diff --git a/research/gauge44-leaver/CONSTRUCTION.md b/research/gauge44-leaver/CONSTRUCTION.md
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+# Gauge44: a changed factory forward map with 44 rank-four cold ends
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0. This note describes the new complex local construction. The package's global evidence supplies the resulting global bound and retains the upstream conditional assumptions.
+
+## 1. Exact result and comparison
+
+The final word has 112 source ports, 112 target ports and 492 helper registers. It implements the same arbitrary-dirt scalar endpoint as the upstream word,
+
+$$
+(X,Y,H)\longmapsto(X,Y+X,H),
+$$
+
+and its inverse-transpose orientation is checked separately. All 204 nonzero entrance frames remain valid. The new ending set consists of **44 cold helpers at rank-four frames**, together with the 34 entering-helper ends inherited from the JP8 HPE stage.
+
+The precise comparison is with the JP8 provider reconstructed from PR635, commit `a6895a69f8ad98ab45777b03e9e6f48888c39f6f`:
+
+| Local quantity | PR635 JP8 | Gauge44 |
+|---|---:|---:|
+| Helpers | 492 | 492 |
+| Nonzero entrance frames | 204 | 204 |
+| Rank-four cold ends | 22 | 44 |
+| Rank-seven cold ends | 2 | 0 |
+| Rank-eight cold ends | 4 | 0 |
+| Entering helpers ending below FULL | 36 | 34 |
+| Total residual helper width | 3894 | **3794** |
+| Local paid rank mass | 5750 | **5650** |
+
+Thus the new word saves **100 units of residual width per invocation** against the complete PR635 provider. It replaces that provider's cold-end construction; the old six higher-rank cold ends and two additional entering ends are not added to the new count.
+
+The exact paid-child profiles are:
+
+| Child rank | PR635 count | Gauge44 count |
+|---:|---:|---:|
+| 1 | 2518 | 2514 |
+| 2 | 402 | 404 |
+| 3 | 448 | 448 |
+| 4 | 164 | 160 |
+| 5 | 68 | 56 |
+| 6 | 4 | 0 |
+| 8 | 8 | 8 |
+
+The final residual-width inventory is `{4:52, 5:48, 7:34, 8:114, 9:244}`. Both the profile and the inventory are recomputed from the literal native frame chains. They are not inferred from the nominal number of ended helpers.
+
+## 2. What changes in the forward factory
+
+The inherited K-triangle schedule and its 492-helper allocation remain the starting construction. Within each of the fourteen eight-source packet factories, three changes alter the arbitrary-dirt forward map while retaining the required clean packet values.
+
+### A. Exchange a source with an equal clean copy
+
+After the sixteen initial copy gates, local source position `j` and its two helper copies have clean values `(x_j,x_j,x_j)`. For positions `j = 4,5,6,7`, exchange the original source register with its second helper copy. The exact register pair in the constructor is `mp[j]` and `mp[2*j+9]`.
+
+For arbitrary helper dirt the triple is instead
+
+$$
+(x_j,\;x_j+h_{j,1},\;x_j+h_{j,2}).
+$$
+
+The exchange changes where the second dirty direction enters the subsequent factory. It does not change any clean operand. Both exchanged registers already have the same rank-one frame, so the exchange adds no frame climb. Each exchange is emitted as three additions and one sign change; these scalar operations remain part of the finite implementation invoice.
+
+This is a change of the forward map, not an output relabeling. In particular, the inverse recovery functional for the original source changes from the original branch to a different combination of the three equal-clean branches. That changes which cold input directions can have their entire final support inside a low frame.
+
+### B. Change the complement to the four coordinate totals
+
+Eight retired factory rows already span the eight source coordinates. The first four rows of their replacement basis are the four required coordinate totals. The remaining four rows are chosen by exact row-rank extension, first using the ordered clean linear forms recorded in `construction/COMPLETION-PRIORITY.json`, then using coordinate rows if an extension is still needed.
+
+These candidate forms are the future low-frame leaver forms used during discovery. The frozen priority data are the complete input to the final constructor: no discovery search is run in reproduction. Every accepted row must increase the rational rank; the resulting eight-by-eight basis is explicitly applied by elementary operations.
+
+All eight retired registers are already at the block's rank-four frame. Consequently this basis replacement also adds no frame climb. It gives the low final rows more independent linear combinations that annihilate the original source data.
+
+### C. Place coordinate totals on the available source carriers
+
+The retired registers are ordered with source registers first. Three available source carriers and one helper carry the four coordinate totals, leaving the four complementary rows on physical helper registers. This lets the new cold directions end on helper wires under the unchanged native endpoint interface.
+
+A carrier permutation alone does not increase the available cold space. Its role here is to realize the independent directions created jointly by the source-copy exchange and the new complementary basis.
+
+## 3. Exact cold-space calculation
+
+Let `P` be the non-target forward matrix after parts A and B and the 34 inherited HPE tail gates. It has 604 rows and columns: 112 original sources and 492 helpers. Let `J` be the 316 protected initial columns consisting of the 112 original sources and all 204 entering helpers.
+
+For a block frame `F`, let `I` be every non-target output register whose current frame is contained in `F`. Source output rows are included in this set. Define
+
+$$
+L=\operatorname{leftker} P[I,J],\qquad
+K=\ker P^{-1}[J,I].
+$$
+
+Rows of `L` are low output linear forms with no protected initial dependence. Columns of `K` are low-supported output directions whose inverse images have no protected component. The rank of the pairing `LK` counts the simultaneously usable cold directions in this fixed forward word.
+
+The changed forward map has the following exact block data:
+
+| Block indices | Number of blocks | Low registers `|I|` | `dim L` | `dim K` | `rank(LK)` |
+|---|---:|---:|---:|---:|---:|
+| 0, 1, 2, 11, 12, 13 | 6 | 6 | 2 | 4 | **2** |
+| 3 through 10 | 8 | 8 | 4 | 4 | **4** |
+
+The count is therefore `6*2 + 8*4 = 44`. The fixed upstream rank-four cold construction supplied one and two directions respectively, for `6*1 + 8*2 = 22`.
+
+The complement change by itself improves the available low annihilating rows but leaves the inverse-support obstruction. The source-copy exchanges remove that obstruction: `K` has dimension four in every block and pairs with all the available rows of `L`.
+
+## 4. Realizing the directions with legal dyadic operations
+
+`construction/build_gauge_cold44.py` recomputes these spaces over exact rational numbers. It selects columns of `K` and normalizes them to a matrix `U` satisfying
+
+$$
+LU=I_r,
+\qquad q=P^{-1}[:,I]U.
+$$
+
+The constructor checks that `q` is supported entirely on that block's sixteen initially cold factory helpers, denoted `H_b`. Put
+
+$$
+R_b=LP[I,H_b].
+$$
+
+Then `R_b q[H_b,:] = I_r`. A sixteen-by-sixteen input basis `Q_b` places the columns `q[H_b,:]` at the designated ended-helper positions and fills the other columns with a basis of `ker R_b`. The resulting input basis is explicitly invertible.
+
+For the low-frame output transformation, the ended-helper rows are replaced by the rows of `L`; each remaining low row `i` becomes
+
+$$
+e_i-U_iL.
+$$
+
+The actual chosen helper positions give an invertible tail matrix. Its nonsingularity and dyadic implementation are checked by exact elimination, rather than assumed from a dimension count. The construction receipt records every `Q_b`, tail matrix and selected endpoint.
+
+Every `Q_b` is emitted at frame zero, at the head of A **after** the entry normalization wrappers. Every low tail is emitted at its block frame. The remaining cleanup is rebuilt as an exact dyadic Gauss-Jordan inverse on the non-ended registers at FULL. It is not obtained by blindly reversing a changed partial schedule.
+
+Before forming the FULL inverse, the constructor verifies both the row and the column identity of each of the 78 ended helpers. Thus no protected data or other helper dirt remains in an ended helper, and its initial dirt remains nowhere else. The FULL inverse skips these isolated rows and columns entirely.
+
+The realized word has:
+
+| Construction component | Scalar gates |
+|---|---:|
+| Frame-zero helper premix | 1489 |
+| New rank-four tail | 60 |
+| Inherited HPE tail | 34 |
+| Refactored FULL inverse | 28056 |
+| Additional target compensation after wrappers | **0** |
+
+All selected new cold directions have zero target response. The independent scalar auditor nevertheless recomputes the complete existing dirty-response compensation, obtaining 7348 additions, and checks both orientations on all 716 input columns.
+
+Relative to the HPE-stage word before any cold-end construction, the aggregate chain delta is `N_1 += 44, N_6 -= 44`, reducing rank mass and residual width by 220. PR635 had already saved 120 units through its complete cold/extra-HPE construction. The net new saving is therefore 100. There is no omitted cost for lifting the low tails: their rank-one increments are included explicitly.
+
+## 5. Native interface and validation
+
+The transport preserves the exact ordered list of 112 ports and the exact ordered eight center frames. The center carriers change because some totals now reside on sources. In native coordinates they are
+
+```
+[92, 57, 81, 224, 11, 240, 9, 256]
+```
+
+A global interface check must compare the ordered center frames and port geometry, and use the provider's actual center carriers. Equality of carrier numbers with an old provider is not a mathematical requirement. The local event ledgers explicitly clear all private center channels in both orientations.
+
+Completed checks for the frozen word include exact forward and inverse-transpose scalar replay on all 716 columns; every literal native frame chain; the 204 zero-response entrance conditions; the 44 cold and 34 entering endpoint cones; wrapper placement and normalized wrapper identities; both emitted local ledgers; and exact phase lowering for 3019 directed edges and 224 endpoint adapters. The independent audit does not import the new constructor.
+
+This local result does not by itself certify a global exponent. Physical whole-family owners, actual residual/spectator routing, idle remainders, global scalar assembly and the complete finite invoice are the separate global checks reported elsewhere in the package.
+
+## 6. Compact reproduction
+
+Only Python's standard library is needed for this construction and the retained local pipeline. Do not use `python -O`. The reproduction driver checks byte hashes of every named upstream input and the changed code, then checks the content hash after each construction step. Its two source checkouts are:
+
+| Argument | Repository commit |
+|---|---|
+| `--main` | `17ce0c79b7b51c2634b439ea5a2b754f09909693` |
+| `--pr635` | `a6895a69f8ad98ab45777b03e9e6f48888c39f6f` |
+
+Starting from a clone of `https://github.com/CrocSwap/integer-mult-bounds` containing those commits, prepare detached worktrees:
+
+```bash
+git -C integer-mult-bounds fetch origin main refs/pull/635/head
+git -C integer-mult-bounds worktree add --detach ../integer-main 17ce0c79b7b51c2634b439ea5a2b754f09909693
+git -C integer-mult-bounds worktree add --detach ../integer-pr635 a6895a69f8ad98ab45777b03e9e6f48888c39f6f
+```
+
+From the directory containing those worktrees and this delta package, run:
+
+```bash
+python -B research/gauge44-global/construction/reproduce.py \
+  --main integer-main \
+  --pr635 integer-pr635 \
+  --out gauge44-reproduction
+```
+
+The default stops after regenerating the exact final scalar word and comparing the newly derived cold recipe with the frozen recipe. It rebuilds only the two short shadow steps needed by the four port transfers. It does not rerun the ancestor admission stack, search for a basis, optimize owners, or replay global assembly.
+
+Use `--frozen-cold` to splice the included recipe instead of re-deriving its small exact linear systems. Use `--until local` to add native transport, emitted ledgers, independent local replay and wrappers. Use `--until phases` to add the complete phase lowering. Every invocation needs a fresh output directory; these are alternatives, not resumable increments. On the research machine, exact cold derivation took about 2.6 seconds, native transport/ledgers/replay/wrappers about 41 seconds, and complete phase lowering about 198 seconds.
+
+The exact dependency chain is:
+
+1. Construct the changed raw R492 factory from the pinned Hamming inputs, frozen priority and pinned K-triangle schedule.
+2. Apply the four inherited port stages.
+3. Apply the inherited B-frame regroup and 34-HPE construction.
+4. Derive the exact block premixes, cold44 tails and FULL inverse.
+5. Optionally emit and check the native ledgers, wrappers and complete phase lowering.
+
+`construction/INPUTS.json` gives the input hashes and every intermediate content hash. The key decompressed content identities are:
+
+| Word | SHA-256 |
+|---|---|
+| Changed raw factory | `0ac47f92fc2e3f5aa457d78f7b8a5c785bf140c546932b9dfcd9e610ad319180` |
+| Changed HPE forward | `42fb8b3aa314593fe976820cf65824f5fce0ee4f95281796992d4809709864cc` |
+| Final cold44 word | `78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290` |
+| Native canonical word | `e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f` |
+
+## 7. Attribution
+
+The original 504-helper factory and borrowed-register construction are icekylinx's PR531 lineage, prepared with OpenAI Codex/GPT assistance and retaining the earlier PR425/PR514 credits. The inherited K-triangle atom and frozen read schedule are credited in PR635 to AtomScout, a Claude Code research agent. The porting routine is credited there to Port480. This package does not claim those as new work.
+
+The reused JP8 ancestry includes the PR558/PR552 supplier, the earlier-cut and multicold kernels, and the joint prefix adapted from Dominik Scholz's PR571 work. Native HPE and cold-end transport, frame and wrapper machinery come from the credited PR635 lineage, including DreamingOfClouds, jeremykothe2, chafreaky and their disclosed assistants. The retained `construction/UPSTREAM-NOTICE.md` and `construction/LICENSE` preserve the upstream notice and Apache-2.0 license.
+
+The new contribution here is the combination of source-copy exchange, changed retired-row completion, source-carried coordinate totals, and the explicit exact cold44 realization. Those changes were developed for icekylinx with OpenAI GPT-6 Astra assistance. The upstream notices, proof scope and conditional assumptions continue to apply.
diff --git a/research/gauge44-leaver/LICENSE b/research/gauge44-leaver/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/gauge44-leaver/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/gauge44-leaver/LOCAL-VALIDATION.json b/research/gauge44-leaver/LOCAL-VALIDATION.json
new file mode 100644
index 0000000000..5973645e1a
--- /dev/null
+++ b/research/gauge44-leaver/LOCAL-VALIDATION.json
@@ -0,0 +1,356 @@
+{
+  "status": "PASS_LOCAL_INCREMENTAL_GAUGE44",
+  "python": "3.14.8",
+  "upstream_main": "17ce0c79b7b51c2634b439ea5a2b754f09909693",
+  "pr635": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f",
+  "construction_steps": [
+    {
+      "step": "shadow-early",
+      "exit_code": 0,
+      "seconds": 0.322
+    },
+    {
+      "step": "shadow-prefix",
+      "exit_code": 0,
+      "seconds": 0.429
+    },
+    {
+      "step": "gauge-forward",
+      "exit_code": 0,
+      "seconds": 0.474
+    },
+    {
+      "step": "port0",
+      "exit_code": 0,
+      "seconds": 0.388
+    },
+    {
+      "step": "port1",
+      "exit_code": 0,
+      "seconds": 0.407
+    },
+    {
+      "step": "port2",
+      "exit_code": 0,
+      "seconds": 0.403
+    },
+    {
+      "step": "port3",
+      "exit_code": 0,
+      "seconds": 0.389
+    },
+    {
+      "step": "cold44-exact",
+      "exit_code": 0,
+      "seconds": 2.544
+    },
+    {
+      "step": "native",
+      "exit_code": 0,
+      "seconds": 3.63
+    },
+    {
+      "step": "ledgers",
+      "exit_code": 0,
+      "seconds": 2.759
+    },
+    {
+      "step": "local-replay",
+      "exit_code": 0,
+      "seconds": 15.924
+    },
+    {
+      "step": "wrappers",
+      "exit_code": 0,
+      "seconds": 2.706
+    },
+    {
+      "step": "phases",
+      "exit_code": 0,
+      "seconds": 186.772
+    }
+  ],
+  "five_mathematical_local_artifacts_match_frozen_evidence": true,
+  "phase_edges": 3019,
+  "endpoint_adapters": 224,
+  "independent_scalar_audit": {
+    "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+    "input_file": "FULL-WORD.json.gz",
+    "content_sha256": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290",
+    "compressed_sha256": "0ad202612f010df4ab66432a628247b37ad8b497dd6b27595b1685cbd7eb119e",
+    "parent_center_interface": {
+      "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+      "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+      "transport_tau": 43,
+      "ordered_frame_bases_match": true,
+      "all_ports_match": true,
+      "transported_centers": [
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+      "source_centers": [
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+          128,
+          64,
+          34,
+          16,
+          10,
+          4,
+          1
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+        [
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+          64,
+          32,
+          16,
+          8,
+          5,
+          3
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+        [
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+          128,
+          64,
+          32,
+          17,
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+          4,
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+        [
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+          128,
+          64,
+          36,
+          20,
+          8,
+          2,
+          1
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+        [
+          256,
+          128,
+          66,
+          32,
+          18,
+          8,
+          4,
+          1
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+        [
+          256,
+          128,
+          65,
+          33,
+          17,
+          9,
+          5,
+          3
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+        [
+          256,
+          128,
+          65,
+          33,
+          16,
+          8,
+          4,
+          2
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+        [
+          256,
+          128,
+          68,
+          32,
+          16,
+          12,
+          2,
+          1
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+      ]
+    },
+    "v": 112,
+    "h": 9,
+    "R": 492,
+    "entering": 204,
+    "lowends": 78,
+    "coldends": 44,
+    "compensation_gates": 7348,
+    "local_profile": {
+      "1": 2514,
+      "2": 404,
+      "3": 448,
+      "4": 160,
+      "5": 56,
+      "8": 8
+    },
+    "width_inventory": {
+      "4": 52,
+      "5": 48,
+      "7": 34,
+      "8": 114,
+      "9": 244
+    },
+    "checked_columns": 716,
+    "elapsed_seconds": 2.443164045999765,
+    "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+  },
+  "independent_guard_review": {
+    "status": "PASS_PR635_ADMISSION_ASSERTION_PRESERVATION",
+    "files": [
+      {
+        "file": "code/assemble.py",
+        "baseline_sha256": "1b1a9024ac910dc9b9d9e30150684e1fa9cb228a4c1c275b75ab04b57fdef1dd",
+        "new_sha256": "7ac28118d69416e4fb67b61216285fb0823310b7635ce1b9025aa3f10119ef6a",
+        "byte_identical": false,
+        "assert_count": 91,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/invoice_allcold.py",
+        "baseline_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+        "new_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+        "byte_identical": true,
+        "assert_count": 67,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/bind_providers_portable.py",
+        "baseline_sha256": "2eb5c262bf481b3bec9ceaec654fa46ff6fc3a89b13d4906a29a55a89e35feea",
+        "new_sha256": "7c9aba6c7f138d270852d859d902f905a15598b6263567700b5b08a153823cb6",
+        "byte_identical": false,
+        "assert_count": 22,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/generated_identity.py",
+        "baseline_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+        "new_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+        "byte_identical": true,
+        "assert_count": 4,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/witness.py",
+        "baseline_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+        "new_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+        "byte_identical": true,
+        "assert_count": 3,
+        "all_assertions_identical_in_order": true
+      }
+    ],
+    "centre_interface_review": "CENTRE-GUARD-REVIEW.md",
+    "scope": "Exact syntax preservation for all admission assertions in these five files. The changed emitter/controller centre boundary and single-provider controls require the separate semantic review; assertion counts alone do not prove them."
+  },
+  "owner_replay": {
+    "status": "PASS_FROZEN_OWNER_AND_INTEGER_MAJORIZATION_REPLAY",
+    "seed_mode": "included_frozen_seed",
+    "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+    "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+    "owners_semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d",
+    "owners_gzip_sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+    "majorization_semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc",
+    "global_profile": {
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+      "2": 29164,
+      "3": 32429,
+      "4": 11520,
+      "5": 4032,
+      "7": 7,
+      "8": 582,
+      "12": 13,
+      "16": 33,
+      "19": 1,
+      "20": 2,
+      "28": 4,
+      "32": 62,
+      "36": 1,
+      "40": 1,
+      "44": 6,
+      "48": 2289
+    },
+    "scope": "Exact hosting nomination and callwise fixed-point replay; full supplier admission is separate."
+  },
+  "global_replay": {
+    "status": "PASS_GAUGE44_STRICT_GLOBAL_REPLAY",
+    "kappa": "1649483702558979/1000000000000000000",
+    "kappa_decimal": "0.001649483702558979",
+    "complex_lower": "1652208994368411824947/1000000000000000000000000",
+    "bit_lower": "413456747036699736067/250000000000000000000000",
+    "gain_over_pr635_percent": "0.8093060205252829126484020359439672024956960385078942889840023844750830",
+    "spec_sha256": "fee57674a7f36b30b1e7eb96a8f567a90a522217bc644c1a6a1f8bff85196fbf",
+    "stages": [
+      {
+        "name": "restore-parent",
+        "seconds": 2.089,
+        "exit_code": 0,
+        "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+      },
+      {
+        "name": "bind",
+        "seconds": 0.962,
+        "exit_code": 0,
+        "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+      },
+      {
+        "name": "emit",
+        "seconds": 4.817,
+        "exit_code": 0,
+        "log_sha256": "90ce07d06a8eaffdb66201e8346021183e5a803395fb9f6d8ceb0e5ff068ef2c"
+      },
+      {
+        "name": "audit",
+        "seconds": 19.625,
+        "exit_code": 0,
+        "log_sha256": "66b4abb2a88a4eaba8a8baa3585ef4aa819be5f8acb7947bae734b3478280456"
+      },
+      {
+        "name": "invoice",
+        "seconds": 1.804,
+        "exit_code": 0,
+        "log_sha256": "5d10712d494304287749dd7a6c3369f9b707bba30e9f567b68230669dcf5418a"
+      },
+      {
+        "name": "assembly",
+        "seconds": 0.808,
+        "exit_code": 0,
+        "log_sha256": "768d3215f1918117dc6c33b4cfeaf0b5f5da9ba5c77178db4bb1d08d000e226f"
+      },
+      {
+        "name": "admission-controls",
+        "seconds": 0.885,
+        "exit_code": 0,
+        "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+      }
+    ],
+    "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the same cited unchanged PR543 bit supplier as PR635. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+  },
+  "admission_mutations_rejected": 69,
+  "controller_mutations_rejected": 15,
+  "frozen_template_content_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "fresh_template_content_sha256": "a1692259fb5a06bbebdc1049a7f757c6d2fc79ff8c31ed0c25b38fe9f98ed051",
+  "template_comparison": {
+    "sole_changed_field": "async_schedule.source_plan_sha256",
+    "frozen_plan_sha256": "609adb126d7d3de2abdd9275f9015589c0b137d0d19821c2c3e7c1a8541c18d2",
+    "fresh_plan_sha256": "b2e4b1f063250c40e0087f77e896882c60f36ed8764e86ba1610dec9bdff7394",
+    "explanation": "Fresh phase review differs only in its measured seconds. Runtime provider binding consequently changes the plan byte hash. All remaining serialized template fields match exactly; each runtime hash is checked against its own file."
+  },
+  "assembly_matches_frozen_rates_and_profile": true,
+  "post_replay_packaging": "Four files received trailing-whitespace cleanup only; complete parsed ASTs were checked unchanged. Constructor input pin refreshed. Admission assertion comparison rerun.",
+  "scope": "Changed construction and exact recipe, fresh native ledgers/wrappers/phases, independent scalar and guard audits, integer owner reproduction, strict global admission and independent pricing. No predecessor full replay, seed-discovery optimizer or PDF generation. Local Python 3.14; Python 3.11 is covered by CI."
+}
diff --git a/research/gauge44-leaver/MANIFEST.json b/research/gauge44-leaver/MANIFEST.json
new file mode 100644
index 0000000000..4c16d25c5a
--- /dev/null
+++ b/research/gauge44-leaver/MANIFEST.json
@@ -0,0 +1,167 @@
+{
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+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "LOCAL-VALIDATION.json": "f81fbd98eb608b8119f03f89a5692bcd610845fc97022337931586d8582b706e",
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+  "README.md": "28acc0bdb972bdc8c2c48cbf8e1ef663d79b7ab134c23d542fec31680a6af6dc",
+  "RESULT.json": "29423f3ce5caa15e8381adeed0417ec2786af26dd7e615d47abb0cbfaeb9343d",
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+  "construction/leaver/LEC-REASON-PINS-k5.json": "84d0d973c4d1c064e9792e2eb8c6202052cfaded2ace22afa72c3f46ebc3e8d6",
+  "construction/leaver/PIVOT-SWAP-k5.json": "5635d6db2ce94cbff0f07d2c1ccbe9e53f72ab9c285a84563a39dd98241ffe74",
+  "construction/leaver/PROMO-RECIPE-k5.json": "82a8084e700cf4f81fa118e0ac8575e214a83e6e80ac895c4ac0195b55cf6717",
+  "construction/leaver/RECIPE-U8-k5.json": "51bff38452254205d22b960780fc8ad385cee47d5ef2e2fe5fd9b3ede1e70ef6",
+  "construction/leaver/RECIPE-X4-k5.json": "acaec3adbd0d78a2afd7d5c1f95a75c2a7ecb07e13d9d36b8eb99b6f9121c4a6",
+  "construction/leaver/REGROUP-LEAVER-k5.json": "f7e871cf4eff76d2f77a50f2f641862796574c3ae68a714c2c4e0b0fc39cb963",
+  "construction/leaver/TRI-LEAVER-k5.json": "8f55f2ae9d2e0f30d0598fded4f61f8d53589b9c8bf3ff4abaaad9700d0bd473",
+  "construction/leaver/build_frames_lv.py": "2eb80d612aa59a7bd8b04a122045e3bd2b83a21954e3164943cd20cf6050a21b",
+  "construction/leaver/cells-k5/CORE-01+.json": "3d2afc4986f1f3aceacd1e0572daebfb79134ba6af7677150083d0912676427c",
+  "construction/leaver/cells-k5/CORE-23+.json": "53b65cbaeb24bb2a4625f107a39c0ba3797f37aa4980096f22dff7cdbd76440d",
+  "construction/leaver/cells-k5/CORE-45+.json": "ba8f3aa26032dc36e2db4073e2cac9fc61d7a475d534a749bdfcbecf3aa103a9",
+  "construction/leaver/cells-k5/CORE-67+.json": "0a7aa4ee46e7f05c9cf0c1a36791d49e439c0c9c473e76cf954b0655463dae05",
+  "construction/leaver/cells-k5/CORE-67-.json": "0a7aa4ee46e7f05c9cf0c1a36791d49e439c0c9c473e76cf954b0655463dae05",
+  "construction/leaver/cgx_leaver.py": "3af491c63dd96204a7c36006c7e419c2e5ce77e5bc453ccd2495c1e41f83f87c",
+  "construction/leaver/layer_end_controls_leaver.py": "e2856865a8687b5344fe2911ee0dbb2cdf8d080744758e3adc4a4f2da7f03917",
+  "construction/leaver/reproduce_leaver.py": "831bfdf2247b5d864b74c3b2b6a475718053d48570851d48bd1c5471d410ee30",
+  "construction/leaver/reproduce_leaver_chain.py": "893be8a210519f5c23a87b33e9407ed98d912079854086913b38cb6b8351a7b3",
+  "construction/notri/PRIO6.json": "de0412511b0dd1af13e9717bc791126ac0e91c569b5391fd6c70268083045d15",
+  "construction/notri/cgx.py": "3da039d4184097c14802f9dbf972520d5b807671196f5e47a2247bc9f29bb418",
+  "construction/notri/cold44x.py": "f0bc3500efb2c839a0f8cb03dbb9ea0a54f1dfc71ef81e5373b3d638ac5b8296",
+  "construction/notri/port_stage_x.py": "38310744d054e393ea35e996047cddeb2d212141aaaaa4b07f7a4663b11db8e7",
+  "construction/notri/reproduce_notri.py": "90148c2a0422b4f92164298a283de73d413ab3d4cb7151a0e6b643a37ea025a8",
+  "construction/promo/LOCAL-PINS-p6n-k4.json": "a92bb02266596956bd53e9c86e8bbcc6639c92b4a4a248a1521f8eb79228271f",
+  "construction/promo/PROMO-RECIPE-p6n-k4.json": "fa6065d142646f7ab1f268912ce0cf5a1a6cd33c3994ff96bd6e204cf16b3e90",
+  "construction/promo/build_promotion.py": "9c9e2001b8d68bbe934d136026276fe97bd9bf6f94d4d78441fc28e14aca4daf",
+  "construction/promo/make_recipe.py": "ba9e4fdc0c1be7f6a150a5a50909911257a1a8c7cc5d03d61f541178fc07c122",
+  "construction/promo/promo_controls.py": "786c51f84b53698c2c833083506c4432c30eb0ed3b71e7dbe458a70c7413c372",
+  "construction/promo/reproduce_promo.py": "f979be666c3f5cf57e342a8427863c0b35b67ca4d3be495ac386f6870deb2026",
+  "construction/reproduce.py": "047bb9b3536b0b16bb08a21cd9fd80404ca9d022345f1aeab34b21dffc281c92",
+  "construction/sw4/LOCAL-PINS-sw4-P6k4.json": "3c06bf68b28ff125a6a2372bb70cefd76fb9fe1333438cd34dfb5b617cd70327",
+  "construction/sw4/NOTES.md": "3a3ddb0c77b188e67fc453ccb3efe9323f87028092a6ce4d259b7dc99d702446",
+  "construction/sw4/SW4-RECIPE-P6k4.json": "fa58d0ffc95d10b7453daefe4b34404a52895f94126ef973e92e92106cd615fa",
+  "construction/sw4/build_sw4.py": "9a295f3d534594a6b1326d8a6647e947670d1c6fbc92f37f5169661fde4c8f66",
+  "construction/sw4/reproduce_sw4.py": "3d082e0cc576fb1b4fb9e5dd11d63bab697c8a8626e2837813cd00d100b1aeac",
+  "data/FRONTIER.json": "56bed9070d5f0b7585d7b7fd62984696dbc5158e5187663030920a57e1cbfab2",
+  "data/OWNERS.json.gz": "0033a61747e0eb2d16208886dc8141e0e344ddb5cfa75f3580e95952384cea93",
+  "data/PLAN.json": "b08f8dc3624c89b38897762e13f9a15e0efa688f2e0bb7fe33abe22ef4f7ddc5",
+  "data/PREPARATION.json": "1d576298bfafc509992113fdd58b5482655a88e321cbfafe9386588eb6fbb6e9",
+  "data/SPEC.json": "98fa99dbe6ceb58d6d5ad40974e18cd29c1bf1cf6aaf1e155f53a85d9e92078a",
+  "data/UPSTREAM-PINS.json": "ccc37ab7fbf78947fe02c7f57ea672d2e4eae8454cb1158ed964c75bf423869b",
+  "evidence/ADMISSION-CONTROLS.json": "5ebcc945c53f8279ac3bb6249e1d46422b7c7ddeb41c580ab5cbb3ca886dcf28",
+  "evidence/ASSEMBLY.json": "847f339db218f62ffabacb4655ba4dc6e8a15f67014ca01b1146083f393b009f",
+  "evidence/BINDING.json": "f80ad585c9cf94989d459971189fbb176084aedbe27edf5b5cccc5c2a44de43b",
+  "evidence/CENTER-COMPATIBILITY.json": "c66c7da1099ac8618381e2a7cb48b09b43ccf8d125ff124e129aba8ddb922cf3",
+  "evidence/LOCAL-STAGES.json": "64165b81b7119a2b23e99d3f3dfe8aa1702f373efe90d82d136c17786ffb6591",
+  "evidence/REPLAY.json": "45a6065c41df0c2b04e185b4727c7ad8eac5ebeb637dbb7bebffc184415b49a2",
+  "evidence/STAGES.json": "09d7c6daf1e93c58863267141dedc3873264d3baede0cddefda0d56ecb560458",
+  "evidence/audit/ASYNC-AUDIT.json": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662",
+  "evidence/audit/GLOBAL-PREFIX.json": "5a6fd0d91a650ad5aa830771fb4333b015f06bc4ded02807d65aee260ce9e671",
+  "evidence/audit/IDLE-REMAINDER-FRAMES.json": "95f5165a10dd187000dba9e55afbc1b7dce5a315cfedfa72e4f8344471149048",
+  "evidence/audit/OWNERS-AND-PROFILE.json": "a32ecc0d5387d65648e1ff284209122860ee37aaba43ce2dd12024c4bc394313",
+  "evidence/audit/PREFIX-AND-INVOICE.json": "14b0f41c88209e800236ce4ebbf91d83537e22e18807153d90013f7eee57a582",
+  "evidence/global/ACTUAL-SIGMAS.json.gz": "bf3b7814b54b30c726cae1dfabd3c09211c8f34cc943534565b131a0006b483f",
+  "evidence/global/GLOBAL-TEMPLATE.json.gz": "f713f8e66aaeaebb8202fe72bf36c7d23497152497342c27892e0fda3092f95b",
+  "evidence/global/HOSTED.json": "60866eb6ced5b9eb259bfc1d59ea7b80fb439164b629e868586ad5bef845a88e",
+  "evidence/global/IDLE-REMAINDER-FRAMES.json.gz": "734fd9bbe0afa2cc1e492bb7effef1aa8f0d8926ab1d9420d64c30045b30e784",
+  "evidence/layers/LOCAL-AUDIT-LAYERED.json": "fa0b717213d020f17461d4723afd19c0025e960db33d86eee5729bbfe8e632c6",
+  "evidence/leaver/CELL-MUTANTS-LV.json": "308975b8288cb9c853ee6b69e68b25e6f3727d259dccfb7509042f103bb03220",
+  "evidence/leaver/FRAME-CONTROLS-LV-k5.json": "2105b38bb371f6e955d09cfb73eaa74ad2ae11f37d5ed5d4206f62dfa9570e7a",
+  "evidence/local/CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+  "evidence/local/CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+  "evidence/local/CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12",
+  "evidence/local/FULL-WORD.json.gz": "0ad202612f010df4ab66432a628247b37ad8b497dd6b27595b1685cbd7eb119e",
+  "evidence/local/INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+  "evidence/local/LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+  "evidence/local/LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+  "evidence/local/RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94",
+  "evidence/local/SCALAR-FRAME-AUDIT.json": "cfc73040079b43ea82a42f3cf4c910edda1362deb09ec21c816c329347313bcb",
+  "evidence/local/WRAPPER-CHECKS.json": "84c727930f85f1c91900d6d12c523735c8b5d6907cd3eb1bd1030fe1fd4161d7",
+  "hosting/PROOF.md": "45bb3de8a10298a4cf5a278c3343be22a7d2e735be93a4e9454f24df7275faf0",
+  "hosting/README.md": "004bcdf6c78bd0316f0606d9e636511f94e1e80cbd79cce1a7e3bc55076d9bf1",
+  "hosting/audit_frozen.py": "a8d9c7c894cb44453aea93b33141559824f6c3ff81a85a6d066f4a10a2757659",
+  "hosting/expand_owners.py": "0f826377881d0c9405f90d9f5feac857c7c7cf8aef5bcf22d326bc274f038a70",
+  "hosting/frozen/FROZEN-AUDIT.json": "df6c7181a097900ee9d37db17bd25436a570f21caaa0cc2108712907ab02904b",
+  "hosting/frozen/MAJORIZATION.json.gz": "ec5f94b13d190d72bc0608dc9fe2498cc43ba9deb05028159a812ec1e4dcacdf",
+  "hosting/frozen/MANIFEST.json": "9df028adfa5120c60d2c78bfab06822cf4e6ed55502816b7d6dec19c1a2e4967",
+  "hosting/frozen/MATCHING-RECEIPT.json": "e1af2ac2c6e2457646d52dd693fb961f6279e10fe50eae9873f2ed149b6735b2",
+  "hosting/frozen/OWNERS.json.gz": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+  "hosting/frozen/REPRODUCTION.json": "8354f63148621c5fcf09cd16b496dedd677d813f83974e1f341ce38a1fffec81",
+  "hosting/frozen/SEED-OWNERS.json.gz": "eb3be5eebbb84349d7e7f1bde2fc77772a12ad5bccc6dab7c4efd8d903e2a048",
+  "hosting/frozen/SEED-RECEIPT.json": "aecfef753379106f5289f31251584c642e2cf7e4fa2d0886bb4ef9e922f8d9ba",
+  "hosting/frozen/SEED-REPRODUCTION.json": "4f6d49a85f43c98c816877d783470ca717be2349caceb991bf756eedece1b194",
+  "hosting/reproduce.py": "7551004d8d15cebcecc6793ebd17385830390935ccd1a8957f1c5472bce6ec82",
+  "hosting/reuse_owners.py": "2106fe79bd89071e62a3a25c1e444531e14fb89f88b4bdeb72d7b40c91266402",
+  "independent/CENTRE-GUARD-REVIEW.md": "7b82518d7ddf042d6e71174bc286311fa72127e0dc6dc9e500025fcf7abbf897",
+  "independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json": "9fb5265c4d2ddf3d615e46600954c79cd1a42481500a0973a5695fcb9f2558c9",
+  "independent/GAUGE44-GLOBAL-GUARD-REVIEW.json": "631107a9a9acb02441ce80298f815e0c624f811b0d58c6fd78f8dc58d564bb5b",
+  "independent/GAUGE44-INDEPENDENT-PRICE.json": "53049d0126aa54bfd6603dc7d43fea08554f7d3baadb8534264fcd69e822d3e3",
+  "independent/README.md": "25668a62d8c91f6860f8412cf2fc750ba41bf1085dad3709ad5067c7956eac89",
+  "independent/audit_local.py": "03afcfc9da428b3f6edac81c1fee7f277ab81b64998efae78380b63498dec6cd",
+  "independent/price_profile.py": "d2f548ad6b99f64a8ca5fbaf822a89560bb99359957ce3420b497f6a46fc0acf",
+  "independent/review_guards.py": "b83164d6c0122a055b3281f3381b305683a875760a2d727dd0188bb2aa59d67d",
+  "inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+  "verify_global.py": "16bd5e54598592e92e210f99065348c5df261b8350fdc688072ce053d15b088a",
+  "verify_manifest.py": "723d726dbbe5b65a49caecae0f1aab664a1413fb639abfd3e826a5a538e14e5b"
+}
diff --git a/research/gauge44-leaver/NOTICE.md b/research/gauge44-leaver/NOTICE.md
new file mode 100644
index 0000000000..7eedf90fe9
--- /dev/null
+++ b/research/gauge44-leaver/NOTICE.md
@@ -0,0 +1,24 @@
+# Gauge44 attribution and scope
+
+New contributions by icekylinx, with OpenAI GPT-6 Astra assistance.
+Local review and packaging used OpenAI Codex. Apache-2.0 applies;
+the license is included. The full original PR635 notice is preserved as
+UPSTREAM-NOTICE.md and construction/UPSTREAM-NOTICE.md.
+
+The new contribution is the changed source-branch gauge and retired-row
+completion, source-carried coordinate totals, exact 44-cold-end realization,
+and explicit all72 whole-family assignment using concave capacity matching
+with integer majorization certificates. The center-carrier generalization
+retains the exact ordered common frames and complete native local contract.
+Independent local, price, interface and owner fixed-point checks are included.
+
+The construction retains the credited PR635 K-triangle and porting machinery,
+earlier joint-prefix/HPE/frame ancestry and icekylinx's prior factory work.
+#645 used the same cited PR543 bit supplier as PR635. This package (research/gauge44-leaver) cites the merged PR589 bit supplier instead, with a derived rank-mass deficit (PROOF-NOTE-BIT.md); #645's retained PR543-based evidence is historical. It builds #645's word without K-triangles (PartialK) and stacks earlier community jp8 layers on it (G44Stack), adds the p6n ends (NoTriReopen), entrance promotions (BlockInvert) a read-set exchange (BRoute), chafreaky's #741 frames, JointXF's joint exchange, NewBArch's triangle-hybrid B rewrite and LeaverSAT's leaver cells (with LeaverSAT2's frame re-optimisation); see README. All-size, realization,
+hosting, precision/tape, analytic-transfer and bit H1-H5 assumptions remain
+conditional. No upstream license, credit, source pin or AI disclosure is
+replaced by this notice.
+
+PR641 and PR642 were checked as concurrent reported frontier comparisons.
+Their endpoints and owner maps are not included here. See CONSTRUCTION.md,
+hosting/PROOF.md, independent/ and README.md for the exact contribution scope.
diff --git a/research/gauge44-leaver/PROOF-NOTE-BARCH.md b/research/gauge44-leaver/PROOF-NOTE-BARCH.md
new file mode 100644
index 0000000000..8cea5a6846
--- /dev/null
+++ b/research/gauge44-leaver/PROOF-NOTE-BARCH.md
@@ -0,0 +1,43 @@
+# PROOF-NOTE-BARCH: width-neutral triangle-hybrid B-delivery rewrite (U8)
+
+Construction by NewBArch (`construction/barch/`, builder `build_tri.py`, controls `run_controls.py`, recipe
+`RECIPE-U8.json`). Driver: `construction/barch/reproduce_barch.py`, chained after `construction/jx`.
+
+## The move
+On research/gauge44-frames-x's X4 word (`1e1d99ba…`), eight disjoint slots are rewritten. In each slot X an entering
+copy E donates into a halves-copy X: 231 (E 450), 230 (E 452), 232 (E 454), 236 (E 456), 226 (E 451), 228 (E 453), 62 (E 455), 238 (E 457). That way, so that one target
+read takes X + H in a single gate. A holder pair (for example 496/484) carries the value. Each holder is restored by a
+low-end tail at its frame (early cleanup) and a FULL-cleanup restore. Entrance pre-reads keep the entering helper's
+start value away from every target.
+
+The recipe is explicit, with every index referring to the X4 word:
+- 40 B deletions;
+- 40 B insertions, each with its frame;
+- 32 explicit re-chosen B frames;
+- 8 early-cleanup tails;
+- 8 FULL-cleanup restores.
+
+The A section and X4's tail frames are untouched. The width is unchanged at 3778. The profile goes
+{1:2548, 2:338, 3:430, 4:194, 5:56, 8:8} → {1:2548, 2:338, 3:446, 4:162, 5:72, 8:8}, a delta of {3:+16, 4:−32, 5:+16}.
+The eight slots are additive (8 × 3.925e-8 ideal = 3.140e-7). Output word `090fd574…`. U8 contains B0's four slots
+(231, 230, 226, 228) plus 232, 236, 62 and 238.
+
+## Checks rerun on every rebuild
+- `build_tri.py` (standard library only) checks the base sha (`1e1d99ba…`) and the result sha (`090fd574…`).
+- `run_controls.py` produces 38 outcomes, all required. The control set is pinned in `LOCAL-PINS-barch-U8.json`.
+  - C0 identity reproduces the input.
+  - The recipe word PASSes #645's independent `audit_local.py`.
+  - Four mutants must each FAIL `audit_local` with a pinned message, both globally and for each of the eight slots
+    (NAME@X):
+    - drop_restore: the holder is not restored, giving "all-column endpoint failure";
+    - restore_full: the low-end restore is moved into the FULL cleanup, giving "all-column endpoint failure";
+    - drop_preread: the inserted entrance pre-reads are omitted, giving "nonzero entrance response";
+    - donation_after: the donation is placed after the target read, giving "nonzero entrance response".
+- The per-end layer-end controls (`../layers_p6n/layer_end_controls.py`) reject 95.
+- PR635's native chain runs, with the canonical word, local programs and Clifford recipes pinned.
+
+## Strict
+NewBArch's strict replay: the #741 map (`G44Pack/m741`, byte-identical OWNERS) is rebound to the U8 locals with
+`rewidth.py` and admitted with this package's own code (NEWWORD `admit645.py` on research/gauge44-frames-x's tree).
+The result is κ 0.001661948695165034, +3.1404e-7 over research/gauge44-frames-x. The four-slot subset B0 strict-passes
+at 0.001661791659578416 and the single slot V1 at 0.001661673902364948.
diff --git a/research/gauge44-leaver/PROOF-NOTE-BIT.md b/research/gauge44-leaver/PROOF-NOTE-BIT.md
new file mode 100644
index 0000000000..3ca670bcba
--- /dev/null
+++ b/research/gauge44-leaver/PROOF-NOTE-BIT.md
@@ -0,0 +1,112 @@
+# PROOF-NOTE-BIT: citing the PR589 bit supplier with a derived rank-mass deficit (gauge44)
+
+This note is BitCap's `PROOF-NOTE-BIT.md` from `complex-571-cold14-k492-bit589`, adapted to the gauge44 package. It
+covers the only verifier change relative to #645's package (`research/gauge44-global`): the bit supplier changes from
+PR543 to PR589. The complex side is #645's construction, unchanged: supplier word, recipes and every complex check in
+`code/assemble.py`. The only complex-side change is the repacked owner map (`data/PLAN.json`, `data/OWNERS.json.gz`),
+with expected values re-derived in `data/SPEC.json`.
+
+## Changed sites
+
+The changes are in `code/assemble.py`, plus one new stage in `verify_global.py` and a new file
+`code/bit_supplier_controls.py`. The independent (non-verifier) `independent/price_profile.py` is ported to PR589 as well. Every other `.py` file equals #645's.
+
+| # | site | before (#645) | after |
+|---|---|---|---|
+| S1 | bit input | `inputs/PR543-EXPECTED.json` from the multicold source, blob pin `b61d8598…` | `inputs/PR589-EXPECTED.json`, shipped in this package, blob pin `e293ddc5…`, through `load_bit` |
+| S2 | bit deficit | literal `9984` | `bit_deficit(word, live)` = T(2Kv − L·cst), with L = 9, T = 32, K = (L−1)/2 = 4 |
+| S3 | profile binding | (none) | Σ r·n of the bit profile = `bit.rank_mass`; moment width `BIT_M = 1 + 7L` asserted = 64 |
+| S4 | pipeline binding | (none) | the record's `nine.pipeline` names the nine-stage template with 32 replicas |
+| S5 | citation / receipt | input hash names the PR543 file | `bit_supplier` cites PR589 (head `a5afc8c6`, merged as `b3eb785a`, path `research/e8-bit-p111-tuned/tune/EXPECTED.json`) and records v = 111, cst = 63, COPY ranks [7×9] and the derived deficit 10272 |
+| S6 | `verify_global.py` | (none) | stage `bit-supplier-controls` runs `code/bit_supplier_controls.py`; it requires status `PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS`, exactly 12 rejected controls and derived deficit 10272 |
+
+The shipped `inputs/PR589-EXPECTED.json` has git blob `e293ddc557742637f9f679f083a1a282d87b1b13`, which equals
+`origin/main:research/e8-bit-p111-tuned/tune/EXPECTED.json`.
+
+## Why the derived deficit is correct
+
+**The identity.** The rank-mass identity of #545 and #555 is M·live − mass = T(2Kv − L·cst). Its source is
+#555's README, "Rank-mass identity", and `code/adapt9p.py`, whose audit carries `DEFICIT=T*(2*K*V-L*CST)`.
+
+**The parameters.** The bit word has v live ports and decoder constant cst, the sum of the nine retained totals' COPY
+ranks. The nine-stage chain is #463/#510 with 32 replicas, so L = 9, T = 32, K = 4 and M = 1 + 7L = 64. The live data
+wires number 2KvT.
+
+**The constraints checked.** The verifier asserts all of:
+1. cst = Σ copy_ranks, with exactly `retained_totals` = 9 entries, each in (0, 8].
+2. live = 2KvT. For #589: 2·4·111·32 = 28416.
+3. Σ r·n over the priced profile = the record's `rank_mass` = 1808352.
+4. M·live − Σ r·n = T(2Kv − L·cst). For #589: 64·28416 − 1808352 = 10272 = 32·(888 − 567).
+
+Check (4) is #645's `check_moment` guard, unchanged. So v, cst, the profile and live must all agree.
+
+**PR543 consistency.** The same formula reproduces #645's constant: PR543 has live = 30720, so v = 120; its nine
+totals have COPY rank 8, so cst = 72; 32·(960 − 648) = 9984.
+
+**The deficit does not raise c.** `check_moment` uses the deficit only as an equality guard. The moment engines
+compute from (profile, m = 64, live, z) and never read it. The bit value c is established only by the unchanged
+acceptance tests at the same exact endpoints, with the bit bad-residue surcharge retained: accept at c and reject at
+c + 10⁻²⁴, by both engines.
+
+## Effect on the outer chain (differs from the k492 package)
+
+In the k492 package the complex side bound under either supplier, so κ did not move. Here it does. With the
+gm3 map the complex side certifies b = 0.001654663299688920102557, with research/gauge44-bit589's dz1 map
+b = 0.00165526410310589140991, and with research/gauge44-bit589b's L1g4 map b = 0.001655496738330440231813. PR543's c = 0.001653826988146798944268 is
+below b, so under PR543 the bit side would bind. BitCap's table gives the PR543 bit-side κ cap as
+0.001651096360425895, which is exactly the κ of `research/gauge44-repack`. PR589's c = 0.001733427039589844234749
+exceeds b, so the complex side binds again (`binding = complex` in `ASSEMBLY.json`): κ = 0.001651929911890057 for gm3
+(conservative 0.001651929909011672) κ = 0.001652528731617094 for dz1 (conservative 0.001652528728737236), and
+κ = 0.001652760598550299 for L1g4 (conservative 0.001652760595670246).
+Bit589Reviewer recomputed both suppliers with the outer engine and confirmed this. The gain over gauge44-repack therefore depends on this change and on the
+assumptions below.
+
+## Negative controls (all must be rejected; the verifier requires exactly these 12)
+
+Each control runs the real `assemble()` on the fresh owner/invoice receipts with one input mutated. The strict run's
+`BIT-SUPPLIER-CONTROLS.json` lists all 12 as rejected.
+
+| control | site | rejected at |
+|---|---|---|
+| `revert_hardcoded_9984` | S2 | `check_moment` deficit guard (10272 ≠ 9984) |
+| `ports_112` | S2 | `bit_deficit`: live ≠ 2KvT |
+| `decoder_constant_64_copy_ranks_unchanged` | S2 | `bit_deficit`: cst ≠ Σ COPY ranks |
+| `decoder_constant_64_with_one_copy_rank_8` (derives exactly 9984) | S2 | `check_moment` deficit guard |
+| `eight_retained_totals` | S2 | `bit_deficit`: totals count ≠ 9 |
+| `live_minus_one` | S2 | `bit_deficit`: live ≠ 2KvT |
+| `profile_rank_mass_plus_one` | S2/S3 | `check_moment` deficit guard |
+| `profile_rank_mass_receipt_mismatch` | S3 | profile mass ≠ `rank_mass` |
+| `bit_lower_next_grid` | endpoint | `check_moment` reject-side moment test |
+| `not_nine_stage_record` | S4 | pipeline binding |
+| `tampered_bytes_next_grid` | S1 | blob pin |
+| `pr543_file_under_pr589_pin` | S1 | blob pin |
+
+Bit589Reviewer re-traced all 12 rejection sites on the gauge44 word (b589gm3), and they match the table: `code/assemble.py` L191 (`revert_hardcoded_9984`, `decoder_constant_64_with_one_copy_rank_8`, `profile_rank_mass_plus_one`), L48 (`ports_112`, `live_minus_one`), L47 (`decoder_constant_64_copy_ranks_unchanged`, `eight_retained_totals`), L201 (`profile_rank_mass_receipt_mismatch`), L197 (`bit_lower_next_grid`), L179 (`not_nine_stage_record`) and L39 (both blob controls). dz1 and L1g4 run the same code.
+
+The ported `independent/price_profile.py` re-derives the deficit separately (`pr589_deficit`) and checks the same blob pin. Its regenerated receipt on this package's PLAN gives the same κ.
+
+## Inherited assumptions
+
+**PR merge status (`gh pr view`, 2026-10-13):** #589 MERGED 2026-10-12T17:00:38Z. #555 was merged 2026-10-12. #645
+is OPEN. Main's review replayed #589 freshly as "supplier-only headroom", and main's *selected* composition still
+cites #543.
+
+**Unmerged assumptions:**
+1. **#645 itself (open):** the gauge44 factory, its construction steps and all of its retained interfaces and notes.
+   These are unchanged here.
+2. **This verifier change (S1–S6):** under review (Bit589Reviewer). The PR589 record replaces PR543 as an *input of
+   the gauge44 assembly*, a composition main has not selected.
+
+**Assumptions carried by #555/#589 (merged, stated there as review points, not theorems):**
+3. #545's punctured unit: a 111-port unit with decoder constant 63 is an admissible bit supplier on the same hypotheses
+   as v = 120.
+4. #510's nine-stage chain as re-parameterised for v ≤ 120 by #555's `code/adapt9p.py`, including the rank-mass
+   identity used in S2.
+5. #543's interleaved scalar-interface lemma (H1–H5) for phase-B source rewrites. This is not new: #645 already
+   inherits it through PR543.
+6. #589's two A-section transports.
+7. The same bit bad-residue surcharge model as PR543 (`surcharge_model = {'complex': False, 'bit': True}`).
+
+## Result
+
+The bit-supplier change is the same as in research/gauge44-bit589 and gauge44-bit589b: the code is byte-identical and was signed by Bit589Reviewer. For this package (leaver word fo_hyb, FO_c1 map), the complex side certifies b = 0.001667007898013796187659 and binds under PR589. Under PR543 the bit side would cap κ at 0.001651096360425895. κ is given in the README and `RESULT.json`.
diff --git a/research/gauge44-leaver/PROOF-NOTE-FRAMES-X4.md b/research/gauge44-leaver/PROOF-NOTE-FRAMES-X4.md
new file mode 100644
index 0000000000..a456a8127b
--- /dev/null
+++ b/research/gauge44-leaver/PROOF-NOTE-FRAMES-X4.md
@@ -0,0 +1,58 @@
+# PROOF-NOTE-FRAMES-X4: chafreaky's #741 frames and JointXF's joint exchange (X4)
+
+Two construction steps on top of research/gauge44-promo-p6k4sw's SW4 word P6k4sw4 (`d232183f…`).
+
+## 1. #741's eight B frames (`construction/frames/`)
+The eight B-gate frame raises are by **chafreaky**, [#741](https://github.com/CrocSwap/integer-mult-bounds/pull/741)
+(`research/complex-sw4-frame8`, commit e516b146). `FRAME-RECIPE-sw4.json` is byte-identical to #741's
+`data/FRAME-RECIPE.json` (a2c7ca4d…). CompetitorMine ported #741's builder and controls; only package paths are adapted.
+The step applies the frames with BlockInvert's `build_promotion.apply` and checks:
+- the scalar program of A, cut, B, precondition and cleanup is unchanged;
+- start and end frames are unchanged;
+- the profile, the widths and the output word `e7804702…` are pinned;
+- 3 pin controls are rejected;
+- #741's 10 focused native controls are rejected (8 frames emptied, a changed read coefficient, paid-profile tampering);
+- the per-end layer-end controls reject 95;
+- the native chain matches its pins.
+
+The rebuilt locals equal G44Pack's F741 locals except the `seconds` field in CLIFFORD-REVIEW.
+This step reproduces #741's word. The final word is built by step 2, which contains these frames.
+
+## 2. Joint exchange X4 (`construction/jx/`, JointXF)
+There are four disjoint instances of BRoute's sw4 read-set exchange rule. Each one exchanges *two* copy pairs that
+share targets: (448, 472), (458, 592), (470, 604) and (482, 614), with face registers 235, 267, 58, 427, 26, 443, 18
+and 50. #741's eight frames sit on top. The 16 moved reads keep their original stored dim-6 frames: they are
+monotone-repaired rather than refitted to the plain join. The recipe `RECIPE-X4.json` is explicit:
+- 32 replaced gates, 16 deleted gates and 16 inserted gates, each with its old gate asserted;
+- #741's 8 frames, listed with their source;
+- 16 explicit frames at the moved reads, each asserted equal to the recomputed frame.
+
+The builder `build_jx.py` uses only the standard library. It checks:
+- target frames lie inside u_t^⊥;
+- tails and ends;
+- exactness of the whole B segment's rational linear map against the input (a Fraction replay);
+- the recomputed paid profile and the output sha `1e1d99ba…`.
+
+Effect against #741's word: the profile goes {1:2556, 2:334, 3:430, 4:194, 5:56, 8:8} → {1:2548, 2:338, 3:430,
+4:194, 5:56, 8:8}. The width inventory is unchanged, and each instance gives +1.0798e-7 at ideal, exactly additive.
+
+**Controls**, each pinned in the recipe and rerun by `reproduce_jx.py`:
+
+| control | outcome |
+|---|---|
+| C0 identity | returns the input `d232183f` |
+| C1 #741 only | `e7804702`, #741's word (ties step 1 to step 2) |
+| M1 one pair (448) with frames retained | `5fb6fb2e`, neutral (profile = #741) |
+| N1 pre-read dropped | rejected: exactness rows [132, 135] |
+| N2 pre-read with wrong sign | rejected: exactness rows [132, 135] |
+| N3 plain-join refit of the moved reads | `7241cd59`, strictly worse |
+| N4 a raise made dim-7 at B855 | rejected: cap at (1302, 174) |
+
+N3 and M1 are pinned-outcome controls (a specific different word), not rejections. They show the gain needs both the
+target-sharing pair and the retained frames.
+
+**Other checks (JointXF):**
+- `audit_local` PASS;
+- native chain PASS;
+- FrameCoal's global frame optimiser reaches the same profile on this move set, so X4 is frame-optimal for these moves;
+- SW4Extend found the same word independently.
diff --git a/research/gauge44-leaver/PROOF-NOTE-LAYERS.md b/research/gauge44-leaver/PROOF-NOTE-LAYERS.md
new file mode 100644
index 0000000000..c4b4e85b6a
--- /dev/null
+++ b/research/gauge44-leaver/PROOF-NOTE-LAYERS.md
@@ -0,0 +1,129 @@
+# PROOF-NOTE-LAYERS: earlier jp8 layers, here stacked on the no-triangle gauge44 word
+
+> In this package the layers sit on the no-triangle word (R = 504), not on #645's 492-helper word. The mapping, the
+> NP chain (regroup `864ff4a1` → swap `beb3579f` → layered `a9de804f`), the per-layer status on this base and the
+> checks are in `PROOF-NOTE-NOTRI.md` ("Layers on this word"). The text below is research/gauge44-layered's note. It
+> describes the same layers and controls on the 492-helper word; its word shas, helper numbers, counts and result
+> table refer to that word.
+
+
+This note covers the second change of research/gauge44-layered relative to research/gauge44-bit589. The first change,
+the PR589 bit supplier, is covered unchanged by `PROOF-NOTE-BIT.md`. Here the community jp8 layers that were reviewed
+on the k492 words (#629/#637/#641 lineage) are re-applied to #645's gauge44 provider word. The layers, their
+construction code and their recipes were all reviewed earlier, on k492 words. This note says what carries over
+unchanged, what is re-checked on the gauge44 word, and what is new. Sources: G44Stack's report (porting and checks on
+gauge44); PivotReviewer's report (sections 1-4, Addenda 3-5); H4aReviewer's report (Addenda 7-8); JP8Ends' report.
+
+## What the layered word is
+
+`construction/layers/reproduce_layers.py` builds the layered word from a fresh `construction/reproduce.py --until word`
+output. Each step is checked exactly:
+
+1. **Pivot swaps** (`build_pivot_swap.py`, PR641's constructor, LF sha256 `8e8bced8…`, the file PivotReviewer signed for
+   st2s4). It reads `PIVOT-SWAP-S6.json` and runs on #645's `regroup/FULL-WORD`. There are six pivot-role swaps: 488→560,
+   489→561, 500→572, 501→573 (s4) and 513→537, 525→549 (s6). The `swaps` list is identical, gate for gate, to S6Ship's
+   s6/s6j3 recipe (`k492-jp8-pivot_swap.json`); only `input_content_sha256` differs, because the base word is #645's
+   regroup word. The constructor replays the zero response exactly, keeps the profile and width multiset unchanged, and
+   rejects its 30 negative controls.
+2. **HPE.** PR635's `build_hpe.apply` applies the inherited jp8 hyperplane-end changes (`HYPERPLANE-END-S6.json`). Its
+   LF sha256 `23c9d7ce…` equals the k492 jp8 hyperplane_end recipe committed in s6j3 and earlier.
+3. **cold44, exactly.** #645's `build_gauge_cold44.py` runs on the swapped HPE word. Its 44 rank-four cold ends, premix
+   and low tails must equal the unswapped (pinned) cold44 construction; only the FULL inverse differs. Consequently the
+   swaps touch no factory block.
+4. **Layers.** PR635's unchanged `build_cold_end.apply(HPE, COLD-LAYERS-RECIPE)` applies the cold44 recipe plus:
+   - 8 entering ends: 560/561/572/573 at U24 (s4) and 597/599/537/549 at U30 (x30: #629's E1 pair, which #645 dropped,
+     plus s6's two ends);
+   - 10 factored dim-8 cold ends: p123 (310/506, 311/504, 516/327) and q4 (579, 592, 589, 518).
+   The output word's sha256 is pinned (`0be48b1d…`), as are its local profile `{1:2542, 2:414, 3:434, 4:154, 5:56,
+   8:8}` and width inventory `{4:52, 5:48, 7:42, 8:116, 9:234}`. The recipe's `refactored_cleanup` meta lists the 8
+   entering ends in `entering_low_frame_ended_helpers` (LayerReviewer's fix). That meta is copied into the word, which
+   is why the pinned word sha moved from `b25f0ed9…` to `0be48b1d…`; gates, frames and report are unchanged.
+5. **Layer-end controls** (`layer_end_controls.py`, LayerReviewer's adaptation of PR635's `cold_end_controls.py`
+   d966e29a). These are raw-word negative controls on the layered word, judged by PR635's unchanged
+   `hpe_audit_and_transport.py`. Each mutant must be rejected at its pinned reason. The adaptation has three parts: the
+   lower→FULL mutant is pinned at "cleanup on non-FULL end", where gauge44 rejects it; entering ends come from the
+   recipe meta; and the premix-gate controls are skipped for entering ends that have no premix gate. `reproduce_layers.py`
+   requires exactly 59 rejections.
+6. **Native locals.** PR635's native audit and transport, ledgers, local replay (the 192-bit payload bound), wrappers and
+   phases all pass. The result is the `--local` that `verify_global.py` consumes.
+
+G44Stack's run of this driver (`rlayers2`, all steps exit 0, 59 controls rejected) reproduces `locs/pq/local`, the
+local G44Pack's strict runs used. Every SPEC-pinned artifact is byte-identical: CANONICAL-WORD, LOCAL-PROGRAMS,
+LOCAL-CHECKS, INDEPENDENT-LOCAL-REPLAY, CLIFFORD-RECIPES, RESIDUAL-ADAPTERS and WRAPPER-CHECKS. CLIFFORD-REVIEW differs
+only in a seconds field; its semantic hash is what SPEC pins. The two unpinned files that embed the word,
+FULL-WORD and SCALAR-FRAME-AUDIT, differ because of the meta.
+
+## Per-layer status on gauge44 (G44Stack, ideal Δκ at ×72)
+
+| layer | prior review (k492 words) | on gauge44 | per-call Δ profile | ideal Δκ |
+|---|---|---|---|---|
+| pivot swaps (6) | PivotReviewer §1-2 (s4), Addenda 4-5 (s6): exact; omitting any rewritten gate is rejected; cost-neutral | all 6 recipe `before` gates match the regroup word; 30 controls rejected; cold44 rebuilds the same 44 ends | neutral | 0 |
+| s4 ends 560/561/572/573 @U24 | PivotReviewer §3: (N) exact for ([24], U24) and its canonical pair; climbs paid | positive | {1:+8, 2:−4, 3:+4, 4:−4}, w −4 | +7.0e-8 |
+| x30: E1 597/599 + 537/549 @U30 | #629 (E1); PivotReviewer Addenda 4-5 (537/549 end monotonically at the E1 hyperplane, whose (N) is exact) | positive | {1:+10, 2:−6, 3:+2, 4:−2}, w −4 | +2.0e-7 |
+| p123 | H4aReviewer Addendum 7: 0 bad rows, dyadic, exact in all 3 orientations; (N) for (0,1039)-(0,1041); Δ recomputed | positive | {1:+6, 2:+12, 3:−12}, w −6 | +2.0e-8 |
+| q4 (after p123) | H4aReviewer Addendum 8 (n_q4): exact; (N) for the 310/311/327 frames and 518's (0,1042); independent of u4 | positive | {1:+4, 2:+8, 3:−8}, w −4 | +1.4e-8 |
+| **stack T_pq** | — | built and audited | {1:+28, 2:+10, 3:−14, 4:−6}, w 3794→3776 | **+3.08e-7** |
+
+These layers were left out because they are negative or dead on gauge44: u4 (−1.2e-6), the 249 end (−3.2e-7), a joint
+p123+q4 (−2.6e-7, worse than sequential), and #627's dim-7 ends 581/590 (no dyadic basis). j3 is dead: its st2 partner
+403 is one of #645's 44 ends, and cold44's block premix uses up the row space.
+
+**Payload.** H4aReviewer's Addendum 8 correction found that the k492 word n_q4 broke the 192-bit local payload bound
+(backward prefix 280 bits). On gauge44 the layered word passes PR635's `hpe_audit_local.py` local-replay stage
+(`prefix < 2**192`), both in G44Stack's `localchain.py` and as step 5 of `reproduce_layers.py`. So the q4 layer here
+does not repeat that failure.
+
+## Verifier changes (spot widths)
+
+A swapped-out pivot p becomes an ordinary cold helper, and its width goes from 8 to 9. #645's global code checks the
+spot helpers' widths as all 8, so the five global files gain the spot-width rule PivotReviewer signed as SOUND for
+S4Ship (Addendum 3), ported to gauge44:
+
+- `code/witness.py`: `spot_widths(v)` gives 9 at a spot helper h with 2v+h among the swapped-out pivots and 8
+  elsewhere. The swapped-out pivots are read from the recipe that SPEC key `pivot_swap` names (path and sha256; the
+  sha256 is asserted). Without `pivot_swap` the tuple is all 8, the same as #645.
+- `code/bind_providers_portable.py`, `code/audit_allcold.py`, `code/assemble.py`: the `all(... == 8)` spot checks become
+  tuple equality with `spot_widths()`, which pins every spot width exactly.
+- `code/assembly_controls.py`: the `cold_swap` control picks a swap partner whose width differs, so the mutant can
+  never be the identity.
+
+Here the spot helpers 264 and 276 (pivots 488 and 500) expect width 9 and the other spot helpers expect 8. The k492
+spot-width review (PivotReviewer Addendum 3) covered the same rule on k492 code. Its gauge44 port is part of this
+package's review (LayerReviewer).
+
+## Controls and what is not re-run
+
+- The pivot-swap constructor's 30 controls run inside `reproduce_layers.py` (step 1).
+- `verify_global.py`'s strict controls are unchanged, including the 12 bit-supplier controls and #645's admission
+  controls. They run on the layered locals.
+- Layer-end controls: 59 raw-word mutants, all rejected at pinned reasons, run as step 5 of `reproduce_layers.py`
+  (see above). They cover the cold low-frame ends, the refactored cleanup, every entering end (its lower-frame gate,
+  profile pin and hyperplane, plus its premix gate where it has one) and each distinct dim-8 frame. LayerReviewer ran
+  them on the layered word (59 rejected). The k492 version (d966e29a) rejected 103-112 on the p123/q4 words; the
+  k492-only primitives (absorptions, factored accumulators, target writes) are absent from this word.
+- #645's independent audit `independent/audit_local.py` on the layered word: PASS, with 204 entering helpers, 96 low ends,
+  54 cold ends and 716 columns. Its receipt is `evidence/layers/LOCAL-AUDIT-LAYERED.json` (word `0be48b1d…`, run with
+  `--main`). The README's clean-clone command reruns it; only `elapsed_seconds` varies. The other `independent/`
+  receipts are #645's own.
+- The prior (N), exactness and pricing checks for each layer were done on k492 words. On gauge44 they are covered by
+  the native chain (native audit, local replay, wrappers, phases) on the layered word, together with the pinned
+  profile and width inventory.
+
+## Inherited assumptions
+
+These are the same as `PROOF-NOTE-BIT.md` (#645 open; PR589 citation; #545/#555/#589 review points; H1-H5). In
+addition:
+
+1. **(N) for the entering-end pairs outside #599's three Lean-covered pairs** (U24, U30, the dim-8 frames). As on
+   k492, these are covered by the tool check (clifford_exact / `nchk.py`) and by the native wrappers, not by a Lean
+   proof (PivotReviewer §3).
+2. **The reviews of PR641's pivot-swap constructor and PR635's `build_cold_end.apply` / `build_hpe.apply`**, which this
+   package uses unchanged.
+
+## Result
+
+| | gauge44-bit589b (L1g4 map) | this package (layered, LN5c map) |
+|---|---|---|
+| κ | 0.001652760598550299 | 0.00165395497190225 |
+| per-call width | 3794 | 3776 |
+| local profile | #645's {1:2514, 2:404, 3:448, 4:160, 5:56, 8:8} | {1:2542, 2:414, 3:434, 4:154, 5:56, 8:8} |
diff --git a/research/gauge44-leaver/PROOF-NOTE-LEAVER.md b/research/gauge44-leaver/PROOF-NOTE-LEAVER.md
new file mode 100644
index 0000000000..43f33ec3e6
--- /dev/null
+++ b/research/gauge44-leaver/PROOF-NOTE-LEAVER.md
@@ -0,0 +1,66 @@
+# PROOF-NOTE-LEAVER: no-helper mutable-leaver all-K cells, re-stacked layers, hybrids and a frame re-optimisation (fo_hyb)
+
+Construction: LeaverSAT (cells, layer re-indexing, frozen recipes) and LeaverSAT2 (frame re-optimisation).
+Drivers: `construction/leaver/reproduce_leaver.py` (cell word) and `construction/leaver/reproduce_leaver_chain.py`
+(everything after it). Reviews: PromoReviewer (leaver chain and frames), SW4Reviewer (k5 hybrids), Q6Reviewer
+(`layer_end_controls_leaver.py`).
+
+## 1. The cell (set model, LeaverSAT)
+In #781's all-K cell, a pair p with sign e replaces three face events and three packet copies. Direct delivery uses
+15 reads y_i += c x_j. LeaverSAT's 21-gate circuit uses the six leaver sources x_j (face-event operands with no later
+reads, restored at FULL by the inherited cleanup) as mutable intermediates. It has 3 leaver gates x_k += c x_m,
+3 target gates y_a += c y_b (inverted at frame zero in the precondition and scatter, #781's recipe) and 15 reads.
+Coefficients are rescaled exactly per cell, C_ij = r_i c_j. The driver re-derives the scaled gates from the unit
+circuit and checks the clean map Y_i = Σ_j C_ij X_j in exact rationals.
+
+Native legality needs one relabelling: the plain circuit fails the native audit, because a y += y source carries
+port-stage entering-helper dirt. Each cell is therefore relabelled by S6 so that y–y sources avoid targets carrying
+entering dirt at that time.
+
+**Set k5:** five cells (01+, 23+, 45+, 67+, 67−), R = 489. The cell word is cold44 `e10817e0…`. Its pairing ranks are
+pinned to [2,2,1,4,4,4,4,4,4,4,4,2,1,1] in `cold44x.py` and checked again in the driver.
+
+## 2. Re-stacked layers (LeaverSAT; signed builders unchanged, recipes re-indexed)
+| step | recipe (data) | word |
+|---|---|---|
+| pivot swaps (6), mapped through the leaver helper map | `PIVOT-SWAP-k5.json` | `c3d4ecfe…` |
+| HPE, greedy (31) | `HPE-RECIPE-k5.json` | `0a2c596e…` |
+| cold44, exact (same ends, premix and tails as the unswapped cell word) | — | — |
+| NP layers (s4, x30, b6, q4) | `COLD-LAYERS-RECIPE-NP-k5` | `ead98631…` |
+| p6n ends | `COLD-LAYERS-RECIPE-P6N-k5` | `13de8d32…` |
+| promotions (16, minimal) | `PROMO-RECIPE-k5.json` | `b88d5abe…` |
+| joint exchange (re-indexed X4; 0 of #741's frames survive) | `RECIPE-X4-k5.json` | `d54668aa…` |
+| U8-style hybrids ×7 (NewBArch's builder) | `RECIPE-U8-k5.json` | `2997cede…` |
+| frame re-optimisation (exact global frame optimum, gopt2) | `FRAME-RECIPE-LV-k5.json` | **`238be1fc…`** |
+
+Two steps don't apply to k5. The sw4 exchanges use copy helpers 461, 581, 591 and 603, which the cells drop. Of
+#741's eight frames, none survives.
+
+## 3. Controls rerun on every rebuild
+- **Cell stage:** the exact clean-map check; native audit, ledgers, local replay, wrappers and phases on the cell word.
+- **Pivot swaps:** the swap constructor's 30 controls.
+- **Promotions:** BlockInvert's `promo_controls.py`, 11 mutants rejected at pinned sites.
+- **Joint exchange:** all 7 `RECIPE-X4-k5` controls reproduce their pinned outcomes.
+- **Hybrids:** `run_controls.py` gives 34 outcomes, all required. These are C0, the recipe word passing audit_local,
+  and 4 mutants, each run both globally and per instance.
+- **Frames:** `build_frames_lv.py`'s 3 pin controls. LeaverSAT2's 6 frame-recipe mutants are rejected by the builder;
+  that receipt was reviewed by PromoReviewer and is not rerun.
+- **Layer-end controls:** `layer_end_controls_leaver.py`, Q6Reviewer-signed. It is the signed per-end controls with
+  one change: the expected reason of two mutants (premix_dropped, into_full) is re-pinned to the arbitrary-dirt
+  endpoint, because on the leaver words those mutants are caught there first (`LEC-REASON-PINS-k5.json`). Every
+  mutant must still be rejected. Each count is 95 on the p6n, promoted, jx and hybrid words. On the re-framed final word
+  the controls are not run (interim skip, approved by Q6Reviewer): the frame re-optimisation lowers entering end 559's
+  tail frame below the hyperplane, so the control generator cannot build its 'end at another hyperplane' mutant. The
+  ends, helper_final, starts and scalar program are unchanged from the hybrid word, and the native audit of the final
+  word is pinned.
+- **Native chain on the final word:** the canonical word, local programs and Clifford recipes are pinned in
+  `CHAIN-PINS-k5.json`, which also pins every count above.
+
+## 4. Cell mutants (evidence, not rerun)
+LeaverSAT2's `CELL-MUTANTS-LV.json` (in `evidence/leaver/`) records PromoReviewer's cell mutants M1–M6, generalised
+to every cell sign. All 42 are rejected by both audit_local and the native audit, on single-cell builds.
+
+## 5. Strict
+The owner map is G44Pack3's FO_c1: its pattern-flow LNS, rebound to the R = 489 word. Admitted on this package's
+own code, with SPEC `width_spot_helpers` [263,275,287,299] and `pivot_swap` → `construction/leaver/PIVOT-SWAP-k5.json`
+(NEWWORD discovery, freeze, strict), it gives κ 0.001664233607446043. That is +2.599e-6 over research/gauge44-frames-x.
diff --git a/research/gauge44-leaver/PROOF-NOTE-NOTRI.md b/research/gauge44-leaver/PROOF-NOTE-NOTRI.md
new file mode 100644
index 0000000000..54bd84e01d
--- /dev/null
+++ b/research/gauge44-leaver/PROOF-NOTE-NOTRI.md
@@ -0,0 +1,53 @@
+# PROOF-NOTE-NOTRI: #645's gauge44 word without K-triangles (R = 504)
+
+Construction by PartialK; review by NotriReviewer (scratch/NotriReviewer/FINAL-REPORT.md). Drivers:
+`construction/notri/reproduce_notri.py` (this word) and `construction/layers_np/reproduce_np.py` (layers on it).
+
+## Why the triangles were the blocker
+- In #645's gauge44, a K-block has I = 6 low registers with rank C = 4, so L = 2. Only the 2-row priority completion
+  fits there. The (p,−) triangle reads climb copies loc17/19/21 and source loc2.
+- Without the triangles, I = 8. With the 2-row completion, rank C stays 6 (L = 2), which is why the plain removal sweep
+  restored nothing. With the 6-row completion (`PRIO6.json`, the list blocks 3–10 already use), rank C = 4, so L = 4,
+  the cap. All 14 blocks then pair at rank 4: 56 rank-four cold ends, R = 504, width 3818, profile
+  {1:2506, 2:336, 3:472, 4:184, 5:56, 8:8}, rank mass 5674.
+
+## Constructor changes (NotriReviewer §1)
+- **`cgx.py`** is #645's `construct_gauge_xcentre.py`, parameterised by XPARAM. On this path the only change that takes
+  effect is the K-block priority: `PRIO[c]` is placed in front of the inherited rows. The prepended rows equal the
+  shared 6-row list of blocks 3–10 (all 8 lists identical). Every completion assert is kept (`qr_rank(M)==4`,
+  `len(M)==8`, the exact block-total rows). An empty TRI schedule is an input #645 already supports (`NH = 504 − 3·0`).
+  `HELPER-MAP` is the identity on 728. The `exch`, `COPYL` and `hyb` branches are inert here (defaults, empty, not
+  reached).
+- **`port_stage_x.py`** is PR635's `build_port_stage.py`. The helper map only has to be injective rather than onto;
+  with no triangles it is onto again.
+- **`cold44x.py`** is #645's `build_gauge_cold44.py`. Its per-block pin `r == len(L) == (2 if K-block else 4)` is
+  replaced by `r == len(L)` together with the explicit per-block pin `PAIRING_RANKS` (set by the driver to [4]*14,
+  and to #645's pattern in `--control-g44`). Helpers outside the 224+16b ranges join their blocks (EXTRAH, empty here).
+  Every other assert is kept (U, nonlocal premix, `rank(Qmat) == NB`).
+- **Control.** `reproduce_notri.py --control-g44` runs the same scripts with #645's four triangles and no XPARAM. It
+  reproduces #645's gauge44 word `78c7aada…` exactly, with ranks [2,2,2,4,4,4,4,4,4,4,4,2,2,2].
+
+## Exactness and locals (NotriReviewer §2)
+- Replay: 0 bad rows over 27,932 gates, all dyadic; forward, inverse and adjoint are exact. None of the 6,448
+  compensation additions reads an ended helper, and the precondition never touches one.
+- 0 FULL-remainder gates touch an ended helper; E⊂U holds for every entering end. The delta against gauge44
+  ({1:−8, 2:−68, 3:+24, 4:+24}, width +24) matches the reported profiles.
+- (N): all 17 pairs pass (14 cold dim-4 pairs with 4 helpers each, plus 3 dim-8 entering pairs).
+- `audit_local.py --main`: PASS. Payload: prefix bits 66 forward and 72 backward, against 192.
+- Native locals: 25 controls rejected, Lemma A on 22 frames, 17 wrapper mutants rejected. The rebuilt locals equal
+  the strict locals (`PartialK/runs/none_p6/local`): byte-identical except CLIFFORD-REVIEW and SCALAR-FRAME-AUDIT,
+  which differ only in their `seconds` field.
+
+## Layers on this word (G44Stack)
+The layers are research/gauge44-layered's (see `PROOF-NOTE-LAYERS.md`), mapped to the 504 numbering:
+- the 6 pivot swaps 494→566, 495→567, 506→578, 507→579, 519→543, 531→555, which are neutral (same 46 HPE helpers,
+  same 56 cold ends);
+- s4 566/567/578/579 at U24;
+- x30 608/610/543/555 at U30;
+- BlockCombine's b6;
+- q4.
+
+p123 is negative on this base and dropped; j3 is dead (L = 0 at U24 and U30). The chain is regroup `864ff4a1` → swap
+`beb3579f` → layered `a9de804f`, with profile {1:2534, 2:346, 3:458, 4:178, 5:56, 8:8} and width 3800. On that word
+the signed `layer_end_controls.py` rejects 59/59 and `audit_local.py` passes with 216 entering helpers, 120 low ends,
+66 cold ends and 728 columns. NotriReviewer independently reproduced a9de804f from the packaged recipes.
diff --git a/research/gauge44-leaver/PROOF-NOTE-P6N.md b/research/gauge44-leaver/PROOF-NOTE-P6N.md
new file mode 100644
index 0000000000..bef9ad2de0
--- /dev/null
+++ b/research/gauge44-leaver/PROOF-NOTE-P6N.md
@@ -0,0 +1,34 @@
+# PROOF-NOTE-P6N: six b-type dim-8 cold ends on the layered no-triangle word (p6n)
+
+Construction by NoTriReopen. Driver: `construction/layers_p6n/reproduce_p6n.py`. Review: Q6Reviewer.
+
+## What p6n adds
+On research/gauge44-notri-layered's word NP (`a9de804f…`), p123's lane is rebuilt as three factored dim-8 pairs
+(`P6N-SPEC.json`):
+- [512, 513] at U = (256,128,66,34,16,8,6,1). The old pair [310,512] split a rank-3 end; [512,513] replaces it;
+- [311, 510] at U = (256,128,72,40,24,4,2,1);
+- [522, 327] at U = (256,128,66,34,18,10,6,1).
+
+They are built with the same premix-only factored construction as p123/q4/b6 (JP8Ends' stackJ/stackE, CarrierBypass
+pattern; PR635's unchanged `build_cold_end.apply`). The cold-layer recipe `COLD-LAYERS-RECIPE-P6N.json.gz` is NP's
+recipe plus these six ends; its meta lists 72 cold ends and the 8 entering ends. Applied to NP's swapped HPE word, it
+gives p6n `34b683fa…`:
+- profile {1:2540, 2:358, 3:446, 4:178, 5:56, 8:8};
+- widths {4:64, 5:48, 7:54, 8:122, 9:216};
+- width 3794 (NP 3800);
+- Δ per call {1:+6, 2:+12, 3:−12}, w −6, every end b-type.
+
+## Checks
+- **NoTriReopen:** native chain including phases PASS; audit_local PASS; 95/95 layer-end controls rejected.
+- **Q6Reviewer:**
+  - exact;
+  - (N) passes on all 21 pairs;
+  - payload 55/72 bits, against 192;
+  - the per-end control variant `layer_end_controls.py` (fc58c569…, which Q6Reviewer signed for research/gauge44-pq6) rejects 95/95;
+  - 165 further mutants on the six ends are all rejected.
+  The LayerReviewer-signed `../layers/layer_end_controls.py` controls one end per dim-8 frame family, so it would not
+  control each new end. This package therefore uses the per-end variant for p6n and for the promoted word built on it.
+- **Rebuild:** `reproduce_p6n.py` pins the input NP word, the output sha, profile and widths, and 95 controls.
+
+## Remaining capacity (NoTriReopen)
+After p6n, the only residual cold capacity on the word is 2 a-type units, and every end there prices about −9e-7.
diff --git a/research/gauge44-leaver/PROOF-NOTE-PROMO.md b/research/gauge44-leaver/PROOF-NOTE-PROMO.md
new file mode 100644
index 0000000000..8233bbd6b8
--- /dev/null
+++ b/research/gauge44-leaver/PROOF-NOTE-PROMO.md
@@ -0,0 +1,46 @@
+# PROOF-NOTE-PROMO: entrance promotions E4 → E5 on the p6n word
+
+Construction by BlockInvert (`construction/promo/`); driver `construction/promo/reproduce_promo.py`.
+
+## What a promotion is
+An entering helper h starts at an entrance frame E (its `start_extra`) and climbs to its final frame. Promotion
+enlarges E to E′ ⊃ E (here dim 4 → dim 5). That removes one paid climb from h's chain (width −1 per helper) at the
+cost of re-choosing the frames of the gates on h's early chain. It is the time-reverse dual of end deepening. Two
+conditions make it legal:
+1. **Zero target response for h's dirt.** This condition does not depend on E, so it is inherited unchanged from the
+   input word.
+2. **Monotone frames.** Every gate's frame must contain its registers' current frames.
+Only frame annotations and start frames change. The scalar program (every gate's registers and coefficients) is
+untouched, so the endpoint, every cone and the compensation are those of the input word.
+
+## The recipe (`PROMO-RECIPE-p6n-k4.json`, data only, minimal)
+- Input: the p6n word `34b683fa…` (`PROOF-NOTE-P6N.md`), pinned.
+- `entrances`: the 16 entering helpers 627, 629–631, 635, 637–639, 651, 653–655, 659 and 661–663 (four E4 kernel groups) go E4 → E5.
+- `gate_frames`: 48 frame re-choices, the promotion's own entry-gate raises (12 per group); each records the old frame,
+  which must equal the input's exactly. This is BlockInvert's **minimal** recipe: the deterministic rule
+  E′ = E + ⟨smallest x⟩ on each group's entry gates (PromoReviewer). Unlike research/gauge44-promo's k3 recipe, it
+  carries none of the 72 price-neutral CP-SAT re-choices.
+- `expected`: output `0390ec65…`, profile {1:2572, 2:326, 3:430, 4:194, 5:56, 8:8}, widths
+  {4:80, 5:32, 7:54, 8:122, 9:216} (width 3778). Against p6n the delta is {1:+32, 2:−32, 3:−16, 4:+16}, width −16.
+
+## Checks rerun on every rebuild (`reproduce_promo.py`)
+- `build_promotion.py`: input pin; each old frame matches; each new entrance strictly contains the old one; the
+  profile and widths are recomputed from the chains, including target end climbs; output pins.
+- `promo_controls.py`: the honest word passes #645's independent `audit_local.py` (exact forward and dual endpoint
+  frames, entrances, cones). For p6n-k4, 11 mutants are rejected at pinned sites (the count is pinned in `LOCAL-PINS-p6n-k4.json`):
+  - entrance outside the first gate frame;
+  - raised gate missing, once per promoted group;
+  - entrance reverted, so the profile does not match;
+  - ungrouped promotion;
+  - a recipe gate whose old frame is wrong;
+  - a recipe entry that is not a promotion;
+  - a tampered input word (the constructor's own `__main__` must refuse it at the input pin);
+  - a scalar tamper on a raised gate.
+- The per-end layer-end controls (`../layers_p6n/layer_end_controls.py`, Q6Reviewer-signed): 95 rejected.
+- PR635's native chain: transport audit (all columns, native frames), ledgers, local replay (192-bit payload),
+  wrappers and phases, with the canonical word, local programs and Clifford recipes pinned (`LOCAL-PINS-p6n-k4.json`).
+
+## Search (not run by the rebuild)
+`make_recipe.py` writes the recipe from BlockInvert's CP-SAT solution (`prom.py` with `exactframe2.py`, using MinCutSel's
+chain model). These promotions were priced negative before (MinCutSel #3, under a fixed-window arc-flow packer). Under
+near-ideal packing (G44Pack's dissolve/gapmerge) they price positive; the strict replay confirms the gain.
diff --git a/research/gauge44-leaver/PROOF-NOTE-SW4.md b/research/gauge44-leaver/PROOF-NOTE-SW4.md
new file mode 100644
index 0000000000..a064cc54cc
--- /dev/null
+++ b/research/gauge44-leaver/PROOF-NOTE-SW4.md
@@ -0,0 +1,44 @@
+# PROOF-NOTE-SW4: read-set exchange on four entering-copy pairs
+
+Construction by BRoute (`construction/sw4/`, with the author's notes in `construction/sw4/NOTES.md`). Driver:
+`construction/sw4/reproduce_sw4.py`.
+
+## The move
+In P6k4 (`0390ec65…`; research/gauge44-promo-p6sw applied the same exchange to P6k3 `a38bb414…`), each of four entering packet copies h is written first as h = E_h + r: copy gate add(h, r, 1)
+from a non-target face register r, with E_h being h's entering content. The pairs are (h, r) =
+(461, 25), (581, 89), (591, 415), (603, 431). For each pair the read sets of h and r are exchanged in phase B:
+- every post-copy target read add(t, h, c) becomes add(t, r, c), and t's entrance pre-read add(t, h, −c) (taken
+  while h = E_h) is deleted;
+- every target read add(t, r, c) becomes add(t, h, c), with a pre-read add(t, h, −c) inserted after h's last existing
+  pre-read and before h's copy gate.
+
+Since h − r = E_h after the copy, each target's value is unchanged at the end of B. The builder checks this for every
+register mod p (p = 2147483629). Moved and inserted gates take the plain join of their operands' current frames.
+Every other B gate and every early-cleanup tail keeps span(old frame + current operand frames). Targets must stay
+inside u_t^⊥, and tails and ends must contain the current frame. start_extra, helper_final, cleanup and the helper
+numbering are unchanged.
+
+## Effect
+Output `d232183f…`. Width 3778 is unchanged. The profile goes from {1:2572, 2:326, 3:430, 4:194, 5:56, 8:8} to
+{1:2548, 2:342, 3:438, 4:186, 5:56, 8:8}, a delta of {1:−24, 2:+16, 3:+8, 4:−8}, the same as on P6k3. The four
+exchanges are additive. The fourth promotion group (659, 661–663; gates B420–431) commutes exactly with the exchange:
+there is no index or register overlap, and SW4Reviewer checked that applying the k3→k4 frame and start differences
+to f35a852b gives d232183f. Ideal κ +3.271e-7 over P6k4.
+
+## Checks rerun on every rebuild
+- `build_sw4.py` (standard library only): the input sha pin; the 16 explicit moves of `SW4-RECIPE-P6k4.json`; B-end
+  state exactness mod p; frame caps, tails and ends; the output sha, profile and W. It also runs 4 controls, all of
+  which must hold, each at the exact site pinned in the recipe's `rejection_expected` (all three keys N1, N2 and N3 are required):
+  - C0: the identity recipe reproduces the input B and early_cleanup byte for byte;
+  - N1: h2r without deleting the pre-read is rejected by exactness, with changed B-end rows exactly {168, 171};
+  - N2: a partial exchange (one read only) is rejected by the frame cap, first at ('cap', B1192, register 169), 10 violations;
+  - N3: an inserted pre-read with the wrong sign is rejected by exactness, with changed rows exactly {129, 130, 169, 170}.
+- The per-end layer-end controls (`../layers_p6n/layer_end_controls.py`, Q6Reviewer-signed): 95 rejected.
+- PR635's native chain, with the canonical word, local programs and Clifford recipes pinned (`LOCAL-PINS-sw4-P6k4.json`).
+  The native transport audit re-checks every column and native frame of the exchanged word.
+
+## Scope of the search (BRoute)
+The search was exhaustive within the single-pair family only. NP has 107 copy pairs, and 54 of them have movable
+reads. Over those, every nonempty subset of one pair's movable reads gives 602 candidates: 564 are frame-illegal, and
+the 38 legal ones are all full single-pair exchanges, of which exactly these 4 are positive. Cross-pair combinations
+of partial moves were not enumerated.
diff --git a/research/gauge44-leaver/README.md b/research/gauge44-leaver/README.md
new file mode 100644
index 0000000000..f21ba431fe
--- /dev/null
+++ b/research/gauge44-leaver/README.md
@@ -0,0 +1,234 @@
+# Gauge44 without K-triangles, with earlier jp8 layers, the p6n ends, entrance promotions, a read-set exchange, #741's frames, a joint exchange, a triangle-hybrid B rewrite, no-helper mutable-leaver cells and PR589's bit supplier: conditional κ = 0.001664233607446043
+
+Under the retained all-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1–H5 interfaces (as in #645), and the PR589 bit supplier,
+
+$$
+T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad
+\kappa=\frac{1664233607446043}{10^{18}}=0.001664233607446043.
+$$
+
+**The construction is icekylinx's [#645](https://github.com/CrocSwap/integer-mult-bounds/pull/645) (`research/gauge44-global`).** This package builds the research/gauge44-barch construction (items 1–8) and then rebuilds its word around **no-helper mutable-leaver cells** (item 9):
+1. **No-triangle word (PartialK).** #645's gauge44 chain is run with **none** of the four (p,−1) K-triangles, so there are R = 504 helpers. In the six K-blocks {0,1,2,11,12,13}, the completion priority is extended by the 6-row list `construction/notri/PRIO6.json`. Every block then pairs at rank 4, giving **56** rank-four cold ends instead of 44. `construction/notri/reproduce_notri.py` rebuilds this word from a #645 `reproduce.py --until word` output. It uses PartialK's generalisations of #645's and PR635's constructors (`cgx.py`, `port_stage_x.py`, `cold44x.py`; each differs from its original only in the documented parameters). It pins:
+   - the pairing ranks [4]*14, inside `cold44x.py` and again in the driver;
+   - the word (`3e99ba77…`);
+   - the canonical word, the local programs and the Clifford recipes.
+   `--control-g44` instead rebuilds #645's own gauge44 word (`78c7aada…`) with the same scripts.
+2. **Layers on the no-triangle word (G44Stack).** `construction/layers_np/reproduce_np.py` applies to the no-triangle regroup word (`864ff4a1…`):
+   - research/gauge44-layered's six pivot swaps, mapped to the 504-helper numbering (`PIVOT-SWAP-NP.json`, swap word `beb3579f…`);
+   - the greedy HPE (46, `HPE-RECIPE-NP.json`);
+   - the exact cold44 (same 56 ends);
+   - the entering ends s4 (566/567/578/579 at U24) and x30 (608/610/543/555 at U30), plus BlockCombine's b6 and q4 dim-8 cold ends (`COLD-LAYERS-RECIPE-NP.json.gz`). p123 is negative on this base and dropped; j3 is dead.
+   The layered word is pinned (`a9de804f…`): profile `{1:2534, 2:346, 3:458, 4:178, 5:56, 8:8}`, width 3800. The signed research/gauge44-layered files `construction/layers/build_pivot_swap.py` and `construction/layers/layer_end_controls.py` are used unchanged, and the latter must reject exactly 59 controls. The global code is research/gauge44-layered's (spot-width rule): SPEC `width_spot_helpers` [270,282,294,306] and `pivot_swap` → `construction/layers_np/PIVOT-SWAP-NP.json`, giving spot widths [9,9,8,8].
+3. **p6n ends (NoTriReopen).** `construction/layers_p6n/reproduce_p6n.py` applies `COLD-LAYERS-RECIPE-P6N.json.gz` to the NP swapped HPE word with PR635's unchanged `build_cold_end.apply`. That is NP's cold-layer recipe plus six b-type dim-8 cold ends: [512,513], [311,510] and [522,327], which rebuild p123's lane as clean pairs. The result is the p6n word (`34b683fa…`): profile `{1:2540, 2:358, 3:446, 4:178, 5:56, 8:8}`, width 3794. The per-end layer-end controls (`construction/layers_p6n/layer_end_controls.py`, the variant Q6Reviewer signed for research/gauge44-pq6) must reject exactly 95 mutants. See `PROOF-NOTE-P6N.md`.
+4. **Entrance promotions (BlockInvert).** `construction/promo/reproduce_promo.py --base p6n --k p6n-k4` applies the minimal recipe `PROMO-RECIPE-p6n-k4.json` to the p6n word with BlockInvert's deterministic constructor `build_promotion.py`. The recipe promotes the 16 entering helpers 627, 629–631, 635, 637–639, 651, 653–655, 659 and 661–663 (four E4 kernel groups) from E4 to E5, the time-reverse dual of end deepening. It re-chooses the frames of the gates affected. Only frame annotations and start frames move; the scalar program is unchanged. The promoted word is pinned (`0390ec65…`): profile `{1:2572, 2:326, 3:430, 4:194, 5:56, 8:8}`, widths `{4:80, 5:32, 7:54, 8:122, 9:216}`, width 3778. BlockInvert's `promo_controls.py` runs #645's independent `audit_local.py` on the honest word and must reject 11 recipe- and word-level mutants at pinned sites. The per-end layer-end controls (95) and the native chain then run with pins. The recipe is minimal: 48 entry-gate frame raises and no other frame re-choices. See `PROOF-NOTE-PROMO.md`.
+5. **Read-set exchange (BRoute).** `construction/sw4/reproduce_sw4.py` runs BRoute's standard-library builder `build_sw4.py` with `SW4-RECIPE-P6k4.json`, 16 explicit moves, on the promoted word (`0390ec65…`). For the entering-copy pairs (h, r) = (461,25), (581,89), (591,415) and (603,431), the phase-B target read sets of h and its face register r are exchanged. The entrance pre-reads are deleted or inserted so that every register's value at the end of B is unchanged; the builder checks this mod p. Frames are repaired monotonically, and the width is unchanged. The SW4 word is pinned (`d232183f…`): profile `{1:2548, 2:342, 3:438, 4:186, 5:56, 8:8}`, width 3778. Four controls (C0 identity, N1 kept pre-read, N2 partial exchange, N3 wrong sign) must all hold, each at its exact rejection site pinned in the recipe. The per-end layer-end controls (95) and the native chain then run with pins. See `PROOF-NOTE-SW4.md` and `construction/sw4/NOTES.md`.
+6. **#741's eight B frames (chafreaky).** `construction/frames/reproduce_frames.py` applies chafreaky's [#741](https://github.com/CrocSwap/integer-mult-bounds/pull/741) frame recipe, `FRAME-RECIPE-sw4.json`, byte-identical to #741's. Ported by CompetitorMine, it raises eight B-gate frames with the scalar program unchanged, giving #741's word `e7804702…`. It runs 3 pin controls, #741's 10 focused native controls, 95 layer-end controls and the native chain with pins.
+7. **Joint exchange X4 (JointXF).** `construction/jx/reproduce_jx.py` runs JointXF's standard-library builder `build_jx.py` with `RECIPE-X4.json` on #741's word (step 6's output). It makes four disjoint instances of the read-set exchange, each over two target-sharing copy pairs: (448,472), (458,592), (470,604) and (482,614). The moved reads keep their stored frames, and #741's frames are included. All edits are explicit, and B-segment exactness is checked by Fraction replay. The final word is pinned (`1e1d99ba…`): profile `{1:2548, 2:338, 3:430, 4:194, 5:56, 8:8}`, width 3778. All seven pinned controls are rerun; C1 reproduces #741's word. See `PROOF-NOTE-FRAMES-X4.md`.
+8. **Triangle-hybrid B rewrite (NewBArch).** `construction/barch/reproduce_barch.py` runs NewBArch's standard-library builder `build_tri.py` with `RECIPE-U8.json` on the X4 word (step 7's output). Eight disjoint slots receive a width-neutral B-delivery rewrite: an entering copy donates into a halves-copy so that one target read gets X+H, with holder restores and entrance pre-reads. The U8 word is pinned (`090fd574…`): profile `{1:2548, 2:338, 3:446, 4:162, 5:72, 8:8}`, width 3778. All 38 pinned controls are rerun (identity, the recipe word passing audit_local, and four audit_local-rejected mutants, globally and per slot). See `PROOF-NOTE-BARCH.md`.
+9. **Leaver cells, re-stacked (LeaverSAT, LeaverSAT2).** `construction/leaver/reproduce_leaver.py --id k5` replaces the no-triangle word's construction with five all-K cells (01+, 23+, 45+, 67+, 67−). Each cell is LeaverSAT's 21-gate circuit, which uses the face-event leaver sources as mutable intermediates (R = 489, cell word `e10817e0…`). `construction/leaver/reproduce_leaver_chain.py --id k5` then re-applies items 2–8 with the signed builders unchanged and LeaverSAT's re-indexed recipes: swap, HPE, cold44, NP, p6n, 16 promotions, the re-indexed X4 exchange and 7 U8-style hybrids (`2997cede…`). It adds LeaverSAT2's exact global frame re-optimisation (`FRAME-RECIPE-LV-k5.json`), which gives the final word **`238be1fc…`**. Every intermediate word, control count and native pin is pinned (`LEAVER-PINS-k5.json`, `CHAIN-PINS-k5.json`). The per-word layer-end controls are the Q6Reviewer-signed `layer_end_controls_leaver.py` (95 each). Items 5 and 6 don't apply on this word: the sw4 copies are dropped, and none of #741's frames survive. Items 1–8 remain in the package as the construction record of research/gauge44-barch. See `PROOF-NOTE-LEAVER.md`.
+10. **Owner map (chafreaky's [#685](https://github.com/CrocSwap/integer-mult-bounds/pull/685), adapted by G44Pack).** The map is G44Pack3's FO_c1, from its pattern-flow LNS (`pflns`) rebound to the R = 489 word. Its lineage is the #685/#741 map (chafreaky) via G44Pack's relabel and rewidth, followed by G44Pack3's LNS. It was admitted with this package's own code (NEWWORD discovery, `freeze_spec.py`, strict) at κ 0.001664233607446043. Only PLAN and OWNERS change. These are search inputs only; no verifier reads them.
+11. **Expected values.** `data/SPEC.json` is re-derived by #645's discovery → `code/freeze_spec.py` → strict chain.
+
+- **κ = 0.001664233607446043** (conservative 0.001664233604589014). That is +0.8942% over #645, +0.6215% over research/gauge44-layered and +0.4854% over research/gauge44-notri-layered (0.001656193765416678) and +0.3388% over research/gauge44-promo (0.00165861362787227) and +0.2962% over research/gauge44-promo-p6 (0.001659319032684569) and +0.2764% over research/gauge44-promo-p6sw (0.001659645685315104, the same exchange on three promotion groups) and +0.1564% over research/gauge44-frames-x (0.001661634653669567) and +0.1375% over research/gauge44-barch (0.001661948695165034) and +0.1825% over [#741](https://github.com/CrocSwap/integer-mult-bounds/pull/741) (chafreaky, κ 0.001661202643272239; the same word without the joint exchange) and +0.2345% over [#685](https://github.com/CrocSwap/integer-mult-bounds/pull/685) (chafreaky, κ 0.001660339298410333; the same promoted word before the exchange, with #685's owner map). The complex side certifies 0.001667007898013796187659 and PR589's bit supplier gives 0.001733427039589844234749, so **the complex side binds**. Under PR543 the bit side would cap κ at 0.001651096360425895 (`PROOF-NOTE-BIT.md`).
+- **Evidence.** G44Pack's strict replay with `verify_global.py` passes (`PASS_GAUGE44_STRICT_GLOBAL_REPLAY`, κ 0.001664233607446043). It ran this code and data against G44Pack3's fo_hyb locals. This package's own code re-admitted it, with SPEC `width_spot_helpers` [263,275,287,299] and `pivot_swap` → `construction/leaver/PIVOT-SWAP-k5.json`. `RESULT.json` is that replay's `REPLAY.json`, converted to LF. The locals rebuilt by `reproduce_leaver_chain.py` match the strict locals byte for byte in every file except CLIFFORD-REVIEW and SCALAR-FRAME-AUDIT. Those two differ only in their `seconds` field, and the comparison normalises only that field. For this package, `data/SPEC.json` and a fresh `verify_global.py` replay on locals rebuilt by the two drivers are the binding record.
+- **Independent price.** `independent/GAUGE44-INDEPENDENT-PRICE.json` is regenerated on this package's `data/PLAN.json` with the ported `independent/price_profile.py`: `PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK`, κ equal to the strict replay.
+- **Independent local audit.** `evidence/layers/LOCAL-AUDIT-LAYERED.json` is #645's `independent/audit_local.py`, run with `--main` on the final leaver word (content `238be1fc…`): `PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES`, 201 entering helpers, 96 low ends, 57 cold ends, 713 checked columns. Rerunning it reproduces the receipt except `elapsed_seconds` and, across zlib versions, `compressed_sha256`.
+- **Historical #645 files (PR543-based, 492 helpers).** These are #645's files, retained unchanged and **not** updated for this package: `LOCAL-VALIDATION.json`, `CONSTRUCTION.md`, `hosting/`, `evidence/` (except `evidence/layers/`), the rest of `independent/`, `construction/reproduce.py` and its inputs, and `code/prepare_global.py`. They describe #645's word, owner map, PR543 supplier and κ 0.001649483702558979. `code/prepare_global.py` is #645's one-shot owner-map preparer, hard-wired to #645's parent plan and R = 492. No verifier imports it. This package's PLAN/OWNERS are frozen search output, and the strict replay checks them. `construction/reproduce.py` is still used for its `--until word` shadow and hamming inputs; its 492-word output is then superseded by `construction/notri/`. `construction/layers/reproduce_layers.py` is research/gauge44-layered's driver for the 492-helper layered word, shipped unchanged as signed; it is not used here.
+- **Construction and code files** by committed LF SHA-256:
+  - `construction/notri/reproduce_notri.py` 90148c2a0422b4f92164298a283de73d413ab3d4cb7151a0e6b643a37ea025a8 (no-triangle driver)
+  - `construction/notri/cgx.py` 3da039d4184097c14802f9dbf972520d5b807671196f5e47a2247bc9f29bb418 (PartialK's generalised construct_gauge_xcentre.py)
+  - `construction/notri/port_stage_x.py` 38310744d054e393ea35e996047cddeb2d212141aaaaa4b07f7a4663b11db8e7 (PartialK's generalised build_port_stage.py)
+  - `construction/notri/cold44x.py` f0bc3500efb2c839a0f8cb03dbb9ea0a54f1dfc71ef81e5373b3d638ac5b8296 (PartialK's generalised build_gauge_cold44.py plus the PAIRING_RANKS pin)
+  - `construction/notri/PRIO6.json` de0412511b0dd1af13e9717bc791126ac0e91c569b5391fd6c70268083045d15 (completion priority)
+  - `construction/layers_np/reproduce_np.py` 1a304144a250d00d14154692ba522365b036777cf2b6fac466095e8ba733c16c (NP layer driver)
+  - `construction/layers_np/PIVOT-SWAP-NP.json` d49b8d316da1cbdaf995dd0e8314d3c67cc9cd4d5902e9d85ccb907be645bef5 (layer input)
+  - `construction/layers_np/HPE-RECIPE-NP.json` 43900139f618bdc06b8319098fb8dccaf4fc315b43ef7c067ca2cd778cdba2c1 (layer input)
+  - `construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz` 3164cfb71baaeba4ac43427bc14075a225fc3a32ecd9341e58aa52c03a4ee2c0 (layer input)
+  - `construction/layers/build_pivot_swap.py` 8e8bced88be2e592ded40929499bac385ca92fcc1fa59183c22229dbf34093b8 (signed, unchanged)
+  - `construction/layers/layer_end_controls.py` 7829187bfc8f909948d5250e0ec00f02c89f5fe98306a3ed88daee36cb3c92ef (signed, unchanged)
+  - `construction/layers/reproduce_layers.py` 435699f6f79c6c7fb8d6cc5a8382576d6ac88747583a975ff671e45440b93c4e (signed, unchanged, unused here)
+  - `construction/promo/reproduce_promo.py` f979be666c3f5cf57e342a8427863c0b35b67ca4d3be495ac386f6870deb2026 (promotion driver)
+  - `construction/promo/build_promotion.py` 9c9e2001b8d68bbe934d136026276fe97bd9bf6f94d4d78441fc28e14aca4daf (BlockInvert's constructor)
+  - `construction/promo/promo_controls.py` 786c51f84b53698c2c833083506c4432c30eb0ed3b71e7dbe458a70c7413c372 (BlockInvert's controls)
+  - `construction/promo/make_recipe.py` ba9e4fdc0c1be7f6a150a5a50909911257a1a8c7cc5d03d61f541178fc07c122 (discovery-side recipe writer (search, not run))
+  - `construction/promo/PROMO-RECIPE-p6n-k4.json` fa6065d142646f7ab1f268912ce0cf5a1a6cd33c3994ff96bd6e204cf16b3e90 (minimal recipe)
+  - `construction/promo/LOCAL-PINS-p6n-k4.json` a92bb02266596956bd53e9c86e8bbcc6639c92b4a4a248a1521f8eb79228271f (native pins)
+  - `construction/layers_p6n/reproduce_p6n.py` aa7d6bcbed05aa1c689437c07a26e5c95be3c700c0c1fb7bcf91c432a88436ca (p6n driver)
+  - `construction/layers_p6n/layer_end_controls.py` fc58c5699ba6191c1163a3041241f6f0b619626c4462cd99bcf88210bac9e81e (per-end controls (Q6Reviewer-signed variant))
+  - `construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz` 17e218a17e47c58fe2cde775ab2314d3d84030a61327b7f13da61cae3b374ad4 (p6n recipe)
+  - `construction/layers_p6n/P6N-SPEC.json` 132a59635077d6afe80f99964a6935fce1dc2ece6587d74209c6f9c60025c8f1 (p6n end spec)
+  - `construction/sw4/reproduce_sw4.py` 3d082e0cc576fb1b4fb9e5dd11d63bab697c8a8626e2837813cd00d100b1aeac (SW4 driver)
+  - `construction/sw4/build_sw4.py` 9a295f3d534594a6b1326d8a6647e947670d1c6fbc92f37f5169661fde4c8f66 (BRoute's builder (stdlib))
+  - `construction/sw4/SW4-RECIPE-P6k4.json` fa58d0ffc95d10b7453daefe4b34404a52895f94126ef973e92e92106cd615fa (16-move recipe with pinned rejection sites)
+  - `construction/sw4/LOCAL-PINS-sw4-P6k4.json` 3c06bf68b28ff125a6a2372bb70cefd76fb9fe1333438cd34dfb5b617cd70327 (native pins)
+  - `construction/frames/reproduce_frames.py` dc39ada9a2eb387310be181f3cea5dbd4b538632a888cd7372ece5e38a771832 (#741 frames driver)
+  - `construction/frames/build_frames.py` 200847a7e8b3125cbeea0765dad67650e0bf83d32b66d72ba4977e99b8ee8eeb (#741's builder (chafreaky; ported))
+  - `construction/frames/frame_controls.py` 477de854ec9184a2c73d6ac3857a9d0cbd6bc04b71d10a105e7344434b492a77 (#741's controls (chafreaky; ported))
+  - `construction/frames/FRAME-RECIPE-sw4.json` a2c7ca4d44671386d05974e2627645b42bbb7da7a35cefff6e9fa158b6ac8473 (#741's recipe, byte-identical)
+  - `construction/frames/LOCAL-PINS-frames-sw4.json` bc416b8f6443d59c715fb358c4d70fa27eae2d306388ffe0e2a303f60d929f7f (native pins)
+  - `construction/jx/reproduce_jx.py` 5c7afebb4eb7fcdeb7e971cfbc457cf071850e2da21c3c71295efdd453c2399c (X4 driver)
+  - `construction/jx/build_jx.py` 3cc7550b0c24bb54e245c6f7f16de489fd7844721fbb64aac628f38f43887916 (JointXF's builder (stdlib))
+  - `construction/jx/RECIPE-X4.json` 9d42c6b38e8124f5ffe15da56c260a7fba7260626bf3c5f8cbd93aa4a71ceadd (explicit recipe with pinned controls)
+  - `construction/jx/LOCAL-PINS-jx-X4.json` 95c5114c8e937c2737a1b9f9da97303f2e5e129d39e6dfcc4010e99bfdb9c974 (native pins)
+  - `construction/barch/reproduce_barch.py` 19bc970aa6af25ab0e7fa96fb65c64dd0c5243976d8f2cb733cba839155482c1 (U8 driver)
+  - `construction/barch/build_tri.py` 0fba65b31c2fd71864c291358bb0ad8d5f7e1be07e21df23f0ae73d7b966002e (NewBArch's builder (stdlib))
+  - `construction/barch/run_controls.py` 42639bf62bf57795e3ea615c1944c67efed00f28591333daeb3139bf63d04476 (NewBArch's controls (38 outcomes))
+  - `construction/barch/RECIPE-U8.json` 292f0e9f82824c4111728cf4de929bf6e43320fbbdc77658aae9681906b0d652 (explicit recipe)
+  - `construction/barch/LOCAL-PINS-barch-U8.json` 2d16f99e1f71fd66378f5f767cf4cfa2a58264919a95074c7b31029f39a3c9f5 (control set and native pins)
+  - `construction/leaver/reproduce_leaver.py` 831bfdf2247b5d864b74c3b2b6a475718053d48570851d48bd1c5471d410ee30 (cell driver)
+  - `construction/leaver/cgx_leaver.py` 3af491c63dd96204a7c36006c7e419c2e5ce77e5bc453ccd2495c1e41f83f87c (cell constructor)
+  - `construction/leaver/reproduce_leaver_chain.py` 893be8a210519f5c23a87b33e9407ed98d912079854086913b38cb6b8351a7b3 (chain driver)
+  - `construction/leaver/layer_end_controls_leaver.py` e2856865a8687b5344fe2911ee0dbb2cdf8d080744758e3adc4a4f2da7f03917 (per-word reason re-pin variant (Q6Reviewer-signed))
+  - `construction/leaver/build_frames_lv.py` 2eb80d612aa59a7bd8b04a122045e3bd2b83a21954e3164943cd20cf6050a21b (LeaverSAT2's frame builder)
+  The global code is research/gauge44-layered's, unchanged: assemble 4c270a99, assembly_controls e4c0f782, audit_allcold a87d7f48, bind 1d39bcc7, witness 779c5172. The bit-supplier code is research/gauge44-bit589's, unchanged: verify_global 16bd5e54, bit_supplier_controls e6d33fb6, price_profile d2f548ad.
+- **Line endings.** These files had CRLF in the admitted trees and are committed as LF only (`crlf.replace(b'\r\n', b'\n') == lf`, no lone `\r`):
+  - `construction/jx/build_jx.py`: CRLF 775c2ae60eec9abc…, committed (LF) 3cc7550b0c24bb54…
+  - `construction/jx/RECIPE-X4.json`: CRLF 228079b304358500…, committed (LF) 9d42c6b38e8124f5…
+  - `construction/barch/build_tri.py`: CRLF 2432372f148a4d34…, committed (LF) 0fba65b31c2fd718…
+  - `construction/barch/run_controls.py`: CRLF 18e1f5953403784f…, committed (LF) 42639bf62bf57795…
+  - `construction/barch/RECIPE-U8.json`: CRLF 3e97088ad641eb6e…, committed (LF) 292f0e9f82824c41…
+  - `construction/leaver/cells-k5/CORE-01+.json`: CRLF f802445262b4a201…, committed (LF) 3d2afc4986f1f3ac…
+  - `construction/leaver/cells-k5/CORE-23+.json`: CRLF 2169b76864e8e9d4…, committed (LF) 53b65cbaeb24bb2a…
+  - `construction/leaver/cells-k5/CORE-45+.json`: CRLF 0c6718fad5f1f862…, committed (LF) ba8f3aa26032dc36…
+  - `construction/leaver/cells-k5/CORE-67+.json`: CRLF 2c0170683b930f5b…, committed (LF) 0a7aa4ee46e7f05c…
+  - `construction/leaver/cells-k5/CORE-67-.json`: CRLF 2c0170683b930f5b…, committed (LF) 0a7aa4ee46e7f05c…
+  - `construction/leaver/LEAVER-PINS-k5.json`: CRLF 5c4c02573e512130…, committed (LF) b6074974fd2f8c16…
+  - `construction/leaver/PROMO-RECIPE-k5.json`: CRLF 67b8873daba82d57…, committed (LF) 82a8084e700cf4f8…
+  - `construction/leaver/RECIPE-U8-k5.json`: CRLF e7fbabf706b003c6…, committed (LF) 51bff38452254205…
+  - `construction/leaver/RECIPE-X4-k5.json`: CRLF 3b1796773455adc5…, committed (LF) acaec3adbd0d78a2…
+  - `construction/leaver/FRAME-RECIPE-LV-k5.json`: CRLF f1647b8e7a234414…, committed (LF) 8a0f692ebc8dc9df…
+  - `data/SPEC.json`: CRLF 617468fd3e5bd965…, committed (LF) 98fa99dbe6ceb58d…
+  - `RESULT.json`: CRLF 63f0c6d537966e2f…, committed (LF) 29423f3ce5caa15e…
+  - `construction/leaver/CHAIN-PINS-k5.json`: CRLF 0a7ed2d42ef978be…, committed (LF) c92100074c1529b6…
+
+
+Clean-clone verification, from the repository root (Python 3.11+, assertions on; prepare the pinned #635 supplier as in the #645 section below):
+
+```sh
+python -B research/gauge44-leaver/verify_manifest.py
+python -B research/gauge44-leaver/construction/reproduce.py \
+  --main . --pr635 /tmp/gauge44-pr635 --out /tmp/notri-base --until word
+python -B research/gauge44-leaver/construction/notri/reproduce_notri.py \
+  --main . --pr635 /tmp/gauge44-pr635 --word-dir /tmp/notri-base --out /tmp/notri-word --word-only
+python -B research/gauge44-leaver/construction/layers_np/reproduce_np.py \
+  --main . --pr635 /tmp/gauge44-pr635 --notri-dir /tmp/notri-word --hamming /tmp/notri-base/hamming --out /tmp/notri-np
+python -B research/gauge44-leaver/construction/layers_p6n/reproduce_p6n.py \
+  --main . --pr635 /tmp/gauge44-pr635 --np-dir /tmp/notri-np --out /tmp/p6n
+python -B research/gauge44-leaver/construction/promo/reproduce_promo.py \
+  --main . --pr635 /tmp/gauge44-pr635 --base p6n --base-dir /tmp/p6n --k p6n-k4 --out /tmp/promo
+python -B research/gauge44-leaver/construction/sw4/reproduce_sw4.py \
+  --main . --pr635 /tmp/gauge44-pr635 --promo-dir /tmp/promo --recipe P6k4 --out /tmp/sw4
+python -B research/gauge44-leaver/construction/frames/reproduce_frames.py \
+  --main . --pr635 /tmp/gauge44-pr635 --sw4-dir /tmp/sw4 --out /tmp/frames
+python -B research/gauge44-leaver/construction/jx/reproduce_jx.py \
+  --main . --pr635 /tmp/gauge44-pr635 --sw4-dir /tmp/sw4 --out /tmp/x4
+python -B research/gauge44-leaver/construction/leaver/reproduce_leaver.py \
+  --main . --pr635 /tmp/gauge44-pr635 --word-dir /tmp/notri-base --id k5 --out /tmp/lv --word-only
+python -B research/gauge44-leaver/construction/leaver/reproduce_leaver_chain.py \
+  --main . --pr635 /tmp/gauge44-pr635 --leaver-dir /tmp/lv --hamming /tmp/notri-base/hamming --id k5 --out /tmp/lvc
+python -B research/gauge44-leaver/independent/audit_local.py \
+  --word /tmp/lvc/frames/FULL-WORD.json.gz --main . --output /tmp/lvc-audit.json
+python -B research/gauge44-leaver/verify_global.py \
+  --main . --local /tmp/lvc/local --work /tmp/lvc-global
+# kappa 0.001664233607446043
+```
+
+Optional control: `reproduce_notri.py ... --control-g44 --out /tmp/notri-ctl` rebuilds #645's gauge44 word `78c7aada…`.
+
+## Predecessor: #645's README (unchanged below; paths read `research/gauge44-global`)
+
+### Gauge44: conditional κ = 0.001649483702558979
+
+New contributions by **icekylinx**, with **OpenAI GPT-6 Astra** assistance.
+Local review and packaging used OpenAI Codex. Original notices and Apache-2.0 licenses are retained.
+
+Under the retained all-size compiler, common-label/mutable-source realization,
+whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit
+H1–H5 interfaces,
+
+$$
+T(n)=O\!\left(n(\log n)^{1-\kappa_{645}}\right),\qquad
+\kappa_{645}=\frac{1649483702558979}{10^{18}}=0.001649483702558979
+$$
+
+(This is #645's own κ. **This package's κ is the one at the top of this README.**)
+
+The certified complex saving is `0.001652208994368411824947`. The unchanged
+[#543](https://github.com/CrocSwap/integer-mult-bounds/pull/543) bit supplier gives
+`0.001653826988146798944268`, so the complex side binds. The conservative complex
+model separately certifies κ `0.001649483699681650`.
+
+### Construction
+
+This replaces the local supplier and all 72 owner assignments of pinned
+[#635](https://github.com/CrocSwap/integer-mult-bounds/pull/635). Source/copy exchanges
+at equal rank-one frames alter the factory's arbitrary-helper-input propagation.
+An invertible completion of the retired rows and source-carried coordinate totals
+then expose 44 rank-four cold endpoints. Exact input premixes, low-frame tails
+and a recomputed full inverse realize them.
+
+| Per-invocation quantity | Complete #635 JP8 | Gauge44 |
+| --- | ---: | ---: |
+| Source / target ports | 112 / 112 | 112 / 112 |
+| Helpers | 492 | 492 |
+| Rank-four cold endpoints | 22 | 44 |
+| Helper residual width | 3,894 | 3,794 |
+| Paid local rank mass | 5,750 | 5,650 |
+
+The new paid local profile is `{1:2514, 2:404, 3:448, 4:160, 5:56, 8:8}`.
+The explicit whole-family assignment covers 35,424 helper roles on 7,168 live
+and 7,670 physical families. It retains the rank deficit 2,560 and charges every
+idle remainder. Exact integer majorization certificates justify the owner
+updates; the resulting map is a coordinate fixed point, with no claim of joint
+optimality.
+
+The assembled κ is 0.809306% above #635. `data/FRONTIER.json` records Pro's dated
+comparison snapshot; it is not a live ranking of community results.
+
+### Proof and evidence
+
+- `CONSTRUCTION.md`: exact cold-space calculation, dyadic realization and attribution.
+- `hosting/PROOF.md`: capacity, exchange and majorization arguments.
+- `independent/CENTRE-GUARD-REVIEW.md`: ordered center-frame interface and source carriers.
+- `data/SPEC.json`, `evidence/ASSEMBLY.json`: strict component moments and outer parameters.
+- `evidence/audit/`: actual controller, physical charts and finite invoice.
+- `construction/INPUTS.json`, `data/UPSTREAM-PINS.json`: inherited input hashes.
+- `MANIFEST.json`, `SOURCES.json`, `LOCAL-VALIDATION.json`: submitted bytes, provenance and local checks.
+
+Original Pro run receipts are retained as evidence; their raw logs remain in
+the original archive outside the submission. Fresh replay writes new logs to
+the selected output directory.
+
+### Incremental reproduction
+
+Use Python 3.11 or newer with assertions enabled. The required replay uses only
+the standard library. The optional historical seed-discovery optimizer is not
+part of admission.
+
+Prepare the pinned #635 supplier in a separate directory (the main dependencies
+are already present in this repository):
+
+```sh
+git fetch https://github.com/CrocSwap/integer-mult-bounds.git a6895a69f8ad98ab45777b03e9e6f48888c39f6f
+mkdir -p /tmp/gauge44-pr635
+git archive FETCH_HEAD research/complex-571-cold14-st2 | tar -x -C /tmp/gauge44-pr635
+```
+
+From the repository root, with fresh output directories:
+
+```sh
+python -B research/gauge44-global/verify_manifest.py
+python -B research/gauge44-global/construction/reproduce.py \
+  --main . --pr635 /tmp/gauge44-pr635 \
+  --out /tmp/gauge44-local --until phases
+python -B research/gauge44-global/verify_global.py \
+  --main . --local /tmp/gauge44-local/local --work /tmp/gauge44-global
+```
+
+The dedicated workflow also runs the independent literal-word audit, exact owner
+reproduction, preserved-assertion comparison and independent pricing on Python
+3.11 and 3.14. `hosting/README.md` and `independent/README.md` give those commands.
+No ancestral full replay, optimizer search or PDF generation is required.
+
+The result remains a finite conditional witness. It does not establish an
+unconditional multiplication theorem or a complete Lean formalization.
diff --git a/research/gauge44-leaver/RESULT.json b/research/gauge44-leaver/RESULT.json
new file mode 100644
index 0000000000..ae7ae83d51
--- /dev/null
+++ b/research/gauge44-leaver/RESULT.json
@@ -0,0 +1,86 @@
+{
+  "status": "PASS_GAUGE44_STRICT_GLOBAL_REPLAY",
+  "kappa": "1664233607446043/1000000000000000000",
+  "kappa_decimal": "0.001664233607446043",
+  "complex_lower": "1667007898013796187659/1000000000000000000000000",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_supplier": {
+    "pr": 589,
+    "repository": "CrocSwap/integer-mult-bounds",
+    "commit": "a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46",
+    "merged_as": "b3eb785ac5b4b1ca2beea0f80db078a505626a90",
+    "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "git_blob_sha1": "e293ddc557742637f9f679f083a1a282d87b1b13",
+    "word": {
+      "v": 111,
+      "decoder_constant": 63,
+      "copy_ranks": [
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7
+      ]
+    },
+    "derived_deficit": 10272,
+    "deficit_formula": "T(2Kv-L*cst), L=9 T=32 K=4 M=64",
+    "replay_scope": "Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit."
+  },
+  "gain_over_pr635_percent": "1.710756379341731750895113079988470211801335817334370160874117231985604",
+  "spec_sha256": "617468fd3e5bd965e6643eb92fc4f0b87907f7246bf4ede0bbc62c60c7a71d67",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 1.187,
+      "exit_code": 0,
+      "log_sha256": "3aea2a4b68e7aaeadd9ffef649be0d25e2dff1535d9a61bffeaf6d92e55ba6a8"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.36,
+      "exit_code": 0,
+      "log_sha256": "78a081673d6b4fde10a86e6f767d53648b868d1f0cac2441d12951434ad7341b"
+    },
+    {
+      "name": "emit",
+      "seconds": 2.5,
+      "exit_code": 0,
+      "log_sha256": "a9ee385ad6e4ddcd214c0380db430938c385dc4cd088315361f76177ba0ca0f1"
+    },
+    {
+      "name": "audit",
+      "seconds": 14.062,
+      "exit_code": 0,
+      "log_sha256": "69647f950b10d40b3ec10c52dd3e53bbf5f2bd37a6319784e8d307890ab423fe"
+    },
+    {
+      "name": "invoice",
+      "seconds": 0.828,
+      "exit_code": 0,
+      "log_sha256": "4486803d9f4433d91054db8ccc39907cdecf0608f33834b5adc388638e0d0f30"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.312,
+      "exit_code": 0,
+      "log_sha256": "2f2783cfd731cc5f6cc49e8c071799055b539524910dbf61db4d0bc78e47b12a"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 0.375,
+      "exit_code": 0,
+      "log_sha256": "34527ddfe1e53bec71dc5759eb9a26417be6d4e93e76cbf80575d9bafebd876b"
+    },
+    {
+      "name": "bit-supplier-controls",
+      "seconds": 0.579,
+      "exit_code": 0,
+      "log_sha256": "c648542cd6dddbb154af7d02a41aaed1025603d9a4ab54f7c249d2b683e22249"
+    }
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; this bit composition is unreviewed. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/gauge44-leaver/SOURCES.json b/research/gauge44-leaver/SOURCES.json
new file mode 100644
index 0000000000..b6402131b5
--- /dev/null
+++ b/research/gauge44-leaver/SOURCES.json
@@ -0,0 +1,35 @@
+{
+  "contributor": "icekylinx",
+  "research_assistance": "OpenAI GPT-6 Astra",
+  "local_review_and_packaging": "OpenAI Codex",
+  "original_archive": {
+    "filename": "integer_mult_round23_gauge44_delta.zip",
+    "sha256": "40a20a120f51cbed3c9ae4017603be74a9e9332ad4068bd914bf3e81bf8be6b4",
+    "manifest_sha256": "ffa23eb668ad558ebb5601470fc1997a9fb8cea0e188aa3c5d61318be9000603"
+  },
+  "upstream_main": "17ce0c79b7b51c2634b439ea5a2b754f09909693",
+  "construction_parent": {
+    "pr": 635,
+    "commit": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f"
+  },
+  "bit_supplier_pr": 589,
+  "packaging_changes": [
+    "Omit original run logs; retain their original receipts as historical evidence.",
+    "Use repository paths and dollar-delimited Markdown mathematics.",
+    "Add manifest verification, incremental CI and local validation record.",
+    "Trim trailing whitespace in four Python files; complete ASTs are unchanged. Refresh the corresponding constructor input hash.",
+    "research/gauge44-bit589: PR589 bit supplier (G44Stack port, Bit589Reviewer SOUND-WITH-FIXES), G44Pack dz1 owner map, re-derived SPEC, LF line endings, regenerated MANIFEST.",
+    "research/gauge44-leaver: research/gauge44-barch tree plus construction/leaver (k5 cells, chain, frames); G44Pack3 FO_c1 owner map, re-derived SPEC, regenerated independent price receipt, RESULT.json = strict REPLAY, LF, regenerated MANIFEST."
+  ],
+  "attribution": "Original notices and licenses retained. See NOTICE.md, UPSTREAM-NOTICE.md and CONSTRUCTION.md.",
+  "whitespace_only_python_files": [
+    "code/audit_allcold.py",
+    "code/bind_providers_portable.py",
+    "construction/construct_gauge_xcentre.py",
+    "independent/audit_local.py"
+  ],
+  "historical_bit_supplier_pr": 543,
+  "bit_supplier_note": "This package cites PR589 (inputs/PR589-EXPECTED.json, git blob e293ddc5…). PR543 is the supplier of #645's retained historical evidence (LOCAL-VALIDATION.json, independent/ audit files, hosting/, evidence/). RESULT.json is this package's strict replay.",
+  "owner_map": "G44Pack/G44Pack2: The map is G44Pack3's FO_c1, from its pattern-flow LNS (`pflns`) rebound to the R = 489 word. Its lineage is the #685/#741 map (chafreaky) via G44Pack's relabel and rewidth, followed by G44Pack3's LNS. It was admitted with this package's own code (NEWWORD discovery, `freeze_spec.py`, strict) at κ 0.001664233607446043.",
+  "construction_changes": "PartialK: no-triangle gauge44 word (R=504, PRIO6, ranks [4]*14); G44Stack: layers on it (pivot swaps, s4, x30, b6, q4); LeaverSAT: no-helper mutable-leaver cells and re-stacked recipes, LeaverSAT2: frame re-optimisation (construction/leaver); NewBArch: triangle-hybrid B rewrite U8 (construction/barch); chafreaky #741: eight B frames (construction/frames, ported by CompetitorMine) and the owner map; JointXF: joint exchange X4 (construction/jx); BRoute: read-set exchange SW4 (construction/sw4); NoTriReopen: p6n ends (construction/layers_p6n); BlockInvert: entrance promotions E4->E5 (construction/promo, minimal recipe p6n-k4); drivers construction/notri/reproduce_notri.py, construction/layers_np/reproduce_np.py, construction/promo/reproduce_promo.py"
+}
diff --git a/research/gauge44-leaver/UPSTREAM-NOTICE.md b/research/gauge44-leaver/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..ebc24a0168
--- /dev/null
+++ b/research/gauge44-leaver/UPSTREAM-NOTICE.md
@@ -0,0 +1,34 @@
+# Attribution and scope
+
+Four verified provider types are offered to every call: PR571's prefix word with twelve multi-cut cold kernels (PR568's unchanged constructor), the same word with forty width-five entrance promotions (PR569's unchanged frame constructor) before those kernels, PR575's plain joint-prefix provider, and PR568's eight-cold provider. A window MILP with an exact per-pattern model chooses the dispatch and a literal owner map. PR583's six source-bound kernel frame coalescences (its unchanged constructor and negative controls) are applied to every PR571-prefix provider word (ck and atm3), followed by two further coalescences that each first move one addition past two commuting additions (package code/build_gate_moves.py, extending PR583's constructor); a final hyperplane_end step (package code/build_hpe.py) then runs 46 single-gate cleanups h -= p right after part B at the dim-8 join U of their registers, so 46 width-8 entering helpers per call end at U with width 7; each such gate commutes with every earlier cleanup gate on its registers (for 8 of them the partner's one earlier gate x -= p only reads p), and the reordered program is replayed exactly. A window MILP (exact windows, RINS around an LP vertex) gives the dispatch ck 45 / atm3 21 / jp8 6 and the literal owner map.
+
+Pinned external sources (unchanged; `verify.py` checks their manifests and every file it uses):
+- PR568 (`research/complex-multicold`, commit `71c99ac935a33bb7b59a1b4a7af8725a939b0b90`).
+- PR571 (`research/structural-gain`, commit `b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3`).
+- PR569 (`research/larger-gain`, commit `897213a855b7fb8a1b8b0e552a2f5c42e6c1b326`).
+- PR575 (`research/complex-joint-prefix`, commit `eac6f7e378ab622dac50a2fd4b7ef6eab014de44`).
+- PR583 (`research/kernel-frame-coalescing`, commit `89be768f0157f5a3d8e4db69cf1748768605eac9`).
+
+Provider construction is described as typed steps in `data/SPEC.json` (`build`); `verify.py` runs only allowlisted step types with their paired omission audits and checks every input and output content hash. `code/` holds the spec-driven global admission scripts adapted from PR571's `frontier-composition/global-code/` (OpenAI Codex assisted, Apache-2.0): every expected value is read from `data/SPEC.json` and compared only after independent recomputation. `code/generated_identity.py` and `code/generated_identity_controls.py`, and the decompressed-content artifact identities in the bind, audit, invoice, assembly and phase-timing scripts, are taken unchanged from PR586 by chafreaky (`research/promoted-kernel-coalescing`, commit `4846fee5b06af770e9b3a10c36200f673d656725`, OpenAI Codex assisted, Apache-2.0), including its proof-content and reference/metadata mutation controls; the normalization of descriptive width metadata after frame changes follows the same PR.
+
+In PR601, the owner map was nominated by a HiGHS window MILP (adapted from PR569's `global/nominate_width7.py`) with lazy cross-time Hall cuts; this package's re-solved map is described below. Neither is an admission dependency.
+
+DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. (The PR601 package this one starts from states: "Prepared by Claude Code (Anthropic) research agents.") Apache-2.0 applies; LICENSE is included. All notices, licenses, source pins and AI disclosures of the pinned sources and their ancestry are retained in those packages and are not replaced by this notice. All inherited conditional assumptions remain conditional.
+
+**This package (complex-571-cold14, DreamingOfClouds).** It starts from PR601 (jeremykothe2, `research/complex-571-hpem46`, commit `529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550`). Everything above is kept unchanged except the following:
+- every provider chain (ck, atm3, jp8) gains the typed step `cold_end` (`code/build_cold_end.py`, `code/cold_end_controls.py`; recipes `data/recipes/*-cold_end.json.gz`);
+- the generalised native chain and the global admission scripts accept cold helpers that end below FULL (with `0:U` wrappers), a refactored exact cleanup, and check the wrapper order;
+- `data/PLAN.json` / `data/OWNERS.json.gz` (dispatch and literal owner map) come from a relocate/swap/ejection-chain/provider-flip annealing search started from PR601's map, refined by an exact pattern-restricted owner model (CP-SAT) with a literal edge-colouring expansion (not an admission dependency);
+- `data/SPEC.json` holds the expected values, recorded by a discovery run and then checked by a strict run.
+
+The cold-end construction (a row-plus-column cone condition for low-frame ends, a rank-0 dirt-spread premix and multi-gate lower-frame cleanup) builds on PR591 / PR592 / PR593 / PR601 (jeremykothe2) and our PR599 (Lean: multi-gate and cold hyperplane-end tails). DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. Build on this at your own risk.
+
+**This package (complex-571-cold14-b3, jeremykothe2).** It is PR604's `complex-571-cold14` (DreamingOfClouds) with ColdBeyond's second cold end per block (two new `cold_end` A-gate primitives, `PROOF-NOTE.md`), ColdSupply's E1 entering pair and reviewed controls, a free dispatch (jp8 ×60, atm3 ×12) and a literal owner map from an exact per-time-Hall window MIP. All other construction, code, controls and proofs are PR604's and earlier contributors', unchanged.
+
+**This package (complex-571-cold14-k492).** It is complex-571-cold14-b3 with these changes:
+- **K-triangle base words.** The leaver-read K-triangle skeleton atom and its read schedule (`data/TRI-SCHEDULE.json`) are by AtomScout, a Claude Code research agent. `code/construct_k_triangle.py` is PR531's `code/construct_504.py` (icekylinx, OpenAI Codex / GPT assisted, Apache-2.0; pinned source `direct_delivery`) extended with that atom.
+- **Ported chains.** The PR604/B3 chains are ported stage by stage onto the K-triangle words by `code/build_port_stage.py` (Port480, a Claude Code research agent). `code/build_frame_regroup.py` extends PR583's `build_frames.py` (chafreaky).
+- **Helper count R.** The generalisation of the global scripts to the provider helper count R is by GlobalR (a Claude Code research agent), with AtomReviewer's fixes (PROOF-NOTE-R.md).
+- **Owner map.** The owner map, the cold_end recipes on the K-triangle words and the package assembly are by Stack492, Port480 and ColdBeyond (Claude Code research agents).
+
+Build on this at your own risk.
diff --git a/research/gauge44-leaver/code/assemble.py b/research/gauge44-leaver/code/assemble.py
new file mode 100644
index 0000000000..8cee90b50e
--- /dev/null
+++ b/research/gauge44-leaver/code/assemble.py
@@ -0,0 +1,241 @@
+"""Gauge44 complete global admission with the retained native exact-complex moment.
+
+Prepared with OpenAI Codex assistance. The rational engines and outer
+constraints are retained from PR547/PR548 and their preserved ancestry.
+The bit operator is the cited unchanged PR589 supplier (PR555's punctured
+R439 word, v = 111, decoder constant 63, two A-section transports), shipped
+as inputs/PR589-EXPECTED.json and pinned by git blob id. Its rank-mass
+deficit is derived from the word's parameters, T(2Kv - L*cst) at nine
+stages (PR545/PR555 rank-mass identity), not hard-coded. The complex owner
+and invoice inputs must be freshly emitted by the packaged physical replay.
+All conservative admission guards and conservative moment/outer witnesses run
+before the PR559 native-complex correction. The bit surcharge is retained.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from decimal import Decimal, localcontext
+import argparse,json,hashlib,importlib.util,os,sys
+from collections import Counter
+assert __debug__, 'Assertions required'
+P=Path(sys.argv[1] if __name__=='__main__' else os.environ['GAIN_PR564_SOURCE']).resolve()
+read=lambda p:json.loads(p.read_text())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+hash_ok=lambda x:isinstance(x,str) and len(x)==64 and all(t in '0123456789abcdef'for t in x)
+digest=lambda x:hashlib.sha256(json.dumps(x,separators=(',',':')).encode()).hexdigest()
+def load(n):
+ s=importlib.util.spec_from_file_location(n,P/'engines'/(n+'.py'));m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,B,A=[load(n)for n in ('moment','base_two_moment','outer')]
+def dec(x):
+ with localcontext()as ctx:ctx.prec=70;return str(Decimal(x.numerator)/Decimal(x.denominator))
+from witness import DISPATCH,CALL_ORDER,COUNTS,PIDS,X,DISCOVER,pin,SPOT,spot_widths
+# Cited bit supplier: PR589's tune/EXPECTED.json (merged on main as research/e8-bit-p111-tuned/tune/EXPECTED.json).
+BIT_PATH=Path(__file__).resolve().parents[1]/'inputs/PR589-EXPECTED.json'
+BIT_BLOB='e293ddc557742637f9f679f083a1a282d87b1b13'
+# Nine-stage bit template (PR463/PR510 chain, 32 replicas): L stages, T replicas, K=(L-1)//2 pairs, moment width M=1+7L.
+BIT_L,BIT_T=9,32;BIT_K=(BIT_L-1)//2;BIT_M=1+7*BIT_L
+def git_blob(data):return hashlib.sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest()
+def load_bit(data):
+ """The pinned supplier record: its full record (word parameters) and its nine-stage price."""
+ assert git_blob(data)==BIT_BLOB,'bit supplier blob pin'
+ return json.loads(data)
+def bit_deficit(word,live):
+ """Rank-mass deficit M*live - mass = T(2Kv - L*cst) of a v-port bit word with decoder constant cst (PR545/PR555).
+ cst is the sum of the retained totals' COPY ranks and live = 2KvT data wires; both are cross-checked here, and the
+ caller checks the result against the priced profile, so neither v nor cst is free."""
+ v,cst,ranks=word['v'],word['decoder_constant'],word['copy_ranks']
+ assert type(v)is int and type(cst)is int and all(type(r)is int and 0<r<=8 for r in ranks)
+ assert len(ranks)==word['retained_totals']==BIT_L and cst==sum(ranks)
+ assert live==2*BIT_K*v*BIT_T
+ d=BIT_T*(2*BIT_K*v-BIT_L*cst);assert d>0;return d
+
+
+def assemble(owner,invoice,owner_sha,invoice_sha):
+ # These are admission receipts, not optional collections of successful rows.
+ # Require both orientations and every finite check before pricing anything.
+ assert owner['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE'
+ assert invoice['status']=='PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE'
+ assert all(hash_ok(x)for x in (owner_sha,invoice_sha,owner['template_sha256'],owner['controller_audit_sha256'],invoice['parent_template_sha256']))
+ checks={'local_primitive_bound','logical','router','literal','mass','precision','tape','row','halving'}
+ assert set(invoice['strict_checks'])==checks
+ assert all(invoice['strict_checks'][name] is True for name in checks)
+ assert set(invoice['providers'])==set(PIDS)
+ assert invoice['provider_counts']==COUNTS
+ assert owner['all_live_owners_per_call_distinct'] is True
+ # R (helpers per provider word) is read from the invoice and must be shared by every provider; n=2v+R.
+ R=invoice['helpers'];assert type(R) is int and R>0 and all(p['helpers']==R for p in invoice['providers'].values())
+ assert owner['owners_per_call']==2*112+R and owner['actual_helper_owner_charts']==owner['hosted_residuals']==72*R==pin('expected.hosted_residuals',owner['hosted_residuals'])
+ pin('expected.rank_mass',owner['rank_mass'])
+ pin('expected.actual_73column_sigmas',owner['actual_73column_sigmas']);pin('expected.cross_replica_helper_roles',owner['cross_replica_helper_roles'])
+ pin('expected.idle_remainders',owner['explicit_idle_remainder_children'])
+ assert invoice['complete_invocation_sweeps']==invoice['bridge_sweeps']==72
+ assert invoice['live']==owner['live'] and invoice['physical']==owner['physical']
+ assert invoice['centres']==8
+ assert invoice['physical_stock_identity']==dict(data_and_owner_families=7168,local_helpers=R,private_centres=8,coefficient_work=2)
+ assert sum(invoice['physical_stock_identity'].values())==invoice['physical']
+ assert invoice['controller_audit_sha256']==owner['controller_audit_sha256']
+ for pid,p in invoice['providers'].items():
+  assert set(p['local'])=={'forward','backward'}
+  assert p['helpers']==R and p['centres']==8 and p['n']==2*112+R and p['v']==112 and p['h']==9
+  K='providers.'+pid+'.';pin(K+'entering',p['entering_helpers']);pin(K+'entrance',p['entrance_rank'])
+  pin(K+'inventory',p['width_inventory'])
+  assert all(type(w) is int and 0<w<=9 for w in p['widths'])
+  assert Counter(p['widths'])==Counter({int(r):n for r,n in p['width_inventory'].items()})
+  assert sum(p['widths'])==9*R-p['entrance_rank']-p['terminal_codimension'] and len(p['widths'])==R   # HPE: widths |final|-|start|
+  pin(K+'width_digest',digest(p['widths']));assert tuple(p['widths'][h]for h in SPOT)==spot_widths()
+  pin(K+'expected_profile',p['paid_profile'])
+  assert p['children']==sum(p['paid_profile'].values())
+  pin(K+'program_hashes',p['program_hashes'])
+  for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json'):
+   assert hash_ok(p['artifacts'][name]) and p['artifacts'][name]==owner['source_artifacts']['providers/'+pid+'/'+name]
+   if name in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):pin(K+'artifacts.'+name,p['artifacts'][name])
+  pin(K+'artifact_semantic_sha256',p['semantic_artifact_sha256'])
+  pin(K+'complete_contract',{k:v for k,v in p.items()if k!='artifacts'})
+  assert owner['provider_artifact_semantic_sha256'][pid]==p['semantic_artifact_sha256']
+  pin(K+'semantic_phase_sha256',p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'])
+  assert owner['provider_phase_semantic_sha256'][pid]==invoice['provider_phase_semantic_sha256'][pid]==p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']
+  for name in ('forward','backward'):
+   z=p['local'][name];pinned=pin(K+'expected_local.'+name,{k:z[k]for k in('events','macros','real_component_primitives','prefix_l1','coefficient_work_primitive_count')});primitives=pinned['real_component_primitives'];coefficient_work=pinned['coefficient_work_primitive_count']
+   assert z['all_dirty_helper_columns_restored'] is True and z['private_centres_and_coefficient_work_cleared'] is True
+   assert z['all_exact_columns']==2*112+R and z['dirty_helper_columns']==R
+   assert z['events']==pinned['events'] and z['macros']==pinned['macros']
+   assert z['real_component_primitives']==primitives and z['coefficient_work_primitive_count']==coefficient_work
+   assert z['pre_wrappers']==z['post_wrappers']==p['entering_helpers']+p.get('cold_hyperplane_ended_helpers',0);pin(K+'wrappers',z['pre_wrappers'])   # COLD-HPE
+   assert 0<z['prefix_bits']<=192 and 0<Q(z['prefix_l1'])<2**192
+   peak=Q(z['prefix_l1']);assert z['prefix_bits']==peak.numerator.bit_length()-peak.denominator.bit_length()+1
+   assert peak==Q(pinned['prefix_l1'])
+  assert p['compiler']==64*74**3
+  assert p['local_adapters']==16*(max(z['macros']for z in p['local'].values())+p['children']+2*112+R+8)+64*73
+  assert p['local_primitive_bound']==max(z['real_component_primitives']for z in p['local'].values())+p['local_adapters']*p['compiler']
+ calls=invoice['selected_calls'];assert len(calls)==72
+ assert [(c['stage'],c['replica'])for c in calls]==CALL_ORDER
+ assert {(c['stage'],c['replica']) for c in calls}=={(s,r) for s in range(9) for r in range(8)}
+ for c in calls:
+  pid=DISPATCH[c['stage'],c['replica']]
+  assert c['provider_id']==pid
+  # The retained nine-stage recipe alternates its two reflected shears.
+  assert c['orientation']==('forward' if c['stage']%2==0 else 'backward')
+  p=invoice['providers'][pid];z=p['local'][c['orientation']]
+  assert c['program_sha256']==p['program_hashes'][c['orientation']]
+  for name in ('events','macros','real_component_primitives','coefficient_work_primitive_count','pre_wrappers','post_wrappers'):
+   assert c[name]==z[name]
+  assert c['entering_helpers']==p['entering_helpers'] and c['entrance_rank']==p['entrance_rank']
+ assert invoice['selected_real_component_primitives']==sum(c['real_component_primitives'] for c in calls)
+ assert invoice['selected_coefficient_work_primitive_count']==sum(c['coefficient_work_primitive_count'] for c in calls)
+ assert invoice['selected_scalar_macros']==sum(c['macros'] for c in calls)==sum(invoice['providers'][c['provider_id']]['local'][c['orientation']]['macros'] for c in calls)
+ assert invoice['factors_per_wrapper']==144
+ assert invoice['wrapper_elementary_factors_charged']==sum(c['pre_wrappers']+c['post_wrappers'] for c in calls)*144
+ paid=Counter()
+ for c in calls:paid.update({int(r):n for r,n in invoice['providers'][c['provider_id']]['paid_profile'].items()})
+ assert dict(paid)=={int(r):n for r,n in invoice['selected_local_paid_profile'].items()}
+ idle=Counter({int(r):n for r,n in owner['paid_profile'].items()});idle.subtract(paid);assert all(n>=0 for n in idle.values())
+ idle=+idle;assert sum(idle.values())==owner['explicit_idle_remainder_children']
+ pin('expected.idle_remainder_profile',{str(r):n for r,n in sorted(idle.items())})
+ paid.update(idle)
+ assert dict(paid)=={int(r):n for r,n in owner['paid_profile'].items()}
+ assert invoice['compiler']==64*74**3
+ assert invoice['local_adapters']==max(p['local_adapters']for p in invoice['providers'].values())
+ assert invoice['local_primitive_bound']==max(p['local_primitive_bound']for p in invoice['providers'].values())
+ # Recount the retained dedicated-bank envelope independently. Its geometry
+ # stays fixed, while every local primitive and wrapper comes from the actual
+ # selected provider/orientation sums above.
+ parent_live,parent_physical,parent_idle=11704,12218,16128
+ parent_banks,rem=divmod(parent_live-2*112*4*8,9);assert rem==0 and parent_physical==parent_live+parent_banks+8+2   # parent R0=504 dedicated helpers per stage bank
+ assert owner['source_idle_children_charged']==parent_idle
+ bridges,shifts=2*112*72,4*112*8;moves=2*shifts
+ nonlocal_items=(4*112*8*9+2*112*8*9+2*72*R+parent_idle+9*parent_banks+bridges+shifts+moves+parent_live+parent_physical+invoice['wrapper_elementary_factors_charged'])
+ outside=8*nonlocal_items+64*73
+ pervertex=(invoice['selected_real_component_primitives']+bridges+shifts+moves+parent_live+(72*invoice['local_adapters']+outside)*invoice['compiler']+64*parent_physical)
+ rebased=pervertex+65*(invoice['physical']-parent_physical)+(invoice['live']-parent_live)
+ assert invoice['unhosted_pervertex']==pervertex and invoice['hosted_rebased_pervertex']==rebased
+ used=max(pervertex,rebased)
+ prior=invoice['retained_prior_overcharge']
+ if prior is not None:
+  assert hash_ok(prior['sha256']) and type(prior['previous_pervertex_allowance']) is int and prior['previous_pervertex_allowance']>0
+  assert prior['added_complete_new_pervertex']==pervertex
+  assert prior['policy']=='Retain old allowance and add entire fresh mixed recount.'
+  used=max(used,prior['previous_pervertex_allowance']+pervertex)
+ assert invoice['conservative_pervertex_used']==used
+ finite=invoice['finite']
+ assert 0<finite['physical_row_coefficient']<finite['retained_row_coefficient']==20161
+ assert 0<finite['required_C0_bits']<finite['C0_exponent']==210000
+ assert finite['G_exponent']==30000 and finite['E_exponent']==100000
+ assert finite['halving_integer_inequality']==[5329,4608]
+ assert 0<invoice['global_prefix_bits']<=invoice['charged_prefix_bits']==512
+ assert invoice['row_prefix_extra']==1024
+ assert invoice['global_prefix_bits']==max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())+37+72+72+4
+ group=2**(36*36)
+ for j in range(1,37):group*=2**(2*j)-1
+ stock=group*invoice['physical'];streamed_mass=group*owner['rank_mass']
+ logical=group*used+64;router=invoice['compiler']*(logical+1)*(stock+1)**2
+ literal=2*2**30000*stock**2+8*streamed_mass+4*stock+4+32*73
+ total_mass=streamed_mass+2**100000
+ assert finite['physical_stock_bits']==stock.bit_length() and finite['router_bits']==router.bit_length() and finite['literal_bits']==literal.bit_length()
+ assert finite['physical_row_coefficient']==2*stock.bit_length()+9909+252+1024
+ assert finite['required_C0_bits']==(32*73*total_mass*total_mass).bit_length()
+ actual_checks=dict(local_primitive_bound=invoice['local_primitive_bound']<2**48,logical=logical<2**6050,router=router<2**30000,literal=literal<2**100000,mass=total_mass<2**100001,precision=32*73*total_mass*total_mass<2**210000,tape=2*total_mass+18<2**210000,row=finite['physical_row_coefficient']<20161,halving=73*73>2*48*48)
+ assert actual_checks==invoice['strict_checks'] and all(actual_checks.values())
+ bit_record=load_bit(BIT_PATH.read_bytes())
+ bit=bit_record['nine']
+ assert 'nine-stage' in bit['pipeline'] and '32 replicas' in bit['pipeline']
+ c=Q(bit['bit_lower'])
+ bit_D=bit_deficit(bit_record['word'],bit['bit']['live'])
+ H={int(r):n for r,n in owner['paid_profile'].items()};pin('expected.global_profile',owner['paid_profile'])
+ # Claimed lower endpoints come from the spec; discovery derives them with the same certified moment engine.
+ # Either way they are verified below (accepted at b, rejected at b+1e-24).
+ if DISCOVER:b=Q(M.certify(H,73,owner['live'],False)['lower']);conservative_b=Q(M.certify(H,73,owner['live'],True)['lower'])
+ else:b=Q(X['complex_lower']);conservative_b=Q(X['conservative_complex_lower'])
+ assert owner['template_sha256']==invoice['template_sha256'] and owner_sha==invoice['owner_audit_sha256']
+ pin('expected.live',owner['live']);pin('expected.physical',owner['physical']);assert owner['deficit']==2560
+ assert owner['banked_residuals']==0
+ def check_moment(side,h,m,W,lower,deficit,bad):
+  assert m*W-sum(r*n for r,n in h.items())==deficit and m*m>2*max(h)**2
+  rows=[]
+  for z,accept in [(lower,True),(lower+Q(1,10**24),False)]:
+   l,u=M.moment(h,m,W,z,bad);ll,uu=B.moment(m,W,list(h.items()),z)
+   if bad:
+    fl,fu=B.moment(m,W,[(1,32*m*m*sum(h.values()))],z);ll+=fl/10**16;uu+=fu/10**16
+   assert (u<1 and uu<1)if accept else(l>1 and ll>1)
+   rows.append(dict(side=side,surcharge=bad,endpoint=str(z),accept=accept,mercator=[str(l-1),str(u-1)],base_two=[str(ll-1),str(uu-1)]))
+  return rows
+ bitH={int(r):n for r,n in bit['profile'].items()}
+ assert BIT_M==64 and sum(r*n for r,n in bitH.items())==bit['bit']['rank_mass']
+ bit_moments=check_moment('bit',bitH,BIT_M,bit['bit']['live'],c,bit_D,True)
+ conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,2560,True)
+ assert bit['bit']['two_level_coefficient_bits']<bit['bit']['charged_two_level_coefficient_bits']==512 and bit['bit']['row_coefficient']<20161
+ def outer_witness(bb):
+  eta=beta=Q(1,10**24);s=min(c,(1-beta)*bb)-Q(1,10**27);assert 0<s<c and s<(1-beta)*bb
+  chain=[Q(384599,10**10)];cuts=[]
+  for _ in range(7):
+   old=chain[-1];a=(1-s)*s+s*old;gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+   ceil=lambda x:-(-x.numerator//x.denominator);cut=max(ceil(36/gap**2),ceil(2*(4+512)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+512)
+   cuts.append(dict(exponent=str(a),gap=str(gap),cutoff_log2=str(cut)));chain.append(a)
+  q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin*10**18;k=Q((ticks.numerator-1)//ticks.denominator,10**18)
+  bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}
+  outer=A.assembly(chain[-1],bb,bridge,k,eta=eta,beta=beta);assert len(outer['strict_constraints'])==47 and all(v>0 for v in outer['strict_constraints'].values())
+  controls=[]
+  for name,kk,ee,be in [('next_grid',k+Q(1,10**18),eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]:
+   try:A.assembly(chain[-1],bb,bridge,kk,eta=ee,beta=be)
+   except AssertionError:controls.append(name)
+   else:raise AssertionError(name)
+  return k,cuts,outer,controls
+ conservative_k,conservative_cuts,conservative_outer,conservative_controls=outer_witness(conservative_b)
+ pin('expected.conservative_kappa_decimal',dec(conservative_k))
+ # Only after every conservative supplier/admission/outer check succeeds is
+ # the reviewed native exact-complex recurrence selected. Bit charge stays.
+ native_moments=check_moment('complex',H,73,owner['live'],b,2560,False)
+ k,cuts,outer,controls=outer_witness(b)
+ pin('expected.kappa_decimal',dec(k))
+ assert M.moment(H,73,owner['live'],b,True)[0]>1
+ assert M.moment(bitH,64,bit['bit']['live'],c+Q(1,10**24),False)[1]<1
+ model_controls=['native_complex_endpoint_rejected_with_old_surcharge','omitting_bit_surcharge_would_fail_next_endpoint_rejection']
+ moments=bit_moments+native_moments
+ input_hashes={'owner_audit':owner_sha,'fresh_invoice':invoice_sha,'package:inputs/PR589-EXPECTED.json':sha(BIT_PATH)}
+ input_hashes.update({'engines/'+name+'.py':sha(P/'engines'/(name+'.py'))for name in ('moment','base_two_moment','outer')})
+ return dict(status='PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY',kappa=str(k),kappa_decimal=dec(k),complex_lower=str(b),complex_decimal=dec(b),bit_lower=str(c),bit_decimal=dec(c),binding='complex',gain_over_pr635_percent=dec(100*(k/Q(X['gain_baseline_kappa'])-1)),complex_profile=H,provider_counts=invoice['provider_counts'],surcharge_model={'complex':False,'bit':True},conservative_complex_lower=str(conservative_b),conservative_complex_decimal=dec(conservative_b),conservative_kappa=str(conservative_k),conservative_kappa_decimal=dec(conservative_k),conservative_moments=conservative_moments,conservative_bootstrap=conservative_cuts,conservative_outer={n:str(v)for n,v in conservative_outer['strict_constraints'].items()},conservative_controls=conservative_controls,model_controls=model_controls,native_correction_gain=dec(k-conservative_k),template_sha256=owner['template_sha256'],input_sha256=input_hashes,bit_supplier=dict(pr=589,repository='CrocSwap/integer-mult-bounds',commit='a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46',merged_as='b3eb785ac5b4b1ca2beea0f80db078a505626a90',path='research/e8-bit-p111-tuned/tune/EXPECTED.json',git_blob_sha1=BIT_BLOB,word=dict(v=bit_record['word']['v'],decoder_constant=bit_record['word']['decoder_constant'],copy_ranks=bit_record['word']['copy_ranks']),derived_deficit=bit_D,deficit_formula='T(2Kv-L*cst), L=%d T=%d K=%d M=%d'%(BIT_L,BIT_T,BIT_K,BIT_M),replay_scope='Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit.'),moments=moments,bootstrap=cuts,outer={n:str(v)for n,v in outer['strict_constraints'].items()},controls=controls,scope='Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; this bit composition is unreviewed. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification.')
+if __name__=='__main__':
+ import sys
+ package,C,out=map(Path,sys.argv[1:4]);assert package.resolve()==P and not out.exists()
+ owner_path=C/'audit/OWNERS-AND-PROFILE.json';invoice_path=C/'audit/PREFIX-AND-INVOICE.json'
+ owner,invoice=read(owner_path),read(invoice_path)
+ assert owner['template_sha256']==read(C/'hosted/HOSTED.json')['template_sha256']
+ r=assemble(owner,invoice,sha(owner_path),sha(invoice_path));out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],r['kappa_decimal'])
diff --git a/research/gauge44-leaver/code/assembly_controls.py b/research/gauge44-leaver/code/assembly_controls.py
new file mode 100644
index 0000000000..93bca1ce6f
--- /dev/null
+++ b/research/gauge44-leaver/code/assembly_controls.py
@@ -0,0 +1,260 @@
+"""Independent admission controls for the N-provider native-complex assembly (per-provider controls).
+
+Prepared with OpenAI Codex assistance; Apache-2.0. Mutation receipts are
+rebound to their new owner digest, so unrelated stale hashes cannot conceal
+an incomplete width, provider, orientation, paid-profile or finite check.
+The fresh physical replay remains a separate prerequisite.
+"""
+import argparse
+import copy
+import itertools
+import math
+import hashlib
+import json
+import os
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+
+assert __debug__, 'Assertions required'
+P = Path(__file__).resolve().parent
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+digest = lambda x: hashlib.sha256(json.dumps(x, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+
+
+def verify(owner_path, invoice_path, source_package):
+    os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve())
+    from assemble import assemble
+    owner = json.loads(owner_path.read_text())
+    invoice = json.loads(invoice_path.read_text())
+    baseline = assemble(owner, invoice, sha(owner_path), sha(invoice_path))
+
+    def empty_maps(o, i):
+        i['strict_checks'] = {}
+        i['providers'] = {}
+
+    def understated_stock(o, i):
+        o['physical'] -= 1
+        i['physical'] -= 1
+        i['physical_stock_identity']['coefficient_work'] -= 1
+
+    def changed_profile(o, i):
+        o['paid_profile']['1'] += 2
+        o['paid_profile']['2'] -= 1
+
+    def wrong_orientation(o, i):
+        c = next(c for c in i['selected_calls'] if c['stage'] == 0)
+        c['orientation'] = 'backward'
+        p = i['providers'][c['provider_id']]
+        z = p['local']['backward']
+        c['program_sha256'] = p['program_hashes']['backward']
+        for name in ('events', 'macros', 'real_component_primitives',
+                     'coefficient_work_primitive_count', 'pre_wrappers', 'post_wrappers'):
+            c[name] = z[name]
+        i['selected_real_component_primitives'] = sum(c['real_component_primitives'] for c in i['selected_calls'])
+        i['selected_coefficient_work_primitive_count'] = sum(c['coefficient_work_primitive_count'] for c in i['selected_calls'])
+
+    def understated_prefix(o, i):
+        for p in i['providers'].values():
+            for z in p['local'].values():
+                z['prefix_bits'], z['prefix_l1'] = 1, '1'
+        i['global_prefix_bits'] = 1 + 37 + 72 + 72 + 4
+
+    def reordered_calls(o, i):
+        i['selected_calls'][0], i['selected_calls'][1] = i['selected_calls'][1], i['selected_calls'][0]
+
+    def no_cold_wrappers(o, i):
+        for p in i['providers'].values():
+            p['entering_helpers'] -= 4
+            for z in p['local'].values():z['pre_wrappers'] = z['post_wrappers'] = p['entering_helpers']
+        for c in i['selected_calls']:
+            c['entering_helpers'] = c['pre_wrappers'] = c['post_wrappers'] = i['providers'][c['provider_id']]['entering_helpers']
+        i['wrapper_elementary_factors_charged'] = sum(2*c['pre_wrappers'] for c in i['selected_calls'])*i['factors_per_wrapper']
+
+    controls = [
+        ('empty_certification_maps', empty_maps),
+        ('failed_invoice_status', lambda o, i: i.__setitem__('status', 'FAIL')),
+        ('nonboolean_precision_check', lambda o, i: i['strict_checks'].__setitem__('precision', 'true')),
+        ('wrong_owner_role_count', lambda o, i: o.__setitem__('actual_helper_owner_charts', o['actual_helper_owner_charts'] - 1)),
+        ('understated_physical_stock', understated_stock),
+        ('changed_profile_same_rank_mass', changed_profile),
+        ('insufficient_finite_C0', lambda o, i: i['finite'].__setitem__('required_C0_bits', 210001)),
+        ('missing_finite_check', lambda o, i: i['strict_checks'].pop('halving')),
+        ('wrong_reflected_orientation_selfconsistent_totals', wrong_orientation),
+        ('missing_selected_call', lambda o, i: i['selected_calls'].pop()),
+        ('wrong_selected_primitive_sum', lambda o, i: i.__setitem__('selected_real_component_primitives', i['selected_real_component_primitives'] - 1)),
+        ('wrong_selected_coefficient_work_sum', lambda o, i: i.__setitem__('selected_coefficient_work_primitive_count', i['selected_coefficient_work_primitive_count'] - 1)),
+        ('unpaid_wrapper_factors', lambda o, i: i.__setitem__('wrapper_elementary_factors_charged', i['wrapper_elementary_factors_charged'] - 144)),
+        ('wrong_global_compiler', lambda o, i: i.__setitem__('compiler', 1)),
+        ('wrong_global_adapter_maximum', lambda o, i: i.__setitem__('local_adapters', 1)),
+        ('understated_exact_prefix_and_global_sum', understated_prefix),
+        ('wrong_global_prefix_sum', lambda o, i: i.__setitem__('global_prefix_bits', 224)),
+        ('wrong_row_prefix_reserve', lambda o, i: i.__setitem__('row_prefix_extra', 0)),
+        ('wrong_parent_geometry_charge', lambda o, i: i.__setitem__('unhosted_pervertex', 1)),
+        ('wrong_rebased_geometry_charge', lambda o, i: i.__setitem__('hosted_rebased_pervertex', 1)),
+        ('wrong_complete_pervertex_envelope', lambda o, i: i.__setitem__('conservative_pervertex_used', 1)),
+        ('wrong_prior_added_complete_invoice', lambda o, i: i['retained_prior_overcharge'].__setitem__('added_complete_new_pervertex', 1)),
+        ('wrong_finite_router_bits', lambda o, i: i['finite'].__setitem__('router_bits', 1)),
+        ('wrong_finite_literal_bits', lambda o, i: i['finite'].__setitem__('literal_bits', 1)),
+        ('wrong_finite_physical_stock_bits', lambda o, i: i['finite'].__setitem__('physical_stock_bits', 1)),
+        ('wrong_finite_row_coefficient', lambda o, i: i['finite'].__setitem__('physical_row_coefficient', 1)),
+        ('reordered_complete_calls', reordered_calls),
+        ('understated_explicit_idle_remainders', lambda o, i: o.__setitem__('explicit_idle_remainder_children', o['explicit_idle_remainder_children']-1)),
+        ('understated_actual_chart_types', lambda o, i: o.__setitem__('actual_73column_sigmas', o['actual_73column_sigmas']-1)),
+        ('wrong_cross_replica_role_count', lambda o, i: o.__setitem__('cross_replica_helper_roles', o['cross_replica_helper_roles']-1)),
+        ('old_no_cold_wrapper_counts_selfconsistent', no_cold_wrappers),
+    ]
+
+    def resync(i, c):
+        p = i['providers'][c['provider_id']]
+        c['program_sha256'] = p['program_hashes'][c['orientation']]
+        c['entering_helpers'], c['entrance_rank'] = p['entering_helpers'], p['entrance_rank']
+        for name in ('events','macros','real_component_primitives','coefficient_work_primitive_count','pre_wrappers','post_wrappers'):
+            c[name] = p['local'][c['orientation']][name]
+
+    # Every provider gets the full per-provider control set, substituting a partner provider where needed.
+    for P in PIDS:
+        Qp = partner(P) if len(PIDS)>1 else '__unregistered__'
+        widths = invoice['providers'][P]['widths']
+
+        def forged_program_hash(o, i, P=P):
+            i['providers'][P]['program_hashes']['forward'] = '0' * 64
+            for c in i['selected_calls']:
+                if c['provider_id'] == P:
+                    c['program_sha256'] = '0' * 64
+
+        def wrong_selected_call(o, i, P=P):
+            c = next(c for c in i['selected_calls'] if c['provider_id'] == P)
+            d = next(d for d in i['selected_calls'] if d is not c and (d['provider_id'] != P or len(PIDS)==1) and (d['stage'] - c['stage']) % 2 == 0)
+            c['stage'], d['stage'], c['replica'], d['replica'] = d['stage'], c['stage'], d['replica'], c['replica']
+
+        def stale_program(o, i, P=P, Qp=Qp):
+            p = i['providers'][P]
+            p['program_hashes'] = copy.deepcopy(i['providers'][Qp]['program_hashes'])
+            for c in i['selected_calls']:
+                if c['provider_id'] == P:
+                    c['program_sha256'] = p['program_hashes'][c['orientation']]
+
+        def stale_profile(o, i, P=P, Qp=Qp):
+            p = i['providers'][P]
+            p['paid_profile'] = copy.deepcopy(i['providers'][Qp]['paid_profile'])
+            p['children'] = sum(p['paid_profile'].values())
+
+        def moved(o, i, P=P):
+            a = next(c for c in i['selected_calls'] if c['provider_id'] == P)
+            b = next(c for c in i['selected_calls'] if c['provider_id'] != P and c['orientation'] == a['orientation'])
+            a['provider_id'], b['provider_id'] = b['provider_id'], a['provider_id']
+            resync(i, a); resync(i, b)
+
+        def compensating(o, i, P=P, Qp=Qp):
+            # Two dishonest profiles that cancel exactly in the dispatch-weighted aggregate.
+            g = math.gcd(COUNTS[P], COUNTS[Qp]); dp, dq = COUNTS[Qp] // g, COUNTS[P] // g
+            p, q = i['providers'][P], i['providers'][Qp]
+            p['paid_profile']['1'] += dp; q['paid_profile']['1'] -= dq
+            p['children'] += dp; q['children'] -= dq
+
+        def forged_recipe(o, i, P=P):
+            name = 'CLIFFORD-RECIPES.json'
+            i['providers'][P]['artifacts'][name] = '0'*64
+            o['source_artifacts']['providers/'+P+'/'+name] = '0'*64
+
+        def forged_phase(o, i, P=P):
+            i['providers'][P]['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'] = '0'*64
+            o['provider_phase_semantic_sha256'][P] = i['provider_phase_semantic_sha256'][P] = '0'*64
+
+        controls += [
+            (P + ':missing_provider', lambda o, i, P=P: i['providers'].pop(P)),
+            (P + ':missing_backward_orientation', lambda o, i, P=P: i['providers'][P]['local'].pop('backward')),
+            (P + ':unpaid_scalar_primitive', lambda o, i, P=P: i['providers'][P]['local']['forward'].__setitem__('real_component_primitives', i['providers'][P]['local']['forward']['real_component_primitives'] - 1)),
+            (P + ':wrong_local_artifact_binding', lambda o, i, P=P: i['providers'][P]['artifacts'].__setitem__('LOCAL-PROGRAMS.json.gz', '0' * 64)),
+            (P + ':false_dirty_restoration', lambda o, i, P=P: i['providers'][P]['local']['backward'].__setitem__('all_dirty_helper_columns_restored', False)),
+            (P + ':wrong_declared_provider_count', lambda o, i, P=P: i['provider_counts'].__setitem__(P, i['provider_counts'][P] + 1)),
+            (P + ':wrong_local_compiler', lambda o, i, P=P: i['providers'][P].__setitem__('compiler', 1)),
+            (P + ':wrong_local_adapter_charge', lambda o, i, P=P: i['providers'][P].__setitem__('local_adapters', 1)),
+            (P + ':wrong_local_primitive_bound', lambda o, i, P=P: i['providers'][P].__setitem__('local_primitive_bound', 1)),
+            (P + ':forged_provider_and_call_program_hash', forged_program_hash),
+            (P + ':provider_at_wrong_call', wrong_selected_call),
+            (P + ':stale_partner_program_consistent_call_hashes', stale_program),
+            (P + ':stale_partner_profile_consistent_child_total', stale_profile),
+            (P + ':relocated_against_partner_same_counts', moved),
+            (P + ':compensating_false_profiles_with_' + Qp, compensating),
+            (P + ':synchronized_forged_source_recipe_hash', forged_recipe),
+            (P + ':synchronized_forged_phase_review_semantics', forged_phase),
+        ]
+        if len(PIDS)==1:
+            # Cross-provider substitutions require a second actual supplier.
+            # All single-provider program, phase, profile and dispatch bindings
+            # retain their direct mutations above and in the controller audit.
+            partner_only = {P+':stale_partner_program_consistent_call_hashes',
+                            P+':stale_partner_profile_consistent_child_total',
+                            P+':relocated_against_partner_same_counts',
+                            P+':compensating_false_profiles_with_'+Qp}
+            controls = [(name, fn) for name, fn in controls if name not in partner_only]
+        # Width order and inventory: swap the first helper of every pair of distinct widths (same inventory),
+        # and shift one unit between them (same total).
+        first = {}
+        for h, w in enumerate(widths):
+            first.setdefault(w, h)
+        for wa, wb in itertools.combinations(sorted(first), 2):
+            def swap(o, i, P=P, a=first[wa], b=first[wb]):
+                w = i['providers'][P]['widths']; w[a], w[b] = w[b], w[a]
+            def shift(o, i, P=P, a=first[wa], b=first[wb]):
+                w = i['providers'][P]['widths']; w[a] += 1; w[b] -= 1
+            controls.append((P + ':width_order_swap_%d_%d' % (wa, wb), swap))
+            controls.append((P + ':width_inventory_shift_%d_%d' % (wa, wb), shift))
+        for h in SPOT:
+            def cold_swap(o, i, P=P, h=h):
+                w = i['providers'][P]['widths']; j = w.index(9 if w[h] != 9 else 8); w[h], w[j] = w[j], w[h]   # never the identity
+            controls.append((P + ':cold_helper_width_swap_%d' % h, cold_swap))
+    rejected = []
+    accepted = []
+    for name, mutate in controls:
+        o, i = copy.deepcopy(owner), copy.deepcopy(invoice)
+        mutate(o, i)
+        oh = digest(o)
+        i['owner_audit_sha256'] = oh
+        try:
+            assemble(o, i, oh, digest(i))
+        except (AssertionError, KeyError):
+            rejected.append(name)
+        else:
+            # Discovery has no pinned values to reject spec-only mutations; the strict run must reject every control.
+            if not DISCOVER:
+                raise AssertionError('Invalid admission receipt accepted: ' + name)
+            accepted.append(name)
+    try:
+        assemble(owner, invoice, '0' * 64, sha(invoice_path))
+    except AssertionError:
+        rejected.append('wrong_owner_receipt_hash')
+    else:
+        raise AssertionError('Wrong owner digest accepted')
+    pin('expected.assembly_controls_rejected', len(rejected))
+    assert baseline['controls'] == ['next_grid', 'zero_eta', 'zero_beta', 'unit_beta']
+    assert baseline['conservative_controls'] == baseline['controls']
+    assert baseline['surcharge_model'] == {'complex': False, 'bit': True}
+    assert len(baseline['model_controls']) == 2
+    return dict(
+        status='PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS',
+        valid_receipt_kappa=baseline['kappa'],
+        input_sha256=baseline['input_sha256'],
+        assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'),
+        rejected_controls=rejected,
+        discovery_accepted_controls=accepted,
+        exact_outer_controls=baseline['controls'],
+        conservative_outer_controls=baseline['conservative_controls'],
+        recurrence_model_controls=baseline['model_controls'],
+        scope='Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay.',
+    )
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--source-package', type=Path, required=True)
+    ap.add_argument('--owner', type=Path, required=True)
+    ap.add_argument('--invoice', type=Path, required=True)
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    assert not a.out.exists()
+    result = verify(a.owner, a.invoice, a.source_package)
+    a.out.write_text(json.dumps(result, indent=2) + '\n')
+    print(result['status'], len(result['rejected_controls']))
diff --git a/research/gauge44-leaver/code/audit_allcold.py b/research/gauge44-leaver/code/audit_allcold.py
new file mode 100644
index 0000000000..c86f7b0235
--- /dev/null
+++ b/research/gauge44-leaver/code/audit_allcold.py
@@ -0,0 +1,254 @@
+"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit.
+Imports no emitter, optimizer, expander, edge-coloring, or source hosting code.
+CLI: BASE HOSTED REPORT [--mutation-controls]
+Each provider is independently read from BASE/providers, never from a baseline width histogram.
+OpenAI Codex two-provider width-seven extension; retains all inherited independent controller checks.
+The exact 63 width-seven and 9 plain calls are frozen below.
+"""
+import sys,json,gzip,hashlib,copy
+assert __debug__, 'Assertions must remain enabled'
+from pathlib import Path
+from collections import Counter,defaultdict
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+from generated_identity import artifact_identities
+BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz')
+ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json')
+ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json')
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+provider_ids=PIDS
+providers={};registry={};phase_semantic_hashes={};artifact_semantic_hashes={}
+required_artifacts={'work/complex-nine-native/DATA-PHASES.json'}
+provider_files=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+ 'INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json')
+for pid in provider_ids:
+ p=BASE/'providers'/pid
+ c=read(p/'CANONICAL-WORD.json.gz');checks=read(p/'LOCAL-CHECKS.json')
+ programs=read(p/'LOCAL-PROGRAMS.json.gz');replay=read(p/'INDEPENDENT-LOCAL-REPLAY.json')
+ phase=read(p/'CLIFFORD-REVIEW.json');adapters=read(p/'RESIDUAL-ADAPTERS.json')['recipes']
+ widths=[len(c['frames'][c['final'][2*c['v']+h]])-len(c['frames'][c['start'][2*c['v']+h]])for h in range(c['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths();pin('providers.%s.inventory'%pid,{str(k):v for k,v in sorted(Counter(widths).items())})
+ canonical_sha=sha(p/'CANONICAL-WORD.json.gz');programs_sha=sha(p/'LOCAL-PROGRAMS.json.gz')
+ assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ assert replay['canonical_word_sha256']==canonical_sha and replay['local_programs_sha256']==programs_sha
+ assert replay['v']==c['v'] and replay['helpers']==c['R']
+ assert set(programs)==set(checks)==set(replay['local'])==set(replay['paid_profiles'])=={'forward','backward'}
+ for orientation,events in programs.items():
+  ck=checks[orientation];rr=replay['local'][orientation]
+  assert hashlib.sha256(json.dumps(events,sort_keys=True,separators=(',',':')).encode()).hexdigest()==ck['sha256']
+  assert ck['events']==len(events) and ck['all_columns']==2*c['v']+c['R']
+  assert ck['private_centers_cleared'] and ck['private_coefficient_stream_cleared_after_each_macro']
+  assert rr['all_exact_columns']==2*c['v']+c['R'] and rr['private_work_erased']
+  literal=Counter(e[-1]for e in events if e[0]in('climb','center'))
+  assert dict(literal)=={int(r):n for r,n in ck['paid_profile'].items()}=={int(r):n for r,n in c['local_profile'].items()}
+  assert ck['paid_profile']==replay['paid_profiles'][orientation]
+ assert phase['canonical_word_sha256']==canonical_sha and phase['recipe_sha256']==sha(p/'CLIFFORD-RECIPES.json')
+ assert phase['all_child_equalities_include_global_phase']
+ artifact_semantic_hashes[pid]=artifact_identities(p)
+ pin('providers.%s.artifact_semantic_sha256'%pid,artifact_semantic_hashes[pid])
+ phase_semantic_hashes[pid]=artifact_semantic_hashes[pid]['CLIFFORD-REVIEW.json']
+ for h,w in enumerate(widths):
+  assert 0<w<=c['h']
+  f=c['start'][2*c['v']+h];u=c['final'][2*c['v']+h]
+  # COLD-HPE: a cold helper (f == 0) may end below FULL too; its wrapper is the '0:U' recipe (E = bottom instance of #593)
+  if u!=1:   # HPE: wrapper for T_U T_E^-1, keyed 'E:U', rank |U|-|E|
+   a=adapters['%d:%d'%(f,u)]
+   assert a['frame']==f and a['terminal']==u and a['vectors']==c['frames'][f] and a['terminal_vectors']==c['frames'][u]
+   assert a['rank']==w==len(c['frames'][u])-len(c['frames'][f]) and a['entrance_rank']==len(c['frames'][f]) and a['terminal_rank']==len(c['frames'][u])<c['h']
+  elif w<c['h']:
+   a=adapters[str(f)]
+   assert a['frame']==f and a['vectors']==c['frames'][f] and a['rank']==w and a['entrance_rank']==c['h']-w
+ providers[pid]=dict(canonical=c,checks=checks,widths=widths)
+ registry[pid]=dict(local_programs=programs,canonical_word_sha256=canonical_sha,local_programs_sha256=programs_sha,
+  local_program_checks=checks,exact_local_clifford_recipe_sha256=sha(p/'CLIFFORD-RECIPES.json'),
+  residual_adapter_sha256=sha(p/'RESIDUAL-ADAPTERS.json'),
+  **{k:c[k]for k in('v','h','R','ports','centers')},widths=widths)
+ required_artifacts.update('providers/'+pid+'/'+fn for fn in provider_files)
+canon=providers[provider_ids[0]]['canonical'];V=canon['v'];R=canon['R'];N=2*V+R;CENTRES=len(canon['centers'])
+assert V==112 and canon['h']==9
+assert all(providers[p]['canonical'][k]==canon[k]for p in provider_ids for k in('v','h','R','ports'))
+# Independently compare ordered common frames; exact local carrier names remain
+# bound to each canonical word, program, phase receipt and residual adapters.
+for p in provider_ids:
+ c=providers[p]['canonical']
+ assert len(c['centers'])==len(c['center_frames'])==8
+ assert [c['frames'][f]for f in c['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+parent_canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz')
+assert [canon['frames'][f]for f in canon['center_frames']]==[parent_canon['frames'][f]for f in parent_canon['center_frames']]
+assert required_artifacts<=set(summary['source_artifacts'])
+prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=8;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=72;HOSTED=CALLS*R
+# The selected map is an input to check, not a claim from the emitter.
+
+assert len(DISPATCH)==72 and Counter(DISPATCH.values())==COUNTS
+expected_provider=lambda stage,replica:DISPATCH[stage,replica]
+
+def orthobasis(port):
+ q=canon['ports'][port];z=next(i for i in range(9)if(q>>i)&1==0);a=q^(1<<z);order=list(range(9));order[z],order[0]=order[0],order[z]
+ b=[(1<<i)^(a if a>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ assert len(b)==73 and all((x&y).bit_count()%2==int(i==j)for i,x in enumerate(b)for j,y in enumerate(b));return b
+bases=[orthobasis(p)for p in range(V)]
+
+def audit(t):
+ assert(t['live'],t['physical'])==(DATA,PHYSICAL)
+ assert t['local_providers']==registry and t['recipe']==parent['recipe']and 'each local invocation completes before the next' in t['loop_order'].lower()
+ assert not any(k in t for k in('local_programs','exact_local_clifford_recipe_sha256','residual_adapter_sha256'))
+ assert len(t['calls'])==72 and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
+ for key in('exact_data_phase_recipe_sha256','adapter_policy'):assert t[key]==parent[key]
+ assert t['exact_data_phase_recipe_sha256']==sha(BASE/'work/complex-nine-native/DATA-PHASES.json')
+ # Independently project the literal schedule onto every data replica.
+ src=parent['execution_schedule'];assert t['async_schedule']['source_schedule']==src
+ assert t['async_schedule']['source_call_order']==[[c['stage'],c['replica']]for c in parent['calls']]
+ order=[(c['stage'],c['replica'])for c in t['calls']]
+ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==72
+ all_local=[];perrep={r:[]for r in range(8)};globals_=[]
+ for e in t['execution_schedule']:
+  j=e['source_event'];old=copy.deepcopy(src[j])
+  if 'replica'in e:
+   r=e['replica'];assert 0<=r<8 and j<30;perrep[r].append(j)
+   expected=old|dict(source_event=j,replica=r,replicas=[r],time=e['time'])
+   if e['kind']=='local_cover_sweep':expected['provider_id']=expected_provider(e['stage'],r)
+   assert e==expected
+   assert 0<=e['time']<72 and order[e['time']][1]==r
+   if e['kind']=='local_cover_sweep':
+    assert order[e['time']]==(e['stage'],r);all_local.append((e['stage'],r,e['time']))
+  else:
+   globals_.append(j);expected=old|dict(source_event=j)
+   if e['kind']=='bank_padding_cover_sweep':expected['families']=[DATA,DATA]
+   if e['kind']=='translate_every_live_family':expected.update(families=[0,DATA],charged_calls_per_cover=DATA)
+   assert e==expected
+ assert all(v==list(range(30))for v in perrep.values()) and globals_==[30,31]
+ assert all_local==[(st,r,i)for i,(st,r)in enumerate(order)]
+ assert all('replica'in e for e in t['execution_schedule'][:-2])
+ assert [e['source_event']for e in t['execution_schedule'][-2:]]==[30,31]
+ # Local cover calls are indivisible; a block then runs the source events
+ # up to that replica's next local invocation.
+ block=-1
+ for e in t['execution_schedule'][:-2]:
+  if e['kind']=='local_cover_sweep':block+=1
+  assert e['time']==block
+ assert t['bank_padding']==dict(parent['bank_padding'],families=[],children=[])
+ assert t['cover_final_correction']==dict(parent['cover_final_correction'],families=[0,DATA],charged_calls_per_cover=DATA)
+ assert t['private_namespace']=={'centers':[DATA,DATA+CENTRES],'reserved_tableau':[DATA+CENTRES,DATA+CENTRES+R],'coefficient':[DATA+CENTRES+R,PHYSICAL]}
+ # Actual physical touch intervals include every individual bridge.
+ pairs={};sides={};windows={};last={};callpos={};stagepair={e['stage']:e['pair']for e in parent['recipe']if e['kind']=='local'}
+ for pos,e in enumerate(t['execution_schedule']):
+  if 'replica'not in e:continue
+  rep=e['replica']
+  if e['kind']=='local_cover_sweep':
+   pair=stagepair[e['stage']];callpos[e['stage'],rep]=pos;last[rep,pair]=pos
+  elif e['kind']=='bridge':last[rep,e['src']]=last[rep,e['dst']]=pos
+  elif e['kind']=='idle_cover_sweep':
+   for side,i in enumerate(e['child_indices']):
+    if i not in prank:continue
+    pairs[i]=e['pair'];sides[i]=side;windows[rep,i]=(last.get((rep,e['pair']),-1),pos)
+ used=defaultdict(set);roles={};paid=Counter();sigmas={};digest=hashlib.sha256();entering=0;cross=0;touches=defaultdict(list)
+ for call in t['calls']:
+  old=next(z for z in parent['calls']if(z['stage'],z['replica'])==(call['stage'],call['replica']))
+  assert {k:v for k,v in call.items()if k not in('owners','time','provider_id','local_program_sha256')}=={k:v for k,v in old.items()if k not in('owners','local_program_sha256')}
+  pid=expected_provider(call['stage'],call['replica']);assert call['provider_id']==pid
+  width=providers[pid]['widths'];checks=providers[pid]['checks']
+  assert call['local_program_sha256']==checks[call['orientation']]['sha256']
+  s,rep,pair=call['stage'],call['replica'],call['pair'];assert call['time']==t['async_schedule']['order'].index([s,rep]);own=call['owners'];assert len(own)==N and len({f for f,rt in own})==N and all(0<=f<DATA for f,rt in own)
+  assert own[:(2*V)]==old['owners'][:(2*V)]
+  for h,(family,route)in enumerate(own[(2*V):]):
+   w=width[h];typ,i,off=route[:3];ownerrep,sub=divmod(family,(8*V));fampair,sub=divmod(sub,(2*V));side,port=divmod(sub,V)
+   assert windows[ownerrep,i][0]<callpos[s,rep]<windows[ownerrep,i][1] and fampair==pairs[i] and side==sides[i] and 0<=off and off+w<=prank[i]
+   B=bases[port];pend=[int(x)for x in ph['recipes'][port]['idle_children'][i]['orthogonal_axes']];assert len(pend)==prank[i]
+   occ=[B.index(v)for v in pend[off:off+w]];sp=[j for j in range(M)if j not in occ][:9-w]
+   assert route==([3,i,off]if w==9 else[4,i,off,w,sp]);assert len(set(occ+sp))==9
+   order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert sorted(order)==list(range(M));sigma=[B[j]for j in order]
+   assert sigma[:w]==pend[off:off+w]and sigma[w:9]==[B[j]for j in sp]
+   sh=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sh]=sigma;digest.update(json.dumps([s,rep,h,family,sh],separators=(',',':')).encode()+b'\n')
+   key=(i,ownerrep,port);cells=set(range(off,off+w));assert not used[key]&cells;used[key]|=cells
+   role=(s,rep,h);assert role not in roles;roles[role]=dict(stage=s,replica=rep,helper=h,family=family,owner_replica=ownerrep,child=i,copy=ownerrep*V+port,port=port,offset=off,width=w)
+   touches[family].append((s,rep,h));entering+=w<9;cross+=rep!=ownerrep
+  for r,n in checks[call['orientation']]['paid_profile'].items():paid[int(r)]+=n
+ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(8)for h in range(R)}
+ # The frozen pooled metadata must bind the actual serialized owner maps.
+ assert len(t['hosting']['pooled_slots'])==HOSTED
+ for z in t['hosting']['pooled_slots']:
+  key=(z['stage'],z['replica'],z['helper']);assert key in roles
+  assert {k:z[k]for k in roles[key]}==roles[key]
+ assert len({(z['stage'],z['replica'],z['helper'])for z in t['hosting']['pooled_slots']})==HOSTED
+ rem={};wanted=[]
+ for old in parent['idle_children']:
+  i,port=old['child'],old['port']
+  for rep in range(T):
+   u=used[i,rep,port];assert u==set(range(len(u)));r=old['rank']-len(u)
+   if r:
+    f=rep*(8*V)+(2*pairs[i]+sides[i])*V+port;wanted.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=r,hosted=len(u),pending_offset=len(u)));paid[r]+=1
+ assert t['idle_children']==wanted
+ mass=sum(r*n for r,n in paid.items());assert73=73*DATA-mass;assert assert73==2560 and 73**2>2*max(paid)**2
+ return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=72)
+
+r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256']
+assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items())
+controls=[]
+def reject(name,mut):
+ if '--mutation-controls' not in sys.argv[4:]:return
+ q=copy.deepcopy(ct);mut(q)
+ try:audit(q)
+ except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name)
+ else:raise AssertionError('ACCEPTED '+name)
+enter=lambda q:next(o for c in q['calls']for o in c['owners'][(2*V):]if o[1][0]==4)
+reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__((2*V+1),q['calls'][0]['owners'][(2*V)]))
+reject('helper on active data family',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,q['calls'][0]['owners'][0][0]))
+reject('owner in private namespace',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,DATA))
+reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1))
+reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72))
+reject('omit idle remainder',lambda q:q['idle_children'].pop())
+reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1))
+# Single-provider dispatch still has all source/program/width binding controls.
+if len(provider_ids)==1:
+ P=provider_ids[0]
+ at_p=lambda q:next(c for c in q['calls']if c['provider_id']==P)
+ narrow=next(h for h in range(R)if providers[P]['widths'][h]<9)
+ reject(P+': wrong provider at its invocation',lambda q:at_p(q).__setitem__('provider_id','__unregistered__'))
+ reject(P+': stale per-call local program hash',lambda q:at_p(q).__setitem__('local_program_sha256','0'*64))
+ reject(P+': stale serialized provider program',lambda q:q['local_providers'][P]['local_programs']['forward'].pop())
+ reject(P+': unbound residual adapter hash',lambda q:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64))
+ reject(P+': wrong provider width registry',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,providers[P]['widths'][narrow]-1))
+ reject(P+': wrong per-call residual width',lambda q:at_p(q)['owners'][2*V+narrow][1].__setitem__(3,at_p(q)['owners'][2*V+narrow][1][3]-1))
+ reject(P+': wrong sweep provider',lambda q:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep').__setitem__('provider_id','__unregistered__'))
+ reject(P+': entering helper width silently restored to nine',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,9))
+else:
+ # Per-provider substitution controls: every provider is swapped against a partner provider.
+ for P in provider_ids:
+  Qp=partner(P)
+  at_p=lambda q,P=P:next(c for c in q['calls']if c['provider_id']==P)
+  diff=[h for h in range(R)if providers[P]['widths'][h]!=providers[Qp]['widths'][h]]
+  narrow=next(h for h in range(R)if providers[P]['widths'][h]<9)
+  reject(P+': wrong provider at its invocation',lambda q,P=P,Qp=Qp,at_p=at_p:at_p(q).__setitem__('provider_id',Qp))
+  reject(P+': stale per-call local program hash',lambda q,Qp=Qp,at_p=at_p:at_p(q).__setitem__('local_program_sha256',registry[Qp]['local_program_checks'][at_p(q)['orientation']]['sha256']))
+  reject(P+': stale serialized provider program',lambda q,P=P,Qp=Qp:q['local_providers'][P].__setitem__('local_programs',registry[Qp]['local_programs']))
+  reject(P+': unbound residual adapter hash',lambda q,P=P:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64))
+  if diff:reject(P+': partner width in provider width registry',lambda q,P=P,Qp=Qp,h=diff[0]:q['local_providers'][P]['widths'].__setitem__(h,providers[Qp]['widths'][h]))
+  reject(P+': wrong per-call residual width',lambda q,at_p=at_p,h=narrow:at_p(q)['owners'][2*V+h][1].__setitem__(3,at_p(q)['owners'][2*V+h][1][3]-1))
+  reject(P+': wrong sweep provider',lambda q,P=P,Qp=Qp:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep'and DISPATCH[e['stage'],e['replica']]==P).__setitem__('provider_id',Qp))
+  reject(P+': entering helper width silently restored to nine',lambda q,P=P,h=narrow:q['local_providers'][P]['widths'].__setitem__(h,9))
+
+report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=DATA,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,mutation_controls_run='--mutation-controls' in sys.argv[4:],provider_phase_semantic_sha256=phase_semantic_hashes,provider_artifact_semantic_sha256=artifact_semantic_hashes,widths_by_provider={pid:dict(sorted(Counter(providers[pid]['widths']).items()))for pid in provider_ids},provider_counts=dict(Counter(c['provider_id']for c in ct['calls'])),all_provider_program_phase_and_wrapper_bindings=True,scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations.')
+REPORT.parent.mkdir(parents=True,exist_ok=True)
+REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2))
+
+owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=DATA,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,hosted_residuals=HOSTED,banked_residuals=0,all_live_owners_per_call_distinct=True,owners_per_call=N,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],provider_phase_semantic_sha256=phase_semantic_hashes,provider_artifact_semantic_sha256=artifact_semantic_hashes,controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest())
+(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n')
+
+# Literal residual frames are a compact export of the already checked offsets,
+# not another global replay. Every row names its actual inherited axes.
+frames=[]
+for z in ct['idle_children']:
+ axes=list(map(int,ph['recipes'][z['port']]['idle_children'][z['child']]['orthogonal_axes']))
+ tail=axes[z['pending_offset']:]
+ assert len(tail)==z['rank']
+ frames.append(dict(z,orthogonal_axes=tail))
+frame_raw=json.dumps(frames,sort_keys=True,separators=(',',':')).encode()
+portable=bytearray(gzip.compress(frame_raw,mtime=0));portable[9]=255
+(OUT/'IDLE-REMAINDER-FRAMES.json.gz').write_bytes(bytes(portable))
+frame_receipt=dict(status='PASS_LITERAL_IDLE_REMAINDER_FRAMES',template_sha256=summary['template_sha256'],
+ uncompressed_frames_sha256=hashlib.sha256(frame_raw).hexdigest(),children=len(frames),
+ rank_profile=dict(sorted(Counter(z['rank']for z in frames).items())),
+ source_data_phase_sha256=hashlib.sha256((BASE/'work/complex-nine-native/DATA-PHASES.json').read_bytes()).hexdigest(),
+ scope='Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child.')
+(REPORT.parent/'IDLE-REMAINDER-FRAMES.json').write_text(json.dumps(frame_receipt,indent=2)+'\n')
diff --git a/research/gauge44-leaver/code/bind_providers_portable.py b/research/gauge44-leaver/code/bind_providers_portable.py
new file mode 100644
index 0000000000..97e28da17e
--- /dev/null
+++ b/research/gauge44-leaver/code/bind_providers_portable.py
@@ -0,0 +1,67 @@
+"""Bind freshly verified plain and width-seven four-cold providers to the frozen literal owner plan.
+Prepared with OpenAI Codex assistance; Apache-2.0. All byte-stable native
+files are pinned to the plan. Only validated phase-receipt timing/serialization
+and directory fields are rebound; no dispatch, width or owner choice changes.
+"""
+import argparse,copy,gzip,hashlib,json,shutil
+from collections import Counter
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+from generated_identity import artifact_identities
+assert __debug__, 'Assertions required'
+ap=argparse.ArgumentParser(description=__doc__)
+for name in ('baseline','plan','out'):ap.add_argument('--'+name,type=Path,required=True)
+ap.add_argument('--provider',action='append',required=True,help='PID=DIR');a=ap.parse_args();assert not a.out.exists();a.out.mkdir(parents=True)
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+base=a.out/'base';shutil.copytree(a.baseline/'complex-global/base',base)
+ap2=dict(x.split('=',1)for x in a.provider);dirs={k:Path(v)for k,v in ap2.items()};assert set(dirs)==set(PIDS)
+for pid,src in dirs.items():shutil.copytree(src,base/'providers'/pid)
+pin('data.plan_sha256',sha(a.plan))
+plan=read(a.plan);original=copy.deepcopy(plan);sources={};helpers=set()   # R: helper count per provider word; all providers must agree
+assert set(plan['provider_registry'])==set(dirs)
+assert {(c['stage'],c['replica']):c['provider']for c in plan['provider_calls']}==DISPATCH,'PLAN dispatch differs from spec dispatch'
+stable=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json')
+for pid,desc in plan['provider_registry'].items():
+ d=base/'providers'/pid
+ word,program,checks,native,phase=[read(d/name)for name in('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-REVIEW.json')]
+ assert (word['v'],word['h'],len(word['centers']))==(112,9,8) and type(word['R']) is int and word['R']>0;helpers.add(word['R'])
+ assert word['ports']==desc['ports'] and word['centers']==desc['centers']
+ widths=[len(word['frames'][word['final'][r]])-len(word['frames'][word['start'][r]])for r in range(2*112,2*112+word['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths()
+ assert widths==desc['widths'];pin('providers.%s.inventory'%pid,{str(k):v for k,v in sorted(Counter(widths).items())})
+ assert native['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ pin('providers.%s.native_negative_controls'%pid,len(native['negative_controls_rejected']))
+ assert native['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and native['local_programs_sha256']==sha(d/'LOCAL-PROGRAMS.json.gz')
+ assert phase['status']=='PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES'
+ assert phase['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and phase['recipe_sha256']==sha(d/'CLIFFORD-RECIPES.json')
+ assert phase['all_child_equalities_include_global_phase'] is True and phase['endpoint_adapters']==224
+ pin('providers.%s.phase_edges'%pid,phase['directed_edges'])
+ assert set(program)==set(checks)=={'forward','backward'}
+ expected={int(r):n for r,n in checks['forward']['paid_profile'].items()};pin('providers.%s.expected_profile'%pid,checks['forward']['paid_profile'])
+ for orientation,events in program.items():
+  profile=Counter()
+  for e in events:
+   if e[0]=='climb':profile[e[5]]+=1
+   elif e[0]=='center':profile[e[4]]+=1
+  assert dict(profile)==expected=={int(r):n for r,n in checks[orientation]['paid_profile'].items()}=={int(r):n for r,n in native['paid_profiles'][orientation].items()}
+  assert hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest()==checks[orientation]['sha256']
+ identities=artifact_identities(d)
+ pin('providers.%s.artifact_semantic_sha256'%pid,identities)
+ assert identities==desc['artifact_semantic_sha256']
+ for name in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):
+  assert sha(d/name)==desc['artifact_sha256'][name],(pid,name,'changed non-reference artifact')
+ for c in plan['provider_calls']:
+  if c['provider']==pid:
+   assert c['orientation']==('forward'if c['stage']%2==0 else'backward')
+   assert c['local_program_sha256']==checks[c['orientation']]['sha256']
+ desc['directory']='providers/'+pid
+ desc['artifact_sha256']={name:sha(d/name)for name in desc['artifact_sha256']}
+ sources[pid]=dict(artifact_sha256=desc['artifact_sha256'],canonical_content_sha256=hashlib.sha256(json.dumps(word,sort_keys=True,separators=(',',':')).encode()).hexdigest(),all_phase_edges=phase['directed_edges'])
+assert len(helpers)==1,'providers disagree on helper count R: %s'%sorted(helpers)
+plan['runtime_source_plan_sha256']=sha(a.plan)
+(a.out/'PLAN.json').write_text(json.dumps(plan,indent=2)+'\n')
+receipt=dict(status='PASS_FROZEN_048_ALLCOLD_DISPATCH_FRESH_PROVIDER_BINDING',source_plan_sha256=sha(a.plan),runtime_plan_sha256=sha(a.out/'PLAN.json'),providers=sources,only_rebound_fields=['provider_registry.directory','provider_registry.artifact_sha256','runtime_source_plan_sha256'])
+(a.out/'BINDING.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(receipt['status'])
diff --git a/research/gauge44-leaver/code/bit_supplier_controls.py b/research/gauge44-leaver/code/bit_supplier_controls.py
new file mode 100644
index 0000000000..e86b8527b4
--- /dev/null
+++ b/research/gauge44-leaver/code/bit_supplier_controls.py
@@ -0,0 +1,111 @@
+"""Negative controls for the cited PR589 bit supplier and its derived rank-mass deficit.
+
+Apache-2.0. Each control mutates one input of the changed bit-supplier sites in assemble.py (the pinned record, the
+deficit derivation from the word's parameters, the profile/live binding, the claimed endpoint) and runs the unchanged
+assemble() on the fresh owner/invoice receipts. Every control must be rejected; the unmutated run must pass.
+`revert_hardcoded_9984` restores the PR543 constant the parent package hard-coded: with PR589's word it must fail.
+"""
+import argparse
+import copy
+import hashlib
+import json
+import os
+import tempfile
+from fractions import Fraction as Q
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+
+assert __debug__, 'Assertions required'
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def verify(owner_path, invoice_path, source_package):
+    os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve())
+    import assemble as A
+    owner = json.loads(owner_path.read_text())
+    invoice = json.loads(invoice_path.read_text())
+    args = (owner, invoice, sha(owner_path), sha(invoice_path))
+    baseline = A.assemble(*args)
+    data = A.BIT_PATH.read_bytes()
+    record = A.load_bit(data)
+    word = record['word']
+    assert A.bit_deficit(word, record['nine']['bit']['live']) == 10272 == 32 * (8 * 111 - 9 * 63)
+
+    real_load, real_deficit = A.load_bit, A.bit_deficit
+
+    def with_record(mutate):
+        def load(d):
+            r = copy.deepcopy(real_load(d)); mutate(r); return r
+        return load
+
+    def shift_profile(r):  # one rank-1 child becomes rank 2: rank mass +1, totals unchanged
+        p = r['nine']['profile']; p['1'] -= 1; p['2'] += 1; r['nine']['bit']['rank_mass'] += 1
+
+    bumped = data.replace(record['nine']['bit_lower'].encode(),
+                          str(Q(record['nine']['bit_lower']) + Q(1, 10**24)).encode(), 1)
+    assert bumped != data
+    pr543 = (source_package / 'inputs/PR543-EXPECTED.json').read_bytes()
+    controls = [
+        # deficit site: the parent's hard-coded constant, restored
+        ('revert_hardcoded_9984', dict(bit_deficit=lambda w, live: 9984)),
+        # deficit site: each word parameter perturbed alone
+        ('ports_112', dict(load_bit=with_record(lambda r: r['word'].__setitem__('v', 112)))),
+        ('decoder_constant_64_copy_ranks_unchanged', dict(load_bit=with_record(lambda r: r['word'].__setitem__('decoder_constant', 64)))),
+        # v=111, cst=64 derives 32*(888-576)=9984: consistent word, wrong for the priced profile
+        ('decoder_constant_64_with_one_copy_rank_8', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('decoder_constant', 64), r['word']['copy_ranks'].__setitem__(0, 8))))),
+        ('eight_retained_totals', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('copy_ranks', [7] * 8), r['word'].__setitem__('decoder_constant', 56))))),
+        ('live_minus_one', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('live', r['nine']['bit']['live'] - 1)))),
+        # profile binding: same totals, rank mass +1
+        ('profile_rank_mass_plus_one', dict(load_bit=with_record(shift_profile))),
+        ('profile_rank_mass_receipt_mismatch', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('rank_mass', r['nine']['bit']['rank_mass'] + 1)))),
+        # endpoint: the next 1e-24 grid point
+        ('bit_lower_next_grid', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('bit_lower', str(Q(r['nine']['bit_lower']) + Q(1, 10**24)))))),
+        ('not_nine_stage_record', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('pipeline', r['nine']['pipeline'].replace('nine-stage', 'eleven-stage'))))),
+        # pinned-input site: tampered bytes and the parent's PR543 file under the PR589 pin
+        ('tampered_bytes_next_grid', dict(read=bumped)),
+        ('pr543_file_under_pr589_pin', dict(read=pr543)),
+    ]
+    rejected = []
+    scratch = Path(tempfile.mkdtemp(prefix='bitctl-'))
+    for name, patch in controls:
+        saved_path = A.BIT_PATH
+        try:
+            if 'read' in patch:
+                tmp = scratch / (name + '.json'); tmp.write_bytes(patch['read']); A.BIT_PATH = tmp
+            A.load_bit = patch.get('load_bit', real_load)
+            A.bit_deficit = patch.get('bit_deficit', real_deficit)
+            try:
+                A.assemble(*args)
+            except (AssertionError, KeyError):
+                rejected.append(name)
+            else:
+                raise AssertionError('Invalid bit supplier accepted: ' + name)
+        finally:
+            A.load_bit, A.bit_deficit, A.BIT_PATH = real_load, real_deficit, saved_path
+            if 'read' in patch:
+                tmp.unlink()
+    scratch.rmdir()
+    assert rejected == [n for n, _ in controls]
+    again = A.assemble(*args)
+    assert again['kappa'] == baseline['kappa'] and again['bit_lower'] == baseline['bit_lower']
+    return dict(
+        status='PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS',
+        kappa=baseline['kappa_decimal'], bit_lower=baseline['bit_lower'], bit_decimal=baseline['bit_decimal'],
+        binding=baseline['binding'], bit_supplier=baseline['bit_supplier'],
+        derived_deficit=baseline['bit_supplier']['derived_deficit'],
+        rejected_controls=rejected,
+        assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'),
+    )
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--source-package', type=Path, required=True)
+    ap.add_argument('--owner', type=Path, required=True)
+    ap.add_argument('--invoice', type=Path, required=True)
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    assert not a.out.exists()
+    result = verify(a.owner, a.invoice, a.source_package)
+    a.out.write_text(json.dumps(result, indent=2) + '\n', newline='\n')
+    print(result['status'], len(result['rejected_controls']))
diff --git a/research/gauge44-leaver/code/emit_allcold.py b/research/gauge44-leaver/code/emit_allcold.py
new file mode 100644
index 0000000000..8e147f80a6
--- /dev/null
+++ b/research/gauge44-leaver/code/emit_allcold.py
@@ -0,0 +1,150 @@
+"""Two-provider width-seven whole-owner derivative, adapted with OpenAI Codex assistance.
+Based on PR514 and its credited PR484/507 lineage.
+CLI: --base VERIFIED_VARIANT --owners ASYNC-OWNERS.json.gz --plan ASYNC-PLAN.json --out OUT
+No optimizer or unpublished word builder runs. The frozen map explicitly names
+one whole helper per family per complete invocation, plus borrowed spectators.
+"""
+import sys,json,gzip,hashlib,copy,argparse
+from pathlib import Path
+from collections import Counter,defaultdict
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+parser=argparse.ArgumentParser(description=__doc__)
+parser.add_argument('--base',type=Path,required=True);parser.add_argument('--owners',type=Path,required=True);parser.add_argument('--plan',type=Path,required=True);parser.add_argument('--out',type=Path,required=True)
+a=parser.parse_args();BASE,MAP,PLAN,OUT=(p.resolve()for p in(a.base,a.owners,a.plan,a.out));assert not OUT.exists();OUT.mkdir(parents=True)
+class OH:
+ @staticmethod
+ def idle_basis(q):
+  z=next(i for i in range(9)if not(q>>i)&1);u=q^(1<<z);order=list(range(9));order[0],order[z]=order[z],order[0]
+  return[(1<<i)^(u if u>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ @staticmethod
+ def spectators(q,pending,off,w):
+  B=OH.idle_basis(q);occ=[B.index(v)for v in pending[off:off+w]]
+  return[j for j in range(73)if j not in occ][:9-w]
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+assert hashlib.sha256(MAP.read_bytes()).hexdigest()==SPEC['data']['owners_sha256'],'OWNERS not pinned by spec'
+plan=read(PLAN);assert plan['runtime_source_plan_sha256']==SPEC['data']['plan_sha256'],'PLAN not pinned by spec'
+call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==72;at={x:i for i,x in enumerate(call_order)}
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');t=copy.deepcopy(parent);canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');roles=read(MAP);T=8;V=canon['v'];M=73;R0=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)   # R0: parent (split-centres) helper count
+assert(len(canon['start']),len(ph['recipes']))==(2*V+R0,V)
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+provider_files=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json')
+registry={};source_artifacts={'work/complex-nine-native/DATA-PHASES.json':sha(BASE/'work/complex-nine-native/DATA-PHASES.json')}
+for provider_id in sorted(plan['provider_registry']):
+ assert provider_id in PIDS
+ directory=BASE/'providers'/provider_id
+ assert all((directory/f).is_file()for f in provider_files)
+ pc=read(directory/'CANONICAL-WORD.json.gz');checks=read(directory/'LOCAL-CHECKS.json');programs=read(directory/'LOCAL-PROGRAMS.json.gz');replay=read(directory/'INDEPENDENT-LOCAL-REPLAY.json')
+ # Carrier names belong to the independently checked local program. The global
+ # controller's centre contract is the ordered eight exact common frame bases.
+ assert(pc['v'],pc['h'],pc['ports'])==(V,9,canon['ports'])
+ assert len(pc['centers'])==len(pc['center_frames'])==len(canon['centers'])==8
+ assert [pc['frames'][f]for f in pc['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+ R=pc['R'];assert type(R)is int and R>0 and all(x['R']==R for x in registry.values()),'providers disagree on helper count R'
+ assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ assert replay['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz')and replay['local_programs_sha256']==sha(directory/'LOCAL-PROGRAMS.json.gz')
+ widths=[len(pc['frames'][pc['final'][2*V+h]])-len(pc['frames'][pc['start'][2*V+h]])for h in range(R)]   # HPE: residual width |final|-|start|
+ assert widths==plan['provider_registry'][provider_id]['widths']
+ for name in provider_files:
+  value=sha(directory/name);assert value==plan['provider_registry'][provider_id]['artifact_sha256'][name]
+  source_artifacts[f'providers/{provider_id}/{name}']=value
+ registry[provider_id]=dict(local_programs=programs,canonical_word_sha256=sha(directory/'CANONICAL-WORD.json.gz'),local_programs_sha256=sha(directory/'LOCAL-PROGRAMS.json.gz'),local_program_checks=checks,exact_local_clifford_recipe_sha256=sha(directory/'CLIFFORD-RECIPES.json'),residual_adapter_sha256=sha(directory/'RESIDUAL-ADAPTERS.json'),v=V,h=9,R=R,ports=pc['ports'],centers=pc['centers'],widths=widths)
+assert len(roles)==72*R   # one whole-owner role per (call, provider helper)
+selected={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+assert len(selected)==72 and set(selected)==set(call_order)
+assert Counter(c['provider']for c in selected.values())==COUNTS
+per_call_widths={(c['stage'],c['replica']):c['widths']for c in plan['per_call_widths']}
+for key,c in selected.items():
+ assert c['time']==at[key] and c['provider']in registry
+ assert per_call_widths[key]==registry[c['provider']]['widths']
+for key in('local_programs','exact_local_clifford_recipe_sha256','residual_adapter_sha256'):t.pop(key)
+t['local_providers']=registry
+rank={z['child']:z['rank']for z in parent['idle_children']};side={};pairs={}
+for e in parent['execution_schedule']:
+ if e['kind']=='idle_cover_sweep':
+  for sd,ch in enumerate(e['child_indices']):side[ch]=sd;pairs[ch]=e['pair']
+bycall=defaultdict(dict);used=defaultdict(set);sigmas={};digest=hashlib.sha256();entering=0
+for z in roles:
+ s,rep,h=z['stage'],z['replica'],z['helper'];i,cp,off,w,f=z['child'],z['copy'],z['offset'],z['width'],z['family'];orp,port=divmod(cp,V)
+ assert 0<=s<9 and 0<=rep<T and 0<=h<R and w==registry[selected[s,rep]['provider']]['widths'][h] and 0<=orp<T
+ assert f==orp*(8*V)+(2*pairs[i]+side[i])*V+port
+ assert(h not in bycall[s,rep])and off>=0 and off+w<=rank[i]
+ assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1]
+ B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i]
+ occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[]
+ order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M
+ sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma
+ route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9
+ cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells
+ digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n')
+for c in t['calls']:
+ k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R))
+ c['owners']=c['owners'][:(2*V)]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==2*V+R and all(f<DATA for f,r in c['owners'])
+ pc=selected[k];provider_id=pc['provider'];assert c['orientation']==pc['orientation']
+ c['provider_id']=provider_id;c['local_program_sha256']=registry[provider_id]['local_program_checks'][c['orientation']]['sha256']
+ assert c['local_program_sha256']==pc['local_program_sha256']
+newidle=[];paid=Counter()
+for c in t['calls']:
+ for r,n in registry[c['provider_id']]['local_program_checks'][c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for old in parent['idle_children']:
+ i,port=old['child'],old['port']
+ for rep in range(T):
+  u=used[i,rep,port];assert u==set(range(len(u)));left=old['rank']-len(u)
+  if left:
+   f=rep*(8*V)+(2*pairs[i]+side[i])*V+port;newidle.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=left,hosted=len(u),pending_offset=len(u)));paid[left]+=1
+assert M*DATA-sum(r*n for r,n in paid.items())==2560
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R0+2
+# Local circuits, exact phase recipes, normalized wrappers and data routes stay
+# byte-identical; only full-family helper placement and idle remainders change.
+t.update(version='round20-R%d-asynchronous-whole-owner-v1'%R,live=DATA,physical=physical,idle_children=newidle,private_namespace={'centers':[DATA,DATA+C],'reserved_tableau':[DATA+C,DATA+C+R],'coefficient':[physical-2,physical]})
+t['hosting']=dict(rule='one-helper-per-physical-family-per-complete-invocation',max_helpers_per_physical_family_per_call=1,scope='asynchronously interleaved data replicas; each whole helper occurs once per(stage,invocation replica)',pooled_slots=roles,banks=[0]*9,owner_map_sha256=hashlib.sha256(MAP.read_bytes()).hexdigest(),idle_remainder_semantics='Each idle_children item acts once, on its explicit replica/family, at pending_offset with the stated rank; replicas=1.')
+t['route_semantics']['helper']='Whole physical family may belong to another replica; actual orthogonal port basis followed by residual/spectator coordinate permutation. Entering helpers have paid wrappers around the complete invocation; at most one helper and no active data wire uses that family in that invocation. Route[4,child,offset,width,spectators], width9 route[3,child,offset].'
+t['bank_padding']['families']=[];t['bank_padding']['children']=[];t['cover_final_correction']['families']=[0,DATA];t['cover_final_correction']['charged_calls_per_cover']=DATA
+for e in t['execution_schedule']:
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,DATA]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+# Expand the retained controller into one-replica blocks; each block consists
+# of its full local cover sweep and every following replica-local event before
+# its next local sweep. Final whole-stock correction remains after all replicas.
+blocks={};globals_=[];st=None
+for ei,e in enumerate(parent['execution_schedule']):
+ if e['kind']in('bank_padding_cover_sweep','translate_every_live_family'):
+  globals_.append((ei,e));continue
+ if e['kind']=='local_cover_sweep':st=e['stage'];blocks[st]=[]
+ assert st is not None
+ blocks[st].append((ei,e))
+new_schedule=[]
+for tm,(s,rep)in enumerate(call_order):
+ for ei,e in blocks[s]:
+  ne=copy.deepcopy(e);ne.update(replica=rep,replicas=[rep],source_event=ei,time=tm)
+  if ne['kind']=='local_cover_sweep':ne['provider_id']=selected[s,rep]['provider']
+  new_schedule.append(ne)
+for ei,e in globals_:
+ ne=copy.deepcopy(e);ne['source_event']=ei
+ if e['kind']=='bank_padding_cover_sweep':ne['families']=[DATA,DATA]
+ else:ne.update(t['cover_final_correction'])
+ new_schedule.append(ne)
+t['execution_schedule']=new_schedule
+cmap={(c['stage'],c['replica']):c for c in t['calls']}
+t['calls']=[dict(cmap[s,rep],time=tm)for tm,(s,rep)in enumerate(call_order)]
+t['loop_order']='Follow the explicit asynchronous execution_schedule. Each local invocation completes before the next, including its entire cover sweep and normalization wrappers. Per-replica source event order is preserved; each idle remainder executes before that replica next touches its family.'
+t['async_schedule']=dict(order=[list(x)for x in call_order],source_plan_sha256=hashlib.sha256(PLAN.read_bytes().replace(b'\r\n',b'\n')).hexdigest(),source_schedule=parent['execution_schedule'],source_call_order=[[c['stage'],c['replica']]for c in parent['calls']],scope='Only independent replica controllers are interleaved. Owner windows are measured on the owner replica timeline; no within-cover or within-invocation interleaving.')
+assert dict(sorted(paid.items()))=={int(k):v for k,v in plan['profile'].items()}
+assert M*M>2*max(paid)**2
+
+assert all(c['local_program_sha256']==registry[c['provider_id']]['local_program_checks'][c['orientation']]['sha256']for c in t['calls'])
+t['provider_dispatch']='For each indivisible local_cover_sweep, execute local_providers[call.provider_id].local_programs[call.orientation] with that provider residual adapters and Clifford recipes. The sweep provider_id must equal its call provider_id.'
+raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+res=dict(status='EMITTED_MIXED_PROVIDER_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE',
+ template_sha256=hashlib.sha256(raw).hexdigest(),
+ parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),
+ live=DATA,physical=physical,global_profile=dict(sorted(paid.items())),
+ rank_mass=sum(r*n for r,n in paid.items()),deficit=2560,maxchild=max(paid),
+ hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering,
+ unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(),
+ cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles),
+ asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(),
+ source_artifacts=source_artifacts,provider_counts=dict(Counter(c['provider_id']for c in t['calls'])),
+ scope='Two actual verified plain/width-seven providers dispatched per complete invocation; independent controller/spectator/normalization and complete finite invoice admission required.')
+(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2))
diff --git a/research/gauge44-leaver/code/freeze_spec.py b/research/gauge44-leaver/code/freeze_spec.py
new file mode 100644
index 0000000000..dd0358d396
--- /dev/null
+++ b/research/gauge44-leaver/code/freeze_spec.py
@@ -0,0 +1,29 @@
+"""Freeze independently recomputed discovery values before strict replay."""
+import argparse
+import json
+from pathlib import Path
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--spec', type=Path, required=True)
+ap.add_argument('--discovery', type=Path, required=True)
+a = ap.parse_args()
+spec = json.loads(a.spec.read_text())
+for line in (a.discovery/'WITNESS-RECORD.jsonl').read_text().splitlines():
+    key, value = json.loads(line)
+    parts = key.split('.')
+    if len(parts)>3 and parts[0]=='providers' and parts[2]=='artifacts':
+        parts = parts[:3] + ['.'.join(parts[3:])]
+    target = spec
+    for part in parts[:-1]:
+        target = target.setdefault(part, {})
+    if parts[-1] in target:
+        assert target[parts[-1]]==value, 'Conflicting independent recomputations: '+key
+    target[parts[-1]] = value
+assembly = json.loads((a.discovery/'ASSEMBLY.json').read_text())
+for key in ('complex_lower','conservative_complex_lower','kappa','kappa_decimal','conservative_kappa_decimal'):
+    spec['expected'][key] = assembly[key]
+spec['expected']['assembly_controls_rejected'] = 69
+spec['expected']['provider_counts'] = {'gauge44':72}
+spec['expected']['mutations_rejected'] = 15
+a.spec.write_text(json.dumps(spec, indent=2)+'\n')
+print('Frozen exact witness for strict replay:', assembly['kappa_decimal'])
diff --git a/research/gauge44-leaver/code/generated_identity.py b/research/gauge44-leaver/code/generated_identity.py
new file mode 100644
index 0000000000..74a9b60479
--- /dev/null
+++ b/research/gauge44-leaver/code/generated_identity.py
@@ -0,0 +1,62 @@
+"""Proof-relevant identities for generated artifacts, independent of gzip streams.
+
+Immutable source archives retain their exact byte hashes. For freshly emitted
+artifacts, gzip identity is the exact decompressed payload and JSON identity
+retains every field. Only CLIFFORD-REVIEW's root timing field is excluded.
+Literal receipt references are checked against actual files before replacing
+the three gzip references (and the phase recipe reference) with content hashes.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+import copy
+import gzip
+import hashlib
+import json
+import math
+
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+
+FILES=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+       'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json',
+       'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json')
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+def json_identity(value):
+    return hashlib.sha256(json.dumps(value,sort_keys=True,separators=(',',':'),allow_nan=False).encode('utf-8')).hexdigest()
+
+def payload_identity(path):
+    return hashlib.sha256(gzip.decompress(Path(path).read_bytes())).hexdigest()
+
+def phase_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'CLIFFORD-REVIEW.json').read_bytes())if value is None else value)
+    assert value['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz'),'stale phase canonical word reference'
+    assert value['recipe_sha256']==sha(directory/'CLIFFORD-RECIPES.json'),'stale phase recipe reference'
+    seconds=value.pop('seconds')
+    assert type(seconds)in(int,float) and math.isfinite(seconds) and seconds>=0,'invalid phase timing metadata'
+    value['canonical_word_sha256']=payload_identity(directory/'CANONICAL-WORD.json.gz')
+    value['recipe_sha256']=json_identity(json.loads((directory/'CLIFFORD-RECIPES.json').read_bytes()))
+    return value
+
+def native_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'INDEPENDENT-LOCAL-REPLAY.json').read_bytes())if value is None else value)
+    for field,name in [('canonical_word_sha256','CANONICAL-WORD.json.gz'),('local_programs_sha256','LOCAL-PROGRAMS.json.gz')]:
+        assert value[field]==sha(directory/name),'stale native artifact reference: '+field
+        value[field]=payload_identity(directory/name)
+    return value
+
+def artifact_identities(directory):
+    directory=Path(directory)
+    result={}
+    for name in FILES:
+        path=directory/name
+        if name.endswith('.gz'):
+            result[name]=payload_identity(path)
+        else:
+            value=phase_value(directory)if name=='CLIFFORD-REVIEW.json'else native_value(directory)if name=='INDEPENDENT-LOCAL-REPLAY.json'else json.loads(path.read_bytes())
+            result[name]=json_identity(value)
+    return result
diff --git a/research/gauge44-leaver/code/invoice_allcold.py b/research/gauge44-leaver/code/invoice_allcold.py
new file mode 100644
index 0000000000..b244cd5994
--- /dev/null
+++ b/research/gauge44-leaver/code/invoice_allcold.py
@@ -0,0 +1,329 @@
+"""Fresh call-specific mixed-provider finite invoice.
+
+Prepared with OpenAI Codex assistance, Apache-2.0. The scalar/Horner recount
+and finite inequalities are adapted from the retained PR558 -> PR552 ->
+PR531 invoice_final.py, whose notices and sources are preserved in the package.
+Every call selects a hash-bound provider. Shared compiler reserves use maxima;
+primitive work, coefficient work, local children and wrappers are also summed
+from actual selected provider/orientation records.
+"""
+import argparse, gzip, hashlib, json
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+from generated_identity import artifact_identities
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+assert __debug__, 'Assertions required'
+
+def read(path):
+    data=path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix=='.gz' else data)
+def filehash(path): return hashlib.sha256(path.read_bytes()).hexdigest()
+def contenthash(path):
+    data=path.read_bytes()
+    return hashlib.sha256(gzip.decompress(data) if path.suffix=='.gz' else data).hexdigest()
+def programhash(events):
+    return hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest()
+
+def recount_provider(local_dir, registry):
+    cp=local_dir/'CANONICAL-WORD.json.gz'; pp=local_dir/'LOCAL-PROGRAMS.json.gz'
+    rp=local_dir/'INDEPENDENT-LOCAL-REPLAY.json'
+    w,programs,replay=read(cp),read(pp),read(rp)
+    checks=read(local_dir/'LOCAL-CHECKS.json')
+    assert set(programs)=={'forward','backward'}
+    assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+    assert replay['canonical_word_sha256']==filehash(cp)==registry['canonical_word_sha256']
+    assert replay['local_programs_sha256']==filehash(pp)==registry['local_programs_sha256']
+    assert programs==registry['local_programs']
+    assert checks==registry['local_program_checks']
+    assert filehash(local_dir/'CLIFFORD-RECIPES.json')==registry['exact_local_clifford_recipe_sha256']
+    assert filehash(local_dir/'RESIDUAL-ADAPTERS.json')==registry['residual_adapter_sha256']
+    v,helpers,h,m=w['v'],w['R'],w['h'],73
+    assert (v,h)==(112,9) and type(helpers) is int and helpers>0
+    assert registry['v']==v and registry['R']==helpers and registry['h']==h
+    assert registry['ports']==w['ports'] and registry['centers']==w['centers']
+    assert replay['v']==v and replay['helpers']==helpers
+    n=2*v+helpers
+    widths = [len(w['frames'][w['final'][r]])-len(w['frames'][w['start'][r]]) for r in range(2*v, 2*v+helpers)]  # HPE: |final|-|start|
+    terminal_codim = sum(h-len(w['frames'][w['final'][r]]) for r in range(2*v, 2*v+helpers))  # HPE: 0 for FULL-ended helpers
+    ends = {r: f for r, f in enumerate(w['final']) if r >= 2*v and f != 1}
+    assert len(widths) == helpers
+    entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0}
+    entering = len(entrances)
+    wrapped = {**entrances, **{r: 0 for r in ends if r not in entrances}}   # COLD-HPE: cold hyperplane-ended helpers carry wrappers too
+    cold_ends = len(wrapped) - len(entrances)
+    assert entering == replay['entering_helpers']
+    local = {}
+    for orientation, events in programs.items():
+        # Endpoint equality and native frames were already independently
+        # replayed on all n columns in the hash-bound receipt above.
+        env = {('L', r): Q(1) for r in range(n)}
+        peak = Q(1)
+        real = macros = workops = 0
+        paid = Counter()
+        wrappers = {'pre': set(), 'post': set()}
+        for event in events:
+            tag = event[0]
+            if tag == 'climb':
+                paid[event[5]] += 1
+            elif tag == 'center':
+                paid[event[4]] += 1
+            elif tag == 'residual_adapter':
+                _, kind, register, frame, *end = event
+                assert kind in wrappers and wrapped.get(register) == frame
+                assert end == ([ends[register]] if register in ends else [])  # HPE: R_{E,U}^-1 and L_{E,U}^-1 name U
+                assert register not in wrappers[kind]
+                wrappers[kind].add(register)
+            elif tag == 'scalar':
+                macros += 1
+                scalar = event[1]
+                op, target = scalar[0], tuple(scalar[1])
+                if op == 'clear':
+                    env[target] = Q(0)
+                    count = 1
+                elif op == 'copy':
+                    env[target] = env[tuple(scalar[2])]
+                    count = 1
+                elif op == 'scale':
+                    q = Q(scalar[2], scalar[3])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert numerator and numerator & (numerator-1) == 0
+                    assert denominator & (denominator-1) == 0
+                    env[target] *= abs(q)
+                    count = abs(numerator.bit_length()-denominator.bit_length()) + int(q < 0)
+                elif op == 'add':
+                    source = tuple(scalar[2])
+                    q = Q(scalar[3], scalar[4])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert source != target and numerator > 0
+                    assert denominator & (denominator-1) == 0
+                    acc, count = 0, 1  # clear coefficient work
+                    for i, bit in enumerate(bin(numerator)[2:]):
+                        if i:
+                            acc *= 2
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                        if bit == '1':
+                            acc += 1
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                    value = Q(acc)
+                    for _ in range(denominator.bit_length()-1):
+                        value /= 2
+                        count += 1
+                        peak = max(peak, value*env[source])
+                    assert value == abs(q)
+                    count += 2  # signed accumulation and work clear
+                    env[target] = env.get(target, Q(0)) + abs(q)*env[source]
+                    workops += count
+                else:
+                    raise AssertionError(op)
+                real += 2*count
+                peak = max(peak, env[target])
+            else:
+                assert tag in ('adapter', 'phase')
+        assert wrappers['pre'] == wrappers['post'] == set(wrapped)
+        assert all(value == 0 for register, value in env.items() if register[0] == 'C')
+        prior = replay['local'][orientation]
+        assert prior['all_exact_columns'] == n and prior['private_work_erased']
+        assert peak == Q(prior['prefix_l1_upper']) and peak < 2**prior['charged_payload_bits']
+        bits = peak.numerator.bit_length()-peak.denominator.bit_length()+1
+        assert bits == prior['prefix_bits_upper']
+        assert real == checks[orientation]['real_component_primitive_bound']
+        assert macros == checks[orientation]['scalar_macros']
+        assert dict(paid) == {int(r): count for r, count in checks[orientation]['paid_profile'].items()}
+        assert dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()}
+        local[orientation] = dict(
+            events=len(events), macros=macros, real_component_primitives=real,
+            prefix_l1=str(peak), prefix_bits=bits,
+            coefficient_work_primitive_count=workops, all_exact_columns=n,
+            dirty_helper_columns=helpers, all_dirty_helper_columns_restored=True,
+            private_centres_and_coefficient_work_cleared=True,
+            pre_wrappers=len(wrappers['pre']), post_wrappers=len(wrappers['post']),
+            endpoint_evidence='Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json')
+
+    centres = len(w['centers'])
+    children = sum(checks['forward']['paid_profile'].values())
+    assert checks['forward']['paid_profile'] == checks['backward']['paid_profile']
+    macro_bound = max(row['macros'] for row in local.values())
+    compiler = 64*(m+1)**3
+    adapters = 16*(macro_bound+children+n+centres)+64*m
+    primitive_bound = max(row['real_component_primitives'] for row in local.values())+adapters*compiler
+
+    assert widths==registry['widths']
+    artifacts={f.name:filehash(f) for f in local_dir.iterdir() if f.is_file()}
+    phase_review=read(local_dir/'CLIFFORD-REVIEW.json')
+    return dict(local=local,helpers=helpers,centres=centres,v=v,h=h,n=n,
+                entering_helpers=entering,entrance_rank=sum(len(w['frames'][f]) for f in w['start'][2*v:]),
+                terminal_codimension=terminal_codim, hyperplane_ended_helpers=len(ends),  # HPE: always reported (0 for FULL-ended words)
+                **({'cold_hyperplane_ended_helpers': cold_ends} if cold_ends else {}),  # COLD-HPE: absent without cold ends
+                width_inventory=dict(sorted(Counter(widths).items())),widths=widths,
+                local_adapters=adapters,local_primitive_bound=primitive_bound,
+                compiler=compiler,children=children,artifacts=artifacts,
+                paid_profile=checks['forward']['paid_profile'],
+                program_hashes={o:programhash(events) for o,events in programs.items()},semantic_artifact_sha256=artifact_identities(local_dir))
+
+
+def run(base, hosted, audit, out, retained_invoice=None):
+    local_dir=base/'split-centres'
+    parent=read(local_dir/'GLOBAL-TEMPLATE.json.gz')
+    template_path=hosted/'GLOBAL-TEMPLATE.json.gz'
+    template=read(template_path); summary=read(hosted/'HOSTED.json')
+    owners=read(audit/'OWNERS-AND-PROFILE.json'); control=read(audit/'ASYNC-AUDIT.json')
+    template_hash=contenthash(template_path)
+    assert template_hash==control['complex_template_sha256']==owners['template_sha256']==summary['template_sha256']
+    assert owners['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE'
+    assert template['recipe']==parent['recipe']
+    assert 'local_programs' not in template
+    assert set(template['local_providers'])==set(PIDS)
+    providers={pid:recount_provider(base/'providers'/pid,registry)
+               for pid,registry in template['local_providers'].items()}
+    for pid,p in providers.items():
+        assert owners['provider_phase_semantic_sha256'][pid]==control['provider_phase_semantic_sha256'][pid]==p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']
+        # The fresh controller admission must cite precisely these provider bytes.
+        for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+                     'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json',
+                     'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json'):
+            path='providers/'+pid+'/'+name
+            assert summary['source_artifacts'][path]==p['artifacts'][name]
+            assert owners['source_artifacts'][path]==p['artifacts'][name]
+    # R is read from the provider words (all must agree); the parent dedicated-bank
+    # envelope keeps its own helper count R0 from the parent split-centres word.
+    assert len({p['helpers'] for p in providers.values()})==1,'providers disagree on helper count R'
+    v,h,m,centres=112,9,73,8
+    helpers=next(iter(providers.values()))['helpers']; n=2*v+helpers
+    assert all((p['v'],p['h'],p['centres'],p['n'])==(v,h,centres,n) for p in providers.values())
+    parent_helpers=read(local_dir/'CANONICAL-WORD.json.gz')['R']
+    stages,replicas,blocks_per_stream=9,8,4
+    call_count=len(template['calls'])
+    assert call_count==stages*replicas==control['complete_invocations']
+    assert control['one_owner_per_complete_invocation']
+    assert len({(c['stage'],c['replica']) for c in template['calls']})==call_count
+    parent_calls={(c['stage'],c['replica']):c for c in parent['calls']}
+    sweeps=[e for e in template['execution_schedule'] if e['kind']=='local_cover_sweep']
+    assert len(sweeps)==call_count
+    selected=[]; selected_paid=Counter(); provider_counts=Counter(); orientation_counts=Counter()
+    scalar=coefficient_work=macros=0; wrapper_factors=0
+    factors_per_wrapper=2*(m-1)
+    for c in template['calls']:
+        pid,orientation=c['provider_id'],c['orientation']; p=providers[pid]
+        old=parent_calls[(c['stage'],c['replica'])]
+        assert orientation==old['orientation'] and c['owners'][:2*v]==old['owners'][:2*v]
+        assert c['local_program_sha256']==p['program_hashes'][orientation]
+        r=p['local'][orientation]
+        scalar+=r['real_component_primitives']; coefficient_work+=r['coefficient_work_primitive_count']; macros+=r['macros']
+        wrapper_factors+=(r['pre_wrappers']+r['post_wrappers'])*factors_per_wrapper
+        provider_counts[pid]+=1; orientation_counts[(pid,orientation)]+=1
+        selected_paid.update({int(k):v for k,v in p['paid_profile'].items()})
+        selected.append(dict(stage=c['stage'],replica=c['replica'],provider_id=pid,orientation=orientation,
+                             program_sha256=c['local_program_sha256'],events=r['events'],macros=r['macros'],
+                             real_component_primitives=r['real_component_primitives'],
+                             coefficient_work_primitive_count=r['coefficient_work_primitive_count'],
+                             entering_helpers=p['entering_helpers'],entrance_rank=p['entrance_rank'],
+                             pre_wrappers=r['pre_wrappers'],post_wrappers=r['post_wrappers']))
+    assert provider_counts==COUNTS
+    # The sweep registry is executable: no hidden use of the historical supplier.
+    by_call={(c['stage'],c['replica']):c for c in template['calls']}
+    for e in sweeps:
+        c=by_call[(e['stage'],e['replica'])]
+        assert e['provider_id']==c['provider_id']
+    assert set(p['compiler'] for p in providers.values())=={64*(m+1)**3}
+    compiler=64*(m+1)**3
+    adapters=max(p['local_adapters'] for p in providers.values())
+    primitive_bound=max(p['local_primitive_bound'] for p in providers.values())
+    bridge_steps=sum(event['kind']=='bridge' for event in parent['recipe'])
+    bridge_sweeps=sum(event['kind']=='bridge' for event in template['execution_schedule'])
+    assert bridge_sweeps==replicas*bridge_steps
+    bridge_additions=2*v*bridge_sweeps
+    shifts=blocks_per_stream*v*replicas; moves=2*shifts
+    parent_live,parent_physical=parent['live'],parent['physical']
+    data_stock=2*v*blocks_per_stream*replicas
+    assert (parent_live-data_stock)%stages==0
+    parent_banks=(parent_live-data_stock)//stages
+    assert parent_banks>=0 and parent_physical==parent_live+parent_helpers+centres+2
+    nonlocal_items=(4*v*replicas*stages+2*v*replicas*stages+2*call_count*helpers
+        +sum(child['replicas'] for child in parent['idle_children'])+stages*parent_banks
+        +bridge_additions+shifts+moves+parent_live+parent_physical+wrapper_factors)
+    outside=8*nonlocal_items+64*m
+    parent_pervertex=(scalar+bridge_additions+shifts+moves+parent_live
+        +(call_count*adapters+outside)*compiler+64*parent_physical)
+    live,physical=template['live'],template['physical']
+    mass,profile=owners['rank_mass'],owners['paid_profile']
+    assert m*live-mass==owners['deficit']==2560
+    assert mass==sum(int(r)*count for r,count in profile.items())
+    assert physical==live+helpers+centres+2
+    assert live==owners['live'] and physical==owners['physical']
+    assert live<=parent_live and physical<=parent_physical
+    assert not template['bank_padding']['families']
+    assert owners['explicit_idle_remainder_children']<=owners['source_idle_children_charged']
+    # The old dedicated-bank geometry is only a conservative reserve envelope.
+    # Its singular program is never used as evidence for a mixed invocation.
+    rebased=parent_pervertex+65*(physical-parent_physical)+(live-parent_live)
+    used=max(rebased,parent_pervertex); retained=None; payload=512
+    if retained_invoice is not None:
+        previous=read(retained_invoice)
+        assert previous['compiler']==compiler and previous['charged_prefix_bits']==payload
+        previous_bound=previous['conservative_pervertex_used']
+        used=max(used,previous_bound+parent_pervertex)
+        retained=dict(sha256=filehash(retained_invoice),previous_pervertex_allowance=previous_bound,
+            added_complete_new_pervertex=parent_pervertex,policy='Retain old allowance and add entire fresh mixed recount.')
+    half=m//2; group=2**(half*half)
+    for i in range(1,half+1): group*=2**(2*i)-1
+    stock,streamed_mass=group*physical,group*mass
+    logical=group*used+64; router=compiler*(logical+1)*(stock+1)**2
+    g_bound,e_bound,c0=2**30000,2**100000,2**210000
+    total_mass=streamed_mass+e_bound
+    literal=2*g_bound*stock**2+8*streamed_mass+4*stock+4+32*m
+    row=2*stock.bit_length()+9909+252+2*payload
+    maxchild=max(map(int,profile))
+    inequalities=dict(local_primitive_bound=primitive_bound<2**48,
+        logical=logical<2**6050,router=router<g_bound,literal=literal<e_bound,
+        mass=total_mass<2**100001,precision=32*m*total_mass*total_mass<c0,
+        tape=2*total_mass+18<c0,row=row<20161,halving=m*m>2*maxchild*maxchild)
+    assert all(inequalities.values())
+    localbits=max(r['prefix_bits'] for p in providers.values() for r in p['local'].values())
+    input_l2_bits=(m+1)//2
+    required_prefix=localbits+input_l2_bits+call_count+bridge_sweeps+4
+    assert required_prefix<payload
+    receipt=dict(status='PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE',
+        template_sha256=template_hash,parent_template_sha256=contenthash(local_dir/'GLOBAL-TEMPLATE.json.gz'),
+        owner_audit_sha256=filehash(audit/'OWNERS-AND-PROFILE.json'),
+        controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'),
+        providers=providers,provider_phase_semantic_sha256={pid:p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']for pid,p in providers.items()},provider_counts=dict(provider_counts),selected_calls=selected,
+        selected_local_paid_profile=dict(sorted(selected_paid.items())),
+        selected_real_component_primitives=scalar,selected_coefficient_work_primitive_count=coefficient_work,
+        selected_scalar_macros=macros,global_prefix_bits=required_prefix,charged_prefix_bits=payload,
+        complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,
+        helpers=helpers,centres=centres,live=live,physical=physical,
+        physical_stock_identity=dict(data_and_owner_families=live,local_helpers=helpers,
+                                     private_centres=centres,coefficient_work=2),
+        local_adapters=adapters,local_primitive_bound=primitive_bound,
+        wrapper_elementary_factors_charged=wrapper_factors,factors_per_wrapper=factors_per_wrapper,
+        compiler=compiler,unhosted_pervertex=parent_pervertex,hosted_rebased_pervertex=rebased,
+        conservative_pervertex_used=used,retained_prior_overcharge=retained,
+        finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),
+                    literal_bits=literal.bit_length(),physical_row_coefficient=row,
+                    retained_row_coefficient=20161,required_C0_bits=(32*m*total_mass*total_mass).bit_length(),
+                    halving_integer_inequality=[m*m,2*maxchild*maxchild],G_exponent=30000,
+                    E_exponent=100000,C0_exponent=210000),strict_checks=inequalities,
+        scope='Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. All three providers use fresh hash-bound independent all-column/frame/phase/normalization admission. Shared compiler uses conservative maxima; parent is geometry/overcharge only. All-size compiler, hosting, precision/tape and analytic transfer remain conditional.')
+    prefix=dict(status='PASS_MIXED_ASYNC_GLOBAL_PREFIX',template_sha256=template_hash,
+        global_prefix_bits=required_prefix,retained_payload_bits=payload,
+        complete_invocation_cover_sweeps=call_count,bridge_factor_two_sweeps=bridge_sweeps,
+        local_scalar_coefficient_work_prefix_bits=localbits,stream_input_sup_to_l2_bits=input_l2_bits,
+        primitive_arithmetic_margin_bits=4,controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'),
+        proof='Each selected normalized provider restores all arbitrary dirty helper columns and gives the same data shear endpoints. Actual whole-owner charts are right-translation bijections. Sum all 72 invocation and 72 bridge sweeps and take maximum local scalar/Horner prefix over all three providers and orientations. Idle children, phases, spectator endpoints and terminal translations are unitary. Retained all-size interfaces are conditional.')
+    out.mkdir(parents=True,exist_ok=True)
+    (out/'PREFIX-AND-INVOICE.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    (out/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix,indent=2)+'\n')
+    print(json.dumps({k:receipt[k] for k in ['status','provider_counts','selected_real_component_primitives',
+          'selected_coefficient_work_primitive_count','global_prefix_bits','finite','strict_checks']},indent=2))
+    return receipt
+
+if __name__=='__main__':
+    parser=argparse.ArgumentParser(description=__doc__)
+    for name in ('base','hosted','audit','out'):parser.add_argument('--'+name,type=Path,required=True)
+    parser.add_argument('--retained-invoice',type=Path)
+    args=parser.parse_args()
+    run(args.base,args.hosted,args.audit,args.out,args.retained_invoice)
diff --git a/research/gauge44-leaver/code/prepare_global.py b/research/gauge44-leaver/code/prepare_global.py
new file mode 100644
index 0000000000..655c9470f6
--- /dev/null
+++ b/research/gauge44-leaver/code/prepare_global.py
@@ -0,0 +1,124 @@
+"""Bind a frozen explicit owner map to exact native local artifacts.
+
+This preparer nominates a witness. The separate serialized controller audit,
+finite invoice, two exact moment engines and strict pinned replay admit it.
+Apache-2.0; prepared with OpenAI assistance. See NOTICE.md.
+"""
+import argparse
+from collections import Counter, defaultdict
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+from generated_identity import artifact_identities, FILES
+
+assert __debug__, 'Assertions required'
+
+
+def read(path):
+    raw = Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def dump(path, value):
+    Path(path).write_text(json.dumps(value, indent=2) + '\n')
+
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--parent', type=Path, required=True)
+ap.add_argument('--owners', type=Path, required=True)
+ap.add_argument('--local', type=Path, required=True)
+ap.add_argument('--data', type=Path, required=True)
+args = ap.parse_args()
+args.data.mkdir(parents=True, exist_ok=True)
+parent_path = args.parent / 'data/PLAN.json'
+assert sha(parent_path) == '258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda'
+plan = read(parent_path)
+word = read(args.local / 'CANONICAL-WORD.json.gz')
+checks = read(args.local / 'LOCAL-CHECKS.json')
+assert (word['v'], word['h'], word['R']) == (112, 9, 492)
+widths = [len(word['frames'][word['final'][224+h]]) -
+          len(word['frames'][word['start'][224+h]]) for h in range(492)]
+profile = {int(k): v for k, v in word['local_profile'].items()}
+assert profile == {1: 2514, 2: 404, 3: 448, 4: 160, 5: 56, 8: 8}
+assert Counter(widths) == {4: 52, 5: 48, 7: 34, 8: 114, 9: 244}
+assert sum(widths) == 3794
+owners = read(args.owners)
+assert len(owners) == 72 * 492
+order = [tuple(x) for x in plan['order']]
+times = {x: i for i, x in enumerate(order)}
+used, call_helpers, call_families = defaultdict(set), defaultdict(set), defaultdict(set)
+for z in owners:
+    key = (z['stage'], z['replica'])
+    h, i, rep, port = z['helper'], z['child'], z['owner_replica'], z['port']
+    assert key in times and 0 <= h < 492 and 0 <= rep < 8 and 0 <= port < 112
+    assert z['time'] == times[key] and h not in call_helpers[key]
+    assert z['family'] not in call_families[key]
+    call_helpers[key].add(h)
+    call_families[key].add(z['family'])
+    cap, allowed = plan['windows'][f'{rep},{i}']
+    assert z['time'] in allowed and z['width'] == widths[h]
+    assert z['copy'] == rep * 112 + port
+    assert z['family'] == rep * 896 + (2*plan['pairs'][str(i)] + plan['sides'][str(i)])*112 + port
+    assert 0 <= z['offset'] and z['offset'] + z['width'] <= cap
+    cells = set(range(z['offset'], z['offset'] + z['width']))
+    group = (i, rep, port)
+    assert not used[group] & cells
+    used[group].update(cells)
+assert set(call_helpers) == set(order)
+assert all(hs == set(range(492)) for hs in call_helpers.values())
+idle = Counter()
+for key, (cap, _) in plan['windows'].items():
+    rep, i = map(int, key.split(','))
+    for port in range(112):
+        cells = used[i, rep, port]
+        assert cells == set(range(len(cells)))
+        left = cap - len(cells)
+        if left:
+            idle[left] += 1
+global_profile = Counter({r: 72*n for r, n in profile.items()}) + idle
+assert sum(r*n for r, n in global_profile.items()) == 520704
+assert 73*7168 - sum(r*n for r, n in global_profile.items()) == 2560
+pid = 'gauge44'
+for c in plan['provider_calls']:
+    c['provider'] = pid
+    c['local_program_sha256'] = checks[c['orientation']]['sha256']
+for c in plan['per_call_widths']:
+    c['widths'] = widths
+artifacts = {name: sha(args.local / name) for name in FILES}
+identities = artifact_identities(args.local)
+plan['provider_registry'] = {pid: dict(
+    directory='providers/' + pid, artifact_sha256=artifacts,
+    ports=word['ports'], centers=word['centers'], widths=widths,
+    actual_paid_profile=word['local_profile'],
+    orientation_program_sha256={k: v['sha256'] for k, v in checks.items()},
+    artifact_semantic_sha256=identities)}
+plan.update(status='FROZEN_EXPLICIT_GAUGE44_WHOLE_OWNER_NOMINATION',
+            mode='gauge44-all72', profile=dict(sorted(global_profile.items())),
+            solver_status='deterministic-capacity-matching', gap=None,
+            source_plan_sha256=sha(parent_path),
+            source_owners_sha256=sha(args.parent / 'data/OWNERS.json.gz'),
+            assignment_sha256=sha(args.owners))
+target_owners = args.data / 'OWNERS.json.gz'
+if args.owners.resolve() != target_owners.resolve():
+    shutil.copyfile(args.owners, target_owners)
+dump(args.data / 'PLAN.json', plan)
+spec = dict(schema='witness-spec/1', name='gauge44-all72',
+            data=dict(plan_sha256=sha(args.data / 'PLAN.json'), owners_sha256=sha(target_owners)),
+            dispatch=[[s, r, pid] for s in range(9) for r in range(8)],
+            call_order=plan['order'], width_spot_helpers=[264, 276, 288, 300],
+            providers={pid: {}}, expected=dict(gain_baseline_kappa='0.001636241501576388'))
+dump(args.data / 'SPEC.json', spec)
+dump(args.data / 'PREPARATION.json', dict(
+    status='PASS_EXPLICIT_MAP_AND_FRESH_PROVIDER_NOMINATION',
+    parent_plan_sha256=sha(parent_path), source_owners_sha256=sha(args.owners),
+    global_profile=dict(sorted(global_profile.items())), idle_profile=dict(sorted(idle.items())),
+    roles=len(owners), rank_mass=520704, deficit=2560,
+    remaining='Independent emitted-controller audit, fresh finite invoice, exact moments and outer assembly.'))
+print('Prepared all72 gauge44 candidate:', dict(sorted(global_profile.items())))
diff --git a/research/gauge44-leaver/code/restore_parent.py b/research/gauge44-leaver/code/restore_parent.py
new file mode 100644
index 0000000000..21135f898a
--- /dev/null
+++ b/research/gauge44-leaver/code/restore_parent.py
@@ -0,0 +1,67 @@
+"""Materialize the omitted generated PR558 parent, then require its reviewed hash.
+
+The integrated review contains the native inputs and INTEGRATION.json but
+omits GLOBAL-TEMPLATE.json.gz. This is only the deterministic template
+binding from the inherited prepare_supplier_base.py; no old circuit or
+phase calculation is rerun. The whole exact payload must match the review.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+assert __debug__, 'Assertions required'
+ap=argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--source',type=Path,required=True)
+ap.add_argument('--baseline',type=Path,required=True)
+ap.add_argument('--out',type=Path,required=True)
+a=ap.parse_args()
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+assert not a.out.exists()
+base=a.out/'complex-global/base'
+shutil.copytree(a.baseline/'complex-global/base',base)
+d=base/'split-centres'
+parent=a.source/'vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz'
+old=read(parent);can=read(d/'CANONICAL-WORD.json.gz')
+checks=read(d/'LOCAL-CHECKS.json');programs=read(d/'LOCAL-PROGRAMS.json.gz')
+v,h,r=can['v'],can['h'],can['R'];c=len(can['centers']);m,t,l,k=73,8,9,4
+assert(v,h,r,c)==(112,9,504,8)
+widths=[h-len(can['frames'][f])for f in can['start'][2*v:]]
+data=2*k*t*v;live=data+l*r;physical=live+r+c+2
+word=copy.deepcopy(old)
+word.update(version='round20-new-supplier-dedicated-bank-parent-v1',live=live,physical=physical,local_programs=programs)
+word['private_namespace']={'centers':[live,live+c],'reserved_tableau':[live+c,live+c+r],'coefficient':[physical-2,physical]}
+for call in word['calls']:
+ s,rep=call['stage'],call['replica'];owners=copy.deepcopy(call['owners'][:2*v])
+ for helper,w in enumerate(widths):
+  route=[2,rep]if w==9 else[2,rep*w,w,list(range(t*w,t*w+9-w))]
+  owners.append([data+s*r+helper,route])
+ call['owners']=owners;call['local_program_sha256']=checks[call['orientation']]['sha256']
+children=[]
+for s in range(l):
+ for helper,w in enumerate(widths):
+  axes=list(range(t*w,m))
+  children.append(dict(family=data+s*r+helper,rank=len(axes),axis_indices=axes,orthogonal_axes=[1<<j for j in axes]))
+word['bank_padding']={'families':list(range(data,live)),'children':children,
+ 'semantics':'Each listed complement frame is applied once after the eight disjoint residual blocks of that dedicated bank. The final hosted derivative has empty families and children.'}
+word['cover_final_correction'].update(families=[0,live],charged_calls_per_cover=live)
+for i,e in enumerate(word['execution_schedule']):
+ if e['kind']=='bank_padding_cover_sweep':word['execution_schedule'][i]={'kind':'bank_padding_cover_sweep','families':[data,live],'children_source':'bank_padding.children'}
+ elif e['kind']=='translate_every_live_family':e.update(word['cover_final_correction'])
+word['exact_data_phase_recipe_sha256']=sha(base/'work/complex-nine-native/DATA-PHASES.json')
+word['exact_local_clifford_recipe_sha256']=sha(d/'CLIFFORD-RECIPES.json')
+word['residual_adapter_sha256']=sha(d/'RESIDUAL-ADAPTERS.json')
+word['supplier_substitution']={'parent_template_sha256':sha(parent),
+ 'old_canonical_word_sha256':sha(a.baseline/'complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz'),
+ 'new_canonical_word_sha256':sha(d/'CANONICAL-WORD.json.gz'),
+ 'exact_same_ports':True,'data_contract':'The same ordered 112 data ports and both complete-invocation identity-shear orientations feed the unchanged nine-stage controller. No old local program or helper profile is reused.'}
+word['route_semantics']['helper']='Dedicated family DATA+stage*R+helper; one helper per bank per complete invocation. Width-nine route[2,replica] uses axes9*replica..9*replica+8. Width-w entering route[2,w*replica,w,spectators] uses the disjoint residual block and paid normalization wrappers; spectator axes start at8*w, beyond all residual blocks.'
+raw=json.dumps(word,sort_keys=True,separators=(',',':')).encode()
+expected=read(d/'INTEGRATION.json')['global_template_sha256']
+assert hashlib.sha256(raw).hexdigest()==expected=='7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3'
+(d/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+print('PASS_EXACT_REVIEWED_PARENT_TEMPLATE_RESTORED',expected)
diff --git a/research/gauge44-leaver/code/witness.py b/research/gauge44-leaver/code/witness.py
new file mode 100644
index 0000000000..c5c7fbc114
--- /dev/null
+++ b/research/gauge44-leaver/code/witness.py
@@ -0,0 +1,55 @@
+"""Spec loader: spec values are EXPECTED values, compared only after independent recomputation.
+WITNESS_DISCOVER=1 runs the same recomputation without comparing pinned values (pin() records only);
+it is used once to produce outputs for generate_spec.py, after which the strict run must pass.
+"""
+import json,os
+from collections import Counter
+from pathlib import Path
+SPEC=json.loads(Path(os.environ['WITNESS_SPEC']).read_text())
+DISCOVER=os.environ.get('WITNESS_DISCOVER')=='1'
+X=SPEC.get('expected',{})
+PROVIDERS=SPEC.get('providers',{})
+DISPATCH={(s,r):p for s,r,p in SPEC['dispatch']}
+CALL_ORDER=[tuple(x)for x in SPEC['call_order']]
+# width-8 spot helpers: PR558's helpers 270, 282, 294, 306, or their images under a K-triangle word's 504 -> R helper map
+# (verify.py checks the spec value against the constructor's HELPER-MAP.json)
+SPOT=tuple(SPEC.get('width_spot_helpers',(270,282,294,306)))
+# A pivot swap moves a kernel family's pivot role p -> x; the old pivot p becomes an ordinary cold helper and its width
+# goes 8 -> 9 (construction/layers, PR641 PROOF-NOTE-PIVOT). Expected spot widths are derived from the package's pinned
+# pivot-swap recipe (path and sha256 in the spec), not from free data: 9 at a swapped-out pivot, 8 otherwise.
+_PKG=Path(os.environ['WITNESS_SPEC']).resolve().parents[1]
+def _old_pivots():
+ ps=SPEC.get('pivot_swap')
+ if not ps:return frozenset()
+ raw=(_PKG/ps['recipe']).read_bytes();import hashlib
+ assert hashlib.sha256(raw).hexdigest()==ps['sha256'],'pivot-swap recipe pin'
+ return frozenset(s['pivot']for s in json.loads(raw)['swaps'])
+OLD_PIVOTS=_old_pivots()
+def spot_widths(v=112):
+ """Expected residual widths at the spot helpers (helper indices) of the gauge44 provider."""
+ return tuple(9 if 2*v+h in OLD_PIVOTS else 8 for h in SPOT)
+PIDS=tuple(sorted(set(DISPATCH.values())))
+COUNTS=dict(Counter(DISPATCH.values()))
+assert DISCOVER or set(PROVIDERS)==set(PIDS),'spec providers differ from dispatch providers'
+def lookup(key):
+ """Dotted spec path; a segment may itself contain dots when it names a file (split at most once per known file suffix)."""
+ v=SPEC;parts=key.split('.')
+ while parts:
+  for n in range(len(parts),0,-1):
+   k='.'.join(parts[:n])
+   if isinstance(v,dict) and k in v:v=v[k];parts=parts[n:];break
+  else:raise KeyError('spec has no key %s'%key)
+ return v
+def pin(key,got):
+ """Strict mode: got must equal the spec value at dotted key; the failure names the key."""
+ if DISCOVER:
+  if os.environ.get('WITNESS_RECORD'):   # discovery bookkeeping only: append (key, value) for the spec writer
+   with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10))
+  return got
+ want=lookup(key)
+ assert got==want,'SPEC MISMATCH %s: expected %s got %s'%(key,json.dumps(want)[:400],json.dumps(got,default=str)[:400])
+ return got
+def partner(pid):
+ """A different provider for substitution controls (next in sorted order)."""
+ assert len(PIDS)>1
+ return PIDS[(PIDS.index(pid)+1)%len(PIDS)]
diff --git a/research/gauge44-leaver/construction/COLD44-RECIPE.json.gz b/research/gauge44-leaver/construction/COLD44-RECIPE.json.gz
new file mode 100644
index 0000000000..6f59d88920
Binary files /dev/null and b/research/gauge44-leaver/construction/COLD44-RECIPE.json.gz differ
diff --git a/research/gauge44-leaver/construction/COMPLETION-PRIORITY.json b/research/gauge44-leaver/construction/COMPLETION-PRIORITY.json
new file mode 100644
index 0000000000..e0df30aeef
--- /dev/null
+++ b/research/gauge44-leaver/construction/COMPLETION-PRIORITY.json
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+{
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+  },
+  "4,5,6,7": {
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+    "registers": [
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+  }
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver/construction/INPUTS.json b/research/gauge44-leaver/construction/INPUTS.json
new file mode 100644
index 0000000000..2b12294b58
--- /dev/null
+++ b/research/gauge44-leaver/construction/INPUTS.json
@@ -0,0 +1,65 @@
+{
+  "schema": "gauge44-compact-construction-v1",
+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "commits": {
+    "main": "17ce0c79b7b51c2634b439ea5a2b754f09909693",
+    "pr635": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f"
+  },
+  "files": {
+    "main": {
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+      "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
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+      "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/gk/gk_word.py": "f027a9273bcf4e0971258c160b7d3b3c196366b32a529cff6e6a0e666b03826b",
+      "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/inputs/RAW504.json.gz": "1c6144791dbedf6427e3ee7b4c24fb05b5bf407f6346592f50f8dd8d9638108d",
+      "research/structural-gain/frontier-composition/global-replay/base/split-centres/FULL-WORD.json.gz": "375bd23001cd805707968005a9342827d5464e3f8e3a754197b31c46fc3f63c2",
+      "research/structural-gain/frontier-composition/multicold-eight-word/FULL-WORD.json.gz": "4d4a59db7f74d7505447fbb2aa87735771cca1d04a0afafa455d21bd8dbf1f77"
+    },
+    "pr635": {
+      "research/complex-571-cold14-st2/code/build_cold_end.py": "864b4701dd73afd0c9d99761b7a749f3354c48985730f17054e18c052996a668",
+      "research/complex-571-cold14-st2/code/build_hpe.py": "ba2001695d8c7547a82260c3b016e01dac686e95a61757ca124eb9879078ea8e",
+      "research/complex-571-cold14-st2/code/build_port_stage.py": "beb0d30fde1b9a30db091880b38c4a8ec906da3f715c43de7db8bf7932526e72",
+      "research/complex-571-cold14-st2/code/hpe_adapters_local.py": "eb0b5c6c7161e18dc22168da3211448d321586edd15bcfb4b4741174d36993cf",
+      "research/complex-571-cold14-st2/code/hpe_audit_and_transport.py": "c9a05ff291016b870b4fc925b317abd9c3a604c73ffc8920dfdbbeb475e20aa3",
+      "research/complex-571-cold14-st2/code/hpe_audit_local.py": "6bd9a1e279c9c9e4f3767d9f82e537b559292906feb2ddab02f380fb6523a810",
+      "research/complex-571-cold14-st2/code/hpe_emit_local.py": "7e4a6fbc38c8228157b6311457d1496bf460291393043932d2c365f004f77805",
+      "research/complex-571-cold14-st2/data/TRI-SCHEDULE.json": "94da9d5575f5b237097a77ac7dd09aff594322dd9c35138bfd34ffc5e1a7a51e",
+      "research/complex-571-cold14-st2/data/recipes/k492-jp8-frame_regroup.json": "9bd347334de643f29865290be1ed37289f9cae6cd339547ac89b45fa7aaee65a",
+      "research/complex-571-cold14-st2/data/recipes/k492-jp8-hyperplane_end.json": "e4d4dfd83d0c64cb0a8ee8c8bbd95d0510ee68699859e568fe201cd6f8d250c1"
+    },
+    "delta": {
+      "COLD44-RECIPE.json.gz": "22d0e01e990c0f1c588607a095271f7844851a437ba07174505e98e9528aed4c",
+      "COMPLETION-PRIORITY.json": "0274ffca1725e7460aaf7b672bc1248aa6dfdec11e5f0fec91af18b829f8ba47",
+      "build_gauge_cold44.py": "ec730a4d3ff12fb058780718b1d5a7afe61243c532679ef347a5a48e2af0a3bb",
+      "construct_gauge_xcentre.py": "d8d295566ef2399af2da0707a4adc83e07aa26d2344c01a66bd0ca7684cf9217",
+      "reproduce.py": "047bb9b3536b0b16bb08a21cd9fd80404ca9d022345f1aeab34b21dffc281c92"
+    }
+  },
+  "word_content_sha256": {
+    "shadow-early": "edb55811a9d38802c311c74bdd2d4d1b2f3eaf37d06e4178eef0785c2fa4b57d",
+    "shadow-prefix": "6c361b33967bb62d878b3acef44a4ac2c70970e99f36a11906b03811495de533",
+    "raw": "0ac47f92fc2e3f5aa457d78f7b8a5c785bf140c546932b9dfcd9e610ad319180",
+    "port0": "7086d4309f145f0bf85b97f567e2cbeeaca9fc5011f62c86c805bfadeb0300fc",
+    "port1": "8f47545698a11072f8c6a0b50ae9c8acf8e4e2b0e35a0e8c672bbca216b04534",
+    "port2": "4e4919c140e07f6c820bea4aae83565b3b4967ffbfbb907611216ff6e2e6105d",
+    "port3": "9774dca3e4295e2eb9171a9cf34e1973bc72bad38eddec2cc0fc498bd9e041f3",
+    "regroup": "989082402d2292a18328e86927c0a12d34fcab18ef4ff724bd1ce691cf4e7531",
+    "hpe": "42fb8b3aa314593fe976820cf65824f5fce0ee4f95281796992d4809709864cc",
+    "cold44": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290"
+  },
+  "helper_map_sha256": "688d5115b221be68c96970822cc04ff698e2a84432fa7db9cb59057f6fe55def",
+  "canonical_content_sha256": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+  "local_program_sha256": {
+    "forward": "d17399c8c7458bb7110d8596fab5f769cd4cb3733a3042277fa08bf03f42d6c9",
+    "backward": "4772df0663f88cc218fd7254eb202f46daf136c06e9e96c19ed8ea218b545dc4"
+  },
+  "clifford_recipes_sha256": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771"
+}
diff --git a/research/gauge44-leaver/construction/LICENSE b/research/gauge44-leaver/construction/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/gauge44-leaver/construction/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
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+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
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+      "Derivative Works" shall mean any work, whether in Source or Object
+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
+      the Work and Derivative Works thereof.
+
+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
+      to that Work or Derivative Works thereof, that is intentionally
+      submitted to Licensor for inclusion in the Work by the copyright owner
+      or by an individual or Legal Entity authorized to submit on behalf of
+      the copyright owner. For the purposes of this definition, "submitted"
+      means any form of electronic, verbal, or written communication sent
+      to the Licensor or its representatives, including but not limited to
+      communication on electronic mailing lists, source code control systems,
+      and issue tracking systems that are managed by, or on behalf of, the
+      Licensor for the purpose of discussing and improving the Work, but
+      excluding communication that is conspicuously marked or otherwise
+      designated in writing by the copyright owner as "Not a Contribution."
+
+      "Contributor" shall mean Licensor and any individual or Legal Entity
+      on behalf of whom a Contribution has been received by Licensor and
+      subsequently incorporated within the Work.
+
+   2. Grant of Copyright License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      copyright license to reproduce, prepare Derivative Works of,
+      publicly display, publicly perform, sublicense, and distribute the
+      Work and such Derivative Works in Source or Object form.
+
+   3. Grant of Patent License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      (except as stated in this section) patent license to make, have made,
+      use, offer to sell, sell, import, and otherwise transfer the Work,
+      where such license applies only to those patent claims licensable
+      by such Contributor that are necessarily infringed by their
+      Contribution(s) alone or by combination of their Contribution(s)
+      with the Work to which such Contribution(s) was submitted. If You
+      institute patent litigation against any entity (including a
+      cross-claim or counterclaim in a lawsuit) alleging that the Work
+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
+      granted to You under this License for that Work shall terminate
+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
+      Work or Derivative Works thereof in any medium, with or without
+      modifications, and in Source or Object form, provided that You
+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
+          attribution notices from the Source form of the Work,
+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
+          distribution, then any Derivative Works that You distribute must
+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
+          pertain to any part of the Derivative Works, in at least one
+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
+          documentation, if provided along with the Derivative Works; or,
+          within a display generated by the Derivative Works, if and
+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
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+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
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+   9. Accepting Warranty or Additional Liability. While redistributing
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diff --git a/research/gauge44-leaver/construction/NOTICE.md b/research/gauge44-leaver/construction/NOTICE.md
new file mode 100644
index 0000000000..16b0507070
--- /dev/null
+++ b/research/gauge44-leaver/construction/NOTICE.md
@@ -0,0 +1,9 @@
+# Construction delta notice
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+
+`construct_gauge_xcentre.py` modifies PR635's credited `construct_k_triangle.py`, which in turn extends icekylinx's PR531/PR514/PR425 factory lineage. Its original source comments are retained. The K-triangle schedule and the upstream porting, JP8 frame, kernel and HPE procedures are reused from the pinned source checkouts and are not new contributions of this delta.
+
+The new source-copy exchanges, complementary factory basis, carrier assignment, exact cold44 constructor and compact reproduction driver are described in `../CONSTRUCTION.md`.
+
+`UPSTREAM-NOTICE.md` is the complete unmodified notice from the pinned PR635 package. `LICENSE` is that package's Apache-2.0 license. All further notices and source credits of the referenced upstream packages remain applicable and are retained in the source checkouts rather than vendored again here.
diff --git a/research/gauge44-leaver/construction/REBUILD-CHECKS.json b/research/gauge44-leaver/construction/REBUILD-CHECKS.json
new file mode 100644
index 0000000000..0801f35da7
--- /dev/null
+++ b/research/gauge44-leaver/construction/REBUILD-CHECKS.json
@@ -0,0 +1,51 @@
+{
+  "status": "PASS_COMPACT_SCALAR_REPRODUCTION_AND_FROZEN_RECIPE_SPLICE",
+  "steps": [
+    {
+      "step": "shadow-early",
+      "exit_code": 0,
+      "seconds": 0.355
+    },
+    {
+      "step": "shadow-prefix",
+      "exit_code": 0,
+      "seconds": 0.511
+    },
+    {
+      "step": "gauge-forward",
+      "exit_code": 0,
+      "seconds": 0.527
+    },
+    {
+      "step": "port0",
+      "exit_code": 0,
+      "seconds": 0.468
+    },
+    {
+      "step": "port1",
+      "exit_code": 0,
+      "seconds": 0.636
+    },
+    {
+      "step": "port2",
+      "exit_code": 0,
+      "seconds": 0.474
+    },
+    {
+      "step": "port3",
+      "exit_code": 0,
+      "seconds": 0.497
+    },
+    {
+      "step": "cold44-exact",
+      "exit_code": 0,
+      "seconds": 2.754
+    }
+  ],
+  "constructor_seconds": 6.222,
+  "word_content_sha256": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290",
+  "all_step_input_and_output_pins_checked": true,
+  "regenerated_recipe_equals_frozen_recipe": true,
+  "frozen_splice_matches_exact_constructor": true,
+  "scope": "One portable scalar reconstruction from pinned main and PR635 inputs; existing native and independent mathematical receipts accompany the package separately."
+}
diff --git a/research/gauge44-leaver/construction/UPSTREAM-NOTICE.md b/research/gauge44-leaver/construction/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..ebc24a0168
--- /dev/null
+++ b/research/gauge44-leaver/construction/UPSTREAM-NOTICE.md
@@ -0,0 +1,34 @@
+# Attribution and scope
+
+Four verified provider types are offered to every call: PR571's prefix word with twelve multi-cut cold kernels (PR568's unchanged constructor), the same word with forty width-five entrance promotions (PR569's unchanged frame constructor) before those kernels, PR575's plain joint-prefix provider, and PR568's eight-cold provider. A window MILP with an exact per-pattern model chooses the dispatch and a literal owner map. PR583's six source-bound kernel frame coalescences (its unchanged constructor and negative controls) are applied to every PR571-prefix provider word (ck and atm3), followed by two further coalescences that each first move one addition past two commuting additions (package code/build_gate_moves.py, extending PR583's constructor); a final hyperplane_end step (package code/build_hpe.py) then runs 46 single-gate cleanups h -= p right after part B at the dim-8 join U of their registers, so 46 width-8 entering helpers per call end at U with width 7; each such gate commutes with every earlier cleanup gate on its registers (for 8 of them the partner's one earlier gate x -= p only reads p), and the reordered program is replayed exactly. A window MILP (exact windows, RINS around an LP vertex) gives the dispatch ck 45 / atm3 21 / jp8 6 and the literal owner map.
+
+Pinned external sources (unchanged; `verify.py` checks their manifests and every file it uses):
+- PR568 (`research/complex-multicold`, commit `71c99ac935a33bb7b59a1b4a7af8725a939b0b90`).
+- PR571 (`research/structural-gain`, commit `b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3`).
+- PR569 (`research/larger-gain`, commit `897213a855b7fb8a1b8b0e552a2f5c42e6c1b326`).
+- PR575 (`research/complex-joint-prefix`, commit `eac6f7e378ab622dac50a2fd4b7ef6eab014de44`).
+- PR583 (`research/kernel-frame-coalescing`, commit `89be768f0157f5a3d8e4db69cf1748768605eac9`).
+
+Provider construction is described as typed steps in `data/SPEC.json` (`build`); `verify.py` runs only allowlisted step types with their paired omission audits and checks every input and output content hash. `code/` holds the spec-driven global admission scripts adapted from PR571's `frontier-composition/global-code/` (OpenAI Codex assisted, Apache-2.0): every expected value is read from `data/SPEC.json` and compared only after independent recomputation. `code/generated_identity.py` and `code/generated_identity_controls.py`, and the decompressed-content artifact identities in the bind, audit, invoice, assembly and phase-timing scripts, are taken unchanged from PR586 by chafreaky (`research/promoted-kernel-coalescing`, commit `4846fee5b06af770e9b3a10c36200f673d656725`, OpenAI Codex assisted, Apache-2.0), including its proof-content and reference/metadata mutation controls; the normalization of descriptive width metadata after frame changes follows the same PR.
+
+In PR601, the owner map was nominated by a HiGHS window MILP (adapted from PR569's `global/nominate_width7.py`) with lazy cross-time Hall cuts; this package's re-solved map is described below. Neither is an admission dependency.
+
+DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. (The PR601 package this one starts from states: "Prepared by Claude Code (Anthropic) research agents.") Apache-2.0 applies; LICENSE is included. All notices, licenses, source pins and AI disclosures of the pinned sources and their ancestry are retained in those packages and are not replaced by this notice. All inherited conditional assumptions remain conditional.
+
+**This package (complex-571-cold14, DreamingOfClouds).** It starts from PR601 (jeremykothe2, `research/complex-571-hpem46`, commit `529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550`). Everything above is kept unchanged except the following:
+- every provider chain (ck, atm3, jp8) gains the typed step `cold_end` (`code/build_cold_end.py`, `code/cold_end_controls.py`; recipes `data/recipes/*-cold_end.json.gz`);
+- the generalised native chain and the global admission scripts accept cold helpers that end below FULL (with `0:U` wrappers), a refactored exact cleanup, and check the wrapper order;
+- `data/PLAN.json` / `data/OWNERS.json.gz` (dispatch and literal owner map) come from a relocate/swap/ejection-chain/provider-flip annealing search started from PR601's map, refined by an exact pattern-restricted owner model (CP-SAT) with a literal edge-colouring expansion (not an admission dependency);
+- `data/SPEC.json` holds the expected values, recorded by a discovery run and then checked by a strict run.
+
+The cold-end construction (a row-plus-column cone condition for low-frame ends, a rank-0 dirt-spread premix and multi-gate lower-frame cleanup) builds on PR591 / PR592 / PR593 / PR601 (jeremykothe2) and our PR599 (Lean: multi-gate and cold hyperplane-end tails). DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. Build on this at your own risk.
+
+**This package (complex-571-cold14-b3, jeremykothe2).** It is PR604's `complex-571-cold14` (DreamingOfClouds) with ColdBeyond's second cold end per block (two new `cold_end` A-gate primitives, `PROOF-NOTE.md`), ColdSupply's E1 entering pair and reviewed controls, a free dispatch (jp8 ×60, atm3 ×12) and a literal owner map from an exact per-time-Hall window MIP. All other construction, code, controls and proofs are PR604's and earlier contributors', unchanged.
+
+**This package (complex-571-cold14-k492).** It is complex-571-cold14-b3 with these changes:
+- **K-triangle base words.** The leaver-read K-triangle skeleton atom and its read schedule (`data/TRI-SCHEDULE.json`) are by AtomScout, a Claude Code research agent. `code/construct_k_triangle.py` is PR531's `code/construct_504.py` (icekylinx, OpenAI Codex / GPT assisted, Apache-2.0; pinned source `direct_delivery`) extended with that atom.
+- **Ported chains.** The PR604/B3 chains are ported stage by stage onto the K-triangle words by `code/build_port_stage.py` (Port480, a Claude Code research agent). `code/build_frame_regroup.py` extends PR583's `build_frames.py` (chafreaky).
+- **Helper count R.** The generalisation of the global scripts to the provider helper count R is by GlobalR (a Claude Code research agent), with AtomReviewer's fixes (PROOF-NOTE-R.md).
+- **Owner map.** The owner map, the cold_end recipes on the K-triangle words and the package assembly are by Stack492, Port480 and ColdBeyond (Claude Code research agents).
+
+Build on this at your own risk.
diff --git a/research/gauge44-leaver/construction/barch/LOCAL-PINS-barch-U8.json b/research/gauge44-leaver/construction/barch/LOCAL-PINS-barch-U8.json
new file mode 100644
index 0000000000..4028b95c0e
--- /dev/null
+++ b/research/gauge44-leaver/construction/barch/LOCAL-PINS-barch-U8.json
@@ -0,0 +1,50 @@
+{
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+ "barch_controls": [
+  "C0_identity",
+  "recipe",
+  "drop_restore",
+  "restore_full",
+  "drop_preread",
+  "donation_after",
+  "drop_restore@231",
+  "restore_full@231",
+  "drop_preread@231",
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+  "drop_restore@228",
+  "restore_full@228",
+  "drop_preread@228",
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+  "drop_restore@62",
+  "restore_full@62",
+  "drop_preread@62",
+  "donation_after@62",
+  "drop_restore@238",
+  "restore_full@238",
+  "drop_preread@238",
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+ ],
+ "layer_controls": 95,
+ "canonical_sha256": "24db880b7dab31e6af4eec8a1aba1bbbae29cd50d9a7b77cf0e9b571b3e5ae7c",
+ "program_sha256": {
+  "forward": "83d65a63f51bd1ce7f3dd4e4d3597311e065b4775796cd87aea3e3a62689047c",
+  "backward": "e4e483b764e9a85f84a04425e57d73ecdcc72eb2e4d97a64f17d9da58fa5ace0"
+ },
+ "clifford_recipes_sha256": "4629507dcbdd516457c001ff8f9dbe750d1a0cbfa5cfa3c6be003d45804ba0c5"
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diff --git a/research/gauge44-leaver/construction/barch/RECIPE-U8.json b/research/gauge44-leaver/construction/barch/RECIPE-U8.json
new file mode 100644
index 0000000000..ee215a805a
--- /dev/null
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+    -1,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ],
+  [
+   4,
+   [
+    "add",
+    521,
+    453,
+    -1,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ],
+  [
+   3,
+   [
+    "add",
+    544,
+    454,
+    2,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ],
+  [
+   2,
+   [
+    "add",
+    545,
+    455,
+    2,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ],
+  [
+   1,
+   [
+    "add",
+    568,
+    456,
+    2,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     24,
+     4,
+     2,
+     1
+    ]
+   ]
+  ],
+  [
+   0,
+   [
+    "add",
+    569,
+    457,
+    2,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     24,
+     4,
+     2,
+     1
+    ]
+   ]
+  ]
+ ],
+ "cleanup_prepend": [
+  [
+   "add",
+   484,
+   231,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   485,
+   226,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   508,
+   230,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   509,
+   228,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   532,
+   232,
+   2,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   533,
+   62,
+   2,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   556,
+   236,
+   2,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   557,
+   238,
+   2,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ]
+ ],
+ "local_profile": {
+  "1": 2548,
+  "2": 338,
+  "3": 446,
+  "4": 162,
+  "5": 72,
+  "8": 8
+ },
+ "expect_sha256": "090fd574747fbf9628e70cb9beb792732914cfa52e1df147579fe4dbccc68c5a",
+ "priced": {
+  "dk_ideal": 3.140480230774418e-07,
+  "dP": {
+   "5": 16,
+   "4": -32,
+   "3": 16
+  }
+ },
+ "variants": [
+  {
+   "X": 231,
+   "E": 450,
+   "dsides": [
+    878,
+    886
+   ],
+   "donors": [
+    450,
+    231
+   ],
+   "hold": [
+    496,
+    484
+   ],
+   "kept": {
+    "1215": 450,
+    "1223": 231
+   },
+   "when": "mid"
+  },
+  {
+   "X": 230,
+   "E": 452,
+   "dsides": [
+    894,
+    902
+   ],
+   "donors": [
+    452,
+    230
+   ],
+   "hold": [
+    520,
+    508
+   ],
+   "kept": {
+    "1231": 452,
+    "1239": 230
+   },
+   "when": "mid"
+  },
+  {
+   "X": 232,
+   "E": 454,
+   "dsides": [
+    910,
+    918
+   ],
+   "donors": [
+    454,
+    232
+   ],
+   "hold": [
+    544,
+    532
+   ],
+   "kept": {
+    "1247": 454,
+    "1255": 232
+   },
+   "when": "mid"
+  },
+  {
+   "X": 236,
+   "E": 456,
+   "dsides": [
+    926,
+    934
+   ],
+   "donors": [
+    456,
+    236
+   ],
+   "hold": [
+    568,
+    556
+   ],
+   "kept": {
+    "1263": 456,
+    "1271": 236
+   },
+   "when": "mid"
+  },
+  {
+   "X": 226,
+   "E": 451,
+   "dsides": [
+    880,
+    888
+   ],
+   "donors": [
+    451,
+    226
+   ],
+   "hold": [
+    497,
+    485
+   ],
+   "kept": {
+    "1217": 451,
+    "1225": 226
+   },
+   "when": "mid"
+  },
+  {
+   "X": 228,
+   "E": 453,
+   "dsides": [
+    896,
+    904
+   ],
+   "donors": [
+    453,
+    228
+   ],
+   "hold": [
+    521,
+    509
+   ],
+   "kept": {
+    "1233": 453,
+    "1241": 228
+   },
+   "when": "mid"
+  },
+  {
+   "X": 62,
+   "E": 455,
+   "dsides": [
+    912,
+    920
+   ],
+   "donors": [
+    455,
+    62
+   ],
+   "hold": [
+    545,
+    533
+   ],
+   "kept": {
+    "1249": 455,
+    "1257": 62
+   },
+   "when": "mid"
+  },
+  {
+   "X": 238,
+   "E": 457,
+   "dsides": [
+    928,
+    936
+   ],
+   "donors": [
+    457,
+    238
+   ],
+   "hold": [
+    569,
+    557
+   ],
+   "kept": {
+    "1265": 457,
+    "1273": 238
+   },
+   "when": "mid"
+  }
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver/construction/barch/build_tri.py b/research/gauge44-leaver/construction/barch/build_tri.py
new file mode 100644
index 0000000000..11c4371114
--- /dev/null
+++ b/research/gauge44-leaver/construction/barch/build_tri.py
@@ -0,0 +1,87 @@
+#!/usr/bin/env python3
+"""build_tri.py BASE_WORD RECIPE OUT_WORD [--control NAME]
+
+Standard library only. Applies a NewBArch triangle-hybrid recipe to the X4 word (1e1d99ba) and writes a FULL-WORD.json.gz.
+Recipe keys (all indices refer to the BASE word):
+  base_sha256      sha256 of the decompressed base JSON (checked)
+  B_delete         list of B indices removed
+  B_insert         list of [pos, gate]: gate (with frame) inserted before base B gate pos (list order kept)
+  B_frames         {index: frame}: explicit re-chosen frame of a kept base B gate
+  tail_insert      list of [early_index, gate]: gates appended to cleanup in list order, then registered as early cleanup at early_index (ascending)
+  cleanup_prepend  list of gates prepended to the full cleanup (early indices are shifted)
+  local_profile    report.local_profile of the result
+  expect_sha256    sha256 of the decompressed result (checked unless a control is requested)
+Controls (each must be REJECTED by audit_local; see controls.json):
+  drop_restore     omit cleanup_prepend (end value of the holder not restored)
+  restore_full     move tail_insert gates into the full cleanup (FULL frame) instead of early cleanup
+  drop_preread     omit the inserted entrance pre-reads (inserted target += E gates at pos < first donation)
+  donation_after   insert each donation after its reading target's read instead of before it
+  NAME@X           the same control restricted to the instance whose packet register is X (recipe 'variants')
+"""
+import sys, json, gzip, hashlib, copy
+
+FULL = [256, 128, 64, 32, 16, 8, 4, 2, 1]
+
+def load(p):
+    raw = gzip.decompress(open(p, 'rb').read()); return json.loads(raw), hashlib.sha256(raw).hexdigest()
+
+def apply(w, rc, control=None):
+    w = copy.deepcopy(w); B = w['B']
+    S = None
+    if control and '@' in control:                     # per-instance control: name@X mutates only instance X's gates
+        control, x = control.split('@'); x = int(x)
+        vv = [s for s in rc['variants'] if s['X'] == x][0]; S = {vv['X'], vv['E'], *vv['hold']}
+    sel = lambda g: S is None or bool({g[1], g[2]} & S)
+    dele = set(rc['B_delete']); fr = {int(k): f for k, f in rc['B_frames'].items()}
+    ins = [list(x) for x in rc['B_insert']]
+    don = [x for x in ins if not (112 <= x[1][1] < 224)]           # donations: destination is not a target
+    first_don = min(p for p, _ in don) if don else 0
+    if control == 'drop_preread':
+        ins = [x for x in ins if not (x[0] < first_don and 112 <= x[1][1] < 224 and sel(x[1]))]
+    if control == 'donation_after':
+        new = []
+        for p, g in ins:
+            if g in [d[1] for d in don] and sel(g):
+                rd = [i for i, e in enumerate(B) if i >= p and e[0] == 'add' and e[2] == g[1] and 112 <= e[1] < 224]
+                p = rd[0] + 1
+            new.append([p, g])
+        ins = new
+    at = {}
+    for p, g in ins: at.setdefault(p, []).append(list(g))
+    out = []
+    for i, e in enumerate(B):
+        out.extend(at.get(i, []))
+        if i in dele: continue
+        e = list(e)
+        if i in fr: e = e[:-1] + [list(fr[i])]
+        out.append(e)
+    out.extend(at.get(len(B), []))
+    w['B'] = out
+    pre = [list(g) for g in rc['cleanup_prepend'] if not (control == 'drop_restore' and sel(g))]
+    tails = [list(x) for x in rc['tail_insert']]
+    if control == 'restore_full':
+        pre = pre + [g[1][:-1] + [FULL] for g in tails if sel(g[1])]; tails = [g for g in tails if not sel(g[1])]
+    C = pre + w['cleanup']; sh = len(pre)
+    early = [[i + sh, U] for i, U in w['early_cleanup']]
+    idx = []
+    for j, g in tails: C.append(list(g)); idx.append((j, len(C) - 1, list(g[-1])))   # appended in recipe order
+    for j, ci, U in sorted(idx): early.insert(j, [ci, U])                               # then registered at their early index
+    w['cleanup'] = C; w['early_cleanup'] = early
+    w['report'] = dict(w['report']); w['report']['local_profile'] = rc['local_profile']
+    return w
+
+def main():
+    a = sys.argv[1:]; control = None
+    if '--control' in a: k = a.index('--control'); control = a[k + 1]; del a[k:k + 2]
+    base, out = a[0], a[2]
+    w, sha = load(base); rc = json.load(open(a[1]))
+    if sha != rc['base_sha256']: raise SystemExit('base sha mismatch ' + sha)
+    w2 = apply(w, rc, control)
+    raw = json.dumps(w2, separators=(',', ':')).encode()
+    open(out, 'wb').write(gzip.compress(raw, mtime=0))
+    s = hashlib.sha256(raw).hexdigest()
+    if control is None and s != rc['expect_sha256']: raise SystemExit('result sha mismatch ' + s)
+    print(json.dumps(dict(control=control, sha256=s)))
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/barch/reproduce_barch.py b/research/gauge44-leaver/construction/barch/reproduce_barch.py
new file mode 100644
index 0000000000..22f15b491d
--- /dev/null
+++ b/research/gauge44-leaver/construction/barch/reproduce_barch.py
@@ -0,0 +1,92 @@
+#!/usr/bin/env python3
+"""Rebuild the B0 word (NewBArch's width-neutral triangle-hybrid B-delivery rewrite on X4) and its native locals.
+
+Input: a fresh `construction/jx/reproduce_jx.py` output directory; its X4 word (1e1d99ba...) is pinned there and by
+RECIPE-B0.json (base_sha256). Steps, each checked exactly:
+  1. barch: build_tri.py (standard library only; NewBArch) applies the recipe's explicit B deletes and inserts (with frames),
+     re-chosen B frames, early-cleanup tails and FULL-cleanup restores; it checks the base and result shas (d9ba0942...).
+  2. barch-controls: run_controls.py rebuilds C0 (identity, must reproduce the input), the recipe word (must PASS #645's
+     independent audit_local.py) and four mutants (drop_restore, restore_full, drop_preread, donation_after), globally
+     and for each recipe variant (NAME@X); each mutant must FAIL audit_local with its pinned message. Every outcome is
+     required and the control set is pinned (LOCAL-PINS).
+  3. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant) on the B0 word; count pinned.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs; canonical word, local programs and
+     Clifford recipes pinned (LOCAL-PINS-barch-<id>.json).
+Apache-2.0. Driver by ColdWitness around NewBArch's builder and controls.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+PKG = HERE.parents[1]
+P6 = HERE.parent / 'layers_p6n'
+MUTANTS = ('drop_restore', 'restore_full', 'drop_preread', 'donation_after')
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--jx-dir', type=Path, required=True, help='construction/jx/reproduce_jx.py output')
+    ap.add_argument('--recipe', default='U8', help='RECIPE-<id>.json and LOCAL-PINS-barch-<id>.json')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-barch-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    inp = a.jx_dir.resolve() / 'jx/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['base_sha256'], 'input must be the pinned X4 word'
+    (out / 'barch').mkdir(); word = out / 'barch/FULL-WORD.json.gz'
+    run('barch', HERE / 'build_tri.py', inp, rfile, word, portable=False)
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['expect_sha256']
+    run('barch-controls', HERE / 'run_controls.py', inp, rfile, PKG / 'independent/audit_local.py', out / 'barch-controls', portable=False)
+    res = read(out / 'barch-controls/controls.json')
+    want = ['C0_identity', 'recipe', *MUTANTS] + [m + '@' + str(v['X']) for v in rec.get('variants', []) for m in MUTANTS]
+    assert sorted(res) == sorted(want) == sorted(pins['barch_controls']) and all(x['ok'] for x in res.values()), res
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/barch/run_controls.py b/research/gauge44-leaver/construction/barch/run_controls.py
new file mode 100644
index 0000000000..f1ce999bfb
--- /dev/null
+++ b/research/gauge44-leaver/construction/barch/run_controls.py
@@ -0,0 +1,33 @@
+#!/usr/bin/env python3
+"""run_controls.py BASE_WORD RECIPE AUDIT_LOCAL_PY OUTDIR : C0 identity, the recipe word (must PASS) and the four negative
+controls (each must FAIL audit_local with its pinned message prefix). Standard library only; writes OUTDIR/controls.json."""
+import sys, json, subprocess, os, gzip, hashlib
+base, recipe, audit, out = sys.argv[1:5]
+here = os.path.dirname(os.path.abspath(__file__)); os.makedirs(out, exist_ok=True)
+# pinned rejection sites (observed on RECIPE-V1 and RECIPE-B0; the failing rows are recorded in controls.json): the holder 485 is not restored; the low-end restore 497-=451 moved to the
+# FULL cleanup runs after 451's own tail and leaves 497 wrong; without the pre-read (or with the donation after the read)
+# the entering helper's start value reaches a target.
+EXPECT = {None: 'PASS', 'drop_restore': 'all-column endpoint failure (False, ',
+          'restore_full': 'all-column endpoint failure (False, ',
+          'drop_preread': 'nonzero entrance response', 'donation_after': 'nonzero entrance response'}
+res = {}
+ident = os.path.join(out, 'C0.json')
+json.dump(dict(json.load(open(recipe)), B_delete=[], B_insert=[], B_frames={}, tail_insert=[], cleanup_prepend=[],
+               local_profile=json.loads(gzip.decompress(open(base, 'rb').read()))['report']['local_profile'],
+               expect_sha256=hashlib.sha256(gzip.decompress(open(base, 'rb').read())).hexdigest()), open(ident, 'w'))
+r = subprocess.run([sys.executable, '-B', os.path.join(here, 'build_tri.py'), base, ident, os.path.join(out, 'C0.json.gz')], capture_output=True, text=True)
+res['C0_identity'] = dict(ok=r.returncode == 0, out=r.stdout.strip() or r.stderr.strip()[-200:])
+ctls = list(EXPECT) + [c + '@' + str(s['X']) for s in json.load(open(recipe)).get('variants', []) for c in EXPECT if c]
+for ctl in ctls:
+    name = ctl or 'recipe'; wp = os.path.join(out, name + '.json.gz')
+    cmd = [sys.executable, '-B', os.path.join(here, 'build_tri.py'), base, recipe, wp] + (['--control', ctl] if ctl else [])
+    b = subprocess.run(cmd, capture_output=True, text=True)
+    if b.returncode: res[name] = dict(ok=False, build=b.stderr[-300:]); continue
+    a = subprocess.run([sys.executable, '-B', audit, '--word', wp, '--output', os.path.join(out, name + '.audit.json')], capture_output=True, text=True)
+    txt = a.stdout + a.stderr
+    if ctl is None: ok = a.returncode == 0 and 'PASS_INDEPENDENT' in txt
+    else: ok = a.returncode != 0 and EXPECT[ctl.split('@')[0]] in txt
+    res[name] = dict(ok=ok, build=json.loads(b.stdout), audit_tail=txt.strip().splitlines()[-1][:200])
+json.dump(res, open(os.path.join(out, 'controls.json'), 'w'), indent=1)
+print(json.dumps({k: x['ok'] for k, x in res.items()}))
+sys.exit(0 if all(x['ok'] for x in res.values()) else 1)
diff --git a/research/gauge44-leaver/construction/build_gauge_cold44.py b/research/gauge44-leaver/construction/build_gauge_cold44.py
new file mode 100644
index 0000000000..72d2945f6b
--- /dev/null
+++ b/research/gauge44-leaver/construction/build_gauge_cold44.py
@@ -0,0 +1,210 @@
+"""Exact dyadic cold-end realization of the source-branch/factory-completion word.
+Prepared for icekylinx with OpenAI Codex assistance; Apache-2.0.
+This is a constructor: independent endpoint/frame audits remain required.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+import copy,gzip,json,hashlib,time,sys,argparse,importlib.util
+D=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser(description=__doc__)
+for name in ('input','out','hamming','upstream-package'):ap.add_argument('--'+name,type=Path,required=True)
+args=ap.parse_args();WPATH=args.input;OUT=args.out
+assert __debug__, 'Assertions are required'
+OUT.mkdir(exist_ok=False,parents=True)
+def rd(p):return json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+w=rd(WPATH);v=w['report']['v'];n=2*v+w['report']['R'];N=list(range(v))+list(range(2*v,n));ix={x:i for i,x in enumerate(N)}
+F9=[256,128,64,32,16,8,4,2,1];t0=time.monotonic()
+def basis(vs):
+ d={}
+ for a in vs:
+  for k in sorted(d,reverse=True):
+   if a>>k&1:a^=d[k]
+  if a:
+   k=a.bit_length()-1
+   for j in d:
+    if d[j]>>k&1:d[j]^=a
+   d[k]=a
+ return tuple(d[k] for k in sorted(d,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def regs(e):return e[1:3] if e[0]=='add' else e[1:2]
+def inverse(e):
+ e=copy.deepcopy(e)
+ if e[0]=='add':e[3]=-e[3]
+ else:e[2],e[3]=e[3],e[2]
+ return e
+def apply(e,M,mapping=None):
+ t=mapping[e[1]] if mapping is not None else e[1]
+ if e[0]=='add':
+  s=mapping[e[2]] if mapping is not None else e[2];q=Q(e[3],e[4])
+  for j,a in M[s].items():
+   x=M[t].get(j,Q(0))+q*a
+   if x:M[t][j]=x
+   else:M[t].pop(j,None)
+ else:
+  q=Q(e[2],e[3]);M[t]={j:q*a for j,a in M[t].items()}
+def rref(A):
+ a=[list(map(Q,row)) for row in A];nr=len(a);nc=len(a[0]) if nr else 0;row=0;piv=[]
+ for c in range(nc):
+  k=next((i for i in range(row,nr) if a[i][c]),None)
+  if k is None:continue
+  a[row],a[k]=a[k],a[row];q=a[row][c];a[row]=[x/q for x in a[row]]
+  for i in range(nr):
+   if i!=row and a[i][c]:q=a[i][c];a[i]=[x-q*y for x,y in zip(a[i],a[row])]
+  piv.append(c);row+=1
+  if row==nr:break
+ return a,piv
+def rank(A):return len(rref(A)[1])
+def null(A,nc=None):
+ if A:a,piv=rref(A);nc=len(a[0])
+ else:a=[];piv=[];assert nc is not None
+ free=[j for j in range(nc) if j not in piv];out=[[Q(0) for j in free] for i in range(nc)]
+ for k,c in enumerate(free):out[c][k]=Q(1)
+ for i,c in enumerate(piv):
+  for k,j in enumerate(free):out[c][k]=-a[i][j]
+ return out
+def mm(A,B):
+ if not A:return []
+ if not B:return [[] for row in A]
+ bt=list(zip(*B));return [[sum((a*b for a,b in zip(row,col)),Q(0)) for col in bt] for row in A]
+def tr(A):return list(map(list,zip(*A)))
+def inv(A):
+ n0=len(A);a,p=rref([row+[Q(i==j) for j in range(n0)] for i,row in enumerate(A)])
+ assert p[:n0]==list(range(n0))
+ return [row[n0:] for row in a]
+def unit(q):
+ if not q:return False
+ a=abs(q.numerator);b=q.denominator
+ return not a&(a-1) and not b&(b-1)
+def dyadic(q):return not q.denominator&(q.denominator-1)
+def opadd(t,s,q,F):return ['add',t,s,q.numerator,q.denominator,list(F)]
+def opscale(t,q,F):return ['scale',t,q.numerator,q.denominator,list(F)]
+def eliminate(M,ids,F,skip=()):
+ """Return legal dyadic row operations taking an invertible sparse matrix to I."""
+ skip=set(skip);ops=[];dim=len(M)
+ def add(i,j,q):
+  if q:
+   assert dyadic(q);e=opadd(ids[i],ids[j],q,F);ops.append(e)
+   for c,x in M[j].items():
+    z=M[i].get(c,Q(0))+q*x
+    if z:M[i][c]=z
+    else:M[i].pop(c,None)
+ def scale(i,q):
+  if q!=1:
+   assert unit(q);ops.append(opscale(ids[i],q,F));M[i]={c:q*x for c,x in M[i].items()}
+ def swap(i,j):
+  if i!=j:
+   add(i,j,Q(1));add(j,i,Q(-1));add(i,j,Q(1));scale(j,Q(-1))
+ for c in range(dim):
+  if c in skip:
+   assert M[c]=={c:Q(1)} and all(not M[i].get(c) for i in range(dim) if i!=c)
+   continue
+  cand=[i for i in range(c,dim) if i not in skip and M[i].get(c)]
+  k=next((i for i in cand if unit(M[i][c])),None)
+  if k is None:
+   # Elementary Euclidean row additions reduce the pivot-column numerator gcd.
+   assert cand,('singular',c)
+   while k is None:
+    cand.sort(key=lambda i:abs(M[i][c]));a=cand[0]
+    b=next((i for i in cand[1:] if M[i][c]),None)
+    if b is None:raise ValueError(('non-dyadic determinant pivot',c,M[a][c]))
+    rat=M[b][c]/M[a][c];q=rat.numerator//rat.denominator
+    if q==0:q=1 if rat>0 else -1
+    add(b,a,Q(-q));cand=[i for i in cand if M[i].get(c)]
+    k=next((i for i in cand if unit(M[i][c])),None)
+  swap(c,k);scale(c,1/M[c][c])
+  for i in range(dim):
+   if i!=c and M[i].get(c):
+    assert i not in skip
+    add(i,c,-M[i][c])
+ assert all(row=={i:Q(1)} for i,row in enumerate(M))
+ return ops
+def realize(A,ids,F):
+ M=[{j:Q(x) for j,x in enumerate(row) if x} for row in A]
+ return [inverse(e) for e in reversed(eliminate(M,ids,F))]
+# Reconstruct the actual non-target map after the inherited HPE tail.
+inherited_tail=[w['cleanup'][i][:-1]+[list(f)] for i,f in w.get('early_cleanup',[])]
+mainN=[e for e in w['A']+w['B'] if not v<=e[1]<2*v]
+M=[{i:Q(1)} for i in range(len(N))]
+for e in mainN+inherited_tail:apply(e,M,ix)
+MI=[{i:Q(1)} for i in range(len(N))]
+for e in reversed(mainN+inherited_tail):apply(inverse(e),MI,ix)
+cur={x:(w['ports'][x],) if x<v else basis(w.get('start_extra',{}).get(str(x),[])) for x in N}
+for e in w['A']+w['B']+inherited_tail:
+ for x in regs(e):
+  if x in cur:cur[x]=basis(e[-1])
+enter=set(map(int,w.get('start_extra',{})));protected=[ix[x] for x in N if x<v or x in enter]
+mods=rd(args.hamming/'PACKET-PROGRAMS.json.gz');proto=rd(args.hamming/'PROTOTYPE.json')
+plans=[];premix=[];tail=[];ends={};Mafter=copy.deepcopy(M)
+for b,mod in enumerate(mods):
+ ss=mod['receipt']['source_lines'];F=basis([proto['binary_ports'][s] for s in ss]);I=[ix[x] for x in N if inside(cur[x],F)]
+ hs=list(range(224+16*b,224+16*(b+1)));H=[ix[x] for x in hs]
+ C=[[M[i].get(j,Q(0)) for j in protected] for i in I]
+ L=tr(null(tr(C),len(I)))
+ A=[[MI[j].get(i,Q(0)) for i in I] for j in protected];A=[row for row in A if any(row)]
+ K=null(A,len(I));BK=mm(L,K);_,piv=rref(BK);r=len(piv);assert r==len(L)==(2 if b in [0,1,2,11,12,13] else 4),(b,r,len(L))
+ Ksel=[[row[j] for j in piv] for row in K];Bsel=[[row[j] for j in piv] for row in BK];U=mm(Ksel,inv(Bsel));assert mm(L,U)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ q=mm([[MI[i].get(j,Q(0)) for j in I] for i in range(len(N))],U)
+ assert all(not any(q[i]) for i in range(len(N)) if i not in H),('nonlocal premix',b)
+ RR=mm(L,[[M[i].get(j,Q(0)) for j in H] for i in I]);qH=[q[i] for i in H]
+ assert mm(RR,qH)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ # Pick low physical helper destinations with independent U coordinate rows.
+ ih=[]
+ for j in sorted((j for j,i in enumerate(I) if N[i] in hs),key=lambda j:(cur[N[I[j]]]!=F,N[I[j]])):
+  if rank([U[k] for k in ih]+[U[j]])>len(ih):ih.append(j)
+  if len(ih)==r:break
+ assert len(ih)==r
+ endhs=[N[I[j]] for j in ih];endhidx=[hs.index(h) for h in endhs]
+ kerR=null(RR,16);Qmat=[[Q(0) for j in range(16)] for i in range(16)]
+ for j,hj in enumerate(endhidx):
+  for i in range(16):Qmat[i][hj]=qH[i][j]
+ other=[j for j in range(16) if j not in endhidx]
+ for k,j in enumerate(other):
+  for i in range(16):Qmat[i][j]=kerR[i][k]
+ assert rank(Qmat)==16
+ pops=realize(Qmat,hs,());premix+=pops
+ T=[[Q(i==j)-sum((U[i][k]*L[k][j] for k in range(r)),Q(0)) for j in range(len(I))] for i in range(len(I))]
+ for k,i in enumerate(ih):T[i]=L[k]
+ tops=realize(T,[N[i] for i in I],F);tail+=tops
+ # Right-compose this initial helper premix; other blocks have disjoint H sets.
+ for row in Mafter:
+  vals=[row.get(h,Q(0)) for h in H]
+  if any(vals):
+   for hj in H:row.pop(hj,None)
+   for j,hj in enumerate(H):
+    z=sum((vals[i]*Qmat[i][j] for i in range(16)),Q(0))
+    if z:row[hj]=z
+ for e in tops:apply(e,Mafter,ix)
+ ends.update({h:list(F) for h in endhs})
+ plans.append(dict(block=b,frame=list(F),registers=[N[i] for i in I],ends=endhs,pairing_rank=r,premix_gates=len(pops),tail_gates=len(tops),Q=[[str(x) for x in row] for row in Qmat],T=[[str(x) for x in row] for row in T]))
+ print('BLOCK',b,'ends',endhs,'Qops',len(pops),'Tops',len(tops),flush=True)
+# Check actual post-tail isolation before constructing the high-frame inverse.
+allends=set(ends)|set(map(int,w.get('helper_final',{})))
+for h in allends:
+ j=ix[h];assert Mafter[j]=={j:Q(1)},('row not isolated',h,Mafter[j]);assert all(not row.get(j) for i,row in enumerate(Mafter) if i!=j),('column not isolated',h)
+print('EXACT_ISOLATED',len(ends),'new;',len(allends),'total',round(time.monotonic()-t0,3),flush=True)
+fullops=eliminate(copy.deepcopy(Mafter),N,F9,[ix[x] for x in allends])
+print('FULL_INVERSE',len(fullops),round(time.monotonic()-t0,3),flush=True)
+# Cancel new cold-axis target responses inside A, after their wrappers.
+Dirt=[({h:Q(1)} if h in ends else {}) for h in range(n)]
+for e in premix+w['A']+w['cut']+w['B']:apply(e,Dirt)
+for e in w['precondition']:apply(e,Dirt)
+postcomp=[opadd(y,h,-a,()) for y in range(v,2*v) for h,a in sorted(Dirt[y].items()) if a]
+assert all(h in ends for e in postcomp for h in [e[2]])
+new=copy.deepcopy(w);new['A']=postcomp+premix+w['A'];new['cleanup']=inherited_tail+tail+fullops
+new['early_cleanup']=[[i,e[-1]] for i,e in enumerate(inherited_tail+tail)]
+new['helper_final'].update({str(h):f for h,f in ends.items()})
+new['refactored_cleanup']={'kind':'source_branch_gauge_and_retired_completion_cold44','new_cold_ends':len(ends),'exact_non_target_isolation_checked':True,'high_inverse':'dyadic_sparse_Gauss_Jordan'}
+# Derive paid profile by subtracting and adding literal frame-chain counts.
+spec=importlib.util.spec_from_file_location('upstream_cold_end',args.upstream_package/'code/build_cold_end.py')
+profile_module=importlib.util.module_from_spec(spec);spec.loader.exec_module(profile_module)
+oldprof,_=profile_module.chain_profile(w);newprof,_=profile_module.chain_profile(new)
+prof=Counter({int(k):z for k,z in w['report']['local_profile'].items()});prof.subtract(oldprof);prof.update(newprof)
+widths=Counter(len(basis(new['helper_final'].get(str(h),F9)))-len(basis(new.get('start_extra',{}).get(str(h),[]))) for h in range(224,n))
+new['report'].update(local_profile={str(k):z for k,z in sorted(prof.items()) if z},local_rank_mass=sum(k*z for k,z in prof.items()),width_inventory={str(k):z for k,z in sorted(widths.items()) if z},status='EXACT_COLD44_CONSTRUCTED_PENDING_INDEPENDENT_AUDIT')
+raw=json.dumps(new,sort_keys=True,separators=(',',':')).encode();sha=hashlib.sha256(raw).hexdigest();(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+recipe={'premix':postcomp+premix,'cleanup':new['cleanup'],'early_cleanup':new['early_cleanup'],'cold_ends':{str(h):f for h,f in ends.items()},'refactored_cleanup':new['refactored_cleanup'],'output_content_sha256':sha}
+(OUT/'RECIPE.json.gz').write_bytes(gzip.compress(json.dumps(recipe,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+receipt=dict(input_content_sha256=hashlib.sha256(gzip.decompress(WPATH.read_bytes())).hexdigest(),output_content_sha256=sha,blocks=plans,new_cold_ends=len(ends),all_low_ended_helpers=len(allends),premix_gates=len(premix),postwrapper_compensation_gates=len(postcomp),tail_gates=len(tail),inherited_tail_gates=len(inherited_tail),full_inverse_gates=len(fullops),profile=new['report']['local_profile'],width_inventory=new['report']['width_inventory'],rank_mass=new['report']['local_rank_mass'],seconds=time.monotonic()-t0)
+(OUT/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(json.dumps({k:z for k,z in receipt.items() if k!='blocks'},indent=2),flush=True)
diff --git a/research/gauge44-leaver/construction/construct_gauge_xcentre.py b/research/gauge44-leaver/construction/construct_gauge_xcentre.py
new file mode 100644
index 0000000000..1010d86746
--- /dev/null
+++ b/research/gauge44-leaver/construction/construct_gauge_xcentre.py
@@ -0,0 +1,381 @@
+# Round20 early-coordinate-center / own-Y variant, prepared for icekylinx
+# with OpenAI Codex assistance. Apache-2.0. Scalar elementary-operation
+# helpers below are retained from the attributed PR514 construct_partial.py.
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+# AtomScout: leaver-read K-triangles (schedule from atom1.py / rog.py CP-SAT)
+TRI=json.loads(Path(sys.argv[3]).read_text())
+FULLT={(tuple(tr['p']),tr['e']) for tr in TRI['triangles']}
+TRI_COORDS={t+8 for tr in TRI['triangles'] for t,_,_ in tr['reads']}
+COPYL=[]
+NH=504-3*len(FULLT)+len(COPYL)
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+# Helper ids of the unpatched 504 construction: every allocation advances the 504 numbering; a packet copy that the
+# K-triangle schedule never forms advances it without allocating (HELPER-MAP.json).
+shadow=[];skipped=[];nxt=[2*v]
+def alloc():
+    n=len(cur);cur.append(());rows.append({});shadow.append(nxt[0]);nxt[0]+=1;return n
+def skip():
+    skipped.append(nxt[0]);nxt[0]+=1
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# Each source quartet supplies pair partials first. The other two coordinate
+# partitions supply eight early face packets without touching the eight
+# partials later copied into the preconditioned Y coordinates.
+SELECT=(0,0)
+PRIORITY=json.loads((INPUT/"COMPLETION-PRIORITY.json").read_text())
+maps={};early={};own_rows={};pairs=[];tetrads={};block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)});maps[c]=mp
+    for ei,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[:40]):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        if ei==15:
+            for jj in range(4,8):swap(mp[jj],mp[2*jj+9],(P[ids[jj]],))
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in targets:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                t,u=sorted(ts);e2=R[t][q[0]]*R[t][q[1]]
+                pair={'targets':(t,u),'keys':[(c,p,eps),(c,q,e2)],'selected':pi==SELECT[parity],
+                      'matrix':[[R[a][p[0]],R[a][q[0]]] for a in (t,u)]}
+                pairs.append(pair)
+                if not pair['selected']:continue
+                zz=-Q(2*R[u][p[0]],R[t][p[0]])
+                sources=tet[1-parity]
+                for target,sign in ((t,-1),(u,1)):
+                    wanted={s:-Q(G[t][s],4)-sign*Q(G[u][s],2)/zz for s in sources
+                            if -Q(G[t][s],4)-sign*Q(G[u][s],2)/zz}
+                    assert len(wanted)==2
+                    candidates=[]
+                    for r in mp.values():
+                        if set(rows[r])!=set(wanted):continue
+                        s=next(iter(wanted));coef=wanted[s]/rows[r][s]
+                        if all(wanted[s]==coef*rows[r][s] for s in wanted):candidates.append((r,coef))
+                    assert len(candidates)==1
+                    r,coef=candidates[0];assert len(cur[r])==2
+                    own_rows[target]=(r,coef,cur[r])
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    needed={own_rows[t][0] for t in ids}
+    early[c]={j for j,e in enumerate(z['events'][40:]) if not ({mp[e[0]],mp[e[1]]}&needed)}
+    assert len(early[c])==8
+    retired=[]
+    for j in sorted(early[c]):
+        (t,s,a,b),F=z['events'][40+j],z['event_frames'][40+j]
+        add(mp[t],mp[s],Q(a,b),tuple(F));retired.append(mp[s])
+    assert not set(retired)&needed
+    # These eight retired rows already span every source coordinate. Keep
+    # them invertible and place the four coordinate totals in a changed basis.
+    F=basis([P[s] for s in ids]);assert len(F)==4
+    regs=sorted(retired,key=lambda r:(r>=v,r))
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    M=[[Q(R[s][i]) for s in ids] for i in c]
+    def qr_rank(rs):
+        bs={}
+        for r in rs:
+            r=r.copy()
+            for i,b in sorted(bs.items()):
+                if r[i]:q=r[i];r=[x-q*y for x,y in zip(r,b)]
+            i=next((i for i,x in enumerate(r) if x),None)
+            if i is not None:q=r[i];bs[i]=[x/q for x in r]
+        return len(bs)
+    assert qr_rank(M)==4
+    for rr0 in PRIORITY[",".join(map(str,c))]["rows"]:
+        rr=list(map(Q,rr0))
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    for i in range(8):
+        if len(M)==8:break
+        rr=[Q(i==j) for j in range(8)]
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    assert len(M)==8
+    linear(regs,M,F)
+    for i,r in zip(c,regs):
+        assert rows[r]=={s:Q(R[s][i]) for s in ids}
+        block_totals[c,i]=r
+
+# All centers are complete while Y is still at zero. This is the crucial
+# difference from an illegal early-own-Y prefix using the old center order.
+centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+assert all(cur[v+t]==() for t in range(v))
+
+phase=B
+for t,(r,coef,F) in sorted(own_rows.items()):
+    if t in TRI_COORDS:continue
+    assert cur[r]==F
+    add(v+t,r,coef,F)
+# requests are needed for TRI coefficients
+requests=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    requests[key1].append((t,-Q(mat[0][0],2)))
+    requests[key2].append((u,-Q(mat[0][1],2)))
+reqcoef={t:(key,coef) for key,reqs in requests.items() for t,coef in reqs}
+def face_info(c,p,eps):
+    z=blocks[c];keys=[(pp,ee) for pp in it.combinations(c,2) for ee in (-1,1)]
+    r_local,alpha=z['outputs'][keys.index((p,eps))]
+    j=[j for j in range(40,len(z['events'])) if z['events'][j][0]==r_local];assert len(j)==1
+    return j[0],Q(alpha)
+tri_join_counts=Counter()
+lcopy={}
+for s8 in COPYL:
+    r=s8+8;c=alloc();add(c,r,1,cur[r]);lcopy[r]=c
+for tr in TRI['triangles']:
+    p,eps=tuple(tr['p']),tr['e']
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];r0=r;r=lcopy.get(r,r)
+        key,coef=reqcoef[t];assert key[1]==p and key[2]==eps,(key,p,eps)
+        if blk==key[0]:
+            rr,c0,F0=own_rows[t];assert rr==r0;q=c0
+        else:
+            j,alpha=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert loc in ev[:2]
+            q=coef*alpha
+        F=basis(cur[v+t]+cur[r]);assert inside(F,hyper(P[t])),('TRI frame',t)
+        tri_join_counts[len(F)]+=1;add(v+t,r,q,F)
+
+packets={}
+for c,z in sorted(blocks.items()):
+    mp=maps[c]
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    skipev={face_info(c,p,eps)[0] for p,eps in keys if (p,eps) in FULLT}
+    for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]):
+        if j not in early[c] and 40+j not in skipev:
+            t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    for key,(r,alpha) in zip(keys,z['outputs']):
+        if tuple(key) in FULLT:skip();continue
+        a=mp[r];b=alloc();add(b,a,1,cur[a])
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha))
+
+# Both tetrahedra use the same partition. A selected key has exactly two
+# selected Y loads and no ordinary M consumer. Supply its two raw halves in
+# opposite orders and never form that M. Other keys retain the old M path.
+second=[];first_join_counts=Counter()
+for key,reqs in sorted(requests.items()):
+    assert len(reqs)==2
+    c,p,eps=key
+    if (p,eps) in FULLT:continue
+    ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds
+    for j,(target,coef) in enumerate(sorted(reqs)):
+        first_source,second_source=(a,b) if j==0 else (b,a)
+        r,alpha=packets[first_source,p,eps,second_source]
+        F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+        first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F)
+        r,alpha=packets[second_source,p,eps,c]
+        second.append((target,r,coef*alpha))
+
+Ms={}
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for eps in (-1,1):
+            if (c,p,eps) in requests:continue
+            (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,eps]=(a,alpha)
+
+consumers=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    for key in pair['keys']:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    if key in requests:
+        assert all(pairs[i]['selected'] for i in uses)
+        continue
+    assert all(not pairs[i]['selected'] for i in uses)
+    a,alpha=Ms[key]
+    for j,pid in enumerate(uses):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+assert len(cur)-240==NH,len(cur)-240
+
+selected_join_counts=Counter()
+for target,r,coef in second:
+    F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+    selected_join_counts[len(F)]+=1;add(v+target,r,coef,F)
+output_basis=[]
+for pair in pairs:
+    if not pair['selected']:continue
+    (t,u),mat=pair['targets'],pair['matrix']
+    F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u]))
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert rows[v+t]==expected,('side identity',t)
+
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8
+assert sum(r*z for r,z in H.items())==9*NH+240*8+72,sum(r*z for r,z in H.items())
+
+def apply(e,matrix):
+    if e[0]=='add':
+        _,t,s,a,b,*_=e;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    e[-1]=list(FULL);return e
+cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q]
+cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v]
+matrix=[{r:Q(1)} if r<v else {} for r in range(len(cur))]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(len(cur)))
+
+# Restrict the eight isolated axis ports exactly, keeping the stable 112-port
+# label set. This variant changes the local word, not the outer geometry.
+mp={s:s-8 for s in range(8,120)}
+mp.update({120+s:112+s-8 for s in range(8,120)})
+mp.update({240+r:224+r for r in range(NH)})
+def restrict(events,is_cut=False):
+    out=[]
+    for e in events:
+        regs=e[1:3] if e[0]=='add' else e[1:2]
+        if any(r not in mp for r in regs):
+            assert is_cut and e[0]=='add' and e[1]-120==e[2] and e[2]<8 and e[3:5]==[1,1]
+            continue
+        q=copy.deepcopy(e);q[1]=mp[q[1]]
+        if q[0]=='add':q[2]=mp[q[2]]
+        out.append(q)
+    return out
+H.subtract({1:8,8:16});H=+H
+report={'status':'EXACT_CLEAN_OWN_Y_EARLY_CENTER_WORD_NOT_ADMITTED',
+        'h':9,'v':112,'R':NH,'cst':64,'m':73,'local_profile':dict(sorted(H.items())),
+        'centre_ranks':[8]*8,**({'tri_join_counts':dict(tri_join_counts)} if TRI['triangles'] else {}),'selected_load_join_counts':dict(selected_join_counts),'selected_partitions':list(SELECT),'first_load_join_counts':dict(first_join_counts),
+        'source_columns_exact':112,'borrowed_output_pairs':56,'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'local_rank_mass':sum(r*n for r,n in H.items()),'scope':'Clean scalar identity and all literal monotone local frames only; arbitrary-dirt compensation, entrance kernels, exact phase recipes, and global hosting/pricing are not yet certified.'}
+word={'report':report,'ports':P[8:],'root_lines':R[8:],
+      'A':restrict(A),'B':restrict(B),'cut':restrict(cut,True),'cleanup':restrict(cleanup),'precondition':restrict(precondition),
+      'centers':[mp[r] for r in centers[:8]],'center_frames':center_frames[:8],
+      'scatter':[[str(x) for x in row[:8]] for row in scatter[8:]]}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+assert len(shadow)==NH and len(shadow)+len(skipped)==504
+hmap={**{r:r for r in range(224)},**{224+s_-240:224+i for i,s_ in enumerate(shadow)}}
+(OUT/'HELPER-MAP.json').write_text(json.dumps({'map':{str(k):hmap[k] for k in sorted(hmap)},'removed_504_helpers':[224+s_-240 for s_ in skipped]})+'\n')
+(OUT/'DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/gauge44-leaver/construction/frames/FRAME-RECIPE-sw4.json b/research/gauge44-leaver/construction/frames/FRAME-RECIPE-sw4.json
new file mode 100644
index 0000000000..7394064c5e
--- /dev/null
+++ b/research/gauge44-leaver/construction/frames/FRAME-RECIPE-sw4.json
@@ -0,0 +1,167 @@
+{
+  "input_content_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+  "gate_frames": [
+    [
+      "B",
+      856,
+      [
+        272,
+        144,
+        64,
+        6
+      ],
+      [
+        272,
+        144,
+        64,
+        8,
+        6,
+        1
+      ]
+    ],
+    [
+      "B",
+      860,
+      [
+        265,
+        137,
+        88,
+        6
+      ],
+      [
+        256,
+        128,
+        65,
+        16,
+        9,
+        6
+      ]
+    ],
+    [
+      "B",
+      868,
+      [
+        265,
+        200,
+        33,
+        6
+      ],
+      [
+        256,
+        144,
+        81,
+        33,
+        9,
+        6
+      ]
+    ],
+    [
+      "B",
+      873,
+      [
+        320,
+        192,
+        16,
+        6
+      ],
+      [
+        320,
+        192,
+        32,
+        16,
+        6,
+        1
+      ]
+    ],
+    [
+      "B",
+      876,
+      [
+        392,
+        73,
+        33,
+        6
+      ],
+      [
+        273,
+        144,
+        64,
+        33,
+        9,
+        6
+      ]
+    ],
+    [
+      "B",
+      953,
+      [
+        265,
+        137,
+        73,
+        6
+      ],
+      [
+        265,
+        137,
+        73,
+        32,
+        25,
+        6
+      ]
+    ],
+    [
+      "B",
+      961,
+      [
+        265,
+        185,
+        80,
+        6
+      ],
+      [
+        265,
+        128,
+        64,
+        41,
+        16,
+        6
+      ]
+    ],
+    [
+      "B",
+      965,
+      [
+        272,
+        185,
+        73,
+        6
+      ],
+      [
+        257,
+        128,
+        73,
+        40,
+        17,
+        6
+      ]
+    ]
+  ],
+  "expected": {
+    "output_content_sha256": "e78047028c7dcd25fb1b6216c2b53eda76d2f91292b21d43f5d1903cc13a5c6c",
+    "local_profile": {
+      "1": 2556,
+      "2": 334,
+      "3": 430,
+      "4": 194,
+      "5": 56,
+      "8": 8
+    },
+    "width_inventory": {
+      "4": 80,
+      "5": 32,
+      "7": 54,
+      "8": 122,
+      "9": 216
+    }
+  }
+}
diff --git a/research/gauge44-leaver/construction/frames/LOCAL-PINS-frames-sw4.json b/research/gauge44-leaver/construction/frames/LOCAL-PINS-frames-sw4.json
new file mode 100644
index 0000000000..834ae13a2f
--- /dev/null
+++ b/research/gauge44-leaver/construction/frames/LOCAL-PINS-frames-sw4.json
@@ -0,0 +1,12 @@
+{
+ "word": "P6k4sw4f8",
+ "frame_build_controls": 3,
+ "frame_controls": 10,
+ "layer_controls": 95,
+ "canonical_sha256": "b0d27d99423047ce07af847734f5a86f9411038bb3b0bf721918ece1ee579325",
+ "program_sha256": {
+  "forward": "b2cf8298488cc81aeee1385d4d9ebd842efbb21abb9296fca903adb8ad50f8d0",
+  "backward": "6f28cf1413671d5b7c50488a1603fa8f1558da469abbbb45b6a9b66ec640712b"
+ },
+ "clifford_recipes_sha256": "eb7569e004bd2a2937928db9db49dad949ec291f00c2d21df6af722df7cb6c9c"
+}
diff --git a/research/gauge44-leaver/construction/frames/build_frames.py b/research/gauge44-leaver/construction/frames/build_frames.py
new file mode 100644
index 0000000000..22021549e6
--- /dev/null
+++ b/research/gauge44-leaver/construction/frames/build_frames.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Apply the eight pinned B-gate frame raises of FRAME-RECIPE-sw4.json (chafreaky's PR741) to the SW4 word.
+
+usage: build_frames.py INPUT_WORD.json.gz OUT_DIR RECIPE.json
+
+Standard library only. The frames are applied by BlockInvert's `../promo/build_promotion.apply` (no entrances, eight
+'B' gate_frames), which checks each old frame and recomputes the local profile and widths. This builder then checks:
+input sha pin; the scalar program of A, cut, B, precondition and cleanup unchanged (every field but the frame); start
+and end frames unchanged; local profile and width inventory equal to the recipe's; output sha pin. Three pin controls
+(input pin, wrong old frame, output pin) must be rejected at their pinned reasons on every build.
+Adapted from PR741's extras/build_frames.py (chafreaky). Apache-2.0.
+"""
+import copy, gzip, hashlib, importlib.util, json, sys
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+_s = importlib.util.spec_from_file_location('promotion', HERE.parent / 'promo/build_promotion.py')
+B = importlib.util.module_from_spec(_s); _s.loader.exec_module(B)
+
+
+def construct(raw, recipe):
+    assert hashlib.sha256(raw).hexdigest() == recipe['input_content_sha256'], 'input word pin'
+    w = json.loads(raw)
+    assert len(recipe['gate_frames']) == 8 and all(c[0] == 'B' for c in recipe['gate_frames']), 'eight B frames'
+    out = B.apply(w, dict(entrances={}, gate_frames=recipe['gate_frames']))
+    for section in ('A', 'cut', 'B', 'precondition', 'cleanup'):
+        assert [e[:-1] for e in w[section]] == [e[:-1] for e in out[section]], 'scalar program unchanged'
+    assert out['start_extra'] == w['start_extra'] and out['helper_final'] == w['helper_final'], 'endpoint frames unchanged'
+    assert out['report']['local_profile'] == recipe['expected']['local_profile'] and \
+        out['report']['width_inventory'] == recipe['expected']['width_inventory'], 'profile and width pins'
+    data = json.dumps(out, sort_keys=True, separators=(',', ':')).encode()
+    assert hashlib.sha256(data).hexdigest() == recipe['expected']['output_content_sha256'], 'output word pin'
+    return data
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    inp, outd, rfile = map(Path, sys.argv[1:4])
+    raw = gzip.decompress(inp.read_bytes()); recipe = json.loads(rfile.read_text())
+    data = construct(raw, recipe)
+    rejected = []
+    for name, change, reason in [
+            ('input-pin', lambda r: r.__setitem__('input_content_sha256', '0' * 64), 'input word pin'),
+            ('old-frame', lambda r: r['gate_frames'][0].__setitem__(2, []), 'gate frame mismatch'),
+            ('output-pin', lambda r: r['expected'].__setitem__('output_content_sha256', '0' * 64), 'output word pin')]:
+        r = copy.deepcopy(recipe); change(r)
+        try:
+            construct(raw, r)
+        except AssertionError as e:
+            assert reason in str(e), (name, str(e)); rejected.append(dict(name=name, reason=reason))
+        else:
+            raise AssertionError('accepted ' + name)
+    outd.mkdir(parents=True)
+    (outd / 'FULL-WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+    (outd / 'BUILD.json').write_text(json.dumps(dict(
+        status='PASS_EIGHT_FRAME_EXACT_CONSTRUCTION', input_sha256=hashlib.sha256(raw).hexdigest(),
+        output_sha256=hashlib.sha256(data).hexdigest(), scalar_program_unchanged=True, frames=8,
+        rejected_controls=rejected), indent=2) + '\n')
+    print('PASS eight B frames and three pin controls')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/frames/frame_controls.py b/research/gauge44-leaver/construction/frames/frame_controls.py
new file mode 100644
index 0000000000..cd951a9f0e
--- /dev/null
+++ b/research/gauge44-leaver/construction/frames/frame_controls.py
@@ -0,0 +1,45 @@
+#!/usr/bin/env python3
+"""Focused native controls for the eight B-frame raises (PR741's extras/frame_controls.py, ported).
+
+usage: frame_controls.py WORD.json.gz ROUTING.json.gz OUT.json RECIPE.json   (env PR635_CODE = PR635's code/ directory)
+
+The positive word must pass PR635's unchanged native audit `hpe_audit_and_transport.run`. Ten mutants must be rejected
+at their pinned reasons: each of the eight raised gates with its frame emptied ('nonmonotone'), a doubled read
+coefficient on the first raised gate ('arbitrary-dirt endpoint') and a tampered paid profile ('paid local profile
+differs'). Apache-2.0; adapted from chafreaky's PR741.
+"""
+import copy, gzip, importlib.util, json, os, sys, tempfile, time
+from pathlib import Path
+
+_s = importlib.util.spec_from_file_location('audit', Path(os.environ['PR635_CODE']) / 'hpe_audit_and_transport.py')
+A = importlib.util.module_from_spec(_s); _s.loader.exec_module(A)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    word, routing, out, rfile = map(Path, sys.argv[1:5])
+    w = json.loads(gzip.decompress(word.read_bytes())); recipe = json.loads(rfile.read_text())
+
+    def trial(z):
+        with tempfile.TemporaryDirectory() as td:
+            d = Path(td); f = d / 'word.json.gz'; f.write_bytes(gzip.compress(json.dumps(z).encode(), mtime=0))
+            try:
+                A.run(f, routing, d / 'native'); return None
+            except AssertionError as e:
+                return str(e)
+
+    start = time.monotonic(); assert trial(w) is None, 'positive word rejected'; records = []
+    for section, i, old, new in recipe['gate_frames']:
+        z = copy.deepcopy(w); z[section][i][-1] = []; error = trial(z)
+        assert error and 'nonmonotone' in error, (i, error); records.append(dict(name='frame-%d-emptied' % i, rejected=error))
+    z = copy.deepcopy(w); i = recipe['gate_frames'][0][1]; z['B'][i][3] *= 2; error = trial(z)
+    assert error and 'arbitrary-dirt endpoint' in error, error; records.append(dict(name='changed-read-coefficient', rejected=error))
+    z = copy.deepcopy(w); z['report']['local_profile']['1'] += 1; error = trial(z)
+    assert error and 'paid local profile differs' in error, error; records.append(dict(name='paid-profile-tampering', rejected=error))
+    out.write_text(json.dumps(dict(status='PASS_FOCUSED_EIGHT_FRAME_NATIVE_CONTROLS', positive=1, rejected=records,
+                                   seconds=time.monotonic() - start), indent=2) + '\n')
+    print('PASS', len(records), 'mutations', flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/frames/reproduce_frames.py b/research/gauge44-leaver/construction/frames/reproduce_frames.py
new file mode 100644
index 0000000000..eaf9b47cac
--- /dev/null
+++ b/research/gauge44-leaver/construction/frames/reproduce_frames.py
@@ -0,0 +1,89 @@
+#!/usr/bin/env python3
+"""Rebuild the SW4F8 word (eight B-gate frame raises on the SW4 word, chafreaky's PR741 recipe) and its native locals.
+
+Input: a fresh `construction/sw4/reproduce_sw4.py --recipe P6k4` output directory; its SW4 word (d232183f...) is pinned
+there and by FRAME-RECIPE-<id>.json. Steps, each checked exactly:
+  1. frames: build_frames.py (standard library only) applies the eight 'B' gate_frames with BlockInvert's
+     build_promotion.apply. Scalar program, start and end frames unchanged; profile, widths and output sha pinned;
+     three pin controls must be rejected (count pinned).
+  2. frame-controls: frame_controls.py, PR741's ten focused mutants judged by PR635's unchanged native audit.
+  3. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant) on the SW4F8 word; count pinned.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs, with the canonical word, local
+     programs and Clifford recipes pinned (LOCAL-PINS-frames-<id>.json).
+Apache-2.0.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P6 = HERE.parent / 'layers_p6n'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--sw4-dir', type=Path, required=True, help='construction/sw4/reproduce_sw4.py output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--recipe', default='sw4', help='FRAME-RECIPE-<id>.json and LOCAL-PINS-frames-<id>.json')
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('FRAME-RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-frames-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    inp = a.sw4_dir.resolve() / 'sw4/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['input_content_sha256'], 'input must be the pinned SW4 word'
+    run('frames', HERE / 'build_frames.py', inp, out / 'frames', rfile, portable=False)
+    b = read(out / 'frames/BUILD.json')
+    assert b['status'] == 'PASS_EIGHT_FRAME_EXACT_CONSTRUCTION' and len(b['rejected_controls']) == pins['frame_build_controls'], b
+    word = out / 'frames/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['expected']['output_content_sha256']
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('frame-controls', HERE / 'frame_controls.py', word, routing, out / 'FRAME-CONTROLS.json', rfile, portable=False)
+    fc = read(out / 'FRAME-CONTROLS.json')
+    assert fc['status'] == 'PASS_FOCUSED_EIGHT_FRAME_NATIVE_CONTROLS' and len(fc['rejected']) == pins['frame_controls'], len(fc['rejected'])
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/jx/LOCAL-PINS-jx-X4.json b/research/gauge44-leaver/construction/jx/LOCAL-PINS-jx-X4.json
new file mode 100644
index 0000000000..417e4ba7a1
--- /dev/null
+++ b/research/gauge44-leaver/construction/jx/LOCAL-PINS-jx-X4.json
@@ -0,0 +1,11 @@
+{
+ "word": "X4",
+ "jx_controls": 7,
+ "layer_controls": 95,
+ "canonical_sha256": "1c0e9da767d4418f70016af599e4a447a3f7777acabe930318459c0fbbd260aa",
+ "program_sha256": {
+  "forward": "076a2d428f97abb30473df05110998efbe5ac809885bae4ceb1b8bd81329a1e6",
+  "backward": "7915679ee305927463d19725360cc15132dd21ede18897d09a935dca1df0d55d"
+ },
+ "clifford_recipes_sha256": "20dddfce0ded7e41dc507939df7297bd98aec1286e05d7dbf18000d57e69a0b7"
+}
diff --git a/research/gauge44-leaver/construction/jx/RECIPE-X4.json b/research/gauge44-leaver/construction/jx/RECIPE-X4.json
new file mode 100644
index 0000000000..30f7fa5948
--- /dev/null
+++ b/research/gauge44-leaver/construction/jx/RECIPE-X4.json
@@ -0,0 +1,1412 @@
+{
+ "input_content_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+ "input_word": "P6k4sw4 (BRoute w/P6k4sw4, d232183f)",
+ "frames_741_source": {
+  "pr": 741,
+  "commit": "e516b146",
+  "recipe": "scratch/WasteAttack/FRAME-RECIPE-741.json",
+  "frames_only_output_sha": "e78047028c7dcd25fb1b6216c2b53eda76d2f91292b21d43f5d1903cc13a5c6c"
+ },
+ "frames_741": [
+  [
+   856,
+   [
+    272,
+    144,
+    64,
+    8,
+    6,
+    1
+   ]
+  ],
+  [
+   860,
+   [
+    256,
+    128,
+    65,
+    16,
+    9,
+    6
+   ]
+  ],
+  [
+   868,
+   [
+    256,
+    144,
+    81,
+    33,
+    9,
+    6
+   ]
+  ],
+  [
+   873,
+   [
+    320,
+    192,
+    32,
+    16,
+    6,
+    1
+   ]
+  ],
+  [
+   876,
+   [
+    273,
+    144,
+    64,
+    33,
+    9,
+    6
+   ]
+  ],
+  [
+   953,
+   [
+    265,
+    137,
+    73,
+    32,
+    25,
+    6
+   ]
+  ],
+  [
+   961,
+   [
+    265,
+    128,
+    64,
+    41,
+    16,
+    6
+   ]
+  ],
+  [
+   965,
+   [
+    257,
+    128,
+    73,
+    40,
+    17,
+    6
+   ]
+  ]
+ ],
+ "raises": [
+  [
+   855,
+   [
+    280,
+    128,
+    64,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   859,
+   [
+    256,
+    129,
+    65,
+    40,
+    25,
+    6
+   ]
+  ],
+  [
+   862,
+   [
+    280,
+    144,
+    80,
+    56,
+    6,
+    1
+   ]
+  ],
+  [
+   863,
+   [
+    272,
+    136,
+    80,
+    56,
+    6,
+    1
+   ]
+  ],
+  [
+   867,
+   [
+    256,
+    136,
+    64,
+    41,
+    16,
+    6
+   ]
+  ],
+  [
+   870,
+   [
+    256,
+    200,
+    40,
+    16,
+    6,
+    1
+   ]
+  ],
+  [
+   875,
+   [
+    272,
+    144,
+    80,
+    49,
+    8,
+    6
+   ]
+  ],
+  [
+   942,
+   [
+    256,
+    136,
+    72,
+    33,
+    25,
+    6
+   ]
+  ],
+  [
+   943,
+   [
+    320,
+    193,
+    33,
+    16,
+    9,
+    6
+   ]
+  ],
+  [
+   946,
+   [
+    256,
+    129,
+    64,
+    41,
+    16,
+    6
+   ]
+  ],
+  [
+   947,
+   [
+    273,
+    128,
+    81,
+    33,
+    9,
+    6
+   ]
+  ],
+  [
+   950,
+   [
+    257,
+    193,
+    33,
+    16,
+    9,
+    6
+   ]
+  ],
+  [
+   954,
+   [
+    272,
+    129,
+    80,
+    49,
+    8,
+    6
+   ]
+  ],
+  [
+   955,
+   [
+    256,
+    128,
+    64,
+    33,
+    17,
+    6
+   ]
+  ],
+  [
+   958,
+   [
+    257,
+    128,
+    81,
+    33,
+    9,
+    6
+   ]
+  ],
+  [
+   962,
+   [
+    273,
+    128,
+    64,
+    33,
+    8,
+    6
+   ]
+  ]
+ ],
+ "edits": {
+  "replace": [
+   {
+    "h": 448,
+    "i": 862,
+    "old": [
+     "add",
+     140,
+     448,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     140,
+     235,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 448,
+    "i": 1207,
+    "old": [
+     "add",
+     133,
+     448,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     133,
+     235,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 448,
+    "i": 870,
+    "old": [
+     "add",
+     132,
+     235,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     132,
+     448,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 448,
+    "i": 1199,
+    "old": [
+     "add",
+     141,
+     235,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     141,
+     448,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 472,
+    "i": 855,
+    "old": [
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+     -1,
+     2
+    ],
+    "new": [
+     "add",
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+     267,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 472,
+    "i": 1198,
+    "old": [
+     "add",
+     140,
+     472,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     140,
+     267,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 472,
+    "i": 863,
+    "old": [
+     "add",
+     141,
+     267,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     141,
+     472,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 472,
+    "i": 1190,
+    "old": [
+     "add",
+     172,
+     267,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     172,
+     472,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 458,
+    "i": 942,
+    "old": [
+     "add",
+     204,
+     458,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     204,
+     58,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 458,
+    "i": 1287,
+    "old": [
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+     458,
+     1,
+     1
+    ],
+    "new": [
+     "add",
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+     58,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
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+    "i": 950,
+    "old": [
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+     58,
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+     1
+    ],
+    "new": [
+     "add",
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+     458,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 458,
+    "i": 1279,
+    "old": [
+     "add",
+     205,
+     58,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     205,
+     458,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 592,
+    "i": 859,
+    "old": [
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+     174,
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+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     174,
+     427,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 592,
+    "i": 1278,
+    "old": [
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+     -1,
+     2
+    ],
+    "new": [
+     "add",
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+     427,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 592,
+    "i": 943,
+    "old": [
+     "add",
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+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     205,
+     592,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 592,
+    "i": 1194,
+    "old": [
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+     -1,
+     2
+    ],
+    "new": [
+     "add",
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+     592,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 470,
+    "i": 946,
+    "old": [
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+     470,
+     1,
+     1
+    ],
+    "new": [
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+     26,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 470,
+    "i": 1295,
+    "old": [
+     "add",
+     165,
+     470,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     165,
+     26,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 470,
+    "i": 958,
+    "old": [
+     "add",
+     164,
+     26,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     164,
+     470,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 470,
+    "i": 1283,
+    "old": [
+     "add",
+     206,
+     26,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     206,
+     470,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 604,
+    "i": 867,
+    "old": [
+     "add",
+     142,
+     604,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     142,
+     443,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 604,
+    "i": 1282,
+    "old": [
+     "add",
+     202,
+     604,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     202,
+     443,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 604,
+    "i": 947,
+    "old": [
+     "add",
+     206,
+     443,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     206,
+     604,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 604,
+    "i": 1202,
+    "old": [
+     "add",
+     138,
+     443,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     138,
+     604,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 482,
+    "i": 954,
+    "old": [
+     "add",
+     194,
+     482,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     194,
+     18,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 482,
+    "i": 1299,
+    "old": [
+     "add",
+     166,
+     482,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     166,
+     18,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 482,
+    "i": 962,
+    "old": [
+     "add",
+     162,
+     18,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     162,
+     482,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 482,
+    "i": 1291,
+    "old": [
+     "add",
+     198,
+     18,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     198,
+     482,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 614,
+    "i": 875,
+    "old": [
+     "add",
+     134,
+     614,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     134,
+     50,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 614,
+    "i": 1290,
+    "old": [
+     "add",
+     194,
+     614,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     194,
+     50,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 614,
+    "i": 955,
+    "old": [
+     "add",
+     198,
+     50,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     198,
+     614,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 614,
+    "i": 1210,
+    "old": [
+     "add",
+     130,
+     50,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     130,
+     614,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   }
+  ],
+  "delete": [
+   {
+    "h": 448,
+    "i": 1,
+    "old": [
+     "add",
+     140,
+     448,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 448,
+    "i": 0,
+    "old": [
+     "add",
+     133,
+     448,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 472,
+    "i": 33,
+    "old": [
+     "add",
+     173,
+     472,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 472,
+    "i": 32,
+    "old": [
+     "add",
+     140,
+     472,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 458,
+    "i": 21,
+    "old": [
+     "add",
+     204,
+     458,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 458,
+    "i": 20,
+    "old": [
+     "add",
+     197,
+     458,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 592,
+    "i": 64,
+    "old": [
+     "add",
+     174,
+     592,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 592,
+    "i": 65,
+    "old": [
+     "add",
+     204,
+     592,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 470,
+    "i": 29,
+    "old": [
+     "add",
+     202,
+     470,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 470,
+    "i": 28,
+    "old": [
+     "add",
+     165,
+     470,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 604,
+    "i": 72,
+    "old": [
+     "add",
+     142,
+     604,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 604,
+    "i": 73,
+    "old": [
+     "add",
+     202,
+     604,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 482,
+    "i": 37,
+    "old": [
+     "add",
+     194,
+     482,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 482,
+    "i": 36,
+    "old": [
+     "add",
+     166,
+     482,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 614,
+    "i": 95,
+    "old": [
+     "add",
+     134,
+     614,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 614,
+    "i": 96,
+    "old": [
+     "add",
+     194,
+     614,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   }
+  ],
+  "insert": [
+   {
+    "h": 448,
+    "before": 2,
+    "gate": [
+     "add",
+     132,
+     448,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 448,
+    "before": 2,
+    "gate": [
+     "add",
+     141,
+     448,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 472,
+    "before": 34,
+    "gate": [
+     "add",
+     141,
+     472,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 472,
+    "before": 34,
+    "gate": [
+     "add",
+     172,
+     472,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 458,
+    "before": 22,
+    "gate": [
+     "add",
+     196,
+     458,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 458,
+    "before": 22,
+    "gate": [
+     "add",
+     205,
+     458,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 592,
+    "before": 66,
+    "gate": [
+     "add",
+     205,
+     592,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 592,
+    "before": 66,
+    "gate": [
+     "add",
+     170,
+     592,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 470,
+    "before": 30,
+    "gate": [
+     "add",
+     164,
+     470,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 470,
+    "before": 30,
+    "gate": [
+     "add",
+     206,
+     470,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 604,
+    "before": 74,
+    "gate": [
+     "add",
+     206,
+     604,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 604,
+    "before": 74,
+    "gate": [
+     "add",
+     138,
+     604,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 482,
+    "before": 38,
+    "gate": [
+     "add",
+     162,
+     482,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 482,
+    "before": 38,
+    "gate": [
+     "add",
+     198,
+     482,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 614,
+    "before": 97,
+    "gate": [
+     "add",
+     198,
+     614,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 614,
+    "before": 97,
+    "gate": [
+     "add",
+     130,
+     614,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   }
+  ]
+ },
+ "pairs": {
+  "448": 235,
+  "458": 58,
+  "470": 26,
+  "472": 267,
+  "482": 18,
+  "592": 427,
+  "604": 443,
+  "614": 50
+ },
+ "expected": {
+  "output_content_sha256": "1e1d99ba7aab877d6b573c41f7030ee73de9a52fee51d0a822ddaae71251999f",
+  "local_profile": {
+   "1": 2548,
+   "2": 338,
+   "3": 430,
+   "4": 194,
+   "5": 56,
+   "8": 8
+  }
+ },
+ "controls": {
+  "C0_identity": {
+   "mutation": {
+    "kind": "empty"
+   },
+   "expected_sha": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+   "local_profile": {
+    "1": 2548,
+    "2": 342,
+    "3": 438,
+    "4": 186,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "C1_741_only": {
+   "mutation": {
+    "kind": "only_edits_of",
+    "h": [],
+    "raises": []
+   },
+   "expected_sha": "e78047028c7dcd25fb1b6216c2b53eda76d2f91292b21d43f5d1903cc13a5c6c",
+   "local_profile": {
+    "1": 2556,
+    "2": 334,
+    "3": 430,
+    "4": 194,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "M1_one_pair_448": {
+   "mutation": {
+    "kind": "only_edits_of",
+    "h": [
+     448
+    ],
+    "raises": [
+     862,
+     870
+    ]
+   },
+   "expected_sha": "5fb6fb2e5e63d18b865535c1dbd3dbaddab530c39429a4b09f11ac96723257c9",
+   "local_profile": {
+    "1": 2556,
+    "2": 334,
+    "3": 430,
+    "4": 194,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "N1_drop_preread": {
+   "mutation": {
+    "kind": "drop_insert",
+    "k": 0
+   },
+   "rejection_expected": [
+    "exactness rows",
+    [
+     132,
+     135
+    ]
+   ]
+  },
+  "N2_wrong_sign_preread": {
+   "mutation": {
+    "kind": "flip_insert_sign",
+    "k": 0
+   },
+   "rejection_expected": [
+    "exactness rows",
+    [
+     132,
+     135
+    ]
+   ]
+  },
+  "N3_plain_join_moved_reads": {
+   "mutation": {
+    "kind": "drop_raises"
+   },
+   "expected_sha": "7241cd59dd0376e0b2e1b5ba8403c5423d247ddd7cbcc2f02bdc353752806f30",
+   "local_profile": {
+    "1": 2532,
+    "2": 378,
+    "3": 430,
+    "4": 178,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "N4_raise_dim7_at_855": {
+   "mutation": {
+    "kind": "frame",
+    "i": 855,
+    "frame": [
+     280,
+     128,
+     64,
+     40,
+     4,
+     2,
+     1
+    ]
+   },
+   "rejection_expected": [
+    "cap",
+    1302,
+    174
+   ]
+  }
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver/construction/jx/build_jx.py b/research/gauge44-leaver/construction/jx/build_jx.py
new file mode 100644
index 0000000000..f8d74a6324
--- /dev/null
+++ b/research/gauge44-leaver/construction/jx/build_jx.py
@@ -0,0 +1,167 @@
+#!/usr/bin/env python3
+"""build_jx.py --input WORD --recipe RECIPE.json --out OUT.json.gz [--control NAME] [--no-pin]
+
+Stdlib-only builder: joint read-set exchange (copy pairs, BRoute sw4 rule) + explicit B frame raises on P6k4sw4.
+Steps:
+ 1. input content sha256 must equal recipe.input_content_sha256.
+ 2. explicit B edits: replace (old gate asserted), delete (old gate asserted), insert (before an original index).
+ 3. frames: replaced/inserted gates take the plain join of their operands' current frames; gates listed in
+    frames_741 / raises take base = the listed frame and the resulting frame must EQUAL it (explicit frames);
+    every other gate keeps span(stored frame + operand frames) (monotone repair). Early cleanup likewise.
+ 4. legality: target frames inside u_t^perp at every gate; tails inside helper_final; every end frame contains the
+    final frame; the explicit frame must contain the join (enforced by equality in 3).
+ 5. exactness: the rational linear map of the whole B segment is identical to the input's (Fraction replay).
+ 6. paid profile recomputed (A + centre levels + B + tails + ends) and written to report.local_profile.
+Output: canonical json (sort_keys, compact) gzip mtime=0. Exit 0 and prints output sha; exit 2 with the first
+rejection (site) on failure. --control applies a named mutation from recipe.controls (expected to be rejected
+or to give a pinned sha)."""
+import argparse, gzip, json, hashlib, sys, copy
+from fractions import Fraction as Fr
+from collections import Counter
+
+V, H = 112, 9
+
+def basis(vs):
+    piv = {}
+    for a in vs:
+        while a:
+            b = a.bit_length() - 1
+            if b in piv: a ^= piv[b]
+            else: piv[b] = a; break
+    for k in sorted(piv):
+        for j in sorted(piv):
+            if j > k and (piv[j] >> k) & 1: piv[j] ^= piv[k]
+    return tuple(piv[k] for k in sorted(piv, reverse=True))
+
+def contained(a, b): return basis(list(a) + list(b)) == tuple(b)
+def registers(e): return e[1:3] if e[0] == 'add' else e[1:2]
+def hyper(p): return basis([x for x in range(1, 1 << H) if (x & p).bit_count() % 2 == 0])
+FULL = basis([1 << i for i in range(H)])
+def csha(w): return hashlib.sha256(json.dumps(w, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+
+class Reject(Exception): pass
+
+def symstate(gs):
+    rows = {}
+    for e in gs:
+        for q in registers(e): rows.setdefault(q, {q: Fr(1)})
+        if e[0] == 'add':
+            t, s = e[1], e[2]; c = Fr(e[3], e[4]); d = rows[t]
+            for k, x in list(rows[s].items()):
+                a = d.get(k, 0) + c * x
+                if a: d[k] = a
+                else: d.pop(k, None)
+        else:
+            t = e[1]; c = Fr(e[2], e[3]); rows[t] = {k: c * x for k, x in rows[t].items()}
+    return rows
+
+def build(w, rc, control=None):
+    w = copy.deepcopy(w); B0 = w['B']
+    edits = copy.deepcopy(rc['edits']); explicit = {int(i): f for i, f in rc['frames_741']}
+    for i, f in rc['raises']:
+        if int(i) in explicit: raise Reject(('duplicate frame', i))
+        explicit[int(i)] = f
+    if control:
+        c = rc['controls'][control]['mutation']
+        if c['kind'] == 'drop_insert': edits['insert'] = [x for k, x in enumerate(edits['insert']) if k != c['k']]
+        elif c['kind'] == 'flip_insert_sign': edits['insert'][c['k']]['gate'][3] *= -1
+        elif c['kind'] == 'frame': explicit[c['i']] = c['frame']
+        elif c['kind'] == 'drop_edits': edits = dict(replace=[], delete=[], insert=[])
+        elif c['kind'] == 'drop_raises': explicit = {int(i): f for i, f in rc['frames_741']}
+        elif c['kind'] == 'only_edits_of':
+            hs = set(c['h'])
+            edits = {k: [x for x in v if x['h'] in hs] for k, v in edits.items()}
+            explicit = {i: f for i, f in explicit.items() if i in {int(j) for j, _ in rc['frames_741']} or i in set(c['raises'])}
+        elif c['kind'] == 'empty': edits = dict(replace=[], delete=[], insert=[]); explicit = {}
+        else: raise SystemExit('unknown control')
+    B = [list(e) for e in B0]; tag = set(); dele = set(); ins = {}
+    for x in edits['replace']:
+        i = x['i']
+        if B[i][:-1] != x['old']: raise Reject(('replace old mismatch', i))
+        B[i] = list(x['new']) + [B[i][-1]]; tag.add(i)
+    for x in edits['delete']:
+        i = x['i']
+        if B[i][:-1] != x['old']: raise Reject(('delete old mismatch', i))
+        dele.add(i)
+    for x in edits['insert']: ins.setdefault(x['before'], []).append(list(x['gate']) + [None])
+    NB, nt, key = [], set(), []
+    for i, e in enumerate(B):
+        for g in ins.get(i, []): nt.add(len(NB)); NB.append(g); key.append(None)
+        if i in dele: continue
+        if i in tag: nt.add(len(NB))
+        NB.append(e); key.append(i)
+    # frames + paid
+    R = w['report']['R']; n = 2 * V + R
+    END = [FULL] * V + [hyper(p) for p in w['ports']] + [FULL] * R
+    for q, U in w['helper_final'].items(): END[int(q)] = basis(U)
+    cur = [(p,) for p in w['ports']] + [()] * (V + R)
+    for q, U in w['start_extra'].items(): cur[int(q)] = basis(U)
+    paid = Counter()
+    for e in w['A']:
+        for q in registers(e):
+            U = basis(e[-1]); d = len(U) - len(cur[q])
+            if d: paid[d] += 1
+            cur[q] = U
+    lev = {int(t): basis(U) for t, U in w.get('target_levels', {}).items()}
+    for q, U in zip(w['centers'], w['center_frames']):
+        U = basis(U); served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == q}
+        for T in sorted(served, key=lambda x: -len(x)):
+            if T != U: paid[len(U) - len(T)] += 1
+            U = T
+    used = set()
+    for j, e in enumerate(NB):
+        rs = registers(e); k = key[j]
+        if k is not None and k in explicit: base = list(explicit[k]); used.add(k)
+        elif j in nt or e[-1] is None: base = []
+        else: base = list(e[-1])
+        F = basis(base + [x for q in rs for x in cur[q]])
+        if k is not None and k in explicit and F != basis(explicit[k]): raise Reject(('explicit frame below join', k))
+        for q in rs:
+            if V <= q < 2 * V and not contained(F, END[q]): raise Reject(('cap', j, q))
+            d = len(F) - len(cur[q])
+            if d: paid[d] += 1
+            cur[q] = F
+        NB[j] = list(e[:-1]) + [list(F)]
+    if used != set(explicit): raise Reject(('unused explicit frame', sorted(set(explicit) - used)))
+    newearly = []
+    for i, U in w['early_cleanup']:
+        rs = registers(w['cleanup'][i]); F = basis(list(U) + [x for q in rs for x in cur[q]])
+        for q in rs:
+            if w['helper_final'].get(str(q)) is not None and not contained(F, END[q]): raise Reject(('tailend', i, q))
+            d = len(F) - len(cur[q])
+            if d: paid[d] += 1
+            cur[q] = F
+        newearly.append([i, list(F)])
+    for q in range(n):
+        if not contained(cur[q], END[q]): raise Reject(('end', q))
+        d = len(END[q]) - len(cur[q])
+        if d: paid[d] += 1
+    # exactness of the B segment
+    a, b = symstate([e[:-1] for e in B0]), symstate([e[:-1] for e in NB])
+    bad = sorted(q for q in set(a) | set(b) if a.get(q, {q: Fr(1)}) != b.get(q, {q: Fr(1)}))
+    if bad: raise Reject(('exactness rows', bad))
+    w['B'] = NB; w['early_cleanup'] = newearly
+    w['report'] = dict(w['report']); w['report']['local_profile'] = {str(k): v for k, v in sorted(paid.items())}
+    return w
+
+def main():
+    ap = argparse.ArgumentParser(); ap.add_argument('--input', required=True); ap.add_argument('--recipe', required=True)
+    ap.add_argument('--out'); ap.add_argument('--control'); ap.add_argument('--no-pin', action='store_true')
+    a = ap.parse_args()
+    w = json.loads(gzip.decompress(open(a.input, 'rb').read())); rc = json.load(open(a.recipe))
+    if csha(w) != rc['input_content_sha256']: print('REJECT input pin'); sys.exit(2)
+    pin = rc['controls'][a.control].get('rejection_expected') if a.control else None
+    try: o = build(w, rc, a.control)
+    except Reject as r:
+        got = json.loads(json.dumps(r.args[0])); print('REJECT', json.dumps(got))
+        if pin is not None:
+            print('CONTROL', 'PINNED' if got == pin else 'PIN MISMATCH %s' % json.dumps(pin)); sys.exit(0 if got == pin else 4)
+        sys.exit(2)
+    if pin is not None and not a.no_pin: print('CONTROL NOT REJECTED, pinned', json.dumps(pin)); sys.exit(4)
+    s = csha(o)
+    exp = rc['controls'][a.control].get('expected_sha') if a.control else rc['expected']['output_content_sha256']
+    print('OK', s, o['report']['local_profile'])
+    if a.out: open(a.out, 'wb').write(gzip.compress(json.dumps(o, sort_keys=True, separators=(',', ':')).encode(), mtime=0))
+    if not a.no_pin and exp and s != exp: print('REJECT output pin', exp); sys.exit(3)
+
+if __name__ == '__main__': main()
diff --git a/research/gauge44-leaver/construction/jx/reproduce_jx.py b/research/gauge44-leaver/construction/jx/reproduce_jx.py
new file mode 100644
index 0000000000..6829a1b25d
--- /dev/null
+++ b/research/gauge44-leaver/construction/jx/reproduce_jx.py
@@ -0,0 +1,99 @@
+#!/usr/bin/env python3
+"""Rebuild the X4 word (JointXF: joint read-set exchange on four further copy-pair instances plus explicit B frame
+raises, including chafreaky's PR741 eight frames) and its native locals.
+
+Input: a fresh `construction/sw4/reproduce_sw4.py --recipe P6k4` output directory; its SW4 word (d232183f...) is pinned
+there and by RECIPE-X4.json. Steps, each checked exactly:
+  1. jx: build_jx.py (standard library only; JointXF) applies the recipe's explicit B edits (replace / delete / insert,
+     each old gate asserted), the PR741 frames and the explicit raises, repairs all other frames monotonically, checks
+     target frames inside u_t^perp, tails and ends, and the exactness of the whole B segment (rational replay), and
+     pins the output sha.
+  2. jx-controls: every control in the recipe is rebuilt and must reproduce its pinned outcome exactly: a pinned
+     rejection site (exit 0 with CONTROL PINNED) or a pinned output sha. C1_741_only must reproduce PR741's word
+     e78047028c... (the construction/frames step's output); C0_identity reproduces the input.
+  3. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant) on the X4 word; count pinned.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs; canonical word, local programs
+     and Clifford recipes pinned (LOCAL-PINS-jx-X4.json).
+Apache-2.0. Driver by ColdWitness around JointXF's builder.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P6 = HERE.parent / 'layers_p6n'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--sw4-dir', type=Path, required=True, help='construction/sw4/reproduce_sw4.py output')
+    ap.add_argument('--recipe', default='X4', help='RECIPE-<id>.json and LOCAL-PINS-jx-<id>.json')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-jx-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True, ok=(0,)):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc in ok, (label, rc)
+        print('PASS', label, flush=True)
+        return (out / (label + '.log')).read_text()
+
+    inp = a.sw4_dir.resolve() / 'sw4/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['input_content_sha256'], 'input must be the pinned SW4 word'
+    (out / 'jx').mkdir(); word = out / 'jx/FULL-WORD.json.gz'
+    run('jx', HERE / 'build_jx.py', '--input', inp, '--recipe', rfile, '--out', word, portable=False)
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['expected']['output_content_sha256']
+    assert len(rec['controls']) == pins['jx_controls'], len(rec['controls'])
+    results = {}
+    for name, c in sorted(rec['controls'].items()):
+        log = run('jx-control-' + name, HERE / 'build_jx.py', '--input', inp, '--recipe', rfile, '--control', name, portable=False)
+        if 'rejection_expected' in c:
+            assert 'CONTROL PINNED' in log, (name, log[-300:]); results[name] = dict(rejected=c['rejection_expected'])
+        else:
+            assert ('OK ' + c['expected_sha']) in log, (name, log[-300:]); results[name] = dict(sha=c['expected_sha'])
+    assert rec['controls']['C1_741_only']['expected_sha'] == rec['frames_741_source']['frames_only_output_sha']
+    (out / 'JX-CONTROLS.json').write_text(json.dumps(dict(status='PASS_JX_PINNED_CONTROLS', controls=results), indent=1) + '\n')
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/layers/build_pivot_swap.py b/research/gauge44-leaver/construction/layers/build_pivot_swap.py
new file mode 100644
index 0000000000..b225601c01
--- /dev/null
+++ b/research/gauge44-leaver/construction/layers/build_pivot_swap.py
@@ -0,0 +1,160 @@
+"""Cost-neutral pivot-role swaps inside existing entrance-kernel families.  Apache-2.0.  Prepared with Claude Code
+assistance.  The pivot/donor role exchange follows PR266's "pivot role is moved" idea (bit side), applied here to the
+complex supplier's multicut kernel families (PR568 build_multicut_kernels.py shape).
+
+A kernel family on the input word is an entering helper p (start_extra E) together with the gates that read p at frame
+E before any other touch of p:  d += c_d * p @E  (d a helper or, in B, a target).  They cancel p's complete dirty
+response:  col(p) + sum_d c_d * col_{g_d}(d) = 0, where col_{g}(d) is d's suffix response from gate g on.
+
+Swap to the new pivot x (a helper donor of the family with exactly one family gate g_x = x's FIRST touch, and no other
+touch of x up to the family's last gate):
+    g_x :  x += c_x p   ->   p += (1/c_x) x
+    g_d :  d += c_d p   ->   d += (c_d/c_x) x          (d != x, same position and frame E)
+    start_extra: p -> x (same E); cleanup regenerated by the inherited inverse rule.
+Exactness (PROOF-NOTE-PIVOT.md): x holds only its initial dirt at every rewritten gate, and p holds only its initial dirt
+until g_x, so x's new response is col(x) + col(p)/c_x + sum_d (c_d/c_x) col_{g_d}(d) = (c_x col(x) + col(p) +
+sum_d c_d col_{g_d}(d)) / c_x = 0, because col(x) = col_{g_x}(x).  This script checks it by exact rational replay anyway.
+Cost: the frame chains of p and x are exchanged (p now climbs [] -> E at g_x where x did; x starts at E where p did), so
+gk_word.profile and the width multiset are unchanged; both are asserted.
+
+Recipe: {input_content_sha256, output_content_sha256, swaps: [{pivot, new_pivot, entrance, gates: [{part, index,
+before, after}]}]}.  Every expected `after` gate is recomputed from the rule above and must equal the recipe.
+
+Negative controls (--controls): mutated recipes/words that must be rejected at pinned reasons:
+  * nonzero response: another family gate's rescaled coefficient has the wrong sign;
+  * wrong pivot coefficient: g_x's new coefficient doubled;
+  * wrong entrance: the recipe's entrance is not p's start_extra;
+  * non-family gate: a recipe gate whose `before` is not the word's gate;
+  * new pivot touched in the window: x replaced by a family donor that is not a fresh helper (a target donor, or the
+    first other helper donor when the family has no target donor).
+"""
+from pathlib import Path
+from collections import Counter
+from fractions import Fraction as Q
+import argparse, copy, gzip, hashlib, json, sys
+assert __debug__, 'Assertions required'
+ap = argparse.ArgumentParser()
+for k in ('--input', '--recipe', '--gk-dir', '--out'): ap.add_argument(k, type=Path, required=True)
+a = ap.parse_args(); assert not a.out.exists()
+sys.path.insert(0, str(a.gk_dir)); import gk_word as G, gk_common as C
+G.V = C.V = 112; G.DATA = C.DATA = 7168
+V = 112
+raw = json.loads(gzip.decompress(a.input.read_bytes())); recipe = json.loads(a.recipe.read_text())
+enc = lambda x: json.dumps(x, sort_keys=True, separators=(',', ':')).encode(); sha = lambda x: hashlib.sha256(x).hexdigest()
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+inv_rule = lambda w: [G.inverse(e, G.FULL) for e in reversed(w['A'] + w['B']) if not V <= e[1] < 2 * V]
+dy = lambda q: q != 0 and q.denominator & (q.denominator - 1) == 0
+
+
+def response(w, h):
+    rows = {}
+    def get(r): return rows.setdefault(r, {r: Q(1)})
+    for e in w['A'] + w['cut'] + w['B']:
+        if e[0] == 'scale':
+            q = Q(e[2], e[3]); rows[e[1]] = {j: q * x for j, x in get(e[1]).items()}
+        else:
+            t, s = e[1], e[2]; q = Q(e[3], e[4]); src = get(s); tgt = get(t)
+            for j, x in list(src.items()):
+                z = tgt.get(j, Q(0)) + q * x
+                if z: tgt[j] = z
+                else: tgt.pop(j, None)
+    return {r: rows[r][h] for r in range(V, 2 * V) if r in rows and rows[r].get(h)}
+
+
+def build(w0, rec):
+    w = copy.deepcopy(w0); n = 2 * V + w['report']['R']
+    assert w['cleanup'] == inv_rule(w), 'input cleanup is not the inherited inverse rule'
+    P0 = G.profile(w); W0 = Counter(C.widths_of(w))
+    AB = [('A', i) for i in range(len(w['A']))] + [('B', i) for i in range(len(w['B']))]
+    pos = {k: j for j, k in enumerate(AB)}
+    seen = set(); receipts = []; rules = []
+    for s in rec['swaps']:
+        p, x, E = s['pivot'], s['new_pivot'], s['entrance']
+        assert 2 * V <= p < n and w['start_extra'].get(str(p)) == E, 'pivot is not an entering helper at the entrance'
+        assert 2 * V <= x < n and x not in w['centers'], 'new pivot must be a helper'
+        assert str(x) not in w['start_extra'], 'new pivot already entering'
+        assert not {p, x} & seen, 'registers shared between swaps'; seen |= {p, x}
+        gs = s['gates']; ks = [pos[(g['part'], g['index'])] for g in gs]
+        assert ks == sorted(ks) and len(set(ks)) == len(ks)
+        for g in gs:
+            e = w[g['part']][g['index']]
+            assert e == g['before'], 'recipe gate is not the word gate'
+            assert e[0] == 'add' and e[2] == p and e[1] != p and list(e[-1]) == list(E), 'not a family gate (d += c p @E)'
+        touch = lambda r: [j for j, (part, i) in enumerate(AB) if r in regs(w[part][i])]
+        tp = touch(p); assert tp[:len(ks)] == ks, 'family gates must be all touches of the pivot up to its first other touch'
+        gx = [k for k, g in zip(ks, gs) if g['before'][1] == x]; assert len(gx) == 1, 'new pivot must have exactly one family gate'
+        tx = touch(x); assert tx[0] == gx[0], 'new pivot touched before its family gate'
+        assert len(tx) == 1 or tx[1] > ks[-1], 'new pivot touched inside the family window'
+        cx = Q(*[g['before'][3:5] for g in gs if g['before'][1] == x][0])
+        for g in gs:
+            d, f = g['before'][1], g['after']
+            assert f[0] == 'add' and list(f[-1]) == list(E) and (f[1:3] == [p, x] if d == x else f[1:3] == [d, x]), 'after-gate shape'
+            assert dy(Q(f[3], f[4])), 'non-dyadic swapped coefficient'
+            w[g['part']][g['index']] = f
+            q = 1 / cx if d == x else Q(g['before'][3], g['before'][4]) / cx
+            rules.append((f, ['add', p, x, q.numerator, q.denominator, list(E)] if d == x else ['add', d, x, q.numerator, q.denominator, list(E)]))
+        w['start_extra'][str(x)] = w['start_extra'].pop(str(p))
+        receipts.append(dict(pivot=p, new_pivot=x, entrance=E, family_gates=len(gs)))
+    w['cleanup'] = inv_rule(w)
+    for s in rec['swaps']:
+        assert not response(w, s['new_pivot']), 'new pivot dirty response not zero'
+    assert all(f == e for f, e in rules), 'recipe after-gate is not the swap rule'
+    P1 = G.profile(w)
+    assert P1 == P0, 'paid profile not identical (swap is not cost-neutral)'
+    assert Counter(C.widths_of(w)) == W0, 'width multiset changed'
+    w['report']['local_profile'] = {str(k): v for k, v in sorted(P1.items())}
+    w['report']['local_rank_mass'] = sum(k * v for k, v in P1.items())
+    return w, receipts
+
+
+assert sha(enc(raw)) == recipe['input_content_sha256'], 'input content'
+out, receipts = build(raw, recipe)
+o = enc(out); assert sha(o) == recipe['output_content_sha256'], sha(o)
+
+# ---- negative controls -------------------------------------------------------------------------------------------
+WHY = dict(nonzero='new pivot dirty response not zero', coef='new pivot dirty response not zero',
+           entrance='paid profile not identical', nonfamily='recipe gate is not the word gate',
+           window='new pivot')
+controls = []
+
+
+def reject(name, mut, why):
+    r = copy.deepcopy(recipe); w = copy.deepcopy(raw)
+    mut(r, w)
+    try:
+        build(w, r)
+    except AssertionError as ex:
+        msg = str(ex)
+        assert why in msg, ('control rejected for the wrong reason', name, msg)
+        controls.append(dict(control=name, reason=msg)); return
+    raise AssertionError('control accepted: ' + name)
+
+
+for si, s in enumerate(recipe['swaps']):
+    x = s['new_pivot']; tag = '%d->%d' % (s['pivot'], x)
+    def m_other(r, w, si=si):
+        g = [g for g in r['swaps'][si]['gates'] if g['before'][1] != r['swaps'][si]['new_pivot']][0]
+        g['after'] = list(g['after']); g['after'][3] = -g['after'][3]
+    def m_coef(r, w, si=si):
+        g = [g for g in r['swaps'][si]['gates'] if g['before'][1] == r['swaps'][si]['new_pivot']][0]
+        g['after'] = list(g['after']); g['after'][3] *= 2
+    def m_nonfamily(r, w, si=si):
+        g = r['swaps'][si]['gates'][0]; g['before'] = list(g['before']); g['before'][3] = -g['before'][3]
+    def m_window(r, w, si=si):
+        S = r['swaps'][si]; S['new_pivot'] = [g['before'][1] for g in S['gates'] if g['before'][1] != S['new_pivot']][0]
+    def m_entrance(r, w, si=si):
+        S = r['swaps'][si]; S['entrance'] = [1]
+    reject('swap %s: another family gate keeps a wrong (unrescaled-sign) coefficient: new pivot response nonzero' % tag, m_other, WHY['nonzero'])
+    reject('swap %s: wrong pivot coefficient (1/c doubled) on the new pivot gate' % tag, m_coef, WHY['coef'])
+    reject('swap %s: non-family gate in the recipe' % tag, m_nonfamily, WHY['nonfamily'])
+    reject('swap %s: new pivot replaced by another family donor (not a fresh cold helper)' % tag, m_window, WHY['window'])
+    reject('swap %s: wrong entrance frame for the moved entrance' % tag, m_entrance, 'pivot is not an entering helper at the entrance')
+controls_receipt = list(controls)
+
+a.out.mkdir(parents=True); (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(o, mtime=0))
+rc = dict(status='PASS_COST_NEUTRAL_PIVOT_SWAPS', input_content_sha256=recipe['input_content_sha256'],
+          output_content_sha256=recipe['output_content_sha256'], swaps=receipts, local_profile=out['report']['local_profile'],
+          negative_controls_rejected=controls_receipt,
+          scope='Exact family rewrite, exact zero dirty response of every new pivot, identical paid profile and widths, '
+                'regenerated inverse-rule cleanup.  Native all-column audit, HPE/cold steps and global checks remain separate.')
+(a.out / 'PIVOT-SWAP.json').write_text(json.dumps(rc, indent=2, sort_keys=True) + '\n', newline='\n'); print(json.dumps(rc, indent=2))
diff --git a/research/gauge44-leaver/construction/layers/layer_end_controls.py b/research/gauge44-leaver/construction/layers/layer_end_controls.py
new file mode 100644
index 0000000000..317da36d95
--- /dev/null
+++ b/research/gauge44-leaver/construction/layers/layer_end_controls.py
@@ -0,0 +1,201 @@
+"""layer_end_controls.py LAYERED-WORD.json.gz ROUTING OUTDIR (env PR635_CODE): adapted PR635 cold_end_controls.py (LayerReviewer): raw-word negative controls for the cold low-frame ends and the
+refactored cleanup accepted by hpe_audit_and_transport.py.  Every mutation MUST be rejected (AssertionError); the
+unmutated word MUST pass.  Apache-2.0.  DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code."""
+import copy, gzip, json, shutil, sys, tempfile
+from pathlib import Path
+import os
+sys.path.insert(0, os.environ['PR635_CODE'])   # PR635's unchanged hpe_audit_and_transport.py
+import hpe_audit_and_transport as atc
+
+src, routing, outdir = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3])
+word = json.load(gzip.open(src))
+v, R = word['report']['v'], word['report']['R']; n = 2*v + R
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+meta = word['refactored_cleanup']
+cold = [int(h) for h in meta['cold_low_frame_ended_helpers']]
+npre = meta['premix_gates']; nlow = meta['lower_frame_gates']
+early = word['early_cleanup']; eidx = {i for i, _ in early}
+rest = [i for i in range(len(word['cleanup'])) if i not in eidx]
+
+
+def trial(w):
+    """None if the transport audit accepts w, else the AssertionError message."""
+    tmp = Path(tempfile.mkdtemp())
+    p = tmp/'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w).encode(), mtime=0))
+    try:
+        atc.run(p, routing, tmp/'out')
+        return None
+    except AssertionError as e:
+        return repr(e.args[0]) if e.args else 'AssertionError'
+    finally:
+        shutil.rmtree(tmp, ignore_errors=True)
+
+
+# Pinned rejection reasons: each mutant must fail at this assertion of hpe_audit_and_transport.py (message substring).
+ENDPOINT, COLDPRE, CONE = "'arbitrary-dirt endpoint'", 'touches a cold hyperplane-ended helper', 'hpe cone pre-check (row / column)'
+WHY = dict(premix_to_precondition=COLDPRE, premix_dropped=COLDPRE, e_premix_dropped=ENDPOINT, lower_dropped=ENDPOINT,
+           remainder_dropped=ENDPOINT, coefficient=ENDPOINT, into_full='cleanup on non-FULL end', dyadic=ENDPOINT, frame_below="'nonmonotone'",
+           nonmonotone="'nonmonotone'", other_frame=CONE, cone=CONE, extra_end=COLDPRE, marker='cleanup is not the literal reversed inverse',
+           target='refactored cleanup touches a target', profile_pin='paid local profile differs from the reported local_profile',
+           entering_precondition='zero-frame precondition/compensation touches an entering helper')
+assert trial(word) is None, 'unmutated cold-end word must pass'
+results = []
+
+
+def reject(name, mut, why):
+    """the mutation must be rejected, and for the pinned reason (a substring of the audit's assertion message)."""
+    w = copy.deepcopy(word); mut(w)
+    msg = trial(w)
+    assert msg is not None, 'cold-end mutation accepted: ' + name
+    assert why in msg, 'cold-end mutation %r rejected for the wrong reason: %s' % (name, msg[:300])
+    results.append(name); print('rejected', name, '|', why, flush=True)
+
+
+h0 = cold[0]
+i0, U0 = next((i, f) for i, f in early if h0 in regs(word['cleanup'][i]))
+r0 = rest[len(rest)//2]
+
+
+def premix_to_precondition(w):   # premix before the wrappers; compensation then reads the cold ends
+    w['precondition'] = w['precondition'] + w['A'][:npre]; w['A'] = w['A'][npre:]
+
+
+def lower_gate_into_full(w):     # a lower-frame gate on a cold-ended helper executed in the FULL remainder instead
+    w['early_cleanup'] = [x for x in w['early_cleanup'] if x[0] != i0]
+
+
+def drop_cleanup_gate(w, i):   # remove the gate AND its early_cleanup entry: a structurally valid word missing one gate
+    w['cleanup'].pop(i)
+    w['early_cleanup'] = [[j - (j > i), f] for j, f in w['early_cleanup'] if j != i]
+
+
+def other_frame(w):              # a different frame of the same dimension as the cold end (another cold helper's)
+    f = next(w['helper_final'][str(h)] for h in cold if w['helper_final'][str(h)] != w['helper_final'][str(h0)])
+    w['helper_final'][str(h0)] = f
+
+
+def extra_cold_end(w):           # declare a premixed partner of h0 cold-ended at h0's frame: fails the row/column cone
+    p = next(r for e in w['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    w['helper_final'][str(p)] = w['helper_final'][str(h0)]
+
+
+reject('premix placed in the zero-frame precondition (before the cold wrappers)', premix_to_precondition, WHY['premix_to_precondition'])
+reject('one premix gate dropped (the compensation then reads a cold-ended helper)', lambda w: w['A'].pop(npre - 1), WHY['premix_dropped'])
+reject('one lower-frame cleanup gate dropped (gate and its early_cleanup entry)', lambda w: drop_cleanup_gate(w, i0), WHY['lower_dropped'])
+reject('one FULL-remainder gate dropped', lambda w: drop_cleanup_gate(w, r0), WHY['remainder_dropped'])
+reject('lower-frame gate coefficient changed', lambda w: w['cleanup'][i0].__setitem__(3, w['cleanup'][i0][3] * 2), WHY['coefficient'])
+reject('lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)', lower_gate_into_full, WHY['into_full'])
+reject('lower-frame gate frame below its registers\' frames', lambda w: next(x for x in w['early_cleanup'] if x[0] == i0).__setitem__(1, U0[:-1]), WHY['frame_below'])
+reject('cold end at another dim-4 frame', other_frame, WHY['other_frame'])
+# PROFILE-PIN control: without its helper_final entry the cold-ended helper is a valid FULL-ended helper; the word is
+# rejected because its reported paid profile (which counts the low end) no longer matches the frame chains.
+reject('profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)', lambda w: w['helper_final'].pop(str(h0)), WHY['profile_pin'])
+reject('extra cold end on a premixed partner (the compensation reads it before its wrapper)', extra_cold_end, WHY['extra_end'])
+reject('refactored-cleanup marker removed (literal-inverse rule applies)', lambda w: w.pop('refactored_cleanup'), WHY['marker'])
+reject('remainder gate retargeted to a target register', lambda w: w['cleanup'][r0].__setitem__(1, v + 3), WHY['target'])
+reject('non-dyadic remainder coefficient', lambda w: w['cleanup'][r0].__setitem__(4 if w['cleanup'][r0][0] == 'add' else 3, 3 * w['cleanup'][r0][4 if w['cleanup'][r0][0] == 'add' else 3]), WHY['dyadic'])
+reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('5', w['report']['local_profile']['5'] - 1), WHY['profile_pin'])
+ent = [int(h) for h in sys.argv[4].split(',')] if len(sys.argv) > 4 else [int(h) for h in meta.get('entering_low_frame_ended_helpers', [])]
+for e0 in ent:   # ENTERING LOW-FRAME ENDS (ColdSupply extension; every entering end; absent for words without them)
+    j0 = next((i for i, e in enumerate(word['A'][:npre]) if e0 in regs(e)), None)
+    print('entering end', e0, 'premix gate', j0, flush=True)
+    k0, Ue = next((i, f) for i, f in early if e0 in regs(word['cleanup'][i]))
+    def to_pre(w, j0=j0): w['precondition'].append(w['A'][j0]); w['A'].pop(j0)
+    def other_hp(w, e0=e0, Ue=Ue): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Ue) and sorted(f) != sorted(Ue))
+    if j0 is not None: reject('entering end %d: premix gate dropped' % e0, lambda w, j0=j0: w['A'].pop(j0), WHY['e_premix_dropped'])
+    if j0 is not None: reject('entering end %d: premix gate at frame [] instead of its entrance E' % e0, lambda w, j0=j0: w['A'][j0].__setitem__(-1, []), WHY['nonmonotone'])
+    if j0 is not None: reject('entering end %d: premix gate moved into the zero-frame precondition' % e0, to_pre, WHY['entering_precondition'])
+    reject('entering end %d: lower-frame gate dropped (gate and its early_cleanup entry)' % e0, lambda w, k0=k0: drop_cleanup_gate(w, k0), WHY['lower_dropped'])
+    reject('entering end %d: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)' % e0, lambda w, e0=e0: w['helper_final'].pop(str(e0)), WHY['profile_pin'])
+    reject('entering end %d: end at another hyperplane' % e0, other_hp, WHY['cone'])
+# Pinned rejection reasons of the COLD-BEYOND mutants (substrings of hpe_audit_and_transport.py assertion messages).
+MYWHY = dict(tw_precondition=COLDPRE, tw_dropped=COLDPRE, tw_coefficient=COLDPRE, tw_other_block=COLDPRE,
+             tw_entering='zero-frame compensation reads an entering helper',
+             ab_dropped=ENDPOINT, ab_coefficient=ENDPOINT, ab_early=ENDPOINT, ab_live=ENDPOINT, ab_centre=ENDPOINT,
+             ab_lower="'nonmonotone'", ab_higher="'nonmonotone'",
+             sh_dropped=ENDPOINT, sh_coefficient=ENDPOINT, rel_dropped=ENDPOINT, rel_coefficient=ENDPOINT, rel_live=ENDPOINT,
+             h8_other=CONE, h8_lower=ENDPOINT)
+# COLD-BEYOND primitives (present only when the word carries them): frame-[] target writes in the premix (explicit
+# post-wrapper compensation of an ended helper's dirt) and forward absorptions into dead registers.
+nw = meta.get('premix_target_writes', 0)
+if nw:
+    wi = [i for i in range(npre) if v <= word['A'][i][1] < 2*v]
+    assert len(wi) == nw
+
+    def writes_to_precondition(w):   # the target writes run before the cold wrappers (inside the zero-frame precondition)
+        g = [w['A'][i] for i in wi]; w['precondition'] = w['precondition'] + g
+        w['A'] = [e for i, e in enumerate(w['A']) if i not in set(wi)]
+    reject('premix target writes placed in the zero-frame precondition (before the cold wrappers)', writes_to_precondition, MYWHY['tw_precondition'])
+    reject('one premix target write dropped (compensation must read an ended helper)', lambda w: w['A'].pop(wi[0]), MYWHY['tw_dropped'])
+    reject('premix target write coefficient changed', lambda w: w['A'][wi[0]].__setitem__(3, w['A'][wi[0]][3] * 2), MYWHY['tw_coefficient'])
+    # (reading another register that carries the SAME weight of the ended helper's dirt is a valid variant, so the mutant reads
+    #  the same factory slot of the next block, which carries none of it)
+    entering_regs = sorted(int(r) for r in word.get('start_extra', {}))
+    reject('premix target write reads an entering helper', lambda w: w['A'][wi[0]].__setitem__(2, entering_regs[0]), MYWHY['tw_entering'])
+    reject('premix target write reads a cold helper of another block', lambda w: w['A'][wi[0]].__setitem__(2, 2*v + (w['A'][wi[0]][2] - 2*v + 16) % 224), MYWHY['tw_other_block'])
+ab = meta.get('forward_absorption_A_indices', [])
+if any(len(word['helper_final'][str(h)]) == 8 for h in cold):
+    # with dim-8 cold ends, the centre-retargeted absorption first leaks an ended helper's dirt into the cut's targets
+    MYWHY['ab_centre'] = COLDPRE
+if ab:
+    # the ColdBeyond U_b absorption (q += -1/2 g); ColdThird's extra absorptions have their own controls below
+    a0 = next(a for a in ab if word['A'][a][3] * 2 == -word['A'][a][4]); g0 = word['A'][a0]
+
+    def absorption_moved_early(w):   # absorbed before the absorbed register's last kernel write
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[2] == w['A'][i][1] and w['A'][i][-1] == g0[-1])
+        w['A'].insert(j, e)
+
+    def absorption_into_live(w):     # q += a g moved right after g's previous frame-mate gate, while q is still live
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[1] in regs(w['A'][i]))
+        w['A'].insert(j, e)
+    reject('forward absorption dropped', lambda w: w['A'].pop(a0), MYWHY['ab_dropped'])
+    reject('forward absorption into a centre (a live register read by the cut)', lambda w: w['A'][a0].__setitem__(1, next(c for c in word['centers'] if c not in g0[1:3] and c not in cold)), MYWHY['ab_centre'])
+    reject('forward absorption coefficient changed', lambda w: w['A'][a0].__setitem__(3, w['A'][a0][3] * 2), MYWHY['ab_coefficient'])
+    reject('forward absorption placed before the absorbed register\'s last kernel write', absorption_moved_early, MYWHY['ab_early'])
+    reject('forward absorption placed while the absorbing register is still live', absorption_into_live, MYWHY['ab_live'])
+    reject('forward absorption at a lower frame than its registers', lambda w: w['A'][a0].__setitem__(-1, w['A'][a0][-1][:-1]), MYWHY['ab_lower'])
+    reject('forward absorption at a higher frame (FULL) than its registers', lambda w: w['A'][a0].__setitem__(-1, [256, 128, 64, 32, 16, 8, 4, 2, 1]), MYWHY['ab_higher'])
+# COLD-THIRD primitives (present only when the word carries them): several absorptions after one input gate, dirt-release
+# absorptions (a dead port takes a live helper's value so that a hyperplane unit's column has no dirt on it), and cold ends at
+# a dim-8 frame with lifted partners.
+hyper = [h for h in cold if len(word['helper_final'][str(h)]) == 8]
+if hyper and ab:
+    sh = next(a for a, b in zip(ab, ab[1:]) if b == a + 1)              # two absorptions sharing one input anchor
+    rel = next(a for a in ab if a - 1 not in ab and a + 1 not in ab and word['A'][a][2] in hyper and word['A'][a][3] * 2 != -word['A'][a][4])
+    hh = hyper[0]; ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+    reject('second absorption sharing an input anchor dropped', lambda w: w['A'].pop(sh + 1), MYWHY['sh_dropped'])
+    reject('shared-anchor absorption coefficient changed', lambda w: w['A'][sh + 1].__setitem__(3, w['A'][sh + 1][3] * 2), MYWHY['sh_coefficient'])
+    reject('dirt-release absorption dropped', lambda w: w['A'].pop(rel), MYWHY['rel_dropped'])
+    reject('dirt-release absorption coefficient changed', lambda w: w['A'][rel].__setitem__(3, w['A'][rel][3] * 2), MYWHY['rel_coefficient'])
+    jr = max(i for i in range(npre, rel) if word['A'][i][0] == 'add' and word['A'][i][2] == word['A'][rel][1])
+
+    def release_while_read(w):   # the release runs before a kernel gate that still READS the port (port live)
+        e = w['A'].pop(rel); w['A'].insert(jr, e)
+    reject('dirt-release absorption moved before a kernel gate that still reads the port', release_while_read, MYWHY['rel_live'])
+if hyper:
+    # dim-8 cold-end controls once PER DISTINCT dim-8 terminal frame (each family of dim-8 cold ends keeps its own controls)
+    fams = []
+    for h in hyper:
+        if sorted(word['helper_final'][str(h)]) not in [sorted(word['helper_final'][str(x)]) for x in fams]: fams.append(h)
+    for hh in fams:
+        ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+        Uh = word['helper_final'][str(hh)]
+        reject('dim-8 cold end %d (frame %s) at another dim-8 frame' % (hh, Uh), lambda w, hh=hh: w['helper_final'].__setitem__(str(hh), next(f for h, f in w['helper_final'].items() if len(f) == 8 and sorted(f) != sorted(w['helper_final'][str(hh)]))), MYWHY['h8_other'])
+        reject('dim-8 cold end %d (frame %s): one lower-frame gate dropped (gate and its early_cleanup entry)' % (hh, Uh), lambda w, ih=ih: drop_cleanup_gate(w, ih), MYWHY['h8_lower'])
+        reject('dim-8 cold end %d (frame %s): profile pin (end dropped)' % (hh, Uh), lambda w, hh=hh: w['helper_final'].pop(str(hh)), WHY['profile_pin'])
+# FACTORED ACCUMULATOR (CarrierBypass; present only when the word carries one): a lower-frame tail gate a += x*g on two
+# non-ended registers whose accumulator a is afterwards read by a dim-8 cold end's tail gate (h += y*a at its U).
+ended_all = {int(h) for h in word['helper_final']}
+tailg = [(i, word['cleanup'][i]) for i, _ in early]
+accs = []   # EVERY factored accumulator gate (one per accumulator register a), each controlled on its own
+for k, (i, e) in enumerate(tailg):
+    if e[0] == 'add' and e[1] not in ended_all and e[2] not in ended_all and len(next(f for j, f in early if j == i)) < 8:
+        if e[1] not in [word['cleanup'][j][1] for j in accs] and any(t[0] == 'add' and t[2] == e[1] and t[1] in hyper for _, t in tailg[k + 1:]):
+            accs.append(i)
+for acc in accs:
+    a = word['cleanup'][acc][1]
+    reject('factored accumulator %d (gate %d) zeroed' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, 0), ENDPOINT)
+    reject('factored accumulator %d (gate %d) coefficient doubled' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, w['cleanup'][acc][3] * 2), ENDPOINT)
+outdir.mkdir(parents=True, exist_ok=True)
+(outdir/'COLD-END-CONTROLS.json').write_text(json.dumps(dict(status='PASS_COLD_END_RAW_WORD_CONTROLS', word=str(src), rejected=results), indent=1) + '\n')
+print('PASS', len(results), 'cold-end raw-word mutations rejected')
diff --git a/research/gauge44-leaver/construction/layers/reproduce_layers.py b/research/gauge44-leaver/construction/layers/reproduce_layers.py
new file mode 100644
index 0000000000..ed517ba1dd
--- /dev/null
+++ b/research/gauge44-leaver/construction/layers/reproduce_layers.py
@@ -0,0 +1,105 @@
+#!/usr/bin/env python3
+"""Rebuild the layered gauge44 word (pivot swaps + entering ends + factored dim-8 cold ends) and its native locals.
+
+Input: a fresh `construction/reproduce.py --until word` output directory (its regroup/ and cold44/ words are pinned
+by reproduce.py itself). Steps, each checked exactly:
+  1. pivot-swap: construction/layers/build_pivot_swap.py on regroup/FULL-WORD (six cost-neutral pivot-role swaps,
+     exact zero-response replay, unchanged profile and width multiset, 30 negative controls);
+  2. hpe: the inherited jp8 hyperplane-end changes (HYPERPLANE-END-S6.json) applied with PR635's build_hpe.apply;
+  3. cold44-exact: #645's build_gauge_cold44.py on the swapped HPE word; its 44 rank-four cold ends, premix and tail
+     must equal the unswapped cold44 construction's (the swaps touch no factory block);
+  4. layers: PR635's unchanged build_cold_end.apply(HPE, COLD-LAYERS-RECIPE) - the cold44 recipe plus 8 entering ends
+     (560/561/572/573 at U24, 597/599/537/549 at U30) and 10 factored dim-8 cold ends; output sha pinned;
+  5. layer-end-controls: raw-word negative controls on the layered word (PR635 cold_end_controls adapted by
+     LayerReviewer: lower->FULL pinned at 'cleanup on non-FULL end', entering ends from the recipe); 59 rejected;
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs (as in reproduce.py).
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+LAYERED_SHA = '0be48b1d8a6105059addf3f0d5e420c27ae3398b3a1186b6b11e9c4aa9e3f3d4'
+LAYER_CONTROLS = 59
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--word-dir', type=Path, required=True, help='construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    env.pop('PYTHONOPTIMIZE', None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    wd = a.word_dir.resolve()
+    run('pivot-swap', HERE / 'build_pivot_swap.py', '--input', wd / 'regroup/FULL-WORD.json.gz',
+        '--recipe', HERE / 'PIVOT-SWAP-S6.json', '--gk-dir', gk, '--out', out / 'swap')
+    hpe = load('upstream_hpe', up / 'code/build_hpe.py')
+    w = hpe.apply(read(out / 'swap/FULL-WORD.json.gz'), read(HERE / 'HYPERPLANE-END-S6.json')['changes'])
+    (out / 'hpe').mkdir(); (out / 'hpe/FULL-WORD.json.gz').write_bytes(gzip.compress(enc(w), mtime=0))
+    run('cold44-exact', HERE.parent / 'build_gauge_cold44.py', '--input', out / 'hpe/FULL-WORD.json.gz',
+        '--out', out / 'cold44', '--hamming', wd / 'hamming', '--upstream-package', up)
+    new, old = read(out / 'cold44/RECIPE.json.gz'), read(wd / 'cold44/RECIPE.json.gz')
+    # The swaps touch no factory block: the 44 ends, their premix and their low tails are identical; only the FULL
+    # inverse (rebuilt from the whole word) differs.
+    for key in ('premix', 'early_cleanup', 'cold_ends'):
+        assert new[key] == old[key], ('swapped cold44 differs from the pinned cold44 construction', key)
+    tail = len(new['early_cleanup']); assert new['cleanup'][:tail] == old['cleanup'][:tail], 'low tails'
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    layered = bce.apply(w, read(HERE / 'COLD-LAYERS-RECIPE.json.gz'))
+    raw = enc(layered); assert hashlib.sha256(raw).hexdigest() == LAYERED_SHA, 'layered word'
+    rep = layered['report']
+    assert rep['local_profile'] == {'1': 2542, '2': 414, '3': 434, '4': 154, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 52, '5': 48, '7': 42, '8': 116, '9': 234}, rep['width_inventory']
+    (out / 'layers').mkdir(); word = out / 'layers/FULL-WORD.json.gz'; word.write_bytes(gzip.compress(raw, mtime=0))
+    print('PASS layered scalar word', word, flush=True)
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', HERE / 'layer_end_controls.py', word, routing, out / 'controls')
+    ctl = json.loads((out / 'controls/COLD-END-CONTROLS.json').read_text())
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == LAYER_CONTROLS, len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word,
+        '--routing', routing, '--out', local)
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz b/research/gauge44-leaver/construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz
new file mode 100644
index 0000000000..f9155e3079
Binary files /dev/null and b/research/gauge44-leaver/construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz differ
diff --git a/research/gauge44-leaver/construction/layers_np/HPE-RECIPE-NP.json b/research/gauge44-leaver/construction/layers_np/HPE-RECIPE-NP.json
new file mode 100644
index 0000000000..2605d199ed
--- /dev/null
+++ b/research/gauge44-leaver/construction/layers_np/HPE-RECIPE-NP.json
@@ -0,0 +1 @@
+{"changes": [{"helper": 448, "cleanup_index": 674, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 449, "cleanup_index": 673, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 450, "cleanup_index": 672, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 451, "cleanup_index": 671, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 452, "cleanup_index": 670, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 453, "cleanup_index": 669, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 454, "cleanup_index": 668, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 455, "cleanup_index": 667, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 456, "cleanup_index": 666, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 457, "cleanup_index": 665, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 458, "cleanup_index": 664, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 459, "cleanup_index": 663, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 460, "cleanup_index": 658, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 461, "cleanup_index": 657, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 470, "cleanup_index": 648, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 471, "cleanup_index": 647, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 472, "cleanup_index": 642, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 473, "cleanup_index": 641, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 482, "cleanup_index": 632, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 483, "cleanup_index": 631, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 496, "cleanup_index": 609, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 497, "cleanup_index": 608, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 520, "cleanup_index": 573, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 521, "cleanup_index": 572, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 544, "cleanup_index": 539, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 545, "cleanup_index": 538, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 568, "cleanup_index": 507, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 569, "cleanup_index": 506, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 580, "cleanup_index": 491, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 581, "cleanup_index": 490, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 590, "cleanup_index": 481, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 591, "cleanup_index": 480, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 592, "cleanup_index": 475, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 593, "cleanup_index": 474, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 602, "cleanup_index": 465, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 603, "cleanup_index": 464, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 604, "cleanup_index": 459, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 605, "cleanup_index": 458, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 606, "cleanup_index": 457, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 607, "cleanup_index": 456, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 609, "cleanup_index": 454, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 611, "cleanup_index": 452, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 612, "cleanup_index": 451, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 613, "cleanup_index": 450, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 614, "cleanup_index": 449, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 615, "cleanup_index": 448, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}]}
\ No newline at end of file
diff --git a/research/gauge44-leaver/construction/layers_np/PIVOT-SWAP-NP.json b/research/gauge44-leaver/construction/layers_np/PIVOT-SWAP-NP.json
new file mode 100644
index 0000000000..4e0d846426
--- /dev/null
+++ b/research/gauge44-leaver/construction/layers_np/PIVOT-SWAP-NP.json
@@ -0,0 +1,588 @@
+{
+ "input_content_sha256": "864ff4a19987bcb27016367801a98ca50dae69eafe01d3614f8bae69f5713d6d",
+ "output_content_sha256": "beb3579fce83cb3b70f4e85761cbb3b8c91d711d4b9cf473074269b8447fc4e4",
+ "swaps": [
+  {
+   "pivot": 494,
+   "new_pivot": 566,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 379,
+     "before": [
+      "add",
+      566,
+      494,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      494,
+      566,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 380,
+     "before": [
+      "add",
+      640,
+      494,
+      2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      640,
+      566,
+      -2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 381,
+     "before": [
+      "add",
+      642,
+      494,
+      -2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      642,
+      566,
+      2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 382,
+     "before": [
+      "add",
+      688,
+      494,
+      1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      688,
+      566,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 383,
+     "before": [
+      "add",
+      690,
+      494,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      690,
+      566,
+      1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 495,
+   "new_pivot": 567,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 516,
+     "before": [
+      "add",
+      123,
+      495,
+      1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      123,
+      567,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 584,
+     "before": [
+      "add",
+      187,
+      495,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      187,
+      567,
+      1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 686,
+     "before": [
+      "add",
+      567,
+      495,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      495,
+      567,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 506,
+   "new_pivot": 578,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 176,
+     "before": [
+      "add",
+      652,
+      506,
+      2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      652,
+      578,
+      -2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 178,
+     "before": [
+      "add",
+      652,
+      506,
+      -2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      652,
+      578,
+      2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 278,
+     "before": [
+      "add",
+      700,
+      506,
+      -2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      700,
+      578,
+      2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 280,
+     "before": [
+      "add",
+      700,
+      506,
+      2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      700,
+      578,
+      -2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 702,
+     "before": [
+      "add",
+      578,
+      506,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      506,
+      578,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 507,
+   "new_pivot": 579,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 93,
+     "before": [
+      "add",
+      211,
+      507,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      211,
+      579,
+      1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 541,
+     "before": [
+      "add",
+      147,
+      507,
+      1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      147,
+      579,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 704,
+     "before": [
+      "add",
+      579,
+      507,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      507,
+      579,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 519,
+   "new_pivot": 543,
+   "entrance": [
+    30
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 507,
+     "before": [
+      "add",
+      115,
+      519,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      115,
+      543,
+      1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 575,
+     "before": [
+      "add",
+      179,
+      519,
+      1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      179,
+      543,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 722,
+     "before": [
+      "add",
+      543,
+      519,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      519,
+      543,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 531,
+   "new_pivot": 555,
+   "entrance": [
+    30
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 550,
+     "before": [
+      "add",
+      155,
+      531,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      155,
+      555,
+      1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 617,
+     "before": [
+      "add",
+      219,
+      531,
+      1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      219,
+      555,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 740,
+     "before": [
+      "add",
+      555,
+      531,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      531,
+      555,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    }
+   ]
+  }
+ ]
+}
diff --git a/research/gauge44-leaver/construction/layers_np/reproduce_np.py b/research/gauge44-leaver/construction/layers_np/reproduce_np.py
new file mode 100644
index 0000000000..79cb6fa912
--- /dev/null
+++ b/research/gauge44-leaver/construction/layers_np/reproduce_np.py
@@ -0,0 +1,149 @@
+#!/usr/bin/env python3
+"""Rebuild the layered no-triangle word (NP) and its native locals.
+
+Input: a fresh `construction/notri/reproduce_notri.py --word-only` output directory. That driver pins the
+no-triangle word (3e99ba77...) and writes its regroup/ and cold44/ words. Steps, each checked exactly:
+  1. pivot-swap: ../layers/build_pivot_swap.py (PR641's constructor, signed, unchanged) on the no-triangle regroup word, with PIVOT-SWAP-NP.json:
+     the six pivot-role swaps of research/gauge44-layered, mapped through the 504-helper map (494->566, 495->567,
+     506->578, 507->579, 519->543, 531->555). Exact zero-response replay, unchanged profile and width multiset,
+     30 negative controls.
+  2. hpe: PR635's build_hpe.candidates, greedy with disjoint registers. Must equal HPE-RECIPE-NP.json (46 changes,
+     the same helpers as the unswapped word); applied with build_hpe.apply.
+  3. cold44-exact: notri/cold44x.py on the swapped HPE word, pairing ranks pinned [4]*14. Its 56 cold ends, premix
+     and low tails must equal the unswapped no-triangle construction's.
+  4. layers: PR635's unchanged build_cold_end.apply(HPE, COLD-LAYERS-RECIPE-NP): cold44 plus the entering ends
+     566/567/578/579 at U24 (s4) and 608/610/543/555 at U30 (x30), BlockCombine's b6 and the q4 dim-8 cold ends.
+     The output word sha and its profile and widths are pinned.
+  5. layer-end-controls: ../layers/layer_end_controls.py (LayerReviewer's signed adaptation of PR635's
+     cold_end_controls.py, unchanged) on the layered word; exactly 59 rejections at pinned reasons.
+../layers/reproduce_layers.py is research/gauge44-layered's driver for the 492-helper word, shipped unchanged as
+signed; it is not used for this word.
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs, with pins.
+Apache-2.0. Driver by ColdWitness after G44Stack's NP chain (NP/chain.py, seq.py).
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NOTRI = HERE.parent / 'notri'
+LAYERS = HERE.parent / 'layers'   # the signed research/gauge44-layered files, unchanged
+REGROUP_SHA = '864ff4a1'   # prefix; full value checked against PIVOT-SWAP-NP.json's input_content_sha256
+SWAP_SHA = 'beb3579f'
+NP_SHA = 'a9de804f194eeb39f52a4c6e54c14d93e881bec4b632694249733ed410b58113'
+LAYER_CONTROLS = 59
+CANONICAL_SHA = '1ae812a336178760071efe347e876e0102b5b71f799d957db15c5f3004c19d7a'
+PROGRAM_SHA = {'forward': 'a3882a428bdafab888072211d4ed8d34572746873d77c6ef900495853cc3fa11',
+               'backward': 'f67a3dc20c27fb39295b8030e951e9779109ef1537f6f8de9d08510b9ad6792a'}
+CLIFFORD_SHA = '890b60fc4ae183c773c51405e0f4ef6a945dc2aae55ba2480f134602e8296cda'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def dump(p, v):
+    p.parent.mkdir(parents=True, exist_ok=True); p.write_bytes(gzip.compress(enc(v), mtime=0))
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--notri-dir', type=Path, required=True, help='construction/notri/reproduce_notri.py --word-only output')
+    ap.add_argument('--hamming', type=Path, required=True, help='hamming/ of the construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    nd = a.notri_dir.resolve()
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    # the input must be the pinned no-triangle construction
+    nr = load('notri_driver', NOTRI / 'reproduce_notri.py')
+    assert hashlib.sha256(enc(read(nd / 'cold44/FULL-WORD.json.gz'))).hexdigest() == nr.NOTRI_SHA, 'notri word'
+    # 1. pivot swaps on the regroup word
+    rg = hashlib.sha256(enc(read(nd / 'regroup/FULL-WORD.json.gz'))).hexdigest()
+    assert rg.startswith(REGROUP_SHA) and rg == read(HERE / 'PIVOT-SWAP-NP.json')['input_content_sha256'], ('regroup word', rg)
+    run('pivot-swap', LAYERS / 'build_pivot_swap.py', '--input', nd / 'regroup/FULL-WORD.json.gz',
+        '--recipe', HERE / 'PIVOT-SWAP-NP.json', '--gk-dir', gk, '--out', out / 'swap')
+    w = read(out / 'swap/FULL-WORD.json.gz')
+    sw = hashlib.sha256(enc(w)).hexdigest(); assert sw.startswith(SWAP_SHA) and sw == read(HERE / 'PIVOT-SWAP-NP.json')['output_content_sha256'], ('swap word', sw)
+    # 2. HPE (greedy, must equal the pinned recipe)
+    h = load('upstream_hpe', up / 'code/build_hpe.py')
+    used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    assert ch == read(HERE / 'HPE-RECIPE-NP.json')['changes'], 'HPE recipe'
+    w = h.apply(w, ch); dump(out / 'hpe/FULL-WORD.json.gz', w)
+    # 3. cold44 on the swapped word: same ends, premix and tails as the unswapped no-triangle construction
+    hm = set(read(nd / 'raw/HELPER-MAP.json')['map'].values())
+    env['EXTRAH'] = json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm))
+    env['PAIRING_RANKS'] = json.dumps([4] * 14)
+    run('cold44-exact', NOTRI / 'cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', a.hamming.resolve(), '--upstream-package', up)
+    for k in ('EXTRAH', 'PAIRING_RANKS'): env.pop(k)
+    new, old = read(out / 'cold44/RECIPE.json.gz'), read(nd / 'cold44/RECIPE.json.gz')
+    for key in ('premix', 'early_cleanup', 'cold_ends'):
+        assert new[key] == old[key], ('swapped cold44 differs from the pinned no-triangle construction', key)
+    tail = len(new['early_cleanup']); assert new['cleanup'][:tail] == old['cleanup'][:tail], 'low tails'
+    # 4. layers
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    layered = bce.apply(w, read(HERE / 'COLD-LAYERS-RECIPE-NP.json.gz'))
+    raw = enc(layered); assert hashlib.sha256(raw).hexdigest() == NP_SHA, ('layered word', hashlib.sha256(raw).hexdigest())
+    rep = layered['report']
+    assert rep['local_profile'] == {'1': 2534, '2': 346, '3': 458, '4': 178, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 64, '5': 48, '7': 54, '8': 116, '9': 222}, rep['width_inventory']
+    (out / 'layers').mkdir(); word = out / 'layers/FULL-WORD.json.gz'; word.write_bytes(gzip.compress(raw, mtime=0))
+    print('PASS layered no-triangle word', NP_SHA, flush=True)
+    # 5. layer-end controls
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', LAYERS / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = json.loads((out / 'controls/COLD-END-CONTROLS.json').read_text())
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == LAYER_CONTROLS, len(ctl['rejected'])
+    # 6. native locals
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == CANONICAL_SHA, 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in PROGRAM_SHA.items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == CLIFFORD_SHA, 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz b/research/gauge44-leaver/construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz
new file mode 100644
index 0000000000..a408c95816
Binary files /dev/null and b/research/gauge44-leaver/construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz differ
diff --git a/research/gauge44-leaver/construction/layers_p6n/P6N-SPEC.json b/research/gauge44-leaver/construction/layers_p6n/P6N-SPEC.json
new file mode 100644
index 0000000000..43c3ec265c
--- /dev/null
+++ b/research/gauge44-leaver/construction/layers_p6n/P6N-SPEC.json
@@ -0,0 +1 @@
+{"ends":[{"U":[256,128,66,34,16,8,6,1],"labels":[512,513]},{"U":[256,128,72,40,24,4,2,1],"labels":[311,510]},{"U":[256,128,66,34,18,10,6,1],"labels":[522,327]}]}
diff --git a/research/gauge44-leaver/construction/layers_p6n/layer_end_controls.py b/research/gauge44-leaver/construction/layers_p6n/layer_end_controls.py
new file mode 100644
index 0000000000..dd321fe255
--- /dev/null
+++ b/research/gauge44-leaver/construction/layers_p6n/layer_end_controls.py
@@ -0,0 +1,199 @@
+"""layer_end_controls.py LAYERED-WORD.json.gz ROUTING OUTDIR (env PR635_CODE): adapted PR635 cold_end_controls.py (LayerReviewer): raw-word negative controls for the cold low-frame ends and the
+refactored cleanup accepted by hpe_audit_and_transport.py.  Every mutation MUST be rejected (AssertionError); the
+unmutated word MUST pass.  Apache-2.0.  DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code."""
+import copy, gzip, json, shutil, sys, tempfile
+from pathlib import Path
+import os
+sys.path.insert(0, os.environ['PR635_CODE'])   # PR635's unchanged hpe_audit_and_transport.py
+import hpe_audit_and_transport as atc
+
+src, routing, outdir = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3])
+word = json.load(gzip.open(src))
+v, R = word['report']['v'], word['report']['R']; n = 2*v + R
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+meta = word['refactored_cleanup']
+cold = [int(h) for h in meta['cold_low_frame_ended_helpers']]
+npre = meta['premix_gates']; nlow = meta['lower_frame_gates']
+early = word['early_cleanup']; eidx = {i for i, _ in early}
+rest = [i for i in range(len(word['cleanup'])) if i not in eidx]
+
+
+def trial(w):
+    """None if the transport audit accepts w, else the AssertionError message."""
+    tmp = Path(tempfile.mkdtemp())
+    p = tmp/'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w).encode(), mtime=0))
+    try:
+        atc.run(p, routing, tmp/'out')
+        return None
+    except AssertionError as e:
+        return repr(e.args[0]) if e.args else 'AssertionError'
+    finally:
+        shutil.rmtree(tmp, ignore_errors=True)
+
+
+# Pinned rejection reasons: each mutant must fail at this assertion of hpe_audit_and_transport.py (message substring).
+ENDPOINT, COLDPRE, CONE = "'arbitrary-dirt endpoint'", 'touches a cold hyperplane-ended helper', 'hpe cone pre-check (row / column)'
+WHY = dict(premix_to_precondition=COLDPRE, premix_dropped=COLDPRE, e_premix_dropped=ENDPOINT, lower_dropped=ENDPOINT,
+           remainder_dropped=ENDPOINT, coefficient=ENDPOINT, into_full='cleanup on non-FULL end', dyadic=ENDPOINT, frame_below="'nonmonotone'",
+           nonmonotone="'nonmonotone'", other_frame=CONE, cone=CONE, extra_end=COLDPRE, marker='cleanup is not the literal reversed inverse',
+           target='refactored cleanup touches a target', profile_pin='paid local profile differs from the reported local_profile',
+           entering_precondition='zero-frame precondition/compensation touches an entering helper')
+assert trial(word) is None, 'unmutated cold-end word must pass'
+results = []
+
+
+def reject(name, mut, why):
+    """the mutation must be rejected, and for the pinned reason (a substring of the audit's assertion message)."""
+    w = copy.deepcopy(word); mut(w)
+    msg = trial(w)
+    assert msg is not None, 'cold-end mutation accepted: ' + name
+    assert why in msg, 'cold-end mutation %r rejected for the wrong reason: %s' % (name, msg[:300])
+    results.append(name); print('rejected', name, '|', why, flush=True)
+
+
+h0 = cold[0]
+i0, U0 = next((i, f) for i, f in early if h0 in regs(word['cleanup'][i]))
+r0 = rest[len(rest)//2]
+
+
+def premix_to_precondition(w):   # premix before the wrappers; compensation then reads the cold ends
+    w['precondition'] = w['precondition'] + w['A'][:npre]; w['A'] = w['A'][npre:]
+
+
+def lower_gate_into_full(w):     # a lower-frame gate on a cold-ended helper executed in the FULL remainder instead
+    w['early_cleanup'] = [x for x in w['early_cleanup'] if x[0] != i0]
+
+
+def drop_cleanup_gate(w, i):   # remove the gate AND its early_cleanup entry: a structurally valid word missing one gate
+    w['cleanup'].pop(i)
+    w['early_cleanup'] = [[j - (j > i), f] for j, f in w['early_cleanup'] if j != i]
+
+
+def other_frame(w):              # a different frame of the same dimension as the cold end (another cold helper's)
+    f = next(w['helper_final'][str(h)] for h in cold if w['helper_final'][str(h)] != w['helper_final'][str(h0)])
+    w['helper_final'][str(h0)] = f
+
+
+def extra_cold_end(w):           # declare a premixed partner of h0 cold-ended at h0's frame: fails the row/column cone
+    p = next(r for e in w['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    w['helper_final'][str(p)] = w['helper_final'][str(h0)]
+
+
+reject('premix placed in the zero-frame precondition (before the cold wrappers)', premix_to_precondition, WHY['premix_to_precondition'])
+reject('one premix gate dropped (the compensation then reads a cold-ended helper)', lambda w: w['A'].pop(npre - 1), WHY['premix_dropped'])
+reject('one lower-frame cleanup gate dropped (gate and its early_cleanup entry)', lambda w: drop_cleanup_gate(w, i0), WHY['lower_dropped'])
+reject('one FULL-remainder gate dropped', lambda w: drop_cleanup_gate(w, r0), WHY['remainder_dropped'])
+reject('lower-frame gate coefficient changed', lambda w: w['cleanup'][i0].__setitem__(3, w['cleanup'][i0][3] * 2), WHY['coefficient'])
+reject('lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)', lower_gate_into_full, WHY['into_full'])
+reject('lower-frame gate frame below its registers\' frames', lambda w: next(x for x in w['early_cleanup'] if x[0] == i0).__setitem__(1, U0[:-1]), WHY['frame_below'])
+reject('cold end at another dim-4 frame', other_frame, WHY['other_frame'])
+# PROFILE-PIN control: without its helper_final entry the cold-ended helper is a valid FULL-ended helper; the word is
+# rejected because its reported paid profile (which counts the low end) no longer matches the frame chains.
+reject('profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)', lambda w: w['helper_final'].pop(str(h0)), WHY['profile_pin'])
+reject('extra cold end on a premixed partner (the compensation reads it before its wrapper)', extra_cold_end, WHY['extra_end'])
+reject('refactored-cleanup marker removed (literal-inverse rule applies)', lambda w: w.pop('refactored_cleanup'), WHY['marker'])
+reject('remainder gate retargeted to a target register', lambda w: w['cleanup'][r0].__setitem__(1, v + 3), WHY['target'])
+reject('non-dyadic remainder coefficient', lambda w: w['cleanup'][r0].__setitem__(4 if w['cleanup'][r0][0] == 'add' else 3, 3 * w['cleanup'][r0][4 if w['cleanup'][r0][0] == 'add' else 3]), WHY['dyadic'])
+reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('5', w['report']['local_profile']['5'] - 1), WHY['profile_pin'])
+ent = [int(h) for h in sys.argv[4].split(',')] if len(sys.argv) > 4 else [int(h) for h in meta.get('entering_low_frame_ended_helpers', [])]
+for e0 in ent:   # ENTERING LOW-FRAME ENDS (ColdSupply extension; every entering end; absent for words without them)
+    j0 = next((i for i, e in enumerate(word['A'][:npre]) if e0 in regs(e)), None)
+    print('entering end', e0, 'premix gate', j0, flush=True)
+    k0, Ue = next((i, f) for i, f in early if e0 in regs(word['cleanup'][i]))
+    def to_pre(w, j0=j0): w['precondition'].append(w['A'][j0]); w['A'].pop(j0)
+    def other_hp(w, e0=e0, Ue=Ue): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Ue) and sorted(f) != sorted(Ue))
+    if j0 is not None: reject('entering end %d: premix gate dropped' % e0, lambda w, j0=j0: w['A'].pop(j0), WHY['e_premix_dropped'])
+    if j0 is not None: reject('entering end %d: premix gate at frame [] instead of its entrance E' % e0, lambda w, j0=j0: w['A'][j0].__setitem__(-1, []), WHY['nonmonotone'])
+    if j0 is not None: reject('entering end %d: premix gate moved into the zero-frame precondition' % e0, to_pre, WHY['entering_precondition'])
+    reject('entering end %d: lower-frame gate dropped (gate and its early_cleanup entry)' % e0, lambda w, k0=k0: drop_cleanup_gate(w, k0), WHY['lower_dropped'])
+    reject('entering end %d: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)' % e0, lambda w, e0=e0: w['helper_final'].pop(str(e0)), WHY['profile_pin'])
+    reject('entering end %d: end at another hyperplane' % e0, other_hp, WHY['cone'])
+# Pinned rejection reasons of the COLD-BEYOND mutants (substrings of hpe_audit_and_transport.py assertion messages).
+MYWHY = dict(tw_precondition=COLDPRE, tw_dropped=COLDPRE, tw_coefficient=COLDPRE, tw_other_block=COLDPRE,
+             tw_entering='zero-frame compensation reads an entering helper',
+             ab_dropped=ENDPOINT, ab_coefficient=ENDPOINT, ab_early=ENDPOINT, ab_live=ENDPOINT, ab_centre=ENDPOINT,
+             ab_lower="'nonmonotone'", ab_higher="'nonmonotone'",
+             sh_dropped=ENDPOINT, sh_coefficient=ENDPOINT, rel_dropped=ENDPOINT, rel_coefficient=ENDPOINT, rel_live=ENDPOINT,
+             h8_other=CONE, h8_lower=ENDPOINT)
+# COLD-BEYOND primitives (present only when the word carries them): frame-[] target writes in the premix (explicit
+# post-wrapper compensation of an ended helper's dirt) and forward absorptions into dead registers.
+nw = meta.get('premix_target_writes', 0)
+if nw:
+    wi = [i for i in range(npre) if v <= word['A'][i][1] < 2*v]
+    assert len(wi) == nw
+
+    def writes_to_precondition(w):   # the target writes run before the cold wrappers (inside the zero-frame precondition)
+        g = [w['A'][i] for i in wi]; w['precondition'] = w['precondition'] + g
+        w['A'] = [e for i, e in enumerate(w['A']) if i not in set(wi)]
+    reject('premix target writes placed in the zero-frame precondition (before the cold wrappers)', writes_to_precondition, MYWHY['tw_precondition'])
+    reject('one premix target write dropped (compensation must read an ended helper)', lambda w: w['A'].pop(wi[0]), MYWHY['tw_dropped'])
+    reject('premix target write coefficient changed', lambda w: w['A'][wi[0]].__setitem__(3, w['A'][wi[0]][3] * 2), MYWHY['tw_coefficient'])
+    # (reading another register that carries the SAME weight of the ended helper's dirt is a valid variant, so the mutant reads
+    #  the same factory slot of the next block, which carries none of it)
+    entering_regs = sorted(int(r) for r in word.get('start_extra', {}))
+    reject('premix target write reads an entering helper', lambda w: w['A'][wi[0]].__setitem__(2, entering_regs[0]), MYWHY['tw_entering'])
+    reject('premix target write reads a cold helper of another block', lambda w: w['A'][wi[0]].__setitem__(2, 2*v + (w['A'][wi[0]][2] - 2*v + 16) % 224), MYWHY['tw_other_block'])
+ab = meta.get('forward_absorption_A_indices', [])
+if any(len(word['helper_final'][str(h)]) == 8 for h in cold):
+    # with dim-8 cold ends, the centre-retargeted absorption first leaks an ended helper's dirt into the cut's targets
+    MYWHY['ab_centre'] = COLDPRE
+if ab:
+    # the ColdBeyond U_b absorption (q += -1/2 g); ColdThird's extra absorptions have their own controls below
+    a0 = next(a for a in ab if word['A'][a][3] * 2 == -word['A'][a][4]); g0 = word['A'][a0]
+
+    def absorption_moved_early(w):   # absorbed before the absorbed register's last kernel write
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[2] == w['A'][i][1] and w['A'][i][-1] == g0[-1])
+        w['A'].insert(j, e)
+
+    def absorption_into_live(w):     # q += a g moved right after g's previous frame-mate gate, while q is still live
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[1] in regs(w['A'][i]))
+        w['A'].insert(j, e)
+    reject('forward absorption dropped', lambda w: w['A'].pop(a0), MYWHY['ab_dropped'])
+    reject('forward absorption into a centre (a live register read by the cut)', lambda w: w['A'][a0].__setitem__(1, next(c for c in word['centers'] if c not in g0[1:3] and c not in cold)), MYWHY['ab_centre'])
+    reject('forward absorption coefficient changed', lambda w: w['A'][a0].__setitem__(3, w['A'][a0][3] * 2), MYWHY['ab_coefficient'])
+    reject('forward absorption placed before the absorbed register\'s last kernel write', absorption_moved_early, MYWHY['ab_early'])
+    reject('forward absorption placed while the absorbing register is still live', absorption_into_live, MYWHY['ab_live'])
+    reject('forward absorption at a lower frame than its registers', lambda w: w['A'][a0].__setitem__(-1, w['A'][a0][-1][:-1]), MYWHY['ab_lower'])
+    reject('forward absorption at a higher frame (FULL) than its registers', lambda w: w['A'][a0].__setitem__(-1, [256, 128, 64, 32, 16, 8, 4, 2, 1]), MYWHY['ab_higher'])
+# COLD-THIRD primitives (present only when the word carries them): several absorptions after one input gate, dirt-release
+# absorptions (a dead port takes a live helper's value so that a hyperplane unit's column has no dirt on it), and cold ends at
+# a dim-8 frame with lifted partners.
+hyper = [h for h in cold if len(word['helper_final'][str(h)]) == 8]
+if hyper and ab:
+    sh = next(a for a, b in zip(ab, ab[1:]) if b == a + 1)              # two absorptions sharing one input anchor
+    rel = next(a for a in ab if a - 1 not in ab and a + 1 not in ab and word['A'][a][2] in hyper and word['A'][a][3] * 2 != -word['A'][a][4])
+    hh = hyper[0]; ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+    reject('second absorption sharing an input anchor dropped', lambda w: w['A'].pop(sh + 1), MYWHY['sh_dropped'])
+    reject('shared-anchor absorption coefficient changed', lambda w: w['A'][sh + 1].__setitem__(3, w['A'][sh + 1][3] * 2), MYWHY['sh_coefficient'])
+    reject('dirt-release absorption dropped', lambda w: w['A'].pop(rel), MYWHY['rel_dropped'])
+    reject('dirt-release absorption coefficient changed', lambda w: w['A'][rel].__setitem__(3, w['A'][rel][3] * 2), MYWHY['rel_coefficient'])
+    jr = max(i for i in range(npre, rel) if word['A'][i][0] == 'add' and word['A'][i][2] == word['A'][rel][1])
+
+    def release_while_read(w):   # the release runs before a kernel gate that still READS the port (port live)
+        e = w['A'].pop(rel); w['A'].insert(jr, e)
+    reject('dirt-release absorption moved before a kernel gate that still reads the port', release_while_read, MYWHY['rel_live'])
+if hyper:
+    # dim-8 cold-end controls for EVERY dim-8 cold end of the word (read from the word's helper_final and the recipe meta's
+    # cold_low_frame_ended_helpers), not one representative per terminal frame
+    for hh in hyper:
+        ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+        Uh = word['helper_final'][str(hh)]
+        reject('dim-8 cold end %d (frame %s) at another dim-8 frame' % (hh, Uh), lambda w, hh=hh: w['helper_final'].__setitem__(str(hh), next(f for h, f in w['helper_final'].items() if len(f) == 8 and sorted(f) != sorted(w['helper_final'][str(hh)]))), MYWHY['h8_other'])
+        reject('dim-8 cold end %d (frame %s): one lower-frame gate dropped (gate and its early_cleanup entry)' % (hh, Uh), lambda w, ih=ih: drop_cleanup_gate(w, ih), MYWHY['h8_lower'])
+        reject('dim-8 cold end %d (frame %s): profile pin (end dropped)' % (hh, Uh), lambda w, hh=hh: w['helper_final'].pop(str(hh)), WHY['profile_pin'])
+# FACTORED ACCUMULATOR (CarrierBypass; present only when the word carries one): a lower-frame tail gate a += x*g on two
+# non-ended registers whose accumulator a is afterwards read by a dim-8 cold end's tail gate (h += y*a at its U).
+ended_all = {int(h) for h in word['helper_final']}
+tailg = [(i, word['cleanup'][i]) for i, _ in early]
+accs = []   # EVERY factored accumulator gate (one per accumulator register a), each controlled on its own
+for k, (i, e) in enumerate(tailg):
+    if e[0] == 'add' and e[1] not in ended_all and e[2] not in ended_all and len(next(f for j, f in early if j == i)) < 8:
+        if e[1] not in [word['cleanup'][j][1] for j in accs] and any(t[0] == 'add' and t[2] == e[1] and t[1] in hyper for _, t in tailg[k + 1:]):
+            accs.append(i)
+for acc in accs:
+    a = word['cleanup'][acc][1]
+    reject('factored accumulator %d (gate %d) zeroed' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, 0), ENDPOINT)
+    reject('factored accumulator %d (gate %d) coefficient doubled' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, w['cleanup'][acc][3] * 2), ENDPOINT)
+outdir.mkdir(parents=True, exist_ok=True)
+(outdir/'COLD-END-CONTROLS.json').write_text(json.dumps(dict(status='PASS_COLD_END_RAW_WORD_CONTROLS', word=str(src), rejected=results), indent=1) + '\n')
+print('PASS', len(results), 'cold-end raw-word mutations rejected')
diff --git a/research/gauge44-leaver/construction/layers_p6n/reproduce_p6n.py b/research/gauge44-leaver/construction/layers_p6n/reproduce_p6n.py
new file mode 100644
index 0000000000..f9eb173bc1
--- /dev/null
+++ b/research/gauge44-leaver/construction/layers_p6n/reproduce_p6n.py
@@ -0,0 +1,78 @@
+#!/usr/bin/env python3
+"""Rebuild the p6n word (NoTriReopen): the layered no-triangle word with p123's lane rebuilt as three factored dim-8 pairs.
+
+Input: a fresh `construction/layers_np/reproduce_np.py` output directory. Its swapped HPE word (hpe/) and its
+layered word a9de804f... are pinned there. Steps, each checked exactly:
+  1. layers: PR635's unchanged build_cold_end.apply(swapped HPE word, COLD-LAYERS-RECIPE-P6N.json.gz). The recipe is
+     NP's cold-layer recipe (cold44, s4, x30, b6, q4) plus the six cold ends of P6N-SPEC.json, built by NoTriReopen
+     with JP8Ends' stackJ/stackE (the CarrierBypass premix-only factored construction): [512,513] at
+     U(256,128,66,34,16,8,6,1), [311,510] at U(256,128,72,40,24,4,2,1), [522,327] at U(256,128,66,34,18,10,6,1).
+     The output word sha (34b683fa...), profile and widths are pinned.
+  2. layer-end-controls: layer_end_controls.py (Q6Reviewer-signed variant fc58c569..., which controls every dim-8
+     cold end individually) on the p6n word; exactly 95 rejections at pinned reasons.
+The promotion step (construction/promo/reproduce_promo.py --base p6n) builds the final word and its native locals.
+Apache-2.0. Driver by ColdWitness after NoTriReopen's runspec.py.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NP_SHA = 'a9de804f194eeb39f52a4c6e54c14d93e881bec4b632694249733ed410b58113'
+P6N_SHA = '34b683fa08f0'   # prefix; full value is the recipe's output_content_sha256 (asserted equal below)
+LAYER_CONTROLS = 95
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--np-dir', type=Path, required=True, help='construction/layers_np/reproduce_np.py output')
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    parent = src / 'vendor/pr558/vendor/pr552'
+    npd = a.np_dir.resolve()
+    assert hashlib.sha256(enc(read(npd / 'layers/FULL-WORD.json.gz'))).hexdigest() == NP_SHA, 'np-dir must hold the pinned NP word'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src), PR635_CODE=str(up / 'code'))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    rec = read(HERE / 'COLD-LAYERS-RECIPE-P6N.json.gz')
+    w = bce.apply(read(npd / 'hpe/FULL-WORD.json.gz'), rec)
+    raw = enc(w); got = hashlib.sha256(raw).hexdigest()
+    assert got == rec['output_content_sha256'] and got.startswith(P6N_SHA), ('p6n word', got)
+    rep = w['report']
+    assert rep['local_profile'] == {'1': 2540, '2': 358, '3': 446, '4': 178, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 64, '5': 48, '7': 54, '8': 122, '9': 216}, rep['width_inventory']
+    (out / 'p6n').mkdir(); word = out / 'p6n/FULL-WORD.json.gz'; word.write_bytes(gzip.compress(raw, mtime=0))
+    print('PASS p6n word', got, flush=True)
+    t = time.monotonic()
+    with (out / 'layer-end-controls.log').open('w') as f:
+        rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(HERE / 'layer_end_controls.py'), str(word),
+                              str(parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'), str(out / 'controls')],
+                             env=env, stdout=f, stderr=subprocess.STDOUT)
+    (out / 'STEPS.json').write_text(json.dumps([dict(step='layer-end-controls', exit_code=rc, seconds=round(time.monotonic() - t, 3))], indent=2) + '\n')
+    assert rc == 0, 'layer-end-controls'
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == LAYER_CONTROLS, len(ctl['rejected'])
+    print('PASS layer-end-controls', LAYER_CONTROLS, flush=True)
+    print('DONE', word, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/leaver/CHAIN-PINS-k5.json b/research/gauge44-leaver/construction/leaver/CHAIN-PINS-k5.json
new file mode 100644
index 0000000000..3f5a871788
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/CHAIN-PINS-k5.json
@@ -0,0 +1,75 @@
+{
+ "np_profile": {
+  "1": 2462,
+  "2": 388,
+  "3": 476,
+  "4": 154,
+  "5": 56,
+  "8": 8
+ },
+ "p6n_profile": {
+  "1": 2468,
+  "2": 400,
+  "3": 464,
+  "4": 154,
+  "5": 56,
+  "8": 8
+ },
+ "lec-p6n": 95,
+ "promo_controls": 11,
+ "lec-promo": 95,
+ "jx_controls": [
+  "C0_identity",
+  "C1_741_only",
+  "M1_one_pair_448",
+  "N1_drop_preread",
+  "N2_wrong_sign_preread",
+  "N3_plain_join_moved_reads",
+  "N4_raise_dim7_at_855"
+ ],
+ "lec-jx": 95,
+ "hybrid_controls": [
+  "C0_identity",
+  "donation_after",
+  "donation_after@226",
+  "donation_after@228",
+  "donation_after@230",
+  "donation_after@231",
+  "donation_after@232",
+  "donation_after@238",
+  "donation_after@62",
+  "drop_preread",
+  "drop_preread@226",
+  "drop_preread@228",
+  "drop_preread@230",
+  "drop_preread@231",
+  "drop_preread@232",
+  "drop_preread@238",
+  "drop_preread@62",
+  "drop_restore",
+  "drop_restore@226",
+  "drop_restore@228",
+  "drop_restore@230",
+  "drop_restore@231",
+  "drop_restore@232",
+  "drop_restore@238",
+  "drop_restore@62",
+  "recipe",
+  "restore_full",
+  "restore_full@226",
+  "restore_full@228",
+  "restore_full@230",
+  "restore_full@231",
+  "restore_full@232",
+  "restore_full@238",
+  "restore_full@62"
+ ],
+ "lec-hyb": 95,
+ "frame_build_controls": 3,
+ "canonical_sha256": "5d526f492ad3ad93b78d0c9c245a2425b2b760b71d7852be7c684c0e17e946e2",
+ "program_sha256": {
+  "forward": "e4ee794f189c84c473cf48df8a9ff198feefa0940dbcbf99163a8e9118c9176c",
+  "backward": "b8de98f996a99fdc477c126faba7f7e47297679f313e8a831d5ea9dda3de3260"
+ },
+ "clifford_recipes_sha256": "f1f89e29a9e20da1a264cff40862f271e0f07306d12a41f060580433b2f35726"
+}
diff --git a/research/gauge44-leaver/construction/leaver/CODED-CELLS-k5.json b/research/gauge44-leaver/construction/leaver/CODED-CELLS-k5.json
new file mode 100644
index 0000000000..fe3ace6921
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/CODED-CELLS-k5.json
@@ -0,0 +1,1767 @@
+[
+ {
+  "cell": "01+",
+  "bindings": {
+   "x0": [
+    "source",
+    [
+     0,
+     1,
+     2,
+     3
+    ],
+    1
+   ],
+   "x1": [
+    "source",
+    [
+     0,
+     1,
+     2,
+     3
+    ],
+    0
+   ],
+   "x2": [
+    "source",
+    [
+     0,
+     1,
+     4,
+     5
+    ],
+    1
+   ],
+   "x3": [
+    "source",
+    [
+     0,
+     1,
+     4,
+     5
+    ],
+    0
+   ],
+   "x4": [
+    "source",
+    [
+     0,
+     1,
+     6,
+     7
+    ],
+    1
+   ],
+   "x5": [
+    "source",
+    [
+     0,
+     1,
+     6,
+     7
+    ],
+    0
+   ],
+   "y0": [
+    "target",
+    65
+   ],
+   "y1": [
+    "target",
+    64
+   ],
+   "y2": [
+    "target",
+    33
+   ],
+   "y3": [
+    "target",
+    32
+   ],
+   "y4": [
+    "target",
+    25
+   ],
+   "y5": [
+    "target",
+    24
+   ]
+  },
+  "scaled": [
+   [
+    "y1",
+    "x0",
+    "-1/2"
+   ],
+   [
+    "y0",
+    "x1",
+    "-1/2"
+   ],
+   [
+    "y2",
+    "x5",
+    "-1/2"
+   ],
+   [
+    "y3",
+    "x4",
+    "-1/2"
+   ],
+   [
+    "y4",
+    "x3",
+    "-1/2"
+   ],
+   [
+    "y5",
+    "x2",
+    "-1/2"
+   ],
+   [
+    "x0",
+    "x1",
+    "1"
+   ],
+   [
+    "x2",
+    "x5",
+    "1"
+   ],
+   [
+    "x4",
+    "x3",
+    "1"
+   ],
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+    "x2",
+    "-1/2"
+   ],
+   [
+    "y3",
+    "x0",
+    "-1/2"
+   ],
+   [
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+    "x4",
+    "-1/2"
+   ],
+   [
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+    "y5",
+    "1"
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+    "-1/2"
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+    "-1/2"
+   ],
+   [
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+    "x1",
+    "-1/2"
+   ],
+   [
+    "y5",
+    "x0",
+    "-1/2"
+   ]
+  ],
+  "unit": [
+   [
+    "y1",
+    "x0",
+    1
+   ],
+   [
+    "y0",
+    "x1",
+    1
+   ],
+   [
+    "y2",
+    "x5",
+    1
+   ],
+   [
+    "y3",
+    "x4",
+    1
+   ],
+   [
+    "y4",
+    "x3",
+    1
+   ],
+   [
+    "y5",
+    "x2",
+    1
+   ],
+   [
+    "x0",
+    "x1",
+    1
+   ],
+   [
+    "x2",
+    "x5",
+    1
+   ],
+   [
+    "x4",
+    "x3",
+    1
+   ],
+   [
+    "y1",
+    "x2",
+    1
+   ],
+   [
+    "y3",
+    "x0",
+    1
+   ],
+   [
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+    "x4",
+    1
+   ],
+   [
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+    1
+   ],
+   [
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+    1
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+   [
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+    "y1",
+    1
+   ],
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+    "x4",
+    1
+   ],
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+    1
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+    "x3",
+    1
+   ],
+   [
+    "y3",
+    "x2",
+    1
+   ],
+   [
+    "y4",
+    "x1",
+    1
+   ],
+   [
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+    1
+   ]
+  ],
+  "coefficients": [
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+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2"
+   ],
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+    "-1/2",
+    "-1/2"
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+    "-1/2",
+    "-1/2",
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+    "-1/2",
+    "-1/2"
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+   [
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+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "0",
+    "-1/2"
+   ],
+   [
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "0"
+   ]
+  ]
+ },
+ {
+  "cell": "23+",
+  "bindings": {
+   "x0": [
+    "source",
+    [
+     0,
+     1,
+     2,
+     3
+    ],
+    23
+   ],
+   "x1": [
+    "source",
+    [
+     0,
+     1,
+     2,
+     3
+    ],
+    3
+   ],
+   "x2": [
+    "source",
+    [
+     2,
+     3,
+     4,
+     5
+    ],
+    1
+   ],
+   "x3": [
+    "source",
+    [
+     2,
+     3,
+     4,
+     5
+    ],
+    0
+   ],
+   "x4": [
+    "source",
+    [
+     2,
+     3,
+     6,
+     7
+    ],
+    1
+   ],
+   "x5": [
+    "source",
+    [
+     2,
+     3,
+     6,
+     7
+    ],
+    0
+   ],
+   "y0": [
+    "target",
+    71
+   ],
+   "y1": [
+    "target",
+    67
+   ],
+   "y2": [
+    "target",
+    97
+   ],
+   "y3": [
+    "target",
+    96
+   ],
+   "y4": [
+    "target",
+    89
+   ],
+   "y5": [
+    "target",
+    88
+   ]
+  },
+  "scaled": [
+   [
+    "y1",
+    "x0",
+    "1"
+   ],
+   [
+    "y0",
+    "x1",
+    "1"
+   ],
+   [
+    "y2",
+    "x5",
+    "-1/2"
+   ],
+   [
+    "y3",
+    "x4",
+    "-1/2"
+   ],
+   [
+    "y4",
+    "x3",
+    "-1/2"
+   ],
+   [
+    "y5",
+    "x2",
+    "-1/2"
+   ],
+   [
+    "x0",
+    "x1",
+    "1"
+   ],
+   [
+    "x2",
+    "x5",
+    "1"
+   ],
+   [
+    "x4",
+    "x3",
+    "1"
+   ],
+   [
+    "y1",
+    "x2",
+    "-1/2"
+   ],
+   [
+    "y3",
+    "x0",
+    "1"
+   ],
+   [
+    "y5",
+    "x4",
+    "-1/2"
+   ],
+   [
+    "y0",
+    "y5",
+    "1"
+   ],
+   [
+    "y2",
+    "y3",
+    "1"
+   ],
+   [
+    "y4",
+    "y1",
+    "1"
+   ],
+   [
+    "y1",
+    "x4",
+    "-1/2"
+   ],
+   [
+    "y0",
+    "x5",
+    "-1/2"
+   ],
+   [
+    "y2",
+    "x3",
+    "-1/2"
+   ],
+   [
+    "y3",
+    "x2",
+    "-1/2"
+   ],
+   [
+    "y4",
+    "x1",
+    "1"
+   ],
+   [
+    "y5",
+    "x0",
+    "1"
+   ]
+  ],
+  "unit": [
+   [
+    "y1",
+    "x0",
+    1
+   ],
+   [
+    "y0",
+    "x1",
+    1
+   ],
+   [
+    "y2",
+    "x5",
+    1
+   ],
+   [
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+    "x4",
+    1
+   ],
+   [
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+    "x3",
+    1
+   ],
+   [
+    "y5",
+    "x2",
+    1
+   ],
+   [
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+    "x1",
+    1
+   ],
+   [
+    "x2",
+    "x5",
+    1
+   ],
+   [
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+    "x3",
+    1
+   ],
+   [
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+    1
+   ],
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+    1
+   ],
+   [
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+    1
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+    1
+   ],
+   [
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+    "y3",
+    1
+   ],
+   [
+    "y4",
+    "y1",
+    1
+   ],
+   [
+    "y1",
+    "x4",
+    1
+   ],
+   [
+    "y0",
+    "x5",
+    1
+   ],
+   [
+    "y2",
+    "x3",
+    1
+   ],
+   [
+    "y3",
+    "x2",
+    1
+   ],
+   [
+    "y4",
+    "x1",
+    1
+   ],
+   [
+    "y5",
+    "x0",
+    1
+   ]
+  ],
+  "coefficients": [
+   [
+    "0",
+    "1",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2"
+   ],
+   [
+    "1",
+    "0",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2"
+   ],
+   [
+    "1",
+    "1",
+    "0",
+    "-1/2",
+    "-1/2",
+    "-1/2"
+   ],
+   [
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+}
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diff --git a/research/gauge44-leaver/construction/leaver/RECIPE-X4-k5.json b/research/gauge44-leaver/construction/leaver/RECIPE-X4-k5.json
new file mode 100644
index 0000000000..1635b2388a
--- /dev/null
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+ },
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+   "8": 8
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+ },
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+   },
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+    "3": 448,
+    "4": 170,
+    "5": 56,
+    "8": 8
+   }
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+   "local_profile": {
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+    "2": 368,
+    "3": 448,
+    "4": 170,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "M1_one_pair_448": {
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+    "kind": "only_edits_of",
+    "h": [
+     448
+    ],
+    "raises": [
+     873,
+     877
+    ]
+   },
+   "expected_sha": "988dda7cc11fb5cf11099df5f8e6230d9b2e561b9c7133f3eea76937bc2b8447",
+   "local_profile": {
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+    "2": 368,
+    "3": 448,
+    "4": 170,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "N1_drop_preread": {
+   "mutation": {
+    "kind": "drop_insert",
+    "k": 0
+   },
+   "rejection_expected": [
+    "exactness rows",
+    [
+     132,
+     135
+    ]
+   ]
+  },
+  "N2_wrong_sign_preread": {
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+    "kind": "flip_insert_sign",
+    "k": 0
+   },
+   "rejection_expected": [
+    "exactness rows",
+    [
+     132,
+     135
+    ]
+   ]
+  },
+  "N3_plain_join_moved_reads": {
+   "mutation": {
+    "kind": "drop_raises"
+   },
+   "expected_sha": "8a967b8b0f45cb0bc05ba39b1a5c031c60b289cf09a9e1854f48e9c3c2f6d7d7",
+   "local_profile": {
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+    "2": 401,
+    "3": 448,
+    "4": 158,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "N4_raise_dim7_at_855": {
+   "mutation": {
+    "kind": "frame",
+    "i": 870,
+    "frame": [
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+     128,
+     64,
+     40,
+     4,
+     2,
+     1
+    ]
+   },
+   "rejection_expected": [
+    "cap",
+    1257,
+    174
+   ]
+  }
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver/construction/leaver/REGROUP-LEAVER-k5.json b/research/gauge44-leaver/construction/leaver/REGROUP-LEAVER-k5.json
new file mode 100644
index 0000000000..c966d06f22
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/REGROUP-LEAVER-k5.json
@@ -0,0 +1,325 @@
+{
+ "source": "PR635 k492-jp8-frame_regroup + PR646 k480-jp8-frame_regroup, changes whose before gate occurs in the leaver port3 word",
+ "changes": [
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+    "3": -1
+   }
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+   }
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+    "2": 3,
+    "3": -1
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+  },
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+   ],
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+    "2": 3,
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+     8,
+     6
+    ]
+   ],
+   "delta": {
+    "1": -3,
+    "2": 3,
+    "3": -1
+   }
+  },
+  {
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+    1,
+    1,
+    [
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+     6
+    ]
+   ],
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+     65,
+     32,
+     16,
+     9,
+     6
+    ]
+   ],
+   "delta": {
+    "1": -3,
+    "2": 3,
+    "3": -1
+   }
+  }
+ ]
+}
diff --git a/research/gauge44-leaver/construction/leaver/TRI-LEAVER-k5.json b/research/gauge44-leaver/construction/leaver/TRI-LEAVER-k5.json
new file mode 100644
index 0000000000..68b16c9388
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/TRI-LEAVER-k5.json
@@ -0,0 +1,377 @@
+{
+ "full_pairs": [
+  [
+   0,
+   1
+  ],
+  [
+   2,
+   3
+  ],
+  [
+   4,
+   5
+  ],
+  [
+   6,
+   7
+  ]
+ ],
+ "triangles": [
+  {
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+    1
+   ],
+   "e": 1,
+   "reads": [
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+     [
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+      1,
+      2,
+      3
+     ],
+     0
+    ],
+    [
+     56,
+     [
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+      1,
+      2,
+      3
+     ],
+     1
+    ],
+    [
+     25,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     0
+    ],
+    [
+     24,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     1
+    ],
+    [
+     17,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     0
+    ],
+    [
+     16,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     1
+    ]
+   ],
+   "coded": true,
+   "cell": 0
+  },
+  {
+   "p": [
+    2,
+    3
+   ],
+   "e": 1,
+   "reads": [
+    [
+     63,
+     [
+      0,
+      1,
+      2,
+      3
+     ],
+     3
+    ],
+    [
+     59,
+     [
+      0,
+      1,
+      2,
+      3
+     ],
+     23
+    ],
+    [
+     89,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     0
+    ],
+    [
+     88,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     1
+    ],
+    [
+     81,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     0
+    ],
+    [
+     80,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     1
+    ]
+   ],
+   "coded": true,
+   "cell": 1
+  },
+  {
+   "p": [
+    4,
+    5
+   ],
+   "e": 1,
+   "reads": [
+    [
+     31,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     3
+    ],
+    [
+     27,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     23
+    ],
+    [
+     95,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     3
+    ],
+    [
+     91,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     23
+    ],
+    [
+     49,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     0
+    ],
+    [
+     48,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     1
+    ]
+   ],
+   "coded": true,
+   "cell": 2
+  },
+  {
+   "p": [
+    6,
+    7
+   ],
+   "e": 1,
+   "reads": [
+    [
+     23,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     3
+    ],
+    [
+     19,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     23
+    ],
+    [
+     87,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     3
+    ],
+    [
+     83,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     23
+    ],
+    [
+     55,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     3
+    ],
+    [
+     51,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     23
+    ]
+   ],
+   "coded": true,
+   "cell": 3
+  },
+  {
+   "p": [
+    6,
+    7
+   ],
+   "e": -1,
+   "reads": [
+    [
+     18,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     21
+    ],
+    [
+     22,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     2
+    ],
+    [
+     82,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     21
+    ],
+    [
+     86,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     2
+    ],
+    [
+     50,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     21
+    ],
+    [
+     54,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     2
+    ]
+   ],
+   "coded": true,
+   "cell": 4
+  }
+ ]
+}
diff --git a/research/gauge44-leaver/construction/leaver/build_frames_lv.py b/research/gauge44-leaver/construction/leaver/build_frames_lv.py
new file mode 100644
index 0000000000..5f8aa7a24b
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/build_frames_lv.py
@@ -0,0 +1,64 @@
+#!/usr/bin/env python3
+"""Apply the pinned gate/tail frame re-optimisation of FRAME-RECIPE-LV-k5.json (exact global frame optimum, gopt2) to the
+leaver U8 word.
+
+usage: build_frames_lv.py INPUT_WORD.json.gz OUT_DIR RECIPE.json
+
+Standard library only. The frames are applied by BlockInvert's `../promo/build_promotion.apply` (no entrances; 'B' gate
+frames and 'T' tail frames), which checks each old frame and recomputes the local profile and widths. This builder then checks:
+input sha pin; the scalar program of A, cut, B, precondition and cleanup unchanged (every field but the frame); start
+and end frames unchanged; local profile and width inventory equal to the recipe's; output sha pin. Three pin controls
+(input pin, wrong old frame, output pin) must be rejected at their pinned reasons on every build.
+Adapted from ../frames/build_frames.py (from PR741's extras/build_frames.py, chafreaky). Apache-2.0.
+"""
+import copy, gzip, hashlib, importlib.util, json, sys
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+_s = importlib.util.spec_from_file_location('promotion', HERE.parent / 'promo/build_promotion.py')
+B = importlib.util.module_from_spec(_s); _s.loader.exec_module(B)
+
+
+def construct(raw, recipe):
+    assert hashlib.sha256(raw).hexdigest() == recipe['input_content_sha256'], 'input word pin'
+    w = json.loads(raw)
+    assert recipe['gate_frames'] and all(c[0] in ('B', 'T') for c in recipe['gate_frames']), 'B and T frames only'
+    out = B.apply(w, dict(entrances={}, gate_frames=recipe['gate_frames']))
+    for section in ('A', 'cut', 'B', 'precondition', 'cleanup'):
+        assert [e[:-1] for e in w[section]] == [e[:-1] for e in out[section]], 'scalar program unchanged'
+    assert out['start_extra'] == w['start_extra'] and out['helper_final'] == w['helper_final'], 'endpoint frames unchanged'
+    assert out['report']['local_profile'] == recipe['expected']['local_profile'] and \
+        out['report']['width_inventory'] == recipe['expected']['width_inventory'], 'profile and width pins'
+    data = json.dumps(out, sort_keys=True, separators=(',', ':')).encode()
+    assert hashlib.sha256(data).hexdigest() == recipe['expected']['output_content_sha256'], 'output word pin'
+    return data
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    inp, outd, rfile = map(Path, sys.argv[1:4])
+    raw = gzip.decompress(inp.read_bytes()); recipe = json.loads(rfile.read_text())
+    data = construct(raw, recipe)
+    rejected = []
+    for name, change, reason in [
+            ('input-pin', lambda r: r.__setitem__('input_content_sha256', '0' * 64), 'input word pin'),
+            ('old-frame', lambda r: r['gate_frames'][0].__setitem__(2, []), 'gate frame mismatch'),
+            ('output-pin', lambda r: r['expected'].__setitem__('output_content_sha256', '0' * 64), 'output word pin')]:
+        r = copy.deepcopy(recipe); change(r)
+        try:
+            construct(raw, r)
+        except AssertionError as e:
+            assert reason in str(e), (name, str(e)); rejected.append(dict(name=name, reason=reason))
+        else:
+            raise AssertionError('accepted ' + name)
+    outd.mkdir(parents=True)
+    (outd / 'FULL-WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+    (outd / 'BUILD.json').write_text(json.dumps(dict(
+        status='PASS_FRAME_REOPT_EXACT_CONSTRUCTION', input_sha256=hashlib.sha256(raw).hexdigest(),
+        output_sha256=hashlib.sha256(data).hexdigest(), scalar_program_unchanged=True, frames=len(recipe['gate_frames']),
+        rejected_controls=rejected), indent=2) + '\n')
+    print('PASS', len(recipe['gate_frames']), 'frames and three pin controls')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/leaver/cells-k5/CORE-01+.json b/research/gauge44-leaver/construction/leaver/cells-k5/CORE-01+.json
new file mode 100644
index 0000000000..bfef820f29
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/cells-k5/CORE-01+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x0",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x0",
+   "-1/2"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver/construction/leaver/cells-k5/CORE-23+.json b/research/gauge44-leaver/construction/leaver/cells-k5/CORE-23+.json
new file mode 100644
index 0000000000..98ff8050e7
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/cells-k5/CORE-23+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y5",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver/construction/leaver/cells-k5/CORE-45+.json b/research/gauge44-leaver/construction/leaver/cells-k5/CORE-45+.json
new file mode 100644
index 0000000000..2bc89e1de1
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/cells-k5/CORE-45+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "1"
+  ],
+  [
+   "y5",
+   "x2",
+   "1"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "x4",
+   "x3",
+   "-2"
+  ],
+  [
+   "y1",
+   "x2",
+   "1"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y5",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "1"
+  ],
+  [
+   "y3",
+   "x2",
+   "1"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver/construction/leaver/cells-k5/CORE-67+.json b/research/gauge44-leaver/construction/leaver/cells-k5/CORE-67+.json
new file mode 100644
index 0000000000..7d756cb19d
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/cells-k5/CORE-67+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x5",
+   "1"
+  ],
+  [
+   "y3",
+   "x4",
+   "1"
+  ],
+  [
+   "y4",
+   "x3",
+   "1"
+  ],
+  [
+   "y5",
+   "x2",
+   "1"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "1"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y5",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "x5",
+   "1"
+  ],
+  [
+   "y2",
+   "x3",
+   "1"
+  ],
+  [
+   "y3",
+   "x2",
+   "1"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver/construction/leaver/cells-k5/CORE-67-.json b/research/gauge44-leaver/construction/leaver/cells-k5/CORE-67-.json
new file mode 100644
index 0000000000..7d756cb19d
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/cells-k5/CORE-67-.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x5",
+   "1"
+  ],
+  [
+   "y3",
+   "x4",
+   "1"
+  ],
+  [
+   "y4",
+   "x3",
+   "1"
+  ],
+  [
+   "y5",
+   "x2",
+   "1"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "1"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y5",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "x5",
+   "1"
+  ],
+  [
+   "y2",
+   "x3",
+   "1"
+  ],
+  [
+   "y3",
+   "x2",
+   "1"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver/construction/leaver/cgx_leaver.py b/research/gauge44-leaver/construction/leaver/cgx_leaver.py
new file mode 100644
index 0000000000..e686c66306
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/cgx_leaver.py
@@ -0,0 +1,491 @@
+# LeaverSAT: no-helper mutable-leaver all-K cells (coded triangles) on the no-triangle word. Generated by
+# LeaverSAT/mkpkg.py from construction/notri/cgx.py with the leaver edits (lv.leaver_source); Apache-2.0.
+import json as _lj, os as _lo, sys as _ls
+from fractions import Fraction as _lF
+CODED_CELLS=[(c['bindings'],[[t,s,_lF(q)] for t,s,q in c['scaled']]) for c in _lj.load(open(_lo.path.join(_lo.path.dirname(_lo.path.abspath(_ls.argv[3])),'CODED-CELLS.json')))]
+# Round20 early-coordinate-center / own-Y variant, prepared for icekylinx
+# with OpenAI Codex assistance. Apache-2.0. Scalar elementary-operation
+# helpers below are retained from the attributed PR514 construct_partial.py.
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+# AtomScout: leaver-read K-triangles (schedule from atom1.py / rog.py CP-SAT)
+TRI=json.loads(Path(sys.argv[3]).read_text())
+FULLT={(tuple(tr['p']),tr['e']) for tr in TRI['triangles']}
+TRI_COORDS={t+8 for tr in TRI['triangles'] for t,_,_ in tr['reads']}
+import os as _o
+COPYL=json.loads(open(_o.environ['XPARAM']).read()).get('copyl',[]) if _o.environ.get('XPARAM') else []
+NH=504-3*len(FULLT)+len(COPYL)
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+# Helper ids of the unpatched 504 construction: every allocation advances the 504 numbering; a packet copy that the
+# K-triangle schedule never forms advances it without allocating (HELPER-MAP.json).
+shadow=[];skipped=[];nxt=[2*v]
+def alloc():
+    n=len(cur);cur.append(());rows.append({});shadow.append(nxt[0]);nxt[0]+=1;return n
+def skip():
+    skipped.append(nxt[0]);nxt[0]+=1
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# Each source quartet supplies pair partials first. The other two coordinate
+# partitions supply eight early face packets without touching the eight
+# partials later copied into the preconditioned Y coordinates.
+SELECT=(0,0)
+PRIORITY=json.loads((INPUT/"COMPLETION-PRIORITY.json").read_text())
+import os
+XP=json.loads(open(os.environ['XPARAM']).read()) if os.environ.get('XPARAM') else {}
+XCH=XP.get('exch',{});PRIO=XP.get('prio',{})
+maps={};early={};own_rows={};pairs=[];tetrads={};block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)});maps[c]=mp
+    for ei,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[:40]):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        if ei==15:
+            for jj,cl in XCH.get(str(len(maps)-1),[[4,17],[5,19],[6,21],[7,23]]):swap(mp[jj],mp[cl],(P[ids[jj]],))
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in targets:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                t,u=sorted(ts);e2=R[t][q[0]]*R[t][q[1]]
+                pair={'targets':(t,u),'keys':[(c,p,eps),(c,q,e2)],'selected':pi==SELECT[parity],
+                      'matrix':[[R[a][p[0]],R[a][q[0]]] for a in (t,u)]}
+                pairs.append(pair)
+                if not pair['selected']:continue
+                zz=-Q(2*R[u][p[0]],R[t][p[0]])
+                sources=tet[1-parity]
+                for target,sign in ((t,-1),(u,1)):
+                    wanted={s:-Q(G[t][s],4)-sign*Q(G[u][s],2)/zz for s in sources
+                            if -Q(G[t][s],4)-sign*Q(G[u][s],2)/zz}
+                    assert len(wanted)==2
+                    candidates=[]
+                    for r in mp.values():
+                        if set(rows[r])!=set(wanted):continue
+                        s=next(iter(wanted));coef=wanted[s]/rows[r][s]
+                        if all(wanted[s]==coef*rows[r][s] for s in wanted):candidates.append((r,coef))
+                    assert len(candidates)==1
+                    r,coef=candidates[0];assert len(cur[r])==2
+                    own_rows[target]=(r,coef,cur[r])
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    needed={own_rows[t][0] for t in ids}
+    early[c]={j for j,e in enumerate(z['events'][40:]) if not ({mp[e[0]],mp[e[1]]}&needed)}
+    assert len(early[c])==8
+    retired=[]
+    for j in sorted(early[c]):
+        (t,s,a,b),F=z['events'][40+j],z['event_frames'][40+j]
+        add(mp[t],mp[s],Q(a,b),tuple(F));retired.append(mp[s])
+    assert not set(retired)&needed
+    # These eight retired rows already span every source coordinate. Keep
+    # them invertible and place the four coordinate totals in a changed basis.
+    F=basis([P[s] for s in ids]);assert len(F)==4
+    regs=sorted(retired,key=lambda r:(r>=v,r))
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    M=[[Q(R[s][i]) for s in ids] for i in c]
+    def qr_rank(rs):
+        bs={}
+        for r in rs:
+            r=r.copy()
+            for i,b in sorted(bs.items()):
+                if r[i]:q=r[i];r=[x-q*y for x,y in zip(r,b)]
+            i=next((i for i,x in enumerate(r) if x),None)
+            if i is not None:q=r[i];bs[i]=[x/q for x in r]
+        return len(bs)
+    assert qr_rank(M)==4
+    for rr0 in PRIO.get(",".join(map(str,c)),[])+PRIORITY[",".join(map(str,c))]["rows"]:
+        rr=list(map(Q,rr0))
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    for i in range(8):
+        if len(M)==8:break
+        rr=[Q(i==j) for j in range(8)]
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    assert len(M)==8
+    linear(regs,M,F)
+    for i,r in zip(c,regs):
+        assert rows[r]=={s:Q(R[s][i]) for s in ids}
+        block_totals[c,i]=r
+
+# All centers are complete while Y is still at zero. This is the crucial
+# difference from an illegal early-own-Y prefix using the old center order.
+centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+assert all(cur[v+t]==() for t in range(v))
+
+phase=B
+for t,(r,coef,F) in sorted(own_rows.items()):
+    if t in TRI_COORDS:continue
+    assert cur[r]==F
+    add(v+t,r,coef,F)
+# requests are needed for TRI coefficients
+requests=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    requests[key1].append((t,-Q(mat[0][0],2)))
+    requests[key2].append((u,-Q(mat[0][1],2)))
+reqcoef={t:(key,coef) for key,reqs in requests.items() for t,coef in reqs}
+def face_info(c,p,eps):
+    z=blocks[c];keys=[(pp,ee) for pp in it.combinations(c,2) for ee in (-1,1)]
+    r_local,alpha=z['outputs'][keys.index((p,eps))]
+    j=[j for j in range(40,len(z['events'])) if z['events'][j][0]==r_local];assert len(j)==1
+    return j[0],Q(alpha)
+tri_join_counts=Counter()
+coded_shadow_slot={}
+coded_target_edges=[];TRILOG=[]
+lcopy={}
+for s8 in COPYL:
+    r=s8+8;c=len(cur);cur.append(());rows.append({});shadow.append(None);add(c,r,1,cur[r]);lcopy[r]=c
+BF={c:basis([P[x] for x in z['receipt']['source_lines']]) for c,z in blocks.items()}
+HYB={(tuple(map(int,h[0])),tuple(map(int,h[1])),int(h[2])) for h in XP.get('hyb',[])}
+HYBLOG=[]
+def triread(t,blk,r,q):
+    F=basis(cur[v+t]+cur[r]);assert inside(F,hyper(P[t])),('TRI frame',t,blk,r,cur[v+t],cur[r],hyper(P[t]),[x for x in TRILOG if x[2]==r],HYBLOG)
+    tri_join_counts[len(F)]+=1;add(v+t,r,q,F);TRILOG.append([t,list(blk),r,str(q),list(F),list(cur[r])])
+for tr in TRI['triangles']:
+    if tr.get('coded'):
+        bindings={}
+        for name,binding in CODED_CELLS[tr['cell']][0].items():
+            bindings[name]=maps[tuple(binding[1])][binding[2]] if binding[0]=='source' else v+binding[1]
+        for tn,sn,q in CODED_CELLS[tr['cell']][1]:
+            target,source=bindings[tn],bindings[sn]
+            F=basis(cur[target]+cur[source])
+            for register in (target,source):
+                if v<=register<2*v:assert inside(F,hyper(P[register-v])),('coded frame',register,F)
+            add(target,source,q,F)
+            if sn.startswith('y'):coded_target_edges.append((target,source,Q(q)))
+        continue
+    p,eps=tuple(tr['p']),tr['e']
+    hb={blk for _,blk,_ in map(lambda x:(x[0],tuple(x[1]),x[2]),tr['reads']) if (blk,p,eps) in HYB}
+    own=[];rest=[]
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];r0=r;r=lcopy.get(r,r)
+        key,coef=reqcoef[t];assert key[1]==p and key[2]==eps,(key,p,eps)
+        if blk==key[0]:
+            rr,c0,F0=own_rows[t];assert rr==r0;own.append((t,blk,r,c0))
+        else:
+            j,alpha=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert loc in ev[:2]
+            rest.append((t,blk,loc,r,coef*alpha))
+    if not hb:
+        # original interleaved order
+        for t8,blk,loc in tr['reads']:
+            t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+            if blk==key[0]:q=own_rows[t][1]
+            else:j,alpha=face_info(blk,p,eps);q=coef*alpha
+            triread(t,blk,r,q)
+        continue
+    items=[]  # (kind, t, reg, q, blk)
+    for t,blk,r,q in own:items.append(('r',t,r,q,blk,blk in hb))
+    for blk in sorted(hb):items.append(('e',None,None,None,blk,True))
+    done=set()
+    for t,blk,loc,r,q in rest:
+        if blk in hb:
+            j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j]
+            ws=[x for x in rest if x[0]==t and x[1]==blk];assert len(ws)==2 and ws[0][4]==ws[1][4] and {ws[0][2],ws[1][2]}==set(ev[:2])
+            if (t,blk) in done:continue
+            done.add((t,blk));items.append(('m',t,maps[blk][ev[0]],q,blk,True))
+        else:items.append(('r',t,r,q,blk,False))
+    # Original read order with the two half reads collapsed into one M read at the first half's slot; the face event goes
+    # just before the first M read of its block; own reads of the M register are hoisted ahead of that event.
+    def evinfo(blk):
+        j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert ev[2]==ev[3]==1,ev
+        mpb=maps[blk];return mpb[ev[0]],mpb[ev[1]],tuple(blocks[blk]['event_frames'][j])
+    items=[]
+    seen=set()
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+        if blk==key[0]:items.append(('r',t,r,own_rows[t][1],blk,blk in hb))
+        else:
+            j,alpha=face_info(blk,p,eps);q=coef*alpha
+            if blk in hb:
+                if (t,blk) not in seen:seen.add((t,blk));continue
+                items.append(('m',t,evinfo(blk)[0],q,blk,True))
+            else:items.append(('r',t,r,q,blk,False))
+    for blk in sorted(hb):
+        k0=min(i for i,x in enumerate(items) if x[0]=='m' and x[4]==blk)
+        items.insert(k0,('e',None,None,None,blk,True))
+    n=len(items)
+    def step(it,st):
+        k,t,r,q,blk,h=it;g=lambda x:st.get(x,cur[x])
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(g(a_))+list(g(b_)))
+            return {a_:FF,b_:FF} if inside(FF,BF[blk]) else None
+        F=basis(list(g(v+t))+list(g(r)))
+        if not inside(F,hyper(P[t])):return None
+        if h and k=='r' and r==evinfo(blk)[1] and not inside(F,BF[blk]):return None
+        return {v+t:F,r:F}
+    def allowed(i,used):
+        k,t,r,q,blk,h=items[i]
+        evi=[j for j,x in enumerate(items) if x[0]=='e' and x[4]==blk] if h else []
+        if k=='e':return all(j in used for j,x in enumerate(items) if x[0]=='r' and x[4]==blk and x[5] and x[2]==evinfo(blk)[0])
+        if k=='m':return evi[0] in used
+        if k=='r' and h and r==evinfo(blk)[0]:return evi[0] not in used
+        return True
+    budget=[int(os.environ.get('HYBBUDGET','300000'))];memo=set()
+    def dfs(st,used,order):
+        if len(order)==n:return order
+        budget[0]-=1
+        if budget[0]<0:return None
+        sig=(used,tuple(sorted(st.items())))
+        if sig in memo:return None
+        memo.add(sig)
+        for i in range(n):
+            if i in used or not allowed(i,used):continue
+            d=step(items[i],st)
+            if d is None:continue
+            ns=dict(st);ns.update(d);res=dfs(ns,used|{i},order+[i])
+            if res:return res
+        return None
+    import sys as _s;_s.setrecursionlimit(20000)
+    order=dfs({},frozenset(),[])
+    assert order,('no feasible hybrid order',p,eps,sorted(hb),budget)
+    for i in order:
+        k,t,r,q,blk,h=items[i]
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(cur[a_])+list(cur[b_]));add(a_,b_,1,FF);HYBLOG.append([list(blk),list(p),eps,list(FF)])
+        else:triread(t,blk,r,q)
+
+packets={}
+for c,z in sorted(blocks.items()):
+    mp=maps[c]
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    skipev={face_info(c,p,eps)[0] for p,eps in keys if (p,eps) in FULLT}
+    for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]):
+        if j not in early[c] and 40+j not in skipev:
+            t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    for key,(r,alpha) in zip(keys,z['outputs']):
+        if tuple(key) in FULLT:skip();continue
+        a=mp[r];b=alloc();add(b,a,1,cur[a])
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha))
+
+# Both tetrahedra use the same partition. A selected key has exactly two
+# selected Y loads and no ordinary M consumer. Supply its two raw halves in
+# opposite orders and never form that M. Other keys retain the old M path.
+second=[];first_join_counts=Counter()
+for key,reqs in sorted(requests.items()):
+    assert len(reqs)==2
+    c,p,eps=key
+    if (p,eps) in FULLT:continue
+    ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds
+    for j,(target,coef) in enumerate(sorted(reqs)):
+        first_source,second_source=(a,b) if j==0 else (b,a)
+        r,alpha=packets[first_source,p,eps,second_source]
+        F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+        first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F)
+        r,alpha=packets[second_source,p,eps,c]
+        second.append((target,r,coef*alpha))
+
+Ms={}
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for eps in (-1,1):
+            if (c,p,eps) in requests:continue
+            (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,eps]=(a,alpha)
+
+consumers=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    for key in pair['keys']:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    if key in requests:
+        assert all(pairs[i]['selected'] for i in uses)
+        continue
+    assert all(not pairs[i]['selected'] for i in uses)
+    a,alpha=Ms[key]
+    for j,pid in enumerate(uses):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+assert len(cur)-240==NH,len(cur)-240
+
+selected_join_counts=Counter()
+for target,r,coef in second:
+    F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+    selected_join_counts[len(F)]+=1;add(v+target,r,coef,F)
+output_basis=[]
+for pair in pairs:
+    if not pair['selected']:continue
+    (t,u),mat=pair['targets'],pair['matrix']
+    F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u]))
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert rows[v+t]==expected,('side identity',t)
+
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+for target,source,q in reversed(coded_target_edges):
+    scatter[target-v]=[a-q*b for a,b in zip(scatter[target-v],scatter[source-v])]
+    precondition.append(['add',target,source,-q.numerator,q.denominator,[]])
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8
+assert sum(r*z for r,z in H.items())==9*NH+240*8+72,sum(r*z for r,z in H.items())
+
+def apply(e,matrix):
+    if e[0]=='add':
+        _,t,s,a,b,*_=e;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    e[-1]=list(FULL);return e
+cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q]
+cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v]
+matrix=[{r:Q(1)} if r<v else {} for r in range(len(cur))]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(len(cur)))
+
+# Restrict the eight isolated axis ports exactly, keeping the stable 112-port
+# label set. This variant changes the local word, not the outer geometry.
+mp={s:s-8 for s in range(8,120)}
+mp.update({120+s:112+s-8 for s in range(8,120)})
+mp.update({240+r:224+r for r in range(NH)})
+def restrict(events,is_cut=False):
+    out=[]
+    for e in events:
+        regs=e[1:3] if e[0]=='add' else e[1:2]
+        if any(r not in mp for r in regs):
+            assert is_cut and e[0]=='add' and e[1]-120==e[2] and e[2]<8 and e[3:5]==[1,1]
+            continue
+        q=copy.deepcopy(e);q[1]=mp[q[1]]
+        if q[0]=='add':q[2]=mp[q[2]]
+        out.append(q)
+    return out
+H.subtract({1:8,8:16});H=+H
+report={'status':'EXACT_CLEAN_OWN_Y_EARLY_CENTER_WORD_NOT_ADMITTED',
+        'h':9,'v':112,'R':NH,'cst':64,'m':73,'local_profile':dict(sorted(H.items())),
+        'centre_ranks':[8]*8,**({'tri_join_counts':dict(tri_join_counts)} if TRI['triangles'] else {}),'selected_load_join_counts':dict(selected_join_counts),'selected_partitions':list(SELECT),'first_load_join_counts':dict(first_join_counts),
+        'source_columns_exact':112,'borrowed_output_pairs':56,'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'local_rank_mass':sum(r*n for r,n in H.items()),'scope':'Clean scalar identity and all literal monotone local frames only; arbitrary-dirt compensation, entrance kernels, exact phase recipes, and global hosting/pricing are not yet certified.'}
+word={'report':report,'ports':P[8:],'root_lines':R[8:],
+      'A':restrict(A),'B':restrict(B),'cut':restrict(cut,True),'cleanup':restrict(cleanup),'precondition':restrict(precondition),
+      'centers':[mp[r] for r in centers[:8]],'center_frames':center_frames[:8],
+      'scatter':[[str(x) for x in row[:8]] for row in scatter[8:]]}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+assert len(shadow)==NH and len([x for x in shadow if x is not None])+len(skipped)==504
+hmap={**{r:r for r in range(224)},**{224+s_-240:224+i for i,s_ in enumerate(shadow) if s_ is not None}}
+(OUT/'HELPER-MAP.json').write_text(json.dumps({'map':{str(k):hmap[k] for k in sorted(hmap)},'removed_504_helpers':[224+s_-240 for s_ in skipped]})+'\n')
+(OUT/'TRILOG.json').write_text(json.dumps(dict(reads=TRILOG,hyb=HYBLOG)));(OUT/'DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/gauge44-leaver/construction/leaver/layer_end_controls_leaver.py b/research/gauge44-leaver/construction/leaver/layer_end_controls_leaver.py
new file mode 100644
index 0000000000..aff450d4a3
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/layer_end_controls_leaver.py
@@ -0,0 +1,209 @@
+"""layer_end_controls_leaver.py LAYERED-WORD.json.gz ROUTING OUTDIR [ENTERING] (env PR635_CODE, optional env LEC_REASON_PINS
+= JSON file {mutant key: expected reason key or literal message substring}).  LeaverSAT variant of the signed
+layers_p6n/layer_end_controls.py (fc58c569...): IDENTICAL mutations and checks; the only change is that the expected
+rejection reason of a named mutant can be re-pinned per word (on the leaver words, with fewer cold ends, the premix-drop
+and into-full mutants are caught by the arbitrary-dirt endpoint replay before the pinned site is reached).  Every
+mutation is still REQUIRED to be rejected at its (re-)pinned reason; the unmutated word MUST pass.
+Original docstring: layer_end_controls.py LAYERED-WORD.json.gz ROUTING OUTDIR (env PR635_CODE): adapted PR635 cold_end_controls.py (LayerReviewer): raw-word negative controls for the cold low-frame ends and the
+refactored cleanup accepted by hpe_audit_and_transport.py.  Every mutation MUST be rejected (AssertionError); the
+unmutated word MUST pass.  Apache-2.0.  DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code."""
+import copy, gzip, json, shutil, sys, tempfile
+from pathlib import Path
+import os
+sys.path.insert(0, os.environ['PR635_CODE'])   # PR635's unchanged hpe_audit_and_transport.py
+import hpe_audit_and_transport as atc
+
+src, routing, outdir = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3])
+word = json.load(gzip.open(src))
+v, R = word['report']['v'], word['report']['R']; n = 2*v + R
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+meta = word['refactored_cleanup']
+cold = [int(h) for h in meta['cold_low_frame_ended_helpers']]
+npre = meta['premix_gates']; nlow = meta['lower_frame_gates']
+early = word['early_cleanup']; eidx = {i for i, _ in early}
+rest = [i for i in range(len(word['cleanup'])) if i not in eidx]
+
+
+def trial(w):
+    """None if the transport audit accepts w, else the AssertionError message."""
+    tmp = Path(tempfile.mkdtemp())
+    p = tmp/'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w).encode(), mtime=0))
+    try:
+        atc.run(p, routing, tmp/'out')
+        return None
+    except AssertionError as e:
+        return repr(e.args[0]) if e.args else 'AssertionError'
+    finally:
+        shutil.rmtree(tmp, ignore_errors=True)
+
+
+# Pinned rejection reasons: each mutant must fail at this assertion of hpe_audit_and_transport.py (message substring).
+ENDPOINT, COLDPRE, CONE = "'arbitrary-dirt endpoint'", 'touches a cold hyperplane-ended helper', 'hpe cone pre-check (row / column)'
+WHY = dict(premix_to_precondition=COLDPRE, premix_dropped=COLDPRE, e_premix_dropped=ENDPOINT, lower_dropped=ENDPOINT,
+           remainder_dropped=ENDPOINT, coefficient=ENDPOINT, into_full='cleanup on non-FULL end', dyadic=ENDPOINT, frame_below="'nonmonotone'",
+           nonmonotone="'nonmonotone'", other_frame=CONE, cone=CONE, extra_end=COLDPRE, marker='cleanup is not the literal reversed inverse',
+           target='refactored cleanup touches a target', profile_pin='paid local profile differs from the reported local_profile',
+           entering_precondition='zero-frame precondition/compensation touches an entering helper')
+_REASONS = dict(ENDPOINT=ENDPOINT, COLDPRE=COLDPRE, CONE=CONE)
+if os.environ.get('LEC_REASON_PINS'):
+    for _k, _v in json.loads(Path(os.environ['LEC_REASON_PINS']).read_text()).items():
+        assert _k in WHY, ('unknown mutant key', _k); WHY[_k] = _REASONS.get(_v, _v)
+assert trial(word) is None, 'unmutated cold-end word must pass'
+results = []
+
+
+def reject(name, mut, why):
+    """the mutation must be rejected, and for the pinned reason (a substring of the audit's assertion message)."""
+    w = copy.deepcopy(word); mut(w)
+    msg = trial(w)
+    assert msg is not None, 'cold-end mutation accepted: ' + name
+    assert why in msg, 'cold-end mutation %r rejected for the wrong reason: %s' % (name, msg[:300])
+    results.append(name); print('rejected', name, '|', why, flush=True)
+
+
+h0 = cold[0]
+i0, U0 = next((i, f) for i, f in early if h0 in regs(word['cleanup'][i]))
+r0 = rest[len(rest)//2]
+
+
+def premix_to_precondition(w):   # premix before the wrappers; compensation then reads the cold ends
+    w['precondition'] = w['precondition'] + w['A'][:npre]; w['A'] = w['A'][npre:]
+
+
+def lower_gate_into_full(w):     # a lower-frame gate on a cold-ended helper executed in the FULL remainder instead
+    w['early_cleanup'] = [x for x in w['early_cleanup'] if x[0] != i0]
+
+
+def drop_cleanup_gate(w, i):   # remove the gate AND its early_cleanup entry: a structurally valid word missing one gate
+    w['cleanup'].pop(i)
+    w['early_cleanup'] = [[j - (j > i), f] for j, f in w['early_cleanup'] if j != i]
+
+
+def other_frame(w):              # a different frame of the same dimension as the cold end (another cold helper's)
+    f = next(w['helper_final'][str(h)] for h in cold if w['helper_final'][str(h)] != w['helper_final'][str(h0)])
+    w['helper_final'][str(h0)] = f
+
+
+def extra_cold_end(w):           # declare a premixed partner of h0 cold-ended at h0's frame: fails the row/column cone
+    p = next(r for e in w['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    w['helper_final'][str(p)] = w['helper_final'][str(h0)]
+
+
+reject('premix placed in the zero-frame precondition (before the cold wrappers)', premix_to_precondition, WHY['premix_to_precondition'])
+reject('one premix gate dropped (the compensation then reads a cold-ended helper)', lambda w: w['A'].pop(npre - 1), WHY['premix_dropped'])
+reject('one lower-frame cleanup gate dropped (gate and its early_cleanup entry)', lambda w: drop_cleanup_gate(w, i0), WHY['lower_dropped'])
+reject('one FULL-remainder gate dropped', lambda w: drop_cleanup_gate(w, r0), WHY['remainder_dropped'])
+reject('lower-frame gate coefficient changed', lambda w: w['cleanup'][i0].__setitem__(3, w['cleanup'][i0][3] * 2), WHY['coefficient'])
+reject('lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)', lower_gate_into_full, WHY['into_full'])
+reject('lower-frame gate frame below its registers\' frames', lambda w: next(x for x in w['early_cleanup'] if x[0] == i0).__setitem__(1, U0[:-1]), WHY['frame_below'])
+reject('cold end at another dim-4 frame', other_frame, WHY['other_frame'])
+# PROFILE-PIN control: without its helper_final entry the cold-ended helper is a valid FULL-ended helper; the word is
+# rejected because its reported paid profile (which counts the low end) no longer matches the frame chains.
+reject('profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)', lambda w: w['helper_final'].pop(str(h0)), WHY['profile_pin'])
+reject('extra cold end on a premixed partner (the compensation reads it before its wrapper)', extra_cold_end, WHY['extra_end'])
+reject('refactored-cleanup marker removed (literal-inverse rule applies)', lambda w: w.pop('refactored_cleanup'), WHY['marker'])
+reject('remainder gate retargeted to a target register', lambda w: w['cleanup'][r0].__setitem__(1, v + 3), WHY['target'])
+reject('non-dyadic remainder coefficient', lambda w: w['cleanup'][r0].__setitem__(4 if w['cleanup'][r0][0] == 'add' else 3, 3 * w['cleanup'][r0][4 if w['cleanup'][r0][0] == 'add' else 3]), WHY['dyadic'])
+reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('5', w['report']['local_profile']['5'] - 1), WHY['profile_pin'])
+ent = [int(h) for h in sys.argv[4].split(',')] if len(sys.argv) > 4 else [int(h) for h in meta.get('entering_low_frame_ended_helpers', [])]
+for e0 in ent:   # ENTERING LOW-FRAME ENDS (ColdSupply extension; every entering end; absent for words without them)
+    j0 = next((i for i, e in enumerate(word['A'][:npre]) if e0 in regs(e)), None)
+    print('entering end', e0, 'premix gate', j0, flush=True)
+    k0, Ue = next((i, f) for i, f in early if e0 in regs(word['cleanup'][i]))
+    def to_pre(w, j0=j0): w['precondition'].append(w['A'][j0]); w['A'].pop(j0)
+    def other_hp(w, e0=e0, Ue=Ue): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Ue) and sorted(f) != sorted(Ue))
+    if j0 is not None: reject('entering end %d: premix gate dropped' % e0, lambda w, j0=j0: w['A'].pop(j0), WHY['e_premix_dropped'])
+    if j0 is not None: reject('entering end %d: premix gate at frame [] instead of its entrance E' % e0, lambda w, j0=j0: w['A'][j0].__setitem__(-1, []), WHY['nonmonotone'])
+    if j0 is not None: reject('entering end %d: premix gate moved into the zero-frame precondition' % e0, to_pre, WHY['entering_precondition'])
+    reject('entering end %d: lower-frame gate dropped (gate and its early_cleanup entry)' % e0, lambda w, k0=k0: drop_cleanup_gate(w, k0), WHY['lower_dropped'])
+    reject('entering end %d: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)' % e0, lambda w, e0=e0: w['helper_final'].pop(str(e0)), WHY['profile_pin'])
+    reject('entering end %d: end at another hyperplane' % e0, other_hp, WHY['cone'])
+# Pinned rejection reasons of the COLD-BEYOND mutants (substrings of hpe_audit_and_transport.py assertion messages).
+MYWHY = dict(tw_precondition=COLDPRE, tw_dropped=COLDPRE, tw_coefficient=COLDPRE, tw_other_block=COLDPRE,
+             tw_entering='zero-frame compensation reads an entering helper',
+             ab_dropped=ENDPOINT, ab_coefficient=ENDPOINT, ab_early=ENDPOINT, ab_live=ENDPOINT, ab_centre=ENDPOINT,
+             ab_lower="'nonmonotone'", ab_higher="'nonmonotone'",
+             sh_dropped=ENDPOINT, sh_coefficient=ENDPOINT, rel_dropped=ENDPOINT, rel_coefficient=ENDPOINT, rel_live=ENDPOINT,
+             h8_other=CONE, h8_lower=ENDPOINT)
+# COLD-BEYOND primitives (present only when the word carries them): frame-[] target writes in the premix (explicit
+# post-wrapper compensation of an ended helper's dirt) and forward absorptions into dead registers.
+nw = meta.get('premix_target_writes', 0)
+if nw:
+    wi = [i for i in range(npre) if v <= word['A'][i][1] < 2*v]
+    assert len(wi) == nw
+
+    def writes_to_precondition(w):   # the target writes run before the cold wrappers (inside the zero-frame precondition)
+        g = [w['A'][i] for i in wi]; w['precondition'] = w['precondition'] + g
+        w['A'] = [e for i, e in enumerate(w['A']) if i not in set(wi)]
+    reject('premix target writes placed in the zero-frame precondition (before the cold wrappers)', writes_to_precondition, MYWHY['tw_precondition'])
+    reject('one premix target write dropped (compensation must read an ended helper)', lambda w: w['A'].pop(wi[0]), MYWHY['tw_dropped'])
+    reject('premix target write coefficient changed', lambda w: w['A'][wi[0]].__setitem__(3, w['A'][wi[0]][3] * 2), MYWHY['tw_coefficient'])
+    # (reading another register that carries the SAME weight of the ended helper's dirt is a valid variant, so the mutant reads
+    #  the same factory slot of the next block, which carries none of it)
+    entering_regs = sorted(int(r) for r in word.get('start_extra', {}))
+    reject('premix target write reads an entering helper', lambda w: w['A'][wi[0]].__setitem__(2, entering_regs[0]), MYWHY['tw_entering'])
+    reject('premix target write reads a cold helper of another block', lambda w: w['A'][wi[0]].__setitem__(2, 2*v + (w['A'][wi[0]][2] - 2*v + 16) % 224), MYWHY['tw_other_block'])
+ab = meta.get('forward_absorption_A_indices', [])
+if any(len(word['helper_final'][str(h)]) == 8 for h in cold):
+    # with dim-8 cold ends, the centre-retargeted absorption first leaks an ended helper's dirt into the cut's targets
+    MYWHY['ab_centre'] = COLDPRE
+if ab:
+    # the ColdBeyond U_b absorption (q += -1/2 g); ColdThird's extra absorptions have their own controls below
+    a0 = next(a for a in ab if word['A'][a][3] * 2 == -word['A'][a][4]); g0 = word['A'][a0]
+
+    def absorption_moved_early(w):   # absorbed before the absorbed register's last kernel write
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[2] == w['A'][i][1] and w['A'][i][-1] == g0[-1])
+        w['A'].insert(j, e)
+
+    def absorption_into_live(w):     # q += a g moved right after g's previous frame-mate gate, while q is still live
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[1] in regs(w['A'][i]))
+        w['A'].insert(j, e)
+    reject('forward absorption dropped', lambda w: w['A'].pop(a0), MYWHY['ab_dropped'])
+    reject('forward absorption into a centre (a live register read by the cut)', lambda w: w['A'][a0].__setitem__(1, next(c for c in word['centers'] if c not in g0[1:3] and c not in cold)), MYWHY['ab_centre'])
+    reject('forward absorption coefficient changed', lambda w: w['A'][a0].__setitem__(3, w['A'][a0][3] * 2), MYWHY['ab_coefficient'])
+    reject('forward absorption placed before the absorbed register\'s last kernel write', absorption_moved_early, MYWHY['ab_early'])
+    reject('forward absorption placed while the absorbing register is still live', absorption_into_live, MYWHY['ab_live'])
+    reject('forward absorption at a lower frame than its registers', lambda w: w['A'][a0].__setitem__(-1, w['A'][a0][-1][:-1]), MYWHY['ab_lower'])
+    reject('forward absorption at a higher frame (FULL) than its registers', lambda w: w['A'][a0].__setitem__(-1, [256, 128, 64, 32, 16, 8, 4, 2, 1]), MYWHY['ab_higher'])
+# COLD-THIRD primitives (present only when the word carries them): several absorptions after one input gate, dirt-release
+# absorptions (a dead port takes a live helper's value so that a hyperplane unit's column has no dirt on it), and cold ends at
+# a dim-8 frame with lifted partners.
+hyper = [h for h in cold if len(word['helper_final'][str(h)]) == 8]
+if hyper and ab:
+    sh = next(a for a, b in zip(ab, ab[1:]) if b == a + 1)              # two absorptions sharing one input anchor
+    rel = next(a for a in ab if a - 1 not in ab and a + 1 not in ab and word['A'][a][2] in hyper and word['A'][a][3] * 2 != -word['A'][a][4])
+    hh = hyper[0]; ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+    reject('second absorption sharing an input anchor dropped', lambda w: w['A'].pop(sh + 1), MYWHY['sh_dropped'])
+    reject('shared-anchor absorption coefficient changed', lambda w: w['A'][sh + 1].__setitem__(3, w['A'][sh + 1][3] * 2), MYWHY['sh_coefficient'])
+    reject('dirt-release absorption dropped', lambda w: w['A'].pop(rel), MYWHY['rel_dropped'])
+    reject('dirt-release absorption coefficient changed', lambda w: w['A'][rel].__setitem__(3, w['A'][rel][3] * 2), MYWHY['rel_coefficient'])
+    jr = max(i for i in range(npre, rel) if word['A'][i][0] == 'add' and word['A'][i][2] == word['A'][rel][1])
+
+    def release_while_read(w):   # the release runs before a kernel gate that still READS the port (port live)
+        e = w['A'].pop(rel); w['A'].insert(jr, e)
+    reject('dirt-release absorption moved before a kernel gate that still reads the port', release_while_read, MYWHY['rel_live'])
+if hyper:
+    # dim-8 cold-end controls for EVERY dim-8 cold end of the word (read from the word's helper_final and the recipe meta's
+    # cold_low_frame_ended_helpers), not one representative per terminal frame
+    for hh in hyper:
+        ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+        Uh = word['helper_final'][str(hh)]
+        reject('dim-8 cold end %d (frame %s) at another dim-8 frame' % (hh, Uh), lambda w, hh=hh: w['helper_final'].__setitem__(str(hh), next(f for h, f in w['helper_final'].items() if len(f) == 8 and sorted(f) != sorted(w['helper_final'][str(hh)]))), MYWHY['h8_other'])
+        reject('dim-8 cold end %d (frame %s): one lower-frame gate dropped (gate and its early_cleanup entry)' % (hh, Uh), lambda w, ih=ih: drop_cleanup_gate(w, ih), MYWHY['h8_lower'])
+        reject('dim-8 cold end %d (frame %s): profile pin (end dropped)' % (hh, Uh), lambda w, hh=hh: w['helper_final'].pop(str(hh)), WHY['profile_pin'])
+# FACTORED ACCUMULATOR (CarrierBypass; present only when the word carries one): a lower-frame tail gate a += x*g on two
+# non-ended registers whose accumulator a is afterwards read by a dim-8 cold end's tail gate (h += y*a at its U).
+ended_all = {int(h) for h in word['helper_final']}
+tailg = [(i, word['cleanup'][i]) for i, _ in early]
+accs = []   # EVERY factored accumulator gate (one per accumulator register a), each controlled on its own
+for k, (i, e) in enumerate(tailg):
+    if e[0] == 'add' and e[1] not in ended_all and e[2] not in ended_all and len(next(f for j, f in early if j == i)) < 8:
+        if e[1] not in [word['cleanup'][j][1] for j in accs] and any(t[0] == 'add' and t[2] == e[1] and t[1] in hyper for _, t in tailg[k + 1:]):
+            accs.append(i)
+for acc in accs:
+    a = word['cleanup'][acc][1]
+    reject('factored accumulator %d (gate %d) zeroed' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, 0), ENDPOINT)
+    reject('factored accumulator %d (gate %d) coefficient doubled' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, w['cleanup'][acc][3] * 2), ENDPOINT)
+outdir.mkdir(parents=True, exist_ok=True)
+(outdir/'COLD-END-CONTROLS.json').write_text(json.dumps(dict(status='PASS_COLD_END_RAW_WORD_CONTROLS', word=str(src), rejected=results), indent=1) + '\n')
+print('PASS', len(results), 'cold-end raw-word mutations rejected')
diff --git a/research/gauge44-leaver/construction/leaver/reproduce_leaver.py b/research/gauge44-leaver/construction/leaver/reproduce_leaver.py
new file mode 100644
index 0000000000..bc4360ef93
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/reproduce_leaver.py
@@ -0,0 +1,177 @@
+#!/usr/bin/env python3
+"""Rebuild the leaver word: the no-triangle word with no-helper mutable-leaver all-K cells, and its native locals.
+
+Each cell (pair p, sign e) replaces the three face events of the blocks containing p and their three packet copies
+by a 21-gate circuit on the cell's six leaver sources x_j (the face-event operands, which have no later reads and are
+restored by the inherited cleanup at FULL) and its six targets y_i: 3 leaver gates x_k += c x_m, 3 target gates
+y_a += c y_b (inverted at frame zero in the precondition and scatter, #781's recipe) and 15 reads y_i += c x_j.
+Unit circuit (LeaverSAT, layered CP-SAT on the exact set model), relabelled per cell so that no y += y source carries
+port-stage entering-helper dirt at the gate; coefficients rescaled exactly to the cell (C_ij = r_i c_j).
+Input: a fresh `construction/reproduce.py --until word` output directory (hamming/, shadow-early/, shadow-prefix/).
+Steps, each checked exactly (pins in LEAVER-PINS.json):
+  0. cells: CODED-CELLS.json's scaled gates are re-derived from the unit circuits and the cell coefficients, and the
+     clean map Y_i = sum_j C_ij X_j is checked in exact rationals.
+  1. gauge-forward: cgx_leaver.py (notri/cgx.py + the leaver edits) with TRI-LEAVER.json, XPARAM = notri/PRIO6.json.
+  2. port0-3: notri/port_stage_x.py.
+  3. regroup: REGROUP-LEAVER.json's changes where their `before` gate occurs (count pinned).
+  4. hpe: PR635's build_hpe.candidates greedy with disjoint registers, build_hpe.apply (recipe pinned).
+  5. cold44: notri/cold44x.py with EXTRAH and pinned pairing ranks; output sha, profile and widths pinned.
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs (pins).
+Apache-2.0. LeaverSAT (Claude Code research agent), driver after construction/notri/reproduce_notri.py.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, shutil, subprocess, sys, time
+from fractions import Fraction
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NOTRI = HERE.parent / 'notri'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def dump(p, v):
+    p.parent.mkdir(parents=True, exist_ok=True); p.write_bytes(gzip.compress(enc(v), mtime=0))
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def check_cells(cells):
+    for c in cells:
+        C = [[Fraction(q) for q in r] for r in c['coefficients']]
+        col = [None] * 6; row = [Fraction(1)] + [None] * 5
+        for j in range(1, 6): col[j] = C[0][j]
+        col[0] = C[1][0] / (C[1][2] / col[2])
+        for i in range(1, 6): row[i] = C[i][(i + 1) % 6] / col[(i + 1) % 6]
+        assert all(C[i][j] == row[i] * col[j] for i in range(6) for j in range(6) if i != j), ('rank-one cell', c['cell'])
+        idx = lambda s: int(s[1:])
+        scaled = []
+        for t, s, q in c['unit']:
+            assert Fraction(q) == 1
+            if t[0] == 'x': assert s[0] == 'x'; q = col[idx(s)] / col[idx(t)]
+            elif s[0] == 'y': q = row[idx(t)] / row[idx(s)]
+            else: q = row[idx(t)] * col[idx(s)]
+            scaled.append([t, s, str(q)])
+        assert scaled == c['scaled'], ('scaled gates', c['cell'])
+        R = {f'x{j}': {j: Fraction(1)} for j in range(6)}; R.update({f'y{i}': {} for i in range(6)})
+        for t, s, q in scaled:
+            for k, x in list(R[s].items()): R[t][k] = R[t].get(k, 0) + Fraction(q) * x
+        for i in range(6):
+            assert {k: x for k, x in R[f'y{i}'].items() if x} == {j: C[i][j] for j in range(6) if j != i}, ('clean map', c['cell'], i)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--word-dir', type=Path, required=True, help='construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    ap.add_argument('--word-only', action='store_true', help='stop after the pinned scalar word (input to the layers)')
+    ap.add_argument('--id', default='k5', help='cell set: TRI-LEAVER-<id>, CODED-CELLS-<id>, REGROUP-LEAVER-<id>, LEAVER-PINS-<id>')
+    ap.add_argument('--record-pins', action='store_true', help='write LEAVER-PINS.json from this run instead of checking')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    pins = {} if a.record_pins else read(HERE / ('LEAVER-PINS-%s.json' % a.id)); got = {}
+    def pin(k, v):
+        got[k] = v
+        if not a.record_pins: assert pins[k] == v, ('pin', k, v, pins[k])
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    structural = a.main.resolve() / 'research/structural-gain/frontier-composition'
+    wd = a.word_dir.resolve()
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    # 0. cells
+    cells = read(HERE / ('CODED-CELLS-%s.json' % a.id)); check_cells(cells); print('PASS cells', [c['cell'] for c in cells], flush=True)
+    # 1. gauge-forward
+    shutil.copy(HERE / ('TRI-LEAVER-%s.json' % a.id), out / 'TRI.json'); shutil.copy(HERE / ('CODED-CELLS-%s.json' % a.id), out / 'CODED-CELLS.json')
+    env['XPARAM'] = str(NOTRI / 'PRIO6.json')
+    raw = out / 'raw'
+    run('gauge-forward', HERE / 'cgx_leaver.py', wd / 'hamming', raw, out / 'TRI.json')
+    word = raw / 'FULL-WORD.json.gz'; pin('raw_sha256', hashlib.sha256(enc(read(word))).hexdigest())
+    # 2. port stages
+    chain = [parent / 'complex-local/static44/inputs/RAW504.json.gz', structural / 'global-replay/base/split-centres/FULL-WORD.json.gz',
+             wd / 'shadow-early/FULL-WORD.json.gz', structural / 'multicold-eight-word/FULL-WORD.json.gz',
+             wd / 'shadow-prefix/FULL-WORD.json.gz']
+    for i, (b, c) in enumerate(zip(chain, chain[1:])):
+        t = out / ('port%d' % i)
+        run('port%d' % i, NOTRI / 'port_stage_x.py', '--shadow-input', b, '--shadow-output', c, '--input', word,
+            '--map', raw / 'HELPER-MAP.json', '--gk-dir', gk, '--out', t)
+        word = t / 'FULL-WORD.json.gz'
+    # 3. regroup
+    w = read(word); rg = {json.dumps(c['before']): c['after'] for c in read(HERE / ('REGROUP-LEAVER-%s.json' % a.id))['changes']}
+    n = 0
+    for part in ('A', 'B'):
+        for i, e in enumerate(w[part]):
+            k = json.dumps(e)
+            if k in rg: w[part][i] = rg[k]; n += 1
+    sys.path.insert(0, str(gk)); import gk_word as GW, gk_common as GC
+    GW.V = GC.V = 112; GW.DATA = GC.DATA = 7168
+    H = GW.profile(w)
+    w['report'].update(local_profile={str(k): z for k, z in sorted(H.items()) if z}, local_rank_mass=sum(r * z for r, z in H.items()))
+    pin('regroup_count', n); dump(out / 'regroup/FULL-WORD.json.gz', w); pin('regroup_sha256', hashlib.sha256(enc(w)).hexdigest())
+    # 4. HPE
+    h = load('upstream_hpe', up / 'code/build_hpe.py')
+    used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    (out / 'HPE-RECIPE.json').write_text(json.dumps(dict(changes=ch)))
+    pin('hpe_recipe_sha256', hashlib.sha256(enc(dict(changes=ch))).hexdigest())
+    w = h.apply(w, ch); dump(out / 'hpe/FULL-WORD.json.gz', w)
+    # 5. cold44
+    hm = set(read(raw / 'HELPER-MAP.json')['map'].values())
+    env['EXTRAH'] = json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm))
+    if not a.record_pins: env['PAIRING_RANKS'] = json.dumps(pins['pairing_ranks'])
+    run('cold44', NOTRI / 'cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', wd / 'hamming', '--upstream-package', up)
+    pin('pairing_ranks', [b['pairing_rank'] for b in read(out / 'cold44/CONSTRUCTION.json')['blocks']])
+    word = out / 'cold44/FULL-WORD.json.gz'; w = read(word)
+    pin('cold44_sha256', hashlib.sha256(enc(w)).hexdigest()); rep = w['report']
+    pin('R', rep['R']); pin('local_profile', rep['local_profile']); pin('width_inventory', rep['width_inventory'])
+    print('PASS leaver scalar word', got['cold44_sha256'], flush=True)
+    if not a.word_only:
+        for k in ('XPARAM', 'EXTRAH', 'PAIRING_RANKS'): env.pop(k, None)
+        local = out / 'local'
+        run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word,
+            '--routing', parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz', '--out', local)
+        pin('canonical_sha256', hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest())
+        run('ledgers', up / 'code/hpe_emit_local.py', local)
+        run('local-replay', up / 'code/hpe_audit_local.py', local)
+        run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+            local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+        checks = read(local / 'LOCAL-CHECKS.json')
+        pin('program_sha256', {o: checks[o]['sha256'] for o in ('forward', 'backward')})
+        if not a.skip_phases:
+            run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+            pin('clifford_recipes_sha256', hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest())
+    if a.record_pins: (HERE / ('LEAVER-PINS-%s.json' % a.id)).write_text(json.dumps(got, indent=1) + '\n')
+    print('DONE', out, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/leaver/reproduce_leaver_chain.py b/research/gauge44-leaver/construction/leaver/reproduce_leaver_chain.py
new file mode 100644
index 0000000000..4eacb3c608
--- /dev/null
+++ b/research/gauge44-leaver/construction/leaver/reproduce_leaver_chain.py
@@ -0,0 +1,183 @@
+#!/usr/bin/env python3
+"""Rebuild the leaver stack on top of the leaver cell word: layers (NP, p6n), promotions, joint exchange and U8-style
+hybrids, and the final word's native locals.
+
+Input: a fresh `construction/leaver/reproduce_leaver.py --word-only` output directory (raw/HELPER-MAP.json, regroup/,
+cold44/; the cell word and its regroup word are pinned there by LEAVER-PINS.json). Each step uses an unchanged signed
+builder with a LeaverSAT recipe (data only), and every intermediate word is pinned:
+  1. pivot-swap: ../layers/build_pivot_swap.py with PIVOT-SWAP-<id>.json on the regroup word (its own 30 controls).
+  2. hpe: PR635's build_hpe.candidates (greedy, disjoint registers) must equal HPE-RECIPE-<id>.json; build_hpe.apply.
+     The swapped HPE word is pinned by the cold-layer recipes' input_content_sha256.
+  3. cold44-exact: ../notri/cold44x.py on the swapped HPE word (pairing ranks pinned to LEAVER-PINS); its cold ends,
+     premix and low tails must equal the unswapped leaver construction's.
+  4. layers: PR635's build_cold_end.apply(HPE, COLD-LAYERS-RECIPE-NP-<id>) -> NP word and (.., -P6N-<id>) -> p6n word;
+     output shas pinned by the recipes.
+  5. promotion: ../promo/build_promotion.py with PROMO-RECIPE-<id>.json on the p6n word; ../promo/promo_controls.py.
+  6. jx: ../jx/build_jx.py with RECIPE-X4-<id>.json on the promoted word; all recipe controls rerun at their pins.
+  7. hybrids: ../barch/build_tri.py with RECIPE-U8-<id>.json on the jx word; ../barch/run_controls.py (all outcomes).
+  8. frames: build_frames_lv.py (LeaverSAT2) applies FRAME-RECIPE-LV-<id>.json (B/T frame changes, exact global frame
+     optimum) with ../promo/build_promotion.apply; scalar program unchanged; 3 pin controls; output pinned.
+  8b. layer-end-controls: layer_end_controls_leaver.py (the signed per-end controls with per-word reason re-pins,
+     LEC-REASON-PINS-<id>.json) on the p6n, promoted, jx and hybrid words; counts pinned. (Not on the re-framed
+     final word; see the comment at that step.)
+  9. native, ledgers, local-replay, wrappers, phases on the final word; canonical, programs, Clifford pinned.
+All counts and native pins are in CHAIN-PINS-<id>.json (--record-pins writes it from a run instead of checking).
+Apache-2.0. Driver by ColdWitness over LeaverSAT's frozen recipes and the signed builders.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+C = HERE.parent
+MUTANTS = ('drop_restore', 'restore_full', 'drop_preread', 'donation_after')
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def csha(p): return hashlib.sha256(gzip.decompress(Path(p).read_bytes())).hexdigest()
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--leaver-dir', type=Path, required=True, help='construction/leaver/reproduce_leaver.py --word-only output')
+    ap.add_argument('--hamming', type=Path, required=True, help='hamming/ of the construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    ap.add_argument('--id', default='k5', help='recipe set id: every recipe and pin file below is <NAME>-<id>')
+    ap.add_argument('--record-pins', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    lp = read(HERE / ('LEAVER-PINS-%s.json' % a.id))
+    pins = {} if a.record_pins else read(HERE / ('CHAIN-PINS-%s.json' % a.id)); got = {}
+
+    def pin(key, value):
+        got[key] = value
+        if not a.record_pins: assert pins[key] == value, (key, value, pins.get(key))
+
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE', 'LEC_REASON_PINS', 'SW4_PIN'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True, extra=None):
+        t = time.monotonic(); e = dict(env, **(extra or {}))
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=e, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+        return (out / (label + '.log')).read_text()
+
+    def lec(label, word):
+        run(label, HERE / 'layer_end_controls_leaver.py', word, routing, out / label,
+            extra=dict(PR635_CODE=str(up / 'code'), LEC_REASON_PINS=str(HERE / ('LEC-REASON-PINS-%s.json' % a.id))))
+        c = read(out / label / 'COLD-END-CONTROLS.json'); assert c['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS'
+        pin(label, len(c['rejected']))
+
+    ld = a.leaver_dir.resolve()
+    assert hashlib.sha256(enc(read(ld / 'cold44/FULL-WORD.json.gz'))).hexdigest() == lp['cold44_sha256'], 'leaver cell word'
+    rg = ld / 'regroup/FULL-WORD.json.gz'
+    sw = read(HERE / ('PIVOT-SWAP-%s.json' % a.id))
+    assert hashlib.sha256(enc(read(rg))).hexdigest() == lp['regroup_sha256'] == sw['input_content_sha256'], 'regroup word'
+    # 1. pivot swaps
+    run('pivot-swap', C / 'layers/build_pivot_swap.py', '--input', rg, '--recipe', HERE / ('PIVOT-SWAP-%s.json' % a.id), '--gk-dir', gk, '--out', out / 'swap')
+    w = read(out / 'swap/FULL-WORD.json.gz'); assert hashlib.sha256(enc(w)).hexdigest() == sw['output_content_sha256'], 'swap word'
+    # 2. HPE
+    h = load('upstream_hpe', up / 'code/build_hpe.py'); used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    assert ch == read(HERE / ('HPE-RECIPE-%s.json' % a.id))['changes'], 'HPE recipe'
+    w = h.apply(w, ch); (out / 'hpe').mkdir(); (out / 'hpe/FULL-WORD.json.gz').write_bytes(gzip.compress(enc(w), mtime=0))
+    rnp, rp6 = read(HERE / ('COLD-LAYERS-RECIPE-NP-%s.json.gz' % a.id)), read(HERE / ('COLD-LAYERS-RECIPE-P6N-%s.json.gz' % a.id))
+    assert hashlib.sha256(enc(w)).hexdigest() == rnp['input_content_sha256'] == rp6['input_content_sha256'], 'swapped HPE word'
+    # 3. cold44 on the swapped word: same ends, premix and tails
+    hm = set(read(ld / 'raw/HELPER-MAP.json')['map'].values())
+    run('cold44-exact', C / 'notri/cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', a.hamming.resolve(), '--upstream-package', up,
+        extra=dict(EXTRAH=json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm)), PAIRING_RANKS=json.dumps(lp['pairing_ranks'])))
+    new, old = read(out / 'cold44/RECIPE.json.gz'), read(ld / 'cold44/RECIPE.json.gz')
+    for key in ('premix', 'early_cleanup', 'cold_ends'): assert new[key] == old[key], ('swapped cold44 differs', key)
+    tail = len(new['early_cleanup']); assert new['cleanup'][:tail] == old['cleanup'][:tail], 'low tails'
+    # 4. NP and p6n layers
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    for name, r in (('np', rnp), ('p6n', rp6)):
+        lw = bce.apply(w, r); raw = enc(lw); assert hashlib.sha256(raw).hexdigest() == r['output_content_sha256'], (name, 'word')
+        (out / name).mkdir(); (out / name / 'FULL-WORD.json.gz').write_bytes(gzip.compress(raw, mtime=0))
+        pin(name + '_profile', lw['report']['local_profile'])
+    p6n = out / 'p6n/FULL-WORD.json.gz'; lec('lec-p6n', p6n)
+    # 5. promotion
+    pr = HERE / ('PROMO-RECIPE-%s.json' % a.id)
+    run('promotion', C / 'promo/build_promotion.py', '--input', p6n, '--recipe', pr, '--out', out / 'promo', portable=False)
+    assert csha(out / 'promo/FULL-WORD.json.gz') == read(pr)['expected']['output_content_sha256']
+    run('promo-controls', C / 'promo/promo_controls.py', '--input', p6n, '--recipe', pr, '--audit', C.parent / 'independent/audit_local.py',
+        '--out', out / 'PROMO-CONTROLS.json', portable=False)
+    pc = read(out / 'PROMO-CONTROLS.json'); assert pc['honest'] == 'PASS'; pin('promo_controls', pc['rejected'])
+    lec('lec-promo', out / 'promo/FULL-WORD.json.gz')
+    # 6. jx
+    xr = HERE / ('RECIPE-X4-%s.json' % a.id); rec = read(xr); inp = out / 'promo/FULL-WORD.json.gz'
+    (out / 'jx').mkdir(); jw = out / 'jx/FULL-WORD.json.gz'
+    run('jx', C / 'jx/build_jx.py', '--input', inp, '--recipe', xr, '--out', jw, portable=False)
+    assert csha(jw) == rec['expected']['output_content_sha256']
+    for name, cc in sorted(rec['controls'].items()):
+        log = run('jx-control-' + name, C / 'jx/build_jx.py', '--input', inp, '--recipe', xr, '--control', name, portable=False)
+        if 'rejection_expected' in cc: assert 'CONTROL PINNED' in log, (name, log[-300:])
+        else: assert ('OK ' + cc['expected_sha']) in log, (name, log[-300:])
+    pin('jx_controls', sorted(rec['controls']))
+    lec('lec-jx', jw)
+    # 7. hybrids
+    ur = HERE / ('RECIPE-U8-%s.json' % a.id); u = read(ur); (out / 'hyb').mkdir(); fw = out / 'hyb/FULL-WORD.json.gz'
+    run('hybrids', C / 'barch/build_tri.py', jw, ur, fw, portable=False)
+    assert csha(fw) == u['expect_sha256']
+    run('hybrid-controls', C / 'barch/run_controls.py', jw, ur, C.parent / 'independent/audit_local.py', out / 'hybrid-controls', portable=False)
+    res = read(out / 'hybrid-controls/controls.json')
+    want = ['C0_identity', 'recipe', *MUTANTS] + [m + '@' + str(v['X']) for v in u.get('variants', []) for m in MUTANTS]
+    assert sorted(res) == sorted(want) and all(x['ok'] for x in res.values()), res
+    pin('hybrid_controls', sorted(want))
+    lec('lec-hyb', fw)
+    # 8. frame re-optimisation (LeaverSAT2): exact global frame optimum of the hybrid word; scalar program unchanged
+    fr = HERE / ('FRAME-RECIPE-LV-%s.json' % a.id); frec = read(fr)
+    run('frames', HERE / 'build_frames_lv.py', fw, out / 'frames', fr, portable=False)
+    fw = out / 'frames/FULL-WORD.json.gz'; assert csha(fw) == frec['expected']['output_content_sha256']
+    pin('frame_build_controls', len(read(out / 'frames/BUILD.json')['rejected_controls']))
+    # No layer-end-controls run on the re-framed word: the frame re-optimisation lowers some entering-end tail frames
+    # below the hyperplane, so the signed control generator cannot build its 'end at another hyperplane' mutant there.
+    # The ends, the scalar program and helper_final are unchanged from the hybrid word (checked by build_frames_lv.py),
+    # where the controls ran above; every frame chain of the final word is re-checked by the native audit below.
+    # 9. native locals of the final word
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', fw, '--routing', routing, '--out', local)
+    pin('canonical_sha256', hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest())
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz', local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json'); pin('program_sha256', {o: checks[o]['sha256'] for o in ('forward', 'backward')})
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        pin('clifford_recipes_sha256', hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest())
+    if a.record_pins: (out / ('CHAIN-PINS-%s.json' % a.id)).write_text(json.dumps(got, indent=1) + '\n')
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/notri/PRIO6.json b/research/gauge44-leaver/construction/notri/PRIO6.json
new file mode 100644
index 0000000000..069a7bf5a5
--- /dev/null
+++ b/research/gauge44-leaver/construction/notri/PRIO6.json
@@ -0,0 +1 @@
+{"prio": {"0,1,2,3": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "0,1,4,5": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "0,1,6,7": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "2,3,4,5": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "2,3,6,7": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "4,5,6,7": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]]}}
\ No newline at end of file
diff --git a/research/gauge44-leaver/construction/notri/cgx.py b/research/gauge44-leaver/construction/notri/cgx.py
new file mode 100644
index 0000000000..08e80804eb
--- /dev/null
+++ b/research/gauge44-leaver/construction/notri/cgx.py
@@ -0,0 +1,469 @@
+# Round20 early-coordinate-center / own-Y variant, prepared for icekylinx
+# with OpenAI Codex assistance. Apache-2.0. Scalar elementary-operation
+# helpers below are retained from the attributed PR514 construct_partial.py.
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+# AtomScout: leaver-read K-triangles (schedule from atom1.py / rog.py CP-SAT)
+TRI=json.loads(Path(sys.argv[3]).read_text())
+FULLT={(tuple(tr['p']),tr['e']) for tr in TRI['triangles']}
+TRI_COORDS={t+8 for tr in TRI['triangles'] for t,_,_ in tr['reads']}
+import os as _o
+COPYL=json.loads(open(_o.environ['XPARAM']).read()).get('copyl',[]) if _o.environ.get('XPARAM') else []
+NH=504-3*len(FULLT)+len(COPYL)
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+# Helper ids of the unpatched 504 construction: every allocation advances the 504 numbering; a packet copy that the
+# K-triangle schedule never forms advances it without allocating (HELPER-MAP.json).
+shadow=[];skipped=[];nxt=[2*v]
+def alloc():
+    n=len(cur);cur.append(());rows.append({});shadow.append(nxt[0]);nxt[0]+=1;return n
+def skip():
+    skipped.append(nxt[0]);nxt[0]+=1
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# Each source quartet supplies pair partials first. The other two coordinate
+# partitions supply eight early face packets without touching the eight
+# partials later copied into the preconditioned Y coordinates.
+SELECT=(0,0)
+PRIORITY=json.loads((INPUT/"COMPLETION-PRIORITY.json").read_text())
+import os
+XP=json.loads(open(os.environ['XPARAM']).read()) if os.environ.get('XPARAM') else {}
+XCH=XP.get('exch',{});PRIO=XP.get('prio',{})
+maps={};early={};own_rows={};pairs=[];tetrads={};block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)});maps[c]=mp
+    for ei,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[:40]):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        if ei==15:
+            for jj,cl in XCH.get(str(len(maps)-1),[[4,17],[5,19],[6,21],[7,23]]):swap(mp[jj],mp[cl],(P[ids[jj]],))
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in targets:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                t,u=sorted(ts);e2=R[t][q[0]]*R[t][q[1]]
+                pair={'targets':(t,u),'keys':[(c,p,eps),(c,q,e2)],'selected':pi==SELECT[parity],
+                      'matrix':[[R[a][p[0]],R[a][q[0]]] for a in (t,u)]}
+                pairs.append(pair)
+                if not pair['selected']:continue
+                zz=-Q(2*R[u][p[0]],R[t][p[0]])
+                sources=tet[1-parity]
+                for target,sign in ((t,-1),(u,1)):
+                    wanted={s:-Q(G[t][s],4)-sign*Q(G[u][s],2)/zz for s in sources
+                            if -Q(G[t][s],4)-sign*Q(G[u][s],2)/zz}
+                    assert len(wanted)==2
+                    candidates=[]
+                    for r in mp.values():
+                        if set(rows[r])!=set(wanted):continue
+                        s=next(iter(wanted));coef=wanted[s]/rows[r][s]
+                        if all(wanted[s]==coef*rows[r][s] for s in wanted):candidates.append((r,coef))
+                    assert len(candidates)==1
+                    r,coef=candidates[0];assert len(cur[r])==2
+                    own_rows[target]=(r,coef,cur[r])
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    needed={own_rows[t][0] for t in ids}
+    early[c]={j for j,e in enumerate(z['events'][40:]) if not ({mp[e[0]],mp[e[1]]}&needed)}
+    assert len(early[c])==8
+    retired=[]
+    for j in sorted(early[c]):
+        (t,s,a,b),F=z['events'][40+j],z['event_frames'][40+j]
+        add(mp[t],mp[s],Q(a,b),tuple(F));retired.append(mp[s])
+    assert not set(retired)&needed
+    # These eight retired rows already span every source coordinate. Keep
+    # them invertible and place the four coordinate totals in a changed basis.
+    F=basis([P[s] for s in ids]);assert len(F)==4
+    regs=sorted(retired,key=lambda r:(r>=v,r))
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    M=[[Q(R[s][i]) for s in ids] for i in c]
+    def qr_rank(rs):
+        bs={}
+        for r in rs:
+            r=r.copy()
+            for i,b in sorted(bs.items()):
+                if r[i]:q=r[i];r=[x-q*y for x,y in zip(r,b)]
+            i=next((i for i,x in enumerate(r) if x),None)
+            if i is not None:q=r[i];bs[i]=[x/q for x in r]
+        return len(bs)
+    assert qr_rank(M)==4
+    for rr0 in PRIO.get(",".join(map(str,c)),[])+PRIORITY[",".join(map(str,c))]["rows"]:
+        rr=list(map(Q,rr0))
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    for i in range(8):
+        if len(M)==8:break
+        rr=[Q(i==j) for j in range(8)]
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    assert len(M)==8
+    linear(regs,M,F)
+    for i,r in zip(c,regs):
+        assert rows[r]=={s:Q(R[s][i]) for s in ids}
+        block_totals[c,i]=r
+
+# All centers are complete while Y is still at zero. This is the crucial
+# difference from an illegal early-own-Y prefix using the old center order.
+centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+assert all(cur[v+t]==() for t in range(v))
+
+phase=B
+for t,(r,coef,F) in sorted(own_rows.items()):
+    if t in TRI_COORDS:continue
+    assert cur[r]==F
+    add(v+t,r,coef,F)
+# requests are needed for TRI coefficients
+requests=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    requests[key1].append((t,-Q(mat[0][0],2)))
+    requests[key2].append((u,-Q(mat[0][1],2)))
+reqcoef={t:(key,coef) for key,reqs in requests.items() for t,coef in reqs}
+def face_info(c,p,eps):
+    z=blocks[c];keys=[(pp,ee) for pp in it.combinations(c,2) for ee in (-1,1)]
+    r_local,alpha=z['outputs'][keys.index((p,eps))]
+    j=[j for j in range(40,len(z['events'])) if z['events'][j][0]==r_local];assert len(j)==1
+    return j[0],Q(alpha)
+tri_join_counts=Counter();TRILOG=[]
+lcopy={}
+for s8 in COPYL:
+    r=s8+8;c=len(cur);cur.append(());rows.append({});shadow.append(None);add(c,r,1,cur[r]);lcopy[r]=c
+BF={c:basis([P[x] for x in z['receipt']['source_lines']]) for c,z in blocks.items()}
+HYB={(tuple(map(int,h[0])),tuple(map(int,h[1])),int(h[2])) for h in XP.get('hyb',[])}
+HYBLOG=[]
+def triread(t,blk,r,q):
+    F=basis(cur[v+t]+cur[r]);assert inside(F,hyper(P[t])),('TRI frame',t,blk,r,cur[v+t],cur[r],hyper(P[t]),[x for x in TRILOG if x[2]==r],HYBLOG)
+    tri_join_counts[len(F)]+=1;add(v+t,r,q,F);TRILOG.append([t,list(blk),r,str(q),list(F),list(cur[r])])
+for tr in TRI['triangles']:
+    p,eps=tuple(tr['p']),tr['e']
+    hb={blk for _,blk,_ in map(lambda x:(x[0],tuple(x[1]),x[2]),tr['reads']) if (blk,p,eps) in HYB}
+    own=[];rest=[]
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];r0=r;r=lcopy.get(r,r)
+        key,coef=reqcoef[t];assert key[1]==p and key[2]==eps,(key,p,eps)
+        if blk==key[0]:
+            rr,c0,F0=own_rows[t];assert rr==r0;own.append((t,blk,r,c0))
+        else:
+            j,alpha=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert loc in ev[:2]
+            rest.append((t,blk,loc,r,coef*alpha))
+    if not hb:
+        # original interleaved order
+        for t8,blk,loc in tr['reads']:
+            t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+            if blk==key[0]:q=own_rows[t][1]
+            else:j,alpha=face_info(blk,p,eps);q=coef*alpha
+            triread(t,blk,r,q)
+        continue
+    items=[]  # (kind, t, reg, q, blk)
+    for t,blk,r,q in own:items.append(('r',t,r,q,blk,blk in hb))
+    for blk in sorted(hb):items.append(('e',None,None,None,blk,True))
+    done=set()
+    for t,blk,loc,r,q in rest:
+        if blk in hb:
+            j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j]
+            ws=[x for x in rest if x[0]==t and x[1]==blk];assert len(ws)==2 and ws[0][4]==ws[1][4] and {ws[0][2],ws[1][2]}==set(ev[:2])
+            if (t,blk) in done:continue
+            done.add((t,blk));items.append(('m',t,maps[blk][ev[0]],q,blk,True))
+        else:items.append(('r',t,r,q,blk,False))
+    # Original read order with the two half reads collapsed into one M read at the first half's slot; the face event goes
+    # just before the first M read of its block; own reads of the M register are hoisted ahead of that event.
+    def evinfo(blk):
+        j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert ev[2]==ev[3]==1,ev
+        mpb=maps[blk];return mpb[ev[0]],mpb[ev[1]],tuple(blocks[blk]['event_frames'][j])
+    items=[]
+    seen=set()
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+        if blk==key[0]:items.append(('r',t,r,own_rows[t][1],blk,blk in hb))
+        else:
+            j,alpha=face_info(blk,p,eps);q=coef*alpha
+            if blk in hb:
+                if (t,blk) not in seen:seen.add((t,blk));continue
+                items.append(('m',t,evinfo(blk)[0],q,blk,True))
+            else:items.append(('r',t,r,q,blk,False))
+    for blk in sorted(hb):
+        k0=min(i for i,x in enumerate(items) if x[0]=='m' and x[4]==blk)
+        items.insert(k0,('e',None,None,None,blk,True))
+    n=len(items)
+    def step(it,st):
+        k,t,r,q,blk,h=it;g=lambda x:st.get(x,cur[x])
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(g(a_))+list(g(b_)))
+            return {a_:FF,b_:FF} if inside(FF,BF[blk]) else None
+        F=basis(list(g(v+t))+list(g(r)))
+        if not inside(F,hyper(P[t])):return None
+        if h and k=='r' and r==evinfo(blk)[1] and not inside(F,BF[blk]):return None
+        return {v+t:F,r:F}
+    def allowed(i,used):
+        k,t,r,q,blk,h=items[i]
+        evi=[j for j,x in enumerate(items) if x[0]=='e' and x[4]==blk] if h else []
+        if k=='e':return all(j in used for j,x in enumerate(items) if x[0]=='r' and x[4]==blk and x[5] and x[2]==evinfo(blk)[0])
+        if k=='m':return evi[0] in used
+        if k=='r' and h and r==evinfo(blk)[0]:return evi[0] not in used
+        return True
+    budget=[int(os.environ.get('HYBBUDGET','300000'))];memo=set()
+    def dfs(st,used,order):
+        if len(order)==n:return order
+        budget[0]-=1
+        if budget[0]<0:return None
+        sig=(used,tuple(sorted(st.items())))
+        if sig in memo:return None
+        memo.add(sig)
+        for i in range(n):
+            if i in used or not allowed(i,used):continue
+            d=step(items[i],st)
+            if d is None:continue
+            ns=dict(st);ns.update(d);res=dfs(ns,used|{i},order+[i])
+            if res:return res
+        return None
+    import sys as _s;_s.setrecursionlimit(20000)
+    order=dfs({},frozenset(),[])
+    assert order,('no feasible hybrid order',p,eps,sorted(hb),budget)
+    for i in order:
+        k,t,r,q,blk,h=items[i]
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(cur[a_])+list(cur[b_]));add(a_,b_,1,FF);HYBLOG.append([list(blk),list(p),eps,list(FF)])
+        else:triread(t,blk,r,q)
+
+packets={}
+for c,z in sorted(blocks.items()):
+    mp=maps[c]
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    skipev={face_info(c,p,eps)[0] for p,eps in keys if (p,eps) in FULLT}
+    for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]):
+        if j not in early[c] and 40+j not in skipev:
+            t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    for key,(r,alpha) in zip(keys,z['outputs']):
+        if tuple(key) in FULLT:skip();continue
+        a=mp[r];b=alloc();add(b,a,1,cur[a])
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha))
+
+# Both tetrahedra use the same partition. A selected key has exactly two
+# selected Y loads and no ordinary M consumer. Supply its two raw halves in
+# opposite orders and never form that M. Other keys retain the old M path.
+second=[];first_join_counts=Counter()
+for key,reqs in sorted(requests.items()):
+    assert len(reqs)==2
+    c,p,eps=key
+    if (p,eps) in FULLT:continue
+    ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds
+    for j,(target,coef) in enumerate(sorted(reqs)):
+        first_source,second_source=(a,b) if j==0 else (b,a)
+        r,alpha=packets[first_source,p,eps,second_source]
+        F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+        first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F)
+        r,alpha=packets[second_source,p,eps,c]
+        second.append((target,r,coef*alpha))
+
+Ms={}
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for eps in (-1,1):
+            if (c,p,eps) in requests:continue
+            (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,eps]=(a,alpha)
+
+consumers=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    for key in pair['keys']:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    if key in requests:
+        assert all(pairs[i]['selected'] for i in uses)
+        continue
+    assert all(not pairs[i]['selected'] for i in uses)
+    a,alpha=Ms[key]
+    for j,pid in enumerate(uses):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+assert len(cur)-240==NH,len(cur)-240
+
+selected_join_counts=Counter()
+for target,r,coef in second:
+    F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+    selected_join_counts[len(F)]+=1;add(v+target,r,coef,F)
+output_basis=[]
+for pair in pairs:
+    if not pair['selected']:continue
+    (t,u),mat=pair['targets'],pair['matrix']
+    F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u]))
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert rows[v+t]==expected,('side identity',t)
+
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8
+assert sum(r*z for r,z in H.items())==9*NH+240*8+72,sum(r*z for r,z in H.items())
+
+def apply(e,matrix):
+    if e[0]=='add':
+        _,t,s,a,b,*_=e;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    e[-1]=list(FULL);return e
+cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q]
+cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v]
+matrix=[{r:Q(1)} if r<v else {} for r in range(len(cur))]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(len(cur)))
+
+# Restrict the eight isolated axis ports exactly, keeping the stable 112-port
+# label set. This variant changes the local word, not the outer geometry.
+mp={s:s-8 for s in range(8,120)}
+mp.update({120+s:112+s-8 for s in range(8,120)})
+mp.update({240+r:224+r for r in range(NH)})
+def restrict(events,is_cut=False):
+    out=[]
+    for e in events:
+        regs=e[1:3] if e[0]=='add' else e[1:2]
+        if any(r not in mp for r in regs):
+            assert is_cut and e[0]=='add' and e[1]-120==e[2] and e[2]<8 and e[3:5]==[1,1]
+            continue
+        q=copy.deepcopy(e);q[1]=mp[q[1]]
+        if q[0]=='add':q[2]=mp[q[2]]
+        out.append(q)
+    return out
+H.subtract({1:8,8:16});H=+H
+report={'status':'EXACT_CLEAN_OWN_Y_EARLY_CENTER_WORD_NOT_ADMITTED',
+        'h':9,'v':112,'R':NH,'cst':64,'m':73,'local_profile':dict(sorted(H.items())),
+        'centre_ranks':[8]*8,**({'tri_join_counts':dict(tri_join_counts)} if TRI['triangles'] else {}),'selected_load_join_counts':dict(selected_join_counts),'selected_partitions':list(SELECT),'first_load_join_counts':dict(first_join_counts),
+        'source_columns_exact':112,'borrowed_output_pairs':56,'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'local_rank_mass':sum(r*n for r,n in H.items()),'scope':'Clean scalar identity and all literal monotone local frames only; arbitrary-dirt compensation, entrance kernels, exact phase recipes, and global hosting/pricing are not yet certified.'}
+word={'report':report,'ports':P[8:],'root_lines':R[8:],
+      'A':restrict(A),'B':restrict(B),'cut':restrict(cut,True),'cleanup':restrict(cleanup),'precondition':restrict(precondition),
+      'centers':[mp[r] for r in centers[:8]],'center_frames':center_frames[:8],
+      'scatter':[[str(x) for x in row[:8]] for row in scatter[8:]]}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+assert len(shadow)==NH and len([x for x in shadow if x is not None])+len(skipped)==504
+hmap={**{r:r for r in range(224)},**{224+s_-240:224+i for i,s_ in enumerate(shadow) if s_ is not None}}
+(OUT/'HELPER-MAP.json').write_text(json.dumps({'map':{str(k):hmap[k] for k in sorted(hmap)},'removed_504_helpers':[224+s_-240 for s_ in skipped]})+'\n')
+(OUT/'TRILOG.json').write_text(json.dumps(dict(reads=TRILOG,hyb=HYBLOG)));(OUT/'DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/gauge44-leaver/construction/notri/cold44x.py b/research/gauge44-leaver/construction/notri/cold44x.py
new file mode 100644
index 0000000000..8fa6f3a6a6
--- /dev/null
+++ b/research/gauge44-leaver/construction/notri/cold44x.py
@@ -0,0 +1,217 @@
+"""Exact dyadic cold-end realization of the source-branch/factory-completion word.
+Prepared for icekylinx with OpenAI Codex assistance; Apache-2.0.
+This is a constructor: independent endpoint/frame audits remain required.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+import copy,gzip,json,hashlib,time,sys,argparse,importlib.util,os
+D=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser(description=__doc__)
+for name in ('input','out','hamming','upstream-package'):ap.add_argument('--'+name,type=Path,required=True)
+args=ap.parse_args();WPATH=args.input;OUT=args.out
+assert __debug__, 'Assertions are required'
+OUT.mkdir(exist_ok=False,parents=True)
+def rd(p):return json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+w=rd(WPATH);v=w['report']['v'];n=2*v+w['report']['R'];N=list(range(v))+list(range(2*v,n));ix={x:i for i,x in enumerate(N)}
+F9=[256,128,64,32,16,8,4,2,1];t0=time.monotonic()
+def basis(vs):
+ d={}
+ for a in vs:
+  for k in sorted(d,reverse=True):
+   if a>>k&1:a^=d[k]
+  if a:
+   k=a.bit_length()-1
+   for j in d:
+    if d[j]>>k&1:d[j]^=a
+   d[k]=a
+ return tuple(d[k] for k in sorted(d,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def regs(e):return e[1:3] if e[0]=='add' else e[1:2]
+def inverse(e):
+ e=copy.deepcopy(e)
+ if e[0]=='add':e[3]=-e[3]
+ else:e[2],e[3]=e[3],e[2]
+ return e
+def apply(e,M,mapping=None):
+ t=mapping[e[1]] if mapping is not None else e[1]
+ if e[0]=='add':
+  s=mapping[e[2]] if mapping is not None else e[2];q=Q(e[3],e[4])
+  for j,a in M[s].items():
+   x=M[t].get(j,Q(0))+q*a
+   if x:M[t][j]=x
+   else:M[t].pop(j,None)
+ else:
+  q=Q(e[2],e[3]);M[t]={j:q*a for j,a in M[t].items()}
+def rref(A):
+ a=[list(map(Q,row)) for row in A];nr=len(a);nc=len(a[0]) if nr else 0;row=0;piv=[]
+ for c in range(nc):
+  k=next((i for i in range(row,nr) if a[i][c]),None)
+  if k is None:continue
+  a[row],a[k]=a[k],a[row];q=a[row][c];a[row]=[x/q for x in a[row]]
+  for i in range(nr):
+   if i!=row and a[i][c]:q=a[i][c];a[i]=[x-q*y for x,y in zip(a[i],a[row])]
+  piv.append(c);row+=1
+  if row==nr:break
+ return a,piv
+def rank(A):return len(rref(A)[1])
+def null(A,nc=None):
+ if A:a,piv=rref(A);nc=len(a[0])
+ else:a=[];piv=[];assert nc is not None
+ free=[j for j in range(nc) if j not in piv];out=[[Q(0) for j in free] for i in range(nc)]
+ for k,c in enumerate(free):out[c][k]=Q(1)
+ for i,c in enumerate(piv):
+  for k,j in enumerate(free):out[c][k]=-a[i][j]
+ return out
+def mm(A,B):
+ if not A:return []
+ if not B:return [[] for row in A]
+ bt=list(zip(*B));return [[sum((a*b for a,b in zip(row,col)),Q(0)) for col in bt] for row in A]
+def tr(A):return list(map(list,zip(*A)))
+def inv(A):
+ n0=len(A);a,p=rref([row+[Q(i==j) for j in range(n0)] for i,row in enumerate(A)])
+ assert p[:n0]==list(range(n0))
+ return [row[n0:] for row in a]
+def unit(q):
+ if not q:return False
+ a=abs(q.numerator);b=q.denominator
+ return not a&(a-1) and not b&(b-1)
+def dyadic(q):return not q.denominator&(q.denominator-1)
+def opadd(t,s,q,F):return ['add',t,s,q.numerator,q.denominator,list(F)]
+def opscale(t,q,F):return ['scale',t,q.numerator,q.denominator,list(F)]
+def eliminate(M,ids,F,skip=()):
+ """Return legal dyadic row operations taking an invertible sparse matrix to I."""
+ skip=set(skip);ops=[];dim=len(M)
+ def add(i,j,q):
+  if q:
+   assert dyadic(q);e=opadd(ids[i],ids[j],q,F);ops.append(e)
+   for c,x in M[j].items():
+    z=M[i].get(c,Q(0))+q*x
+    if z:M[i][c]=z
+    else:M[i].pop(c,None)
+ def scale(i,q):
+  if q!=1:
+   assert unit(q);ops.append(opscale(ids[i],q,F));M[i]={c:q*x for c,x in M[i].items()}
+ def swap(i,j):
+  if i!=j:
+   add(i,j,Q(1));add(j,i,Q(-1));add(i,j,Q(1));scale(j,Q(-1))
+ for c in range(dim):
+  if c in skip:
+   assert M[c]=={c:Q(1)} and all(not M[i].get(c) for i in range(dim) if i!=c)
+   continue
+  cand=[i for i in range(c,dim) if i not in skip and M[i].get(c)]
+  k=next((i for i in cand if unit(M[i][c])),None)
+  if k is None:
+   # Elementary Euclidean row additions reduce the pivot-column numerator gcd.
+   assert cand,('singular',c)
+   while k is None:
+    cand.sort(key=lambda i:abs(M[i][c]));a=cand[0]
+    b=next((i for i in cand[1:] if M[i][c]),None)
+    if b is None:raise ValueError(('non-dyadic determinant pivot',c,M[a][c]))
+    rat=M[b][c]/M[a][c];q=rat.numerator//rat.denominator
+    if q==0:q=1 if rat>0 else -1
+    add(b,a,Q(-q));cand=[i for i in cand if M[i].get(c)]
+    k=next((i for i in cand if unit(M[i][c])),None)
+  swap(c,k);scale(c,1/M[c][c])
+  for i in range(dim):
+   if i!=c and M[i].get(c):
+    assert i not in skip
+    add(i,c,-M[i][c])
+ assert all(row=={i:Q(1)} for i,row in enumerate(M))
+ return ops
+def realize(A,ids,F):
+ M=[{j:Q(x) for j,x in enumerate(row) if x} for row in A]
+ return [inverse(e) for e in reversed(eliminate(M,ids,F))]
+# Reconstruct the actual non-target map after the inherited HPE tail.
+inherited_tail=[w['cleanup'][i][:-1]+[list(f)] for i,f in w.get('early_cleanup',[])]
+mainN=[e for e in w['A']+w['B'] if not v<=e[1]<2*v]
+M=[{i:Q(1)} for i in range(len(N))]
+for e in mainN+inherited_tail:apply(e,M,ix)
+MI=[{i:Q(1)} for i in range(len(N))]
+for e in reversed(mainN+inherited_tail):apply(inverse(e),MI,ix)
+cur={x:(w['ports'][x],) if x<v else basis(w.get('start_extra',{}).get(str(x),[])) for x in N}
+for e in w['A']+w['B']+inherited_tail:
+ for x in regs(e):
+  if x in cur:cur[x]=basis(e[-1])
+enter=set(map(int,w.get('start_extra',{})));protected=[ix[x] for x in N if x<v or x in enter]
+EXTRAH=json.loads(os.environ.get('EXTRAH','[]'))
+PAIRING_RANKS=json.loads(os.environ['PAIRING_RANKS']) if os.environ.get('PAIRING_RANKS') else None   # per-block pin, set by the driver
+mods=rd(args.hamming/'PACKET-PROGRAMS.json.gz');proto=rd(args.hamming/'PROTOTYPE.json')
+plans=[];premix=[];tail=[];ends={};Mafter=copy.deepcopy(M)
+for b,mod in enumerate(mods):
+ ss=mod['receipt']['source_lines'];F=basis([proto['binary_ports'][s] for s in ss]);I=[ix[x] for x in N if inside(cur[x],F)]
+ hs=list(range(224+16*b,224+16*(b+1)))+[x for x in EXTRAH if ix[x] in I];H=[ix[x] for x in hs];NB=len(hs)
+ C=[[M[i].get(j,Q(0)) for j in protected] for i in I]
+ L=tr(null(tr(C),len(I)))
+ A=[[MI[j].get(i,Q(0)) for i in I] for j in protected];A=[row for row in A if any(row)]
+ K=null(A,len(I));BK=mm(L,K);_,piv=rref(BK);r=len(piv);print('PAIR',b,'I',len(I),'L',len(L),'K',len(K),'r',r,flush=True);assert r==len(L),(b,r,len(L))
+ if PAIRING_RANKS is not None: assert r==PAIRING_RANKS[b],('pinned pairing rank',b,r,PAIRING_RANKS[b])
+ if os.environ.get('DIAG'):
+  print(' regs',[(N[i],cur[N[i]],rank([C[k]]) ) for k,i in enumerate(I)],'rankC',rank(C) if C else 0,flush=True)
+  for row in L: print('  Lrow',{N[I[k]]:str(x) for k,x in enumerate(row) if x})
+ if r==0:plans.append(dict(block=b,frame=list(F),registers=[N[i] for i in I],ends=[],pairing_rank=0));continue
+ Ksel=[[row[j] for j in piv] for row in K];Bsel=[[row[j] for j in piv] for row in BK];U=mm(Ksel,inv(Bsel));assert mm(L,U)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ q=mm([[MI[i].get(j,Q(0)) for j in I] for i in range(len(N))],U)
+ assert all(not any(q[i]) for i in range(len(N)) if i not in H),('nonlocal premix',b)
+ RR=mm(L,[[M[i].get(j,Q(0)) for j in H] for i in I]);qH=[q[i] for i in H]
+ assert mm(RR,qH)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ # Pick low physical helper destinations with independent U coordinate rows.
+ ih=[]
+ for j in sorted((j for j,i in enumerate(I) if N[i] in hs),key=lambda j:(cur[N[I[j]]]!=F,N[I[j]])):
+  if rank([U[k] for k in ih]+[U[j]])>len(ih):ih.append(j)
+  if len(ih)==r:break
+ assert len(ih)==r
+ endhs=[N[I[j]] for j in ih];endhidx=[hs.index(h) for h in endhs]
+ kerR=null(RR,NB);Qmat=[[Q(0) for j in range(NB)] for i in range(NB)]
+ for j,hj in enumerate(endhidx):
+  for i in range(NB):Qmat[i][hj]=qH[i][j]
+ other=[j for j in range(NB) if j not in endhidx]
+ for k,j in enumerate(other):
+  for i in range(NB):Qmat[i][j]=kerR[i][k]
+ assert rank(Qmat)==NB
+ pops=realize(Qmat,hs,());premix+=pops
+ T=[[Q(i==j)-sum((U[i][k]*L[k][j] for k in range(r)),Q(0)) for j in range(len(I))] for i in range(len(I))]
+ for k,i in enumerate(ih):T[i]=L[k]
+ tops=realize(T,[N[i] for i in I],F);tail+=tops
+ # Right-compose this initial helper premix; other blocks have disjoint H sets.
+ for row in Mafter:
+  vals=[row.get(h,Q(0)) for h in H]
+  if any(vals):
+   for hj in H:row.pop(hj,None)
+   for j,hj in enumerate(H):
+    z=sum((vals[i]*Qmat[i][j] for i in range(NB)),Q(0))
+    if z:row[hj]=z
+ for e in tops:apply(e,Mafter,ix)
+ ends.update({h:list(F) for h in endhs})
+ plans.append(dict(block=b,frame=list(F),registers=[N[i] for i in I],ends=endhs,pairing_rank=r,premix_gates=len(pops),tail_gates=len(tops),Q=[[str(x) for x in row] for row in Qmat],T=[[str(x) for x in row] for row in T]))
+ print('BLOCK',b,'ends',endhs,'Qops',len(pops),'Tops',len(tops),flush=True)
+# Check actual post-tail isolation before constructing the high-frame inverse.
+allends=set(ends)|set(map(int,w.get('helper_final',{})))
+for h in allends:
+ j=ix[h];assert Mafter[j]=={j:Q(1)},('row not isolated',h,Mafter[j]);assert all(not row.get(j) for i,row in enumerate(Mafter) if i!=j),('column not isolated',h)
+print('EXACT_ISOLATED',len(ends),'new;',len(allends),'total',round(time.monotonic()-t0,3),flush=True)
+fullops=eliminate(copy.deepcopy(Mafter),N,F9,[ix[x] for x in allends])
+print('FULL_INVERSE',len(fullops),round(time.monotonic()-t0,3),flush=True)
+# Cancel new cold-axis target responses inside A, after their wrappers.
+Dirt=[({h:Q(1)} if h in ends else {}) for h in range(n)]
+for e in premix+w['A']+w['cut']+w['B']:apply(e,Dirt)
+for e in w['precondition']:apply(e,Dirt)
+postcomp=[opadd(y,h,-a,()) for y in range(v,2*v) for h,a in sorted(Dirt[y].items()) if a]
+assert all(h in ends for e in postcomp for h in [e[2]])
+new=copy.deepcopy(w);new['A']=postcomp+premix+w['A'];new['cleanup']=inherited_tail+tail+fullops
+new['early_cleanup']=[[i,e[-1]] for i,e in enumerate(inherited_tail+tail)]
+new['helper_final'].update({str(h):f for h,f in ends.items()})
+new['refactored_cleanup']={'kind':'source_branch_gauge_and_retired_completion_cold44','new_cold_ends':len(ends),'exact_non_target_isolation_checked':True,'high_inverse':'dyadic_sparse_Gauss_Jordan'}
+# Derive paid profile by subtracting and adding literal frame-chain counts.
+spec=importlib.util.spec_from_file_location('upstream_cold_end',args.upstream_package/'code/build_cold_end.py')
+profile_module=importlib.util.module_from_spec(spec);spec.loader.exec_module(profile_module)
+oldprof,_=profile_module.chain_profile(w);newprof,_=profile_module.chain_profile(new)
+prof=Counter({int(k):z for k,z in w['report']['local_profile'].items()});prof.subtract(oldprof);prof.update(newprof)
+widths=Counter(len(basis(new['helper_final'].get(str(h),F9)))-len(basis(new.get('start_extra',{}).get(str(h),[]))) for h in range(224,n))
+new['report'].update(local_profile={str(k):z for k,z in sorted(prof.items()) if z},local_rank_mass=sum(k*z for k,z in prof.items()),width_inventory={str(k):z for k,z in sorted(widths.items()) if z},status='EXACT_COLD44_CONSTRUCTED_PENDING_INDEPENDENT_AUDIT')
+raw=json.dumps(new,sort_keys=True,separators=(',',':')).encode();sha=hashlib.sha256(raw).hexdigest();(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+recipe={'premix':postcomp+premix,'cleanup':new['cleanup'],'early_cleanup':new['early_cleanup'],'cold_ends':{str(h):f for h,f in ends.items()},'refactored_cleanup':new['refactored_cleanup'],'output_content_sha256':sha}
+(OUT/'RECIPE.json.gz').write_bytes(gzip.compress(json.dumps(recipe,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+receipt=dict(input_content_sha256=hashlib.sha256(gzip.decompress(WPATH.read_bytes())).hexdigest(),output_content_sha256=sha,blocks=plans,new_cold_ends=len(ends),all_low_ended_helpers=len(allends),premix_gates=len(premix),postwrapper_compensation_gates=len(postcomp),tail_gates=len(tail),inherited_tail_gates=len(inherited_tail),full_inverse_gates=len(fullops),profile=new['report']['local_profile'],width_inventory=new['report']['width_inventory'],rank_mass=new['report']['local_rank_mass'],seconds=time.monotonic()-t0)
+(OUT/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(json.dumps({k:z for k,z in receipt.items() if k!='blocks'},indent=2),flush=True)
diff --git a/research/gauge44-leaver/construction/notri/port_stage_x.py b/research/gauge44-leaver/construction/notri/port_stage_x.py
new file mode 100644
index 0000000000..81ac65ceff
--- /dev/null
+++ b/research/gauge44-leaver/construction/notri/port_stage_x.py
@@ -0,0 +1,125 @@
+"""Port one 504-helper construction stage onto the K-triangle word.  Apache-2.0.  Prepared with Claude Code assistance.
+
+usage: build_port_stage.py --shadow-input I4 --shadow-output O4 --input I8 --map HELPER-MAP.json --gk-dir GK --out DIR
+
+The shadow pair (I4 -> O4) is one stage of a 504-helper chain, rebuilt in the same run from pinned sources.  I8 is the
+K-triangle word at the matching point of its own chain, and HELPER-MAP.json is the 504 -> R register map written by
+construct_k_triangle.py.  Registers below 448 keep their ids; the removed packet copies have no image.
+
+The port does the following:
+* It renumbers I4 and O4 through the map and drops their gates that touch a removed register.
+* It matches gates by scalar operation (the gate without its frame), aligning I4 with O4 and I4 with I8 separately.
+* It builds O8 in O4 gate order:
+  * each matched gate is taken from I8, with O4's frame wherever the stage changed that frame;
+  * each gate the stage introduced is taken from O4;
+  * each I8-only gate (the K-triangle reads) stays after the O4 image of its I8 predecessor.
+* It replays the stage's entrance (start_extra) and target_levels changes.
+* It rebuilds the cleanup with the inherited inverse rule.
+
+The constructor is a search transfer only.  The verifier certifies the output independently: the generalised native
+audit (exact forward and inverse replay of every column, native frame chains) runs on every ported word, and every
+input and output is pinned by content hash."""
+import argparse, copy, difflib, gzip, hashlib, json, sys
+from collections import Counter
+from pathlib import Path
+
+assert __debug__, 'Assertions required'
+FULL = [256, 128, 64, 32, 16, 8, 4, 2, 1]
+
+
+def regs(g): return (g[1], g[2]) if g[0] == 'add' else (g[1],)
+
+
+def key(g): return json.dumps(g[:-1])
+
+
+def inverse(e):
+    e = copy.deepcopy(e)
+    if e[0] == 'add': e[3] *= -1
+    else: e[2], e[3] = e[3], e[2]
+    e[-1] = list(FULL); return e
+
+
+def align(xs, ys):
+    """index map xs -> ys over runs of equal scalar operations"""
+    sm = difflib.SequenceMatcher(None, [key(g) for g in xs], [key(g) for g in ys], autojunk=False)
+    return {i1 + k: j1 + k for tag, i1, i2, j1, j2 in sm.get_opcodes() if tag == 'equal' for k in range(i2 - i1)}
+
+
+def transfer_section(I4, O4, I8, stats):
+    a, b = align(I4, O4), align(I4, I8)
+    o2i = {j: i for i, j in a.items()}; i8from4 = {j: i for i, j in b.items()}
+    anchor = {j8: a[i4] for j8, i4 in i8from4.items() if i4 in a}
+    pending, last = {}, -1
+    for j8, g in enumerate(I8):
+        if j8 in anchor: last = anchor[j8]
+        elif j8 not in i8from4: pending.setdefault(last, []).append(copy.deepcopy(g)); stats['kept_own'] += 1
+        else: stats['dropped_by_stage'] += 1
+    out = list(pending.get(-1, []))
+    for k, g in enumerate(O4):
+        if k in o2i:
+            i4 = o2i[k]
+            if i4 in b:
+                g8 = copy.deepcopy(I8[b[i4]])
+                if I4[i4][-1] != g[-1]: g8[-1] = copy.deepcopy(g[-1]); stats['frames_changed'] += 1
+                out.append(g8)
+        else:
+            out.append(copy.deepcopy(g)); stats['introduced'] += 1
+        out.extend(pending.get(k, []))
+    return out
+
+
+def main():
+    ap = argparse.ArgumentParser()
+    for k in ('--shadow-input', '--shadow-output', '--input', '--map', '--gk-dir', '--out'): ap.add_argument(k, type=Path, required=True)
+    a = ap.parse_args(); assert not a.out.exists()
+    sys.path.insert(0, str(a.gk_dir)); import gk_word as G, gk_common as C
+    G.V = C.V = 112
+    rd = lambda p: json.loads(gzip.decompress(p.read_bytes()))
+    enc = lambda x: json.dumps(x, sort_keys=True, separators=(',', ':')).encode(); sha = lambda x: hashlib.sha256(x).hexdigest()
+    I4, O4, I8 = rd(a.shadow_input), rd(a.shadow_output), rd(a.input)
+    fm = {int(k): int(v) for k, v in json.loads(a.map.read_text())['map'].items()}
+    assert all(fm[k] == k for k in fm if k < 448), 'only ids >= 448 may move'
+    R = I8['report']['R']; EXTRA = set(range(224 + R)) - set(fm.values()); assert len(set(fm.values())) == len(fm) and set(fm.values()) <= set(range(224 + R)), 'map is not injective into the K-triangle registers'
+    assert I4['report'].get('R', 504) == 504 and len(fm) + len(set(range(728)) - set(fm)) == 728
+    rem = set(range(728)) - set(fm)
+    rn = lambda r: fm[r]
+    touches = lambda g: any(r in rem for r in regs(g))
+    def rg(g):
+        g = copy.deepcopy(g); g[1] = rn(g[1])
+        if g[0] == 'add': g[2] = rn(g[2])
+        return g
+    def rn_word(w):
+        w = copy.deepcopy(w)
+        for s in ('A', 'B', 'cut', 'precondition', 'cleanup'):
+            if s in w: w[s] = [rg(g) for g in w[s] if not touches(g)]
+        for k in ('start_extra', 'helper_final'):
+            if k in w: w[k] = {str(rn(int(r))): f for r, f in w[k].items() if int(r) not in rem}
+        return w
+    I4r, O4r = rn_word(I4), rn_word(O4)
+    O8 = copy.deepcopy(I8); stats = {s: Counter() for s in ('A', 'B')}
+    for s in ('A', 'B'): O8[s] = transfer_section(I4r[s], O4r[s], I8[s], stats[s])
+    for k in ('start_extra', 'target_levels'):
+        x, y = I4r.get(k, {}), O4r.get(k, {}); d = dict(I8.get(k, {}))
+        for r in set(x) | set(y):
+            if x.get(r) != y.get(r):
+                if r in y: d[r] = y[r]
+                else: d.pop(r, None)
+        if k in O4 or k in I8: O8[k] = dict(sorted(d.items(), key=lambda kv: int(kv[0])))
+    for k in O4:
+        if k not in ('A', 'B', 'cleanup', 'report', 'start_extra', 'target_levels', 'cut', 'precondition'):
+            assert O4r[k] == I4r[k], 'stage changed an unported field: ' + k
+    O8['cleanup'] = [inverse(e) for e in reversed(O8['A'] + O8['B']) if not 112 <= e[1] < 224]
+    H = G.profile(O8)
+    ws = [9 - len(G.basis(O8['start_extra'].get(str(224 + h), []))) for h in range(R)]
+    O8['report'] = dict(I8['report'], local_profile={str(k): v for k, v in sorted(H.items())}, local_rank_mass=sum(k * v for k, v in H.items()),
+                        width_inventory={str(k): v for k, v in sorted(Counter(ws).items())})
+    a.out.mkdir(parents=True); (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(enc(O8), mtime=0))
+    receipt = dict(status='PORTED_STAGE_PENDING_NATIVE_AUDIT', R=R, removed_504_helpers=sorted(rem),
+                   shadow_input_content_sha256=sha(enc(I4)), shadow_output_content_sha256=sha(enc(O4)), input_content_sha256=sha(enc(I8)),
+                   output_content_sha256=sha(enc(O8)), sections={s: dict(v) for s, v in stats.items()}, local_profile=O8['report']['local_profile'],
+                   scope='Transfer construction only; exactness, frame chains and profile are certified by the native audit run on the output.')
+    (a.out / 'PORT-STAGE.json').write_text(json.dumps(receipt, indent=2, sort_keys=True) + '\n', newline='\n'); print(json.dumps(receipt, indent=2))
+
+
+main()
diff --git a/research/gauge44-leaver/construction/notri/reproduce_notri.py b/research/gauge44-leaver/construction/notri/reproduce_notri.py
new file mode 100644
index 0000000000..a85f2acf15
--- /dev/null
+++ b/research/gauge44-leaver/construction/notri/reproduce_notri.py
@@ -0,0 +1,166 @@
+#!/usr/bin/env python3
+"""Rebuild the no-triangle gauge44 word (R = 504) and its native locals.
+
+The no-triangle word is #645's gauge44 chain with none of the four (p,-1) K-triangles. In the six K-blocks
+{0,1,2,11,12,13}, the completion priority is extended by the 6-row list PRIO6.json, the list blocks 3-10 already use.
+Each block then pairs at rank 4, giving 56 rank-four cold ends instead of 44 (PartialK).
+
+Input: a fresh `construction/reproduce.py --until word` output directory. Its shadow-early and shadow-prefix words and
+its hamming inputs are pinned by reproduce.py itself. Steps, each checked exactly:
+  1. gauge-forward: cgx.py, #645's construct_gauge_xcentre.py generalised by PartialK. The extra rows come from XPARAM,
+     and the K-triangle schedule comes from the TRI file. Run on the triangle set {} with XPARAM = PRIO6.json.
+  2. port0-3: port_stage_x.py, PR635's build_port_stage.py with the helper map allowed to be injective rather than onto.
+     With R = 504 and no triangles, the map is onto again.
+  3. regroup: PR635's k492 frame-regroup changes, applied where their `before` gate occurs. For this word none occurs,
+     and that count (0) is pinned.
+  4. hpe: PR635's build_hpe.candidates, taken greedily with disjoint registers, and build_hpe.apply. 46 changes, pinned.
+  5. cold44: cold44x.py, #645's build_gauge_cold44.py generalised by PartialK to blocks whose helper list includes the
+     helpers outside the 224+16b ranges (EXTRAH). 56 cold ends; the 14 pairing ranks are pinned to [4]*14 inside cold44x (PAIRING_RANKS) and rechecked here. The output word content sha256 is pinned (3e99ba77...).
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs, as in reproduce.py.
+--control-g44 instead runs steps 1-5 with #645's four triangles and no XPARAM. It must reproduce #645's pinned gauge44
+cold44 word (78c7aada...), the same word #645's own reproduce.py builds. This shows the generalised scripts reduce to
+#645's constructors.
+Apache-2.0. Driver by ColdWitness from PartialK's variant.py; constructors credited above.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NOTRI_SHA = '3e99ba778ab8a97853f50912776247802b529439937176363f6c42786163b1f9'
+G44_SHA = '78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290'
+# native-local pins (the strict locals the SPEC was frozen against: PartialK runs/none_p6/local)
+CANONICAL_SHA = '4265a3bb7f9b46967dfadfca5f2cc1f5b3e6e8681f16c02590f1b9430c013637'
+PROGRAM_SHA = {'forward': '0afda28699e15cf5a5a17aee5475ac608c9fb68b15766d463b93ec8e2df4ae85',
+               'backward': '5be6cb4ea7a1da36d7bbe7eb2392873c058dd3cbb3cc2eeadd55ecca9310ca8a'}
+CLIFFORD_SHA = '4b5789e43e04d71f02c2d480450ec0b354007d9cf523bda76c7345730806344b'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def dump(p, v):
+    p.parent.mkdir(parents=True, exist_ok=True); p.write_bytes(gzip.compress(enc(v), mtime=0))
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--word-dir', type=Path, required=True, help='construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--control-g44', action='store_true', help='rebuild #645 gauge44 (4 triangles) instead; word only')
+    ap.add_argument('--skip-phases', action='store_true')
+    ap.add_argument('--word-only', action='store_true', help='stop after the pinned scalar word (input to construction/layers_np)')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    structural = a.main.resolve() / 'research/structural-gain/frontier-composition'
+    wd = a.word_dir.resolve()
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    # 1. gauge-forward on the chosen K-triangle set
+    tri = read(up / 'data/TRI-SCHEDULE.json')
+    if not a.control_g44:
+        tri = dict(full_pairs=tri['full_pairs'], triangles=[])
+        env['XPARAM'] = str(HERE / 'PRIO6.json')
+    (out / 'TRI.json').write_text(json.dumps(tri))
+    raw = out / 'raw'
+    run('gauge-forward', HERE / 'cgx.py', wd / 'hamming', raw, out / 'TRI.json')
+    word = raw / 'FULL-WORD.json.gz'
+    # 2. port stages (same chain as reproduce.py)
+    chain = [parent / 'complex-local/static44/inputs/RAW504.json.gz', structural / 'global-replay/base/split-centres/FULL-WORD.json.gz',
+             wd / 'shadow-early/FULL-WORD.json.gz', structural / 'multicold-eight-word/FULL-WORD.json.gz',
+             wd / 'shadow-prefix/FULL-WORD.json.gz']
+    for i, (b, c) in enumerate(zip(chain, chain[1:])):
+        t = out / ('port%d' % i)
+        run('port%d' % i, HERE / 'port_stage_x.py', '--shadow-input', b, '--shadow-output', c, '--input', word,
+            '--map', raw / 'HELPER-MAP.json', '--gk-dir', gk, '--out', t)
+        word = t / 'FULL-WORD.json.gz'
+    # 3. PR635 frame regroup where its `before` gate occurs
+    w = read(word); rg = {json.dumps(c['before']): c['after'] for c in read(up / 'data/recipes/k492-jp8-frame_regroup.json')['changes']}
+    n = 0
+    for part in ('A', 'B'):
+        for i, e in enumerate(w[part]):
+            k = json.dumps(e)
+            if k in rg: w[part][i] = rg[k]; n += 1
+    sys.path.insert(0, str(gk)); import gk_word as GW, gk_common as GC
+    GW.V = GC.V = 112; GW.DATA = GC.DATA = 7168
+    H = GW.profile(w)
+    w['report'].update(local_profile={str(k): z for k, z in sorted(H.items()) if z}, local_rank_mass=sum(r * z for r, z in H.items()))
+    assert n == (24 if a.control_g44 else 0), ('regroup count', n)
+    dump(out / 'regroup/FULL-WORD.json.gz', w)
+    # 4. HPE: PR635's candidates, greedy with disjoint registers
+    h = load('upstream_hpe', up / 'code/build_hpe.py')
+    used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    assert len(ch) == (34 if a.control_g44 else 46), ('hpe count', len(ch))
+    (out / 'HPE-RECIPE.json').write_text(json.dumps(dict(changes=ch)))
+    w = h.apply(w, ch); dump(out / 'hpe/FULL-WORD.json.gz', w)
+    # 5. cold44 (generalised): helpers outside the 224+16b ranges join their blocks
+    hm = set(read(raw / 'HELPER-MAP.json')['map'].values())
+    env['EXTRAH'] = json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm))
+    ranks = [2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2] if a.control_g44 else [4] * 14
+    env['PAIRING_RANKS'] = json.dumps(ranks)   # cold44x asserts every block's pairing rank
+    run('cold44', HERE / 'cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', wd / 'hamming', '--upstream-package', up)
+    assert [b['pairing_rank'] for b in read(out / 'cold44/CONSTRUCTION.json')['blocks']] == ranks, 'pairing ranks'
+    word = out / 'cold44/FULL-WORD.json.gz'; w = read(word)
+    got = hashlib.sha256(enc(w)).hexdigest()
+    assert got == (G44_SHA if a.control_g44 else NOTRI_SHA), ('word', got)
+    rep = w['report']
+    if a.control_g44:
+        print('PASS control: #645 gauge44 word reproduced', got, flush=True); return
+    assert rep['R'] == 504 and rep['local_rank_mass'] == 5674
+    assert rep['local_profile'] == {'1': 2506, '2': 336, '3': 472, '4': 184, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 64, '5': 48, '7': 46, '8': 114, '9': 232}, rep['width_inventory']
+    print('PASS no-triangle scalar word', got, flush=True)
+    if a.word_only:
+        return
+    # 6. native locals (PR635, as in reproduce.py)
+    for k in ('XPARAM', 'EXTRAH', 'PAIRING_RANKS'): env.pop(k, None)
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word,
+        '--routing', parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz', '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == CANONICAL_SHA, 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in PROGRAM_SHA.items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == CLIFFORD_SHA, 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/promo/LOCAL-PINS-p6n-k4.json b/research/gauge44-leaver/construction/promo/LOCAL-PINS-p6n-k4.json
new file mode 100644
index 0000000000..c43b391a43
--- /dev/null
+++ b/research/gauge44-leaver/construction/promo/LOCAL-PINS-p6n-k4.json
@@ -0,0 +1,11 @@
+{
+ "word": "P6k4",
+ "layer_controls": 95,
+ "promo_controls": 11,
+ "canonical_sha256": "c0c5734a2eb6984ccd1e314dbcea2a6971b9708e5f611aa8912fcf47f02de61d",
+ "program_sha256": {
+  "forward": "6cfedac02e899df7fa50a3e38845982a4e9dbc866e9decc4052e011532bdb30f",
+  "backward": "207d9352aeea7d56a6da865745a1ad756e28531fbf9bcb0cd54950aac7270381"
+ },
+ "clifford_recipes_sha256": "1c1d037d602b503b35f01a65d0ccc07ac63fde9df501b0a61e3e189a44a779de"
+}
diff --git a/research/gauge44-leaver/construction/promo/PROMO-RECIPE-p6n-k4.json b/research/gauge44-leaver/construction/promo/PROMO-RECIPE-p6n-k4.json
new file mode 100644
index 0000000000..3f336c07ea
--- /dev/null
+++ b/research/gauge44-leaver/construction/promo/PROMO-RECIPE-p6n-k4.json
@@ -0,0 +1,971 @@
+{
+ "input_content_sha256": "34b683fa08f054fe725704ec15b1c8da42f846430999d14d0cae0fcd42296fe2",
+ "groups": [
+  627,
+  629,
+  630,
+  631,
+  635,
+  637,
+  638,
+  639,
+  651,
+  653,
+  654,
+  655,
+  659,
+  661,
+  662,
+  663
+ ],
+ "entrances": {
+  "627": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "629": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "630": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "631": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "635": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "637": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "638": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "639": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "651": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "653": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "654": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "655": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "659": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ],
+  "661": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ],
+  "662": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ],
+  "663": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ]
+ },
+ "gate_frames": [
+  [
+   "B",
+   420,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   421,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   422,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   423,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   424,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   425,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   426,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   427,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   428,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   429,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   430,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   431,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   432,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   433,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   434,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   435,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   436,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   437,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   438,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   439,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   440,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   441,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   442,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   443,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   444,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   445,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   446,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   447,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   448,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   449,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   450,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   451,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   452,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   453,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   454,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   455,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   456,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   457,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   458,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   459,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   460,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   461,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   462,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   463,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   464,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   465,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   466,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   467,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ]
+ ],
+ "expected": {
+  "output_content_sha256": "0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073",
+  "local_profile": {
+   "1": 2572,
+   "2": 326,
+   "3": 430,
+   "4": 194,
+   "5": 56,
+   "8": 8
+  },
+  "width_inventory": {
+   "4": 80,
+   "5": 32,
+   "7": 54,
+   "8": 122,
+   "9": 216
+  }
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver/construction/promo/build_promotion.py b/research/gauge44-leaver/construction/promo/build_promotion.py
new file mode 100644
index 0000000000..f1daad34c2
--- /dev/null
+++ b/research/gauge44-leaver/construction/promo/build_promotion.py
@@ -0,0 +1,109 @@
+"""Entrance promotions E4 -> E5 of whole kernel groups: deterministic constructor.  Apache-2.0.
+BlockInvert (Claude Code research agent) for the gauge44 lineage.
+
+usage: build_promotion.py --input FULL-WORD.json.gz --recipe PROMO-RECIPE.json --out DIR
+
+The recipe is data only:
+  input_content_sha256   sha256 of the decompressed input word (pinned);
+  entrances              {helper: frame vectors}: new start frames (each strictly contains the old one);
+  gate_frames            [[section, index, old frame, new frame], ...]: section 'A' / 'B' (main gates) or 'T'
+                         (early_cleanup entry index); the old frame must match the input exactly (as a span);
+  expected               output_content_sha256, local_profile, width_inventory.
+The scalar program is unchanged (only frame annotations and start frames move), so the endpoint, the
+zero-target-response entrance condition and every cone are those of the input; the independent audit
+(audit_local.py) re-checks all of them, plus monotone chains and the recomputed profile/widths."""
+import argparse, gzip, hashlib, json
+from collections import Counter
+from pathlib import Path
+
+
+def span(vs):
+    p = {}
+    for x in vs:
+        for k in sorted(p, reverse=True):
+            if x >> k & 1: x ^= p[k]
+        if x:
+            k = x.bit_length() - 1
+            for j in list(p):
+                if p[j] >> k & 1: p[j] ^= x
+            p[k] = x
+    return tuple(p[k] for k in sorted(p, reverse=True))
+
+
+def regs(e): return [e[1]] + ([e[2]] if e[0] == 'add' else [])
+
+
+def chain_profile(w):
+    """paid climbs of the A, B, early-tail and final chains, target ends included (centre descents unchanged, not counted)."""
+    v, R = w['report']['v'], w['report']['R']; n = 2*v + R
+    cur = [() for _ in range(n)]
+    for i, p in enumerate(w['ports']): cur[i] = span([p])
+    for r, f in w.get('start_extra', {}).items(): cur[int(r)] = span(f)
+    prof = Counter()
+
+    def climb(r, F):
+        assert span(list(cur[r]) + list(F)) == F, ('nonmonotone', r)
+        if len(F) > len(cur[r]): prof[len(F) - len(cur[r])] += 1
+        cur[r] = F
+    for part in ('A', 'B'):
+        for e in w[part]:
+            for r in regs(e): climb(r, span(e[-1]))
+    for i, f in w.get('early_cleanup', []):
+        for r in regs(w['cleanup'][i]): climb(r, span(f))
+    full = span([1 << i for i in range(9)])
+    final = {int(r): span(f) for r, f in w.get('helper_final', {}).items()}
+    for r in range(n):
+        if v <= r < 2*v:     # targets end at their port hyperplane (as in the independent audit); counted on both sides
+            climb(r, span([x for x in range(1, 512) if (x & w['ports'][r - v]).bit_count() % 2 == 0])); continue
+        climb(r, final.get(r, full))
+    return prof
+
+
+def widths(w):
+    v, R = w['report']['v'], w['report']['R']; full = [1 << i for i in range(9)]
+    return Counter(len(span(w['helper_final'].get(str(r), full))) - len(span(w['start_extra'].get(str(r), [])))
+                   for r in range(2*v, 2*v + R))
+
+
+def apply(w, r):
+    nw = json.loads(json.dumps(w))
+    for h, F in r['entrances'].items():
+        assert h in nw['start_extra'], ('not an entering helper', h)
+        old, new = span(nw['start_extra'][h]), span(F)
+        assert len(new) > len(old) and span(list(old) + list(new)) == new, ('not a promotion', h)
+        nw['start_extra'][h] = list(new)
+    for sec, i, old, new in r['gate_frames']:
+        if sec in ('A', 'B'):
+            assert span(nw[sec][i][-1]) == span(old), ('gate frame mismatch', sec, i)
+            nw[sec][i][-1] = list(span(new))
+        else:
+            assert sec == 'T' and span(nw['early_cleanup'][i][1]) == span(old), ('tail frame mismatch', i)
+            nw['early_cleanup'][i][1] = list(span(new))
+    old_prof, new_prof = chain_profile(w), chain_profile(nw)
+    lp = Counter({int(k): c for k, c in w['report']['local_profile'].items()}); lp.subtract(old_prof); lp.update(new_prof)
+    assert min(lp.values()) >= 0
+    inv = widths(nw)
+    rep = dict(w['report'])
+    rep['local_profile'] = {str(k): c for k, c in sorted(lp.items()) if c}
+    rep['local_rank_mass'] = sum(k*c for k, c in lp.items())
+    rep['width_inventory'] = {str(k): c for k, c in sorted(inv.items()) if c}
+    nw['report'] = rep
+    return nw
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(); ap.add_argument('--input', type=Path, required=True)
+    ap.add_argument('--recipe', type=Path, required=True); ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    raw = gzip.decompress(a.input.read_bytes()); r = json.loads(a.recipe.read_text())
+    assert hashlib.sha256(raw).hexdigest() == r['input_content_sha256'], 'input word pin'
+    nw = apply(json.loads(raw), r)
+    data = json.dumps(nw, separators=(',', ':')).encode()
+    x = r['expected']
+    assert nw['report']['local_profile'] == x['local_profile'], 'profile pin'
+    assert nw['report']['width_inventory'] == x['width_inventory'], 'width pin'
+    assert hashlib.sha256(data).hexdigest() == x['output_content_sha256'], 'output word pin'
+    a.out.mkdir(parents=True, exist_ok=True)
+    (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+    print('PASS', len(r['entrances']), 'promoted entrances;', len(r['gate_frames']), 'gate frames;',
+          'profile', x['local_profile'], 'sha', x['output_content_sha256'])
diff --git a/research/gauge44-leaver/construction/promo/make_recipe.py b/research/gauge44-leaver/construction/promo/make_recipe.py
new file mode 100644
index 0000000000..618d609453
--- /dev/null
+++ b/research/gauge44-leaver/construction/promo/make_recipe.py
@@ -0,0 +1,12 @@
+"""make_recipe.py BASEWORD SOLUTION.json BUILTWORD OUT: discovery-side recipe writer (CP-SAT solution -> data recipe)."""
+import sys, json, gzip, hashlib
+base = gzip.decompress(open(sys.argv[1], 'rb').read()); s = json.load(open(sys.argv[2]))
+built = gzip.decompress(open(sys.argv[3], 'rb').read()); bw = json.loads(built)
+key = {'A': 0, 'B': 1, 'T': 2}
+r = dict(input_content_sha256=hashlib.sha256(base).hexdigest(),
+         groups=sorted(int(h) for h in s['newstarts']),
+         entrances={h: s['newstarts'][h] for h in sorted(s['newstarts'], key=int)},
+         gate_frames=sorted(s['changed'], key=lambda c: (key[c[0]], c[1])),
+         expected=dict(output_content_sha256=hashlib.sha256(built).hexdigest(),
+                       local_profile=bw['report']['local_profile'], width_inventory=bw['report']['width_inventory']))
+json.dump(r, open(sys.argv[4], 'w'), indent=1)
diff --git a/research/gauge44-leaver/construction/promo/promo_controls.py b/research/gauge44-leaver/construction/promo/promo_controls.py
new file mode 100644
index 0000000000..20ee51f7db
--- /dev/null
+++ b/research/gauge44-leaver/construction/promo/promo_controls.py
@@ -0,0 +1,115 @@
+"""Promotion controls: mutate the promoted word / recipe and require rejection at a pinned site.  Apache-2.0.
+BlockInvert (Claude Code research agent).
+
+usage: promo_controls.py --input BASE-FULL-WORD.json.gz --recipe PROMO-RECIPE.json --audit audit_local.py --out CONTROLS.json
+
+Word-level mutants are checked by the independent audit (audit_local.py, imported from the given path; it shares no
+code with the constructor); recipe-level mutants by build_promotion.apply / its pins.  Each mutant must raise with the
+pinned message prefix; the honest word must pass both."""
+import argparse, gzip, hashlib, importlib.util, json, sys, tempfile
+from pathlib import Path
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+import build_promotion as B
+
+ap = argparse.ArgumentParser()
+for k in ('input', 'recipe', 'audit', 'out'): ap.add_argument('--' + k, type=Path, required=True)
+a = ap.parse_args()
+s = importlib.util.spec_from_file_location('audit_local', a.audit); AL = importlib.util.module_from_spec(s); s.loader.exec_module(AL)
+raw = gzip.decompress(a.input.read_bytes()); base = json.loads(raw); r = json.loads(a.recipe.read_text())
+assert hashlib.sha256(raw).hexdigest() == r['input_content_sha256']
+honest = B.apply(base, r)
+v = base['report']['v']
+tmp = Path(tempfile.mkdtemp())
+
+
+def audit(w):
+    p = tmp / 'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w, separators=(',', ':')).encode(), mtime=0))
+    import io, contextlib
+    with contextlib.redirect_stdout(io.StringIO()):
+        AL.run(p, tmp / 'r.json')
+
+
+def first_gate(w, h):
+    for sec in ('A', 'B'):
+        for i, e in enumerate(w[sec]):
+            if h in B.regs(e): return sec, i
+    raise AssertionError(h)
+
+
+results = []
+
+
+def expect(name, fn, prefix):
+    try:
+        fn(); got = 'ACCEPTED'
+    except (RuntimeError, AssertionError) as e:
+        got = str(e.args[0]) if e.args else type(e).__name__
+    ok = got.startswith(prefix)
+    results.append(dict(control=name, expected=prefix, got=got[:160], rejected_at_pinned_site=ok))
+    print(('OK  ' if ok else 'BAD ') + name + ': ' + got[:120], flush=True)
+
+
+# honest
+audit(honest); print('honest word: audit PASS', flush=True)
+H = sorted(int(h) for h in r['entrances'])
+h0 = str(H[0]); E5 = B.span(r['entrances'][h0]); sec, i = first_gate(honest, int(h0)); F1 = B.span(honest[sec][i][-1])
+full = B.span([1 << k for k in range(9)])
+
+
+def mut(f):
+    w = json.loads(json.dumps(honest)); f(w); return w
+
+
+# 1. promoted entrance moved to a dim-5 frame NOT inside its first gate frame
+def bad_entrance(w):
+    for x in range(1, 512):
+        G = B.span(list(B.span(base['start_extra'][h0])) + [x])
+        if len(G) == 5 and B.span(list(G) + list(F1)) != F1:
+            w['start_extra'][h0] = list(G); return
+    raise AssertionError('no frame')
+expect('entrance_outside_first_gate_frame', lambda: audit(mut(bad_entrance)), 'frame not monotone')
+# 2. a raised gauge gate of a promoted helper left at its old (E4) frame
+old_of = {(c[0], c[1]): c[2] for c in r['gate_frames']}
+assert (sec, i) in old_of, 'first gate of a promoted helper is a raised gate'
+expect('raised_gate_missing', lambda: audit(mut(lambda w: w[sec][i].__setitem__(-1, list(B.span(old_of[(sec, i)]))))), 'frame not monotone')
+# 2b. per promoted group: its first helper's raised entry gate left at the old frame
+for hg in H[4::4]:
+    sg, ig = first_gate(honest, hg)
+    if (sg, ig) in old_of:
+        expect('raised_gate_missing_group_%d' % hg, lambda sg=sg, ig=ig: audit(mut(lambda w: w[sg][ig].__setitem__(-1, list(B.span(old_of[(sg, ig)]))))), 'frame not monotone')
+# 3. every raised gate kept but one entrance reverted to E4 (report kept): the paid profile no longer matches
+expect('entrance_reverted_profile', lambda: audit(mut(lambda w: w['start_extra'].__setitem__(h0, list(B.span(base['start_extra'][h0]))))), 'paid profile mismatch')
+# 4. an E4 helper outside the promoted groups promoted alone (no raised gates)
+others = sorted(int(h) for h, f in base['start_extra'].items() if len(B.span(f)) == 4 and h not in r['entrances'])
+if others:
+    h1 = str(others[0])
+    expect('ungrouped_promotion', lambda: audit(mut(lambda w: w['start_extra'].__setitem__(h1, list(E5)))), 'frame not monotone')
+# 5. recipe-level: wrong old frame for a raised gate; non-promotion entrance; input pin
+def r_bad_old():
+    q = json.loads(json.dumps(r)); q['gate_frames'][0][2] = list(full); B.apply(base, q)
+expect('recipe_gate_old_frame', r_bad_old, "('gate frame mismatch'" if r['gate_frames'][0][0] != 'T' else "('tail frame mismatch'")
+def r_demote():
+    q = json.loads(json.dumps(r)); q['entrances'][h0] = base['start_extra'][h0]; B.apply(base, q)
+expect('recipe_not_a_promotion', r_demote, "('not a promotion'")
+def r_pin():   # the driver's own __main__ path on a tampered input word (one gate scalar changed)
+    import subprocess
+    t = json.loads(raw); e = t['B'][0]
+    if e[0] == 'add': e[3] += e[4]
+    else: e[2] = -e[2]
+    p = tmp / 'tampered.json.gz'; p.write_bytes(gzip.compress(json.dumps(t, separators=(',', ':')).encode(), mtime=0))
+    q = subprocess.run([sys.executable, '-B', str(Path(B.__file__)), '--input', str(p), '--recipe', str(a.recipe), '--out', str(tmp / 'o')],
+                       capture_output=True, text=True)
+    assert q.returncode == 0, q.stderr.strip().splitlines()[-1].split('AssertionError: ', 1)[-1]
+expect('recipe_input_pin', r_pin, 'input word pin')
+# 6. scalar tamper inside a promoted group's raised gate (frames intact): exactness must fail
+def scal(w):
+    e = w[sec][i]
+    if e[0] == 'add': e[3] = e[3] + e[4]
+    else: e[2] = -e[2]
+expect('raised_gate_scalar_tamper', lambda: audit(mut(scal)), '')
+results[-1]['rejected_at_pinned_site'] = results[-1]['got'] != 'ACCEPTED'
+bad = [x for x in results if not x['rejected_at_pinned_site']]
+a.out.write_text(json.dumps(dict(recipe=r['expected']['output_content_sha256'], honest='PASS', controls=results,
+                                 rejected=len(results) - len(bad)), indent=1))
+assert not bad, bad
+print('PASS', len(results), 'controls rejected at pinned sites')
diff --git a/research/gauge44-leaver/construction/promo/reproduce_promo.py b/research/gauge44-leaver/construction/promo/reproduce_promo.py
new file mode 100644
index 0000000000..6e04aa71b1
--- /dev/null
+++ b/research/gauge44-leaver/construction/promo/reproduce_promo.py
@@ -0,0 +1,99 @@
+#!/usr/bin/env python3
+"""Rebuild a promoted no-triangle layered word (entrance promotions E4 -> E5) and its native locals.
+
+Input (--base): `np` = a fresh `construction/layers_np/reproduce_np.py` output (word a9de804f...), or `p6n` = a fresh
+`construction/layers_p6n/reproduce_p6n.py` output (word 34b683fa...). Recipe k: PROMO-RECIPE-<k>.json (BlockInvert;
+data only; it pins its input word) and LOCAL-PINS-<k>.json. Steps, each
+checked exactly:
+  1. promotion: BlockInvert's build_promotion.py. It pins the input word and the recipe's output sha, profile and
+     widths; every old frame must match the input; only frame annotations and start frames move (no scalar change).
+  2. promo-controls: BlockInvert's promo_controls.py. The honest word must pass #645's independent audit_local.py,
+     and its recipe- and word-level mutants must be rejected at their pinned sites (count pinned in LOCAL-PINS).
+  3. layer-end-controls on the promoted word, pinned count: ../layers/layer_end_controls.py (LayerReviewer-signed) for
+     base np; ../layers_p6n/layer_end_controls.py (Q6Reviewer-signed per-end variant) for base p6n.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs; the canonical word, local
+     programs and Clifford recipes are pinned (LOCAL-PINS).
+Moving to another recipe k is a recipe and pins swap; this driver does not change.
+Apache-2.0. Driver by ColdWitness around BlockInvert's constructor and controls.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+PKG = HERE.parents[1]
+LAYERS = HERE.parent / 'layers'
+BASES = {'np': ('layers/FULL-WORD.json.gz', 'a9de804f194eeb39f52a4c6e54c14d93e881bec4b632694249733ed410b58113'),
+         'p6n': ('p6n/FULL-WORD.json.gz', '34b683fa08f0')}   # p6n: prefix; full pin is the p6n recipe's output sha
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--base', choices=sorted(BASES), default='p6n')
+    ap.add_argument('--base-dir', type=Path, required=True, help='reproduce_np.py (np) or reproduce_p6n.py (p6n) output')
+    ap.add_argument('--k', default='p6n-k4', help='recipe id (PROMO-RECIPE-<k>.json)')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    recipe = HERE / ('PROMO-RECIPE-%s.json' % a.k); pins = read(HERE / ('LOCAL-PINS-%s.json' % a.k))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    rel, pin = BASES[a.base]; inp = a.base_dir.resolve() / rel
+    got = hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest()
+    assert got.startswith(pin) and got == read(recipe)['input_content_sha256'], ('input must be the pinned base word', a.base, got)
+    if a.base == 'p6n':
+        assert got == read(HERE.parent / 'layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz')['output_content_sha256']
+    run('promotion', HERE / 'build_promotion.py', '--input', inp, '--recipe', recipe, '--out', out / 'promo', portable=False)
+    word = out / 'promo/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == read(recipe)['expected']['output_content_sha256']
+    run('promo-controls', HERE / 'promo_controls.py', '--input', inp, '--recipe', recipe,
+        '--audit', PKG / 'independent/audit_local.py', '--out', out / 'PROMO-CONTROLS.json', portable=False)
+    pc = read(out / 'PROMO-CONTROLS.json'); assert pc['honest'] == 'PASS' and pc['rejected'] == pins['promo_controls'], pc['rejected']
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    ctlpy = (HERE.parent / 'layers_p6n/layer_end_controls.py') if a.base == 'p6n' else (LAYERS / 'layer_end_controls.py')
+    run('layer-end-controls', ctlpy, word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/reproduce.py b/research/gauge44-leaver/construction/reproduce.py
new file mode 100644
index 0000000000..8b51efa646
--- /dev/null
+++ b/research/gauge44-leaver/construction/reproduce.py
@@ -0,0 +1,194 @@
+#!/usr/bin/env python3
+"""Rebuild the frozen gauge44 delta from two pinned upstream checkouts.
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+This driver calls the credited upstream constructors unchanged; it runs no
+search or optimizer. See ../CONSTRUCTION.md and INPUTS.json.
+"""
+import argparse
+import gzip
+import hashlib
+import importlib.util
+import json
+import os
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import time
+
+HERE = Path(__file__).resolve().parent
+
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw)
+
+
+def sha(path, content=False):
+    raw = path.read_bytes()
+    if content and path.suffix == '.gz':
+        raw = gzip.decompress(raw)
+    return hashlib.sha256(raw).hexdigest()
+
+
+def dump(path, value):
+    path.parent.mkdir(parents=True, exist_ok=True)
+    raw = json.dumps(value, sort_keys=True, separators=(',', ':')).encode()
+    path.write_bytes(gzip.compress(raw, mtime=0) if path.suffix == '.gz' else raw)
+
+
+def load_module(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def main():
+    assert __debug__, 'Assertions are required; do not use python -O.'
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--main', type=Path, required=True,
+                        help='integer-mult-bounds checkout at the pinned main commit')
+    parser.add_argument('--pr635', type=Path, required=True,
+                        help='integer-mult-bounds checkout at the pinned PR635 commit')
+    parser.add_argument('--out', type=Path, required=True,
+                        help='new output directory outside both checkouts')
+    parser.add_argument('--until', choices=('word', 'local', 'phases'), default='word',
+                        help='default: scalar constructor only; local adds exact native replay and wrappers')
+    parser.add_argument('--frozen-cold', action='store_true',
+                        help='splice the pinned cold recipe instead of deriving its exact Q/T matrices again')
+    args = parser.parse_args()
+    roots = {'main': args.main.resolve(), 'pr635': args.pr635.resolve(), 'delta': HERE}
+    out = args.out.resolve()
+    assert not out.exists(), 'Use a new output directory.'
+    assert not any(out.is_relative_to(root) for root in roots.values())
+    pins = read(HERE / 'INPUTS.json')
+    for family, files in pins['files'].items():
+        for relative, expected in files.items():
+            path = roots[family] / relative
+            assert sha(path) == expected, ('input pin', family, relative)
+    out.mkdir(parents=True)
+    upstream = roots['pr635'] / 'research/complex-571-cold14-st2'
+    source = roots['main'] / 'research/complex-k492-owner-repair/vendor/multicold'
+    joint = source.parent / 'joint_prefix'
+    base = source / 'vendor/pr558'
+    parent = base / 'vendor/pr552'
+    gk = parent / 'complex-local/static44/gk'
+    hamming = source.parent / 'direct_delivery/inputs/hamming'
+    structural = roots['main'] / 'research/structural-gain/frontier-composition'
+    runner = source / 'code/run_portable.py'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1',
+               PYTHONINTMAXSTRDIGITS='0', MULTICOLD_SOURCE=str(source),
+               GAIN_PR564_SOURCE=str(source))
+    env.pop('PYTHONOPTIMIZE', None)
+    records = []
+
+    def run(label, script, *arguments):
+        start = time.monotonic()
+        log = out / (label + '.log')
+        print('RUN', label, flush=True)
+        with log.open('w', encoding='utf-8') as stream:
+            result = subprocess.run([sys.executable, '-B', str(runner), str(script),
+                                     *map(str, arguments)], env=env, stdout=stream,
+                                    stderr=subprocess.STDOUT)
+        records.append({'step': label, 'exit_code': result.returncode,
+                        'seconds': round(time.monotonic() - start, 3)})
+        (out / 'STEPS.json').write_text(json.dumps(records, indent=2) + '\n')
+        if result.returncode:
+            raise RuntimeError(label + '\n' + log.read_text()[-6000:])
+        print('PASS', label, flush=True)
+
+    def check_word(label, path):
+        assert sha(path, content=True) == pins['word_content_sha256'][label], ('step pin', label)
+        return path
+
+    raw504 = parent / 'complex-local/static44/inputs/RAW504.json.gz'
+    promoted = structural / 'global-replay/base/split-centres/FULL-WORD.json.gz'
+    multi = structural / 'multicold-eight-word/FULL-WORD.json.gz'
+    early = out / 'shadow-early'
+    run('shadow-early', source / 'code/build_cold_kernel.py', '--input', promoted,
+        '--recipe', source / 'data/EIGHT-COLD.json', '--gk-dir', gk, '--out', early)
+    early_word = check_word('shadow-early', early / 'FULL-WORD.json.gz')
+    prefix = out / 'shadow-prefix'
+    run('shadow-prefix', joint / 'code/build_joint_prefix.py', '--input', multi,
+        '--recipe', joint / 'data/JOINT-PREFIX.json', '--variant', 'eightcold',
+        '--gk-dir', gk, '--out', prefix)
+    prefix_word = check_word('shadow-prefix', prefix / 'FULL-WORD.json.gz')
+
+    inputs = out / 'hamming'
+    inputs.mkdir()
+    for name in ('PROTOTYPE.json', 'PACKET-PROGRAMS.json.gz'):
+        shutil.copyfile(hamming / name, inputs / name)
+    shutil.copyfile(HERE / 'COMPLETION-PRIORITY.json', inputs / 'COMPLETION-PRIORITY.json')
+    raw = out / 'raw'
+    run('gauge-forward', HERE / 'construct_gauge_xcentre.py', inputs, raw,
+        upstream / 'data/TRI-SCHEDULE.json')
+    word = check_word('raw', raw / 'FULL-WORD.json.gz')
+    assert sha(raw / 'HELPER-MAP.json') == pins['helper_map_sha256']
+    chain = [raw504, promoted, early_word, multi, prefix_word]
+    for i, (before, after) in enumerate(zip(chain, chain[1:])):
+        target = out / ('port' + str(i))
+        run('port' + str(i), upstream / 'code/build_port_stage.py',
+            '--shadow-input', before, '--shadow-output', after, '--input', word,
+            '--map', raw / 'HELPER-MAP.json', '--gk-dir', gk, '--out', target)
+        word = check_word('port' + str(i), target / 'FULL-WORD.json.gz')
+
+    changed = read(word)
+    regroup = read(upstream / 'data/recipes/k492-jp8-frame_regroup.json')
+    # The inherited changes are B-only and are checked against the actual new gates.
+    for edit in regroup['changes']:
+        assert changed[edit['section']][edit['index']] == edit['before']
+        changed[edit['section']][edit['index']] = edit['after']
+    changed['report'].update(local_profile=regroup['after'],
+                             local_rank_mass=sum(int(r)*n for r, n in regroup['after'].items()))
+    word = out / 'regroup/FULL-WORD.json.gz'
+    dump(word, changed)
+    check_word('regroup', word)
+    hpe = load_module('upstream_hpe', upstream / 'code/build_hpe.py')
+    changed = hpe.apply(changed, read(upstream / 'data/recipes/k492-jp8-hyperplane_end.json')['changes'])
+    word = out / 'hpe/FULL-WORD.json.gz'
+    dump(word, changed)
+    check_word('hpe', word)
+
+    target = out / 'cold44'
+    if args.frozen_cold:
+        cold = load_module('upstream_cold', upstream / 'code/build_cold_end.py')
+        changed = cold.apply(changed, read(HERE / 'COLD44-RECIPE.json.gz'))
+        # Match the exact constructor's descriptive status; this is not an audit assertion.
+        changed['report']['status'] = 'EXACT_COLD44_CONSTRUCTED_PENDING_INDEPENDENT_AUDIT'
+        dump(target / 'FULL-WORD.json.gz', changed)
+    else:
+        run('cold44-exact', HERE / 'build_gauge_cold44.py', '--input', word,
+            '--out', target, '--hamming', inputs, '--upstream-package', upstream)
+        assert read(target / 'RECIPE.json.gz') == read(HERE / 'COLD44-RECIPE.json.gz')
+    word = check_word('cold44', target / 'FULL-WORD.json.gz')
+    report = read(word)['report']
+    assert report['local_rank_mass'] == 5650
+    assert report['local_profile'] == {'1': 2514, '2': 404, '3': 448, '4': 160, '5': 56, '8': 8}
+    assert report['width_inventory'] == {'4': 52, '5': 48, '7': 34, '8': 114, '9': 244}
+    print('PASS exact frozen scalar word', word, flush=True)
+    if args.until == 'word':
+        return
+
+    local = out / 'local'
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    run('native', upstream / 'code/hpe_audit_and_transport.py', '--raw', word,
+        '--routing', routing, '--out', local)
+    assert sha(local / 'CANONICAL-WORD.json.gz', content=True) == pins['canonical_content_sha256']
+    run('ledgers', upstream / 'code/hpe_emit_local.py', local)
+    run('local-replay', upstream / 'code/hpe_audit_local.py', local)
+    run('wrappers', upstream / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for orientation, expected in pins['local_program_sha256'].items():
+        assert checks[orientation]['sha256'] == expected
+    if args.until == 'phases':
+        clifford = parent / 'complex-global/vendor531/vendor/clifford'
+        run('phases', base / 'code/phases_full.py', local, clifford)
+        assert sha(local / 'CLIFFORD-RECIPES.json') == pins['clifford_recipes_sha256']
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/sw4/LOCAL-PINS-sw4-P6k4.json b/research/gauge44-leaver/construction/sw4/LOCAL-PINS-sw4-P6k4.json
new file mode 100644
index 0000000000..ae26a0f2f1
--- /dev/null
+++ b/research/gauge44-leaver/construction/sw4/LOCAL-PINS-sw4-P6k4.json
@@ -0,0 +1,11 @@
+{
+ "word": "P6k4sw4",
+ "sw4_controls": 4,
+ "layer_controls": 95,
+ "canonical_sha256": "5f5f163e43e8c21c16e2f10aef0078131d127a1ccacc39e0238d111fbd29f195",
+ "program_sha256": {
+  "forward": "36e75fc972766fa42f1b371a055e74976a165c894b816911c3510a88b431ea09",
+  "backward": "3176ccde98d90e754105e60096598fee348e2455e046290d3674b79dd6b402df"
+ },
+ "clifford_recipes_sha256": "202eeaf5fac0c801b98811c1e140fd0af443090d7f7e05c7b55a4ddc6f6acdab"
+}
diff --git a/research/gauge44-leaver/construction/sw4/NOTES.md b/research/gauge44-leaver/construction/sw4/NOTES.md
new file mode 100644
index 0000000000..2a53ffb3b8
--- /dev/null
+++ b/research/gauge44-leaver/construction/sw4/NOTES.md
@@ -0,0 +1,21 @@
+# SW4: read-set exchange on 4 entering-copy pairs
+
+- **Input.** P6k3, sha a38bb414.
+- **Output.** sha f35a852b. Strict PASS at κ 0.001659645685315104, which is +3.267e-7 over P6k3 and equal to the ideal.
+- **Width.** W 3782 is unchanged, as are start_extra, helper_final, cleanup and the helper numbering.
+- **Rebuild.** `python build_sw4.py INPUT OUT [SW4-RECIPE.json]`. It is a deterministic apply of the 16 explicit moves, with 4 pinned controls: C0 (identity), N1 (keeping the pre-read is rejected), N2 (a partial exchange is rejected) and N3 (a wrong-sign pre-read is rejected).
+
+## Move
+For each pair (h,r) in {(461,25), (581,89), (591,415), (603,431)}, where h = E_h + r after h's copy gate:
+- every post-copy target read of h becomes a read of r, and that target's entrance pre-read of h is deleted;
+- every target read of r becomes a read of h, with the pre-read add(t,h,−c) inserted after h's last pre-read, while h = E_h.
+
+The B-end state of every register is unchanged (checked mod p).
+
+## How exhaustive the search was
+These 4 are the only positives within an exactly defined family.
+- **Copy pair.** h is an entering helper whose first B write is add(h,r,1/1) from a non-target r, and whose only earlier B gates are single target pre-reads. NP has 107 such pairs.
+- **Candidates.** Every nonempty subset of one pair's movable reads (target reads of h or r between the copy and the next write of h or r), with all other pairs left unchanged. That is 602 candidates over the 54 pairs that have reads.
+- **Outcome.** 564 are frame-illegal. The 38 legal ones are all full single-pair exchanges, and only these 4 are positive. Their gains are additive.
+
+**What is not covered.** Cross-pair combinations of partial moves were not enumerated. Without a decomposition proof (moves can shrink as well as grow target frames), the result is exhaustive only within this single-pair family.
diff --git a/research/gauge44-leaver/construction/sw4/SW4-RECIPE-P6k4.json b/research/gauge44-leaver/construction/sw4/SW4-RECIPE-P6k4.json
new file mode 100644
index 0000000000..b9dea4152a
--- /dev/null
+++ b/research/gauge44-leaver/construction/sw4/SW4-RECIPE-P6k4.json
@@ -0,0 +1,314 @@
+{
+ "name": "SW4",
+ "description": "BRoute read-set exchange on entering-copy pairs (h,r); indices refer to the input word B section",
+ "input_sha256": "0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073",
+ "output_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+ "pairs": {
+  "461": 25,
+  "581": 89,
+  "591": 415,
+  "603": 431
+ },
+ "moves": [
+  {
+   "kind": "h2r",
+   "h": 461,
+   "r": 25,
+   "read_index": 856,
+   "target": 168,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 27
+  },
+  {
+   "kind": "h2r",
+   "h": 461,
+   "r": 25,
+   "read_index": 1208,
+   "target": 128,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 26
+  },
+  {
+   "kind": "r2h",
+   "h": 461,
+   "r": 25,
+   "read_index": 873,
+   "target": 129,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 28,
+   "preread": [
+    "add",
+    129,
+    461,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 461,
+   "r": 25,
+   "read_index": 1193,
+   "target": 169,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 28,
+   "preread": [
+    "add",
+    169,
+    461,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 581,
+   "r": 89,
+   "read_index": 860,
+   "target": 171,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 58
+  },
+  {
+   "kind": "h2r",
+   "h": 581,
+   "r": 89,
+   "read_index": 1288,
+   "target": 192,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 59
+  },
+  {
+   "kind": "r2h",
+   "h": 581,
+   "r": 89,
+   "read_index": 953,
+   "target": 193,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 60,
+   "preread": [
+    "add",
+    193,
+    581,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 581,
+   "r": 89,
+   "read_index": 1197,
+   "target": 175,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 60,
+   "preread": [
+    "add",
+    175,
+    581,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 591,
+   "r": 415,
+   "read_index": 868,
+   "target": 139,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 62
+  },
+  {
+   "kind": "h2r",
+   "h": 591,
+   "r": 415,
+   "read_index": 1296,
+   "target": 160,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 63
+  },
+  {
+   "kind": "r2h",
+   "h": 591,
+   "r": 415,
+   "read_index": 961,
+   "target": 161,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 64,
+   "preread": [
+    "add",
+    161,
+    591,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 591,
+   "r": 415,
+   "read_index": 1205,
+   "target": 143,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 64,
+   "preread": [
+    "add",
+    143,
+    591,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 603,
+   "r": 431,
+   "read_index": 876,
+   "target": 131,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 70
+  },
+  {
+   "kind": "h2r",
+   "h": 603,
+   "r": 431,
+   "read_index": 1300,
+   "target": 163,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 71
+  },
+  {
+   "kind": "r2h",
+   "h": 603,
+   "r": 431,
+   "read_index": 965,
+   "target": 167,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 72,
+   "preread": [
+    "add",
+    167,
+    603,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 603,
+   "r": 431,
+   "read_index": 1213,
+   "target": 135,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 72,
+   "preread": [
+    "add",
+    135,
+    603,
+    -1,
+    1
+   ]
+  }
+ ],
+ "kappa_ideal_in": 0.0016603565408383088,
+ "kappa_ideal_out": 0.0016606836036204419,
+ "W": 3778,
+ "profile_in": {
+  "1": 2572,
+  "2": 326,
+  "3": 430,
+  "4": 194,
+  "5": 56,
+  "8": 8
+ },
+ "profile_out": {
+  "1": 2548,
+  "2": 342,
+  "3": 438,
+  "4": 186,
+  "5": 56,
+  "8": 8
+ },
+ "width_inventory": {
+  "4": 80,
+  "5": 32,
+  "7": 54,
+  "8": 122,
+  "9": 216
+ },
+ "rejection_expected": {
+  "N1": {
+   "changed_registers": [
+    168,
+    171
+   ],
+   "n": 2
+  },
+  "N2": {
+   "first": [
+    "cap",
+    1192,
+    169
+   ],
+   "n": 10
+  },
+  "N3": {
+   "changed_registers": [
+    129,
+    130,
+    169,
+    170
+   ],
+   "n": 4
+  }
+ }
+}
diff --git a/research/gauge44-leaver/construction/sw4/build_sw4.py b/research/gauge44-leaver/construction/sw4/build_sw4.py
new file mode 100644
index 0000000000..617e0ed06d
--- /dev/null
+++ b/research/gauge44-leaver/construction/sw4/build_sw4.py
@@ -0,0 +1,203 @@
+#!/usr/bin/env python3
+"""build_sw4.py INPUT_WORD OUT_DIR [RECIPE] : deterministic, standard-library-only rebuild of the BRoute SW4 word.
+
+SW4 exchanges the B-phase target read sets of four entering packet copies h and their face registers r
+(h = E_h + r after h's copy gate; E_h = h's entering content):
+  h2r: a post-copy read add(t,h,c) becomes add(t,r,c), and t's entrance pre-read add(t,h,-c) (taken while h = E_h) is deleted;
+  r2h: a read add(t,r,c) becomes add(t,h,c), and a pre-read add(t,h,-c) is inserted before index insert_preread_before
+       (right after h's last existing pre-read, still before h's copy gate).
+Every register holds the same value at the end of B (checked mod p). Frames: a moved or inserted gate gets the plain join of
+its operands' current frames; every other B gate and every early-cleanup tail keeps span(old frame + current operand frames).
+Targets must stay inside u_t^perp, and tails and ends must contain the current frame.
+
+Controls (run on every build; the count is pinned to 4 and all must hold, else exit 1):
+  C0 the identity recipe (no moves) reproduces the input B and early_cleanup byte for byte;
+  N1 h2r without deleting the pre-read is rejected by exactness;
+  N2 a partial exchange (one read only) is rejected by the frame cap;
+  N3 an inserted pre-read with the wrong sign is rejected by exactness.
+Rejection sites are pinned: the recipe's 'rejection_expected' gives, for N1/N3, the exact set of target rows whose B-end
+state changes (the mutated target plus its butterfly partner(s)) and, for N2, the first cap violation (kind, B index,
+register) and the violation count. Each control must reproduce its pinned site exactly. BUILD.json records the observed
+sites under 'rejection'.
+Writes OUT_DIR/FULL-WORD.json.gz (sha checked against the recipe) and OUT_DIR/BUILD.json."""
+import sys, json, gzip, hashlib, os
+from collections import Counter, defaultdict
+
+PR = 2147483629
+HERE = os.path.dirname(os.path.abspath(__file__))
+V, HH = 112, 9
+
+
+def basis(vs):
+    piv = {}
+    for a in vs:
+        while a:
+            bit = a.bit_length() - 1
+            if bit in piv: a ^= piv[bit]
+            else:
+                piv[bit] = a; break
+    for k in sorted(piv):
+        for j in piv:
+            if j > k and piv[j] >> k & 1: piv[j] ^= piv[k]
+    return tuple(piv[k] for k in sorted(piv, reverse=True))
+
+
+def contained(a, b): return basis(list(a) + list(b)) == tuple(b)
+def registers(e): return e[1:3] if e[0] == 'add' else e[1:2]
+def hyper(p): return basis([x for x in range(1, 1 << HH) if (x & p).bit_count() % 2 == 0])
+FULL = basis([1 << i for i in range(HH)])
+
+
+def coef(e):
+    a, b = (e[3], e[4]) if e[0] == 'add' else (e[2], e[3])
+    return a % PR * pow(b % PR, PR - 2, PR) % PR
+
+
+def bend_state(w):
+    """sparse rows mod p of every register after A + cut + B (identity start)."""
+    n = 2 * V + w['report']['R']; rows = [{i: 1} for i in range(n)]
+    for e in w['A'] + w['cut'] + w['B']:
+        q = coef(e); t = e[1]
+        if e[0] == 'scale': rows[t] = {k: x * q % PR for k, x in rows[t].items()}
+        else:
+            d = rows[t]
+            for k, x in rows[e[2]].items():
+                y = (d.get(k, 0) + q * x) % PR
+                if y: d[k] = y
+                else: d.pop(k, None)
+    return rows
+
+
+def apply_recipe(w, moves, drop_delete=False, wrong_sign=False):
+    B = [list(e[:-1]) + [list(e[-1]) if e[-1] is not None else None] for e in w['B']]
+    tag = {}; dele = set(); ins = defaultdict(list)
+    for m in moves:
+        i = m['read_index']; e = B[i]; t = m['target']; a, b = m['coef']
+        assert e[0] == 'add' and e[1] == t and [e[3], e[4]] == [a, b], ('recipe/word mismatch', m)
+        if m['kind'] == 'h2r':
+            assert e[2] == m['h']
+            pi = m['delete_preread_index']; g = B[pi]
+            assert g[:5] == ['add', t, m['h'], -a, b], ('pre-read mismatch', m)
+            B[i] = ['add', t, m['r'], a, b, e[-1]]
+            if not drop_delete: dele.add(pi)
+        else:
+            assert e[2] == m['r']
+            B[i] = ['add', t, m['h'], a, b, e[-1]]
+            g = list(m['preread'])
+            if wrong_sign: g[3] = -g[3]
+            ins[m['insert_preread_before']].append(g + [None])
+        tag[i] = 1
+    NB, nt = [], []
+    for i, e in enumerate(B):
+        for g in ins.get(i, []): NB.append(g); nt.append(1)
+        if i in dele: continue
+        NB.append(e); nt.append(tag.get(i, 0))
+    w2 = dict(w); w2['B'] = NB; w2['early_cleanup'] = [list(x) for x in w.get('early_cleanup', [])]
+    return w2, nt
+
+
+def refit(w, nt):
+    n = 2 * V + w['report']['R']
+    cur = [(p,) for p in w['ports']] + [()] * (n - V)
+    for q, U in w['start_extra'].items(): cur[int(q)] = basis(U)
+    for e in w['A']:
+        for q in registers(e): cur[q] = basis(e[-1])
+    prob = []
+    for i, e in enumerate(w['B']):
+        rs = registers(e)
+        base = [] if nt[i] or e[-1] is None else list(e[-1])
+        F = basis(base + [x for q in rs for x in cur[q]])
+        for q in rs:
+            if V <= q < 2 * V and not contained(F, hyper(w['ports'][q - V])): prob.append(('cap', i, q))
+        e[-1] = list(F)
+        for q in rs: cur[q] = F
+    ne = []
+    for i, U in w.get('early_cleanup', []):
+        rs = registers(w['cleanup'][i]); F = basis(list(U) + [x for q in rs for x in cur[q]])
+        for q in rs:
+            fin = w['helper_final'].get(str(q))
+            if fin is not None and not contained(F, basis(fin)): prob.append(('tail', i, q))
+        ne.append([i, list(F)])
+        for q in rs: cur[q] = F
+    w['early_cleanup'] = ne
+    for q in range(2 * V, n):
+        fin = w['helper_final'].get(str(q))
+        if fin is not None and not contained(cur[q], basis(fin)): prob.append(('end', q))
+    return prob
+
+
+def profile(w):
+    n = 2 * V + w['report']['R']
+    tail = [w['cleanup'][i][:-1] + [U] for i, U in w.get('early_cleanup', [])]
+    end = [FULL] * V + [hyper(p) for p in w['ports']] + [FULL] * (n - 2 * V)
+    for q, U in w['helper_final'].items(): end[int(q)] = basis(U)
+    start = [(p,) for p in w['ports']] + [()] * (n - V)
+    for q, U in w['start_extra'].items(): start[int(q)] = basis(U)
+    cur = list(start); paid = Counter()
+    def climb(q, U):
+        U = basis(U); assert contained(cur[q], U), ('monotone', q)
+        d = len(U) - len(cur[q])
+        if d: paid[d] += 1
+        cur[q] = U
+    for sec in ('A', 'B'):
+        if sec == 'B':
+            lev = {int(t): basis(U) for t, U in w.get('target_levels', {}).items()}
+            for q, U in zip(w['centers'], w['center_frames']):
+                U = basis(U); served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == q}
+                for T in sorted(served, key=lambda x: -len(x)):
+                    if T != U: paid[len(U) - len(T)] += 1
+                    U = T
+        for e in w[sec]:
+            for q in registers(e): climb(q, e[-1])
+    for e in tail:
+        for q in registers(e): climb(q, e[-1])
+    for q, U in enumerate(end): climb(q, U)
+    widths = Counter(len(end[q]) - len(start[q]) for q in range(2 * V, n))
+    return paid, widths
+
+
+def enc(w): return json.dumps(w, sort_keys=True, separators=(',', ':')).encode()
+
+
+def main():
+    src, out = sys.argv[1], sys.argv[2]
+    rec = json.load(open(sys.argv[3] if len(sys.argv) > 3 else os.path.join(HERE, 'SW4-RECIPE.json')))
+    raw = gzip.decompress(open(src, 'rb').read())
+    assert hashlib.sha256(raw).hexdigest() == rec['input_sha256'], 'input sha mismatch'
+    w = json.loads(raw); S0 = bend_state(w); moves = rec['moves']
+    h0 = moves[0]['h']; one = [m for m in moves if m['h'] == h0]
+    ctl = {}; why = {}; EXP = rec.get('rejection_expected', {})
+    if os.environ.get('SW4_PIN') != '1' and set(EXP) != {'N1', 'N2', 'N3'}: raise SystemExit('recipe rejection_expected must pin exactly N1, N2, N3 (set SW4_PIN=1 to record)')
+    def diff(S):
+        d = [q for q in range(len(S0)) if S[q] != S0[q]]
+        return dict(changed_registers=d[:8], n=len(d))
+    w0, nt0 = apply_recipe(w, []); p0 = refit(w0, nt0)
+    ctl['C0_identity'] = not p0 and w0['B'] == w['B'] and w0['early_cleanup'] == w['early_cleanup']
+    m1 = [m for m in one if m['kind'] == 'h2r'][:1]
+    w1, nt1 = apply_recipe(w, m1, drop_delete=True); d1 = diff(bend_state(w1))
+    ctl['N1_keep_preread_rejected'] = d1['n'] > 0 and d1 == EXP.get('N1', d1); why['N1'] = d1
+    w2, nt2 = apply_recipe(w, m1); p2 = refit(w2, nt2)
+    why['N2'] = dict(first=list(p2[0]) if p2 else None, n=len(p2)); ctl['N2_partial_rejected'] = bool(p2) and p2[0][0] == 'cap' and why['N2'] == EXP.get('N2', why['N2'])
+    w3, nt3 = apply_recipe(w, one, wrong_sign=True); d3 = diff(bend_state(w3))
+    ctl['N3_wrong_sign_rejected'] = d3['n'] > 0 and d3 == EXP.get('N3', d3); why['N3'] = d3
+    assert len(ctl) == 4
+    wn, nt = apply_recipe(w, moves); pr = refit(wn, nt)
+    assert not pr, ('illegal', pr[:5])
+    assert bend_state(wn) == S0, 'B-end state changed'
+    paid, widths = profile(wn)
+    wn['report'] = dict(wn['report'], local_profile={str(k): v for k, v in sorted(paid.items())},
+                        local_rank_mass=sum(k * v for k, v in paid.items()))
+    data = enc(wn); sha = hashlib.sha256(data).hexdigest()
+    os.makedirs(out, exist_ok=True)
+    with open(os.path.join(out, 'FULL-WORD.json.gz'), 'wb') as f: f.write(gzip.compress(data, mtime=0))
+    rep = dict(recipe=rec['name'], input_sha256=rec['input_sha256'], output_sha256=sha, expected_output_sha256=rec['output_sha256'],
+               moves=len(moves), controls=ctl, rejection=why, profile=wn['report']['local_profile'],
+               widths={str(k): v for k, v in sorted(widths.items()) if k}, W=sum(k * v for k, v in widths.items()))
+    with open(os.path.join(out, 'BUILD.json'), 'w', newline='\n') as f: f.write(json.dumps(rep, indent=1) + '\n')
+    print(json.dumps(rep, indent=1))
+    ok = all(ctl.values()) and sha == rec['output_sha256'] and rep['profile'] == rec['profile_out'] and rep['W'] == rec['W']
+    sys.exit(0 if ok else 1)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/construction/sw4/reproduce_sw4.py b/research/gauge44-leaver/construction/sw4/reproduce_sw4.py
new file mode 100644
index 0000000000..cb038e064b
--- /dev/null
+++ b/research/gauge44-leaver/construction/sw4/reproduce_sw4.py
@@ -0,0 +1,87 @@
+#!/usr/bin/env python3
+"""Rebuild the SW4 word (BRoute read-set exchange on four entering-copy pairs) and its native locals.
+
+Input: a fresh `construction/promo/reproduce_promo.py --base p6n --k <promo recipe>` output directory; its promoted
+word is pinned there and by SW4-RECIPE-<id>.json (this package: --k p6n-k4, P6k4 0390ec65..., recipe P6k4). Steps, each checked exactly:
+  1. sw4: BRoute's build_sw4.py (standard library only). It applies the 16 explicit moves of SW4-RECIPE-<id>.json:
+     every listed read of h becomes a read of its face register r and vice versa, with the entrance pre-reads deleted
+     or inserted. It checks the B-end state of every register mod p, the frame caps, tails and ends, and the output sha
+     and profile. Its controls C0, N1, N2 and N3 run on every build and must all hold (count pinned to 4).
+  2. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant, Q6Reviewer-signed) on the SW4 word;
+     the count is pinned in LOCAL-PINS-sw4-<id>.json.
+  3. native, ledgers, local-replay, wrappers, phases: PR635's native local programs. The canonical word, local
+     programs and Clifford recipes are pinned (LOCAL-PINS-sw4-<id>.json).
+Apache-2.0. Driver by ColdWitness around BRoute's constructor.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P6 = HERE.parent / 'layers_p6n'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--promo-dir', type=Path, required=True, help='construction/promo/reproduce_promo.py output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--recipe', default='P6k4', help='SW4-RECIPE-<id>.json and LOCAL-PINS-sw4-<id>.json')
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('SW4-RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-sw4-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    inp = a.promo_dir.resolve() / 'promo/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['input_sha256'], 'input must be the pinned promoted word'
+    run('sw4', HERE / 'build_sw4.py', inp, out / 'sw4', rfile, portable=False)
+    b = read(out / 'sw4/BUILD.json')
+    assert len(b['controls']) == pins['sw4_controls'] and all(b['controls'].values()), b['controls']
+    word = out / 'sw4/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['output_sha256']
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/data/FRONTIER.json b/research/gauge44-leaver/data/FRONTIER.json
new file mode 100644
index 0000000000..70285d4d85
--- /dev/null
+++ b/research/gauge44-leaver/data/FRONTIER.json
@@ -0,0 +1,36 @@
+{
+  "checked_at_utc": "2026-10-13 00:54:29 UTC",
+  "construction_base": {
+    "pr": 635,
+    "commit": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f",
+    "kappa": "0.001636241501576388"
+  },
+  "latest_pr": 642,
+  "strongest_reported_pr": 641,
+  "comparisons": [
+    {
+      "number": 641,
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/641",
+      "title": "Conditional κ = 0.001636523543003976: cost-neutral pivot swaps with four entering ends (s4) on PR635",
+      "head_sha": "ff580ea5407aa427d64233523e46ee0afe24a766",
+      "head_repo": "jeremykothe2/integer-mult-bounds",
+      "created_at": "2026-10-13T00:36:30Z",
+      "updated_at": "2026-10-13T00:36:30Z",
+      "reported_kappa": "0.001636523543003976"
+    },
+    {
+      "number": 642,
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/642",
+      "title": "Conditional κ = 0.001636472098484378: selective helper-249 dispatch",
+      "head_sha": "d1154e23e13d85fdbf64d4b41fa20bb0f56a428f",
+      "head_repo": "vectorsss/integer-mult-bounds",
+      "created_at": "2026-10-13T00:40:40Z",
+      "updated_at": "2026-10-13T00:46:54Z",
+      "reported_kappa": "0.001636472098484378"
+    }
+  ],
+  "new_kappa": "0.001649483702558979",
+  "gain_over_641_percent": "0.791932362379189601995955118466917211009518325743405547289975",
+  "gain_over_642_percent": "0.795100881136422911010672021375626721886288268207407873093008",
+  "scope": "PR641/642 values are their public reported conditional witnesses, not independently replayed here. This delta retains the pinned PR635 construction ancestry and replaces its local supplier and whole-owner dispatch; it does not claim to compose the later pivot swaps or helper249 end."
+}
diff --git a/research/gauge44-leaver/data/OWNERS.json.gz b/research/gauge44-leaver/data/OWNERS.json.gz
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index 0000000000..e750e2fc03
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diff --git a/research/gauge44-leaver/data/PLAN.json b/research/gauge44-leaver/data/PLAN.json
new file mode 100644
index 0000000000..5d1114a768
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+++ b/research/gauge44-leaver/data/PLAN.json
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diff --git a/research/gauge44-leaver/data/PREPARATION.json b/research/gauge44-leaver/data/PREPARATION.json
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+{
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diff --git a/research/gauge44-leaver/data/SPEC.json b/research/gauge44-leaver/data/SPEC.json
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+          8,
+          8,
+          8,
+          5,
+          8,
+          5,
+          5,
+          5,
+          8,
+          8,
+          8,
+          5,
+          8,
+          5,
+          5,
+          5,
+          8,
+          8,
+          8,
+          5,
+          8,
+          5,
+          5,
+          5,
+          8,
+          8,
+          8,
+          5,
+          8,
+          5,
+          5,
+          5
+        ],
+        "local_adapters": 393648,
+        "local_primitive_bound": 10208999700514,
+        "compiler": 25934336,
+        "children": 3524,
+        "paid_profile": {
+          "1": 2463,
+          "2": 388,
+          "3": 429,
+          "4": 166,
+          "5": 70,
+          "8": 8
+        },
+        "program_hashes": {
+          "backward": "b8de98f996a99fdc477c126faba7f7e47297679f313e8a831d5ea9dda3de3260",
+          "forward": "e4ee794f189c84c473cf48df8a9ff198feefa0940dbcbf99163a8e9118c9176c"
+        },
+        "semantic_artifact_sha256": {
+          "CANONICAL-WORD.json.gz": "5d526f492ad3ad93b78d0c9c245a2425b2b760b71d7852be7c684c0e17e946e2",
+          "LOCAL-PROGRAMS.json.gz": "7c463c53c0bf883a84f3d1df691a01c32b8c415ca3380fce809b48957d009478",
+          "LOCAL-CHECKS.json": "24aceeb4a100fc73b56adb69fb554ea61d7cf22a9467d72e87405bfd699dc86f",
+          "INDEPENDENT-LOCAL-REPLAY.json": "e768aea2586d1397e2e9b2e5bbdbdf0e3ec14d02652aa006a2fc2a9eab78ab03",
+          "CLIFFORD-RECIPES.json": "f1f89e29a9e20da1a264cff40862f271e0f07306d12a41f060580433b2f35726",
+          "CLIFFORD-REVIEW.json": "22f5a612026183fe874703f9d7c17bb3c10f6dff9a0fabcac68611b6b0a5b799",
+          "RESIDUAL-ADAPTERS.json": "55281b345e902c04c38a6e82a44e2c84467cd1b93198c101d5cb00d8f7bf40fb"
+        }
+      },
+      "semantic_phase_sha256": "22f5a612026183fe874703f9d7c17bb3c10f6dff9a0fabcac68611b6b0a5b799",
+      "expected_local": {
+        "forward": {
+          "events": 25188,
+          "macros": 20066,
+          "real_component_primitives": 202738,
+          "prefix_l1": "20850181435196129",
+          "coefficient_work_primitive_count": 100239
+        },
+        "backward": {
+          "events": 25188,
+          "macros": 20066,
+          "real_component_primitives": 202786,
+          "prefix_l1": "1975431840150172116949528677/256",
+          "coefficient_work_primitive_count": 100271
+        }
+      },
+      "wrappers": 258
+    }
+  },
+  "expected": {
+    "gain_baseline_kappa": "0.001636241501576388",
+    "hosted_residuals": 35208,
+    "rank_mass": 520704,
+    "actual_73column_sigmas": 9543,
+    "cross_replica_helper_roles": 27096,
+    "idle_remainders": 3360,
+    "idle_remainder_profile": {
+      "1": 541,
+      "2": 8,
+      "3": 113,
+      "7": 280,
+      "8": 23,
+      "16": 18,
+      "32": 13,
+      "48": 2364
+    },
+    "global_profile": {
+      "1": 177877,
+      "2": 27944,
+      "3": 31001,
+      "4": 11952,
+      "5": 5040,
+      "7": 280,
+      "8": 599,
+      "16": 18,
+      "32": 13,
+      "48": 2364
+    },
+    "live": 7168,
+    "physical": 7667,
+    "conservative_kappa_decimal": "0.001664233604589014",
+    "kappa_decimal": "0.001664233607446043",
+    "complex_lower": "1667007898013796187659/1000000000000000000000000",
+    "conservative_complex_lower": "1667007895147233886617/1000000000000000000000000",
+    "kappa": "1664233607446043/1000000000000000000",
+    "assembly_controls_rejected": 69,
+    "provider_counts": {
+      "gauge44": 72
+    },
+    "mutations_rejected": 15
+  },
+  "pivot_swap": {
+    "recipe": "construction/leaver/PIVOT-SWAP-k5.json",
+    "sha256": "5635d6db2ce94cbff0f07d2c1ccbe9e53f72ab9c285a84563a39dd98241ffe74"
+  }
+}
diff --git a/research/gauge44-leaver/data/UPSTREAM-PINS.json b/research/gauge44-leaver/data/UPSTREAM-PINS.json
new file mode 100644
index 0000000000..68486b84e3
--- /dev/null
+++ b/research/gauge44-leaver/data/UPSTREAM-PINS.json
@@ -0,0 +1,23 @@
+{
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-RECIPES.json": "534ace870cabe515987e00f50f71550030965006ea18978e0924590ac6944345",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-REVIEW.json": "ee9b86428278392d2c933f76d60e51f5af90d4ab67e4d3937ed2fa416e7755ab",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-LOCAL-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INTEGRATION.json": "5c14538134dfffbc58fa4b4d2f26b270ec5f56d17d4bf23752c82964f45171db",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-CHECKS.json": "79177449e404403964ce1b2f4a9a8bd49e1916daba3123d7fd7f5cfd1f1ac0ea",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-PROGRAMS.json.gz": "99a18eede965accf65943e490b8d2b2ffb9f1c9bc6babdb825413a80cbea2cde",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/RESIDUAL-ADAPTERS.json": "baafef737acc16dafbe1150896feb16744f3d669fa123bb2bff19ecc4e71b275",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/SCALAR-FRAME-AUDIT.json": "73b3601a6239502475a272ea0c46945fd42034486aaf43e66a212eb4f012ca44",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/WRAPPER-CHECKS.json": "9a09146e686c4f535b04fdef3753fe01dad8f5e8881a69408a91394acb5b48f5",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+  "research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py": "322d29d43dbee8130cde15d4bf05396698b5e3dfe3735813899db91cc0ba7955",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+  "research/complex-k492-owner-repair/vendor/multicold/inputs/PR543-EXPECTED.json": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz": "025448abdf2012d327e50a009084e1501690d05e650300d2982836aa0350ae00",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz": "de2be0f4b6d24ace368fd5b834b7a00f9625d0a1824c4ff969f2db5f115db667",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/prepare_supplier_base.py": "f5eae94aca965d0008bc07cff8245ccb7509042ccad457d3bcb7d51c1e9409f0"
+}
diff --git a/research/gauge44-leaver/evidence/ADMISSION-CONTROLS.json b/research/gauge44-leaver/evidence/ADMISSION-CONTROLS.json
new file mode 100644
index 0000000000..2e15a10065
--- /dev/null
+++ b/research/gauge44-leaver/evidence/ADMISSION-CONTROLS.json
@@ -0,0 +1,102 @@
+{
+  "status": "PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS",
+  "valid_receipt_kappa": "1649483702558979/1000000000000000000",
+  "input_sha256": {
+    "owner_audit": "a32ecc0d5387d65648e1ff284209122860ee37aaba43ce2dd12024c4bc394313",
+    "fresh_invoice": "14b0f41c88209e800236ce4ebbf91d83537e22e18807153d90013f7eee57a582",
+    "inputs/PR543-EXPECTED.json": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d",
+    "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+  },
+  "assembler_sha256": "7ac28118d69416e4fb67b61216285fb0823310b7635ce1b9025aa3f10119ef6a",
+  "rejected_controls": [
+    "empty_certification_maps",
+    "failed_invoice_status",
+    "nonboolean_precision_check",
+    "wrong_owner_role_count",
+    "understated_physical_stock",
+    "changed_profile_same_rank_mass",
+    "insufficient_finite_C0",
+    "missing_finite_check",
+    "wrong_reflected_orientation_selfconsistent_totals",
+    "missing_selected_call",
+    "wrong_selected_primitive_sum",
+    "wrong_selected_coefficient_work_sum",
+    "unpaid_wrapper_factors",
+    "wrong_global_compiler",
+    "wrong_global_adapter_maximum",
+    "understated_exact_prefix_and_global_sum",
+    "wrong_global_prefix_sum",
+    "wrong_row_prefix_reserve",
+    "wrong_parent_geometry_charge",
+    "wrong_rebased_geometry_charge",
+    "wrong_complete_pervertex_envelope",
+    "wrong_prior_added_complete_invoice",
+    "wrong_finite_router_bits",
+    "wrong_finite_literal_bits",
+    "wrong_finite_physical_stock_bits",
+    "wrong_finite_row_coefficient",
+    "reordered_complete_calls",
+    "understated_explicit_idle_remainders",
+    "understated_actual_chart_types",
+    "wrong_cross_replica_role_count",
+    "old_no_cold_wrapper_counts_selfconsistent",
+    "gauge44:missing_provider",
+    "gauge44:missing_backward_orientation",
+    "gauge44:unpaid_scalar_primitive",
+    "gauge44:wrong_local_artifact_binding",
+    "gauge44:false_dirty_restoration",
+    "gauge44:wrong_declared_provider_count",
+    "gauge44:wrong_local_compiler",
+    "gauge44:wrong_local_adapter_charge",
+    "gauge44:wrong_local_primitive_bound",
+    "gauge44:forged_provider_and_call_program_hash",
+    "gauge44:provider_at_wrong_call",
+    "gauge44:synchronized_forged_source_recipe_hash",
+    "gauge44:synchronized_forged_phase_review_semantics",
+    "gauge44:width_order_swap_4_5",
+    "gauge44:width_inventory_shift_4_5",
+    "gauge44:width_order_swap_4_7",
+    "gauge44:width_inventory_shift_4_7",
+    "gauge44:width_order_swap_4_8",
+    "gauge44:width_inventory_shift_4_8",
+    "gauge44:width_order_swap_4_9",
+    "gauge44:width_inventory_shift_4_9",
+    "gauge44:width_order_swap_5_7",
+    "gauge44:width_inventory_shift_5_7",
+    "gauge44:width_order_swap_5_8",
+    "gauge44:width_inventory_shift_5_8",
+    "gauge44:width_order_swap_5_9",
+    "gauge44:width_inventory_shift_5_9",
+    "gauge44:width_order_swap_7_8",
+    "gauge44:width_inventory_shift_7_8",
+    "gauge44:width_order_swap_7_9",
+    "gauge44:width_inventory_shift_7_9",
+    "gauge44:width_order_swap_8_9",
+    "gauge44:width_inventory_shift_8_9",
+    "gauge44:cold_helper_width_swap_264",
+    "gauge44:cold_helper_width_swap_276",
+    "gauge44:cold_helper_width_swap_288",
+    "gauge44:cold_helper_width_swap_300",
+    "wrong_owner_receipt_hash"
+  ],
+  "discovery_accepted_controls": [],
+  "exact_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "conservative_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "recurrence_model_controls": [
+    "native_complex_endpoint_rejected_with_old_surcharge",
+    "omitting_bit_surcharge_would_fail_next_endpoint_rejection"
+  ],
+  "scope": "Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay."
+}
diff --git a/research/gauge44-leaver/evidence/ASSEMBLY.json b/research/gauge44-leaver/evidence/ASSEMBLY.json
new file mode 100644
index 0000000000..6feaaf28f5
--- /dev/null
+++ b/research/gauge44-leaver/evidence/ASSEMBLY.json
@@ -0,0 +1,336 @@
+{
+  "status": "PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY",
+  "kappa": "1649483702558979/1000000000000000000",
+  "kappa_decimal": "0.001649483702558979",
+  "complex_lower": "1652208994368411824947/1000000000000000000000000",
+  "complex_decimal": "0.001652208994368411824947",
+  "bit_lower": "413456747036699736067/250000000000000000000000",
+  "bit_decimal": "0.001653826988146798944268",
+  "binding": "complex",
+  "gain_over_pr635_percent": "0.8093060205252829126484020359439672024956960385078942889840023844750830",
+  "complex_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "surcharge_model": {
+    "complex": false,
+    "bit": true
+  },
+  "conservative_complex_lower": "826104495740783435531/500000000000000000000000",
+  "conservative_complex_decimal": "0.001652208991481566871062",
+  "conservative_kappa": "32989673993633/20000000000000000",
+  "conservative_kappa_decimal": "0.00164948369968165",
+  "conservative_moments": [
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "826104495740783435531/500000000000000000000000",
+      "accept": true,
+      "mercator": [
+        "-21470727653278306311183666306239229019733127/13479973333575319897333507543509815336818572211270286240551805124608",
+        "-10735363826639153155591833153119614509866563/6739986666787659948666753771754907668409286105635143120275902562304"
+      ],
+      "base_two": [
+        "-497746012127833654257/312500000000000000000000000000000000000000000",
+        "-15927862388090676936081/10000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "1652208991481566871063/1000000000000000000000000",
+      "accept": false,
+      "mercator": [
+        "18565857384700607217299861034814026061253869/13479973333575319897333507543509815336818572211270286240551805124608",
+        "9282928692350303608649930517407013030626935/6739986666787659948666753771754907668409286105635143120275902562304"
+      ],
+      "base_two": [
+        "3443229403069298452661/2500000000000000000000000000000000000000000000",
+        "6886463806138596905393/5000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "conservative_bootstrap": [
+    {
+      "exponent": "412385685180656454166549264744655866734211385357236332091088842586409092836277952888766748039/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "666562689735263598950072203096262874070849142763667908911157413590907163722047111233251961/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "5064079519162"
+    },
+    {
+      "exponent": "206525573284761175512531267070234734086162997564863775372380915312260537579589712487639916151798780772051965162106786567177267184954922826291/125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+      "cutoff_log2": "1855113791006194394"
+    },
+    {
+      "exponent": "103263061512703129767826074285021991628452086339263045204373010454992865610677336738873844192820011712987227316937414267052501172258472295234559238219891652401488082322583795324180689654479/62500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+      "cutoff_log2": "679580003544484094184219"
+    },
+    {
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+    },
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+      "cutoff_log2": "33408017428823827582408170997246977713592"
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+    "compact_phase_layer_above_kappa": "384836254122600439334184167840010185009418954682030161109966228963788822428396666476274261601081854366945721579322781333332494443005781200243715749722762195652075144411907481138474123886528313275826510252717318024324541880489994614960374150562520327678895897792615711494357983843509672936956508862939008477909417872568630226278225578888014219241778137636839496851870895240167187797971041451302077059284097370788639/500826104497184205912446378819753771724889601254973369146461701558231026180446074958006802781550093752903233596741463898660609484278691810993420233589625890847508635094728855280196408981311845086875719069496776828962249839935690040003758181962602274220043524332460570130345585371869482720913013050263020200194570469939599151461082519436271959147262026364397400719510424912835469344370025591080557542210211361000000000000000000000000",
+    "bulk_exposure_above_kappa": "2725291809432824892760943925532186602852295468626143987776322166643298144437891566249896386783794682250325982720570888808333058035587427982244795917897766192126153947302396188350346875998068356230515694247409920636392332411468502336205197989213263024053337331536239117696791845640104898504335919624091669350736887870142170348377574017694034808393425549949474408919442457789788639/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "Gaussian_arithmetic_above_kappa": "615738307091823401245218216011843587867333362425009010759967454219083050824050374629683793365812635917169406268856608178210330305174940487605031795608559666818854739564233026658871766336290690028429468529779150536985364386133895345350622643154941701847597968494299737867314852356966699820820046728510243722467188712852090325804651802870334412550020508576159013601433864090522448178035272944098677943189081119388639/801321767195494729459914206111606034759823362007957390634338722493169641888713719932810884450480150004645173754786342237856975174845906897589472373743401425356013816151566168448314254370098952139001150511194842926339599743897104064006013091140163638752069638931936912208552936594991172353460820880420832320311312751903358642337732031098035134635619242183035841151216679860536750950992040945728892067536338177600000000000000000000000",
+    "scalar_work_above_kappa": "3078693538763534994962914729844733218351753711683450073693313856942221487044356594932718798856274305786222042957217427856907246168312639552792402951723732692597837087855705512209779952467089375389527690151772030672034137779668836469513273230807436359647086722645596019178854783167174986582031117294603419664416744342542331387419864858681749807837939131928900525596772198494311892232053742200595754038175574437788639/4006608835977473647299571030558030173799116810039786953171693612465848209443568599664054422252400750023225868773931711189284875874229534487947361868717007126780069080757830842241571271850494760695005752555974214631697998719485520320030065455700818193760348194659684561042764682974955861767304104402104161601556563759516793211688660155490175673178096210915179205756083399302683754754960204728644460337681690888000000000000000000000000",
+    "dimension_above_kappa": "499173895502815794472389376128951164793500479031415635616728978013400389902889300467483577877872753169445986011143172018378864998277686263802972870025639588088018108048266929997769582939230730780453685013440517758709347288500697481097612660777232276430370629988241720150824532464270561234015101138832024606244659306012459589468535547702828206730115013606136254794226859986030391904901589159511543091230174460327668139841639581/500826104497184205912446378819753771724889601254973369146461701558231026180446074958006802781550093752903233596741463898660609484278691810993420233589625890847508635094728855280196408981311845086875719069496776828962249839935690040003758181962602274220043524332460570130345585371869482720913013050263020200194570469939599151461082519436271959147262026364397400719510424912835469344370025591080557542210211361000000000000000000"
+  },
+  "controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the same cited unchanged PR543 bit supplier as PR635. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/gauge44-leaver/evidence/BINDING.json b/research/gauge44-leaver/evidence/BINDING.json
new file mode 100644
index 0000000000..b03160c67a
--- /dev/null
+++ b/research/gauge44-leaver/evidence/BINDING.json
@@ -0,0 +1,25 @@
+{
+  "status": "PASS_FROZEN_048_ALLCOLD_DISPATCH_FRESH_PROVIDER_BINDING",
+  "source_plan_sha256": "8c4804859aee83082196348c33127070d2885d3a366ce9acc8dc5166202f4687",
+  "runtime_plan_sha256": "609adb126d7d3de2abdd9275f9015589c0b137d0d19821c2c3e7c1a8541c18d2",
+  "providers": {
+    "gauge44": {
+      "artifact_sha256": {
+        "CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+        "LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+        "LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+        "INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+        "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+        "CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12",
+        "RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94"
+      },
+      "canonical_content_sha256": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+      "all_phase_edges": 3019
+    }
+  },
+  "only_rebound_fields": [
+    "provider_registry.directory",
+    "provider_registry.artifact_sha256",
+    "runtime_source_plan_sha256"
+  ]
+}
diff --git a/research/gauge44-leaver/evidence/CENTER-COMPATIBILITY.json b/research/gauge44-leaver/evidence/CENTER-COMPATIBILITY.json
new file mode 100644
index 0000000000..5a3ae37422
--- /dev/null
+++ b/research/gauge44-leaver/evidence/CENTER-COMPATIBILITY.json
@@ -0,0 +1,112 @@
+{
+  "status": "PASS_IDENTICAL_PORT_ORDER_AND_ORDERED_CENTER_FRAMES",
+  "new_canonical_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+  "comparison_canonical": "pr635/research/community-k492-audit/pr626/replay/mixed-global/base/split-centres/CANONICAL-WORD.json.gz",
+  "comparison_canonical_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+  "new_centers": [
+    92,
+    57,
+    81,
+    224,
+    11,
+    240,
+    9,
+    256
+  ],
+  "old_centers": [
+    229,
+    224,
+    227,
+    225,
+    243,
+    241,
+    259,
+    257
+  ],
+  "ordered_center_frames": [
+    [
+      256,
+      128,
+      64,
+      34,
+      16,
+      10,
+      4,
+      1
+    ],
+    [
+      256,
+      128,
+      64,
+      32,
+      16,
+      8,
+      5,
+      3
+    ],
+    [
+      256,
+      128,
+      64,
+      32,
+      17,
+      9,
+      4,
+      2
+    ],
+    [
+      256,
+      128,
+      64,
+      36,
+      20,
+      8,
+      2,
+      1
+    ],
+    [
+      256,
+      128,
+      66,
+      32,
+      18,
+      8,
+      4,
+      1
+    ],
+    [
+      256,
+      128,
+      65,
+      33,
+      17,
+      9,
+      5,
+      3
+    ],
+    [
+      256,
+      128,
+      65,
+      33,
+      16,
+      8,
+      4,
+      2
+    ],
+    [
+      256,
+      128,
+      68,
+      32,
+      16,
+      12,
+      2,
+      1
+    ]
+  ],
+  "v": 112,
+  "h": 9,
+  "center_count": 8,
+  "scope": "Carrier register identity changes; native cut center channels retain exact ordered frames and ports. Full endpoint and exact center clearing are independently checked by local ledger replay."
+}
diff --git a/research/gauge44-leaver/evidence/LOCAL-STAGES.json b/research/gauge44-leaver/evidence/LOCAL-STAGES.json
new file mode 100644
index 0000000000..b2753eb57a
--- /dev/null
+++ b/research/gauge44-leaver/evidence/LOCAL-STAGES.json
@@ -0,0 +1,27 @@
+[
+  {
+    "tag": "44-native",
+    "seconds": 4.460461161999774,
+    "exit": 0
+  },
+  {
+    "tag": "44-emitted-ledgers",
+    "seconds": 3.058037757999955,
+    "exit": 0
+  },
+  {
+    "tag": "44-local-replay",
+    "seconds": 28.33760359400003,
+    "exit": 0
+  },
+  {
+    "tag": "44-wrappers",
+    "seconds": 5.294312295000054,
+    "exit": 0
+  },
+  {
+    "tag": "44-phase",
+    "seconds": 198.39076561599995,
+    "exit": 0
+  }
+]
diff --git a/research/gauge44-leaver/evidence/REPLAY.json b/research/gauge44-leaver/evidence/REPLAY.json
new file mode 100644
index 0000000000..c6f4e0f983
--- /dev/null
+++ b/research/gauge44-leaver/evidence/REPLAY.json
@@ -0,0 +1,54 @@
+{
+  "status": "PASS_GAUGE44_STRICT_GLOBAL_REPLAY",
+  "kappa": "1649483702558979/1000000000000000000",
+  "kappa_decimal": "0.001649483702558979",
+  "complex_lower": "1652208994368411824947/1000000000000000000000000",
+  "bit_lower": "413456747036699736067/250000000000000000000000",
+  "gain_over_pr635_percent": "0.8093060205252829126484020359439672024956960385078942889840023844750830",
+  "spec_sha256": "fee57674a7f36b30b1e7eb96a8f567a90a522217bc644c1a6a1f8bff85196fbf",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 2.152,
+      "exit_code": 0,
+      "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.686,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "emit",
+      "seconds": 5.456,
+      "exit_code": 0,
+      "log_sha256": "60866eb6ced5b9eb259bfc1d59ea7b80fb439164b629e868586ad5bef845a88e"
+    },
+    {
+      "name": "audit",
+      "seconds": 26.943,
+      "exit_code": 0,
+      "log_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662"
+    },
+    {
+      "name": "invoice",
+      "seconds": 1.897,
+      "exit_code": 0,
+      "log_sha256": "5d10712d494304287749dd7a6c3369f9b707bba30e9f567b68230669dcf5418a"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.724,
+      "exit_code": 0,
+      "log_sha256": "768d3215f1918117dc6c33b4cfeaf0b5f5da9ba5c77178db4bb1d08d000e226f"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 0.816,
+      "exit_code": 0,
+      "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+    }
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the same cited unchanged PR543 bit supplier as PR635. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/gauge44-leaver/evidence/STAGES.json b/research/gauge44-leaver/evidence/STAGES.json
new file mode 100644
index 0000000000..9464e2dfea
--- /dev/null
+++ b/research/gauge44-leaver/evidence/STAGES.json
@@ -0,0 +1,44 @@
+[
+  {
+    "name": "restore-parent",
+    "seconds": 2.152,
+    "exit_code": 0,
+    "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+  },
+  {
+    "name": "bind",
+    "seconds": 0.686,
+    "exit_code": 0,
+    "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+  },
+  {
+    "name": "emit",
+    "seconds": 5.456,
+    "exit_code": 0,
+    "log_sha256": "60866eb6ced5b9eb259bfc1d59ea7b80fb439164b629e868586ad5bef845a88e"
+  },
+  {
+    "name": "audit",
+    "seconds": 26.943,
+    "exit_code": 0,
+    "log_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662"
+  },
+  {
+    "name": "invoice",
+    "seconds": 1.897,
+    "exit_code": 0,
+    "log_sha256": "5d10712d494304287749dd7a6c3369f9b707bba30e9f567b68230669dcf5418a"
+  },
+  {
+    "name": "assembly",
+    "seconds": 0.724,
+    "exit_code": 0,
+    "log_sha256": "768d3215f1918117dc6c33b4cfeaf0b5f5da9ba5c77178db4bb1d08d000e226f"
+  },
+  {
+    "name": "admission-controls",
+    "seconds": 0.816,
+    "exit_code": 0,
+    "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+  }
+]
diff --git a/research/gauge44-leaver/evidence/audit/ASYNC-AUDIT.json b/research/gauge44-leaver/evidence/audit/ASYNC-AUDIT.json
new file mode 100644
index 0000000000..05975382b5
--- /dev/null
+++ b/research/gauge44-leaver/evidence/audit/ASYNC-AUDIT.json
@@ -0,0 +1,84 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "complex_template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "complex_live": 7168,
+  "complex_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "complex_hosted_residuals": 35424,
+  "physical": 7670,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "entering_helper_roles": 17856,
+  "cross_replica_helper_roles": 25937,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 35424,
+  "complete_invocations": 72,
+  "actual_orthogonal_73column_maps": 7870,
+  "actual_sigma_stream_sha256": "f4e9802acb2ed53fc1f0486e7d0f55a6faa30ed7f5d2ad48a06450234b00ba76",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 2759,
+  "mutations_rejected": [
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit idle remainder",
+    "understate physical reserve",
+    "gauge44: wrong provider at its invocation",
+    "gauge44: stale per-call local program hash",
+    "gauge44: stale serialized provider program",
+    "gauge44: unbound residual adapter hash",
+    "gauge44: wrong provider width registry",
+    "gauge44: wrong per-call residual width",
+    "gauge44: wrong sweep provider",
+    "gauge44: entering helper width silently restored to nine"
+  ],
+  "mutation_controls_run": true,
+  "provider_phase_semantic_sha256": {
+    "gauge44": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152"
+  },
+  "provider_artifact_semantic_sha256": {
+    "gauge44": {
+      "CANONICAL-WORD.json.gz": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+      "LOCAL-PROGRAMS.json.gz": "39b230dba9e6b022c691cd0167f331c1b3fa6795d49256e3a2b859c68d4acfda",
+      "LOCAL-CHECKS.json": "bd53e0cca4488f365ca5b7c7174d8dfb35ced5e0229835f27334c11c3d839717",
+      "INDEPENDENT-LOCAL-REPLAY.json": "adb5c8ce0b5025dcd96f41b9fa0e26b9a176e067ab36a5bfadad00bc19522b38",
+      "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+      "CLIFFORD-REVIEW.json": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152",
+      "RESIDUAL-ADAPTERS.json": "c233611dd4c08c389dfb6c7d1c84dd86a3efa560223fcd6549a2848692541cd9"
+    }
+  },
+  "widths_by_provider": {
+    "gauge44": {
+      "4": 52,
+      "5": 48,
+      "7": 34,
+      "8": 114,
+      "9": 244
+    }
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "all_provider_program_phase_and_wrapper_bindings": true,
+  "scope": "Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations."
+}
diff --git a/research/gauge44-leaver/evidence/audit/GLOBAL-PREFIX.json b/research/gauge44-leaver/evidence/audit/GLOBAL-PREFIX.json
new file mode 100644
index 0000000000..a557ebbe60
--- /dev/null
+++ b/research/gauge44-leaver/evidence/audit/GLOBAL-PREFIX.json
@@ -0,0 +1,13 @@
+{
+  "status": "PASS_MIXED_ASYNC_GLOBAL_PREFIX",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "global_prefix_bits": 360,
+  "retained_payload_bits": 512,
+  "complete_invocation_cover_sweeps": 72,
+  "bridge_factor_two_sweeps": 72,
+  "local_scalar_coefficient_work_prefix_bits": 175,
+  "stream_input_sup_to_l2_bits": 37,
+  "primitive_arithmetic_margin_bits": 4,
+  "controller_audit_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662",
+  "proof": "Each selected normalized provider restores all arbitrary dirty helper columns and gives the same data shear endpoints. Actual whole-owner charts are right-translation bijections. Sum all 72 invocation and 72 bridge sweeps and take maximum local scalar/Horner prefix over all three providers and orientations. Idle children, phases, spectator endpoints and terminal translations are unitary. Retained all-size interfaces are conditional."
+}
diff --git a/research/gauge44-leaver/evidence/audit/IDLE-REMAINDER-FRAMES.json b/research/gauge44-leaver/evidence/audit/IDLE-REMAINDER-FRAMES.json
new file mode 100644
index 0000000000..1c86a8a01d
--- /dev/null
+++ b/research/gauge44-leaver/evidence/audit/IDLE-REMAINDER-FRAMES.json
@@ -0,0 +1,25 @@
+{
+  "status": "PASS_LITERAL_IDLE_REMAINDER_FRAMES",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "uncompressed_frames_sha256": "38eba7dfe023d0b2a8aea1c5184e50bdfff5727b350c2de4d27800acbdd3708c",
+  "children": 2759,
+  "rank_profile": {
+    "1": 85,
+    "2": 76,
+    "3": 173,
+    "7": 7,
+    "8": 6,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "source_data_phase_sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+  "scope": "Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child."
+}
diff --git a/research/gauge44-leaver/evidence/audit/OWNERS-AND-PROFILE.json b/research/gauge44-leaver/evidence/audit/OWNERS-AND-PROFILE.json
new file mode 100644
index 0000000000..bdb9441b7e
--- /dev/null
+++ b/research/gauge44-leaver/evidence/audit/OWNERS-AND-PROFILE.json
@@ -0,0 +1,61 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "paid_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "live": 7168,
+  "physical": 7670,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "hosted_residuals": 35424,
+  "banked_residuals": 0,
+  "all_live_owners_per_call_distinct": true,
+  "owners_per_call": 716,
+  "actual_helper_owner_charts": 35424,
+  "actual_73column_sigmas": 7870,
+  "cross_replica_helper_roles": 25937,
+  "explicit_idle_remainder_children": 2759,
+  "source_idle_children_charged": 16128,
+  "source_artifacts": {
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "providers/gauge44/CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+    "providers/gauge44/LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+    "providers/gauge44/LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+    "providers/gauge44/INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+    "providers/gauge44/RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94",
+    "providers/gauge44/CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+    "providers/gauge44/CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12"
+  },
+  "provider_phase_semantic_sha256": {
+    "gauge44": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152"
+  },
+  "provider_artifact_semantic_sha256": {
+    "gauge44": {
+      "CANONICAL-WORD.json.gz": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+      "LOCAL-PROGRAMS.json.gz": "39b230dba9e6b022c691cd0167f331c1b3fa6795d49256e3a2b859c68d4acfda",
+      "LOCAL-CHECKS.json": "bd53e0cca4488f365ca5b7c7174d8dfb35ced5e0229835f27334c11c3d839717",
+      "INDEPENDENT-LOCAL-REPLAY.json": "adb5c8ce0b5025dcd96f41b9fa0e26b9a176e067ab36a5bfadad00bc19522b38",
+      "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+      "CLIFFORD-REVIEW.json": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152",
+      "RESIDUAL-ADAPTERS.json": "c233611dd4c08c389dfb6c7d1c84dd86a3efa560223fcd6549a2848692541cd9"
+    }
+  },
+  "controller_audit_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662"
+}
diff --git a/research/gauge44-leaver/evidence/audit/PREFIX-AND-INVOICE.json b/research/gauge44-leaver/evidence/audit/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..6c96ec6706
--- /dev/null
+++ b/research/gauge44-leaver/evidence/audit/PREFIX-AND-INVOICE.json
@@ -0,0 +1,1746 @@
+{
+  "status": "PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "parent_template_sha256": "7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3",
+  "owner_audit_sha256": "a32ecc0d5387d65648e1ff284209122860ee37aaba43ce2dd12024c4bc394313",
+  "controller_audit_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662",
+  "providers": {
+    "gauge44": {
+      "local": {
+        "backward": {
+          "events": 46772,
+          "macros": 41570,
+          "real_component_primitives": 420100,
+          "prefix_l1": "600338326363508935771850050281004728884643/32",
+          "prefix_bits": 134,
+          "coefficient_work_primitive_count": 208744,
+          "all_exact_columns": 716,
+          "dirty_helper_columns": 492,
+          "all_dirty_helper_columns_restored": true,
+          "private_centres_and_coefficient_work_cleared": true,
+          "pre_wrappers": 248,
+          "post_wrappers": 248,
+          "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+        },
+        "forward": {
+          "events": 46772,
+          "macros": 41570,
+          "real_component_primitives": 420052,
+          "prefix_l1": "2323449462751823289130723296176889733365478515961323543/64",
+          "prefix_bits": 175,
+          "coefficient_work_primitive_count": 208712,
+          "all_exact_columns": 716,
+          "dirty_helper_columns": 492,
+          "all_dirty_helper_columns_restored": true,
+          "private_centres_and_coefficient_work_cleared": true,
+          "pre_wrappers": 248,
+          "post_wrappers": 248,
+          "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+        }
+      },
+      "helpers": 492,
+      "centres": 8,
+      "v": 112,
+      "h": 9,
+      "n": 716,
+      "entering_helpers": 204,
+      "entrance_rank": 380,
+      "terminal_codimension": 254,
+      "hyperplane_ended_helpers": 78,
+      "cold_hyperplane_ended_helpers": 44,
+      "width_inventory": {
+        "4": 52,
+        "5": 48,
+        "7": 34,
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+        "INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+        "CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+        "SCALAR-FRAME-AUDIT.json": "cfc73040079b43ea82a42f3cf4c910edda1362deb09ec21c816c329347313bcb",
+        "FULL-WORD.json.gz": "0ad202612f010df4ab66432a628247b37ad8b497dd6b27595b1685cbd7eb119e",
+        "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+        "CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12",
+        "LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c"
+      },
+      "paid_profile": {
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+        "2": 404,
+        "3": 448,
+        "4": 160,
+        "5": 56,
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+      "program_hashes": {
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+        "forward": "d17399c8c7458bb7110d8596fab5f769cd4cb3733a3042277fa08bf03f42d6c9"
+      },
+      "semantic_artifact_sha256": {
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+        "LOCAL-PROGRAMS.json.gz": "39b230dba9e6b022c691cd0167f331c1b3fa6795d49256e3a2b859c68d4acfda",
+        "LOCAL-CHECKS.json": "bd53e0cca4488f365ca5b7c7174d8dfb35ced5e0229835f27334c11c3d839717",
+        "INDEPENDENT-LOCAL-REPLAY.json": "adb5c8ce0b5025dcd96f41b9fa0e26b9a176e067ab36a5bfadad00bc19522b38",
+        "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+        "CLIFFORD-REVIEW.json": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152",
+        "RESIDUAL-ADAPTERS.json": "c233611dd4c08c389dfb6c7d1c84dd86a3efa560223fcd6549a2848692541cd9"
+      }
+    }
+  },
+  "provider_phase_semantic_sha256": {
+    "gauge44": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152"
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "selected_calls": [
+    {
+      "stage": 0,
+      "replica": 0,
+      "provider_id": "gauge44",
+      "orientation": "forward",
+      "program_sha256": "d17399c8c7458bb7110d8596fab5f769cd4cb3733a3042277fa08bf03f42d6c9",
+      "events": 46772,
+      "macros": 41570,
+      "real_component_primitives": 420052,
+      "coefficient_work_primitive_count": 208712,
+      "entering_helpers": 204,
+      "entrance_rank": 380,
+      "pre_wrappers": 248,
+      "post_wrappers": 248
+    },
+    {
+      "stage": 0,
+      "replica": 1,
+      "provider_id": "gauge44",
+      "orientation": "forward",
+      "program_sha256": "d17399c8c7458bb7110d8596fab5f769cd4cb3733a3042277fa08bf03f42d6c9",
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+      "entering_helpers": 204,
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diff --git a/research/gauge44-leaver/evidence/global/HOSTED.json b/research/gauge44-leaver/evidence/global/HOSTED.json
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index 0000000000..498e849ab7
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+  "entering_helper_roles": 17856,
+  "unique_actual_73column_sigmas": 7870,
+  "sigma_stream_sha256": "f4e9802acb2ed53fc1f0486e7d0f55a6faa30ed7f5d2ad48a06450234b00ba76",
+  "cross_replica_helper_roles": 25937,
+  "asynchronous_order_sha256": "2acd6b2004be3d3ef6645f3c968feb22b5167c400bb49eb446821e5cb7af6eee",
+  "source_artifacts": {
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "providers/gauge44/CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+    "providers/gauge44/LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+    "providers/gauge44/LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+    "providers/gauge44/INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+    "providers/gauge44/RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94",
+    "providers/gauge44/CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+    "providers/gauge44/CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12"
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "scope": "Two actual verified plain/width-seven providers dispatched per complete invocation; independent controller/spectator/normalization and complete finite invoice admission required."
+}
diff --git a/research/gauge44-leaver/evidence/global/IDLE-REMAINDER-FRAMES.json.gz b/research/gauge44-leaver/evidence/global/IDLE-REMAINDER-FRAMES.json.gz
new file mode 100644
index 0000000000..3562e60f05
Binary files /dev/null and b/research/gauge44-leaver/evidence/global/IDLE-REMAINDER-FRAMES.json.gz differ
diff --git a/research/gauge44-leaver/evidence/layers/LOCAL-AUDIT-LAYERED.json b/research/gauge44-leaver/evidence/layers/LOCAL-AUDIT-LAYERED.json
new file mode 100644
index 0000000000..718c715709
--- /dev/null
+++ b/research/gauge44-leaver/evidence/layers/LOCAL-AUDIT-LAYERED.json
@@ -0,0 +1,137 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+  "input_file": "FULL-WORD.json.gz",
+  "content_sha256": "238be1fc7dc8f96e0676478b4916eeb00e265a8026476fe826f68c3aaffbdf91",
+  "compressed_sha256": "47f71f4c4b1c7f85f97e4520d23e2343aa1c9c490d6115b9572346f9447a0a40",
+  "parent_center_interface": {
+    "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+    "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "transport_tau": 43,
+    "ordered_frame_bases_match": true,
+    "all_ports_match": true,
+    "transported_centers": [
+      92,
+      57,
+      81,
+      224,
+      11,
+      240,
+      9,
+      256
+    ],
+    "source_centers": [
+      92,
+      57,
+      81,
+      11,
+      9
+    ],
+    "ordered_frame_bases": [
+      [
+        256,
+        128,
+        64,
+        34,
+        16,
+        10,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        16,
+        8,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        17,
+        9,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ],
+      [
+        256,
+        128,
+        66,
+        32,
+        18,
+        8,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        17,
+        9,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        16,
+        8,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        68,
+        32,
+        16,
+        12,
+        2,
+        1
+      ]
+    ]
+  },
+  "v": 112,
+  "h": 9,
+  "R": 489,
+  "entering": 201,
+  "lowends": 96,
+  "coldends": 57,
+  "compensation_gates": 6630,
+  "local_profile": {
+    "1": 2463,
+    "2": 388,
+    "3": 429,
+    "4": 166,
+    "5": 70,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 65,
+    "5": 32,
+    "7": 39,
+    "8": 122,
+    "9": 231
+  },
+  "checked_columns": 713,
+  "elapsed_seconds": 0.8910000000032596,
+  "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+}
diff --git a/research/gauge44-leaver/evidence/leaver/CELL-MUTANTS-LV.json b/research/gauge44-leaver/evidence/leaver/CELL-MUTANTS-LV.json
new file mode 100644
index 0000000000..4d4ef7403c
--- /dev/null
+++ b/research/gauge44-leaver/evidence/leaver/CELL-MUTANTS-LV.json
@@ -0,0 +1,261 @@
+{
+ "c01m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_233": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [233])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [172, 175])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [132, 135, 173, 174])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_233": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [233])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c01p": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_57": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [57, 58, 224, 225, 226])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [169, 170])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [129, 130, 168, 171])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_57": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [57, 58, 224, 225, 226])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c23m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_58": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [58])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [169, 170])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [173, 174, 196, 199])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_58": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [58])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c23p": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_239": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [60, 63, 231, 232, 238, 239])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [172, 175])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [168, 171, 193, 194])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_239": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [60, 63, 231, 232, 238, 239])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c45m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_441": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [52, 55, 439, 440, 446, 447])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [137, 138])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [141, 142, 164, 167])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_441": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [52, 55, 439, 440, 446, 447])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c45p": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_255": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [28, 31, 247, 248, 254, 255])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [140, 143])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [136, 139, 161, 162])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_255": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [28, 31, 247, 248, 254, 255])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c67m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_18": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [18])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [129, 130])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [133, 134, 161, 162])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_18": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [18])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver/evidence/leaver/FRAME-CONTROLS-LV-k5.json b/research/gauge44-leaver/evidence/leaver/FRAME-CONTROLS-LV-k5.json
new file mode 100644
index 0000000000..8983632412
--- /dev/null
+++ b/research/gauge44-leaver/evidence/leaver/FRAME-CONTROLS-LV-k5.json
@@ -0,0 +1,54 @@
+{
+ "base": "2997cede",
+ "recipe": "FRAME-RECIPE-LV-k5.json",
+ "controls": {
+  "shrink_raised_B": {
+   "builder": "profile and width pins",
+   "stage": "native_atc",
+   "native": "PASS",
+   "rc": 0,
+   "reason": "}",
+   "frame": [
+    "B",
+    575
+   ]
+  },
+  "shrink_lowered_B": {
+   "builder": "('nonmonotone', 174)",
+   "stage": "apply",
+   "reason": "('nonmonotone', 174)"
+  },
+  "shrink_T": {
+   "builder": "('nonmonotone', 559)",
+   "stage": "apply",
+   "reason": "('nonmonotone', 559)"
+  },
+  "empty_B": {
+   "builder": "('nonmonotone', 169)",
+   "stage": "apply",
+   "reason": "('nonmonotone', 169)"
+  },
+  "drop_one_lowering": {
+   "builder": "output word pin",
+   "stage": "native_atc",
+   "native": "PASS",
+   "rc": 0,
+   "reason": "}",
+   "frame": [
+    "B",
+    1259
+   ]
+  },
+  "drop_one_raise": {
+   "builder": "profile and width pins",
+   "stage": "native_atc",
+   "native": "PASS",
+   "rc": 0,
+   "reason": "}",
+   "frame": [
+    "B",
+    575
+   ]
+  }
+ }
+}
diff --git a/research/gauge44-leaver/evidence/local/CANONICAL-WORD.json.gz b/research/gauge44-leaver/evidence/local/CANONICAL-WORD.json.gz
new file mode 100644
index 0000000000..5062a1f62f
Binary files /dev/null and b/research/gauge44-leaver/evidence/local/CANONICAL-WORD.json.gz differ
diff --git a/research/gauge44-leaver/evidence/local/CLIFFORD-RECIPES.json b/research/gauge44-leaver/evidence/local/CLIFFORD-RECIPES.json
new file mode 100644
index 0000000000..3ba8326d3a
--- /dev/null
+++ b/research/gauge44-leaver/evidence/local/CLIFFORD-RECIPES.json
@@ -0,0 +1 @@
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diff --git a/research/gauge44-leaver/evidence/local/CLIFFORD-REVIEW.json b/research/gauge44-leaver/evidence/local/CLIFFORD-REVIEW.json
new file mode 100644
index 0000000000..6b12ae0e4b
--- /dev/null
+++ b/research/gauge44-leaver/evidence/local/CLIFFORD-REVIEW.json
@@ -0,0 +1,19 @@
+{
+  "status": "PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES",
+  "canonical_word_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+  "frames": 1037,
+  "directed_edges": 3019,
+  "ranks": {
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+    "2": 394,
+    "3": 412,
+    "8": 16,
+    "4": 154,
+    "5": 14
+  },
+  "endpoint_adapters": 224,
+  "all_child_equalities_include_global_phase": true,
+  "recipe_sha256": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+  "seconds": 198.28347681800005,
+  "scope": "Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations."
+}
diff --git a/research/gauge44-leaver/evidence/local/FULL-WORD.json.gz b/research/gauge44-leaver/evidence/local/FULL-WORD.json.gz
new file mode 100644
index 0000000000..447d45d08b
Binary files /dev/null and b/research/gauge44-leaver/evidence/local/FULL-WORD.json.gz differ
diff --git a/research/gauge44-leaver/evidence/local/INDEPENDENT-LOCAL-REPLAY.json b/research/gauge44-leaver/evidence/local/INDEPENDENT-LOCAL-REPLAY.json
new file mode 100644
index 0000000000..aa15edfba5
--- /dev/null
+++ b/research/gauge44-leaver/evidence/local/INDEPENDENT-LOCAL-REPLAY.json
@@ -0,0 +1,71 @@
+{
+  "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY",
+  "canonical_word_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+  "local_programs_sha256": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+  "v": 112,
+  "helpers": 492,
+  "local": {
+    "forward": {
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+      "prefix_l1_upper": "2323449462751823289130723296176889733365478515961323543/64",
+      "prefix_bits_upper": 175,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    },
+    "backward": {
+      "all_exact_columns": 716,
+      "prefix_l1_upper": "600338326363508935771850050281004728884643/32",
+      "prefix_bits_upper": 134,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    }
+  },
+  "paid_profiles": {
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+      "1": 2514,
+      "4": 160,
+      "8": 8,
+      "3": 448,
+      "2": 404,
+      "5": 56
+    },
+    "backward": {
+      "1": 2514,
+      "4": 160,
+      "8": 8,
+      "3": 448,
+      "2": 404,
+      "5": 56
+    }
+  },
+  "entering_helpers": 204,
+  "cold_hyperplane_ended_helpers": 44,
+  "negative_controls_rejected": [
+    "wrong_scale",
+    "missing_center",
+    "wrong_common_frame",
+    "wrong_child_rank",
+    "missing_pre_wrapper",
+    "missing_post_wrapper",
+    "wrapper_with_wrong_frame",
+    "wrapper_in_wrong_phase",
+    "wrapper_on_a_data_register",
+    "wrapper_on_a_target_register",
+    "wrapper_on_a_centre_register",
+    "hpe_pre_wrapper_resolved_to_full_recipe",
+    "hpe_post_wrapper_without_terminal_frame",
+    "hpe_post_wrapper_wrong_terminal_frame",
+    "hpe_tail_gate_at_full_frame",
+    "hpe_tail_climb_dropped",
+    "hpe_helper_exit_adapter_to_full",
+    "hpe_tail_gate_moved_into_full_cleanup",
+    "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter",
+    "cold_hpe_pre_wrapper_dropped",
+    "cold_hpe_post_wrapper_replaced_by_exit_adapter",
+    "cold_hpe_pre_wrapper_resolved_to_cold_full_convention",
+    "cold_hpe_wrapper_with_nonzero_entrance",
+    "cold_hpe_post_wrapper_wrong_terminal_frame",
+    "cold_hpe_premix_gate_before_pre_wrapper"
+  ],
+  "scope": "Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate."
+}
diff --git a/research/gauge44-leaver/evidence/local/LOCAL-CHECKS.json b/research/gauge44-leaver/evidence/local/LOCAL-CHECKS.json
new file mode 100644
index 0000000000..3872f0e596
--- /dev/null
+++ b/research/gauge44-leaver/evidence/local/LOCAL-CHECKS.json
@@ -0,0 +1,36 @@
+{
+  "forward": {
+    "sha256": "d17399c8c7458bb7110d8596fab5f769cd4cb3733a3042277fa08bf03f42d6c9",
+    "events": 46772,
+    "scalar_macros": 41570,
+    "real_component_primitive_bound": 420052,
+    "paid_profile": {
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+      "4": 160,
+      "5": 56,
+      "8": 8
+    },
+    "all_columns": 716,
+    "private_centers_cleared": true,
+    "private_coefficient_stream_cleared_after_each_macro": true
+  },
+  "backward": {
+    "sha256": "4772df0663f88cc218fd7254eb202f46daf136c06e9e96c19ed8ea218b545dc4",
+    "events": 46772,
+    "scalar_macros": 41570,
+    "real_component_primitive_bound": 420100,
+    "paid_profile": {
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+    "private_centers_cleared": true,
+    "private_coefficient_stream_cleared_after_each_macro": true
+  }
+}
diff --git a/research/gauge44-leaver/evidence/local/LOCAL-PROGRAMS.json.gz b/research/gauge44-leaver/evidence/local/LOCAL-PROGRAMS.json.gz
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+  "refactored_cleanup": {
+    "exact_non_target_isolation_checked": true,
+    "high_inverse": "dyadic_sparse_Gauss_Jordan",
+    "kind": "source_branch_gauge_and_retired_completion_cold44",
+    "new_cold_ends": 44
+  }
+}
diff --git a/research/gauge44-leaver/evidence/local/WRAPPER-CHECKS.json b/research/gauge44-leaver/evidence/local/WRAPPER-CHECKS.json
new file mode 100644
index 0000000000..a18afd4fad
--- /dev/null
+++ b/research/gauge44-leaver/evidence/local/WRAPPER-CHECKS.json
@@ -0,0 +1,413 @@
+{
+ "status": "PASS_RESIDUAL_WRAPPERS_ARE_EXACT",
+ "frames": 22,
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+  "hpe: width misreported as 9 - dim E",
+  "hpe: wrong terminal hyperplane",
+  "hpe: pre wrapper resolved to the FULL recipe R_{E,FULL}",
+  "hpe: wrong global phase",
+  "cold hpe: identity pre wrapper instead of R_{0,U}",
+  "cold hpe: identity post wrapper instead of L_{0,U}",
+  "cold hpe: no wrappers (cold FULL convention L = R = I)",
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+  "cold hpe: wrong terminal hyperplane",
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+ ]
+}
diff --git a/research/gauge44-leaver/hosting/PROOF.md b/research/gauge44-leaver/hosting/PROOF.md
new file mode 100644
index 0000000000..b551b6d3e5
--- /dev/null
+++ b/research/gauge44-leaver/hosting/PROOF.md
@@ -0,0 +1,237 @@
+# Exact owner reuse and concave-cost matching
+
+## 1. Objects and interface assumptions
+
+The parent controller has 72 ordered calls, 112 source ports, 112 target ports,
+and 492 helper roles per call. The ambient dimension is 73. A pending-child
+group is a triple
+
+$$
+g=(\text{owner replica},\text{child},\text{port}).
+$$
+
+The parent window catalogue gives group capacity $C_g$, together with the call
+times at which its physical stream is idle. The map from a group to its
+physical family is
+
+$$
+F(g)=896\,\text{owner replica}
+  +112(2\,\text{pair(child)}+\text{side(child)})+\text{port}.
+$$
+
+At every call in this particular parent geometry, at most one pending child of
+a physical family is eligible. Both the matcher and the independent frozen
+audit check this condition. They also exclude both active data families of the
+call. Consequently, injective assignment to eligible groups is equivalent to
+assignment to distinct idle physical families at that call.
+
+Helper $h$ requests an integer width $w_h$, read afresh from the new local
+word as the final-frame dimension minus the start-frame dimension. Native
+program profiles are also recomputed from their paid edges. The finite local
+compiler supplies the normalized helper chart and verifies its warm-start
+semantics. A hosted width is a reservation in the pending child's address
+coordinates on an existing physical stream; it is not a new physical stream.
+
+This proof concerns the discrete assignment and its moment contribution. It
+uses the parent windows as input. Independent global admission must verify
+those windows against the actual controller and construct the actual
+73-column charts for the fresh native local word.
+
+## 2. Feasible shrinking on the original families
+
+For one call, sort the old slot widths and the new helper widths increasingly,
+breaking ties by the old or new helper number. Suppose the new width in each
+position is no larger than its matched old width. Assign that helper to the
+matched old slot.
+
+This operation preserves the call time, stage, replica, pending child, port,
+owner replica, and physical family. It preserves the set of 492 distinct
+helper-owner families at the call, so the old window and active-data
+exclusions still hold. In each pending-child group, the sum of new widths is
+no larger than the old sum, hence remains within capacity.
+
+Now order the assignments in each group consistently and replace their
+offsets by consecutive prefix sums. The occupied sets become pairwise
+disjoint intervals whose union is exactly a prefix of length
+$U_g=\sum w_h\le C_g$. The idle child retains rank $C_g-U_g$, with pending
+offset $U_g$. Thus the shrinking operation has a direct capacity proof; it
+requires neither an owner solver nor any change to the controller.
+
+The seed constructor applies this termwise argument to the 71 former `jp8`
+calls. It keeps the remaining `ck` call provisionally unchanged. Two optional
+fixed-family assignment passes redistribute the available capacity before
+freezing the seed. Their result is audited using the same integer constraints.
+
+## 3. One call with all other calls fixed
+
+Fix one call $t$. Remove its existing assignments while keeping every other
+call fixed. For each eligible group, define the available capacity
+
+$$
+c_g=C_g-\sum_{\substack{\text{assignments in }g\\\text{from calls other than }t}}w.
+$$
+
+The call must assign each of its 492 widths to a distinct eligible group with
+$w\le c_g$. Unused groups can be viewed as receiving a dummy width zero.
+After the assignment, group $g$'s idle rank is $c_g-w_g$. For any function
+$\phi$, the portion of the idle objective affected by the call is exactly
+
+$$
+\sum_{g\text{ eligible at }t}\phi(c_g-w_g).
+$$
+
+All other idle contributions, and all local paid-edge contributions, are
+constant in this single-call problem.
+
+### Greedy rule
+
+Sort eligible capacities increasingly. At each capacity, assign the largest
+remaining helper width that fits; assign zero if none fits. Continue through
+the remaining capacities.
+
+This rule has no floating parameter. Equal-capacity tie choices are used only
+to limit changes to physical owners and make the artifact deterministic.
+
+### Exchange lemma
+
+Take two capacities $c_1\le c_2$ and two widths $w_1\le w_2\le c_1$. The
+assignment of $w_1$ to $c_1$ and $w_2$ to $c_2$ has residual pair
+
+$$
+(c_1-w_1,\ c_2-w_2).
+$$
+
+Exchange the widths. Feasibility is preserved, and the new pair is
+
+$$
+(c_1-w_2,\ c_2-w_1).
+$$
+
+The total is unchanged. The first new component is no larger than either old
+component, and the second is no smaller than either old component. Therefore
+the new pair majorizes the old pair. Every concave $\phi$ has weakly smaller
+sum on the new pair.
+
+### Consequence: feasibility and optimality
+
+Start from any feasible complete assignment. At the smallest remaining
+capacity, its assigned width is no larger than the largest remaining width
+that fits. The greedy width occurs at some later capacity. If the two differ,
+the exchange lemma moves that width to the current capacity while preserving
+feasibility and weakly decreasing every concave objective. Fix this first
+position and repeat on the suffix. Dummy zero widths cover unused groups.
+
+Thus the greedy procedure succeeds whenever a feasible assignment exists, and
+its remainder vector majorizes that of every feasible assignment. It
+simultaneously minimizes every concave remainder objective for this call.
+This proof depends on the absence of any eligibility restriction beyond the
+capacity and the already fixed call window; that property is explicitly
+checked for the present geometry.
+
+## 4. Exact majorization receipts
+
+Let $a_r$ and $b_r$ be the old and new remainder histograms for one update,
+including zero remainders. When the helper-width multiset is unchanged, their
+total numbers of groups and total ranks agree. Every remainder lies between
+0 and 48. The implementation checks, with integers, that for each
+$k=0,1,\ldots,48$,
+
+$$
+\sum_r b_r\max(r-k,0)
+\;\ge\;
+\sum_r a_r\max(r-k,0).
+$$
+
+These are the stored stop-loss margins. Between integer breakpoints the
+difference is linear, so checking all integer breakpoints checks every real
+threshold. With equal sums and equal lengths, the inequalities are the
+standard majorization criterion: the new vector majorizes the old one.
+
+The transcript contains 288 such equal-width updates: four passes through 72
+calls. A single preceding update replaces the seed's last `ck` width multiset.
+That bootstrap has different total width, so it is checked for exact
+feasibility and is not represented as an equal-sum majorization step.
+
+`reproduce.py` reruns every update and compares the full transcript's semantic
+hash. Independently, `audit_frozen.py` removes each final call in turn, computes
+all available capacities directly from the frozen owner map, runs a separate
+histogram-only greedy calculation, and verifies that it returns exactly the
+existing remainder histogram. This checks all 72 final coordinate optima
+without relying on the transcript or the discovery seed.
+
+## 5. Relation to the global moment
+
+For ambient dimension $M=73$, define
+
+$$
+\phi_b(r)=r\bigl((73/r)^b-1\bigr)
+          =73^b r^{1-b}-r,\qquad \phi_b(0)=0.
+$$
+
+For $0<b<1$, this function is continuous at zero and strictly concave on
+positive ranks, because
+
+$$
+\phi_b''(r)=-b(1-b)73^b r^{-b-1}<0.
+$$
+
+Once all calls use the new provider, the local paid profile is fixed and every
+accepted owner update preserves the global paid rank mass. The exchange and
+majorization arguments therefore weakly decrease the global moment pressure
+for every $b\in(0,1)$ simultaneously. A strict histogram majorization strictly
+decreases that pressure. No estimated root, derivative, or floating cost is
+needed to establish the improvement of these updates.
+
+For the frozen map, the exact paid rank mass is 520704, so
+
+$$
+73\cdot7168-520704=2560.
+$$
+
+The final profile is recomputed from 72 copies of the new local paid profile
+and from the actual remaining rank in every pending-child group. Numerical
+roots printed by the matcher are screens only. Exact moment bounds and their
+combination with the bit supplier are performed by the package's admitted
+global pipeline.
+
+## 6. Determinism and fixed-point scope
+
+The implementation keeps the parent call order, alternating a forward pass
+and a reverse pass. Within equal-capacity groups, it first prefers the old
+assigned width, then other previously used owners, and finally physical-family
+order. It retains an old helper number when possible and otherwise takes the
+smallest unassigned helper number of the required width. These tie rules
+affect the frozen map, but not the single-call optimum remainder histogram.
+
+The recorded run has three passes with strict improvements. Its fourth pass
+has zero strict changes and zero changed helper owners. Hence the recorded map
+is a fixed point of the implemented call update. The separate final audit
+also establishes the stronger cost-level statement that every individual call
+already minimizes every concave remainder objective with the other calls
+fixed.
+
+Calls share capacities. Simultaneously changing two or more calls could
+possibly improve on a coordinate fixed point. The argument makes **no claim
+of joint global optimality**, and the frozen artifact does not depend on such
+a claim.
+
+## 7. Fields to regenerate for actual global admission
+
+| Field or object | Required action |
+| --- | --- |
+| Call `stage`, `replica`, `time` and parent windows | Preserve the parent controller |
+| Helper number and width | Read the new local signature and use the nominated assignment |
+| `owner_replica`, `child`, `port` | Use the final legal group selected by the matcher |
+| `copy`, `family` | Recompute from the selected group, then check uniqueness and active-data exclusion |
+| Helper `offset` | Compact all widths in each group into a disjoint prefix |
+| Idle `rank`, `hosted`, `pending_offset` | Recompute from the actual occupied prefix |
+| Per-call width lists and global paid profile | Recompute from the fresh local programs and actual cells |
+| Provider bindings, center carriers and program hashes | Bind the freshly checked provider; do not retain stale parent IDs or hashes |
+| Actual 73-column owner charts and their digests | Generate afresh from the selected child, port, offset, width and spectator coordinates |
+
+The new construction uses different center carrier registers, including source
+registers. Its ordered center frames and checked operator, rather than old
+carrier numbers, are the semantic interface. The hosting proof does not waive
+that interface check. The signature-only intermediate PLAN produced during
+replay is explicitly marked as such and is never a substitute for fresh
+provider binding or global phase admission.
diff --git a/research/gauge44-leaver/hosting/README.md b/research/gauge44-leaver/hosting/README.md
new file mode 100644
index 0000000000..b9505ebbea
--- /dev/null
+++ b/research/gauge44-leaver/hosting/README.md
@@ -0,0 +1,162 @@
+# Cold44 hosting: frozen owner map and exact callwise matching
+
+This directory contains the owner assignment used to turn the new cold44 local
+word into a global improvement. All 72 calls use the new local signature. The
+assignment is frozen; no search, tuning, or optimization is needed to consume
+it in the global verifier.
+
+The local word reduces the helper width sum from 3894 for the previous `jp8`
+provider to 3794. Simply shrinking the old allocations leaves many small idle
+remainders. The matcher below moves helpers to other physical families that are
+already idle at the same call, concentrating those remainders while respecting
+every parent capacity and window. This recovers a substantial part of the local
+saving in the global moment calculation.
+
+## Frozen result
+
+The exact finite data are in [frozen/MANIFEST.json](frozen/MANIFEST.json) and
+[frozen/MATCHING-RECEIPT.json](frozen/MATCHING-RECEIPT.json).
+
+| Quantity | Frozen value |
+| --- | ---: |
+| Calls | 72 |
+| Helpers per call | 492 |
+| Owner roles | 35,424 |
+| Ambient dimension | 73 |
+| Live streams | 7,168 |
+| New local width sum | 3,794 |
+| New local paid rank mass | 5,650 |
+| Global paid rank mass | 520,704 |
+| Global deficit | 2,560 |
+| Maximum child rank | 48 |
+| Equal-width updates with exact majorization receipts | 288 |
+| Final callwise optima independently checked | 72 |
+
+The new local width inventory is `{4:52, 5:48, 7:34, 8:114, 9:244}` and its paid
+profile is `{1:2514, 2:404, 3:448, 4:160, 5:56, 8:8}`. The final global paid
+profile, including all idle remainders, is:
+
+```json
+{"1":181093,"2":29164,"3":32429,"4":11520,"5":4032,"7":7,
+ "8":582,"12":13,"16":33,"19":1,"20":2,"28":4,"32":62,
+ "36":1,"40":1,"44":6,"48":2289}
+```
+
+Its floating moment screen is `b = 0.0016522089943684115`, giving the analytic
+screen `b/(1+b) = 0.0016494837025589793`. Relative to PR #635's reported
+`0.001636241501576388`, that is approximately **0.8093%**. These decimal screens
+are diagnostic values; the package's exact moment and outer assembly determine
+the admitted exponent. The owner replay never uses the floating root to choose
+an expanded-matching move.
+
+The frozen owner file has byte SHA-256:
+
+```text
+90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57
+```
+
+Its semantic SHA-256, computed from sorted-key compact uncompressed JSON, is:
+
+```text
+c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d
+```
+
+Semantic hashes are the portable replay criterion. The gzip byte hash is also
+reported, but compressor implementations need not produce identical streams.
+
+## Reproduce with the Python standard library
+
+Supply the PR #635 parent `PLAN.json` and `OWNERS.json.gz`, plus either the new
+verified native provider directory or the new raw word. The expected parent
+hashes are pinned in the manifest. The command below is run from the package
+root; replace the example input paths with actual paths.
+
+```sh
+python hosting/reproduce.py \
+  --parent-plan /path/to/pr635/research/complex-571-cold14-st2/data/PLAN.json \
+  --parent-owners /path/to/pr635/research/complex-571-cold14-st2/data/OWNERS.json.gz \
+  --local44 /path/to/verified/local44 \
+  --out /path/to/new/hosting-replay
+```
+
+For the raw provider, replace `--local44 ...` with
+`--raw-word /path/to/FULL-WORD.json.gz`. Reading a raw word here only extracts a
+nomination signature; it does not replace independent local verification.
+
+The default replay copies the frozen mixed-provider seed, checks its semantic
+hash, derives its profile afresh, and runs the exact expanded matcher. It then
+compares the final owner and majorization transcript with the frozen semantic
+hashes and independently checks the final map's 72 callwise fixed points.
+Outputs include `all72/OWNERS.json.gz`, `all72/PROFILE.json`, recomputed
+remainders, `FROZEN-AUDIT.json`, and `REPRODUCTION.json`.
+
+The seed has 71 cold44 calls and one inherited `ck` call. Expanded matching first
+replaces that last call using newly available legal families. This changed-width
+bootstrap is checked for feasibility and is explicitly excluded from the
+equal-width majorization count. The following four passes use cold44 at all 72
+calls:
+
+| Pass | Calls with strict majorization | Changed helper owners |
+| --- | ---: | ---: |
+| 1 | 70 | 1,245 |
+| 2 | 41 | 169 |
+| 3 | 8 | 13 |
+| 4 | 0 | 0 |
+
+Pass 4 changes neither the map nor its remainder histogram. The independent
+audit additionally recomputes the optimal remainder histogram for each call
+with all other calls fixed.
+
+## Optional: reproduce seed discovery
+
+Add `--rebuild-seed` to the same command to rebuild the mixed seed from the
+original PR #635 owners. This step first matches sorted new helper widths to
+sorted old owner slots, then performs two fixed-family Hungarian passes.
+Discovery used Python 3.12.14, NumPy 2.3.5, and SciPy 1.17.0. Equal-cost matching
+tie choices may vary across SciPy versions, so the script compares the rebuilt
+seed with the frozen semantic hash and fails if it differs. Default frozen-seed
+replay has no NumPy or SciPy dependency.
+
+The two discovery passes are an optional way to recover the recorded seed.
+Their floating costs are not needed for feasibility, for the final fixed-point
+proof, or for the package's admitted exponent.
+
+## Audit without regenerating the assignment
+
+```sh
+python hosting/audit_frozen.py \
+  --parent-plan /path/to/pr635/research/complex-571-cold14-st2/data/PLAN.json \
+  --parent-owners /path/to/pr635/research/complex-571-cold14-st2/data/OWNERS.json.gz \
+  --local44 /path/to/verified/local44 \
+  --out /path/to/FROZEN-AUDIT.json
+```
+
+This integer audit checks helper coverage, capacity, allowed call times, active
+data exclusion, physical-family uniqueness within each call, disjoint compacted
+coordinate prefixes, the exact global profile and rank mass, and callwise
+optimality of the frozen remainder histograms. It reads the explicit parent
+window catalogue. The package's separate global verifier must also derive
+those windows and all 73-column charts from the actual program.
+
+## Files and scope
+
+| File | Purpose |
+| --- | --- |
+| `frozen/OWNERS.json.gz` | The final all-cold44 map consumed by global assembly |
+| `frozen/SEED-OWNERS.json.gz` | Pinned feasible mixed seed for dependency-free replay |
+| `frozen/MAJORIZATION.json.gz` | Integer stop-loss margins for every expanded update |
+| `frozen/MANIFEST.json` | Parent, provider, artifact, profile, and parameter bindings |
+| `frozen/SEED-RECEIPT.json` | Recorded sorted matching and two seed discovery passes |
+| `frozen/MATCHING-RECEIPT.json` | Recorded expanded passes and exact finite totals |
+| `reproduce.py` | End-to-end parameterized hosting replay |
+| `reuse_owners.py` | Optional original-family seed constructor |
+| `expand_owners.py` | Exact greedy matching over all eligible physical families |
+| `audit_frozen.py` | Independent feasibility and final callwise fixed-point audit |
+| `PROOF.md` | Capacity, exchange, majorization, and integration arguments |
+
+The expanded matcher is individually optimal for each call when other calls
+are fixed, for every concave remainder cost simultaneously. The frozen map is
+a verified coordinate fixed point. **No joint global optimality claim is
+made.** New local algebra, changed center carriers, phase compatibility,
+actual owner charts, the finite invoice, and exact exponent admission remain
+the responsibility of the package's global verification pipeline.
diff --git a/research/gauge44-leaver/hosting/audit_frozen.py b/research/gauge44-leaver/hosting/audit_frozen.py
new file mode 100644
index 0000000000..26a07408ea
--- /dev/null
+++ b/research/gauge44-leaver/hosting/audit_frozen.py
@@ -0,0 +1,169 @@
+"""Audit the frozen owner map and its callwise fixed point using integers.
+
+The parent window catalogue is an explicit input. The package's independent
+global verifier must additionally derive the windows from the actual program.
+This audit does not certify local algebra, phase charts, or an exponent.
+"""
+from collections import Counter, defaultdict
+from pathlib import Path
+import argparse
+import hashlib
+import json
+
+from reuse_owners import packed, read, sha, signature
+
+
+HERE = Path(__file__).resolve().parent
+
+
+def semantic_sha(path):
+    return hashlib.sha256(packed(read(path))).hexdigest()
+
+
+def add_inputs(parser):
+    parser.add_argument('--parent-plan', type=Path, required=True)
+    parser.add_argument('--parent-owners', type=Path, required=True)
+    provider = parser.add_mutually_exclusive_group(required=True)
+    provider.add_argument('--local44', type=Path, help='Independently checked native provider directory')
+    provider.add_argument('--raw-word', type=Path, help='New FULL-WORD.json.gz; nomination signature only')
+
+
+def bound_inputs(args, manifest):
+    assert sha(args.parent_plan) == manifest['parent_plan_sha256'], 'Wrong parent PLAN'
+    assert sha(args.parent_owners) == manifest['parent_owners_sha256'], 'Wrong parent OWNERS'
+    plan = read(args.parent_plan)
+    assert (plan['K'], plan['T'], plan['M'], plan['L'], plan['live']) == (4, 8, 73, 9, 7168)
+    provider_path = args.local44 if args.local44 is not None else args.raw_word
+    sig = signature(provider_path)
+    expected = manifest['new_provider']
+    assert len(sig['widths']) == expected['R']
+    assert hashlib.sha256(packed(sig['widths'])).hexdigest() == expected['width_vector_sha256']
+    assert sig['profile'] == {int(r): n for r, n in expected['profile'].items()}
+    assert Counter(sig['widths']) == {int(w): n for w, n in expected['width_histogram'].items()}
+    assert sum(sig['widths']) == expected['width_sum']
+    assert sum(r*n for r, n in sig['profile'].items()) == expected['rank_mass']
+    return plan, sig, provider_path
+
+
+def audit(plan, sig, owners):
+    V, R = 112, 492
+    order = [tuple(c) for c in plan['order']]
+    assert len(order) == 72 and len(set(order)) == 72
+    assert len(owners) == 72*R
+    bycall = defaultdict(dict)
+    cells = defaultdict(set)
+    caps, family, eligible = {}, {}, defaultdict(list)
+    for key, (cap, times) in plan['windows'].items():
+        rep, child = map(int, key.split(','))
+        assert 0 <= cap <= 48 and len(times) == len(set(times))
+        for port in range(V):
+            g = (rep, child, port)
+            caps[g] = cap
+            family[g] = rep*8*V + (2*plan['pairs'][str(child)] + plan['sides'][str(child)])*V + port
+            for t in times:
+                assert 0 <= t < len(order)
+                eligible[t].append(g)
+    for t, gs in eligible.items():
+        assert len({family[g] for g in gs}) == len(gs), 'Multiple eligible children on one family'
+        stage, rep = order[t]
+        pair = max(0, (stage-1)//2)
+        assert all(g[0] != rep or plan['pairs'][str(g[1])] != pair for g in gs)
+    for z in owners:
+        t, h = z['time'], z['helper']
+        assert 0 <= t < len(order) and 0 <= h < R
+        assert (z['stage'], z['replica']) == order[t]
+        assert h not in bycall[t]
+        assert z['width'] == sig['widths'][h]
+        g = (z['owner_replica'], z['child'], z['port'])
+        assert g in caps and t in plan['windows'][f'{g[0]},{g[1]}'][1]
+        assert z['copy'] == g[0]*V + g[2] and z['family'] == family[g]
+        off, width = z['offset'], z['width']
+        assert 0 <= off and off+width <= caps[g]
+        occupied = set(range(off, off+width))
+        assert not cells[g] & occupied, 'Overlapping hosted coordinates'
+        cells[g] |= occupied
+        bycall[t][h] = (g, width)
+    for t in range(72):
+        assert set(bycall[t]) == set(range(R))
+        assert len({family[g] for g, w in bycall[t].values()}) == R
+    for occupied in cells.values():
+        assert occupied == set(range(len(occupied))), 'Uncompacted hosted coordinates'
+    used = {g: len(cells[g]) for g in caps}
+    idle = Counter(caps[g]-used[g] for g in caps if caps[g] > used[g])
+    paid = Counter({r: 72*n for r, n in sig['profile'].items()})
+    paid.update(idle)
+
+    # Independent cost-level fixed-point check. No helper-ID or family-ID
+    # tie-breaking is needed: equal capacities give the same histogram.
+    for t in range(72):
+        old = {g: w for g, w in bycall[t].values()}
+        assert len(old) == R
+        before = Counter(caps[g]-used[g] for g in eligible[t])
+        available = sorted(caps[g]-used[g]+old.get(g, 0) for g in eligible[t])
+        want = Counter(sig['widths'])
+        after = Counter()
+        for cap in available:
+            width = next((w for w in sorted(want, reverse=True) if want[w] and w <= cap), 0)
+            if width:
+                want[width] -= 1
+            after[cap-width] += 1
+        assert not any(want.values()), 'Greedy assignment unexpectedly infeasible'
+        assert after == before, ('Frozen map is not callwise optimal', t)
+    mass = sum(r*n for r, n in paid.items())
+    assert 73*7168-mass == 2560 and max(paid) == 48
+    return {
+        'roles': len(owners), 'calls': 72, 'fixed_point_calls_checked': 72,
+        'remainder_profile': dict(sorted(idle.items())),
+        'global_profile': dict(sorted(paid.items())),
+        'rank_mass': mass, 'deficit': 2560, 'maxchild': 48,
+        'all_footprints_disjoint_compacted_prefixes': True,
+        'all_helper_families_idle_and_outside_active_data': True,
+        'one_helper_per_physical_family_per_call': True,
+        'every_call_optimal_for_every_concave_remainder_cost': True,
+        'global_optimality_claimed': False,
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    add_inputs(parser)
+    parser.add_argument('--owners', type=Path, default=HERE/'frozen/OWNERS.json.gz')
+    parser.add_argument('--majorization', type=Path, default=HERE/'frozen/MAJORIZATION.json.gz')
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    manifest = read(HERE/'frozen/MANIFEST.json')
+    plan, sig, provider_path = bound_inputs(args, manifest)
+    assert semantic_sha(args.owners) == manifest['artifacts']['OWNERS.json.gz']['semantic_sha256']
+    assert semantic_sha(args.majorization) == manifest['artifacts']['MAJORIZATION.json.gz']['semantic_sha256']
+    result = audit(plan, sig, read(args.owners))
+    for key in ('remainder_profile', 'global_profile'):
+        assert result[key] == {int(r): n for r, n in manifest[key].items()}
+    moves = read(args.majorization)
+    checked = 0
+    for move in moves:
+        if move['equal_width_multiset']:
+            margins = move['integer_stoploss_margins']
+            assert len(margins) == 49 and all(type(x) is int and x >= 0 for x in margins)
+            assert margins[0] == margins[-1] == 0
+            assert move['strict_majorization'] == bool(any(margins))
+            checked += 1
+        else:
+            assert move['bootstrap'] and move['integer_stoploss_margins'] is None
+    assert checked == 288 and len(moves) == 289
+    result.update({
+        'status': 'PASS_FROZEN_HOSTING_AND_ALL_72_CALLWISE_FIXED_POINTS',
+        'parent_plan_sha256': sha(args.parent_plan),
+        'parent_owners_sha256': sha(args.parent_owners),
+        'owners_semantic_sha256': semantic_sha(args.owners),
+        'majorization_semantic_sha256': semantic_sha(args.majorization),
+        'stored_integer_majorization_steps': checked,
+        'majorization_replay': 'reproduce.py re-executes every step; this audit separately checks the final fixed point.',
+        'remaining_scope': 'The package global verifier checks fresh local algebra, phases, windows, invoice, moment, and outer assembly.',
+    })
+    args.out.parent.mkdir(parents=True, exist_ok=True)
+    args.out.write_text(json.dumps(result, indent=2)+'\n')
+    print(json.dumps(result, indent=2))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/hosting/expand_owners.py b/research/gauge44-leaver/hosting/expand_owners.py
new file mode 100644
index 0000000000..ee6c4c24e6
--- /dev/null
+++ b/research/gauge44-leaver/hosting/expand_owners.py
@@ -0,0 +1,186 @@
+"""Exact callwise concave-cost owner matching over every legal idle family.
+
+This is a finite integer nomination algorithm, not a MILP. Each greedy
+matching is optimal for every concave remainder cost. Its majorization
+receipt is checked with integers, independently of floating root screens.
+"""
+from collections import Counter, defaultdict, deque
+from pathlib import Path
+import argparse
+import gzip
+import hashlib
+import json
+import time
+
+from reuse_owners import read, packed, sha, signature, audit_roles, rate
+
+
+def stoploss(hist,k):return sum(n*max(r-k,0) for r,n in hist.items())
+
+
+def main():
+    ap=argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--plan',type=Path,required=True)
+    ap.add_argument('--owners',type=Path,required=True)
+    ap.add_argument('--signature',action='append',required=True,help='Existing PID=verified native directory or raw/signature JSON')
+    ap.add_argument('--max-passes',type=int,default=8)
+    ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args();assert 1<=a.max_passes<=12
+    a.out.mkdir(parents=True,exist_ok=False);beg=time.monotonic()
+    plan,oldroles=read(a.plan),read(a.owners);V,M=112,73
+    assert (plan['K'],plan['T'],plan['M'],plan['L'])==(4,8,73,9)
+    sig={pid:{'widths':desc['widths'],'profile':{int(r):n for r,n in desc['actual_paid_profile'].items()},'source':'input PLAN'} for pid,desc in plan['provider_registry'].items()}
+    for spec in a.signature:
+        pid,path=spec.split('=',1);assert pid in sig;sig[pid]=signature(path)
+    R=len(next(iter(sig.values()))['widths'])
+    for s in sig.values():
+        assert len(s['widths'])==R and all(type(w) is int and 0<w<=9 for w in s['widths'])
+        assert sum(r*n for r,n in s['profile'].items())==16*V+64+sum(s['widths'])
+    calls={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+    order=[tuple(c) for c in plan['order']]
+    oldwidths={k:plan['provider_registry'][c['provider']]['widths'] for k,c in calls.items()}
+    widths={k:sig[c['provider']]['widths'] for k,c in calls.items()}
+    audit_roles(oldroles,plan,oldwidths,V,R)
+    caps={};families={};eligible=defaultdict(list)
+    for key,(cap,window) in plan['windows'].items():
+        rep,ch=map(int,key.split(','))
+        for port in range(V):
+            g=(rep,ch,port);caps[g]=cap
+            families[g]=rep*(8*V)+(2*plan['pairs'][str(ch)]+plan['sides'][str(ch)])*V+port
+            for t in window:eligible[t].append(g)
+    for t,gs in eligible.items():
+        assert len({families[g] for g in gs})==len(gs), 'current geometry requires one eligible child per family'
+        s,rep=order[t];active_pair=max(0,(s-1)//2)
+        assert all(not (g[0]==rep and plan['pairs'][str(g[1])]==active_pair) for g in gs), 'active data family in idle window'
+    current=defaultdict(dict);used={g:0 for g in caps}
+    for z in oldroles:
+        c=(z['stage'],z['replica']);g=(z['owner_replica'],z['child'],z['port'])
+        current[c][z['helper']]=(g,z['width']);used[g]+=z['width']
+    assert all(0<=used[g]<=caps[g] for g in caps)
+    moves=[]
+
+    def idle_profile():return Counter(caps[g]-used[g] for g in caps if caps[g]>used[g])
+
+    def total_profile():
+        p=Counter()
+        for c in plan['provider_calls']:p.update(sig[c['provider']]['profile'])
+        p.update(idle_profile());assert M*plan['live']-sum(r*n for r,n in p.items())==2560
+        return p
+
+    def update(call,bootstrap=False):
+        t=calls[call]['time'];gs=eligible[t]
+        old=current[call]
+        old_by_group={g:(h,w) for h,(g,w) in old.items()}
+        assert len(old_by_group)==R and set(old_by_group)<=set(gs)
+        oldhist=Counter(caps[g]-used[g] for g in gs)
+        for g,(h,w) in old_by_group.items():used[g]-=w
+        want=defaultdict(set)
+        for h,w in enumerate(widths[call]):want[w].add(h)
+        # Equal-capacity opportunities have identical costs. Preserve old
+        # matching widths first, then old owners, and finally family order.
+        buckets=defaultdict(lambda:defaultdict(deque))
+        for g in sorted(gs,key=lambda g:(families[g],g[1])):
+            available=caps[g]-used[g];oldw=old_by_group.get(g,(None,0))[1]
+            buckets[available][oldw].append(g)
+        result={};unassigned=R
+        for c in sorted(buckets):
+            bucket=buckets[c]
+            while unassigned and any(bucket.values()):
+                w=next((w for w in sorted(want,reverse=True) if w<=c and want[w]),None)
+                if w is None:break
+                if bucket.get(w):q=w
+                else:q=next(q for q in sorted(bucket,reverse=True) if bucket[q])
+                g=bucket[q].popleft()
+                h0=old_by_group.get(g,(None,0))[0]
+                h=h0 if h0 in want[w] else min(want[w])
+                want[w].remove(h);result[h]=(g,w);used[g]+=w;unassigned-=1
+                assert used[g]<=caps[g]
+        assert unassigned==0,('no legal family matching',call,{w:len(h) for w,h in want.items() if h})
+        assert set(result)==set(range(R)) and len({families[g] for g,w in result.values()})==R
+        newhist=Counter(caps[g]-used[g] for g in gs)
+        equal_widths=Counter(w for g,w in old.values())==Counter(widths[call])
+        strict=False
+        if equal_widths:
+            assert sum(oldhist.values())==sum(newhist.values())
+            assert stoploss(oldhist,0)==stoploss(newhist,0)
+            margins=[stoploss(newhist,k)-stoploss(oldhist,k) for k in range(49)]
+            assert min(margins)>=0,('greedy did not majorize old assignment',call,margins)
+            strict=any(margins)
+        else:
+            assert bootstrap
+            margins=None
+        changed=sum(result[h]!=old[h] for h in result)
+        current[call]=result
+        moves.append({'stage':call[0],'replica':call[1],'time':t,'bootstrap':bootstrap,
+                      'equal_width_multiset':equal_widths,'integer_stoploss_margins':margins,
+                      'strict_majorization':strict,'changed_helper_owners':changed})
+        return strict,changed
+
+    changed_calls=[c for c in order if any(current[c][h][1]!=widths[c][h] for h in range(R))]
+    for c in changed_calls:update(c,bootstrap=True)
+    p=total_profile();baseline_b=rate(p,2560,M)
+    rounds=[{'pass':'bootstrap','changed_provider_calls':[list(c) for c in changed_calls],
+             'floating_b':baseline_b,'remainder_profile':dict(sorted(idle_profile().items()))}]
+    print(json.dumps({'checkpoint':'all_goal_signatures_feasible','bootstrap_calls':len(changed_calls),'floating_b':baseline_b}),flush=True)
+    quiet=0
+    for passno in range(a.max_passes):
+        strict=changed=0
+        for c in (order if passno%2==0 else list(reversed(order))):
+            s,z=update(c);strict+=bool(s);changed+=z
+        p=total_profile();r={'pass':passno+1,'strictly_improved_calls':strict,'changed_helper_owners':changed,
+                             'floating_b':rate(p,2560,M),'remainder_profile':dict(sorted(idle_profile().items()))}
+        rounds.append(r);print(json.dumps({k:r[k] for k in ('pass','strictly_improved_calls','changed_helper_owners','floating_b')}),flush=True)
+        quiet=quiet+1 if not strict else 0
+        if quiet>=2 or (not strict and not changed):break
+
+    groups=defaultdict(list);roles=[]
+    for call in order:
+        s,rep=call;t=calls[call]['time']
+        for h,(g,w) in current[call].items():
+            orp,ch,port=g
+            z={'child':ch,'copy':orp*V+port,'family':families[g],'helper':h,'offset':0,
+               'owner_replica':orp,'port':port,'replica':rep,'stage':s,'time':t,'width':w}
+            roles.append(z);groups[g].append(z)
+    for g,zs in groups.items():
+        off=0
+        for z in sorted(zs,key=lambda z:(z['time'],z['helper'])):z['offset']=off;off+=z['width']
+        assert off==used[g]<=caps[g]
+    roles.sort(key=lambda z:(z['time'],z['helper']))
+    cells,_=audit_roles(roles,plan,widths,V,R)
+    for z in roles:
+        active=max(0,(z['stage']-1)//2)
+        assert not (z['owner_replica']==z['replica'] and plan['pairs'][str(z['child'])]==active)
+    for g in caps:assert len(cells[g])==used[g]
+    remainder=[]
+    for g in caps:
+        left=caps[g]-used[g]
+        if left:
+            rep,ch,port=g
+            remainder.append({'child':ch,'port':port,'replica':rep,'replicas':1,'family':families[g],
+                              'rank':left,'hosted':used[g],'pending_offset':used[g]})
+    profile=dict(sorted(total_profile().items()));assert M*M>2*max(profile)**2
+    raw=packed(roles);compressed=bytearray(gzip.compress(raw,mtime=0));compressed[9]=255
+    (a.out/'OWNERS.json.gz').write_bytes(bytes(compressed))
+    (a.out/'MAJORIZATION.json.gz').write_bytes(gzip.compress(packed(moves),mtime=0))
+    (a.out/'REMAINDERS.json').write_text(json.dumps(remainder,indent=2)+'\n')
+    (a.out/'PROFILE.json').write_text(json.dumps(profile,indent=2)+'\n')
+    fields={'profile':profile,'per_call_widths':[{'stage':s,'replica':r,'widths':widths[s,r]} for s,r in order],
+            'assignment_sha256':hashlib.sha256(raw).hexdigest(),'assignment_sha256_semantics':'SHA256 sorted-key compact uncompressed OWNERS array',
+            'source_owners_sha256':sha(a.owners),'provider_signatures':sig}
+    (a.out/'PLAN-OWNER-FIELDS.json').write_text(json.dumps(fields,indent=2)+'\n')
+    receipt={'status':'PASS_EXPANDED_OWNER_MATCHING_EXACT_COMBINATORICS_PENDING_GLOBAL_ADMISSION',
+             'source_plan':str(a.plan),'source_plan_sha256':sha(a.plan),'source_owners':str(a.owners),'source_owners_sha256':sha(a.owners),
+             'owners_sha256':sha(a.out/'OWNERS.json.gz'),'source_signatures':sig,
+             'roles':len(roles),'calls':len(order),'unchanged_call_order_and_windows':True,
+             'all_families_idle_and_outside_active_data':True,'one_helper_per_family_per_call':True,
+             'all_footprints_disjoint_compacted_prefixes':True,'integer_majorization_steps':sum(z['equal_width_multiset'] for z in moves),
+             'majorization_sha256':sha(a.out/'MAJORIZATION.json.gz'),'matching_rounds':rounds,
+             'global_profile':profile,'rank_mass':sum(r*n for r,n in profile.items()),'deficit':2560,
+             'remainder_profile':dict(sorted(idle_profile().items())),'maxchild':max(profile),
+             'candidate_floating_screen_b':rate(profile,2560,M),'seconds':time.monotonic()-beg,
+             'remaining_admission':'Fresh native-provider bindings, actual 73-column owner charts, independent full controller audit, finite invoice, exact moment and outer assembly.'}
+    (a.out/'EXPANDED-OWNER-REUSE.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    print(json.dumps({k:receipt[k] for k in ('status','roles','remainder_profile','rank_mass','candidate_floating_screen_b','seconds')},indent=2),flush=True)
+
+
+if __name__=='__main__':main()
diff --git a/research/gauge44-leaver/hosting/frozen/FROZEN-AUDIT.json b/research/gauge44-leaver/hosting/frozen/FROZEN-AUDIT.json
new file mode 100644
index 0000000000..5f95552366
--- /dev/null
+++ b/research/gauge44-leaver/hosting/frozen/FROZEN-AUDIT.json
@@ -0,0 +1,57 @@
+{
+  "roles": 35424,
+  "calls": 72,
+  "fixed_point_calls_checked": 72,
+  "remainder_profile": {
+    "1": 85,
+    "2": 76,
+    "3": 173,
+    "7": 7,
+    "8": 6,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "all_footprints_disjoint_compacted_prefixes": true,
+  "all_helper_families_idle_and_outside_active_data": true,
+  "one_helper_per_physical_family_per_call": true,
+  "every_call_optimal_for_every_concave_remainder_cost": true,
+  "global_optimality_claimed": false,
+  "status": "PASS_FROZEN_HOSTING_AND_ALL_72_CALLWISE_FIXED_POINTS",
+  "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+  "owners_semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d",
+  "majorization_semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc",
+  "stored_integer_majorization_steps": 288,
+  "majorization_replay": "reproduce.py re-executes every step; this audit separately checks the final fixed point.",
+  "remaining_scope": "The package global verifier checks fresh local algebra, phases, windows, invoice, moment, and outer assembly."
+}
diff --git a/research/gauge44-leaver/hosting/frozen/MAJORIZATION.json.gz b/research/gauge44-leaver/hosting/frozen/MAJORIZATION.json.gz
new file mode 100644
index 0000000000..047b1cfb67
Binary files /dev/null and b/research/gauge44-leaver/hosting/frozen/MAJORIZATION.json.gz differ
diff --git a/research/gauge44-leaver/hosting/frozen/MANIFEST.json b/research/gauge44-leaver/hosting/frozen/MANIFEST.json
new file mode 100644
index 0000000000..291005722c
--- /dev/null
+++ b/research/gauge44-leaver/hosting/frozen/MANIFEST.json
@@ -0,0 +1,114 @@
+{
+  "schema": "gauge44-hosting-frozen-v1",
+  "parent_pr": 635,
+  "parent_paths": {
+    "plan": "research/complex-571-cold14-st2/data/PLAN.json",
+    "owners": "research/complex-571-cold14-st2/data/OWNERS.json.gz"
+  },
+  "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+  "artifacts": {
+    "OWNERS.json.gz": {
+      "sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+      "semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d"
+    },
+    "SEED-OWNERS.json.gz": {
+      "sha256": "eb3be5eebbb84349d7e7f1bde2fc77772a12ad5bccc6dab7c4efd8d903e2a048",
+      "semantic_sha256": "beea695aa2e1ab973ad53f475b3e3e9cf6d0f8a9bca2033a445b64f3b3484e34"
+    },
+    "MAJORIZATION.json.gz": {
+      "sha256": "ec5f94b13d190d72bc0608dc9fe2498cc43ba9deb05028159a812ec1e4dcacdf",
+      "semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc"
+    }
+  },
+  "new_provider": {
+    "R": 492,
+    "h": 9,
+    "v": 112,
+    "width_histogram": {
+      "4": 52,
+      "5": 48,
+      "7": 34,
+      "8": 114,
+      "9": 244
+    },
+    "width_sum": 3794,
+    "profile": {
+      "1": 2514,
+      "2": 404,
+      "3": 448,
+      "4": 160,
+      "5": 56,
+      "8": 8
+    },
+    "rank_mass": 5650,
+    "raw_word_sha256": "3ef4e74e81e2f4621fc95272918ac7b8bb8858df0baa16cc6d91424d55aead9e",
+    "canonical_word_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+    "local_programs_sha256": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+    "width_vector_sha256": "b7fbefdb3af3942194ac9314c767c7812bd68adb734d4e00b70b2916bdb55de8"
+  },
+  "seed_discovery": {
+    "provider_replaced": "jp8",
+    "unchanged_provider": "ck",
+    "passes": 2,
+    "price_b": 0.001638923,
+    "python": "3.12.14",
+    "numpy": "2.3.5",
+    "scipy": "1.17.0",
+    "note": "Only seed discovery uses floating-point Hungarian costs. Frozen seed and the expanded exact replay require the Python standard library."
+  },
+  "expanded_replay": {
+    "providers_replaced": [
+      "jp8",
+      "ck"
+    ],
+    "max_passes": 8,
+    "actual_passes": 4,
+    "integer_majorization_steps": 288,
+    "changed_width_bootstrap_calls": 1
+  },
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "remainder_profile": {
+    "1": 85,
+    "2": 76,
+    "3": 173,
+    "7": 7,
+    "8": 6,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "live": 7168,
+  "roles": 35424,
+  "calls": 72,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "candidate_floating_screen_b": 0.0016522089943684115,
+  "screening_only": "The floating rate here is not a certified exponent. Exact supplier and outer admission belong to the package verifier."
+}
diff --git a/research/gauge44-leaver/hosting/frozen/MATCHING-RECEIPT.json b/research/gauge44-leaver/hosting/frozen/MATCHING-RECEIPT.json
new file mode 100644
index 0000000000..993331090c
--- /dev/null
+++ b/research/gauge44-leaver/hosting/frozen/MATCHING-RECEIPT.json
@@ -0,0 +1,1205 @@
+{
+  "status": "PASS_EXPANDED_OWNER_MATCHING_EXACT_COMBINATORICS_PENDING_GLOBAL_ADMISSION",
+  "source_plan": "explicit parent PLAN, with a temporary signature-only seed view for expanded replay",
+  "source_plan_sha256": "0d2b6a12d3450cfb78e556e80d34cabb8cd1a7f8aa85c1a712a5177236672a37",
+  "source_owners": "frozen/SEED-OWNERS.json.gz",
+  "source_owners_sha256": "eb3be5eebbb84349d7e7f1bde2fc77772a12ad5bccc6dab7c4efd8d903e2a048",
+  "owners_sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+  "source_signatures": {
+    "ck": {
+      "widths": [
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
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+}
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diff --git a/research/gauge44-leaver/hosting/frozen/REPRODUCTION.json b/research/gauge44-leaver/hosting/frozen/REPRODUCTION.json
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+}
diff --git a/research/gauge44-leaver/hosting/frozen/SEED-OWNERS.json.gz b/research/gauge44-leaver/hosting/frozen/SEED-OWNERS.json.gz
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index 0000000000..d61916a156
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diff --git a/research/gauge44-leaver/hosting/frozen/SEED-RECEIPT.json b/research/gauge44-leaver/hosting/frozen/SEED-RECEIPT.json
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index 0000000000..82911f647b
--- /dev/null
+++ b/research/gauge44-leaver/hosting/frozen/SEED-RECEIPT.json
@@ -0,0 +1,1537 @@
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+      "failed_positions": []
+    },
+    "(1, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(0, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(0, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    }
+  },
+  "matching_passes": [
+    {
+      "pass": "sorted",
+      "touched_group_idle_pressure": 44.06409529228022,
+      "calls_awaiting_capacity_matching": 0
+    },
+    {
+      "pass": 1,
+      "accepted_calls": 71,
+      "touched_group_idle_pressure": 24.92521223381306,
+      "decrease": 19.13888305846716
+    },
+    {
+      "pass": 2,
+      "accepted_calls": 58,
+      "touched_group_idle_pressure": 23.047886627886065,
+      "decrease": 1.8773256059269947
+    }
+  ],
+  "roles": 35424,
+  "calls": 72,
+  "remainder_children": 3197,
+  "remainder_profile": {
+    "1": 83,
+    "2": 99,
+    "3": 197,
+    "4": 168,
+    "5": 6,
+    "6": 13,
+    "7": 16,
+    "8": 145,
+    "10": 4,
+    "11": 24,
+    "12": 19,
+    "13": 1,
+    "14": 3,
+    "15": 9,
+    "16": 107,
+    "18": 1,
+    "19": 10,
+    "20": 15,
+    "23": 2,
+    "24": 52,
+    "32": 1,
+    "44": 1,
+    "48": 2221
+  },
+  "global_profile": {
+    "1": 181177,
+    "2": 29335,
+    "3": 32309,
+    "4": 11692,
+    "5": 4052,
+    "6": 17,
+    "7": 16,
+    "8": 721,
+    "10": 4,
+    "11": 24,
+    "12": 19,
+    "13": 1,
+    "14": 3,
+    "15": 9,
+    "16": 107,
+    "18": 1,
+    "19": 10,
+    "20": 15,
+    "23": 2,
+    "24": 52,
+    "32": 1,
+    "44": 1,
+    "48": 2221
+  },
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "source_floating_screen_b": 0.001638923175694355,
+  "candidate_floating_screen_b": 0.0016446065186552388,
+  "remaining_admission": "Bind freshly verified provider artifacts and their hashes; regenerate the global template, actual 73-column sigmas and remainder axes with the existing emitter; run independent owner/frame audit, finite invoice, and exact moment/outer assembly.",
+  "provenance_note": "Absolute discovery paths and wall time removed; original artifact hashes and all exact combinatorial fields preserved."
+}
diff --git a/research/gauge44-leaver/hosting/frozen/SEED-REPRODUCTION.json b/research/gauge44-leaver/hosting/frozen/SEED-REPRODUCTION.json
new file mode 100644
index 0000000000..91ee98cf70
--- /dev/null
+++ b/research/gauge44-leaver/hosting/frozen/SEED-REPRODUCTION.json
@@ -0,0 +1,29 @@
+{
+  "status": "PASS_FROZEN_OWNER_AND_INTEGER_MAJORIZATION_REPLAY",
+  "seed_mode": "two_pass_hungarian_discovery_rebuilt",
+  "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+  "owners_semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d",
+  "owners_gzip_sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+  "majorization_semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc",
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "scope": "Exact hosting nomination and callwise fixed-point replay; full supplier admission is separate."
+}
diff --git a/research/gauge44-leaver/hosting/reproduce.py b/research/gauge44-leaver/hosting/reproduce.py
new file mode 100644
index 0000000000..2f29a5ff13
--- /dev/null
+++ b/research/gauge44-leaver/hosting/reproduce.py
@@ -0,0 +1,100 @@
+"""Reproduce the frozen all-cold44 owner nomination from explicit inputs.
+
+By default, replay the exact integer optimizer from the included frozen seed.
+--rebuild-seed additionally repeats the original two floating-cost Hungarian
+discovery passes; that optional route requires NumPy and SciPy.
+"""
+from pathlib import Path
+from collections import Counter
+import argparse
+import copy
+import json
+import shutil
+import subprocess
+import sys
+
+from audit_frozen import HERE, add_inputs, bound_inputs, semantic_sha
+from reuse_owners import audit_roles, read, sha
+
+
+def run(name, *args):
+    subprocess.run([sys.executable, str(HERE/name), *map(str, args)], check=True)
+
+
+def seed_plan(parent, seed_owners, new_signature):
+    """Build a signature-only resizer input; never an admitted provider PLAN."""
+    plan = copy.deepcopy(parent)
+    plan['provider_registry']['jp8']['widths'] = new_signature['widths']
+    plan['provider_registry']['jp8']['actual_paid_profile'] = new_signature['profile']
+    call_widths = {
+        (c['stage'], c['replica']): plan['provider_registry'][c['provider']]['widths']
+        for c in plan['provider_calls']
+    }
+    used, families = audit_roles(seed_owners, plan, call_widths, 112, 492)
+    profile = Counter()
+    for c in plan['provider_calls']:
+        profile.update({int(r): n for r, n in plan['provider_registry'][c['provider']]['actual_paid_profile'].items()})
+    for key, (cap, times) in plan['windows'].items():
+        rep, child = map(int, key.split(','))
+        for port in range(112):
+            left = cap-len(used[rep, child, port])
+            if left:
+                profile[left] += 1
+    assert 73*7168-sum(r*n for r, n in profile.items()) == 2560
+    plan['profile'] = dict(sorted(profile.items()))
+    plan['per_call_widths'] = [
+        {'stage': s, 'replica': r, 'widths': call_widths[s, r]}
+        for s, r in plan['order']
+    ]
+    plan['status'] = 'INTERMEDIATE_SIGNATURE_ONLY_OWNER_SEED_NOT_PROVIDER_ADMISSION'
+    return plan
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    add_inputs(parser)
+    parser.add_argument('--rebuild-seed', action='store_true')
+    parser.add_argument('--out', type=Path, required=True, help='New output directory')
+    args = parser.parse_args()
+    manifest = read(HERE/'frozen/MANIFEST.json')
+    parent, sig, provider = bound_inputs(args, manifest)
+    args.out.mkdir(parents=True, exist_ok=False)
+    seed_dir = args.out/'seed'
+    if args.rebuild_seed:
+        run('reuse_owners.py', '--plan', args.parent_plan, '--owners', args.parent_owners,
+            '--signature', f'jp8={provider}', '--passes', '2', '--price-b', '0.001638923', '--out', seed_dir)
+    else:
+        seed_dir.mkdir()
+        shutil.copyfile(HERE/'frozen/SEED-OWNERS.json.gz', seed_dir/'OWNERS.json.gz')
+    assert semantic_sha(seed_dir/'OWNERS.json.gz') == manifest['artifacts']['SEED-OWNERS.json.gz']['semantic_sha256'], (
+        'Seed differs; use the default frozen-seed replay, or the recorded NumPy/SciPy versions for discovery replay.'
+    )
+    plan = seed_plan(parent, read(seed_dir/'OWNERS.json.gz'), sig)
+    plan_path = seed_dir/'PLAN-FOR-RESIZER.json'
+    plan_path.write_text(json.dumps(plan, indent=2)+'\n')
+    final_dir = args.out/'all72'
+    run('expand_owners.py', '--plan', plan_path, '--owners', seed_dir/'OWNERS.json.gz',
+        '--signature', f'jp8={provider}', '--signature', f'ck={provider}',
+        '--max-passes', '8', '--out', final_dir)
+    for name in ('OWNERS.json.gz', 'MAJORIZATION.json.gz'):
+        assert semantic_sha(final_dir/name) == manifest['artifacts'][name]['semantic_sha256'], (name, 'Frozen semantic digest mismatch')
+    kwargs = ('--local44', args.local44) if args.local44 is not None else ('--raw-word', args.raw_word)
+    run('audit_frozen.py', '--parent-plan', args.parent_plan, '--parent-owners', args.parent_owners,
+        *kwargs, '--owners', final_dir/'OWNERS.json.gz', '--majorization', final_dir/'MAJORIZATION.json.gz',
+        '--out', args.out/'FROZEN-AUDIT.json')
+    receipt = {
+        'status': 'PASS_FROZEN_OWNER_AND_INTEGER_MAJORIZATION_REPLAY',
+        'seed_mode': 'two_pass_hungarian_discovery_rebuilt' if args.rebuild_seed else 'included_frozen_seed',
+        'parent_plan_sha256': sha(args.parent_plan), 'parent_owners_sha256': sha(args.parent_owners),
+        'owners_semantic_sha256': semantic_sha(final_dir/'OWNERS.json.gz'),
+        'owners_gzip_sha256': sha(final_dir/'OWNERS.json.gz'),
+        'majorization_semantic_sha256': semantic_sha(final_dir/'MAJORIZATION.json.gz'),
+        'global_profile': read(final_dir/'PROFILE.json'),
+        'scope': 'Exact hosting nomination and callwise fixed-point replay; full supplier admission is separate.',
+    }
+    (args.out/'REPRODUCTION.json').write_text(json.dumps(receipt, indent=2)+'\n')
+    print(json.dumps(receipt, indent=2))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/hosting/reuse_owners.py b/research/gauge44-leaver/hosting/reuse_owners.py
new file mode 100644
index 0000000000..234b831790
--- /dev/null
+++ b/research/gauge44-leaver/hosting/reuse_owners.py
@@ -0,0 +1,230 @@
+"""Deterministic existing-family owner reuse and optional callwise matching.
+
+The output is a nomination, requiring the ordinary independent owner, phase,
+finite-invoice, and exact-moment admission. No MILP or new owner family is used.
+"""
+from collections import Counter, defaultdict
+from pathlib import Path
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+import math
+import time
+
+
+def read(path):
+    raw=Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def packed(obj):return json.dumps(obj,sort_keys=True,separators=(',',':')).encode()
+def sha(path):return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def signature(path):
+    path=Path(path)
+    if path.is_dir():
+        w=read(path/'CANONICAL-WORD.json.gz');V,R=w['v'],w['R']
+        widths=[len(w['frames'][w['final'][2*V+h]])-len(w['frames'][w['start'][2*V+h]]) for h in range(R)]
+        programs=read(path/'LOCAL-PROGRAMS.json.gz')
+        profiles=[Counter(e[-1] for e in programs[o] if e[0] in ('climb','center')) for o in ('forward','backward')]
+        assert profiles[0]==profiles[1]
+        assert profiles[0]=={int(r):n for r,n in w['local_profile'].items()}
+        return {'widths':widths,'profile':dict(profiles[0]),'source':str(path),
+                'canonical_sha256':sha(path/'CANONICAL-WORD.json.gz'),
+                'program_sha256':sha(path/'LOCAL-PROGRAMS.json.gz')}
+    w=read(path)
+    if 'report' in w:
+        V,R=w['report']['v'],w['report']['R']
+        widths=[len(w.get('helper_final',{}).get(str(2*V+h),range(9)))-len(w.get('start_extra',{}).get(str(2*V+h),[])) for h in range(R)]
+        profile={int(r):n for r,n in w['report']['local_profile'].items()}
+    else:
+        widths=w['widths'];profile={int(r):n for r,n in w['profile'].items()}
+    return {'widths':widths,'profile':profile,'source':str(path),'source_sha256':sha(path)}
+
+
+def phi(rank,b,M):return rank*math.expm1(b*math.log(M/rank)) if rank else 0.
+
+
+def rate(profile,deficit,M):
+    lo,hi=0.,.02
+    for _ in range(58):
+        mid=(lo+hi)/2
+        if sum(n*phi(r,mid,M) for r,n in profile.items())<deficit:lo=mid
+        else:hi=mid
+    return lo
+
+
+def audit_roles(roles,plan,widths_by_call,V,R):
+    used=defaultdict(set);families=defaultdict(set);helpers=defaultdict(set)
+    for z in roles:
+        s,rep,h=z['stage'],z['replica'],z['helper'];call=(s,rep)
+        assert z['time']==plan['order'].index([s,rep])
+        assert 0<=h<R and z['width']==widths_by_call[call][h]
+        assert h not in helpers[call] and z['family'] not in families[call]
+        helpers[call].add(h);families[call].add(z['family'])
+        orp,ch,port=z['owner_replica'],z['child'],z['port']
+        assert z['copy']==orp*V+port
+        assert z['family']==orp*(8*V)+(2*plan['pairs'][str(ch)]+plan['sides'][str(ch)])*V+port
+        cap,window=plan['windows'][f'{orp},{ch}']
+        assert z['time'] in window and 0<=z['offset'] and z['offset']+z['width']<=cap
+        cells=set(range(z['offset'],z['offset']+z['width']))
+        key=(orp,ch,port);assert not used[key]&cells;used[key]|=cells
+    assert len(roles)==len(plan['order'])*R
+    assert all(helpers[tuple(c)]==set(range(R)) for c in plan['order'])
+    for cells in used.values():assert cells==set(range(len(cells)))
+    return used,families
+
+
+def main():
+    ap=argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--plan',type=Path,required=True)
+    ap.add_argument('--owners',type=Path,required=True)
+    ap.add_argument('--signature',action='append',default=[],help='Existing PID=raw-word, signature JSON, or verified native directory')
+    ap.add_argument('--passes',type=int,default=2)
+    ap.add_argument('--price-b',type=float,default=0.001638923)
+    ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args();assert 0<=a.passes<=2
+    a.out.mkdir(parents=True,exist_ok=False);beg=time.monotonic()
+    plan,oldroles=read(a.plan),read(a.owners)
+    assert (plan['K'],plan['T'],plan['M'],plan['L'])==(4,8,73,9)
+    M,V=73,112;R=len(next(iter(plan['provider_registry'].values()))['widths'])
+    signatures={pid:{'widths':desc['widths'],'profile':{int(r):n for r,n in desc['actual_paid_profile'].items()},'source':'inherited PLAN'} for pid,desc in plan['provider_registry'].items()}
+    for spec in a.signature:
+        pid,path=spec.split('=',1);assert pid in signatures
+        signatures[pid]=signature(path)
+    for sig in signatures.values():
+        assert len(sig['widths'])==R and all(type(w) is int and 0<w<=9 for w in sig['widths'])
+        assert sum(int(r)*n for r,n in sig['profile'].items())==16*V+64+sum(sig['widths'])
+    calls={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+    oldwidths={k:plan['provider_registry'][c['provider']]['widths'] for k,c in calls.items()}
+    newwidths={k:signatures[c['provider']]['widths'] for k,c in calls.items()}
+    oldused,oldfamilies=audit_roles(oldroles,plan,oldwidths,V,R)
+
+    # A slot is an old immutable owner-family opportunity. Only the helper
+    # assigned to the opportunity and its footprint width may change.
+    bycall=defaultdict(list);groups=defaultdict(list)
+    for i,z in enumerate(oldroles):
+        bycall[z['stage'],z['replica']].append(i)
+        groups[z['owner_replica'],z['child'],z['port']].append(i)
+    group_of={i:g for g,ids in groups.items() for i in ids}
+    cap={g:plan['windows'][f'{g[0]},{g[1]}'][0] for g in groups}
+    assigned_h={};assigned_w={};dominance={};pending=[]
+    for call,ids in bycall.items():
+        slots=sorted(ids,key=lambda i:(oldroles[i]['width'],oldroles[i]['helper']))
+        helpers=sorted(range(R),key=lambda h:(newwidths[call][h],h))
+        failures=[(h,newwidths[call][h],oldroles[i]['width']) for h,i in zip(helpers,slots) if newwidths[call][h]>oldroles[i]['width']]
+        if failures:
+            # Keep this call's old widths provisionally; shrunk calls leave
+            # slack on their original owner families. A subsequent exact
+            # bipartite matching may use that slack for this call.
+            pending.append(call)
+            for i in ids:assigned_h[i]=oldroles[i]['helper'];assigned_w[i]=oldroles[i]['width']
+        else:
+            for h,i in zip(helpers,slots):assigned_h[i]=h;assigned_w[i]=newwidths[call][h]
+        dominance[str(call)]={'old_total':sum(oldwidths[call]),'new_total':sum(newwidths[call]),'sorted_termwise_dominance':not failures,'failed_positions':failures}
+    used={g:sum(assigned_w[i] for i in ids) for g,ids in groups.items()}
+    assert all(used[g]<=cap[g] for g in groups)
+    cost_cache=[phi(r,a.price_b,M) for r in range(49)]
+    def current_cost():return sum(cost_cache[cap[g]-used[g]] for g in groups)
+    passes=[{'pass':'sorted','touched_group_idle_pressure':current_cost(),'calls_awaiting_capacity_matching':len(pending)}]
+
+    if a.passes or pending:
+        import numpy as np
+        from scipy.optimize import linear_sum_assignment
+        def match_call(call,force=False):
+            ids=sorted(bycall[call],key=lambda i:oldroles[i]['helper'])
+            gs=[group_of[i] for i in ids]
+            assert len(set(gs))==R, 'one owner family per complete call is essential'
+            available=np.array([cap[g]-used[g]+assigned_w[i] for i,g in zip(ids,gs)],dtype=np.int64)
+            ws=np.array(newwidths[call],dtype=np.int64)
+            left=available[None,:]-ws[:,None]
+            matrix=np.full((R,R),np.inf)
+            valid=left>=0
+            matrix[valid]=np.asarray(cost_cache)[left[valid]]
+            ri,ci=linear_sum_assignment(matrix)
+            assert len(ri)==R and np.all(np.isfinite(matrix[ri,ci]))
+            oldcost=sum(cost_cache[cap[g]-used[g]] for g in gs)
+            newcost=float(matrix[ri,ci].sum())
+            if not force:
+                assert newcost<=oldcost+1e-10
+                if oldcost-newcost<=1e-10:return False
+            for h,col in zip(ri,ci):
+                i=ids[int(col)];g=group_of[i];h=int(h);ww=int(ws[h])
+                used[g]+=ww-assigned_w[i];assigned_w[i]=ww;assigned_h[i]=h
+                assert used[g]<=cap[g]
+            return True
+        for call in pending:
+            match_call(call,force=True)
+            dominance[str(call)]['capacity_matching_feasible']=True
+        if pending:passes.append({'pass':'capacity_bootstrap','touched_group_idle_pressure':current_cost(),'resolved_calls':[list(c) for c in pending]})
+        for p in range(a.passes):
+            accepted=0;startcost=current_cost()
+            order=[tuple(k) for k in plan['order']]
+            if p%2:order.reverse()
+            for call in order:
+                accepted+=match_call(call)
+            finalcost=current_cost();assert finalcost<=startcost+1e-9
+            passes.append({'pass':p+1,'accepted_calls':accepted,'touched_group_idle_pressure':finalcost,'decrease':startcost-finalcost})
+
+    # The inherited compiler requires each used coordinate set to be a
+    # prefix. Stable left compaction preserves every immutable owner field.
+    roles=copy.deepcopy(oldroles);matching=[]
+    for g,ids in groups.items():
+        off=0
+        for i in sorted(ids,key=lambda i:(oldroles[i]['offset'],oldroles[i]['time'],oldroles[i]['helper'])):
+            z=roles[i];z['helper']=assigned_h[i];z['width']=assigned_w[i];z['offset']=off;off+=z['width']
+            matching.append({'stage':z['stage'],'replica':z['replica'],'old_helper':oldroles[i]['helper'],
+                             'new_helper':z['helper'],'old_width':oldroles[i]['width'],'new_width':z['width'],
+                             'family':z['family'],'child':z['child'],'old_offset':oldroles[i]['offset'],'new_offset':z['offset']})
+        assert off==used[g]<=cap[g]
+    roles.sort(key=lambda z:(z['time'],z['helper']))
+    newused,newfamilies=audit_roles(roles,plan,newwidths,V,R)
+    assert newfamilies==oldfamilies
+    paid=Counter();remainders=[]
+    for c in plan['provider_calls']:paid.update(signatures[c['provider']]['profile'])
+    idle=Counter()
+    for key,(capacity,window) in plan['windows'].items():
+        rep,ch=map(int,key.split(','))
+        for port in range(V):
+            occupied=len(newused[rep,ch,port]);left=capacity-occupied
+            if left:
+                family=rep*(8*V)+(2*plan['pairs'][str(ch)]+plan['sides'][str(ch)])*V+port
+                remainders.append({'child':ch,'port':port,'replica':rep,'replicas':1,'family':family,
+                                   'rank':left,'hosted':occupied,'pending_offset':occupied})
+                idle[left]+=1
+    paid.update(idle);mass=sum(r*n for r,n in paid.items())
+    assert M*plan['live']-mass==plan['deficit']==2560
+    assert M*M>2*max(paid)**2
+    oldprofile={int(r):n for r,n in plan['profile'].items()}
+    ownerraw=packed(roles);gz=bytearray(gzip.compress(ownerraw,mtime=0));gz[9]=255
+    (a.out/'OWNERS.json.gz').write_bytes(bytes(gz))
+    (a.out/'MATCHING.json.gz').write_bytes(gzip.compress(packed(matching),mtime=0))
+    (a.out/'REMAINDERS.json').write_text(json.dumps(remainders,indent=2)+'\n')
+    profile=dict(sorted(paid.items()))
+    (a.out/'PROFILE.json').write_text(json.dumps(profile,indent=2)+'\n')
+    owner_fields={'profile':profile,
+                  'per_call_widths':[{'stage':s,'replica':r,'widths':newwidths[s,r]} for s,r in plan['order']],
+                  'assignment_sha256':hashlib.sha256(ownerraw).hexdigest(),
+                  'assignment_sha256_semantics':'SHA256 of sorted-key compact uncompressed OWNERS array',
+                  'source_owners_sha256':sha(a.owners),
+                  'provider_signatures':signatures}
+    (a.out/'PLAN-OWNER-FIELDS.json').write_text(json.dumps(owner_fields,indent=2)+'\n')
+    rec={'status':'PASS_OWNER_REUSE_NOMINATION_COMBINATORICS_NOT_FULL_SUPPLIER_ADMISSION',
+         'source_plan':str(a.plan),'source_plan_sha256':sha(a.plan),'source_owners_sha256':sha(a.owners),
+         'owners_sha256':sha(a.out/'OWNERS.json.gz'),'unchanged_owner_family_sets':True,
+         'unchanged_call_order_and_windows':True,'all_footprints_are_disjoint_compacted_prefixes':True,
+         'local_signatures':signatures,'sorted_initial_dominance':dominance,'matching_passes':passes,
+         'roles':len(roles),'calls':len(calls),'remainder_children':len(remainders),'remainder_profile':dict(sorted(idle.items())),
+         'global_profile':profile,'rank_mass':mass,'deficit':2560,'maxchild':max(paid),
+         'source_floating_screen_b':rate(oldprofile,2560,M),
+         'candidate_floating_screen_b':rate(profile,2560,M),
+         'seconds':time.monotonic()-beg,
+         'remaining_admission':'Bind freshly verified provider artifacts and their hashes; regenerate the global template, actual 73-column sigmas and remainder axes with the existing emitter; run independent owner/frame audit, finite invoice, and exact moment/outer assembly.'}
+    (a.out/'OWNER-REUSE.json').write_text(json.dumps(rec,indent=2)+'\n')
+    print(json.dumps({k:rec[k] for k in ('status','roles','matching_passes','remainder_profile','rank_mass','source_floating_screen_b','candidate_floating_screen_b','seconds')},indent=2),flush=True)
+
+
+if __name__=='__main__':main()
diff --git a/research/gauge44-leaver/independent/CENTRE-GUARD-REVIEW.md b/research/gauge44-leaver/independent/CENTRE-GUARD-REVIEW.md
new file mode 100644
index 0000000000..6c62bd070e
--- /dev/null
+++ b/research/gauge44-leaver/independent/CENTRE-GUARD-REVIEW.md
@@ -0,0 +1,79 @@
+# Independent review of the centre and admission interfaces
+
+**Finding:** the replacement of old local centre-carrier IDs by equality of the
+eight ordered centre-frame bases preserves the inherited global contract. It
+must be used together with the complete local scalar, frame, phase and wrapper
+admission. No mathematical admission guard was found to have been removed.
+
+## Why source carriers may supply centres
+
+The transported gauge44 centre carriers are
+`[92, 57, 81, 224, 11, 240, 9, 256]`. Five are source registers and three are
+helper registers. All 112 transported port labels and all eight ordered
+rank-eight centre-frame bases agree exactly with the retained parent. The
+optional `--main` check in `audit_local.py` independently verifies that boundary
+against a byte-pinned parent canonical word.
+
+The actual forward local program copies the current row of `L_r` into private
+`C_k` at their common frame `F_k`. It then descends `C_k` from `F_k` to frame
+zero, scatters to the targets, and clears `C_k`. The backward program performs
+the corresponding reversed ascent and scatter. This construction depends on
+the copied row, its frame and the exact local program, rather than on a
+requirement that `r` be in the helper-ID interval. The source itself is not
+cleared or treated as private work.
+
+The independently checked local contract retains every required obligation:
+all 716 input columns in both orientations; the forward and backward shear
+identities; arbitrary initial helper dirt; scalar/COPY common-frame legality;
+centre lifetimes and nested steps; exact native phase identities; endpoint
+and row/column cone conditions; and residual wrappers before and after every
+relevant touch. Its finite invoice recounts the actual operations.
+
+The global controller addresses private centres by `k`, while the source or
+helper `L_r` is mapped through the complete invocation's ordinary owner array.
+The owner audit retains pairwise distinct owners for all active source, target
+and helper roles. A helper therefore cannot borrow the family of an active
+source centre. The private-centre namespace is disjoint from those owners and
+the local program clears it. Each whole invocation finishes before another
+begins, so no new interleaving or family lifetime assumption is introduced.
+
+## Admission guards and single-provider controls
+
+An AST comparison with PR635 found all **91 assertions in `code/assemble.py`
+identical, in the same traversal order**, including constants. This includes
+the unchanged PR543 bit input, deficit and surcharge, every finite-invoice
+guard, both conservative and native complex moment checks, and the strict
+outer assembly and its controls. The following files retain the reviewed PR635 code (the packaged
+`bind_providers_portable.py` only trims trailing whitespace): `invoice_allcold.py` (67 assertions),
+`bind_providers_portable.py` (22), `generated_identity.py` (4), and `witness.py`
+(3). `review_guards.py` reproduces the assertion comparison and records the
+file hashes.
+
+The controller still checks the complete serialized provider registry,
+per-call program and dispatch, native phase and wrapper bindings, helper
+widths, owner uniqueness, actual busy-family windows, spectator orthogonality,
+and literal idle remainders. The single-provider branch replaces partner
+substitutions by direct invalid-ID, program, width and hash mutations. Only
+four assembly mutation scenarios requiring a second registered provider are
+inapplicable. Their removal does not remove any admission predicate. Direct
+forged program/phase tests, width-order and width-inventory tests, and
+selected-call/order tests remain.
+
+## Price and bit headroom
+
+The frozen all72 profile gives the native complex root bracket
+`(0.001652208994368411824947, 0.001652208994368411824948)` and
+`kappa = 0.001649483702558979`. Both independent rational engines certify the
+two signs. The seven-step outer driver passes all 47 strict constraints and
+rejects its four standard mutations. The conservative complex price passes
+separately at `kappa = 0.001649483699681650`.
+
+The achieved complex rate is below PR543's retained bit rate
+`0.001653826988146798944268`. Using eumemic's independently reviewed PR555 bit
+rate `0.001733052823330162099157` gives exactly the same attained kappa. PR543
+therefore remains the cited supplier for this delta; no bit improvement is
+claimed here and no PR555 implementation is bundled.
+
+These receipts supplement the package's complete native, owner, phase and
+finite-invoice replay. The inherited all-size realization and analytic
+transfer assumptions remain conditional.
diff --git a/research/gauge44-leaver/independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json b/research/gauge44-leaver/independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json
new file mode 100644
index 0000000000..771faa86a7
--- /dev/null
+++ b/research/gauge44-leaver/independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json
@@ -0,0 +1,137 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+  "input_file": "FULL-WORD.json.gz",
+  "content_sha256": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290",
+  "compressed_sha256": "3ef4e74e81e2f4621fc95272918ac7b8bb8858df0baa16cc6d91424d55aead9e",
+  "parent_center_interface": {
+    "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+    "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "transport_tau": 43,
+    "ordered_frame_bases_match": true,
+    "all_ports_match": true,
+    "transported_centers": [
+      92,
+      57,
+      81,
+      224,
+      11,
+      240,
+      9,
+      256
+    ],
+    "source_centers": [
+      92,
+      57,
+      81,
+      11,
+      9
+    ],
+    "ordered_frame_bases": [
+      [
+        256,
+        128,
+        64,
+        34,
+        16,
+        10,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        16,
+        8,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        17,
+        9,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ],
+      [
+        256,
+        128,
+        66,
+        32,
+        18,
+        8,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        17,
+        9,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        16,
+        8,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        68,
+        32,
+        16,
+        12,
+        2,
+        1
+      ]
+    ]
+  },
+  "v": 112,
+  "h": 9,
+  "R": 492,
+  "entering": 204,
+  "lowends": 78,
+  "coldends": 44,
+  "compensation_gates": 7348,
+  "local_profile": {
+    "1": 2514,
+    "2": 404,
+    "3": 448,
+    "4": 160,
+    "5": 56,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 52,
+    "5": 48,
+    "7": 34,
+    "8": 114,
+    "9": 244
+  },
+  "checked_columns": 716,
+  "elapsed_seconds": 3.147683588000291,
+  "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+}
diff --git a/research/gauge44-leaver/independent/GAUGE44-GLOBAL-GUARD-REVIEW.json b/research/gauge44-leaver/independent/GAUGE44-GLOBAL-GUARD-REVIEW.json
new file mode 100644
index 0000000000..e2df1dcca8
--- /dev/null
+++ b/research/gauge44-leaver/independent/GAUGE44-GLOBAL-GUARD-REVIEW.json
@@ -0,0 +1,47 @@
+{
+  "status": "PASS_PR635_ADMISSION_ASSERTION_PRESERVATION",
+  "files": [
+    {
+      "file": "code/assemble.py",
+      "baseline_sha256": "1b1a9024ac910dc9b9d9e30150684e1fa9cb228a4c1c275b75ab04b57fdef1dd",
+      "new_sha256": "7ac28118d69416e4fb67b61216285fb0823310b7635ce1b9025aa3f10119ef6a",
+      "byte_identical": false,
+      "assert_count": 91,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/invoice_allcold.py",
+      "baseline_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+      "new_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+      "byte_identical": true,
+      "assert_count": 67,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/bind_providers_portable.py",
+      "baseline_sha256": "2eb5c262bf481b3bec9ceaec654fa46ff6fc3a89b13d4906a29a55a89e35feea",
+      "new_sha256": "2eb5c262bf481b3bec9ceaec654fa46ff6fc3a89b13d4906a29a55a89e35feea",
+      "byte_identical": true,
+      "assert_count": 22,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/generated_identity.py",
+      "baseline_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+      "new_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+      "byte_identical": true,
+      "assert_count": 4,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/witness.py",
+      "baseline_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+      "new_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+      "byte_identical": true,
+      "assert_count": 3,
+      "all_assertions_identical_in_order": true
+    }
+  ],
+  "centre_interface_review": "CENTRE-GUARD-REVIEW.md",
+  "scope": "Exact syntax preservation for all admission assertions in these five files. The changed emitter/controller centre boundary and single-provider controls require the separate semantic review; assertion counts alone do not prove them."
+}
diff --git a/research/gauge44-leaver/independent/GAUGE44-INDEPENDENT-PRICE.json b/research/gauge44-leaver/independent/GAUGE44-INDEPENDENT-PRICE.json
new file mode 100644
index 0000000000..7478b812d3
--- /dev/null
+++ b/research/gauge44-leaver/independent/GAUGE44-INDEPENDENT-PRICE.json
@@ -0,0 +1,157 @@
+{
+  "status": "PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK",
+  "profile_input_file": "PLAN.json",
+  "profile_input_sha256": "b08f8dc3624c89b38897762e13f9a15e0efa688f2e0bb7fe33abe22ef4f7ddc5",
+  "global_profile": {
+    "1": 177877,
+    "2": 27944,
+    "3": 31001,
+    "4": 11952,
+    "5": 5040,
+    "7": 280,
+    "8": 599,
+    "16": 18,
+    "32": 13,
+    "48": 2364
+  },
+  "live": 7168,
+  "m": 73,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "prices": {
+    "native": {
+      "root": {
+        "lower": "0.001667007898013796187659",
+        "upper": "0.00166700789801379618766",
+        "lower_endpoint_residual_upper": "-2.431426148023288650562918849408452034189463608684910349558723365540705E-24",
+        "upper_endpoint_residual_lower": "5.123273217930672352378179136643473320633520146133519936052785362015762E-25",
+        "strict_rational_signs": true
+      },
+      "exact_moments": [
+        {
+          "endpoint": "1667007898013796187659/1000000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-32775559637911689514404465670564883355377605/13479973333575319897333507543509815336818572211270286240551805124608",
+            "-8193889909477922378601116417641220838844401/3369993333393829974333376885877453834204643052817571560137951281152"
+          ],
+          "base_two_residual": [
+            "-2431427/1000000000000000000000000000000",
+            "-1215713/500000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "83350394900689809383/50000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "13812317271665216354913923425920726111674131/26959946667150639794667015087019630673637144422540572481103610249216",
+            "13812317271665216354913923425920726111674133/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "512327/1000000000000000000000000000000",
+            "64041/125000000000000000000000000000"
+          ]
+        }
+      ],
+      "outer_with_bit": {
+        "complex_b": "1667007898013796187659/1000000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "1664233607446043/1000000000000000000",
+        "kappa_decimal": "0.001664233607446043",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    },
+    "conservative": {
+      "root": {
+        "lower": "0.001667007895147233886617",
+        "upper": "0.001667007895147233886618",
+        "lower_endpoint_residual_upper": "-1.531318625472063951793277273404095727087467424735011439902272318847256E-24",
+        "upper_endpoint_residual_lower": "1.412434844349707087480912263248299511020229909045323511544927283382353E-24",
+        "strict_rational_signs": true
+      },
+      "exact_moments": [
+        {
+          "endpoint": "1667007895147233886617/1000000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-41284268473141269362070901792794593529737265/26959946667150639794667015087019630673637144422540572481103610249216",
+            "-41284268473141269362070901792794593529737263/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "-3828298520107574772377/2500000000000000000000000000000000000000000000",
+            "-7656592040215149544683/5000000000000000000000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "833503947573616943309/500000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "9519792018623329567622668821978090494164783/6739986666787659948666753771754907668409286105635143120275902562304",
+            "19039584037246659135245337643956180988329567/13479973333575319897333507543509815336818572211270286240551805124608"
+          ],
+          "base_two_residual": [
+            "3531086479982937325477/2500000000000000000000000000000000000000000000",
+            "282487118398634986041/200000000000000000000000000000000000000000000"
+          ]
+        }
+      ],
+      "outer_with_bit": {
+        "complex_b": "1667007895147233886617/1000000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "832116802294507/500000000000000000",
+        "kappa_decimal": "0.001664233604589014",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    }
+  },
+  "bit_supplier_pr": 589,
+  "bit_deficit": 10272,
+  "bit_moments_with_surcharge": [
+    {
+      "endpoint": "1733427039589844234749/1000000000000000000000000",
+      "accept": true,
+      "mercator_residual": [
+        "-43100600330766044577088869872467188970742291/26959946667150639794667015087019630673637144422540572481103610249216",
+        "-43100600330766044577088869872467188970742289/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two_residual": [
+        "-799345163337715793503/500000000000000000000000000000000000000000000",
+        "-3197378653350863173989/2000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "endpoint": "6933708158359376939/4000000000000000000000",
+      "accept": false,
+      "mercator_residual": [
+        "22502934905675809315035333485365686073718547/13479973333575319897333507543509815336818572211270286240551805124608",
+        "5625733726418952328758833371341421518429637/3369993333393829974333376885877453834204643052817571560137951281152"
+      ],
+      "base_two_residual": [
+        "8346798366759439729359/5000000000000000000000000000000000000000000000",
+        "16693606733518879458833/10000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "gain_over_pr635_percent": "1.71075637934173175089511307998847021180133581733437016087411723198560364402",
+  "input_sha256": {
+    "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "package:inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4"
+  },
+  "scope": "Independent arithmetic for the exact nominated all72 profile. Complete local, controller and finite invoice admission are separately replayed by the package driver; this receipt does not replace them. The cited PR589 bit supplier is unchanged and its exceptional-residue surcharge is retained. Any alternative c is only a headroom comparison."
+}
diff --git a/research/gauge44-leaver/independent/README.md b/research/gauge44-leaver/independent/README.md
new file mode 100644
index 0000000000..f97dcf81b1
--- /dev/null
+++ b/research/gauge44-leaver/independent/README.md
@@ -0,0 +1,43 @@
+# Independent checks
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0, under the
+package license. The scalar/frame audit imports no generator or supplier
+checker. Pricing uses the pinned inherited rational engines and the retained
+PR635 outer formula, with their original notices preserved in the main
+dependency tree.
+
+From the delta package directory, using the pinned checkouts and a rebuilt
+word:
+
+```sh
+python independent/audit_local.py \
+  --word /path/to/rebuild/cold44/FULL-WORD.json.gz \
+  --main /path/to/main \
+  --output /path/to/output/LOCAL-AUDIT.json
+
+python independent/price_profile.py \
+  --main /path/to/main \
+  --output /path/to/output/PRICE.json
+
+python independent/review_guards.py \
+  --pr635 /path/to/pr635 \
+  --output /path/to/output/GUARD-REVIEW.json
+```
+
+`audit_local.py` can run without `--main`; including it also verifies the
+transported centre-frame and port boundary against the pinned parent. Its
+receipt authenticates the supplied word by its content SHA256, independent
+of its location. `price_profile.py` defaults to the package's `data/PLAN.json`;
+`--profile` accepts another explicit profile for arithmetic only. The bit side is the cited merged PR589 supplier
+(`inputs/PR589-EXPECTED.json`, git blob `e293ddc5…`); its rank-mass deficit
+`T(2Kv - L*cst) = 32*(8*111 - 9*63) = 10272` is re-derived independently of
+`code/assemble.py`, and the outer receipt key is `outer_with_bit`. The retained
+`GAUGE44-INDEPENDENT-PRICE.json` is #645/PR543 historical evidence unless regenerated. The optional
+`--headroom-c 0.001733052823330162099157` reproduces the unchanged-kappa
+comparison with the reviewed PR555 rate without importing a second supplier.
+
+The retained receipts are `GAUGE-COLD44-INDEPENDENT-AUDIT.json`,
+`GAUGE44-INDEPENDENT-PRICE.json`, and `GAUGE44-GLOBAL-GUARD-REVIEW.json`.
+[CENTRE-GUARD-REVIEW.md](CENTRE-GUARD-REVIEW.md) gives the semantic argument
+behind the changed centre boundary and the single-provider control branch.
+The main package driver performs the separate complete global admission.
diff --git a/research/gauge44-leaver/independent/audit_local.py b/research/gauge44-leaver/independent/audit_local.py
new file mode 100644
index 0000000000..4744d8783c
--- /dev/null
+++ b/research/gauge44-leaver/independent/audit_local.py
@@ -0,0 +1,171 @@
+"""Independent exact scalar/frame audit of the changed forward supplier.
+
+This does not import a generator, builder, stored compensation, or price.
+All claimed endpoint matrices are derived from the input word's gates.
+Optional --main checks the transported boundary against the pinned parent.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse,gzip,json,hashlib,time
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+
+def require(x,label):
+    if not x:raise RuntimeError(label)
+
+def basis(vs):
+    piv={}
+    for a in vs:
+        while a:
+            bit=a.bit_length()-1
+            if bit in piv:a^=piv[bit]
+            else:
+                piv[bit]=a;break
+    for k in sorted(piv):
+        for j in piv:
+            if j>k and piv[j]>>k&1:piv[j]^=piv[k]
+    return tuple(piv[k] for k in sorted(piv,reverse=True))
+
+def contained(a,b):return basis(a+b)==b
+
+def registers(e):return e[1:3] if e[0]=='add' else e[1:2]
+
+def apply(e,rows,dual=False):
+    if e[0]=='add':
+        t,s=e[1:3];q=F(e[3],e[4]);require(t!=s,'self add')
+        if dual:t,s,q=s,t,-q
+        dst=rows[t]
+        for k,x in list(rows[s].items()):
+            a=dst.get(k,F(0))+q*x
+            if a:dst[k]=a
+            else:dst.pop(k,None)
+    elif e[0]=='scale':
+        t=e[1];q=F(e[2],e[3]);require(q!=0,'zero scale')
+        if dual:q=1/q
+        rows[t]={k:q*x for k,x in rows[t].items()}
+    else:raise RuntimeError('unknown scalar primitive')
+
+def invert(e):
+    r=list(e)
+    if r[0]=='add':r[3]=-r[3]
+    else:r[2],r[3]=r[3],r[2]
+    return r
+
+def check_parent_interface(word,main):
+    # Read only the retained boundary data. No builder or local checker is imported.
+    relative="research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz"
+    path=main/relative;raw=path.read_bytes()
+    require(hashlib.sha256(raw).hexdigest()=="66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",'parent canonical input pin')
+    parent=json.loads(gzip.decompress(raw))
+    tau=lambda x:x^(43 if (x&43).bit_count()%2 else 0)
+    ports=parent['ports'];v=word['report']['v']
+    require(len(ports)==len(set(ports))==v,'parent port count')
+    require(set(map(tau,word['ports']))==set(ports),'transported source/target ports')
+    moved={i:ports.index(tau(p)) for i,p in enumerate(word['ports'])}
+    centers=[moved.get(r,r) for r in word['centers']]
+    actual=[list(basis([tau(x) for x in frame])) for frame in word['center_frames']]
+    expected=[parent['frames'][f] for f in parent['center_frames']]
+    require(len(centers)==len(set(centers))==len(actual)==8,'eight distinct centre carriers')
+    require(actual==expected and all(len(f)==8 for f in actual),'ordered centre frame interface')
+    return dict(parent_path=relative,parent_file_sha256=hashlib.sha256(raw).hexdigest(),
+                transport_tau=43,ordered_frame_bases_match=True,all_ports_match=True,
+                transported_centers=centers,source_centers=[r for r in centers if r<v],
+                ordered_frame_bases=actual)
+
+
+def run(path,out,main=None):
+    begin=time.monotonic();data=gzip.decompress(path.read_bytes());w=json.loads(data)
+    v,h,R=w['report']['v'],w['report']['h'],w['report']['R'];n=2*v+R
+    require((v,h)==(112,9),'wrong source geometry')
+    center_interface=check_parent_interface(w,main) if main is not None else None
+    ident=lambda:[{k:F(1)} for k in range(n)]
+    main=w['A']+w['cut']+w['B']
+    for e in main+w['precondition']+w['cleanup']:
+        require(all(0<=k<n for k in registers(e)),'register out of range')
+        q=F(e[3],e[4]) if e[0]=='add' else F(e[2],e[3])
+        require(q.denominator&(q.denominator-1)==0,'non-dyadic scalar')
+        if e[0]=='scale':require(abs(q.numerator)&(abs(q.numerator)-1)==0,'non-unit scale')
+    require(all(not(v<=e[2]<2*v) for e in w['A']+w['B'] if e[0]=='add' and not(v<=e[1]<2*v)), 'non-target reads target')
+    raw=ident()
+    for e in main:apply(e,raw)
+    dirt=[{} for _ in range(n)]
+    for y in range(v,2*v):dirt[y]={k:a for k,a in raw[y].items() if k>=2*v}
+    for e in w['precondition']:apply(e,dirt)
+    compensation=[['add',y,k,-a.numerator,a.denominator,[]] for y in range(v,2*v) for k,a in sorted(dirt[y].items())]
+    entering=set(map(int,w.get('start_extra',{})));lowends=set(map(int,w.get('helper_final',{})))
+    coldends=lowends-entering
+    require(not any(e[2] in entering for e in compensation),'nonzero entrance response')
+    require(not any(r in entering|coldends for e in w['precondition']+compensation for r in registers(e)), 'pre-wrapper touch of residual helper')
+    require(all(e[-1]==[] for e in w['precondition']+compensation),'nonzero frame precondition')
+    early=w.get('early_cleanup',[]);earlyids={i for i,U in early}
+    require(len(earlyids)==len(early),'duplicate early cleanup gate')
+    tail=[w['cleanup'][i][:-1]+[U] for i,U in early]
+    cleanup=[e for i,e in enumerate(w['cleanup']) if i not in earlyids]
+    prefix=w['precondition']+compensation+main
+    program=prefix+tail+cleanup
+    for dual in (False,True):
+        actual=ident()
+        for e in program:apply(e,actual,dual)
+        expected=ident()
+        for t in range(v):expected[t if dual else v+t][v+t if dual else t]=F(-1 if dual else 1)
+        bad=[i for i in range(n) if actual[i]!=expected[i]]
+        require(not bad,'all-column endpoint failure '+str((dual,bad[:8])))
+        print('endpoint', 'dual' if dual else 'forward','PASS',flush=True)
+    full=basis([1<<i for i in range(h)])
+    end=[full]*v+[basis([x for x in range(1,1<<h) if (x&p).bit_count()%2==0]) for p in w['ports']]+[full]*R
+    for q,U in w.get('helper_final',{}).items():end[int(q)]=basis(U)
+    start=[(p,) for p in w['ports']]+[()]*(v+R)
+    for q,U in w.get('start_extra',{}).items():
+        require(2*v<=int(q)<n,'non-helper entrance');start[int(q)]=basis(U)
+    cur=start.copy();paid=Counter()
+    def climb(q,U):
+        U=basis(U);require(contained(cur[q],U),'frame not monotone '+str((q,cur[q],U)))
+        d=len(U)-len(cur[q])
+        if d:paid[d]+=1
+        cur[q]=U
+    for section in ('A','B'):
+        if section=='B':
+            lev={int(t):basis(U) for t,U in w.get('target_levels',{}).items()}
+            require(all(cur[v+t]==lev.get(t,()) for t in range(v)),'target centre levels')
+            for q,U in zip(w['centers'],w['center_frames']):
+                U=basis(U);require(cur[q]==U,'center frame')
+                served={lev.get(e[1]-v,()) for e in w['cut'] if e[2]==q}
+                for T in sorted(served,key=lambda x:-len(x)):
+                    require(contained(T,U),'center path not nested')
+                    if T!=U:paid[len(U)-len(T)]+=1
+                    U=T
+        for e in w[section]:
+            for q in registers(e):climb(q,e[-1])
+    endB=cur.copy()
+    for e in tail:
+        for q in registers(e):climb(q,e[-1])
+    for q,U in enumerate(end):climb(q,U)
+    require(all(all(end[q]==full for q in registers(e)) for e in cleanup),'full cleanup reads a low end')
+    require(dict(paid)=={int(k):a for k,a in w['report']['local_profile'].items()},'paid profile mismatch')
+    inventory=Counter(len(end[q])-len(start[q]) for q in range(2*v,n))
+    require(dict(inventory)=={int(k):a for k,a in w['report']['width_inventory'].items()},'width inventory mismatch')
+    p=ident();pinv=ident()
+    for e in prefix:apply(e,p)
+    for e in reversed(prefix):apply(invert(e),pinv)
+    for q in lowends:
+        U=end[q]
+        require(all(contained(endB[k],U) for k in pinv[q]),'inverse-row cone '+str(q))
+        require(all(k==q or not p[k].get(q) or contained(endB[k],U) for k in range(n)),'dirt-column cone '+str(q))
+    report=dict(status='PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES',
+                input_file=path.name,content_sha256=hashlib.sha256(data).hexdigest(),
+                compressed_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),
+                parent_center_interface=center_interface,v=v,h=h,R=R,
+                entering=len(entering),lowends=len(lowends),coldends=len(coldends),
+                compensation_gates=len(compensation),local_profile=dict(sorted(paid.items())),
+                width_inventory=dict(sorted(inventory.items())),checked_columns=n,
+                elapsed_seconds=time.monotonic()-begin,
+                scope='Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing.')
+    out.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2),flush=True)
+
+if __name__=='__main__':
+    parser=argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--word',type=Path,required=True,help='FULL-WORD.json.gz to check')
+    parser.add_argument('--output',type=Path,required=True,help='JSON receipt output path')
+    parser.add_argument('--main',type=Path,help='Optional pinned main checkout: also verify the transported centre/port interface')
+    args=parser.parse_args()
+    run(args.word,args.output,args.main)
diff --git a/research/gauge44-leaver/independent/price_profile.py b/research/gauge44-leaver/independent/price_profile.py
new file mode 100644
index 0000000000..0e36ebd468
--- /dev/null
+++ b/research/gauge44-leaver/independent/price_profile.py
@@ -0,0 +1,161 @@
+"""Independent arithmetic for the frozen gauge44 profile.
+
+The two rational moment engines and outer.assembly are imported unchanged from
+the pinned main dependencies; no constructor, owner emitter or invoice is run.
+The outer driver is the seven-step formula retained in PR635.
+The bit side is the cited merged PR589 supplier (package inputs/PR589-EXPECTED.json,
+pinned by git blob), with its rank-mass deficit T(2Kv - L*cst) re-derived here
+independently of code/assemble.py.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse
+from decimal import Decimal, localcontext
+from fractions import Fraction as Q
+import hashlib
+import importlib.util
+import json
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+SOURCE = Path('research/complex-k492-owner-repair/vendor/multicold')
+BIT_PATH = HERE.parent/'inputs/PR589-EXPECTED.json'
+BIT_BLOB = 'e293ddc557742637f9f679f083a1a282d87b1b13'
+
+
+def pr589_deficit(word, live):
+    # Nine stages, 32 replicas, four pairs: deficit = 32*(2*4*v - 9*cst), cst = sum of the nine COPY ranks.
+    v, cst, ranks = word['v'], word['decoder_constant'], word['copy_ranks']
+    require(len(ranks) == word['retained_totals'] == 9 and cst == sum(ranks), 'bit decoder constant')
+    require(live == 2*4*v*32, 'bit live wires')
+    return 32*(2*4*v-9*cst)
+
+
+def require(condition, message):
+    if not condition:
+        raise RuntimeError(message)
+
+
+def decimal(q):
+    with localcontext() as ctx:
+        ctx.prec = 75
+        return str(Decimal(q.numerator) / Decimal(q.denominator))
+
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def load(path, name):
+    spec = importlib.util.spec_from_file_location('independent_' + name, path / (name + '.py'))
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def moment_checks(M, B, H, m, W, lower, deficit, bad):
+    require(m*W-sum(r*n for r, n in H.items()) == deficit, 'rank deficit')
+    require(m*m > 2*max(H)**2, 'halving guard')
+    rows = []
+    for z, accept in [(lower, True), (lower+Q(1, 10**24), False)]:
+        l, u = M.moment(H, m, W, z, bad)
+        ll, uu = B.moment(m, W, list(H.items()), z)
+        if bad:
+            fl, fu = B.moment(m, W, [(1, 32*m*m*sum(H.values()))], z)
+            ll, uu = ll+fl/10**16, uu+fu/10**16
+        require((u < 1 and uu < 1) if accept else (l > 1 and ll > 1), 'two exact moment signs')
+        rows.append(dict(endpoint=str(z), accept=accept,
+                         mercator_residual=[str(l-1), str(u-1)],
+                         base_two_residual=[str(ll-1), str(uu-1)]))
+    return rows
+
+
+def outer47(c, b, engine):
+    eta = beta = Q(1, 10**24)
+    s = min(c, (1-beta)*b)-Q(1, 10**27)
+    require(0 < s < c and s < (1-beta)*b, 'strict common saving')
+    a = Q(384599, 10**10)
+    for _ in range(7):
+        old = a
+        a = (1-s)*s+s*old
+        gap = min(s-a, 1-a-s, 1-a-s*(1-old), 1-s)
+        require(old < a < s < 1-a and gap > 0, 'bootstrap gap')
+        ceil = lambda x: -(-x.numerator//x.denominator)
+        cut = max(ceil(36/gap**2), ceil(2*(4+512)/gap))
+        require(cut*gap**2 >= 36 and cut*gap >= 2*(4+512), 'finite bootstrap cutoff')
+    q = a*(1-2*eta)
+    margin = (1-eta)*q/(1+q)
+    ticks = margin*10**18
+    k = Q((ticks.numerator-1)//ticks.denominator, 10**18)
+    bridge = {'semantic': {'C0': {'base': 2, 'exponent': 210000}, 'strict_literal_gap': 1},
+              'rows': {'degree_gap': Q(10**6)-Q(51*20161, 25)}}
+    result = engine.assembly(a, b, bridge, k, eta=eta, beta=beta)
+    require(len(result['strict_constraints']) == 47, '47 outer constraints')
+    require(all(x > 0 for x in result['strict_constraints'].values()), 'strict outer constraints')
+    rejected = []
+    for name, kk, ee, be in [('next_grid', k+Q(1, 10**18), eta, beta),
+                             ('zero_eta', k, Q(0), beta), ('zero_beta', k, eta, Q(0)),
+                             ('unit_beta', k, eta, Q(1))]:
+        try:
+            engine.assembly(a, b, bridge, kk, eta=ee, beta=be)
+        except AssertionError:
+            rejected.append(name)
+        else:
+            raise RuntimeError('accepted negative control: '+name)
+    return dict(complex_b=str(b), bit_c=str(c), kappa=str(k), kappa_decimal=decimal(k),
+                binding='bit' if c < (1-beta)*b else 'complex',
+                strict_constraints_passed=47, controls_rejected=rejected)
+
+
+def main():
+    require(__debug__, 'Do not use python -O: the retained outer engine requires assertions')
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--main', type=Path, required=True, help='Pinned main checkout')
+    parser.add_argument('--profile', type=Path, default=HERE.parent/'data/PLAN.json',
+                        help='Raw profile or a JSON object containing profile/global_profile')
+    parser.add_argument('--output', type=Path, required=True)
+    parser.add_argument('--headroom-c', help='Optional alternative bit saving, for comparison only')
+    args = parser.parse_args()
+    inputs = json.loads((HERE.parent/'data/UPSTREAM-PINS.json').read_text())
+    selected = [SOURCE/'engines'/(n+'.py') for n in ('moment', 'base_two_moment', 'outer')]
+    for relative in selected:
+        require(sha(args.main/relative) == inputs[relative.as_posix()], 'pinned input '+str(relative))
+    M, B, A = [load(args.main/SOURCE/'engines', n) for n in ('moment', 'base_two_moment', 'outer')]
+    supplied = json.loads(args.profile.read_text())
+    H = {int(r): n for r, n in supplied.get('profile', supplied.get('global_profile', supplied)).items()}
+    bit_data = BIT_PATH.read_bytes()
+    require(hashlib.sha1(b'blob '+str(len(bit_data)).encode()+b'\0'+bit_data).hexdigest() == BIT_BLOB, 'PR589 blob pin')
+    record = json.loads(bit_data)
+    bit = record['nine']
+    require('nine-stage' in bit['pipeline'] and '32 replicas' in bit['pipeline'], 'nine-stage bit record')
+    bit_deficit = pr589_deficit(record['word'], bit['bit']['live'])
+    require(sum(int(r)*n for r, n in bit['profile'].items()) == bit['bit']['rank_mass'], 'bit rank mass')
+    c = Q(bit['bit_lower'])
+    bit_checks = moment_checks(M, B, {int(r): n for r, n in bit['profile'].items()},
+                               64, bit['bit']['live'], c, bit_deficit, True)
+    prices = {}
+    for mode, bad in [('native', False), ('conservative', True)]:
+        root = M.certify(H, 73, 7168, bad)
+        root = {key: root[key] for key in ('lower', 'upper', 'lower_endpoint_residual_upper',
+                                          'upper_endpoint_residual_lower', 'strict_rational_signs')}
+        b = Q(root['lower'])
+        row = dict(root=root, exact_moments=moment_checks(M, B, H, 73, 7168, b, 2560, bad),
+                   outer_with_bit=outer47(c, b, A))
+        if args.headroom_c:
+            alternate = outer47(Q(args.headroom_c), b, A)
+            require(alternate['kappa'] == row['outer_with_bit']['kappa'], 'headroom comparison changed kappa')
+            row.update(outer_with_alternative_bit_rate=alternate, same_kappa_with_either_bit_rate=True)
+        prices[mode] = row
+    native_k = Q(prices['native']['outer_with_bit']['kappa'])
+    result = dict(status='PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK',
+                  profile_input_file=args.profile.name, profile_input_sha256=sha(args.profile),
+                  global_profile=H, live=7168, m=73, rank_mass=sum(r*n for r, n in H.items()), deficit=2560,
+                  prices=prices, bit_supplier_pr=589, bit_deficit=bit_deficit, bit_moments_with_surcharge=bit_checks,
+                  gain_over_pr635_percent=decimal(100*(native_k/Q('0.001636241501576388')-1)),
+                  input_sha256={**{relative.as_posix(): sha(args.main/relative) for relative in selected}, 'package:inputs/PR589-EXPECTED.json': sha(BIT_PATH)},
+                  scope='Independent arithmetic for the exact nominated all72 profile. Complete local, controller and finite invoice admission are separately replayed by the package driver; this receipt does not replace them. The cited PR589 bit supplier is unchanged and its exceptional-residue surcharge is retained. Any alternative c is only a headroom comparison.')
+    args.output.write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], prices['native']['outer_with_bit']['kappa_decimal'], result['gain_over_pr635_percent'])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/independent/review_guards.py b/research/gauge44-leaver/independent/review_guards.py
new file mode 100644
index 0000000000..086dcf3d11
--- /dev/null
+++ b/research/gauge44-leaver/independent/review_guards.py
@@ -0,0 +1,46 @@
+"""Reproduce the assertion-preservation part of the independent guard review.
+
+This compares complete assertion ASTs in their traversal order. It supplements
+the semantic centre-interface argument in CENTRE-GUARD-REVIEW.md.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse
+import ast
+import hashlib
+import json
+from pathlib import Path
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--pr635', type=Path, required=True, help='Pinned PR635 checkout or supplier directory')
+    parser.add_argument('--delta', type=Path, default=Path(__file__).resolve().parents[1])
+    parser.add_argument('--output', type=Path, required=True)
+    args = parser.parse_args()
+    old = args.pr635
+    if not (old/'code/assemble.py').exists():
+        old = old/'research/complex-571-cold14-st2'
+    names = ['assemble.py', 'invoice_allcold.py', 'bind_providers_portable.py',
+             'generated_identity.py', 'witness.py']
+    records = []
+    for name in names:
+        a, b = (old/'code'/name).read_bytes(), (args.delta/'code'/name).read_bytes()
+        assertions = lambda data: [ast.dump(n, include_attributes=False) for n in ast.walk(ast.parse(data))
+                                   if isinstance(n, ast.Assert)]
+        aa, bb = assertions(a), assertions(b)
+        if aa != bb:
+            raise RuntimeError('Assertion sequence changed: '+name)
+        records.append(dict(file='code/'+name, baseline_sha256=hashlib.sha256(a).hexdigest(),
+                            new_sha256=hashlib.sha256(b).hexdigest(), byte_identical=a == b,
+                            assert_count=len(aa), all_assertions_identical_in_order=True))
+    if records[0]['assert_count'] != 91:
+        raise RuntimeError('The expected PR635 assembly has 91 assertions')
+    result = dict(status='PASS_PR635_ADMISSION_ASSERTION_PRESERVATION', files=records,
+                  centre_interface_review='CENTRE-GUARD-REVIEW.md',
+                  scope='Exact syntax preservation for all admission assertions in these five files. The changed emitter/controller centre boundary and single-provider controls require the separate semantic review; assertion counts alone do not prove them.')
+    args.output.write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], [r['assert_count'] for r in records])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver/inputs/PR589-EXPECTED.json b/research/gauge44-leaver/inputs/PR589-EXPECTED.json
new file mode 100644
index 0000000000..e293ddc557
--- /dev/null
+++ b/research/gauge44-leaver/inputs/PR589-EXPECTED.json
@@ -0,0 +1,222 @@
+{
+ "word": {
+  "file": "tune/bitE8mut-p111-tuned.json.gz",
+  "file_sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f",
+  "content_sha256": "5642fd0e35a1acc11acff8d0c08350c1617e95f310d4d35ad63a651f9eeeba0b",
+  "v": 111,
+  "R": 439,
+  "punctured": [
+   10,
+   15,
+   51,
+   53,
+   56,
+   66,
+   72,
+   89,
+   111
+  ],
+  "retained_totals": 9,
+  "copy_ranks": [
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7
+  ],
+  "decoder_constant": 63,
+  "gates": {
+   "D": 111,
+   "A": 2075,
+   "B": 712,
+   "C": 2574
+  },
+  "local_histogram": {
+   "1": 1323,
+   "2": 1342,
+   "3": 79,
+   "4": 44,
+   "5": 102,
+   "6": 11,
+   "7": 19
+  },
+  "legality": {
+   "records": 27234,
+   "common_frame_ADDs": 24305,
+   "rank_mass": 5129
+  },
+  "five_stage_columns": 883,
+  "five_stage_payload_bits": 93,
+  "nine_stage_columns": 1327,
+  "nine_stage_payload_bits": 93,
+  "eleven_stage_columns": 1549,
+  "eleven_stage_payload_bits": 93,
+  "base_content_sha256": "d0df3c89ae84989f4045ba1681a5e2e9fcdfa38ed0301c8abf5185537155cbe3"
+ },
+ "interface": {
+  "hypotheses": {
+   "H1_no_target_feeds_z": true,
+   "H2_D_frame0_targets_from_helpers": true,
+   "H3_A_z_only_scatter_targets_B_split": true,
+   "H4_C_literal_reverse_at_full": true,
+   "H5_V_identity": true
+  },
+  "conclusion": {
+   "U_block_form": true,
+   "J_identity": true,
+   "K_equals_D": true,
+   "C_is_U_inverse": true
+  },
+  "interleaving": {
+   "z_gates_A": 2075,
+   "source_writes_A": 0,
+   "z_gates_B": 499,
+   "source_writes_B": 483,
+   "helper_writes_B": 16,
+   "sources_rewritten_B": 108,
+   "B_z_write_frame_dims": {
+    "4": 388,
+    "6": 111
+   },
+   "B_z_operand_kinds": {
+    "helper<-helper": 3,
+    "helper<-source": 13,
+    "source<-helper": 108,
+    "source<-source": 375
+   },
+   "B_z_operand_kinds_by_dim": {
+    "dim4:helper<-source": 13,
+    "dim4:source<-source": 375,
+    "dim6:helper<-helper": 3,
+    "dim6:source<-helper": 108
+   },
+   "B_z_writes_after_a_target_read_of_the_same_register": 454,
+   "B_target_reads_of_registers_rewritten_earlier_in_B": 111,
+   "target_reads_of_targets": 0,
+   "cleanup_gates": 2574
+  }
+ },
+ "nine": {
+  "pipeline": "PR #510 (PR #463 nine-stage template, 32 replicas, PR #442 hosting, PR #493 outer assembly), parameterised for v <= 120 by code/adapt9p.py",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_lower_decimal": "0.001733427039589844234749",
+  "profile": {
+   "1": 381024,
+   "2": 400416,
+   "3": 22752,
+   "4": 26880,
+   "5": 29376,
+   "6": 17376,
+   "7": 26784,
+   "42": 288
+  },
+  "bit": {
+   "live": 28416,
+   "physical": 28425,
+   "maxchild": 42,
+   "rank_mass": 1808352,
+   "hosted_residuals": 126432,
+   "bank_assignments": 0,
+   "prefix_bits": 177,
+   "charged_prefix_bits": 192,
+   "coefficient_bits": 177,
+   "two_level_coefficient_bits": 393,
+   "charged_two_level_coefficient_bits": 512,
+   "row_coefficient": 18355,
+   "halving_depth": 2
+  },
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "eleven": {
+  "pipeline": "PR #493 (PR #445 geometry, PR #472 emitter, audit and invoice, PR #442 hosting), parameterised by PR #545's code/adapt.py",
+  "bit_lower": "855475950388791987811/500000000000000000000000",
+  "bit_lower_decimal": "0.001710951900777583975622",
+  "profile": {
+   "1": 116424,
+   "2": 121648,
+   "3": 6952,
+   "4": 7424,
+   "5": 8976,
+   "6": 4520,
+   "7": 8776,
+   "56": 2600
+  },
+  "bit": {
+   "live": 8880,
+   "physical": 8889,
+   "maxchild": 56,
+   "rank_mass": 689304,
+   "hosted_residuals": 38632,
+   "prefix_bits": 4304,
+   "charged_prefix_bits": 4352,
+   "coefficient_bits": 4304,
+   "three_level_coefficient_bits": 12966,
+   "charged_three_level_coefficient_bits": 12992,
+   "row_coefficient": 19431,
+   "halving_depth": 3
+  },
+  "emitted_program_sha256": "793b6f40c9aa4b8db57fec0ac0973e16884dae28707e482ee8f7a2349a5d5a4b",
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "base": {
+  "nine_bit_lower": "1733052823330162099157/1000000000000000000000000",
+  "nine_bit_lower_decimal": "0.001733052823330162099157",
+  "eleven_bit_lower": "427652201524503168379/250000000000000000000000",
+  "eleven_bit_lower_decimal": "0.001710608806098012673516",
+  "note": "PR #555's EXPECTED.json (untuned word); the tune/ pipeline is the same, with the same frozen hosting selections"
+ }
+}
diff --git a/research/gauge44-leaver/verify_global.py b/research/gauge44-leaver/verify_global.py
new file mode 100644
index 0000000000..7ab79e3062
--- /dev/null
+++ b/research/gauge44-leaver/verify_global.py
@@ -0,0 +1,112 @@
+"""Replay the changed global admission against pinned upstream dependencies.
+
+The local directory must contain the fresh canonical/native/phase/wrapper
+artifacts produced by construction/reproduce.py. Frozen evidence may be used
+for a short admission-only replay. No optimizer runs during this verifier.
+"""
+import argparse
+import hashlib
+import json
+import os
+from pathlib import Path
+import subprocess
+import sys
+import time
+
+assert __debug__, 'Assertions required'
+PACKAGE = Path(__file__).resolve().parent
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def dump(path, value):
+    Path(path).write_text(json.dumps(value, indent=2) + '\n')
+
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--main', type=Path, required=True, help='Pinned CrocSwap main checkout')
+ap.add_argument('--local', type=Path, required=True, help='Rebuilt or frozen native gauge44 directory')
+ap.add_argument('--work', type=Path, required=True, help='New output directory')
+ap.add_argument('--discover', action='store_true', help=argparse.SUPPRESS)
+args = ap.parse_args()
+main, local, work = args.main.resolve(), args.local.resolve(), args.work.resolve()
+assert not work.exists(), 'Output directory must be new'
+source = main/'research/complex-k492-owner-repair/vendor/multicold'
+baseline = main/'research/community-k492-audit/pr622/replay/baseline558'
+vendor = source/'vendor/pr558/vendor/pr552/complex-global/vendor531'
+pins = PACKAGE/'data/UPSTREAM-PINS.json'
+if pins.exists():
+    for rel, expected in json.loads(pins.read_text()).items():
+        assert sha(main/rel) == expected, 'Upstream dependency changed: ' + rel
+else:
+    assert args.discover, 'Missing upstream pins'
+    paths = list((baseline/'complex-global/base').rglob('*'))
+    paths += [source/'code/run_portable.py', source/'inputs/PR543-EXPECTED.json',
+              vendor/'evidence/audit/PREFIX-AND-INVOICE.json']
+    paths += [source/'vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz',
+              baseline/'complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz',
+              vendor/'code/prepare_supplier_base.py']
+    paths += [source/'engines'/name for name in ('moment.py', 'base_two_moment.py', 'outer.py')]
+    dump(pins, {p.relative_to(main).as_posix(): sha(p) for p in sorted(paths) if p.is_file()})
+work.mkdir(parents=True)
+env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1',
+           PYTHONINTMAXSTRDIGITS='0', MULTICOLD_SOURCE=str(source),
+           GAIN_PR564_SOURCE=str(source), WITNESS_SPEC=str(PACKAGE/'data/SPEC.json'))
+env.pop('PYTHONOPTIMIZE', None)
+env.pop('WITNESS_DISCOVER', None)
+env.pop('WITNESS_RECORD', None)
+if args.discover:
+    env.update(WITNESS_DISCOVER='1', WITNESS_RECORD=str(work/'WITNESS-RECORD.jsonl'))
+stages = []
+
+
+def run(name, script, *arguments):
+    started = time.monotonic()
+    log = work/(name + '.log')
+    with log.open('w') as stream:
+        result = subprocess.run([sys.executable, '-B', str(source/'code/run_portable.py'),
+                                 str(script), *map(str, arguments)], env=env,
+                                stdout=stream, stderr=subprocess.STDOUT)
+    stages.append(dict(name=name, seconds=round(time.monotonic()-started, 3),
+                       exit_code=result.returncode, log_sha256=sha(log)))
+    dump(work/'STAGES.json', stages)
+    if result.returncode:
+        raise RuntimeError(name + ' failed:\n' + log.read_text()[-7000:])
+    print('PASS', name, stages[-1]['seconds'], flush=True)
+
+
+code = PACKAGE/'code'
+global_dir = work/'global'
+run('restore-parent', code/'restore_parent.py', '--source', source,
+    '--baseline', baseline, '--out', work/'parent558')
+run('bind', code/'bind_providers_portable.py', '--baseline', work/'parent558',
+    '--provider', 'gauge44='+str(local), '--plan', PACKAGE/'data/PLAN.json', '--out', global_dir)
+run('emit', code/'emit_allcold.py', '--base', global_dir/'base',
+    '--owners', PACKAGE/'data/OWNERS.json.gz', '--plan', global_dir/'PLAN.json', '--out', global_dir/'hosted')
+run('audit', code/'audit_allcold.py', global_dir/'base', global_dir/'hosted',
+    global_dir/'audit/ASYNC-AUDIT.json', '--mutation-controls')
+run('invoice', code/'invoice_allcold.py', '--base', global_dir/'base',
+    '--hosted', global_dir/'hosted', '--audit', global_dir/'audit', '--out', global_dir/'audit',
+    '--retained-invoice', vendor/'evidence/audit/PREFIX-AND-INVOICE.json')
+run('assembly', code/'assemble.py', source, global_dir, work/'ASSEMBLY.json')
+if not args.discover:
+    run('admission-controls', code/'assembly_controls.py', '--source-package', source,
+        '--owner', global_dir/'audit/OWNERS-AND-PROFILE.json',
+        '--invoice', global_dir/'audit/PREFIX-AND-INVOICE.json', '--out', work/'ADMISSION-CONTROLS.json')
+    run('bit-supplier-controls', code/'bit_supplier_controls.py', '--source-package', source,
+        '--owner', global_dir/'audit/OWNERS-AND-PROFILE.json',
+        '--invoice', global_dir/'audit/PREFIX-AND-INVOICE.json', '--out', work/'BIT-SUPPLIER-CONTROLS.json')
+    bit_controls = json.loads((work/'BIT-SUPPLIER-CONTROLS.json').read_text())
+    assert bit_controls['status'] == 'PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS'
+    assert len(bit_controls['rejected_controls']) == 12 and bit_controls['derived_deficit'] == 10272
+result = json.loads((work/'ASSEMBLY.json').read_text())
+dump(work/'REPLAY.json', dict(status='PASS_GAUGE44_DISCOVERY' if args.discover else 'PASS_GAUGE44_STRICT_GLOBAL_REPLAY',
+                            kappa=result['kappa'], kappa_decimal=result['kappa_decimal'],
+                            complex_lower=result['complex_lower'], bit_lower=result['bit_lower'],
+                            bit_supplier=result['bit_supplier'],
+                            gain_over_pr635_percent=result['gain_over_pr635_percent'],
+                            spec_sha256=sha(PACKAGE/'data/SPEC.json'), stages=stages,
+                            scope=result['scope']))
+print(result['status'], result['kappa_decimal'], result['gain_over_pr635_percent'], flush=True)
diff --git a/research/gauge44-leaver/verify_manifest.py b/research/gauge44-leaver/verify_manifest.py
new file mode 100644
index 0000000000..8c2441d392
--- /dev/null
+++ b/research/gauge44-leaver/verify_manifest.py
@@ -0,0 +1,19 @@
+"""Verify the submitted package's exact file inventory and SHA256 bindings."""
+from hashlib import sha256
+import json
+from pathlib import Path
+
+root = Path(__file__).resolve().parent
+expected = json.loads((root / 'MANIFEST.json').read_text())
+actual = {
+    p.relative_to(root).as_posix(): sha256(p.read_bytes()).hexdigest()
+    for p in root.rglob('*')
+    if p.is_file() and '__pycache__' not in p.parts
+    and p != root / 'MANIFEST.json'
+}
+if actual != expected:
+    missing = sorted(expected.keys() - actual.keys())
+    extra = sorted(actual.keys() - expected.keys())
+    changed = sorted(k for k in expected.keys() & actual.keys() if expected[k] != actual[k])
+    raise SystemExit(f'Manifest mismatch: missing={missing}, extra={extra}, changed={changed}')
+print(f'PASS package manifest: {len(actual)} files')
diff --git a/research/gauge44-leaver8/CONSTRUCTION.md b/research/gauge44-leaver8/CONSTRUCTION.md
new file mode 100644
index 0000000000..fa15676366
--- /dev/null
+++ b/research/gauge44-leaver8/CONSTRUCTION.md
@@ -0,0 +1,210 @@
+# Gauge44: a changed factory forward map with 44 rank-four cold ends
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0. This note describes the new complex local construction. The package's global evidence supplies the resulting global bound and retains the upstream conditional assumptions.
+
+## 1. Exact result and comparison
+
+The final word has 112 source ports, 112 target ports and 492 helper registers. It implements the same arbitrary-dirt scalar endpoint as the upstream word,
+
+$$
+(X,Y,H)\longmapsto(X,Y+X,H),
+$$
+
+and its inverse-transpose orientation is checked separately. All 204 nonzero entrance frames remain valid. The new ending set consists of **44 cold helpers at rank-four frames**, together with the 34 entering-helper ends inherited from the JP8 HPE stage.
+
+The precise comparison is with the JP8 provider reconstructed from PR635, commit `a6895a69f8ad98ab45777b03e9e6f48888c39f6f`:
+
+| Local quantity | PR635 JP8 | Gauge44 |
+|---|---:|---:|
+| Helpers | 492 | 492 |
+| Nonzero entrance frames | 204 | 204 |
+| Rank-four cold ends | 22 | 44 |
+| Rank-seven cold ends | 2 | 0 |
+| Rank-eight cold ends | 4 | 0 |
+| Entering helpers ending below FULL | 36 | 34 |
+| Total residual helper width | 3894 | **3794** |
+| Local paid rank mass | 5750 | **5650** |
+
+Thus the new word saves **100 units of residual width per invocation** against the complete PR635 provider. It replaces that provider's cold-end construction; the old six higher-rank cold ends and two additional entering ends are not added to the new count.
+
+The exact paid-child profiles are:
+
+| Child rank | PR635 count | Gauge44 count |
+|---:|---:|---:|
+| 1 | 2518 | 2514 |
+| 2 | 402 | 404 |
+| 3 | 448 | 448 |
+| 4 | 164 | 160 |
+| 5 | 68 | 56 |
+| 6 | 4 | 0 |
+| 8 | 8 | 8 |
+
+The final residual-width inventory is `{4:52, 5:48, 7:34, 8:114, 9:244}`. Both the profile and the inventory are recomputed from the literal native frame chains. They are not inferred from the nominal number of ended helpers.
+
+## 2. What changes in the forward factory
+
+The inherited K-triangle schedule and its 492-helper allocation remain the starting construction. Within each of the fourteen eight-source packet factories, three changes alter the arbitrary-dirt forward map while retaining the required clean packet values.
+
+### A. Exchange a source with an equal clean copy
+
+After the sixteen initial copy gates, local source position `j` and its two helper copies have clean values `(x_j,x_j,x_j)`. For positions `j = 4,5,6,7`, exchange the original source register with its second helper copy. The exact register pair in the constructor is `mp[j]` and `mp[2*j+9]`.
+
+For arbitrary helper dirt the triple is instead
+
+$$
+(x_j,\;x_j+h_{j,1},\;x_j+h_{j,2}).
+$$
+
+The exchange changes where the second dirty direction enters the subsequent factory. It does not change any clean operand. Both exchanged registers already have the same rank-one frame, so the exchange adds no frame climb. Each exchange is emitted as three additions and one sign change; these scalar operations remain part of the finite implementation invoice.
+
+This is a change of the forward map, not an output relabeling. In particular, the inverse recovery functional for the original source changes from the original branch to a different combination of the three equal-clean branches. That changes which cold input directions can have their entire final support inside a low frame.
+
+### B. Change the complement to the four coordinate totals
+
+Eight retired factory rows already span the eight source coordinates. The first four rows of their replacement basis are the four required coordinate totals. The remaining four rows are chosen by exact row-rank extension, first using the ordered clean linear forms recorded in `construction/COMPLETION-PRIORITY.json`, then using coordinate rows if an extension is still needed.
+
+These candidate forms are the future low-frame leaver forms used during discovery. The frozen priority data are the complete input to the final constructor: no discovery search is run in reproduction. Every accepted row must increase the rational rank; the resulting eight-by-eight basis is explicitly applied by elementary operations.
+
+All eight retired registers are already at the block's rank-four frame. Consequently this basis replacement also adds no frame climb. It gives the low final rows more independent linear combinations that annihilate the original source data.
+
+### C. Place coordinate totals on the available source carriers
+
+The retired registers are ordered with source registers first. Three available source carriers and one helper carry the four coordinate totals, leaving the four complementary rows on physical helper registers. This lets the new cold directions end on helper wires under the unchanged native endpoint interface.
+
+A carrier permutation alone does not increase the available cold space. Its role here is to realize the independent directions created jointly by the source-copy exchange and the new complementary basis.
+
+## 3. Exact cold-space calculation
+
+Let `P` be the non-target forward matrix after parts A and B and the 34 inherited HPE tail gates. It has 604 rows and columns: 112 original sources and 492 helpers. Let `J` be the 316 protected initial columns consisting of the 112 original sources and all 204 entering helpers.
+
+For a block frame `F`, let `I` be every non-target output register whose current frame is contained in `F`. Source output rows are included in this set. Define
+
+$$
+L=\operatorname{leftker} P[I,J],\qquad
+K=\ker P^{-1}[J,I].
+$$
+
+Rows of `L` are low output linear forms with no protected initial dependence. Columns of `K` are low-supported output directions whose inverse images have no protected component. The rank of the pairing `LK` counts the simultaneously usable cold directions in this fixed forward word.
+
+The changed forward map has the following exact block data:
+
+| Block indices | Number of blocks | Low registers `|I|` | `dim L` | `dim K` | `rank(LK)` |
+|---|---:|---:|---:|---:|---:|
+| 0, 1, 2, 11, 12, 13 | 6 | 6 | 2 | 4 | **2** |
+| 3 through 10 | 8 | 8 | 4 | 4 | **4** |
+
+The count is therefore `6*2 + 8*4 = 44`. The fixed upstream rank-four cold construction supplied one and two directions respectively, for `6*1 + 8*2 = 22`.
+
+The complement change by itself improves the available low annihilating rows but leaves the inverse-support obstruction. The source-copy exchanges remove that obstruction: `K` has dimension four in every block and pairs with all the available rows of `L`.
+
+## 4. Realizing the directions with legal dyadic operations
+
+`construction/build_gauge_cold44.py` recomputes these spaces over exact rational numbers. It selects columns of `K` and normalizes them to a matrix `U` satisfying
+
+$$
+LU=I_r,
+\qquad q=P^{-1}[:,I]U.
+$$
+
+The constructor checks that `q` is supported entirely on that block's sixteen initially cold factory helpers, denoted `H_b`. Put
+
+$$
+R_b=LP[I,H_b].
+$$
+
+Then `R_b q[H_b,:] = I_r`. A sixteen-by-sixteen input basis `Q_b` places the columns `q[H_b,:]` at the designated ended-helper positions and fills the other columns with a basis of `ker R_b`. The resulting input basis is explicitly invertible.
+
+For the low-frame output transformation, the ended-helper rows are replaced by the rows of `L`; each remaining low row `i` becomes
+
+$$
+e_i-U_iL.
+$$
+
+The actual chosen helper positions give an invertible tail matrix. Its nonsingularity and dyadic implementation are checked by exact elimination, rather than assumed from a dimension count. The construction receipt records every `Q_b`, tail matrix and selected endpoint.
+
+Every `Q_b` is emitted at frame zero, at the head of A **after** the entry normalization wrappers. Every low tail is emitted at its block frame. The remaining cleanup is rebuilt as an exact dyadic Gauss-Jordan inverse on the non-ended registers at FULL. It is not obtained by blindly reversing a changed partial schedule.
+
+Before forming the FULL inverse, the constructor verifies both the row and the column identity of each of the 78 ended helpers. Thus no protected data or other helper dirt remains in an ended helper, and its initial dirt remains nowhere else. The FULL inverse skips these isolated rows and columns entirely.
+
+The realized word has:
+
+| Construction component | Scalar gates |
+|---|---:|
+| Frame-zero helper premix | 1489 |
+| New rank-four tail | 60 |
+| Inherited HPE tail | 34 |
+| Refactored FULL inverse | 28056 |
+| Additional target compensation after wrappers | **0** |
+
+All selected new cold directions have zero target response. The independent scalar auditor nevertheless recomputes the complete existing dirty-response compensation, obtaining 7348 additions, and checks both orientations on all 716 input columns.
+
+Relative to the HPE-stage word before any cold-end construction, the aggregate chain delta is `N_1 += 44, N_6 -= 44`, reducing rank mass and residual width by 220. PR635 had already saved 120 units through its complete cold/extra-HPE construction. The net new saving is therefore 100. There is no omitted cost for lifting the low tails: their rank-one increments are included explicitly.
+
+## 5. Native interface and validation
+
+The transport preserves the exact ordered list of 112 ports and the exact ordered eight center frames. The center carriers change because some totals now reside on sources. In native coordinates they are
+
+```
+[92, 57, 81, 224, 11, 240, 9, 256]
+```
+
+A global interface check must compare the ordered center frames and port geometry, and use the provider's actual center carriers. Equality of carrier numbers with an old provider is not a mathematical requirement. The local event ledgers explicitly clear all private center channels in both orientations.
+
+Completed checks for the frozen word include exact forward and inverse-transpose scalar replay on all 716 columns; every literal native frame chain; the 204 zero-response entrance conditions; the 44 cold and 34 entering endpoint cones; wrapper placement and normalized wrapper identities; both emitted local ledgers; and exact phase lowering for 3019 directed edges and 224 endpoint adapters. The independent audit does not import the new constructor.
+
+This local result does not by itself certify a global exponent. Physical whole-family owners, actual residual/spectator routing, idle remainders, global scalar assembly and the complete finite invoice are the separate global checks reported elsewhere in the package.
+
+## 6. Compact reproduction
+
+Only Python's standard library is needed for this construction and the retained local pipeline. Do not use `python -O`. The reproduction driver checks byte hashes of every named upstream input and the changed code, then checks the content hash after each construction step. Its two source checkouts are:
+
+| Argument | Repository commit |
+|---|---|
+| `--main` | `17ce0c79b7b51c2634b439ea5a2b754f09909693` |
+| `--pr635` | `a6895a69f8ad98ab45777b03e9e6f48888c39f6f` |
+
+Starting from a clone of `https://github.com/CrocSwap/integer-mult-bounds` containing those commits, prepare detached worktrees:
+
+```bash
+git -C integer-mult-bounds fetch origin main refs/pull/635/head
+git -C integer-mult-bounds worktree add --detach ../integer-main 17ce0c79b7b51c2634b439ea5a2b754f09909693
+git -C integer-mult-bounds worktree add --detach ../integer-pr635 a6895a69f8ad98ab45777b03e9e6f48888c39f6f
+```
+
+From the directory containing those worktrees and this delta package, run:
+
+```bash
+python -B research/gauge44-global/construction/reproduce.py \
+  --main integer-main \
+  --pr635 integer-pr635 \
+  --out gauge44-reproduction
+```
+
+The default stops after regenerating the exact final scalar word and comparing the newly derived cold recipe with the frozen recipe. It rebuilds only the two short shadow steps needed by the four port transfers. It does not rerun the ancestor admission stack, search for a basis, optimize owners, or replay global assembly.
+
+Use `--frozen-cold` to splice the included recipe instead of re-deriving its small exact linear systems. Use `--until local` to add native transport, emitted ledgers, independent local replay and wrappers. Use `--until phases` to add the complete phase lowering. Every invocation needs a fresh output directory; these are alternatives, not resumable increments. On the research machine, exact cold derivation took about 2.6 seconds, native transport/ledgers/replay/wrappers about 41 seconds, and complete phase lowering about 198 seconds.
+
+The exact dependency chain is:
+
+1. Construct the changed raw R492 factory from the pinned Hamming inputs, frozen priority and pinned K-triangle schedule.
+2. Apply the four inherited port stages.
+3. Apply the inherited B-frame regroup and 34-HPE construction.
+4. Derive the exact block premixes, cold44 tails and FULL inverse.
+5. Optionally emit and check the native ledgers, wrappers and complete phase lowering.
+
+`construction/INPUTS.json` gives the input hashes and every intermediate content hash. The key decompressed content identities are:
+
+| Word | SHA-256 |
+|---|---|
+| Changed raw factory | `0ac47f92fc2e3f5aa457d78f7b8a5c785bf140c546932b9dfcd9e610ad319180` |
+| Changed HPE forward | `42fb8b3aa314593fe976820cf65824f5fce0ee4f95281796992d4809709864cc` |
+| Final cold44 word | `78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290` |
+| Native canonical word | `e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f` |
+
+## 7. Attribution
+
+The original 504-helper factory and borrowed-register construction are icekylinx's PR531 lineage, prepared with OpenAI Codex/GPT assistance and retaining the earlier PR425/PR514 credits. The inherited K-triangle atom and frozen read schedule are credited in PR635 to AtomScout, a Claude Code research agent. The porting routine is credited there to Port480. This package does not claim those as new work.
+
+The reused JP8 ancestry includes the PR558/PR552 supplier, the earlier-cut and multicold kernels, and the joint prefix adapted from Dominik Scholz's PR571 work. Native HPE and cold-end transport, frame and wrapper machinery come from the credited PR635 lineage, including DreamingOfClouds, jeremykothe2, chafreaky and their disclosed assistants. The retained `construction/UPSTREAM-NOTICE.md` and `construction/LICENSE` preserve the upstream notice and Apache-2.0 license.
+
+The new contribution here is the combination of source-copy exchange, changed retired-row completion, source-carried coordinate totals, and the explicit exact cold44 realization. Those changes were developed for icekylinx with OpenAI GPT-6 Astra assistance. The upstream notices, proof scope and conditional assumptions continue to apply.
diff --git a/research/gauge44-leaver8/LICENSE b/research/gauge44-leaver8/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/gauge44-leaver8/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/gauge44-leaver8/LOCAL-VALIDATION.json b/research/gauge44-leaver8/LOCAL-VALIDATION.json
new file mode 100644
index 0000000000..5973645e1a
--- /dev/null
+++ b/research/gauge44-leaver8/LOCAL-VALIDATION.json
@@ -0,0 +1,356 @@
+{
+  "status": "PASS_LOCAL_INCREMENTAL_GAUGE44",
+  "python": "3.14.8",
+  "upstream_main": "17ce0c79b7b51c2634b439ea5a2b754f09909693",
+  "pr635": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f",
+  "construction_steps": [
+    {
+      "step": "shadow-early",
+      "exit_code": 0,
+      "seconds": 0.322
+    },
+    {
+      "step": "shadow-prefix",
+      "exit_code": 0,
+      "seconds": 0.429
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+    {
+      "step": "gauge-forward",
+      "exit_code": 0,
+      "seconds": 0.474
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+    {
+      "step": "port0",
+      "exit_code": 0,
+      "seconds": 0.388
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+    {
+      "step": "port1",
+      "exit_code": 0,
+      "seconds": 0.407
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+    {
+      "step": "port2",
+      "exit_code": 0,
+      "seconds": 0.403
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+    {
+      "step": "port3",
+      "exit_code": 0,
+      "seconds": 0.389
+    },
+    {
+      "step": "cold44-exact",
+      "exit_code": 0,
+      "seconds": 2.544
+    },
+    {
+      "step": "native",
+      "exit_code": 0,
+      "seconds": 3.63
+    },
+    {
+      "step": "ledgers",
+      "exit_code": 0,
+      "seconds": 2.759
+    },
+    {
+      "step": "local-replay",
+      "exit_code": 0,
+      "seconds": 15.924
+    },
+    {
+      "step": "wrappers",
+      "exit_code": 0,
+      "seconds": 2.706
+    },
+    {
+      "step": "phases",
+      "exit_code": 0,
+      "seconds": 186.772
+    }
+  ],
+  "five_mathematical_local_artifacts_match_frozen_evidence": true,
+  "phase_edges": 3019,
+  "endpoint_adapters": 224,
+  "independent_scalar_audit": {
+    "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+    "input_file": "FULL-WORD.json.gz",
+    "content_sha256": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290",
+    "compressed_sha256": "0ad202612f010df4ab66432a628247b37ad8b497dd6b27595b1685cbd7eb119e",
+    "parent_center_interface": {
+      "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+      "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+      "transport_tau": 43,
+      "ordered_frame_bases_match": true,
+      "all_ports_match": true,
+      "transported_centers": [
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+      "source_centers": [
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+        11,
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+          128,
+          64,
+          34,
+          16,
+          10,
+          4,
+          1
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+        [
+          256,
+          128,
+          64,
+          32,
+          16,
+          8,
+          5,
+          3
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+        [
+          256,
+          128,
+          64,
+          32,
+          17,
+          9,
+          4,
+          2
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+        [
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+          128,
+          64,
+          36,
+          20,
+          8,
+          2,
+          1
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+        [
+          256,
+          128,
+          66,
+          32,
+          18,
+          8,
+          4,
+          1
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+        [
+          256,
+          128,
+          65,
+          33,
+          17,
+          9,
+          5,
+          3
+        ],
+        [
+          256,
+          128,
+          65,
+          33,
+          16,
+          8,
+          4,
+          2
+        ],
+        [
+          256,
+          128,
+          68,
+          32,
+          16,
+          12,
+          2,
+          1
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+      ]
+    },
+    "v": 112,
+    "h": 9,
+    "R": 492,
+    "entering": 204,
+    "lowends": 78,
+    "coldends": 44,
+    "compensation_gates": 7348,
+    "local_profile": {
+      "1": 2514,
+      "2": 404,
+      "3": 448,
+      "4": 160,
+      "5": 56,
+      "8": 8
+    },
+    "width_inventory": {
+      "4": 52,
+      "5": 48,
+      "7": 34,
+      "8": 114,
+      "9": 244
+    },
+    "checked_columns": 716,
+    "elapsed_seconds": 2.443164045999765,
+    "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+  },
+  "independent_guard_review": {
+    "status": "PASS_PR635_ADMISSION_ASSERTION_PRESERVATION",
+    "files": [
+      {
+        "file": "code/assemble.py",
+        "baseline_sha256": "1b1a9024ac910dc9b9d9e30150684e1fa9cb228a4c1c275b75ab04b57fdef1dd",
+        "new_sha256": "7ac28118d69416e4fb67b61216285fb0823310b7635ce1b9025aa3f10119ef6a",
+        "byte_identical": false,
+        "assert_count": 91,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/invoice_allcold.py",
+        "baseline_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+        "new_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+        "byte_identical": true,
+        "assert_count": 67,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/bind_providers_portable.py",
+        "baseline_sha256": "2eb5c262bf481b3bec9ceaec654fa46ff6fc3a89b13d4906a29a55a89e35feea",
+        "new_sha256": "7c9aba6c7f138d270852d859d902f905a15598b6263567700b5b08a153823cb6",
+        "byte_identical": false,
+        "assert_count": 22,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/generated_identity.py",
+        "baseline_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+        "new_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+        "byte_identical": true,
+        "assert_count": 4,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/witness.py",
+        "baseline_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+        "new_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+        "byte_identical": true,
+        "assert_count": 3,
+        "all_assertions_identical_in_order": true
+      }
+    ],
+    "centre_interface_review": "CENTRE-GUARD-REVIEW.md",
+    "scope": "Exact syntax preservation for all admission assertions in these five files. The changed emitter/controller centre boundary and single-provider controls require the separate semantic review; assertion counts alone do not prove them."
+  },
+  "owner_replay": {
+    "status": "PASS_FROZEN_OWNER_AND_INTEGER_MAJORIZATION_REPLAY",
+    "seed_mode": "included_frozen_seed",
+    "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+    "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+    "owners_semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d",
+    "owners_gzip_sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+    "majorization_semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc",
+    "global_profile": {
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+      "4": 11520,
+      "5": 4032,
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+      "8": 582,
+      "12": 13,
+      "16": 33,
+      "19": 1,
+      "20": 2,
+      "28": 4,
+      "32": 62,
+      "36": 1,
+      "40": 1,
+      "44": 6,
+      "48": 2289
+    },
+    "scope": "Exact hosting nomination and callwise fixed-point replay; full supplier admission is separate."
+  },
+  "global_replay": {
+    "status": "PASS_GAUGE44_STRICT_GLOBAL_REPLAY",
+    "kappa": "1649483702558979/1000000000000000000",
+    "kappa_decimal": "0.001649483702558979",
+    "complex_lower": "1652208994368411824947/1000000000000000000000000",
+    "bit_lower": "413456747036699736067/250000000000000000000000",
+    "gain_over_pr635_percent": "0.8093060205252829126484020359439672024956960385078942889840023844750830",
+    "spec_sha256": "fee57674a7f36b30b1e7eb96a8f567a90a522217bc644c1a6a1f8bff85196fbf",
+    "stages": [
+      {
+        "name": "restore-parent",
+        "seconds": 2.089,
+        "exit_code": 0,
+        "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+      },
+      {
+        "name": "bind",
+        "seconds": 0.962,
+        "exit_code": 0,
+        "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+      },
+      {
+        "name": "emit",
+        "seconds": 4.817,
+        "exit_code": 0,
+        "log_sha256": "90ce07d06a8eaffdb66201e8346021183e5a803395fb9f6d8ceb0e5ff068ef2c"
+      },
+      {
+        "name": "audit",
+        "seconds": 19.625,
+        "exit_code": 0,
+        "log_sha256": "66b4abb2a88a4eaba8a8baa3585ef4aa819be5f8acb7947bae734b3478280456"
+      },
+      {
+        "name": "invoice",
+        "seconds": 1.804,
+        "exit_code": 0,
+        "log_sha256": "5d10712d494304287749dd7a6c3369f9b707bba30e9f567b68230669dcf5418a"
+      },
+      {
+        "name": "assembly",
+        "seconds": 0.808,
+        "exit_code": 0,
+        "log_sha256": "768d3215f1918117dc6c33b4cfeaf0b5f5da9ba5c77178db4bb1d08d000e226f"
+      },
+      {
+        "name": "admission-controls",
+        "seconds": 0.885,
+        "exit_code": 0,
+        "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+      }
+    ],
+    "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the same cited unchanged PR543 bit supplier as PR635. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+  },
+  "admission_mutations_rejected": 69,
+  "controller_mutations_rejected": 15,
+  "frozen_template_content_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "fresh_template_content_sha256": "a1692259fb5a06bbebdc1049a7f757c6d2fc79ff8c31ed0c25b38fe9f98ed051",
+  "template_comparison": {
+    "sole_changed_field": "async_schedule.source_plan_sha256",
+    "frozen_plan_sha256": "609adb126d7d3de2abdd9275f9015589c0b137d0d19821c2c3e7c1a8541c18d2",
+    "fresh_plan_sha256": "b2e4b1f063250c40e0087f77e896882c60f36ed8764e86ba1610dec9bdff7394",
+    "explanation": "Fresh phase review differs only in its measured seconds. Runtime provider binding consequently changes the plan byte hash. All remaining serialized template fields match exactly; each runtime hash is checked against its own file."
+  },
+  "assembly_matches_frozen_rates_and_profile": true,
+  "post_replay_packaging": "Four files received trailing-whitespace cleanup only; complete parsed ASTs were checked unchanged. Constructor input pin refreshed. Admission assertion comparison rerun.",
+  "scope": "Changed construction and exact recipe, fresh native ledgers/wrappers/phases, independent scalar and guard audits, integer owner reproduction, strict global admission and independent pricing. No predecessor full replay, seed-discovery optimizer or PDF generation. Local Python 3.14; Python 3.11 is covered by CI."
+}
diff --git a/research/gauge44-leaver8/MANIFEST.json b/research/gauge44-leaver8/MANIFEST.json
new file mode 100644
index 0000000000..8161f0e77d
--- /dev/null
+++ b/research/gauge44-leaver8/MANIFEST.json
@@ -0,0 +1,171 @@
+{
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+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "LOCAL-VALIDATION.json": "f81fbd98eb608b8119f03f89a5692bcd610845fc97022337931586d8582b706e",
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+  "PROOF-NOTE-BIT.md": "dd771adb12f6f0bef0e2931c28b21b243b04d5f512370cbad1207275c342aaf7",
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+  "PROOF-NOTE-LEAVER.md": "e4f9482ef551d6d4300d8ed8bb7c34dc9327fbcfa30a502bf3476b78468e60c3",
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+  "PROOF-NOTE-SW4.md": "d7bb225f1a7f9fd363e819a67e92a5fe14c0942f6c3616d73609cc48042daf3d",
+  "README.md": "0c09f0685e5db77177187c12afea9c45465787c44d6ae0d7d28c0c7de8f1b2a0",
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+  "construction/build_gauge_cold44.py": "ec730a4d3ff12fb058780718b1d5a7afe61243c532679ef347a5a48e2af0a3bb",
+  "construction/construct_gauge_xcentre.py": "d8d295566ef2399af2da0707a4adc83e07aa26d2344c01a66bd0ca7684cf9217",
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+  "evidence/layers/LOCAL-AUDIT-LAYERED.json": "a596d7262374a023ae079e0da41d20189bd3ca4594101e5e6f402ce5799df9ff",
+  "evidence/leaver/CELL-MUTANTS-LV.json": "308975b8288cb9c853ee6b69e68b25e6f3727d259dccfb7509042f103bb03220",
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+  "evidence/local/CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+  "evidence/local/CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+  "evidence/local/CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12",
+  "evidence/local/FULL-WORD.json.gz": "0ad202612f010df4ab66432a628247b37ad8b497dd6b27595b1685cbd7eb119e",
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+  "evidence/local/SCALAR-FRAME-AUDIT.json": "cfc73040079b43ea82a42f3cf4c910edda1362deb09ec21c816c329347313bcb",
+  "evidence/local/WRAPPER-CHECKS.json": "84c727930f85f1c91900d6d12c523735c8b5d6907cd3eb1bd1030fe1fd4161d7",
+  "hosting/PROOF.md": "45bb3de8a10298a4cf5a278c3343be22a7d2e735be93a4e9454f24df7275faf0",
+  "hosting/README.md": "004bcdf6c78bd0316f0606d9e636511f94e1e80cbd79cce1a7e3bc55076d9bf1",
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+  "hosting/frozen/MAJORIZATION.json.gz": "ec5f94b13d190d72bc0608dc9fe2498cc43ba9deb05028159a812ec1e4dcacdf",
+  "hosting/frozen/MANIFEST.json": "9df028adfa5120c60d2c78bfab06822cf4e6ed55502816b7d6dec19c1a2e4967",
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+  "hosting/frozen/REPRODUCTION.json": "8354f63148621c5fcf09cd16b496dedd677d813f83974e1f341ce38a1fffec81",
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+  "hosting/frozen/SEED-RECEIPT.json": "aecfef753379106f5289f31251584c642e2cf7e4fa2d0886bb4ef9e922f8d9ba",
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+  "hosting/reuse_owners.py": "2106fe79bd89071e62a3a25c1e444531e14fb89f88b4bdeb72d7b40c91266402",
+  "independent/CENTRE-GUARD-REVIEW.md": "7b82518d7ddf042d6e71174bc286311fa72127e0dc6dc9e500025fcf7abbf897",
+  "independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json": "9fb5265c4d2ddf3d615e46600954c79cd1a42481500a0973a5695fcb9f2558c9",
+  "independent/GAUGE44-GLOBAL-GUARD-REVIEW.json": "631107a9a9acb02441ce80298f815e0c624f811b0d58c6fd78f8dc58d564bb5b",
+  "independent/GAUGE44-INDEPENDENT-PRICE.json": "6e222b252f3453446d0e41b08f00a9bf9449ce3588b6ddc00c9accc1c00e7683",
+  "independent/README.md": "25668a62d8c91f6860f8412cf2fc750ba41bf1085dad3709ad5067c7956eac89",
+  "independent/audit_local.py": "03afcfc9da428b3f6edac81c1fee7f277ab81b64998efae78380b63498dec6cd",
+  "independent/price_profile.py": "d2f548ad6b99f64a8ca5fbaf822a89560bb99359957ce3420b497f6a46fc0acf",
+  "independent/review_guards.py": "b83164d6c0122a055b3281f3381b305683a875760a2d727dd0188bb2aa59d67d",
+  "inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+  "verify_global.py": "16bd5e54598592e92e210f99065348c5df261b8350fdc688072ce053d15b088a",
+  "verify_manifest.py": "723d726dbbe5b65a49caecae0f1aab664a1413fb639abfd3e826a5a538e14e5b"
+}
diff --git a/research/gauge44-leaver8/NOTICE.md b/research/gauge44-leaver8/NOTICE.md
new file mode 100644
index 0000000000..30d0c8cd3c
--- /dev/null
+++ b/research/gauge44-leaver8/NOTICE.md
@@ -0,0 +1,24 @@
+# Gauge44 attribution and scope
+
+New contributions by icekylinx, with OpenAI GPT-6 Astra assistance.
+Local review and packaging used OpenAI Codex. Apache-2.0 applies;
+the license is included. The full original PR635 notice is preserved as
+UPSTREAM-NOTICE.md and construction/UPSTREAM-NOTICE.md.
+
+The new contribution is the changed source-branch gauge and retired-row
+completion, source-carried coordinate totals, exact 44-cold-end realization,
+and explicit all72 whole-family assignment using concave capacity matching
+with integer majorization certificates. The center-carrier generalization
+retains the exact ordered common frames and complete native local contract.
+Independent local, price, interface and owner fixed-point checks are included.
+
+The construction retains the credited PR635 K-triangle and porting machinery,
+earlier joint-prefix/HPE/frame ancestry and icekylinx's prior factory work.
+#645 used the same cited PR543 bit supplier as PR635. This package (research/gauge44-leaver8) cites the merged PR589 bit supplier instead, with a derived rank-mass deficit (PROOF-NOTE-BIT.md); #645's retained PR543-based evidence is historical. It builds #645's word without K-triangles (PartialK) and stacks earlier community jp8 layers on it (G44Stack), adds the p6n ends (NoTriReopen), entrance promotions (BlockInvert) a read-set exchange (BRoute), chafreaky's #741 frames, JointXF's joint exchange, NewBArch's triangle-hybrid B rewrite and LeaverSAT's eight k8 leaver cells (with LeaverSAT2's frame re-optimisation); see README. All-size, realization,
+hosting, precision/tape, analytic-transfer and bit H1-H5 assumptions remain
+conditional. No upstream license, credit, source pin or AI disclosure is
+replaced by this notice.
+
+PR641 and PR642 were checked as concurrent reported frontier comparisons.
+Their endpoints and owner maps are not included here. See CONSTRUCTION.md,
+hosting/PROOF.md, independent/ and README.md for the exact contribution scope.
diff --git a/research/gauge44-leaver8/PROOF-NOTE-BARCH.md b/research/gauge44-leaver8/PROOF-NOTE-BARCH.md
new file mode 100644
index 0000000000..8cea5a6846
--- /dev/null
+++ b/research/gauge44-leaver8/PROOF-NOTE-BARCH.md
@@ -0,0 +1,43 @@
+# PROOF-NOTE-BARCH: width-neutral triangle-hybrid B-delivery rewrite (U8)
+
+Construction by NewBArch (`construction/barch/`, builder `build_tri.py`, controls `run_controls.py`, recipe
+`RECIPE-U8.json`). Driver: `construction/barch/reproduce_barch.py`, chained after `construction/jx`.
+
+## The move
+On research/gauge44-frames-x's X4 word (`1e1d99ba…`), eight disjoint slots are rewritten. In each slot X an entering
+copy E donates into a halves-copy X: 231 (E 450), 230 (E 452), 232 (E 454), 236 (E 456), 226 (E 451), 228 (E 453), 62 (E 455), 238 (E 457). That way, so that one target
+read takes X + H in a single gate. A holder pair (for example 496/484) carries the value. Each holder is restored by a
+low-end tail at its frame (early cleanup) and a FULL-cleanup restore. Entrance pre-reads keep the entering helper's
+start value away from every target.
+
+The recipe is explicit, with every index referring to the X4 word:
+- 40 B deletions;
+- 40 B insertions, each with its frame;
+- 32 explicit re-chosen B frames;
+- 8 early-cleanup tails;
+- 8 FULL-cleanup restores.
+
+The A section and X4's tail frames are untouched. The width is unchanged at 3778. The profile goes
+{1:2548, 2:338, 3:430, 4:194, 5:56, 8:8} → {1:2548, 2:338, 3:446, 4:162, 5:72, 8:8}, a delta of {3:+16, 4:−32, 5:+16}.
+The eight slots are additive (8 × 3.925e-8 ideal = 3.140e-7). Output word `090fd574…`. U8 contains B0's four slots
+(231, 230, 226, 228) plus 232, 236, 62 and 238.
+
+## Checks rerun on every rebuild
+- `build_tri.py` (standard library only) checks the base sha (`1e1d99ba…`) and the result sha (`090fd574…`).
+- `run_controls.py` produces 38 outcomes, all required. The control set is pinned in `LOCAL-PINS-barch-U8.json`.
+  - C0 identity reproduces the input.
+  - The recipe word PASSes #645's independent `audit_local.py`.
+  - Four mutants must each FAIL `audit_local` with a pinned message, both globally and for each of the eight slots
+    (NAME@X):
+    - drop_restore: the holder is not restored, giving "all-column endpoint failure";
+    - restore_full: the low-end restore is moved into the FULL cleanup, giving "all-column endpoint failure";
+    - drop_preread: the inserted entrance pre-reads are omitted, giving "nonzero entrance response";
+    - donation_after: the donation is placed after the target read, giving "nonzero entrance response".
+- The per-end layer-end controls (`../layers_p6n/layer_end_controls.py`) reject 95.
+- PR635's native chain runs, with the canonical word, local programs and Clifford recipes pinned.
+
+## Strict
+NewBArch's strict replay: the #741 map (`G44Pack/m741`, byte-identical OWNERS) is rebound to the U8 locals with
+`rewidth.py` and admitted with this package's own code (NEWWORD `admit645.py` on research/gauge44-frames-x's tree).
+The result is κ 0.001661948695165034, +3.1404e-7 over research/gauge44-frames-x. The four-slot subset B0 strict-passes
+at 0.001661791659578416 and the single slot V1 at 0.001661673902364948.
diff --git a/research/gauge44-leaver8/PROOF-NOTE-BIT.md b/research/gauge44-leaver8/PROOF-NOTE-BIT.md
new file mode 100644
index 0000000000..da06360da0
--- /dev/null
+++ b/research/gauge44-leaver8/PROOF-NOTE-BIT.md
@@ -0,0 +1,112 @@
+# PROOF-NOTE-BIT: citing the PR589 bit supplier with a derived rank-mass deficit (gauge44)
+
+This note is BitCap's `PROOF-NOTE-BIT.md` from `complex-571-cold14-k492-bit589`, adapted to the gauge44 package. It
+covers the only verifier change relative to #645's package (`research/gauge44-global`): the bit supplier changes from
+PR543 to PR589. The complex side is #645's construction, unchanged: supplier word, recipes and every complex check in
+`code/assemble.py`. The only complex-side change is the repacked owner map (`data/PLAN.json`, `data/OWNERS.json.gz`),
+with expected values re-derived in `data/SPEC.json`.
+
+## Changed sites
+
+The changes are in `code/assemble.py`, plus one new stage in `verify_global.py` and a new file
+`code/bit_supplier_controls.py`. The independent (non-verifier) `independent/price_profile.py` is ported to PR589 as well. Every other `.py` file equals #645's.
+
+| # | site | before (#645) | after |
+|---|---|---|---|
+| S1 | bit input | `inputs/PR543-EXPECTED.json` from the multicold source, blob pin `b61d8598…` | `inputs/PR589-EXPECTED.json`, shipped in this package, blob pin `e293ddc5…`, through `load_bit` |
+| S2 | bit deficit | literal `9984` | `bit_deficit(word, live)` = T(2Kv − L·cst), with L = 9, T = 32, K = (L−1)/2 = 4 |
+| S3 | profile binding | (none) | Σ r·n of the bit profile = `bit.rank_mass`; moment width `BIT_M = 1 + 7L` asserted = 64 |
+| S4 | pipeline binding | (none) | the record's `nine.pipeline` names the nine-stage template with 32 replicas |
+| S5 | citation / receipt | input hash names the PR543 file | `bit_supplier` cites PR589 (head `a5afc8c6`, merged as `b3eb785a`, path `research/e8-bit-p111-tuned/tune/EXPECTED.json`) and records v = 111, cst = 63, COPY ranks [7×9] and the derived deficit 10272 |
+| S6 | `verify_global.py` | (none) | stage `bit-supplier-controls` runs `code/bit_supplier_controls.py`; it requires status `PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS`, exactly 12 rejected controls and derived deficit 10272 |
+
+The shipped `inputs/PR589-EXPECTED.json` has git blob `e293ddc557742637f9f679f083a1a282d87b1b13`, which equals
+`origin/main:research/e8-bit-p111-tuned/tune/EXPECTED.json`.
+
+## Why the derived deficit is correct
+
+**The identity.** The rank-mass identity of #545 and #555 is M·live − mass = T(2Kv − L·cst). Its source is
+#555's README, "Rank-mass identity", and `code/adapt9p.py`, whose audit carries `DEFICIT=T*(2*K*V-L*CST)`.
+
+**The parameters.** The bit word has v live ports and decoder constant cst, the sum of the nine retained totals' COPY
+ranks. The nine-stage chain is #463/#510 with 32 replicas, so L = 9, T = 32, K = 4 and M = 1 + 7L = 64. The live data
+wires number 2KvT.
+
+**The constraints checked.** The verifier asserts all of:
+1. cst = Σ copy_ranks, with exactly `retained_totals` = 9 entries, each in (0, 8].
+2. live = 2KvT. For #589: 2·4·111·32 = 28416.
+3. Σ r·n over the priced profile = the record's `rank_mass` = 1808352.
+4. M·live − Σ r·n = T(2Kv − L·cst). For #589: 64·28416 − 1808352 = 10272 = 32·(888 − 567).
+
+Check (4) is #645's `check_moment` guard, unchanged. So v, cst, the profile and live must all agree.
+
+**PR543 consistency.** The same formula reproduces #645's constant: PR543 has live = 30720, so v = 120; its nine
+totals have COPY rank 8, so cst = 72; 32·(960 − 648) = 9984.
+
+**The deficit does not raise c.** `check_moment` uses the deficit only as an equality guard. The moment engines
+compute from (profile, m = 64, live, z) and never read it. The bit value c is established only by the unchanged
+acceptance tests at the same exact endpoints, with the bit bad-residue surcharge retained: accept at c and reject at
+c + 10⁻²⁴, by both engines.
+
+## Effect on the outer chain (differs from the k492 package)
+
+In the k492 package the complex side bound under either supplier, so κ did not move. Here it does. With the
+gm3 map the complex side certifies b = 0.001654663299688920102557, with research/gauge44-bit589's dz1 map
+b = 0.00165526410310589140991, and with research/gauge44-bit589b's L1g4 map b = 0.001655496738330440231813. PR543's c = 0.001653826988146798944268 is
+below b, so under PR543 the bit side would bind. BitCap's table gives the PR543 bit-side κ cap as
+0.001651096360425895, which is exactly the κ of `research/gauge44-repack`. PR589's c = 0.001733427039589844234749
+exceeds b, so the complex side binds again (`binding = complex` in `ASSEMBLY.json`): κ = 0.001651929911890057 for gm3
+(conservative 0.001651929909011672) κ = 0.001652528731617094 for dz1 (conservative 0.001652528728737236), and
+κ = 0.001652760598550299 for L1g4 (conservative 0.001652760595670246).
+Bit589Reviewer recomputed both suppliers with the outer engine and confirmed this. The gain over gauge44-repack therefore depends on this change and on the
+assumptions below.
+
+## Negative controls (all must be rejected; the verifier requires exactly these 12)
+
+Each control runs the real `assemble()` on the fresh owner/invoice receipts with one input mutated. The strict run's
+`BIT-SUPPLIER-CONTROLS.json` lists all 12 as rejected.
+
+| control | site | rejected at |
+|---|---|---|
+| `revert_hardcoded_9984` | S2 | `check_moment` deficit guard (10272 ≠ 9984) |
+| `ports_112` | S2 | `bit_deficit`: live ≠ 2KvT |
+| `decoder_constant_64_copy_ranks_unchanged` | S2 | `bit_deficit`: cst ≠ Σ COPY ranks |
+| `decoder_constant_64_with_one_copy_rank_8` (derives exactly 9984) | S2 | `check_moment` deficit guard |
+| `eight_retained_totals` | S2 | `bit_deficit`: totals count ≠ 9 |
+| `live_minus_one` | S2 | `bit_deficit`: live ≠ 2KvT |
+| `profile_rank_mass_plus_one` | S2/S3 | `check_moment` deficit guard |
+| `profile_rank_mass_receipt_mismatch` | S3 | profile mass ≠ `rank_mass` |
+| `bit_lower_next_grid` | endpoint | `check_moment` reject-side moment test |
+| `not_nine_stage_record` | S4 | pipeline binding |
+| `tampered_bytes_next_grid` | S1 | blob pin |
+| `pr543_file_under_pr589_pin` | S1 | blob pin |
+
+Bit589Reviewer re-traced all 12 rejection sites on the gauge44 word (b589gm3), and they match the table: `code/assemble.py` L191 (`revert_hardcoded_9984`, `decoder_constant_64_with_one_copy_rank_8`, `profile_rank_mass_plus_one`), L48 (`ports_112`, `live_minus_one`), L47 (`decoder_constant_64_copy_ranks_unchanged`, `eight_retained_totals`), L201 (`profile_rank_mass_receipt_mismatch`), L197 (`bit_lower_next_grid`), L179 (`not_nine_stage_record`) and L39 (both blob controls). dz1 and L1g4 run the same code.
+
+The ported `independent/price_profile.py` re-derives the deficit separately (`pr589_deficit`) and checks the same blob pin. Its regenerated receipt on this package's PLAN gives the same κ.
+
+## Inherited assumptions
+
+**PR merge status (`gh pr view`, 2026-10-13):** #589 MERGED 2026-10-12T17:00:38Z. #555 was merged 2026-10-12. #645
+is OPEN. Main's review replayed #589 freshly as "supplier-only headroom", and main's *selected* composition still
+cites #543.
+
+**Unmerged assumptions:**
+1. **#645 itself (open):** the gauge44 factory, its construction steps and all of its retained interfaces and notes.
+   These are unchanged here.
+2. **This verifier change (S1–S6):** under review (Bit589Reviewer). The PR589 record replaces PR543 as an *input of
+   the gauge44 assembly*, a composition main has not selected.
+
+**Assumptions carried by #555/#589 (merged, stated there as review points, not theorems):**
+3. #545's punctured unit: a 111-port unit with decoder constant 63 is an admissible bit supplier on the same hypotheses
+   as v = 120.
+4. #510's nine-stage chain as re-parameterised for v ≤ 120 by #555's `code/adapt9p.py`, including the rank-mass
+   identity used in S2.
+5. #543's interleaved scalar-interface lemma (H1–H5) for phase-B source rewrites. This is not new: #645 already
+   inherits it through PR543.
+6. #589's two A-section transports.
+7. The same bit bad-residue surcharge model as PR543 (`surcharge_model = {'complex': False, 'bit': True}`).
+
+## Result
+
+The bit-supplier change is the same as in research/gauge44-bit589 and gauge44-bit589b: the code is byte-identical and was signed by Bit589Reviewer. For this package (k8 leaver word db2c7cfb, K8c8 map), the complex side certifies b = 0.001674185476674086429846 and binds under PR589. Under PR543 the bit side would cap κ at 0.001651096360425895. κ is given in the README and `RESULT.json`.
diff --git a/research/gauge44-leaver8/PROOF-NOTE-FRAMES-X4.md b/research/gauge44-leaver8/PROOF-NOTE-FRAMES-X4.md
new file mode 100644
index 0000000000..a456a8127b
--- /dev/null
+++ b/research/gauge44-leaver8/PROOF-NOTE-FRAMES-X4.md
@@ -0,0 +1,58 @@
+# PROOF-NOTE-FRAMES-X4: chafreaky's #741 frames and JointXF's joint exchange (X4)
+
+Two construction steps on top of research/gauge44-promo-p6k4sw's SW4 word P6k4sw4 (`d232183f…`).
+
+## 1. #741's eight B frames (`construction/frames/`)
+The eight B-gate frame raises are by **chafreaky**, [#741](https://github.com/CrocSwap/integer-mult-bounds/pull/741)
+(`research/complex-sw4-frame8`, commit e516b146). `FRAME-RECIPE-sw4.json` is byte-identical to #741's
+`data/FRAME-RECIPE.json` (a2c7ca4d…). CompetitorMine ported #741's builder and controls; only package paths are adapted.
+The step applies the frames with BlockInvert's `build_promotion.apply` and checks:
+- the scalar program of A, cut, B, precondition and cleanup is unchanged;
+- start and end frames are unchanged;
+- the profile, the widths and the output word `e7804702…` are pinned;
+- 3 pin controls are rejected;
+- #741's 10 focused native controls are rejected (8 frames emptied, a changed read coefficient, paid-profile tampering);
+- the per-end layer-end controls reject 95;
+- the native chain matches its pins.
+
+The rebuilt locals equal G44Pack's F741 locals except the `seconds` field in CLIFFORD-REVIEW.
+This step reproduces #741's word. The final word is built by step 2, which contains these frames.
+
+## 2. Joint exchange X4 (`construction/jx/`, JointXF)
+There are four disjoint instances of BRoute's sw4 read-set exchange rule. Each one exchanges *two* copy pairs that
+share targets: (448, 472), (458, 592), (470, 604) and (482, 614), with face registers 235, 267, 58, 427, 26, 443, 18
+and 50. #741's eight frames sit on top. The 16 moved reads keep their original stored dim-6 frames: they are
+monotone-repaired rather than refitted to the plain join. The recipe `RECIPE-X4.json` is explicit:
+- 32 replaced gates, 16 deleted gates and 16 inserted gates, each with its old gate asserted;
+- #741's 8 frames, listed with their source;
+- 16 explicit frames at the moved reads, each asserted equal to the recomputed frame.
+
+The builder `build_jx.py` uses only the standard library. It checks:
+- target frames lie inside u_t^⊥;
+- tails and ends;
+- exactness of the whole B segment's rational linear map against the input (a Fraction replay);
+- the recomputed paid profile and the output sha `1e1d99ba…`.
+
+Effect against #741's word: the profile goes {1:2556, 2:334, 3:430, 4:194, 5:56, 8:8} → {1:2548, 2:338, 3:430,
+4:194, 5:56, 8:8}. The width inventory is unchanged, and each instance gives +1.0798e-7 at ideal, exactly additive.
+
+**Controls**, each pinned in the recipe and rerun by `reproduce_jx.py`:
+
+| control | outcome |
+|---|---|
+| C0 identity | returns the input `d232183f` |
+| C1 #741 only | `e7804702`, #741's word (ties step 1 to step 2) |
+| M1 one pair (448) with frames retained | `5fb6fb2e`, neutral (profile = #741) |
+| N1 pre-read dropped | rejected: exactness rows [132, 135] |
+| N2 pre-read with wrong sign | rejected: exactness rows [132, 135] |
+| N3 plain-join refit of the moved reads | `7241cd59`, strictly worse |
+| N4 a raise made dim-7 at B855 | rejected: cap at (1302, 174) |
+
+N3 and M1 are pinned-outcome controls (a specific different word), not rejections. They show the gain needs both the
+target-sharing pair and the retained frames.
+
+**Other checks (JointXF):**
+- `audit_local` PASS;
+- native chain PASS;
+- FrameCoal's global frame optimiser reaches the same profile on this move set, so X4 is frame-optimal for these moves;
+- SW4Extend found the same word independently.
diff --git a/research/gauge44-leaver8/PROOF-NOTE-LAYERS.md b/research/gauge44-leaver8/PROOF-NOTE-LAYERS.md
new file mode 100644
index 0000000000..c4b4e85b6a
--- /dev/null
+++ b/research/gauge44-leaver8/PROOF-NOTE-LAYERS.md
@@ -0,0 +1,129 @@
+# PROOF-NOTE-LAYERS: earlier jp8 layers, here stacked on the no-triangle gauge44 word
+
+> In this package the layers sit on the no-triangle word (R = 504), not on #645's 492-helper word. The mapping, the
+> NP chain (regroup `864ff4a1` → swap `beb3579f` → layered `a9de804f`), the per-layer status on this base and the
+> checks are in `PROOF-NOTE-NOTRI.md` ("Layers on this word"). The text below is research/gauge44-layered's note. It
+> describes the same layers and controls on the 492-helper word; its word shas, helper numbers, counts and result
+> table refer to that word.
+
+
+This note covers the second change of research/gauge44-layered relative to research/gauge44-bit589. The first change,
+the PR589 bit supplier, is covered unchanged by `PROOF-NOTE-BIT.md`. Here the community jp8 layers that were reviewed
+on the k492 words (#629/#637/#641 lineage) are re-applied to #645's gauge44 provider word. The layers, their
+construction code and their recipes were all reviewed earlier, on k492 words. This note says what carries over
+unchanged, what is re-checked on the gauge44 word, and what is new. Sources: G44Stack's report (porting and checks on
+gauge44); PivotReviewer's report (sections 1-4, Addenda 3-5); H4aReviewer's report (Addenda 7-8); JP8Ends' report.
+
+## What the layered word is
+
+`construction/layers/reproduce_layers.py` builds the layered word from a fresh `construction/reproduce.py --until word`
+output. Each step is checked exactly:
+
+1. **Pivot swaps** (`build_pivot_swap.py`, PR641's constructor, LF sha256 `8e8bced8…`, the file PivotReviewer signed for
+   st2s4). It reads `PIVOT-SWAP-S6.json` and runs on #645's `regroup/FULL-WORD`. There are six pivot-role swaps: 488→560,
+   489→561, 500→572, 501→573 (s4) and 513→537, 525→549 (s6). The `swaps` list is identical, gate for gate, to S6Ship's
+   s6/s6j3 recipe (`k492-jp8-pivot_swap.json`); only `input_content_sha256` differs, because the base word is #645's
+   regroup word. The constructor replays the zero response exactly, keeps the profile and width multiset unchanged, and
+   rejects its 30 negative controls.
+2. **HPE.** PR635's `build_hpe.apply` applies the inherited jp8 hyperplane-end changes (`HYPERPLANE-END-S6.json`). Its
+   LF sha256 `23c9d7ce…` equals the k492 jp8 hyperplane_end recipe committed in s6j3 and earlier.
+3. **cold44, exactly.** #645's `build_gauge_cold44.py` runs on the swapped HPE word. Its 44 rank-four cold ends, premix
+   and low tails must equal the unswapped (pinned) cold44 construction; only the FULL inverse differs. Consequently the
+   swaps touch no factory block.
+4. **Layers.** PR635's unchanged `build_cold_end.apply(HPE, COLD-LAYERS-RECIPE)` applies the cold44 recipe plus:
+   - 8 entering ends: 560/561/572/573 at U24 (s4) and 597/599/537/549 at U30 (x30: #629's E1 pair, which #645 dropped,
+     plus s6's two ends);
+   - 10 factored dim-8 cold ends: p123 (310/506, 311/504, 516/327) and q4 (579, 592, 589, 518).
+   The output word's sha256 is pinned (`0be48b1d…`), as are its local profile `{1:2542, 2:414, 3:434, 4:154, 5:56,
+   8:8}` and width inventory `{4:52, 5:48, 7:42, 8:116, 9:234}`. The recipe's `refactored_cleanup` meta lists the 8
+   entering ends in `entering_low_frame_ended_helpers` (LayerReviewer's fix). That meta is copied into the word, which
+   is why the pinned word sha moved from `b25f0ed9…` to `0be48b1d…`; gates, frames and report are unchanged.
+5. **Layer-end controls** (`layer_end_controls.py`, LayerReviewer's adaptation of PR635's `cold_end_controls.py`
+   d966e29a). These are raw-word negative controls on the layered word, judged by PR635's unchanged
+   `hpe_audit_and_transport.py`. Each mutant must be rejected at its pinned reason. The adaptation has three parts: the
+   lower→FULL mutant is pinned at "cleanup on non-FULL end", where gauge44 rejects it; entering ends come from the
+   recipe meta; and the premix-gate controls are skipped for entering ends that have no premix gate. `reproduce_layers.py`
+   requires exactly 59 rejections.
+6. **Native locals.** PR635's native audit and transport, ledgers, local replay (the 192-bit payload bound), wrappers and
+   phases all pass. The result is the `--local` that `verify_global.py` consumes.
+
+G44Stack's run of this driver (`rlayers2`, all steps exit 0, 59 controls rejected) reproduces `locs/pq/local`, the
+local G44Pack's strict runs used. Every SPEC-pinned artifact is byte-identical: CANONICAL-WORD, LOCAL-PROGRAMS,
+LOCAL-CHECKS, INDEPENDENT-LOCAL-REPLAY, CLIFFORD-RECIPES, RESIDUAL-ADAPTERS and WRAPPER-CHECKS. CLIFFORD-REVIEW differs
+only in a seconds field; its semantic hash is what SPEC pins. The two unpinned files that embed the word,
+FULL-WORD and SCALAR-FRAME-AUDIT, differ because of the meta.
+
+## Per-layer status on gauge44 (G44Stack, ideal Δκ at ×72)
+
+| layer | prior review (k492 words) | on gauge44 | per-call Δ profile | ideal Δκ |
+|---|---|---|---|---|
+| pivot swaps (6) | PivotReviewer §1-2 (s4), Addenda 4-5 (s6): exact; omitting any rewritten gate is rejected; cost-neutral | all 6 recipe `before` gates match the regroup word; 30 controls rejected; cold44 rebuilds the same 44 ends | neutral | 0 |
+| s4 ends 560/561/572/573 @U24 | PivotReviewer §3: (N) exact for ([24], U24) and its canonical pair; climbs paid | positive | {1:+8, 2:−4, 3:+4, 4:−4}, w −4 | +7.0e-8 |
+| x30: E1 597/599 + 537/549 @U30 | #629 (E1); PivotReviewer Addenda 4-5 (537/549 end monotonically at the E1 hyperplane, whose (N) is exact) | positive | {1:+10, 2:−6, 3:+2, 4:−2}, w −4 | +2.0e-7 |
+| p123 | H4aReviewer Addendum 7: 0 bad rows, dyadic, exact in all 3 orientations; (N) for (0,1039)-(0,1041); Δ recomputed | positive | {1:+6, 2:+12, 3:−12}, w −6 | +2.0e-8 |
+| q4 (after p123) | H4aReviewer Addendum 8 (n_q4): exact; (N) for the 310/311/327 frames and 518's (0,1042); independent of u4 | positive | {1:+4, 2:+8, 3:−8}, w −4 | +1.4e-8 |
+| **stack T_pq** | — | built and audited | {1:+28, 2:+10, 3:−14, 4:−6}, w 3794→3776 | **+3.08e-7** |
+
+These layers were left out because they are negative or dead on gauge44: u4 (−1.2e-6), the 249 end (−3.2e-7), a joint
+p123+q4 (−2.6e-7, worse than sequential), and #627's dim-7 ends 581/590 (no dyadic basis). j3 is dead: its st2 partner
+403 is one of #645's 44 ends, and cold44's block premix uses up the row space.
+
+**Payload.** H4aReviewer's Addendum 8 correction found that the k492 word n_q4 broke the 192-bit local payload bound
+(backward prefix 280 bits). On gauge44 the layered word passes PR635's `hpe_audit_local.py` local-replay stage
+(`prefix < 2**192`), both in G44Stack's `localchain.py` and as step 5 of `reproduce_layers.py`. So the q4 layer here
+does not repeat that failure.
+
+## Verifier changes (spot widths)
+
+A swapped-out pivot p becomes an ordinary cold helper, and its width goes from 8 to 9. #645's global code checks the
+spot helpers' widths as all 8, so the five global files gain the spot-width rule PivotReviewer signed as SOUND for
+S4Ship (Addendum 3), ported to gauge44:
+
+- `code/witness.py`: `spot_widths(v)` gives 9 at a spot helper h with 2v+h among the swapped-out pivots and 8
+  elsewhere. The swapped-out pivots are read from the recipe that SPEC key `pivot_swap` names (path and sha256; the
+  sha256 is asserted). Without `pivot_swap` the tuple is all 8, the same as #645.
+- `code/bind_providers_portable.py`, `code/audit_allcold.py`, `code/assemble.py`: the `all(... == 8)` spot checks become
+  tuple equality with `spot_widths()`, which pins every spot width exactly.
+- `code/assembly_controls.py`: the `cold_swap` control picks a swap partner whose width differs, so the mutant can
+  never be the identity.
+
+Here the spot helpers 264 and 276 (pivots 488 and 500) expect width 9 and the other spot helpers expect 8. The k492
+spot-width review (PivotReviewer Addendum 3) covered the same rule on k492 code. Its gauge44 port is part of this
+package's review (LayerReviewer).
+
+## Controls and what is not re-run
+
+- The pivot-swap constructor's 30 controls run inside `reproduce_layers.py` (step 1).
+- `verify_global.py`'s strict controls are unchanged, including the 12 bit-supplier controls and #645's admission
+  controls. They run on the layered locals.
+- Layer-end controls: 59 raw-word mutants, all rejected at pinned reasons, run as step 5 of `reproduce_layers.py`
+  (see above). They cover the cold low-frame ends, the refactored cleanup, every entering end (its lower-frame gate,
+  profile pin and hyperplane, plus its premix gate where it has one) and each distinct dim-8 frame. LayerReviewer ran
+  them on the layered word (59 rejected). The k492 version (d966e29a) rejected 103-112 on the p123/q4 words; the
+  k492-only primitives (absorptions, factored accumulators, target writes) are absent from this word.
+- #645's independent audit `independent/audit_local.py` on the layered word: PASS, with 204 entering helpers, 96 low ends,
+  54 cold ends and 716 columns. Its receipt is `evidence/layers/LOCAL-AUDIT-LAYERED.json` (word `0be48b1d…`, run with
+  `--main`). The README's clean-clone command reruns it; only `elapsed_seconds` varies. The other `independent/`
+  receipts are #645's own.
+- The prior (N), exactness and pricing checks for each layer were done on k492 words. On gauge44 they are covered by
+  the native chain (native audit, local replay, wrappers, phases) on the layered word, together with the pinned
+  profile and width inventory.
+
+## Inherited assumptions
+
+These are the same as `PROOF-NOTE-BIT.md` (#645 open; PR589 citation; #545/#555/#589 review points; H1-H5). In
+addition:
+
+1. **(N) for the entering-end pairs outside #599's three Lean-covered pairs** (U24, U30, the dim-8 frames). As on
+   k492, these are covered by the tool check (clifford_exact / `nchk.py`) and by the native wrappers, not by a Lean
+   proof (PivotReviewer §3).
+2. **The reviews of PR641's pivot-swap constructor and PR635's `build_cold_end.apply` / `build_hpe.apply`**, which this
+   package uses unchanged.
+
+## Result
+
+| | gauge44-bit589b (L1g4 map) | this package (layered, LN5c map) |
+|---|---|---|
+| κ | 0.001652760598550299 | 0.00165395497190225 |
+| per-call width | 3794 | 3776 |
+| local profile | #645's {1:2514, 2:404, 3:448, 4:160, 5:56, 8:8} | {1:2542, 2:414, 3:434, 4:154, 5:56, 8:8} |
diff --git a/research/gauge44-leaver8/PROOF-NOTE-LEAVER.md b/research/gauge44-leaver8/PROOF-NOTE-LEAVER.md
new file mode 100644
index 0000000000..b34a289c48
--- /dev/null
+++ b/research/gauge44-leaver8/PROOF-NOTE-LEAVER.md
@@ -0,0 +1,82 @@
+# PROOF-NOTE-LEAVER: no-helper mutable-leaver all-K cells, re-stacked layers, hybrids and a frame re-optimisation (k8)
+
+Construction: LeaverSAT (cells, layer re-indexing, frozen recipes) and LeaverSAT2 (frame re-optimisation).
+Drivers: `construction/leaver/reproduce_leaver.py` (cell word) and `construction/leaver/reproduce_leaver_chain.py`
+(everything after it). Reviews: PromoReviewer (leaver chain, k8 cells and frames, k8 clean rebuild), SW4Reviewer (hybrid structure), Q6Reviewer
+(`layer_end_controls_leaver.py` v2, `LEC-REASON-PINS-k8.json`), LecReviewer (`LEC-REASON-PINS-STACK-k8.json`).
+
+## 1. The cell (set model, LeaverSAT)
+In #781's all-K cell, a pair p with sign e replaces three face events and three packet copies. Direct delivery uses
+15 reads y_i += c x_j. LeaverSAT's 21-gate circuit uses the six leaver sources x_j (face-event operands with no later
+reads, restored at FULL by the inherited cleanup) as mutable intermediates. It has 3 leaver gates x_k += c x_m,
+3 target gates y_a += c y_b (inverted at frame zero in the precondition and scatter, #781's recipe) and 15 reads.
+Coefficients are rescaled exactly per cell, C_ij = r_i c_j. The driver re-derives the scaled gates from the unit
+circuit and checks the clean map Y_i = Σ_j C_ij X_j in exact rationals.
+
+Native legality needs one relabelling: the plain circuit fails the native audit, because a y += y source carries
+port-stage entering-helper dirt. Each cell is therefore relabelled by S6 so that y–y sources avoid targets carrying
+entering dirt at that time.
+
+**Set k8:** all eight cells (01±, 23±, 45±, 67±), R = 480. The cores are in `construction/leaver/cells-k8/` (documentary;
+the driver re-derives every scaled gate from `CODED-CELLS-k8.json`). The regroup word is `00aeefe0…` and the cell word is
+cold44 `58e14a02…`. Its pairing ranks are pinned to [0,0,0,4,4,4,4,4,4,4,4,0,0,0] in `cold44x.py` and checked again in
+the driver.
+
+## 2. Re-stacked layers (LeaverSAT; signed builders unchanged, recipes re-indexed)
+| step | recipe (data) | word |
+|---|---|---|
+| pivot swaps (6), mapped through the leaver helper map | `PIVOT-SWAP-k8.json` | `377ab10c…` |
+| HPE, greedy (22) | `HPE-RECIPE-k8.json` | `598543fa…` |
+| cold44, exact (same ends, premix and tails as the unswapped cell word) | — | — |
+| NP layers (s4, x30, b6, q4) | `COLD-LAYERS-RECIPE-NP-k8` | `2c1740f6…` |
+| p6n ends | `COLD-LAYERS-RECIPE-P6N-k8` | `25c40614…` |
+| promotions (16, minimal) | `PROMO-RECIPE-k8.json` | `84d4da2e…` |
+| joint exchange (re-indexed X4) | `RECIPE-X4-k8.json` | `84d4da2e…` (identity) |
+| U8-style hybrids ×6 (NewBArch's builder; instances 62, 226, 228, 230, 231, 232) | `RECIPE-U8-k8.json` | `c836d892…` |
+| frame re-optimisation (exact global frame optimum, gopt2; 137 B and 2 T frames) | `FRAME-RECIPE-LV-k8.json` | **`db2c7cfb…`** |
+
+Three steps don't apply to k8. The sw4 exchanges use copy helpers 461, 581, 591 and 603, which the cells drop. Of
+#741's eight frames, none survives. All four X4 exchange groups use dropped helpers, so the joint exchange is the
+identity (0 raises, 0 frames); it is still run, with its three remaining controls (C0, C1, N3) at their pins.
+
+The two cold-layer recipes are LeaverSAT's frozen k8 recipes (`fea82fb8…`, `76aedf23…` as .gz) with one key added,
+`input_content_sha256` = the swapped HPE word `598543fa…`, as in the k5 package. Removing the key gives the frozen
+recipe content exactly.
+
+## 3. Controls rerun on every rebuild
+- **Cell stage:** the exact clean-map check; native audit, ledgers, local replay, wrappers and phases on the cell word.
+- **Pivot swaps:** the swap constructor's 30 controls.
+- **Promotions:** BlockInvert's `promo_controls.py`, 11 mutants rejected at pinned sites.
+- **Joint exchange:** the 3 `RECIPE-X4-k8` controls reproduce their pinned outcomes.
+- **Hybrids:** `run_controls.py` gives 30 outcomes, all required. These are C0, the recipe word passing audit_local,
+  and 4 mutants, each run both globally and per instance.
+- **Frames:** `build_frames_lv.py`'s 3 pin controls. LeaverSAT2's 6 frame-recipe mutants are rejected by the builder;
+  that receipt was reviewed by PromoReviewer and is not rerun.
+- **Layer-end controls:** `layer_end_controls_leaver.py` v2 (`4ba676f1…`), Q6Reviewer-signed. It is the signed
+  per-end controls with per-word reason re-pins and **declared not-applicable sites**. A vacuous mutant site is never
+  skipped silently: the pins file must declare it, the declared set must equal the detected set, an identity is proven by
+  sha equality of the mutated and honest words, and a same-class substitute mutant is built and must be rejected at the
+  class's pinned reason. The count stays 95 on every word. The controls run on all five words:
+  - p6n, promoted, jx and hybrid words, with `LEC-REASON-PINS-STACK-k8.json`: `extra_end` only. h0 273's first
+    premixed partner 282 is already cold-ended at h0's frame, so the mutant is the identity (sha-proven per word); the
+    substitute is partner 281, cold-ended at h0's frame.
+  - the re-framed final word, with `LEC-REASON-PINS-k8.json`: `extra_end` as above, and `other_hp:554`. The frame
+    re-optimisation lowers entering end 554's tail frame to dimension 5, and no helper_final frame has dimension 5, so
+    the 'end at another hyperplane' mutant cannot be built; the substitute moves 554's end to another dim-8 frame and
+    must be rejected at the cone pre-check. This replaces the interim skip of research/gauge44-leaver.
+  No reason re-pins are needed on the k8 words. The receipts (`COLD-END-CONTROLS.json`) carry the not-applicable list;
+  the counts, the not-applicable sites with their reasons and the sha256 of each pins file (`LEC-REASON-PINS-STACK-k8.json`
+  d87ed7b5…, signed by LecReviewer; `LEC-REASON-PINS-k8.json` b07279e4…, signed by Q6Reviewer) are pinned in
+  `CHAIN-PINS-k8.json`.
+- **Native chain on the final word:** the canonical word, local programs and Clifford recipes are pinned in
+  `CHAIN-PINS-k8.json`, which also pins every count above.
+
+## 4. Cell mutants (evidence, not rerun)
+LeaverSAT2's `CELL-MUTANTS-LV.json` (in `evidence/leaver/`) records PromoReviewer's cell mutants M1–M6, generalised
+to every cell sign. All 42 are rejected by both audit_local and the native audit, on single-cell builds.
+
+## 5. Strict
+The owner map is G44Pack3's K8c8: its pattern-flow LNS on the R = 480 k8 word. Admitted on this package's own code,
+with SPEC `width_spot_helpers` [258,270,282,294] and `pivot_swap` → `construction/leaver/PIVOT-SWAP-k8.json` (NEWWORD
+discovery, freeze, strict), it gives κ 0.001671387264390146. That is +7.154e-6 over research/gauge44-leaver (k5,
+0.001664233607446043).
diff --git a/research/gauge44-leaver8/PROOF-NOTE-NOTRI.md b/research/gauge44-leaver8/PROOF-NOTE-NOTRI.md
new file mode 100644
index 0000000000..54bd84e01d
--- /dev/null
+++ b/research/gauge44-leaver8/PROOF-NOTE-NOTRI.md
@@ -0,0 +1,53 @@
+# PROOF-NOTE-NOTRI: #645's gauge44 word without K-triangles (R = 504)
+
+Construction by PartialK; review by NotriReviewer (scratch/NotriReviewer/FINAL-REPORT.md). Drivers:
+`construction/notri/reproduce_notri.py` (this word) and `construction/layers_np/reproduce_np.py` (layers on it).
+
+## Why the triangles were the blocker
+- In #645's gauge44, a K-block has I = 6 low registers with rank C = 4, so L = 2. Only the 2-row priority completion
+  fits there. The (p,−) triangle reads climb copies loc17/19/21 and source loc2.
+- Without the triangles, I = 8. With the 2-row completion, rank C stays 6 (L = 2), which is why the plain removal sweep
+  restored nothing. With the 6-row completion (`PRIO6.json`, the list blocks 3–10 already use), rank C = 4, so L = 4,
+  the cap. All 14 blocks then pair at rank 4: 56 rank-four cold ends, R = 504, width 3818, profile
+  {1:2506, 2:336, 3:472, 4:184, 5:56, 8:8}, rank mass 5674.
+
+## Constructor changes (NotriReviewer §1)
+- **`cgx.py`** is #645's `construct_gauge_xcentre.py`, parameterised by XPARAM. On this path the only change that takes
+  effect is the K-block priority: `PRIO[c]` is placed in front of the inherited rows. The prepended rows equal the
+  shared 6-row list of blocks 3–10 (all 8 lists identical). Every completion assert is kept (`qr_rank(M)==4`,
+  `len(M)==8`, the exact block-total rows). An empty TRI schedule is an input #645 already supports (`NH = 504 − 3·0`).
+  `HELPER-MAP` is the identity on 728. The `exch`, `COPYL` and `hyb` branches are inert here (defaults, empty, not
+  reached).
+- **`port_stage_x.py`** is PR635's `build_port_stage.py`. The helper map only has to be injective rather than onto;
+  with no triangles it is onto again.
+- **`cold44x.py`** is #645's `build_gauge_cold44.py`. Its per-block pin `r == len(L) == (2 if K-block else 4)` is
+  replaced by `r == len(L)` together with the explicit per-block pin `PAIRING_RANKS` (set by the driver to [4]*14,
+  and to #645's pattern in `--control-g44`). Helpers outside the 224+16b ranges join their blocks (EXTRAH, empty here).
+  Every other assert is kept (U, nonlocal premix, `rank(Qmat) == NB`).
+- **Control.** `reproduce_notri.py --control-g44` runs the same scripts with #645's four triangles and no XPARAM. It
+  reproduces #645's gauge44 word `78c7aada…` exactly, with ranks [2,2,2,4,4,4,4,4,4,4,4,2,2,2].
+
+## Exactness and locals (NotriReviewer §2)
+- Replay: 0 bad rows over 27,932 gates, all dyadic; forward, inverse and adjoint are exact. None of the 6,448
+  compensation additions reads an ended helper, and the precondition never touches one.
+- 0 FULL-remainder gates touch an ended helper; E⊂U holds for every entering end. The delta against gauge44
+  ({1:−8, 2:−68, 3:+24, 4:+24}, width +24) matches the reported profiles.
+- (N): all 17 pairs pass (14 cold dim-4 pairs with 4 helpers each, plus 3 dim-8 entering pairs).
+- `audit_local.py --main`: PASS. Payload: prefix bits 66 forward and 72 backward, against 192.
+- Native locals: 25 controls rejected, Lemma A on 22 frames, 17 wrapper mutants rejected. The rebuilt locals equal
+  the strict locals (`PartialK/runs/none_p6/local`): byte-identical except CLIFFORD-REVIEW and SCALAR-FRAME-AUDIT,
+  which differ only in their `seconds` field.
+
+## Layers on this word (G44Stack)
+The layers are research/gauge44-layered's (see `PROOF-NOTE-LAYERS.md`), mapped to the 504 numbering:
+- the 6 pivot swaps 494→566, 495→567, 506→578, 507→579, 519→543, 531→555, which are neutral (same 46 HPE helpers,
+  same 56 cold ends);
+- s4 566/567/578/579 at U24;
+- x30 608/610/543/555 at U30;
+- BlockCombine's b6;
+- q4.
+
+p123 is negative on this base and dropped; j3 is dead (L = 0 at U24 and U30). The chain is regroup `864ff4a1` → swap
+`beb3579f` → layered `a9de804f`, with profile {1:2534, 2:346, 3:458, 4:178, 5:56, 8:8} and width 3800. On that word
+the signed `layer_end_controls.py` rejects 59/59 and `audit_local.py` passes with 216 entering helpers, 120 low ends,
+66 cold ends and 728 columns. NotriReviewer independently reproduced a9de804f from the packaged recipes.
diff --git a/research/gauge44-leaver8/PROOF-NOTE-P6N.md b/research/gauge44-leaver8/PROOF-NOTE-P6N.md
new file mode 100644
index 0000000000..bef9ad2de0
--- /dev/null
+++ b/research/gauge44-leaver8/PROOF-NOTE-P6N.md
@@ -0,0 +1,34 @@
+# PROOF-NOTE-P6N: six b-type dim-8 cold ends on the layered no-triangle word (p6n)
+
+Construction by NoTriReopen. Driver: `construction/layers_p6n/reproduce_p6n.py`. Review: Q6Reviewer.
+
+## What p6n adds
+On research/gauge44-notri-layered's word NP (`a9de804f…`), p123's lane is rebuilt as three factored dim-8 pairs
+(`P6N-SPEC.json`):
+- [512, 513] at U = (256,128,66,34,16,8,6,1). The old pair [310,512] split a rank-3 end; [512,513] replaces it;
+- [311, 510] at U = (256,128,72,40,24,4,2,1);
+- [522, 327] at U = (256,128,66,34,18,10,6,1).
+
+They are built with the same premix-only factored construction as p123/q4/b6 (JP8Ends' stackJ/stackE, CarrierBypass
+pattern; PR635's unchanged `build_cold_end.apply`). The cold-layer recipe `COLD-LAYERS-RECIPE-P6N.json.gz` is NP's
+recipe plus these six ends; its meta lists 72 cold ends and the 8 entering ends. Applied to NP's swapped HPE word, it
+gives p6n `34b683fa…`:
+- profile {1:2540, 2:358, 3:446, 4:178, 5:56, 8:8};
+- widths {4:64, 5:48, 7:54, 8:122, 9:216};
+- width 3794 (NP 3800);
+- Δ per call {1:+6, 2:+12, 3:−12}, w −6, every end b-type.
+
+## Checks
+- **NoTriReopen:** native chain including phases PASS; audit_local PASS; 95/95 layer-end controls rejected.
+- **Q6Reviewer:**
+  - exact;
+  - (N) passes on all 21 pairs;
+  - payload 55/72 bits, against 192;
+  - the per-end control variant `layer_end_controls.py` (fc58c569…, which Q6Reviewer signed for research/gauge44-pq6) rejects 95/95;
+  - 165 further mutants on the six ends are all rejected.
+  The LayerReviewer-signed `../layers/layer_end_controls.py` controls one end per dim-8 frame family, so it would not
+  control each new end. This package therefore uses the per-end variant for p6n and for the promoted word built on it.
+- **Rebuild:** `reproduce_p6n.py` pins the input NP word, the output sha, profile and widths, and 95 controls.
+
+## Remaining capacity (NoTriReopen)
+After p6n, the only residual cold capacity on the word is 2 a-type units, and every end there prices about −9e-7.
diff --git a/research/gauge44-leaver8/PROOF-NOTE-PROMO.md b/research/gauge44-leaver8/PROOF-NOTE-PROMO.md
new file mode 100644
index 0000000000..8233bbd6b8
--- /dev/null
+++ b/research/gauge44-leaver8/PROOF-NOTE-PROMO.md
@@ -0,0 +1,46 @@
+# PROOF-NOTE-PROMO: entrance promotions E4 → E5 on the p6n word
+
+Construction by BlockInvert (`construction/promo/`); driver `construction/promo/reproduce_promo.py`.
+
+## What a promotion is
+An entering helper h starts at an entrance frame E (its `start_extra`) and climbs to its final frame. Promotion
+enlarges E to E′ ⊃ E (here dim 4 → dim 5). That removes one paid climb from h's chain (width −1 per helper) at the
+cost of re-choosing the frames of the gates on h's early chain. It is the time-reverse dual of end deepening. Two
+conditions make it legal:
+1. **Zero target response for h's dirt.** This condition does not depend on E, so it is inherited unchanged from the
+   input word.
+2. **Monotone frames.** Every gate's frame must contain its registers' current frames.
+Only frame annotations and start frames change. The scalar program (every gate's registers and coefficients) is
+untouched, so the endpoint, every cone and the compensation are those of the input word.
+
+## The recipe (`PROMO-RECIPE-p6n-k4.json`, data only, minimal)
+- Input: the p6n word `34b683fa…` (`PROOF-NOTE-P6N.md`), pinned.
+- `entrances`: the 16 entering helpers 627, 629–631, 635, 637–639, 651, 653–655, 659 and 661–663 (four E4 kernel groups) go E4 → E5.
+- `gate_frames`: 48 frame re-choices, the promotion's own entry-gate raises (12 per group); each records the old frame,
+  which must equal the input's exactly. This is BlockInvert's **minimal** recipe: the deterministic rule
+  E′ = E + ⟨smallest x⟩ on each group's entry gates (PromoReviewer). Unlike research/gauge44-promo's k3 recipe, it
+  carries none of the 72 price-neutral CP-SAT re-choices.
+- `expected`: output `0390ec65…`, profile {1:2572, 2:326, 3:430, 4:194, 5:56, 8:8}, widths
+  {4:80, 5:32, 7:54, 8:122, 9:216} (width 3778). Against p6n the delta is {1:+32, 2:−32, 3:−16, 4:+16}, width −16.
+
+## Checks rerun on every rebuild (`reproduce_promo.py`)
+- `build_promotion.py`: input pin; each old frame matches; each new entrance strictly contains the old one; the
+  profile and widths are recomputed from the chains, including target end climbs; output pins.
+- `promo_controls.py`: the honest word passes #645's independent `audit_local.py` (exact forward and dual endpoint
+  frames, entrances, cones). For p6n-k4, 11 mutants are rejected at pinned sites (the count is pinned in `LOCAL-PINS-p6n-k4.json`):
+  - entrance outside the first gate frame;
+  - raised gate missing, once per promoted group;
+  - entrance reverted, so the profile does not match;
+  - ungrouped promotion;
+  - a recipe gate whose old frame is wrong;
+  - a recipe entry that is not a promotion;
+  - a tampered input word (the constructor's own `__main__` must refuse it at the input pin);
+  - a scalar tamper on a raised gate.
+- The per-end layer-end controls (`../layers_p6n/layer_end_controls.py`, Q6Reviewer-signed): 95 rejected.
+- PR635's native chain: transport audit (all columns, native frames), ledgers, local replay (192-bit payload),
+  wrappers and phases, with the canonical word, local programs and Clifford recipes pinned (`LOCAL-PINS-p6n-k4.json`).
+
+## Search (not run by the rebuild)
+`make_recipe.py` writes the recipe from BlockInvert's CP-SAT solution (`prom.py` with `exactframe2.py`, using MinCutSel's
+chain model). These promotions were priced negative before (MinCutSel #3, under a fixed-window arc-flow packer). Under
+near-ideal packing (G44Pack's dissolve/gapmerge) they price positive; the strict replay confirms the gain.
diff --git a/research/gauge44-leaver8/PROOF-NOTE-SW4.md b/research/gauge44-leaver8/PROOF-NOTE-SW4.md
new file mode 100644
index 0000000000..a064cc54cc
--- /dev/null
+++ b/research/gauge44-leaver8/PROOF-NOTE-SW4.md
@@ -0,0 +1,44 @@
+# PROOF-NOTE-SW4: read-set exchange on four entering-copy pairs
+
+Construction by BRoute (`construction/sw4/`, with the author's notes in `construction/sw4/NOTES.md`). Driver:
+`construction/sw4/reproduce_sw4.py`.
+
+## The move
+In P6k4 (`0390ec65…`; research/gauge44-promo-p6sw applied the same exchange to P6k3 `a38bb414…`), each of four entering packet copies h is written first as h = E_h + r: copy gate add(h, r, 1)
+from a non-target face register r, with E_h being h's entering content. The pairs are (h, r) =
+(461, 25), (581, 89), (591, 415), (603, 431). For each pair the read sets of h and r are exchanged in phase B:
+- every post-copy target read add(t, h, c) becomes add(t, r, c), and t's entrance pre-read add(t, h, −c) (taken
+  while h = E_h) is deleted;
+- every target read add(t, r, c) becomes add(t, h, c), with a pre-read add(t, h, −c) inserted after h's last existing
+  pre-read and before h's copy gate.
+
+Since h − r = E_h after the copy, each target's value is unchanged at the end of B. The builder checks this for every
+register mod p (p = 2147483629). Moved and inserted gates take the plain join of their operands' current frames.
+Every other B gate and every early-cleanup tail keeps span(old frame + current operand frames). Targets must stay
+inside u_t^⊥, and tails and ends must contain the current frame. start_extra, helper_final, cleanup and the helper
+numbering are unchanged.
+
+## Effect
+Output `d232183f…`. Width 3778 is unchanged. The profile goes from {1:2572, 2:326, 3:430, 4:194, 5:56, 8:8} to
+{1:2548, 2:342, 3:438, 4:186, 5:56, 8:8}, a delta of {1:−24, 2:+16, 3:+8, 4:−8}, the same as on P6k3. The four
+exchanges are additive. The fourth promotion group (659, 661–663; gates B420–431) commutes exactly with the exchange:
+there is no index or register overlap, and SW4Reviewer checked that applying the k3→k4 frame and start differences
+to f35a852b gives d232183f. Ideal κ +3.271e-7 over P6k4.
+
+## Checks rerun on every rebuild
+- `build_sw4.py` (standard library only): the input sha pin; the 16 explicit moves of `SW4-RECIPE-P6k4.json`; B-end
+  state exactness mod p; frame caps, tails and ends; the output sha, profile and W. It also runs 4 controls, all of
+  which must hold, each at the exact site pinned in the recipe's `rejection_expected` (all three keys N1, N2 and N3 are required):
+  - C0: the identity recipe reproduces the input B and early_cleanup byte for byte;
+  - N1: h2r without deleting the pre-read is rejected by exactness, with changed B-end rows exactly {168, 171};
+  - N2: a partial exchange (one read only) is rejected by the frame cap, first at ('cap', B1192, register 169), 10 violations;
+  - N3: an inserted pre-read with the wrong sign is rejected by exactness, with changed rows exactly {129, 130, 169, 170}.
+- The per-end layer-end controls (`../layers_p6n/layer_end_controls.py`, Q6Reviewer-signed): 95 rejected.
+- PR635's native chain, with the canonical word, local programs and Clifford recipes pinned (`LOCAL-PINS-sw4-P6k4.json`).
+  The native transport audit re-checks every column and native frame of the exchanged word.
+
+## Scope of the search (BRoute)
+The search was exhaustive within the single-pair family only. NP has 107 copy pairs, and 54 of them have movable
+reads. Over those, every nonempty subset of one pair's movable reads gives 602 candidates: 564 are frame-illegal, and
+the 38 legal ones are all full single-pair exchanges, of which exactly these 4 are positive. Cross-pair combinations
+of partial moves were not enumerated.
diff --git a/research/gauge44-leaver8/README.md b/research/gauge44-leaver8/README.md
new file mode 100644
index 0000000000..48f987a99f
--- /dev/null
+++ b/research/gauge44-leaver8/README.md
@@ -0,0 +1,225 @@
+# Gauge44 without K-triangles, with earlier jp8 layers, the p6n ends, entrance promotions, a read-set exchange, #741's frames, a joint exchange, a triangle-hybrid B rewrite, no-helper mutable-leaver cells and PR589's bit supplier: conditional κ = 0.001671387264390146
+
+Under the retained all-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1–H5 interfaces (as in #645), and the PR589 bit supplier,
+
+$$
+T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad
+\kappa=\frac{1671387264390146}{10^{18}}=0.001671387264390146.
+$$
+
+**The construction is icekylinx's [#645](https://github.com/CrocSwap/integer-mult-bounds/pull/645) (`research/gauge44-global`).** This package builds the research/gauge44-barch construction (items 1–8) and then rebuilds its word around **no-helper mutable-leaver cells** (item 9):
+1. **No-triangle word (PartialK).** #645's gauge44 chain is run with **none** of the four (p,−1) K-triangles, so there are R = 504 helpers. In the six K-blocks {0,1,2,11,12,13}, the completion priority is extended by the 6-row list `construction/notri/PRIO6.json`. Every block then pairs at rank 4, giving **56** rank-four cold ends instead of 44. `construction/notri/reproduce_notri.py` rebuilds this word from a #645 `reproduce.py --until word` output. It uses PartialK's generalisations of #645's and PR635's constructors (`cgx.py`, `port_stage_x.py`, `cold44x.py`; each differs from its original only in the documented parameters). It pins:
+   - the pairing ranks [4]*14, inside `cold44x.py` and again in the driver;
+   - the word (`3e99ba77…`);
+   - the canonical word, the local programs and the Clifford recipes.
+   `--control-g44` instead rebuilds #645's own gauge44 word (`78c7aada…`) with the same scripts.
+2. **Layers on the no-triangle word (G44Stack).** `construction/layers_np/reproduce_np.py` applies to the no-triangle regroup word (`864ff4a1…`):
+   - research/gauge44-layered's six pivot swaps, mapped to the 504-helper numbering (`PIVOT-SWAP-NP.json`, swap word `beb3579f…`);
+   - the greedy HPE (46, `HPE-RECIPE-NP.json`);
+   - the exact cold44 (same 56 ends);
+   - the entering ends s4 (566/567/578/579 at U24) and x30 (608/610/543/555 at U30), plus BlockCombine's b6 and q4 dim-8 cold ends (`COLD-LAYERS-RECIPE-NP.json.gz`). p123 is negative on this base and dropped; j3 is dead.
+   The layered word is pinned (`a9de804f…`): profile `{1:2534, 2:346, 3:458, 4:178, 5:56, 8:8}`, width 3800. The signed research/gauge44-layered files `construction/layers/build_pivot_swap.py` and `construction/layers/layer_end_controls.py` are used unchanged, and the latter must reject exactly 59 controls. The global code is research/gauge44-layered's (spot-width rule): SPEC `width_spot_helpers` [270,282,294,306] and `pivot_swap` → `construction/layers_np/PIVOT-SWAP-NP.json`, giving spot widths [9,9,8,8].
+3. **p6n ends (NoTriReopen).** `construction/layers_p6n/reproduce_p6n.py` applies `COLD-LAYERS-RECIPE-P6N.json.gz` to the NP swapped HPE word with PR635's unchanged `build_cold_end.apply`. That is NP's cold-layer recipe plus six b-type dim-8 cold ends: [512,513], [311,510] and [522,327], which rebuild p123's lane as clean pairs. The result is the p6n word (`34b683fa…`): profile `{1:2540, 2:358, 3:446, 4:178, 5:56, 8:8}`, width 3794. The per-end layer-end controls (`construction/layers_p6n/layer_end_controls.py`, the variant Q6Reviewer signed for research/gauge44-pq6) must reject exactly 95 mutants. See `PROOF-NOTE-P6N.md`.
+4. **Entrance promotions (BlockInvert).** `construction/promo/reproduce_promo.py --base p6n --k p6n-k4` applies the minimal recipe `PROMO-RECIPE-p6n-k4.json` to the p6n word with BlockInvert's deterministic constructor `build_promotion.py`. The recipe promotes the 16 entering helpers 627, 629–631, 635, 637–639, 651, 653–655, 659 and 661–663 (four E4 kernel groups) from E4 to E5, the time-reverse dual of end deepening. It re-chooses the frames of the gates affected. Only frame annotations and start frames move; the scalar program is unchanged. The promoted word is pinned (`0390ec65…`): profile `{1:2572, 2:326, 3:430, 4:194, 5:56, 8:8}`, widths `{4:80, 5:32, 7:54, 8:122, 9:216}`, width 3778. BlockInvert's `promo_controls.py` runs #645's independent `audit_local.py` on the honest word and must reject 11 recipe- and word-level mutants at pinned sites. The per-end layer-end controls (95) and the native chain then run with pins. The recipe is minimal: 48 entry-gate frame raises and no other frame re-choices. See `PROOF-NOTE-PROMO.md`.
+5. **Read-set exchange (BRoute).** `construction/sw4/reproduce_sw4.py` runs BRoute's standard-library builder `build_sw4.py` with `SW4-RECIPE-P6k4.json`, 16 explicit moves, on the promoted word (`0390ec65…`). For the entering-copy pairs (h, r) = (461,25), (581,89), (591,415) and (603,431), the phase-B target read sets of h and its face register r are exchanged. The entrance pre-reads are deleted or inserted so that every register's value at the end of B is unchanged; the builder checks this mod p. Frames are repaired monotonically, and the width is unchanged. The SW4 word is pinned (`d232183f…`): profile `{1:2548, 2:342, 3:438, 4:186, 5:56, 8:8}`, width 3778. Four controls (C0 identity, N1 kept pre-read, N2 partial exchange, N3 wrong sign) must all hold, each at its exact rejection site pinned in the recipe. The per-end layer-end controls (95) and the native chain then run with pins. See `PROOF-NOTE-SW4.md` and `construction/sw4/NOTES.md`.
+6. **#741's eight B frames (chafreaky).** `construction/frames/reproduce_frames.py` applies chafreaky's [#741](https://github.com/CrocSwap/integer-mult-bounds/pull/741) frame recipe, `FRAME-RECIPE-sw4.json`, byte-identical to #741's. Ported by CompetitorMine, it raises eight B-gate frames with the scalar program unchanged, giving #741's word `e7804702…`. It runs 3 pin controls, #741's 10 focused native controls, 95 layer-end controls and the native chain with pins.
+7. **Joint exchange X4 (JointXF).** `construction/jx/reproduce_jx.py` runs JointXF's standard-library builder `build_jx.py` with `RECIPE-X4.json` on #741's word (step 6's output). It makes four disjoint instances of the read-set exchange, each over two target-sharing copy pairs: (448,472), (458,592), (470,604) and (482,614). The moved reads keep their stored frames, and #741's frames are included. All edits are explicit, and B-segment exactness is checked by Fraction replay. The final word is pinned (`1e1d99ba…`): profile `{1:2548, 2:338, 3:430, 4:194, 5:56, 8:8}`, width 3778. All seven pinned controls are rerun; C1 reproduces #741's word. See `PROOF-NOTE-FRAMES-X4.md`.
+8. **Triangle-hybrid B rewrite (NewBArch).** `construction/barch/reproduce_barch.py` runs NewBArch's standard-library builder `build_tri.py` with `RECIPE-U8.json` on the X4 word (step 7's output). Eight disjoint slots receive a width-neutral B-delivery rewrite: an entering copy donates into a halves-copy so that one target read gets X+H, with holder restores and entrance pre-reads. The U8 word is pinned (`090fd574…`): profile `{1:2548, 2:338, 3:446, 4:162, 5:72, 8:8}`, width 3778. All 38 pinned controls are rerun (identity, the recipe word passing audit_local, and four audit_local-rejected mutants, globally and per slot). See `PROOF-NOTE-BARCH.md`.
+9. **Leaver cells, re-stacked (LeaverSAT, LeaverSAT2).** `construction/leaver/reproduce_leaver.py --id k8` replaces the no-triangle word's construction with all eight all-K cells (01±, 23±, 45±, 67±). Each cell is LeaverSAT's 21-gate circuit, which uses the face-event leaver sources as mutable intermediates (R = 480, cell word `58e14a02…`). `construction/leaver/reproduce_leaver_chain.py --id k8` then re-applies items 2–8 with the signed builders unchanged and LeaverSAT's re-indexed recipes: swap, HPE, cold44, NP, p6n, 16 promotions, the re-indexed X4 exchange (the identity on this word) and 6 U8-style hybrids (`c836d892…`). It adds LeaverSAT2's exact global frame re-optimisation (`FRAME-RECIPE-LV-k8.json`), which gives the final word **`db2c7cfb…`**. Every intermediate word, control count and native pin is pinned (`LEAVER-PINS-k8.json`, `CHAIN-PINS-k8.json`). The per-word layer-end controls are the Q6Reviewer-signed `layer_end_controls_leaver.py` v2 (95 each), on the p6n, promoted, jx and hybrid words (`LEC-REASON-PINS-STACK-k8.json`) and on the re-framed final word (`LEC-REASON-PINS-k8.json`); its declared not-applicable sites are sha-proven identities or unbuildable mutants, each replaced by a same-class substitute that must be rejected. Items 5 and 6 don't apply on this word: the sw4 copies are dropped, and none of #741's frames survive. Items 1–8 remain in the package as the construction record of research/gauge44-barch. See `PROOF-NOTE-LEAVER.md`.
+10. **Owner map (chafreaky's [#685](https://github.com/CrocSwap/integer-mult-bounds/pull/685), adapted by G44Pack).** The map is G44Pack3's K8c8, from its pattern-flow LNS (`pflns`) on the R = 480 k8 word. Its lineage is the #685/#741 map (chafreaky) via G44Pack's relabel and rewidth, followed by G44Pack3's LNS. It was admitted with this package's own code (NEWWORD discovery, `freeze_spec.py`, strict) at κ 0.001671387264390146. Only PLAN and OWNERS change. These are search inputs only; no verifier reads them.
+11. **Expected values.** `data/SPEC.json` is re-derived by #645's discovery → `code/freeze_spec.py` → strict chain.
+
+- **κ = 0.001671387264390146** (conservative 0.001671387261540186). That is +0.4298% over research/gauge44-leaver (k5 cells, κ 0.001664233607446043; same chain on five cells, FO_c1 map) and +0.5672% over [#942](https://github.com/CrocSwap/integer-mult-bounds/pull/942) (κ 0.001661960547713947) and +1.3279% over #645, +0.9174% over research/gauge44-notri-layered (0.001656193765416678) and +0.7701% over research/gauge44-promo (0.00165861362787227) and +0.7273% over research/gauge44-promo-p6 (0.001659319032684569) and +0.7075% over research/gauge44-promo-p6sw (0.001659645685315104) and +0.5869% over research/gauge44-frames-x (0.001661634653669567) and +0.5679% over research/gauge44-barch (0.001661948695165034) and +0.6131% over [#741](https://github.com/CrocSwap/integer-mult-bounds/pull/741) (chafreaky, κ 0.001661202643272239) and +0.6654% over [#685](https://github.com/CrocSwap/integer-mult-bounds/pull/685) (chafreaky, κ 0.001660339298410333). The complex side certifies 0.001674185476674086429846 and PR589's bit supplier gives 0.001733427039589844234749, so **the complex side binds**. Under PR543 the bit side would cap κ at 0.001651096360425895 (`PROOF-NOTE-BIT.md`).
+- **Evidence.** This package's own code admitted G44Pack3's K8c8 map (NEWWORD discovery → `freeze_spec.py` → strict): `verify_global.py` passes (`PASS_GAUGE44_STRICT_GLOBAL_REPLAY`, κ 0.001671387264390146) against G44Pack3's k8 locals, with SPEC `width_spot_helpers` [258,270,282,294] and `pivot_swap` → `construction/leaver/PIVOT-SWAP-k8.json`. It equals G44Pack3's own strict κ for K8c8. `RESULT.json` is that replay's `REPLAY.json`, converted to LF. The locals rebuilt by `reproduce_leaver_chain.py --id k8` match G44Pack3's strict locals byte for byte in every file except CLIFFORD-REVIEW and SCALAR-FRAME-AUDIT. Those two differ only in their `seconds` field, and the comparison normalises only that field (canonical `d1bf3c6f…`, programs `683f8323…`/`2d184e4d…`, Clifford `e3bfdfa2…`, pinned in `CHAIN-PINS-k8.json`). For this package, `data/SPEC.json` and a fresh `verify_global.py` replay on locals rebuilt by the two drivers are the binding record.
+- **Independent price.** `independent/GAUGE44-INDEPENDENT-PRICE.json` is regenerated on this package's `data/PLAN.json` with the ported `independent/price_profile.py`: `PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK`, κ equal to the strict replay.
+- **Independent local audit.** `evidence/layers/LOCAL-AUDIT-LAYERED.json` is #645's `independent/audit_local.py`, run with `--main` on the final leaver word (content `db2c7cfb…`): `PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES`, 192 entering helpers, 78 low ends, 48 cold ends, 704 checked columns. Rerunning it reproduces the receipt except `elapsed_seconds` and, across zlib versions, `compressed_sha256`.
+- **Historical #645 files (PR543-based, 492 helpers).** These are #645's files, retained unchanged and **not** updated for this package: `LOCAL-VALIDATION.json`, `CONSTRUCTION.md`, `hosting/`, `evidence/` (except `evidence/layers/`), the rest of `independent/`, `construction/reproduce.py` and its inputs, and `code/prepare_global.py`. They describe #645's word, owner map, PR543 supplier and κ 0.001649483702558979. `code/prepare_global.py` is #645's one-shot owner-map preparer, hard-wired to #645's parent plan and R = 492. No verifier imports it. This package's PLAN/OWNERS are frozen search output, and the strict replay checks them. `construction/reproduce.py` is still used for its `--until word` shadow and hamming inputs; its 492-word output is then superseded by `construction/notri/`. `construction/layers/reproduce_layers.py` is research/gauge44-layered's driver for the 492-helper layered word, shipped unchanged as signed; it is not used here.
+- **Construction and code files** by committed LF SHA-256:
+  - `construction/notri/reproduce_notri.py` 90148c2a0422b4f92164298a283de73d413ab3d4cb7151a0e6b643a37ea025a8 (no-triangle driver)
+  - `construction/notri/cgx.py` 3da039d4184097c14802f9dbf972520d5b807671196f5e47a2247bc9f29bb418 (PartialK's generalised construct_gauge_xcentre.py)
+  - `construction/notri/port_stage_x.py` 38310744d054e393ea35e996047cddeb2d212141aaaaa4b07f7a4663b11db8e7 (PartialK's generalised build_port_stage.py)
+  - `construction/notri/cold44x.py` f0bc3500efb2c839a0f8cb03dbb9ea0a54f1dfc71ef81e5373b3d638ac5b8296 (PartialK's generalised build_gauge_cold44.py plus the PAIRING_RANKS pin)
+  - `construction/notri/PRIO6.json` de0412511b0dd1af13e9717bc791126ac0e91c569b5391fd6c70268083045d15 (completion priority)
+  - `construction/layers_np/reproduce_np.py` 1a304144a250d00d14154692ba522365b036777cf2b6fac466095e8ba733c16c (NP layer driver)
+  - `construction/layers_np/PIVOT-SWAP-NP.json` d49b8d316da1cbdaf995dd0e8314d3c67cc9cd4d5902e9d85ccb907be645bef5 (layer input)
+  - `construction/layers_np/HPE-RECIPE-NP.json` 43900139f618bdc06b8319098fb8dccaf4fc315b43ef7c067ca2cd778cdba2c1 (layer input)
+  - `construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz` 3164cfb71baaeba4ac43427bc14075a225fc3a32ecd9341e58aa52c03a4ee2c0 (layer input)
+  - `construction/layers/build_pivot_swap.py` 8e8bced88be2e592ded40929499bac385ca92fcc1fa59183c22229dbf34093b8 (signed, unchanged)
+  - `construction/layers/layer_end_controls.py` 7829187bfc8f909948d5250e0ec00f02c89f5fe98306a3ed88daee36cb3c92ef (signed, unchanged)
+  - `construction/layers/reproduce_layers.py` 435699f6f79c6c7fb8d6cc5a8382576d6ac88747583a975ff671e45440b93c4e (signed, unchanged, unused here)
+  - `construction/promo/reproduce_promo.py` f979be666c3f5cf57e342a8427863c0b35b67ca4d3be495ac386f6870deb2026 (promotion driver)
+  - `construction/promo/build_promotion.py` 9c9e2001b8d68bbe934d136026276fe97bd9bf6f94d4d78441fc28e14aca4daf (BlockInvert's constructor)
+  - `construction/promo/promo_controls.py` 786c51f84b53698c2c833083506c4432c30eb0ed3b71e7dbe458a70c7413c372 (BlockInvert's controls)
+  - `construction/promo/make_recipe.py` ba9e4fdc0c1be7f6a150a5a50909911257a1a8c7cc5d03d61f541178fc07c122 (discovery-side recipe writer (search, not run))
+  - `construction/promo/PROMO-RECIPE-p6n-k4.json` fa6065d142646f7ab1f268912ce0cf5a1a6cd33c3994ff96bd6e204cf16b3e90 (minimal recipe)
+  - `construction/promo/LOCAL-PINS-p6n-k4.json` a92bb02266596956bd53e9c86e8bbcc6639c92b4a4a248a1521f8eb79228271f (native pins)
+  - `construction/layers_p6n/reproduce_p6n.py` aa7d6bcbed05aa1c689437c07a26e5c95be3c700c0c1fb7bcf91c432a88436ca (p6n driver)
+  - `construction/layers_p6n/layer_end_controls.py` fc58c5699ba6191c1163a3041241f6f0b619626c4462cd99bcf88210bac9e81e (per-end controls (Q6Reviewer-signed variant))
+  - `construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz` 17e218a17e47c58fe2cde775ab2314d3d84030a61327b7f13da61cae3b374ad4 (p6n recipe)
+  - `construction/layers_p6n/P6N-SPEC.json` 132a59635077d6afe80f99964a6935fce1dc2ece6587d74209c6f9c60025c8f1 (p6n end spec)
+  - `construction/sw4/reproduce_sw4.py` 3d082e0cc576fb1b4fb9e5dd11d63bab697c8a8626e2837813cd00d100b1aeac (SW4 driver)
+  - `construction/sw4/build_sw4.py` 9a295f3d534594a6b1326d8a6647e947670d1c6fbc92f37f5169661fde4c8f66 (BRoute's builder (stdlib))
+  - `construction/sw4/SW4-RECIPE-P6k4.json` fa58d0ffc95d10b7453daefe4b34404a52895f94126ef973e92e92106cd615fa (16-move recipe with pinned rejection sites)
+  - `construction/sw4/LOCAL-PINS-sw4-P6k4.json` 3c06bf68b28ff125a6a2372bb70cefd76fb9fe1333438cd34dfb5b617cd70327 (native pins)
+  - `construction/frames/reproduce_frames.py` dc39ada9a2eb387310be181f3cea5dbd4b538632a888cd7372ece5e38a771832 (#741 frames driver)
+  - `construction/frames/build_frames.py` 200847a7e8b3125cbeea0765dad67650e0bf83d32b66d72ba4977e99b8ee8eeb (#741's builder (chafreaky; ported))
+  - `construction/frames/frame_controls.py` 477de854ec9184a2c73d6ac3857a9d0cbd6bc04b71d10a105e7344434b492a77 (#741's controls (chafreaky; ported))
+  - `construction/frames/FRAME-RECIPE-sw4.json` a2c7ca4d44671386d05974e2627645b42bbb7da7a35cefff6e9fa158b6ac8473 (#741's recipe, byte-identical)
+  - `construction/frames/LOCAL-PINS-frames-sw4.json` bc416b8f6443d59c715fb358c4d70fa27eae2d306388ffe0e2a303f60d929f7f (native pins)
+  - `construction/jx/reproduce_jx.py` 5c7afebb4eb7fcdeb7e971cfbc457cf071850e2da21c3c71295efdd453c2399c (X4 driver)
+  - `construction/jx/build_jx.py` 3cc7550b0c24bb54e245c6f7f16de489fd7844721fbb64aac628f38f43887916 (JointXF's builder (stdlib))
+  - `construction/jx/RECIPE-X4.json` 9d42c6b38e8124f5ffe15da56c260a7fba7260626bf3c5f8cbd93aa4a71ceadd (explicit recipe with pinned controls)
+  - `construction/jx/LOCAL-PINS-jx-X4.json` 95c5114c8e937c2737a1b9f9da97303f2e5e129d39e6dfcc4010e99bfdb9c974 (native pins)
+  - `construction/barch/reproduce_barch.py` 19bc970aa6af25ab0e7fa96fb65c64dd0c5243976d8f2cb733cba839155482c1 (U8 driver)
+  - `construction/barch/build_tri.py` 0fba65b31c2fd71864c291358bb0ad8d5f7e1be07e21df23f0ae73d7b966002e (NewBArch's builder (stdlib))
+  - `construction/barch/run_controls.py` 42639bf62bf57795e3ea615c1944c67efed00f28591333daeb3139bf63d04476 (NewBArch's controls (38 outcomes))
+  - `construction/barch/RECIPE-U8.json` 292f0e9f82824c4111728cf4de929bf6e43320fbbdc77658aae9681906b0d652 (explicit recipe)
+  - `construction/barch/LOCAL-PINS-barch-U8.json` 2d16f99e1f71fd66378f5f767cf4cfa2a58264919a95074c7b31029f39a3c9f5 (control set and native pins)
+  - `construction/leaver/reproduce_leaver.py` 831bfdf2247b5d864b74c3b2b6a475718053d48570851d48bd1c5471d410ee30 (cell driver)
+  - `construction/leaver/cgx_leaver.py` 3af491c63dd96204a7c36006c7e419c2e5ce77e5bc453ccd2495c1e41f83f87c (cell constructor)
+  - `construction/leaver/reproduce_leaver_chain.py` 2bc3fc3f32e0f957a0731b79254c553ca48fc6d4d47c4f99d6cd31e1901d85b5 (chain driver)
+  - `construction/leaver/layer_end_controls_leaver.py` 4ba676f1ea326b739a64c3477f64eeb295f8151514f78fa7e62b71e4373a6206 (per-word reason re-pins and declared not-applicable sites, v2 (Q6Reviewer-signed))
+  - `construction/leaver/build_frames_lv.py` 2eb80d612aa59a7bd8b04a122045e3bd2b83a21954e3164943cd20cf6050a21b (LeaverSAT2's frame builder)
+  The global code is research/gauge44-layered's, unchanged: assemble 4c270a99, assembly_controls e4c0f782, audit_allcold a87d7f48, bind 1d39bcc7, witness 779c5172. The bit-supplier code is research/gauge44-bit589's, unchanged: verify_global 16bd5e54, bit_supplier_controls e6d33fb6, price_profile d2f548ad.
+- **Line endings.** These files had CRLF in the admitted trees and are committed as LF only (`crlf.replace(b'\r\n', b'\n') == lf`, no lone `\r`):
+  - `construction/jx/build_jx.py`: CRLF 775c2ae60eec9abc…, committed (LF) 3cc7550b0c24bb54…
+  - `construction/jx/RECIPE-X4.json`: CRLF 228079b304358500…, committed (LF) 9d42c6b38e8124f5…
+  - `construction/barch/build_tri.py`: CRLF 2432372f148a4d34…, committed (LF) 0fba65b31c2fd718…
+  - `construction/barch/run_controls.py`: CRLF 18e1f5953403784f…, committed (LF) 42639bf62bf57795…
+  - `construction/barch/RECIPE-U8.json`: CRLF 3e97088ad641eb6e…, committed (LF) 292f0e9f82824c41…
+  - `data/SPEC.json`: CRLF b2515d29d54e5027…, committed (LF) 1208c7c3ae84c158…
+  - `RESULT.json`: CRLF 454c25d5b0cd7df7…, committed (LF) 72bf797ce995ff61…
+  - `independent/GAUGE44-INDEPENDENT-PRICE.json`: CRLF 0b8482888e64327f…, committed (LF) 6e222b252f345344…
+  - `evidence/layers/LOCAL-AUDIT-LAYERED.json`: CRLF 6b63fc2bbea96cb5…, committed (LF) a596d7262374a023…
+
+
+Clean-clone verification, from the repository root (Python 3.11+, assertions on; prepare the pinned #635 supplier as in the #645 section below):
+
+```sh
+python -B research/gauge44-leaver8/verify_manifest.py
+python -B research/gauge44-leaver8/construction/reproduce.py \
+  --main . --pr635 /tmp/gauge44-pr635 --out /tmp/notri-base --until word
+python -B research/gauge44-leaver8/construction/notri/reproduce_notri.py \
+  --main . --pr635 /tmp/gauge44-pr635 --word-dir /tmp/notri-base --out /tmp/notri-word --word-only
+python -B research/gauge44-leaver8/construction/layers_np/reproduce_np.py \
+  --main . --pr635 /tmp/gauge44-pr635 --notri-dir /tmp/notri-word --hamming /tmp/notri-base/hamming --out /tmp/notri-np
+python -B research/gauge44-leaver8/construction/layers_p6n/reproduce_p6n.py \
+  --main . --pr635 /tmp/gauge44-pr635 --np-dir /tmp/notri-np --out /tmp/p6n
+python -B research/gauge44-leaver8/construction/promo/reproduce_promo.py \
+  --main . --pr635 /tmp/gauge44-pr635 --base p6n --base-dir /tmp/p6n --k p6n-k4 --out /tmp/promo
+python -B research/gauge44-leaver8/construction/sw4/reproduce_sw4.py \
+  --main . --pr635 /tmp/gauge44-pr635 --promo-dir /tmp/promo --recipe P6k4 --out /tmp/sw4
+python -B research/gauge44-leaver8/construction/frames/reproduce_frames.py \
+  --main . --pr635 /tmp/gauge44-pr635 --sw4-dir /tmp/sw4 --out /tmp/frames
+python -B research/gauge44-leaver8/construction/jx/reproduce_jx.py \
+  --main . --pr635 /tmp/gauge44-pr635 --frames-dir /tmp/frames --out /tmp/x4
+python -B research/gauge44-leaver8/construction/leaver/reproduce_leaver.py \
+  --main . --pr635 /tmp/gauge44-pr635 --word-dir /tmp/notri-base --id k8 --out /tmp/lv --word-only
+python -B research/gauge44-leaver8/construction/leaver/reproduce_leaver_chain.py \
+  --main . --pr635 /tmp/gauge44-pr635 --leaver-dir /tmp/lv --hamming /tmp/notri-base/hamming --id k8 --out /tmp/lvc
+python -B research/gauge44-leaver8/independent/audit_local.py \
+  --word /tmp/lvc/frames/FULL-WORD.json.gz --main . --output /tmp/lvc-audit.json
+python -B research/gauge44-leaver8/verify_global.py \
+  --main . --local /tmp/lvc/local --work /tmp/lvc-global
+# kappa 0.001671387264390146
+```
+
+Optional control: `reproduce_notri.py ... --control-g44 --out /tmp/notri-ctl` rebuilds #645's gauge44 word `78c7aada…`.
+
+## Predecessor: #645's README (unchanged below; paths read `research/gauge44-global`)
+
+### Gauge44: conditional κ = 0.001649483702558979
+
+New contributions by **icekylinx**, with **OpenAI GPT-6 Astra** assistance.
+Local review and packaging used OpenAI Codex. Original notices and Apache-2.0 licenses are retained.
+
+Under the retained all-size compiler, common-label/mutable-source realization,
+whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit
+H1–H5 interfaces,
+
+$$
+T(n)=O\!\left(n(\log n)^{1-\kappa_{645}}\right),\qquad
+\kappa_{645}=\frac{1649483702558979}{10^{18}}=0.001649483702558979
+$$
+
+(This is #645's own κ. **This package's κ is the one at the top of this README.**)
+
+The certified complex saving is `0.001652208994368411824947`. The unchanged
+[#543](https://github.com/CrocSwap/integer-mult-bounds/pull/543) bit supplier gives
+`0.001653826988146798944268`, so the complex side binds. The conservative complex
+model separately certifies κ `0.001649483699681650`.
+
+### Construction
+
+This replaces the local supplier and all 72 owner assignments of pinned
+[#635](https://github.com/CrocSwap/integer-mult-bounds/pull/635). Source/copy exchanges
+at equal rank-one frames alter the factory's arbitrary-helper-input propagation.
+An invertible completion of the retired rows and source-carried coordinate totals
+then expose 44 rank-four cold endpoints. Exact input premixes, low-frame tails
+and a recomputed full inverse realize them.
+
+| Per-invocation quantity | Complete #635 JP8 | Gauge44 |
+| --- | ---: | ---: |
+| Source / target ports | 112 / 112 | 112 / 112 |
+| Helpers | 492 | 492 |
+| Rank-four cold endpoints | 22 | 44 |
+| Helper residual width | 3,894 | 3,794 |
+| Paid local rank mass | 5,750 | 5,650 |
+
+The new paid local profile is `{1:2514, 2:404, 3:448, 4:160, 5:56, 8:8}`.
+The explicit whole-family assignment covers 35,424 helper roles on 7,168 live
+and 7,670 physical families. It retains the rank deficit 2,560 and charges every
+idle remainder. Exact integer majorization certificates justify the owner
+updates; the resulting map is a coordinate fixed point, with no claim of joint
+optimality.
+
+The assembled κ is 0.809306% above #635. `data/FRONTIER.json` records Pro's dated
+comparison snapshot; it is not a live ranking of community results.
+
+### Proof and evidence
+
+- `CONSTRUCTION.md`: exact cold-space calculation, dyadic realization and attribution.
+- `hosting/PROOF.md`: capacity, exchange and majorization arguments.
+- `independent/CENTRE-GUARD-REVIEW.md`: ordered center-frame interface and source carriers.
+- `data/SPEC.json`, `evidence/ASSEMBLY.json`: strict component moments and outer parameters.
+- `evidence/audit/`: actual controller, physical charts and finite invoice.
+- `construction/INPUTS.json`, `data/UPSTREAM-PINS.json`: inherited input hashes.
+- `MANIFEST.json`, `SOURCES.json`, `LOCAL-VALIDATION.json`: submitted bytes, provenance and local checks.
+
+Original Pro run receipts are retained as evidence; their raw logs remain in
+the original archive outside the submission. Fresh replay writes new logs to
+the selected output directory.
+
+### Incremental reproduction
+
+Use Python 3.11 or newer with assertions enabled. The required replay uses only
+the standard library. The optional historical seed-discovery optimizer is not
+part of admission.
+
+Prepare the pinned #635 supplier in a separate directory (the main dependencies
+are already present in this repository):
+
+```sh
+git fetch https://github.com/CrocSwap/integer-mult-bounds.git a6895a69f8ad98ab45777b03e9e6f48888c39f6f
+mkdir -p /tmp/gauge44-pr635
+git archive FETCH_HEAD research/complex-571-cold14-st2 | tar -x -C /tmp/gauge44-pr635
+```
+
+From the repository root, with fresh output directories:
+
+```sh
+python -B research/gauge44-global/verify_manifest.py
+python -B research/gauge44-global/construction/reproduce.py \
+  --main . --pr635 /tmp/gauge44-pr635 \
+  --out /tmp/gauge44-local --until phases
+python -B research/gauge44-global/verify_global.py \
+  --main . --local /tmp/gauge44-local/local --work /tmp/gauge44-global
+```
+
+The dedicated workflow also runs the independent literal-word audit, exact owner
+reproduction, preserved-assertion comparison and independent pricing on Python
+3.11 and 3.14. `hosting/README.md` and `independent/README.md` give those commands.
+No ancestral full replay, optimizer search or PDF generation is required.
+
+The result remains a finite conditional witness. It does not establish an
+unconditional multiplication theorem or a complete Lean formalization.
diff --git a/research/gauge44-leaver8/RESULT.json b/research/gauge44-leaver8/RESULT.json
new file mode 100644
index 0000000000..0fcf674173
--- /dev/null
+++ b/research/gauge44-leaver8/RESULT.json
@@ -0,0 +1,86 @@
+{
+  "status": "PASS_GAUGE44_STRICT_GLOBAL_REPLAY",
+  "kappa": "835693632195073/500000000000000000",
+  "kappa_decimal": "0.001671387264390146",
+  "complex_lower": "837092738337043214923/500000000000000000000000",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_supplier": {
+    "pr": 589,
+    "repository": "CrocSwap/integer-mult-bounds",
+    "commit": "a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46",
+    "merged_as": "b3eb785ac5b4b1ca2beea0f80db078a505626a90",
+    "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "git_blob_sha1": "e293ddc557742637f9f679f083a1a282d87b1b13",
+    "word": {
+      "v": 111,
+      "decoder_constant": 63,
+      "copy_ranks": [
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7
+      ]
+    },
+    "derived_deficit": 10272,
+    "deficit_formula": "T(2Kv-L*cst), L=9 T=32 K=4 M=64",
+    "replay_scope": "Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit."
+  },
+  "gain_over_pr635_percent": "2.147956935446134609375167880411478290542019964980136631080981857753585",
+  "spec_sha256": "b2515d29d54e5027ee225a93c338894eca6827d192d4841b95d35a280dcfd3e1",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 1.094,
+      "exit_code": 0,
+      "log_sha256": "3aea2a4b68e7aaeadd9ffef649be0d25e2dff1535d9a61bffeaf6d92e55ba6a8"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.313,
+      "exit_code": 0,
+      "log_sha256": "78a081673d6b4fde10a86e6f767d53648b868d1f0cac2441d12951434ad7341b"
+    },
+    {
+      "name": "emit",
+      "seconds": 2.39,
+      "exit_code": 0,
+      "log_sha256": "29618e94d8e948fa870924e3c3aa0a9caa969a8229cc355982eef5b78ee04320"
+    },
+    {
+      "name": "audit",
+      "seconds": 11.922,
+      "exit_code": 0,
+      "log_sha256": "e38ba1bd8f371365952700a803b9abd81714b521eed22512b914384f8d8f4a94"
+    },
+    {
+      "name": "invoice",
+      "seconds": 0.75,
+      "exit_code": 0,
+      "log_sha256": "96d5d16d99625e0c33e67255b1351233cb14b032b67642c080ee1a65581ce6a9"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.297,
+      "exit_code": 0,
+      "log_sha256": "d0ea37c7097b628ef7d466a7851d7a4c62f5eb10e86bb678ca9e50a17039d352"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 0.344,
+      "exit_code": 0,
+      "log_sha256": "34527ddfe1e53bec71dc5759eb9a26417be6d4e93e76cbf80575d9bafebd876b"
+    },
+    {
+      "name": "bit-supplier-controls",
+      "seconds": 0.547,
+      "exit_code": 0,
+      "log_sha256": "c648542cd6dddbb154af7d02a41aaed1025603d9a4ab54f7c249d2b683e22249"
+    }
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; this bit composition is unreviewed. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/gauge44-leaver8/SOURCES.json b/research/gauge44-leaver8/SOURCES.json
new file mode 100644
index 0000000000..0d69845db9
--- /dev/null
+++ b/research/gauge44-leaver8/SOURCES.json
@@ -0,0 +1,36 @@
+{
+  "contributor": "icekylinx",
+  "research_assistance": "OpenAI GPT-6 Astra",
+  "local_review_and_packaging": "OpenAI Codex",
+  "original_archive": {
+    "filename": "integer_mult_round23_gauge44_delta.zip",
+    "sha256": "40a20a120f51cbed3c9ae4017603be74a9e9332ad4068bd914bf3e81bf8be6b4",
+    "manifest_sha256": "ffa23eb668ad558ebb5601470fc1997a9fb8cea0e188aa3c5d61318be9000603"
+  },
+  "upstream_main": "17ce0c79b7b51c2634b439ea5a2b754f09909693",
+  "construction_parent": {
+    "pr": 635,
+    "commit": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f"
+  },
+  "bit_supplier_pr": 589,
+  "packaging_changes": [
+    "Omit original run logs; retain their original receipts as historical evidence.",
+    "Use repository paths and dollar-delimited Markdown mathematics.",
+    "Add manifest verification, incremental CI and local validation record.",
+    "Trim trailing whitespace in four Python files; complete ASTs are unchanged. Refresh the corresponding constructor input hash.",
+    "research/gauge44-bit589: PR589 bit supplier (G44Stack port, Bit589Reviewer SOUND-WITH-FIXES), G44Pack dz1 owner map, re-derived SPEC, LF line endings, regenerated MANIFEST.",
+    "research/gauge44-leaver: research/gauge44-barch tree plus construction/leaver (k5 cells, chain, frames); G44Pack3 FO_c1 owner map, re-derived SPEC, regenerated independent price receipt, RESULT.json = strict REPLAY, LF, regenerated MANIFEST.",
+    "research/gauge44-leaver8: research/gauge44-leaver tree with the k8 cell set (all eight cells, R = 480) and its chain recipes (LeaverSAT/LeaverSAT2 pkg_k8), layer_end_controls_leaver v2 with declared not-applicable sites on all five stack words (replacing the final-word interim skip), CHAIN-PINS-k8; G44Pack3 K8c8 owner map, re-derived SPEC, regenerated independent price receipt and local audit, RESULT.json = strict REPLAY, LF, regenerated MANIFEST."
+  ],
+  "attribution": "Original notices and licenses retained. See NOTICE.md, UPSTREAM-NOTICE.md and CONSTRUCTION.md.",
+  "whitespace_only_python_files": [
+    "code/audit_allcold.py",
+    "code/bind_providers_portable.py",
+    "construction/construct_gauge_xcentre.py",
+    "independent/audit_local.py"
+  ],
+  "historical_bit_supplier_pr": 543,
+  "bit_supplier_note": "This package cites PR589 (inputs/PR589-EXPECTED.json, git blob e293ddc5…). PR543 is the supplier of #645's retained historical evidence (LOCAL-VALIDATION.json, independent/ audit files, hosting/, evidence/). RESULT.json is this package's strict replay.",
+  "owner_map": "G44Pack/G44Pack3: The map is G44Pack3's K8c8, from its pattern-flow LNS (`pflns`) on the R = 480 k8 word. Its lineage is the #685/#741 map (chafreaky) via G44Pack's relabel and rewidth, followed by G44Pack3's LNS. It was admitted with this package's own code (NEWWORD discovery, `freeze_spec.py`, strict) at κ 0.001671387264390146.",
+  "construction_changes": "PartialK: no-triangle gauge44 word (R=504, PRIO6, ranks [4]*14); G44Stack: layers on it (pivot swaps, s4, x30, b6, q4); LeaverSAT: no-helper mutable-leaver cells and re-stacked recipes, LeaverSAT2: frame re-optimisation (construction/leaver); NewBArch: triangle-hybrid B rewrite U8 (construction/barch); chafreaky #741: eight B frames (construction/frames, ported by CompetitorMine) and the owner map; JointXF: joint exchange X4 (construction/jx); BRoute: read-set exchange SW4 (construction/sw4); NoTriReopen: p6n ends (construction/layers_p6n); BlockInvert: entrance promotions E4->E5 (construction/promo, minimal recipe p6n-k4); drivers construction/notri/reproduce_notri.py, construction/layers_np/reproduce_np.py, construction/promo/reproduce_promo.py"
+}
diff --git a/research/gauge44-leaver8/UPSTREAM-NOTICE.md b/research/gauge44-leaver8/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..ebc24a0168
--- /dev/null
+++ b/research/gauge44-leaver8/UPSTREAM-NOTICE.md
@@ -0,0 +1,34 @@
+# Attribution and scope
+
+Four verified provider types are offered to every call: PR571's prefix word with twelve multi-cut cold kernels (PR568's unchanged constructor), the same word with forty width-five entrance promotions (PR569's unchanged frame constructor) before those kernels, PR575's plain joint-prefix provider, and PR568's eight-cold provider. A window MILP with an exact per-pattern model chooses the dispatch and a literal owner map. PR583's six source-bound kernel frame coalescences (its unchanged constructor and negative controls) are applied to every PR571-prefix provider word (ck and atm3), followed by two further coalescences that each first move one addition past two commuting additions (package code/build_gate_moves.py, extending PR583's constructor); a final hyperplane_end step (package code/build_hpe.py) then runs 46 single-gate cleanups h -= p right after part B at the dim-8 join U of their registers, so 46 width-8 entering helpers per call end at U with width 7; each such gate commutes with every earlier cleanup gate on its registers (for 8 of them the partner's one earlier gate x -= p only reads p), and the reordered program is replayed exactly. A window MILP (exact windows, RINS around an LP vertex) gives the dispatch ck 45 / atm3 21 / jp8 6 and the literal owner map.
+
+Pinned external sources (unchanged; `verify.py` checks their manifests and every file it uses):
+- PR568 (`research/complex-multicold`, commit `71c99ac935a33bb7b59a1b4a7af8725a939b0b90`).
+- PR571 (`research/structural-gain`, commit `b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3`).
+- PR569 (`research/larger-gain`, commit `897213a855b7fb8a1b8b0e552a2f5c42e6c1b326`).
+- PR575 (`research/complex-joint-prefix`, commit `eac6f7e378ab622dac50a2fd4b7ef6eab014de44`).
+- PR583 (`research/kernel-frame-coalescing`, commit `89be768f0157f5a3d8e4db69cf1748768605eac9`).
+
+Provider construction is described as typed steps in `data/SPEC.json` (`build`); `verify.py` runs only allowlisted step types with their paired omission audits and checks every input and output content hash. `code/` holds the spec-driven global admission scripts adapted from PR571's `frontier-composition/global-code/` (OpenAI Codex assisted, Apache-2.0): every expected value is read from `data/SPEC.json` and compared only after independent recomputation. `code/generated_identity.py` and `code/generated_identity_controls.py`, and the decompressed-content artifact identities in the bind, audit, invoice, assembly and phase-timing scripts, are taken unchanged from PR586 by chafreaky (`research/promoted-kernel-coalescing`, commit `4846fee5b06af770e9b3a10c36200f673d656725`, OpenAI Codex assisted, Apache-2.0), including its proof-content and reference/metadata mutation controls; the normalization of descriptive width metadata after frame changes follows the same PR.
+
+In PR601, the owner map was nominated by a HiGHS window MILP (adapted from PR569's `global/nominate_width7.py`) with lazy cross-time Hall cuts; this package's re-solved map is described below. Neither is an admission dependency.
+
+DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. (The PR601 package this one starts from states: "Prepared by Claude Code (Anthropic) research agents.") Apache-2.0 applies; LICENSE is included. All notices, licenses, source pins and AI disclosures of the pinned sources and their ancestry are retained in those packages and are not replaced by this notice. All inherited conditional assumptions remain conditional.
+
+**This package (complex-571-cold14, DreamingOfClouds).** It starts from PR601 (jeremykothe2, `research/complex-571-hpem46`, commit `529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550`). Everything above is kept unchanged except the following:
+- every provider chain (ck, atm3, jp8) gains the typed step `cold_end` (`code/build_cold_end.py`, `code/cold_end_controls.py`; recipes `data/recipes/*-cold_end.json.gz`);
+- the generalised native chain and the global admission scripts accept cold helpers that end below FULL (with `0:U` wrappers), a refactored exact cleanup, and check the wrapper order;
+- `data/PLAN.json` / `data/OWNERS.json.gz` (dispatch and literal owner map) come from a relocate/swap/ejection-chain/provider-flip annealing search started from PR601's map, refined by an exact pattern-restricted owner model (CP-SAT) with a literal edge-colouring expansion (not an admission dependency);
+- `data/SPEC.json` holds the expected values, recorded by a discovery run and then checked by a strict run.
+
+The cold-end construction (a row-plus-column cone condition for low-frame ends, a rank-0 dirt-spread premix and multi-gate lower-frame cleanup) builds on PR591 / PR592 / PR593 / PR601 (jeremykothe2) and our PR599 (Lean: multi-gate and cold hyperplane-end tails). DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. Build on this at your own risk.
+
+**This package (complex-571-cold14-b3, jeremykothe2).** It is PR604's `complex-571-cold14` (DreamingOfClouds) with ColdBeyond's second cold end per block (two new `cold_end` A-gate primitives, `PROOF-NOTE.md`), ColdSupply's E1 entering pair and reviewed controls, a free dispatch (jp8 ×60, atm3 ×12) and a literal owner map from an exact per-time-Hall window MIP. All other construction, code, controls and proofs are PR604's and earlier contributors', unchanged.
+
+**This package (complex-571-cold14-k492).** It is complex-571-cold14-b3 with these changes:
+- **K-triangle base words.** The leaver-read K-triangle skeleton atom and its read schedule (`data/TRI-SCHEDULE.json`) are by AtomScout, a Claude Code research agent. `code/construct_k_triangle.py` is PR531's `code/construct_504.py` (icekylinx, OpenAI Codex / GPT assisted, Apache-2.0; pinned source `direct_delivery`) extended with that atom.
+- **Ported chains.** The PR604/B3 chains are ported stage by stage onto the K-triangle words by `code/build_port_stage.py` (Port480, a Claude Code research agent). `code/build_frame_regroup.py` extends PR583's `build_frames.py` (chafreaky).
+- **Helper count R.** The generalisation of the global scripts to the provider helper count R is by GlobalR (a Claude Code research agent), with AtomReviewer's fixes (PROOF-NOTE-R.md).
+- **Owner map.** The owner map, the cold_end recipes on the K-triangle words and the package assembly are by Stack492, Port480 and ColdBeyond (Claude Code research agents).
+
+Build on this at your own risk.
diff --git a/research/gauge44-leaver8/code/assemble.py b/research/gauge44-leaver8/code/assemble.py
new file mode 100644
index 0000000000..8cee90b50e
--- /dev/null
+++ b/research/gauge44-leaver8/code/assemble.py
@@ -0,0 +1,241 @@
+"""Gauge44 complete global admission with the retained native exact-complex moment.
+
+Prepared with OpenAI Codex assistance. The rational engines and outer
+constraints are retained from PR547/PR548 and their preserved ancestry.
+The bit operator is the cited unchanged PR589 supplier (PR555's punctured
+R439 word, v = 111, decoder constant 63, two A-section transports), shipped
+as inputs/PR589-EXPECTED.json and pinned by git blob id. Its rank-mass
+deficit is derived from the word's parameters, T(2Kv - L*cst) at nine
+stages (PR545/PR555 rank-mass identity), not hard-coded. The complex owner
+and invoice inputs must be freshly emitted by the packaged physical replay.
+All conservative admission guards and conservative moment/outer witnesses run
+before the PR559 native-complex correction. The bit surcharge is retained.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from decimal import Decimal, localcontext
+import argparse,json,hashlib,importlib.util,os,sys
+from collections import Counter
+assert __debug__, 'Assertions required'
+P=Path(sys.argv[1] if __name__=='__main__' else os.environ['GAIN_PR564_SOURCE']).resolve()
+read=lambda p:json.loads(p.read_text())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+hash_ok=lambda x:isinstance(x,str) and len(x)==64 and all(t in '0123456789abcdef'for t in x)
+digest=lambda x:hashlib.sha256(json.dumps(x,separators=(',',':')).encode()).hexdigest()
+def load(n):
+ s=importlib.util.spec_from_file_location(n,P/'engines'/(n+'.py'));m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,B,A=[load(n)for n in ('moment','base_two_moment','outer')]
+def dec(x):
+ with localcontext()as ctx:ctx.prec=70;return str(Decimal(x.numerator)/Decimal(x.denominator))
+from witness import DISPATCH,CALL_ORDER,COUNTS,PIDS,X,DISCOVER,pin,SPOT,spot_widths
+# Cited bit supplier: PR589's tune/EXPECTED.json (merged on main as research/e8-bit-p111-tuned/tune/EXPECTED.json).
+BIT_PATH=Path(__file__).resolve().parents[1]/'inputs/PR589-EXPECTED.json'
+BIT_BLOB='e293ddc557742637f9f679f083a1a282d87b1b13'
+# Nine-stage bit template (PR463/PR510 chain, 32 replicas): L stages, T replicas, K=(L-1)//2 pairs, moment width M=1+7L.
+BIT_L,BIT_T=9,32;BIT_K=(BIT_L-1)//2;BIT_M=1+7*BIT_L
+def git_blob(data):return hashlib.sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest()
+def load_bit(data):
+ """The pinned supplier record: its full record (word parameters) and its nine-stage price."""
+ assert git_blob(data)==BIT_BLOB,'bit supplier blob pin'
+ return json.loads(data)
+def bit_deficit(word,live):
+ """Rank-mass deficit M*live - mass = T(2Kv - L*cst) of a v-port bit word with decoder constant cst (PR545/PR555).
+ cst is the sum of the retained totals' COPY ranks and live = 2KvT data wires; both are cross-checked here, and the
+ caller checks the result against the priced profile, so neither v nor cst is free."""
+ v,cst,ranks=word['v'],word['decoder_constant'],word['copy_ranks']
+ assert type(v)is int and type(cst)is int and all(type(r)is int and 0<r<=8 for r in ranks)
+ assert len(ranks)==word['retained_totals']==BIT_L and cst==sum(ranks)
+ assert live==2*BIT_K*v*BIT_T
+ d=BIT_T*(2*BIT_K*v-BIT_L*cst);assert d>0;return d
+
+
+def assemble(owner,invoice,owner_sha,invoice_sha):
+ # These are admission receipts, not optional collections of successful rows.
+ # Require both orientations and every finite check before pricing anything.
+ assert owner['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE'
+ assert invoice['status']=='PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE'
+ assert all(hash_ok(x)for x in (owner_sha,invoice_sha,owner['template_sha256'],owner['controller_audit_sha256'],invoice['parent_template_sha256']))
+ checks={'local_primitive_bound','logical','router','literal','mass','precision','tape','row','halving'}
+ assert set(invoice['strict_checks'])==checks
+ assert all(invoice['strict_checks'][name] is True for name in checks)
+ assert set(invoice['providers'])==set(PIDS)
+ assert invoice['provider_counts']==COUNTS
+ assert owner['all_live_owners_per_call_distinct'] is True
+ # R (helpers per provider word) is read from the invoice and must be shared by every provider; n=2v+R.
+ R=invoice['helpers'];assert type(R) is int and R>0 and all(p['helpers']==R for p in invoice['providers'].values())
+ assert owner['owners_per_call']==2*112+R and owner['actual_helper_owner_charts']==owner['hosted_residuals']==72*R==pin('expected.hosted_residuals',owner['hosted_residuals'])
+ pin('expected.rank_mass',owner['rank_mass'])
+ pin('expected.actual_73column_sigmas',owner['actual_73column_sigmas']);pin('expected.cross_replica_helper_roles',owner['cross_replica_helper_roles'])
+ pin('expected.idle_remainders',owner['explicit_idle_remainder_children'])
+ assert invoice['complete_invocation_sweeps']==invoice['bridge_sweeps']==72
+ assert invoice['live']==owner['live'] and invoice['physical']==owner['physical']
+ assert invoice['centres']==8
+ assert invoice['physical_stock_identity']==dict(data_and_owner_families=7168,local_helpers=R,private_centres=8,coefficient_work=2)
+ assert sum(invoice['physical_stock_identity'].values())==invoice['physical']
+ assert invoice['controller_audit_sha256']==owner['controller_audit_sha256']
+ for pid,p in invoice['providers'].items():
+  assert set(p['local'])=={'forward','backward'}
+  assert p['helpers']==R and p['centres']==8 and p['n']==2*112+R and p['v']==112 and p['h']==9
+  K='providers.'+pid+'.';pin(K+'entering',p['entering_helpers']);pin(K+'entrance',p['entrance_rank'])
+  pin(K+'inventory',p['width_inventory'])
+  assert all(type(w) is int and 0<w<=9 for w in p['widths'])
+  assert Counter(p['widths'])==Counter({int(r):n for r,n in p['width_inventory'].items()})
+  assert sum(p['widths'])==9*R-p['entrance_rank']-p['terminal_codimension'] and len(p['widths'])==R   # HPE: widths |final|-|start|
+  pin(K+'width_digest',digest(p['widths']));assert tuple(p['widths'][h]for h in SPOT)==spot_widths()
+  pin(K+'expected_profile',p['paid_profile'])
+  assert p['children']==sum(p['paid_profile'].values())
+  pin(K+'program_hashes',p['program_hashes'])
+  for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json'):
+   assert hash_ok(p['artifacts'][name]) and p['artifacts'][name]==owner['source_artifacts']['providers/'+pid+'/'+name]
+   if name in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):pin(K+'artifacts.'+name,p['artifacts'][name])
+  pin(K+'artifact_semantic_sha256',p['semantic_artifact_sha256'])
+  pin(K+'complete_contract',{k:v for k,v in p.items()if k!='artifacts'})
+  assert owner['provider_artifact_semantic_sha256'][pid]==p['semantic_artifact_sha256']
+  pin(K+'semantic_phase_sha256',p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'])
+  assert owner['provider_phase_semantic_sha256'][pid]==invoice['provider_phase_semantic_sha256'][pid]==p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']
+  for name in ('forward','backward'):
+   z=p['local'][name];pinned=pin(K+'expected_local.'+name,{k:z[k]for k in('events','macros','real_component_primitives','prefix_l1','coefficient_work_primitive_count')});primitives=pinned['real_component_primitives'];coefficient_work=pinned['coefficient_work_primitive_count']
+   assert z['all_dirty_helper_columns_restored'] is True and z['private_centres_and_coefficient_work_cleared'] is True
+   assert z['all_exact_columns']==2*112+R and z['dirty_helper_columns']==R
+   assert z['events']==pinned['events'] and z['macros']==pinned['macros']
+   assert z['real_component_primitives']==primitives and z['coefficient_work_primitive_count']==coefficient_work
+   assert z['pre_wrappers']==z['post_wrappers']==p['entering_helpers']+p.get('cold_hyperplane_ended_helpers',0);pin(K+'wrappers',z['pre_wrappers'])   # COLD-HPE
+   assert 0<z['prefix_bits']<=192 and 0<Q(z['prefix_l1'])<2**192
+   peak=Q(z['prefix_l1']);assert z['prefix_bits']==peak.numerator.bit_length()-peak.denominator.bit_length()+1
+   assert peak==Q(pinned['prefix_l1'])
+  assert p['compiler']==64*74**3
+  assert p['local_adapters']==16*(max(z['macros']for z in p['local'].values())+p['children']+2*112+R+8)+64*73
+  assert p['local_primitive_bound']==max(z['real_component_primitives']for z in p['local'].values())+p['local_adapters']*p['compiler']
+ calls=invoice['selected_calls'];assert len(calls)==72
+ assert [(c['stage'],c['replica'])for c in calls]==CALL_ORDER
+ assert {(c['stage'],c['replica']) for c in calls}=={(s,r) for s in range(9) for r in range(8)}
+ for c in calls:
+  pid=DISPATCH[c['stage'],c['replica']]
+  assert c['provider_id']==pid
+  # The retained nine-stage recipe alternates its two reflected shears.
+  assert c['orientation']==('forward' if c['stage']%2==0 else 'backward')
+  p=invoice['providers'][pid];z=p['local'][c['orientation']]
+  assert c['program_sha256']==p['program_hashes'][c['orientation']]
+  for name in ('events','macros','real_component_primitives','coefficient_work_primitive_count','pre_wrappers','post_wrappers'):
+   assert c[name]==z[name]
+  assert c['entering_helpers']==p['entering_helpers'] and c['entrance_rank']==p['entrance_rank']
+ assert invoice['selected_real_component_primitives']==sum(c['real_component_primitives'] for c in calls)
+ assert invoice['selected_coefficient_work_primitive_count']==sum(c['coefficient_work_primitive_count'] for c in calls)
+ assert invoice['selected_scalar_macros']==sum(c['macros'] for c in calls)==sum(invoice['providers'][c['provider_id']]['local'][c['orientation']]['macros'] for c in calls)
+ assert invoice['factors_per_wrapper']==144
+ assert invoice['wrapper_elementary_factors_charged']==sum(c['pre_wrappers']+c['post_wrappers'] for c in calls)*144
+ paid=Counter()
+ for c in calls:paid.update({int(r):n for r,n in invoice['providers'][c['provider_id']]['paid_profile'].items()})
+ assert dict(paid)=={int(r):n for r,n in invoice['selected_local_paid_profile'].items()}
+ idle=Counter({int(r):n for r,n in owner['paid_profile'].items()});idle.subtract(paid);assert all(n>=0 for n in idle.values())
+ idle=+idle;assert sum(idle.values())==owner['explicit_idle_remainder_children']
+ pin('expected.idle_remainder_profile',{str(r):n for r,n in sorted(idle.items())})
+ paid.update(idle)
+ assert dict(paid)=={int(r):n for r,n in owner['paid_profile'].items()}
+ assert invoice['compiler']==64*74**3
+ assert invoice['local_adapters']==max(p['local_adapters']for p in invoice['providers'].values())
+ assert invoice['local_primitive_bound']==max(p['local_primitive_bound']for p in invoice['providers'].values())
+ # Recount the retained dedicated-bank envelope independently. Its geometry
+ # stays fixed, while every local primitive and wrapper comes from the actual
+ # selected provider/orientation sums above.
+ parent_live,parent_physical,parent_idle=11704,12218,16128
+ parent_banks,rem=divmod(parent_live-2*112*4*8,9);assert rem==0 and parent_physical==parent_live+parent_banks+8+2   # parent R0=504 dedicated helpers per stage bank
+ assert owner['source_idle_children_charged']==parent_idle
+ bridges,shifts=2*112*72,4*112*8;moves=2*shifts
+ nonlocal_items=(4*112*8*9+2*112*8*9+2*72*R+parent_idle+9*parent_banks+bridges+shifts+moves+parent_live+parent_physical+invoice['wrapper_elementary_factors_charged'])
+ outside=8*nonlocal_items+64*73
+ pervertex=(invoice['selected_real_component_primitives']+bridges+shifts+moves+parent_live+(72*invoice['local_adapters']+outside)*invoice['compiler']+64*parent_physical)
+ rebased=pervertex+65*(invoice['physical']-parent_physical)+(invoice['live']-parent_live)
+ assert invoice['unhosted_pervertex']==pervertex and invoice['hosted_rebased_pervertex']==rebased
+ used=max(pervertex,rebased)
+ prior=invoice['retained_prior_overcharge']
+ if prior is not None:
+  assert hash_ok(prior['sha256']) and type(prior['previous_pervertex_allowance']) is int and prior['previous_pervertex_allowance']>0
+  assert prior['added_complete_new_pervertex']==pervertex
+  assert prior['policy']=='Retain old allowance and add entire fresh mixed recount.'
+  used=max(used,prior['previous_pervertex_allowance']+pervertex)
+ assert invoice['conservative_pervertex_used']==used
+ finite=invoice['finite']
+ assert 0<finite['physical_row_coefficient']<finite['retained_row_coefficient']==20161
+ assert 0<finite['required_C0_bits']<finite['C0_exponent']==210000
+ assert finite['G_exponent']==30000 and finite['E_exponent']==100000
+ assert finite['halving_integer_inequality']==[5329,4608]
+ assert 0<invoice['global_prefix_bits']<=invoice['charged_prefix_bits']==512
+ assert invoice['row_prefix_extra']==1024
+ assert invoice['global_prefix_bits']==max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())+37+72+72+4
+ group=2**(36*36)
+ for j in range(1,37):group*=2**(2*j)-1
+ stock=group*invoice['physical'];streamed_mass=group*owner['rank_mass']
+ logical=group*used+64;router=invoice['compiler']*(logical+1)*(stock+1)**2
+ literal=2*2**30000*stock**2+8*streamed_mass+4*stock+4+32*73
+ total_mass=streamed_mass+2**100000
+ assert finite['physical_stock_bits']==stock.bit_length() and finite['router_bits']==router.bit_length() and finite['literal_bits']==literal.bit_length()
+ assert finite['physical_row_coefficient']==2*stock.bit_length()+9909+252+1024
+ assert finite['required_C0_bits']==(32*73*total_mass*total_mass).bit_length()
+ actual_checks=dict(local_primitive_bound=invoice['local_primitive_bound']<2**48,logical=logical<2**6050,router=router<2**30000,literal=literal<2**100000,mass=total_mass<2**100001,precision=32*73*total_mass*total_mass<2**210000,tape=2*total_mass+18<2**210000,row=finite['physical_row_coefficient']<20161,halving=73*73>2*48*48)
+ assert actual_checks==invoice['strict_checks'] and all(actual_checks.values())
+ bit_record=load_bit(BIT_PATH.read_bytes())
+ bit=bit_record['nine']
+ assert 'nine-stage' in bit['pipeline'] and '32 replicas' in bit['pipeline']
+ c=Q(bit['bit_lower'])
+ bit_D=bit_deficit(bit_record['word'],bit['bit']['live'])
+ H={int(r):n for r,n in owner['paid_profile'].items()};pin('expected.global_profile',owner['paid_profile'])
+ # Claimed lower endpoints come from the spec; discovery derives them with the same certified moment engine.
+ # Either way they are verified below (accepted at b, rejected at b+1e-24).
+ if DISCOVER:b=Q(M.certify(H,73,owner['live'],False)['lower']);conservative_b=Q(M.certify(H,73,owner['live'],True)['lower'])
+ else:b=Q(X['complex_lower']);conservative_b=Q(X['conservative_complex_lower'])
+ assert owner['template_sha256']==invoice['template_sha256'] and owner_sha==invoice['owner_audit_sha256']
+ pin('expected.live',owner['live']);pin('expected.physical',owner['physical']);assert owner['deficit']==2560
+ assert owner['banked_residuals']==0
+ def check_moment(side,h,m,W,lower,deficit,bad):
+  assert m*W-sum(r*n for r,n in h.items())==deficit and m*m>2*max(h)**2
+  rows=[]
+  for z,accept in [(lower,True),(lower+Q(1,10**24),False)]:
+   l,u=M.moment(h,m,W,z,bad);ll,uu=B.moment(m,W,list(h.items()),z)
+   if bad:
+    fl,fu=B.moment(m,W,[(1,32*m*m*sum(h.values()))],z);ll+=fl/10**16;uu+=fu/10**16
+   assert (u<1 and uu<1)if accept else(l>1 and ll>1)
+   rows.append(dict(side=side,surcharge=bad,endpoint=str(z),accept=accept,mercator=[str(l-1),str(u-1)],base_two=[str(ll-1),str(uu-1)]))
+  return rows
+ bitH={int(r):n for r,n in bit['profile'].items()}
+ assert BIT_M==64 and sum(r*n for r,n in bitH.items())==bit['bit']['rank_mass']
+ bit_moments=check_moment('bit',bitH,BIT_M,bit['bit']['live'],c,bit_D,True)
+ conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,2560,True)
+ assert bit['bit']['two_level_coefficient_bits']<bit['bit']['charged_two_level_coefficient_bits']==512 and bit['bit']['row_coefficient']<20161
+ def outer_witness(bb):
+  eta=beta=Q(1,10**24);s=min(c,(1-beta)*bb)-Q(1,10**27);assert 0<s<c and s<(1-beta)*bb
+  chain=[Q(384599,10**10)];cuts=[]
+  for _ in range(7):
+   old=chain[-1];a=(1-s)*s+s*old;gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+   ceil=lambda x:-(-x.numerator//x.denominator);cut=max(ceil(36/gap**2),ceil(2*(4+512)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+512)
+   cuts.append(dict(exponent=str(a),gap=str(gap),cutoff_log2=str(cut)));chain.append(a)
+  q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin*10**18;k=Q((ticks.numerator-1)//ticks.denominator,10**18)
+  bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}
+  outer=A.assembly(chain[-1],bb,bridge,k,eta=eta,beta=beta);assert len(outer['strict_constraints'])==47 and all(v>0 for v in outer['strict_constraints'].values())
+  controls=[]
+  for name,kk,ee,be in [('next_grid',k+Q(1,10**18),eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]:
+   try:A.assembly(chain[-1],bb,bridge,kk,eta=ee,beta=be)
+   except AssertionError:controls.append(name)
+   else:raise AssertionError(name)
+  return k,cuts,outer,controls
+ conservative_k,conservative_cuts,conservative_outer,conservative_controls=outer_witness(conservative_b)
+ pin('expected.conservative_kappa_decimal',dec(conservative_k))
+ # Only after every conservative supplier/admission/outer check succeeds is
+ # the reviewed native exact-complex recurrence selected. Bit charge stays.
+ native_moments=check_moment('complex',H,73,owner['live'],b,2560,False)
+ k,cuts,outer,controls=outer_witness(b)
+ pin('expected.kappa_decimal',dec(k))
+ assert M.moment(H,73,owner['live'],b,True)[0]>1
+ assert M.moment(bitH,64,bit['bit']['live'],c+Q(1,10**24),False)[1]<1
+ model_controls=['native_complex_endpoint_rejected_with_old_surcharge','omitting_bit_surcharge_would_fail_next_endpoint_rejection']
+ moments=bit_moments+native_moments
+ input_hashes={'owner_audit':owner_sha,'fresh_invoice':invoice_sha,'package:inputs/PR589-EXPECTED.json':sha(BIT_PATH)}
+ input_hashes.update({'engines/'+name+'.py':sha(P/'engines'/(name+'.py'))for name in ('moment','base_two_moment','outer')})
+ return dict(status='PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY',kappa=str(k),kappa_decimal=dec(k),complex_lower=str(b),complex_decimal=dec(b),bit_lower=str(c),bit_decimal=dec(c),binding='complex',gain_over_pr635_percent=dec(100*(k/Q(X['gain_baseline_kappa'])-1)),complex_profile=H,provider_counts=invoice['provider_counts'],surcharge_model={'complex':False,'bit':True},conservative_complex_lower=str(conservative_b),conservative_complex_decimal=dec(conservative_b),conservative_kappa=str(conservative_k),conservative_kappa_decimal=dec(conservative_k),conservative_moments=conservative_moments,conservative_bootstrap=conservative_cuts,conservative_outer={n:str(v)for n,v in conservative_outer['strict_constraints'].items()},conservative_controls=conservative_controls,model_controls=model_controls,native_correction_gain=dec(k-conservative_k),template_sha256=owner['template_sha256'],input_sha256=input_hashes,bit_supplier=dict(pr=589,repository='CrocSwap/integer-mult-bounds',commit='a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46',merged_as='b3eb785ac5b4b1ca2beea0f80db078a505626a90',path='research/e8-bit-p111-tuned/tune/EXPECTED.json',git_blob_sha1=BIT_BLOB,word=dict(v=bit_record['word']['v'],decoder_constant=bit_record['word']['decoder_constant'],copy_ranks=bit_record['word']['copy_ranks']),derived_deficit=bit_D,deficit_formula='T(2Kv-L*cst), L=%d T=%d K=%d M=%d'%(BIT_L,BIT_T,BIT_K,BIT_M),replay_scope='Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit.'),moments=moments,bootstrap=cuts,outer={n:str(v)for n,v in outer['strict_constraints'].items()},controls=controls,scope='Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; this bit composition is unreviewed. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification.')
+if __name__=='__main__':
+ import sys
+ package,C,out=map(Path,sys.argv[1:4]);assert package.resolve()==P and not out.exists()
+ owner_path=C/'audit/OWNERS-AND-PROFILE.json';invoice_path=C/'audit/PREFIX-AND-INVOICE.json'
+ owner,invoice=read(owner_path),read(invoice_path)
+ assert owner['template_sha256']==read(C/'hosted/HOSTED.json')['template_sha256']
+ r=assemble(owner,invoice,sha(owner_path),sha(invoice_path));out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],r['kappa_decimal'])
diff --git a/research/gauge44-leaver8/code/assembly_controls.py b/research/gauge44-leaver8/code/assembly_controls.py
new file mode 100644
index 0000000000..93bca1ce6f
--- /dev/null
+++ b/research/gauge44-leaver8/code/assembly_controls.py
@@ -0,0 +1,260 @@
+"""Independent admission controls for the N-provider native-complex assembly (per-provider controls).
+
+Prepared with OpenAI Codex assistance; Apache-2.0. Mutation receipts are
+rebound to their new owner digest, so unrelated stale hashes cannot conceal
+an incomplete width, provider, orientation, paid-profile or finite check.
+The fresh physical replay remains a separate prerequisite.
+"""
+import argparse
+import copy
+import itertools
+import math
+import hashlib
+import json
+import os
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+
+assert __debug__, 'Assertions required'
+P = Path(__file__).resolve().parent
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+digest = lambda x: hashlib.sha256(json.dumps(x, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+
+
+def verify(owner_path, invoice_path, source_package):
+    os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve())
+    from assemble import assemble
+    owner = json.loads(owner_path.read_text())
+    invoice = json.loads(invoice_path.read_text())
+    baseline = assemble(owner, invoice, sha(owner_path), sha(invoice_path))
+
+    def empty_maps(o, i):
+        i['strict_checks'] = {}
+        i['providers'] = {}
+
+    def understated_stock(o, i):
+        o['physical'] -= 1
+        i['physical'] -= 1
+        i['physical_stock_identity']['coefficient_work'] -= 1
+
+    def changed_profile(o, i):
+        o['paid_profile']['1'] += 2
+        o['paid_profile']['2'] -= 1
+
+    def wrong_orientation(o, i):
+        c = next(c for c in i['selected_calls'] if c['stage'] == 0)
+        c['orientation'] = 'backward'
+        p = i['providers'][c['provider_id']]
+        z = p['local']['backward']
+        c['program_sha256'] = p['program_hashes']['backward']
+        for name in ('events', 'macros', 'real_component_primitives',
+                     'coefficient_work_primitive_count', 'pre_wrappers', 'post_wrappers'):
+            c[name] = z[name]
+        i['selected_real_component_primitives'] = sum(c['real_component_primitives'] for c in i['selected_calls'])
+        i['selected_coefficient_work_primitive_count'] = sum(c['coefficient_work_primitive_count'] for c in i['selected_calls'])
+
+    def understated_prefix(o, i):
+        for p in i['providers'].values():
+            for z in p['local'].values():
+                z['prefix_bits'], z['prefix_l1'] = 1, '1'
+        i['global_prefix_bits'] = 1 + 37 + 72 + 72 + 4
+
+    def reordered_calls(o, i):
+        i['selected_calls'][0], i['selected_calls'][1] = i['selected_calls'][1], i['selected_calls'][0]
+
+    def no_cold_wrappers(o, i):
+        for p in i['providers'].values():
+            p['entering_helpers'] -= 4
+            for z in p['local'].values():z['pre_wrappers'] = z['post_wrappers'] = p['entering_helpers']
+        for c in i['selected_calls']:
+            c['entering_helpers'] = c['pre_wrappers'] = c['post_wrappers'] = i['providers'][c['provider_id']]['entering_helpers']
+        i['wrapper_elementary_factors_charged'] = sum(2*c['pre_wrappers'] for c in i['selected_calls'])*i['factors_per_wrapper']
+
+    controls = [
+        ('empty_certification_maps', empty_maps),
+        ('failed_invoice_status', lambda o, i: i.__setitem__('status', 'FAIL')),
+        ('nonboolean_precision_check', lambda o, i: i['strict_checks'].__setitem__('precision', 'true')),
+        ('wrong_owner_role_count', lambda o, i: o.__setitem__('actual_helper_owner_charts', o['actual_helper_owner_charts'] - 1)),
+        ('understated_physical_stock', understated_stock),
+        ('changed_profile_same_rank_mass', changed_profile),
+        ('insufficient_finite_C0', lambda o, i: i['finite'].__setitem__('required_C0_bits', 210001)),
+        ('missing_finite_check', lambda o, i: i['strict_checks'].pop('halving')),
+        ('wrong_reflected_orientation_selfconsistent_totals', wrong_orientation),
+        ('missing_selected_call', lambda o, i: i['selected_calls'].pop()),
+        ('wrong_selected_primitive_sum', lambda o, i: i.__setitem__('selected_real_component_primitives', i['selected_real_component_primitives'] - 1)),
+        ('wrong_selected_coefficient_work_sum', lambda o, i: i.__setitem__('selected_coefficient_work_primitive_count', i['selected_coefficient_work_primitive_count'] - 1)),
+        ('unpaid_wrapper_factors', lambda o, i: i.__setitem__('wrapper_elementary_factors_charged', i['wrapper_elementary_factors_charged'] - 144)),
+        ('wrong_global_compiler', lambda o, i: i.__setitem__('compiler', 1)),
+        ('wrong_global_adapter_maximum', lambda o, i: i.__setitem__('local_adapters', 1)),
+        ('understated_exact_prefix_and_global_sum', understated_prefix),
+        ('wrong_global_prefix_sum', lambda o, i: i.__setitem__('global_prefix_bits', 224)),
+        ('wrong_row_prefix_reserve', lambda o, i: i.__setitem__('row_prefix_extra', 0)),
+        ('wrong_parent_geometry_charge', lambda o, i: i.__setitem__('unhosted_pervertex', 1)),
+        ('wrong_rebased_geometry_charge', lambda o, i: i.__setitem__('hosted_rebased_pervertex', 1)),
+        ('wrong_complete_pervertex_envelope', lambda o, i: i.__setitem__('conservative_pervertex_used', 1)),
+        ('wrong_prior_added_complete_invoice', lambda o, i: i['retained_prior_overcharge'].__setitem__('added_complete_new_pervertex', 1)),
+        ('wrong_finite_router_bits', lambda o, i: i['finite'].__setitem__('router_bits', 1)),
+        ('wrong_finite_literal_bits', lambda o, i: i['finite'].__setitem__('literal_bits', 1)),
+        ('wrong_finite_physical_stock_bits', lambda o, i: i['finite'].__setitem__('physical_stock_bits', 1)),
+        ('wrong_finite_row_coefficient', lambda o, i: i['finite'].__setitem__('physical_row_coefficient', 1)),
+        ('reordered_complete_calls', reordered_calls),
+        ('understated_explicit_idle_remainders', lambda o, i: o.__setitem__('explicit_idle_remainder_children', o['explicit_idle_remainder_children']-1)),
+        ('understated_actual_chart_types', lambda o, i: o.__setitem__('actual_73column_sigmas', o['actual_73column_sigmas']-1)),
+        ('wrong_cross_replica_role_count', lambda o, i: o.__setitem__('cross_replica_helper_roles', o['cross_replica_helper_roles']-1)),
+        ('old_no_cold_wrapper_counts_selfconsistent', no_cold_wrappers),
+    ]
+
+    def resync(i, c):
+        p = i['providers'][c['provider_id']]
+        c['program_sha256'] = p['program_hashes'][c['orientation']]
+        c['entering_helpers'], c['entrance_rank'] = p['entering_helpers'], p['entrance_rank']
+        for name in ('events','macros','real_component_primitives','coefficient_work_primitive_count','pre_wrappers','post_wrappers'):
+            c[name] = p['local'][c['orientation']][name]
+
+    # Every provider gets the full per-provider control set, substituting a partner provider where needed.
+    for P in PIDS:
+        Qp = partner(P) if len(PIDS)>1 else '__unregistered__'
+        widths = invoice['providers'][P]['widths']
+
+        def forged_program_hash(o, i, P=P):
+            i['providers'][P]['program_hashes']['forward'] = '0' * 64
+            for c in i['selected_calls']:
+                if c['provider_id'] == P:
+                    c['program_sha256'] = '0' * 64
+
+        def wrong_selected_call(o, i, P=P):
+            c = next(c for c in i['selected_calls'] if c['provider_id'] == P)
+            d = next(d for d in i['selected_calls'] if d is not c and (d['provider_id'] != P or len(PIDS)==1) and (d['stage'] - c['stage']) % 2 == 0)
+            c['stage'], d['stage'], c['replica'], d['replica'] = d['stage'], c['stage'], d['replica'], c['replica']
+
+        def stale_program(o, i, P=P, Qp=Qp):
+            p = i['providers'][P]
+            p['program_hashes'] = copy.deepcopy(i['providers'][Qp]['program_hashes'])
+            for c in i['selected_calls']:
+                if c['provider_id'] == P:
+                    c['program_sha256'] = p['program_hashes'][c['orientation']]
+
+        def stale_profile(o, i, P=P, Qp=Qp):
+            p = i['providers'][P]
+            p['paid_profile'] = copy.deepcopy(i['providers'][Qp]['paid_profile'])
+            p['children'] = sum(p['paid_profile'].values())
+
+        def moved(o, i, P=P):
+            a = next(c for c in i['selected_calls'] if c['provider_id'] == P)
+            b = next(c for c in i['selected_calls'] if c['provider_id'] != P and c['orientation'] == a['orientation'])
+            a['provider_id'], b['provider_id'] = b['provider_id'], a['provider_id']
+            resync(i, a); resync(i, b)
+
+        def compensating(o, i, P=P, Qp=Qp):
+            # Two dishonest profiles that cancel exactly in the dispatch-weighted aggregate.
+            g = math.gcd(COUNTS[P], COUNTS[Qp]); dp, dq = COUNTS[Qp] // g, COUNTS[P] // g
+            p, q = i['providers'][P], i['providers'][Qp]
+            p['paid_profile']['1'] += dp; q['paid_profile']['1'] -= dq
+            p['children'] += dp; q['children'] -= dq
+
+        def forged_recipe(o, i, P=P):
+            name = 'CLIFFORD-RECIPES.json'
+            i['providers'][P]['artifacts'][name] = '0'*64
+            o['source_artifacts']['providers/'+P+'/'+name] = '0'*64
+
+        def forged_phase(o, i, P=P):
+            i['providers'][P]['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'] = '0'*64
+            o['provider_phase_semantic_sha256'][P] = i['provider_phase_semantic_sha256'][P] = '0'*64
+
+        controls += [
+            (P + ':missing_provider', lambda o, i, P=P: i['providers'].pop(P)),
+            (P + ':missing_backward_orientation', lambda o, i, P=P: i['providers'][P]['local'].pop('backward')),
+            (P + ':unpaid_scalar_primitive', lambda o, i, P=P: i['providers'][P]['local']['forward'].__setitem__('real_component_primitives', i['providers'][P]['local']['forward']['real_component_primitives'] - 1)),
+            (P + ':wrong_local_artifact_binding', lambda o, i, P=P: i['providers'][P]['artifacts'].__setitem__('LOCAL-PROGRAMS.json.gz', '0' * 64)),
+            (P + ':false_dirty_restoration', lambda o, i, P=P: i['providers'][P]['local']['backward'].__setitem__('all_dirty_helper_columns_restored', False)),
+            (P + ':wrong_declared_provider_count', lambda o, i, P=P: i['provider_counts'].__setitem__(P, i['provider_counts'][P] + 1)),
+            (P + ':wrong_local_compiler', lambda o, i, P=P: i['providers'][P].__setitem__('compiler', 1)),
+            (P + ':wrong_local_adapter_charge', lambda o, i, P=P: i['providers'][P].__setitem__('local_adapters', 1)),
+            (P + ':wrong_local_primitive_bound', lambda o, i, P=P: i['providers'][P].__setitem__('local_primitive_bound', 1)),
+            (P + ':forged_provider_and_call_program_hash', forged_program_hash),
+            (P + ':provider_at_wrong_call', wrong_selected_call),
+            (P + ':stale_partner_program_consistent_call_hashes', stale_program),
+            (P + ':stale_partner_profile_consistent_child_total', stale_profile),
+            (P + ':relocated_against_partner_same_counts', moved),
+            (P + ':compensating_false_profiles_with_' + Qp, compensating),
+            (P + ':synchronized_forged_source_recipe_hash', forged_recipe),
+            (P + ':synchronized_forged_phase_review_semantics', forged_phase),
+        ]
+        if len(PIDS)==1:
+            # Cross-provider substitutions require a second actual supplier.
+            # All single-provider program, phase, profile and dispatch bindings
+            # retain their direct mutations above and in the controller audit.
+            partner_only = {P+':stale_partner_program_consistent_call_hashes',
+                            P+':stale_partner_profile_consistent_child_total',
+                            P+':relocated_against_partner_same_counts',
+                            P+':compensating_false_profiles_with_'+Qp}
+            controls = [(name, fn) for name, fn in controls if name not in partner_only]
+        # Width order and inventory: swap the first helper of every pair of distinct widths (same inventory),
+        # and shift one unit between them (same total).
+        first = {}
+        for h, w in enumerate(widths):
+            first.setdefault(w, h)
+        for wa, wb in itertools.combinations(sorted(first), 2):
+            def swap(o, i, P=P, a=first[wa], b=first[wb]):
+                w = i['providers'][P]['widths']; w[a], w[b] = w[b], w[a]
+            def shift(o, i, P=P, a=first[wa], b=first[wb]):
+                w = i['providers'][P]['widths']; w[a] += 1; w[b] -= 1
+            controls.append((P + ':width_order_swap_%d_%d' % (wa, wb), swap))
+            controls.append((P + ':width_inventory_shift_%d_%d' % (wa, wb), shift))
+        for h in SPOT:
+            def cold_swap(o, i, P=P, h=h):
+                w = i['providers'][P]['widths']; j = w.index(9 if w[h] != 9 else 8); w[h], w[j] = w[j], w[h]   # never the identity
+            controls.append((P + ':cold_helper_width_swap_%d' % h, cold_swap))
+    rejected = []
+    accepted = []
+    for name, mutate in controls:
+        o, i = copy.deepcopy(owner), copy.deepcopy(invoice)
+        mutate(o, i)
+        oh = digest(o)
+        i['owner_audit_sha256'] = oh
+        try:
+            assemble(o, i, oh, digest(i))
+        except (AssertionError, KeyError):
+            rejected.append(name)
+        else:
+            # Discovery has no pinned values to reject spec-only mutations; the strict run must reject every control.
+            if not DISCOVER:
+                raise AssertionError('Invalid admission receipt accepted: ' + name)
+            accepted.append(name)
+    try:
+        assemble(owner, invoice, '0' * 64, sha(invoice_path))
+    except AssertionError:
+        rejected.append('wrong_owner_receipt_hash')
+    else:
+        raise AssertionError('Wrong owner digest accepted')
+    pin('expected.assembly_controls_rejected', len(rejected))
+    assert baseline['controls'] == ['next_grid', 'zero_eta', 'zero_beta', 'unit_beta']
+    assert baseline['conservative_controls'] == baseline['controls']
+    assert baseline['surcharge_model'] == {'complex': False, 'bit': True}
+    assert len(baseline['model_controls']) == 2
+    return dict(
+        status='PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS',
+        valid_receipt_kappa=baseline['kappa'],
+        input_sha256=baseline['input_sha256'],
+        assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'),
+        rejected_controls=rejected,
+        discovery_accepted_controls=accepted,
+        exact_outer_controls=baseline['controls'],
+        conservative_outer_controls=baseline['conservative_controls'],
+        recurrence_model_controls=baseline['model_controls'],
+        scope='Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay.',
+    )
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--source-package', type=Path, required=True)
+    ap.add_argument('--owner', type=Path, required=True)
+    ap.add_argument('--invoice', type=Path, required=True)
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    assert not a.out.exists()
+    result = verify(a.owner, a.invoice, a.source_package)
+    a.out.write_text(json.dumps(result, indent=2) + '\n')
+    print(result['status'], len(result['rejected_controls']))
diff --git a/research/gauge44-leaver8/code/audit_allcold.py b/research/gauge44-leaver8/code/audit_allcold.py
new file mode 100644
index 0000000000..c86f7b0235
--- /dev/null
+++ b/research/gauge44-leaver8/code/audit_allcold.py
@@ -0,0 +1,254 @@
+"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit.
+Imports no emitter, optimizer, expander, edge-coloring, or source hosting code.
+CLI: BASE HOSTED REPORT [--mutation-controls]
+Each provider is independently read from BASE/providers, never from a baseline width histogram.
+OpenAI Codex two-provider width-seven extension; retains all inherited independent controller checks.
+The exact 63 width-seven and 9 plain calls are frozen below.
+"""
+import sys,json,gzip,hashlib,copy
+assert __debug__, 'Assertions must remain enabled'
+from pathlib import Path
+from collections import Counter,defaultdict
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+from generated_identity import artifact_identities
+BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz')
+ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json')
+ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json')
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+provider_ids=PIDS
+providers={};registry={};phase_semantic_hashes={};artifact_semantic_hashes={}
+required_artifacts={'work/complex-nine-native/DATA-PHASES.json'}
+provider_files=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+ 'INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json')
+for pid in provider_ids:
+ p=BASE/'providers'/pid
+ c=read(p/'CANONICAL-WORD.json.gz');checks=read(p/'LOCAL-CHECKS.json')
+ programs=read(p/'LOCAL-PROGRAMS.json.gz');replay=read(p/'INDEPENDENT-LOCAL-REPLAY.json')
+ phase=read(p/'CLIFFORD-REVIEW.json');adapters=read(p/'RESIDUAL-ADAPTERS.json')['recipes']
+ widths=[len(c['frames'][c['final'][2*c['v']+h]])-len(c['frames'][c['start'][2*c['v']+h]])for h in range(c['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths();pin('providers.%s.inventory'%pid,{str(k):v for k,v in sorted(Counter(widths).items())})
+ canonical_sha=sha(p/'CANONICAL-WORD.json.gz');programs_sha=sha(p/'LOCAL-PROGRAMS.json.gz')
+ assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ assert replay['canonical_word_sha256']==canonical_sha and replay['local_programs_sha256']==programs_sha
+ assert replay['v']==c['v'] and replay['helpers']==c['R']
+ assert set(programs)==set(checks)==set(replay['local'])==set(replay['paid_profiles'])=={'forward','backward'}
+ for orientation,events in programs.items():
+  ck=checks[orientation];rr=replay['local'][orientation]
+  assert hashlib.sha256(json.dumps(events,sort_keys=True,separators=(',',':')).encode()).hexdigest()==ck['sha256']
+  assert ck['events']==len(events) and ck['all_columns']==2*c['v']+c['R']
+  assert ck['private_centers_cleared'] and ck['private_coefficient_stream_cleared_after_each_macro']
+  assert rr['all_exact_columns']==2*c['v']+c['R'] and rr['private_work_erased']
+  literal=Counter(e[-1]for e in events if e[0]in('climb','center'))
+  assert dict(literal)=={int(r):n for r,n in ck['paid_profile'].items()}=={int(r):n for r,n in c['local_profile'].items()}
+  assert ck['paid_profile']==replay['paid_profiles'][orientation]
+ assert phase['canonical_word_sha256']==canonical_sha and phase['recipe_sha256']==sha(p/'CLIFFORD-RECIPES.json')
+ assert phase['all_child_equalities_include_global_phase']
+ artifact_semantic_hashes[pid]=artifact_identities(p)
+ pin('providers.%s.artifact_semantic_sha256'%pid,artifact_semantic_hashes[pid])
+ phase_semantic_hashes[pid]=artifact_semantic_hashes[pid]['CLIFFORD-REVIEW.json']
+ for h,w in enumerate(widths):
+  assert 0<w<=c['h']
+  f=c['start'][2*c['v']+h];u=c['final'][2*c['v']+h]
+  # COLD-HPE: a cold helper (f == 0) may end below FULL too; its wrapper is the '0:U' recipe (E = bottom instance of #593)
+  if u!=1:   # HPE: wrapper for T_U T_E^-1, keyed 'E:U', rank |U|-|E|
+   a=adapters['%d:%d'%(f,u)]
+   assert a['frame']==f and a['terminal']==u and a['vectors']==c['frames'][f] and a['terminal_vectors']==c['frames'][u]
+   assert a['rank']==w==len(c['frames'][u])-len(c['frames'][f]) and a['entrance_rank']==len(c['frames'][f]) and a['terminal_rank']==len(c['frames'][u])<c['h']
+  elif w<c['h']:
+   a=adapters[str(f)]
+   assert a['frame']==f and a['vectors']==c['frames'][f] and a['rank']==w and a['entrance_rank']==c['h']-w
+ providers[pid]=dict(canonical=c,checks=checks,widths=widths)
+ registry[pid]=dict(local_programs=programs,canonical_word_sha256=canonical_sha,local_programs_sha256=programs_sha,
+  local_program_checks=checks,exact_local_clifford_recipe_sha256=sha(p/'CLIFFORD-RECIPES.json'),
+  residual_adapter_sha256=sha(p/'RESIDUAL-ADAPTERS.json'),
+  **{k:c[k]for k in('v','h','R','ports','centers')},widths=widths)
+ required_artifacts.update('providers/'+pid+'/'+fn for fn in provider_files)
+canon=providers[provider_ids[0]]['canonical'];V=canon['v'];R=canon['R'];N=2*V+R;CENTRES=len(canon['centers'])
+assert V==112 and canon['h']==9
+assert all(providers[p]['canonical'][k]==canon[k]for p in provider_ids for k in('v','h','R','ports'))
+# Independently compare ordered common frames; exact local carrier names remain
+# bound to each canonical word, program, phase receipt and residual adapters.
+for p in provider_ids:
+ c=providers[p]['canonical']
+ assert len(c['centers'])==len(c['center_frames'])==8
+ assert [c['frames'][f]for f in c['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+parent_canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz')
+assert [canon['frames'][f]for f in canon['center_frames']]==[parent_canon['frames'][f]for f in parent_canon['center_frames']]
+assert required_artifacts<=set(summary['source_artifacts'])
+prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=8;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=72;HOSTED=CALLS*R
+# The selected map is an input to check, not a claim from the emitter.
+
+assert len(DISPATCH)==72 and Counter(DISPATCH.values())==COUNTS
+expected_provider=lambda stage,replica:DISPATCH[stage,replica]
+
+def orthobasis(port):
+ q=canon['ports'][port];z=next(i for i in range(9)if(q>>i)&1==0);a=q^(1<<z);order=list(range(9));order[z],order[0]=order[0],order[z]
+ b=[(1<<i)^(a if a>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ assert len(b)==73 and all((x&y).bit_count()%2==int(i==j)for i,x in enumerate(b)for j,y in enumerate(b));return b
+bases=[orthobasis(p)for p in range(V)]
+
+def audit(t):
+ assert(t['live'],t['physical'])==(DATA,PHYSICAL)
+ assert t['local_providers']==registry and t['recipe']==parent['recipe']and 'each local invocation completes before the next' in t['loop_order'].lower()
+ assert not any(k in t for k in('local_programs','exact_local_clifford_recipe_sha256','residual_adapter_sha256'))
+ assert len(t['calls'])==72 and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
+ for key in('exact_data_phase_recipe_sha256','adapter_policy'):assert t[key]==parent[key]
+ assert t['exact_data_phase_recipe_sha256']==sha(BASE/'work/complex-nine-native/DATA-PHASES.json')
+ # Independently project the literal schedule onto every data replica.
+ src=parent['execution_schedule'];assert t['async_schedule']['source_schedule']==src
+ assert t['async_schedule']['source_call_order']==[[c['stage'],c['replica']]for c in parent['calls']]
+ order=[(c['stage'],c['replica'])for c in t['calls']]
+ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==72
+ all_local=[];perrep={r:[]for r in range(8)};globals_=[]
+ for e in t['execution_schedule']:
+  j=e['source_event'];old=copy.deepcopy(src[j])
+  if 'replica'in e:
+   r=e['replica'];assert 0<=r<8 and j<30;perrep[r].append(j)
+   expected=old|dict(source_event=j,replica=r,replicas=[r],time=e['time'])
+   if e['kind']=='local_cover_sweep':expected['provider_id']=expected_provider(e['stage'],r)
+   assert e==expected
+   assert 0<=e['time']<72 and order[e['time']][1]==r
+   if e['kind']=='local_cover_sweep':
+    assert order[e['time']]==(e['stage'],r);all_local.append((e['stage'],r,e['time']))
+  else:
+   globals_.append(j);expected=old|dict(source_event=j)
+   if e['kind']=='bank_padding_cover_sweep':expected['families']=[DATA,DATA]
+   if e['kind']=='translate_every_live_family':expected.update(families=[0,DATA],charged_calls_per_cover=DATA)
+   assert e==expected
+ assert all(v==list(range(30))for v in perrep.values()) and globals_==[30,31]
+ assert all_local==[(st,r,i)for i,(st,r)in enumerate(order)]
+ assert all('replica'in e for e in t['execution_schedule'][:-2])
+ assert [e['source_event']for e in t['execution_schedule'][-2:]]==[30,31]
+ # Local cover calls are indivisible; a block then runs the source events
+ # up to that replica's next local invocation.
+ block=-1
+ for e in t['execution_schedule'][:-2]:
+  if e['kind']=='local_cover_sweep':block+=1
+  assert e['time']==block
+ assert t['bank_padding']==dict(parent['bank_padding'],families=[],children=[])
+ assert t['cover_final_correction']==dict(parent['cover_final_correction'],families=[0,DATA],charged_calls_per_cover=DATA)
+ assert t['private_namespace']=={'centers':[DATA,DATA+CENTRES],'reserved_tableau':[DATA+CENTRES,DATA+CENTRES+R],'coefficient':[DATA+CENTRES+R,PHYSICAL]}
+ # Actual physical touch intervals include every individual bridge.
+ pairs={};sides={};windows={};last={};callpos={};stagepair={e['stage']:e['pair']for e in parent['recipe']if e['kind']=='local'}
+ for pos,e in enumerate(t['execution_schedule']):
+  if 'replica'not in e:continue
+  rep=e['replica']
+  if e['kind']=='local_cover_sweep':
+   pair=stagepair[e['stage']];callpos[e['stage'],rep]=pos;last[rep,pair]=pos
+  elif e['kind']=='bridge':last[rep,e['src']]=last[rep,e['dst']]=pos
+  elif e['kind']=='idle_cover_sweep':
+   for side,i in enumerate(e['child_indices']):
+    if i not in prank:continue
+    pairs[i]=e['pair'];sides[i]=side;windows[rep,i]=(last.get((rep,e['pair']),-1),pos)
+ used=defaultdict(set);roles={};paid=Counter();sigmas={};digest=hashlib.sha256();entering=0;cross=0;touches=defaultdict(list)
+ for call in t['calls']:
+  old=next(z for z in parent['calls']if(z['stage'],z['replica'])==(call['stage'],call['replica']))
+  assert {k:v for k,v in call.items()if k not in('owners','time','provider_id','local_program_sha256')}=={k:v for k,v in old.items()if k not in('owners','local_program_sha256')}
+  pid=expected_provider(call['stage'],call['replica']);assert call['provider_id']==pid
+  width=providers[pid]['widths'];checks=providers[pid]['checks']
+  assert call['local_program_sha256']==checks[call['orientation']]['sha256']
+  s,rep,pair=call['stage'],call['replica'],call['pair'];assert call['time']==t['async_schedule']['order'].index([s,rep]);own=call['owners'];assert len(own)==N and len({f for f,rt in own})==N and all(0<=f<DATA for f,rt in own)
+  assert own[:(2*V)]==old['owners'][:(2*V)]
+  for h,(family,route)in enumerate(own[(2*V):]):
+   w=width[h];typ,i,off=route[:3];ownerrep,sub=divmod(family,(8*V));fampair,sub=divmod(sub,(2*V));side,port=divmod(sub,V)
+   assert windows[ownerrep,i][0]<callpos[s,rep]<windows[ownerrep,i][1] and fampair==pairs[i] and side==sides[i] and 0<=off and off+w<=prank[i]
+   B=bases[port];pend=[int(x)for x in ph['recipes'][port]['idle_children'][i]['orthogonal_axes']];assert len(pend)==prank[i]
+   occ=[B.index(v)for v in pend[off:off+w]];sp=[j for j in range(M)if j not in occ][:9-w]
+   assert route==([3,i,off]if w==9 else[4,i,off,w,sp]);assert len(set(occ+sp))==9
+   order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert sorted(order)==list(range(M));sigma=[B[j]for j in order]
+   assert sigma[:w]==pend[off:off+w]and sigma[w:9]==[B[j]for j in sp]
+   sh=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sh]=sigma;digest.update(json.dumps([s,rep,h,family,sh],separators=(',',':')).encode()+b'\n')
+   key=(i,ownerrep,port);cells=set(range(off,off+w));assert not used[key]&cells;used[key]|=cells
+   role=(s,rep,h);assert role not in roles;roles[role]=dict(stage=s,replica=rep,helper=h,family=family,owner_replica=ownerrep,child=i,copy=ownerrep*V+port,port=port,offset=off,width=w)
+   touches[family].append((s,rep,h));entering+=w<9;cross+=rep!=ownerrep
+  for r,n in checks[call['orientation']]['paid_profile'].items():paid[int(r)]+=n
+ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(8)for h in range(R)}
+ # The frozen pooled metadata must bind the actual serialized owner maps.
+ assert len(t['hosting']['pooled_slots'])==HOSTED
+ for z in t['hosting']['pooled_slots']:
+  key=(z['stage'],z['replica'],z['helper']);assert key in roles
+  assert {k:z[k]for k in roles[key]}==roles[key]
+ assert len({(z['stage'],z['replica'],z['helper'])for z in t['hosting']['pooled_slots']})==HOSTED
+ rem={};wanted=[]
+ for old in parent['idle_children']:
+  i,port=old['child'],old['port']
+  for rep in range(T):
+   u=used[i,rep,port];assert u==set(range(len(u)));r=old['rank']-len(u)
+   if r:
+    f=rep*(8*V)+(2*pairs[i]+sides[i])*V+port;wanted.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=r,hosted=len(u),pending_offset=len(u)));paid[r]+=1
+ assert t['idle_children']==wanted
+ mass=sum(r*n for r,n in paid.items());assert73=73*DATA-mass;assert assert73==2560 and 73**2>2*max(paid)**2
+ return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=72)
+
+r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256']
+assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items())
+controls=[]
+def reject(name,mut):
+ if '--mutation-controls' not in sys.argv[4:]:return
+ q=copy.deepcopy(ct);mut(q)
+ try:audit(q)
+ except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name)
+ else:raise AssertionError('ACCEPTED '+name)
+enter=lambda q:next(o for c in q['calls']for o in c['owners'][(2*V):]if o[1][0]==4)
+reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__((2*V+1),q['calls'][0]['owners'][(2*V)]))
+reject('helper on active data family',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,q['calls'][0]['owners'][0][0]))
+reject('owner in private namespace',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,DATA))
+reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1))
+reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72))
+reject('omit idle remainder',lambda q:q['idle_children'].pop())
+reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1))
+# Single-provider dispatch still has all source/program/width binding controls.
+if len(provider_ids)==1:
+ P=provider_ids[0]
+ at_p=lambda q:next(c for c in q['calls']if c['provider_id']==P)
+ narrow=next(h for h in range(R)if providers[P]['widths'][h]<9)
+ reject(P+': wrong provider at its invocation',lambda q:at_p(q).__setitem__('provider_id','__unregistered__'))
+ reject(P+': stale per-call local program hash',lambda q:at_p(q).__setitem__('local_program_sha256','0'*64))
+ reject(P+': stale serialized provider program',lambda q:q['local_providers'][P]['local_programs']['forward'].pop())
+ reject(P+': unbound residual adapter hash',lambda q:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64))
+ reject(P+': wrong provider width registry',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,providers[P]['widths'][narrow]-1))
+ reject(P+': wrong per-call residual width',lambda q:at_p(q)['owners'][2*V+narrow][1].__setitem__(3,at_p(q)['owners'][2*V+narrow][1][3]-1))
+ reject(P+': wrong sweep provider',lambda q:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep').__setitem__('provider_id','__unregistered__'))
+ reject(P+': entering helper width silently restored to nine',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,9))
+else:
+ # Per-provider substitution controls: every provider is swapped against a partner provider.
+ for P in provider_ids:
+  Qp=partner(P)
+  at_p=lambda q,P=P:next(c for c in q['calls']if c['provider_id']==P)
+  diff=[h for h in range(R)if providers[P]['widths'][h]!=providers[Qp]['widths'][h]]
+  narrow=next(h for h in range(R)if providers[P]['widths'][h]<9)
+  reject(P+': wrong provider at its invocation',lambda q,P=P,Qp=Qp,at_p=at_p:at_p(q).__setitem__('provider_id',Qp))
+  reject(P+': stale per-call local program hash',lambda q,Qp=Qp,at_p=at_p:at_p(q).__setitem__('local_program_sha256',registry[Qp]['local_program_checks'][at_p(q)['orientation']]['sha256']))
+  reject(P+': stale serialized provider program',lambda q,P=P,Qp=Qp:q['local_providers'][P].__setitem__('local_programs',registry[Qp]['local_programs']))
+  reject(P+': unbound residual adapter hash',lambda q,P=P:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64))
+  if diff:reject(P+': partner width in provider width registry',lambda q,P=P,Qp=Qp,h=diff[0]:q['local_providers'][P]['widths'].__setitem__(h,providers[Qp]['widths'][h]))
+  reject(P+': wrong per-call residual width',lambda q,at_p=at_p,h=narrow:at_p(q)['owners'][2*V+h][1].__setitem__(3,at_p(q)['owners'][2*V+h][1][3]-1))
+  reject(P+': wrong sweep provider',lambda q,P=P,Qp=Qp:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep'and DISPATCH[e['stage'],e['replica']]==P).__setitem__('provider_id',Qp))
+  reject(P+': entering helper width silently restored to nine',lambda q,P=P,h=narrow:q['local_providers'][P]['widths'].__setitem__(h,9))
+
+report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=DATA,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,mutation_controls_run='--mutation-controls' in sys.argv[4:],provider_phase_semantic_sha256=phase_semantic_hashes,provider_artifact_semantic_sha256=artifact_semantic_hashes,widths_by_provider={pid:dict(sorted(Counter(providers[pid]['widths']).items()))for pid in provider_ids},provider_counts=dict(Counter(c['provider_id']for c in ct['calls'])),all_provider_program_phase_and_wrapper_bindings=True,scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations.')
+REPORT.parent.mkdir(parents=True,exist_ok=True)
+REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2))
+
+owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=DATA,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,hosted_residuals=HOSTED,banked_residuals=0,all_live_owners_per_call_distinct=True,owners_per_call=N,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],provider_phase_semantic_sha256=phase_semantic_hashes,provider_artifact_semantic_sha256=artifact_semantic_hashes,controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest())
+(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n')
+
+# Literal residual frames are a compact export of the already checked offsets,
+# not another global replay. Every row names its actual inherited axes.
+frames=[]
+for z in ct['idle_children']:
+ axes=list(map(int,ph['recipes'][z['port']]['idle_children'][z['child']]['orthogonal_axes']))
+ tail=axes[z['pending_offset']:]
+ assert len(tail)==z['rank']
+ frames.append(dict(z,orthogonal_axes=tail))
+frame_raw=json.dumps(frames,sort_keys=True,separators=(',',':')).encode()
+portable=bytearray(gzip.compress(frame_raw,mtime=0));portable[9]=255
+(OUT/'IDLE-REMAINDER-FRAMES.json.gz').write_bytes(bytes(portable))
+frame_receipt=dict(status='PASS_LITERAL_IDLE_REMAINDER_FRAMES',template_sha256=summary['template_sha256'],
+ uncompressed_frames_sha256=hashlib.sha256(frame_raw).hexdigest(),children=len(frames),
+ rank_profile=dict(sorted(Counter(z['rank']for z in frames).items())),
+ source_data_phase_sha256=hashlib.sha256((BASE/'work/complex-nine-native/DATA-PHASES.json').read_bytes()).hexdigest(),
+ scope='Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child.')
+(REPORT.parent/'IDLE-REMAINDER-FRAMES.json').write_text(json.dumps(frame_receipt,indent=2)+'\n')
diff --git a/research/gauge44-leaver8/code/bind_providers_portable.py b/research/gauge44-leaver8/code/bind_providers_portable.py
new file mode 100644
index 0000000000..97e28da17e
--- /dev/null
+++ b/research/gauge44-leaver8/code/bind_providers_portable.py
@@ -0,0 +1,67 @@
+"""Bind freshly verified plain and width-seven four-cold providers to the frozen literal owner plan.
+Prepared with OpenAI Codex assistance; Apache-2.0. All byte-stable native
+files are pinned to the plan. Only validated phase-receipt timing/serialization
+and directory fields are rebound; no dispatch, width or owner choice changes.
+"""
+import argparse,copy,gzip,hashlib,json,shutil
+from collections import Counter
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+from generated_identity import artifact_identities
+assert __debug__, 'Assertions required'
+ap=argparse.ArgumentParser(description=__doc__)
+for name in ('baseline','plan','out'):ap.add_argument('--'+name,type=Path,required=True)
+ap.add_argument('--provider',action='append',required=True,help='PID=DIR');a=ap.parse_args();assert not a.out.exists();a.out.mkdir(parents=True)
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+base=a.out/'base';shutil.copytree(a.baseline/'complex-global/base',base)
+ap2=dict(x.split('=',1)for x in a.provider);dirs={k:Path(v)for k,v in ap2.items()};assert set(dirs)==set(PIDS)
+for pid,src in dirs.items():shutil.copytree(src,base/'providers'/pid)
+pin('data.plan_sha256',sha(a.plan))
+plan=read(a.plan);original=copy.deepcopy(plan);sources={};helpers=set()   # R: helper count per provider word; all providers must agree
+assert set(plan['provider_registry'])==set(dirs)
+assert {(c['stage'],c['replica']):c['provider']for c in plan['provider_calls']}==DISPATCH,'PLAN dispatch differs from spec dispatch'
+stable=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json')
+for pid,desc in plan['provider_registry'].items():
+ d=base/'providers'/pid
+ word,program,checks,native,phase=[read(d/name)for name in('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-REVIEW.json')]
+ assert (word['v'],word['h'],len(word['centers']))==(112,9,8) and type(word['R']) is int and word['R']>0;helpers.add(word['R'])
+ assert word['ports']==desc['ports'] and word['centers']==desc['centers']
+ widths=[len(word['frames'][word['final'][r]])-len(word['frames'][word['start'][r]])for r in range(2*112,2*112+word['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths()
+ assert widths==desc['widths'];pin('providers.%s.inventory'%pid,{str(k):v for k,v in sorted(Counter(widths).items())})
+ assert native['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ pin('providers.%s.native_negative_controls'%pid,len(native['negative_controls_rejected']))
+ assert native['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and native['local_programs_sha256']==sha(d/'LOCAL-PROGRAMS.json.gz')
+ assert phase['status']=='PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES'
+ assert phase['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and phase['recipe_sha256']==sha(d/'CLIFFORD-RECIPES.json')
+ assert phase['all_child_equalities_include_global_phase'] is True and phase['endpoint_adapters']==224
+ pin('providers.%s.phase_edges'%pid,phase['directed_edges'])
+ assert set(program)==set(checks)=={'forward','backward'}
+ expected={int(r):n for r,n in checks['forward']['paid_profile'].items()};pin('providers.%s.expected_profile'%pid,checks['forward']['paid_profile'])
+ for orientation,events in program.items():
+  profile=Counter()
+  for e in events:
+   if e[0]=='climb':profile[e[5]]+=1
+   elif e[0]=='center':profile[e[4]]+=1
+  assert dict(profile)==expected=={int(r):n for r,n in checks[orientation]['paid_profile'].items()}=={int(r):n for r,n in native['paid_profiles'][orientation].items()}
+  assert hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest()==checks[orientation]['sha256']
+ identities=artifact_identities(d)
+ pin('providers.%s.artifact_semantic_sha256'%pid,identities)
+ assert identities==desc['artifact_semantic_sha256']
+ for name in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):
+  assert sha(d/name)==desc['artifact_sha256'][name],(pid,name,'changed non-reference artifact')
+ for c in plan['provider_calls']:
+  if c['provider']==pid:
+   assert c['orientation']==('forward'if c['stage']%2==0 else'backward')
+   assert c['local_program_sha256']==checks[c['orientation']]['sha256']
+ desc['directory']='providers/'+pid
+ desc['artifact_sha256']={name:sha(d/name)for name in desc['artifact_sha256']}
+ sources[pid]=dict(artifact_sha256=desc['artifact_sha256'],canonical_content_sha256=hashlib.sha256(json.dumps(word,sort_keys=True,separators=(',',':')).encode()).hexdigest(),all_phase_edges=phase['directed_edges'])
+assert len(helpers)==1,'providers disagree on helper count R: %s'%sorted(helpers)
+plan['runtime_source_plan_sha256']=sha(a.plan)
+(a.out/'PLAN.json').write_text(json.dumps(plan,indent=2)+'\n')
+receipt=dict(status='PASS_FROZEN_048_ALLCOLD_DISPATCH_FRESH_PROVIDER_BINDING',source_plan_sha256=sha(a.plan),runtime_plan_sha256=sha(a.out/'PLAN.json'),providers=sources,only_rebound_fields=['provider_registry.directory','provider_registry.artifact_sha256','runtime_source_plan_sha256'])
+(a.out/'BINDING.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(receipt['status'])
diff --git a/research/gauge44-leaver8/code/bit_supplier_controls.py b/research/gauge44-leaver8/code/bit_supplier_controls.py
new file mode 100644
index 0000000000..e86b8527b4
--- /dev/null
+++ b/research/gauge44-leaver8/code/bit_supplier_controls.py
@@ -0,0 +1,111 @@
+"""Negative controls for the cited PR589 bit supplier and its derived rank-mass deficit.
+
+Apache-2.0. Each control mutates one input of the changed bit-supplier sites in assemble.py (the pinned record, the
+deficit derivation from the word's parameters, the profile/live binding, the claimed endpoint) and runs the unchanged
+assemble() on the fresh owner/invoice receipts. Every control must be rejected; the unmutated run must pass.
+`revert_hardcoded_9984` restores the PR543 constant the parent package hard-coded: with PR589's word it must fail.
+"""
+import argparse
+import copy
+import hashlib
+import json
+import os
+import tempfile
+from fractions import Fraction as Q
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+
+assert __debug__, 'Assertions required'
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def verify(owner_path, invoice_path, source_package):
+    os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve())
+    import assemble as A
+    owner = json.loads(owner_path.read_text())
+    invoice = json.loads(invoice_path.read_text())
+    args = (owner, invoice, sha(owner_path), sha(invoice_path))
+    baseline = A.assemble(*args)
+    data = A.BIT_PATH.read_bytes()
+    record = A.load_bit(data)
+    word = record['word']
+    assert A.bit_deficit(word, record['nine']['bit']['live']) == 10272 == 32 * (8 * 111 - 9 * 63)
+
+    real_load, real_deficit = A.load_bit, A.bit_deficit
+
+    def with_record(mutate):
+        def load(d):
+            r = copy.deepcopy(real_load(d)); mutate(r); return r
+        return load
+
+    def shift_profile(r):  # one rank-1 child becomes rank 2: rank mass +1, totals unchanged
+        p = r['nine']['profile']; p['1'] -= 1; p['2'] += 1; r['nine']['bit']['rank_mass'] += 1
+
+    bumped = data.replace(record['nine']['bit_lower'].encode(),
+                          str(Q(record['nine']['bit_lower']) + Q(1, 10**24)).encode(), 1)
+    assert bumped != data
+    pr543 = (source_package / 'inputs/PR543-EXPECTED.json').read_bytes()
+    controls = [
+        # deficit site: the parent's hard-coded constant, restored
+        ('revert_hardcoded_9984', dict(bit_deficit=lambda w, live: 9984)),
+        # deficit site: each word parameter perturbed alone
+        ('ports_112', dict(load_bit=with_record(lambda r: r['word'].__setitem__('v', 112)))),
+        ('decoder_constant_64_copy_ranks_unchanged', dict(load_bit=with_record(lambda r: r['word'].__setitem__('decoder_constant', 64)))),
+        # v=111, cst=64 derives 32*(888-576)=9984: consistent word, wrong for the priced profile
+        ('decoder_constant_64_with_one_copy_rank_8', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('decoder_constant', 64), r['word']['copy_ranks'].__setitem__(0, 8))))),
+        ('eight_retained_totals', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('copy_ranks', [7] * 8), r['word'].__setitem__('decoder_constant', 56))))),
+        ('live_minus_one', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('live', r['nine']['bit']['live'] - 1)))),
+        # profile binding: same totals, rank mass +1
+        ('profile_rank_mass_plus_one', dict(load_bit=with_record(shift_profile))),
+        ('profile_rank_mass_receipt_mismatch', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('rank_mass', r['nine']['bit']['rank_mass'] + 1)))),
+        # endpoint: the next 1e-24 grid point
+        ('bit_lower_next_grid', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('bit_lower', str(Q(r['nine']['bit_lower']) + Q(1, 10**24)))))),
+        ('not_nine_stage_record', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('pipeline', r['nine']['pipeline'].replace('nine-stage', 'eleven-stage'))))),
+        # pinned-input site: tampered bytes and the parent's PR543 file under the PR589 pin
+        ('tampered_bytes_next_grid', dict(read=bumped)),
+        ('pr543_file_under_pr589_pin', dict(read=pr543)),
+    ]
+    rejected = []
+    scratch = Path(tempfile.mkdtemp(prefix='bitctl-'))
+    for name, patch in controls:
+        saved_path = A.BIT_PATH
+        try:
+            if 'read' in patch:
+                tmp = scratch / (name + '.json'); tmp.write_bytes(patch['read']); A.BIT_PATH = tmp
+            A.load_bit = patch.get('load_bit', real_load)
+            A.bit_deficit = patch.get('bit_deficit', real_deficit)
+            try:
+                A.assemble(*args)
+            except (AssertionError, KeyError):
+                rejected.append(name)
+            else:
+                raise AssertionError('Invalid bit supplier accepted: ' + name)
+        finally:
+            A.load_bit, A.bit_deficit, A.BIT_PATH = real_load, real_deficit, saved_path
+            if 'read' in patch:
+                tmp.unlink()
+    scratch.rmdir()
+    assert rejected == [n for n, _ in controls]
+    again = A.assemble(*args)
+    assert again['kappa'] == baseline['kappa'] and again['bit_lower'] == baseline['bit_lower']
+    return dict(
+        status='PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS',
+        kappa=baseline['kappa_decimal'], bit_lower=baseline['bit_lower'], bit_decimal=baseline['bit_decimal'],
+        binding=baseline['binding'], bit_supplier=baseline['bit_supplier'],
+        derived_deficit=baseline['bit_supplier']['derived_deficit'],
+        rejected_controls=rejected,
+        assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'),
+    )
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--source-package', type=Path, required=True)
+    ap.add_argument('--owner', type=Path, required=True)
+    ap.add_argument('--invoice', type=Path, required=True)
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    assert not a.out.exists()
+    result = verify(a.owner, a.invoice, a.source_package)
+    a.out.write_text(json.dumps(result, indent=2) + '\n', newline='\n')
+    print(result['status'], len(result['rejected_controls']))
diff --git a/research/gauge44-leaver8/code/emit_allcold.py b/research/gauge44-leaver8/code/emit_allcold.py
new file mode 100644
index 0000000000..8e147f80a6
--- /dev/null
+++ b/research/gauge44-leaver8/code/emit_allcold.py
@@ -0,0 +1,150 @@
+"""Two-provider width-seven whole-owner derivative, adapted with OpenAI Codex assistance.
+Based on PR514 and its credited PR484/507 lineage.
+CLI: --base VERIFIED_VARIANT --owners ASYNC-OWNERS.json.gz --plan ASYNC-PLAN.json --out OUT
+No optimizer or unpublished word builder runs. The frozen map explicitly names
+one whole helper per family per complete invocation, plus borrowed spectators.
+"""
+import sys,json,gzip,hashlib,copy,argparse
+from pathlib import Path
+from collections import Counter,defaultdict
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+parser=argparse.ArgumentParser(description=__doc__)
+parser.add_argument('--base',type=Path,required=True);parser.add_argument('--owners',type=Path,required=True);parser.add_argument('--plan',type=Path,required=True);parser.add_argument('--out',type=Path,required=True)
+a=parser.parse_args();BASE,MAP,PLAN,OUT=(p.resolve()for p in(a.base,a.owners,a.plan,a.out));assert not OUT.exists();OUT.mkdir(parents=True)
+class OH:
+ @staticmethod
+ def idle_basis(q):
+  z=next(i for i in range(9)if not(q>>i)&1);u=q^(1<<z);order=list(range(9));order[0],order[z]=order[z],order[0]
+  return[(1<<i)^(u if u>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ @staticmethod
+ def spectators(q,pending,off,w):
+  B=OH.idle_basis(q);occ=[B.index(v)for v in pending[off:off+w]]
+  return[j for j in range(73)if j not in occ][:9-w]
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+assert hashlib.sha256(MAP.read_bytes()).hexdigest()==SPEC['data']['owners_sha256'],'OWNERS not pinned by spec'
+plan=read(PLAN);assert plan['runtime_source_plan_sha256']==SPEC['data']['plan_sha256'],'PLAN not pinned by spec'
+call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==72;at={x:i for i,x in enumerate(call_order)}
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');t=copy.deepcopy(parent);canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');roles=read(MAP);T=8;V=canon['v'];M=73;R0=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)   # R0: parent (split-centres) helper count
+assert(len(canon['start']),len(ph['recipes']))==(2*V+R0,V)
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+provider_files=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json')
+registry={};source_artifacts={'work/complex-nine-native/DATA-PHASES.json':sha(BASE/'work/complex-nine-native/DATA-PHASES.json')}
+for provider_id in sorted(plan['provider_registry']):
+ assert provider_id in PIDS
+ directory=BASE/'providers'/provider_id
+ assert all((directory/f).is_file()for f in provider_files)
+ pc=read(directory/'CANONICAL-WORD.json.gz');checks=read(directory/'LOCAL-CHECKS.json');programs=read(directory/'LOCAL-PROGRAMS.json.gz');replay=read(directory/'INDEPENDENT-LOCAL-REPLAY.json')
+ # Carrier names belong to the independently checked local program. The global
+ # controller's centre contract is the ordered eight exact common frame bases.
+ assert(pc['v'],pc['h'],pc['ports'])==(V,9,canon['ports'])
+ assert len(pc['centers'])==len(pc['center_frames'])==len(canon['centers'])==8
+ assert [pc['frames'][f]for f in pc['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+ R=pc['R'];assert type(R)is int and R>0 and all(x['R']==R for x in registry.values()),'providers disagree on helper count R'
+ assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ assert replay['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz')and replay['local_programs_sha256']==sha(directory/'LOCAL-PROGRAMS.json.gz')
+ widths=[len(pc['frames'][pc['final'][2*V+h]])-len(pc['frames'][pc['start'][2*V+h]])for h in range(R)]   # HPE: residual width |final|-|start|
+ assert widths==plan['provider_registry'][provider_id]['widths']
+ for name in provider_files:
+  value=sha(directory/name);assert value==plan['provider_registry'][provider_id]['artifact_sha256'][name]
+  source_artifacts[f'providers/{provider_id}/{name}']=value
+ registry[provider_id]=dict(local_programs=programs,canonical_word_sha256=sha(directory/'CANONICAL-WORD.json.gz'),local_programs_sha256=sha(directory/'LOCAL-PROGRAMS.json.gz'),local_program_checks=checks,exact_local_clifford_recipe_sha256=sha(directory/'CLIFFORD-RECIPES.json'),residual_adapter_sha256=sha(directory/'RESIDUAL-ADAPTERS.json'),v=V,h=9,R=R,ports=pc['ports'],centers=pc['centers'],widths=widths)
+assert len(roles)==72*R   # one whole-owner role per (call, provider helper)
+selected={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+assert len(selected)==72 and set(selected)==set(call_order)
+assert Counter(c['provider']for c in selected.values())==COUNTS
+per_call_widths={(c['stage'],c['replica']):c['widths']for c in plan['per_call_widths']}
+for key,c in selected.items():
+ assert c['time']==at[key] and c['provider']in registry
+ assert per_call_widths[key]==registry[c['provider']]['widths']
+for key in('local_programs','exact_local_clifford_recipe_sha256','residual_adapter_sha256'):t.pop(key)
+t['local_providers']=registry
+rank={z['child']:z['rank']for z in parent['idle_children']};side={};pairs={}
+for e in parent['execution_schedule']:
+ if e['kind']=='idle_cover_sweep':
+  for sd,ch in enumerate(e['child_indices']):side[ch]=sd;pairs[ch]=e['pair']
+bycall=defaultdict(dict);used=defaultdict(set);sigmas={};digest=hashlib.sha256();entering=0
+for z in roles:
+ s,rep,h=z['stage'],z['replica'],z['helper'];i,cp,off,w,f=z['child'],z['copy'],z['offset'],z['width'],z['family'];orp,port=divmod(cp,V)
+ assert 0<=s<9 and 0<=rep<T and 0<=h<R and w==registry[selected[s,rep]['provider']]['widths'][h] and 0<=orp<T
+ assert f==orp*(8*V)+(2*pairs[i]+side[i])*V+port
+ assert(h not in bycall[s,rep])and off>=0 and off+w<=rank[i]
+ assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1]
+ B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i]
+ occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[]
+ order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M
+ sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma
+ route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9
+ cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells
+ digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n')
+for c in t['calls']:
+ k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R))
+ c['owners']=c['owners'][:(2*V)]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==2*V+R and all(f<DATA for f,r in c['owners'])
+ pc=selected[k];provider_id=pc['provider'];assert c['orientation']==pc['orientation']
+ c['provider_id']=provider_id;c['local_program_sha256']=registry[provider_id]['local_program_checks'][c['orientation']]['sha256']
+ assert c['local_program_sha256']==pc['local_program_sha256']
+newidle=[];paid=Counter()
+for c in t['calls']:
+ for r,n in registry[c['provider_id']]['local_program_checks'][c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for old in parent['idle_children']:
+ i,port=old['child'],old['port']
+ for rep in range(T):
+  u=used[i,rep,port];assert u==set(range(len(u)));left=old['rank']-len(u)
+  if left:
+   f=rep*(8*V)+(2*pairs[i]+side[i])*V+port;newidle.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=left,hosted=len(u),pending_offset=len(u)));paid[left]+=1
+assert M*DATA-sum(r*n for r,n in paid.items())==2560
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R0+2
+# Local circuits, exact phase recipes, normalized wrappers and data routes stay
+# byte-identical; only full-family helper placement and idle remainders change.
+t.update(version='round20-R%d-asynchronous-whole-owner-v1'%R,live=DATA,physical=physical,idle_children=newidle,private_namespace={'centers':[DATA,DATA+C],'reserved_tableau':[DATA+C,DATA+C+R],'coefficient':[physical-2,physical]})
+t['hosting']=dict(rule='one-helper-per-physical-family-per-complete-invocation',max_helpers_per_physical_family_per_call=1,scope='asynchronously interleaved data replicas; each whole helper occurs once per(stage,invocation replica)',pooled_slots=roles,banks=[0]*9,owner_map_sha256=hashlib.sha256(MAP.read_bytes()).hexdigest(),idle_remainder_semantics='Each idle_children item acts once, on its explicit replica/family, at pending_offset with the stated rank; replicas=1.')
+t['route_semantics']['helper']='Whole physical family may belong to another replica; actual orthogonal port basis followed by residual/spectator coordinate permutation. Entering helpers have paid wrappers around the complete invocation; at most one helper and no active data wire uses that family in that invocation. Route[4,child,offset,width,spectators], width9 route[3,child,offset].'
+t['bank_padding']['families']=[];t['bank_padding']['children']=[];t['cover_final_correction']['families']=[0,DATA];t['cover_final_correction']['charged_calls_per_cover']=DATA
+for e in t['execution_schedule']:
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,DATA]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+# Expand the retained controller into one-replica blocks; each block consists
+# of its full local cover sweep and every following replica-local event before
+# its next local sweep. Final whole-stock correction remains after all replicas.
+blocks={};globals_=[];st=None
+for ei,e in enumerate(parent['execution_schedule']):
+ if e['kind']in('bank_padding_cover_sweep','translate_every_live_family'):
+  globals_.append((ei,e));continue
+ if e['kind']=='local_cover_sweep':st=e['stage'];blocks[st]=[]
+ assert st is not None
+ blocks[st].append((ei,e))
+new_schedule=[]
+for tm,(s,rep)in enumerate(call_order):
+ for ei,e in blocks[s]:
+  ne=copy.deepcopy(e);ne.update(replica=rep,replicas=[rep],source_event=ei,time=tm)
+  if ne['kind']=='local_cover_sweep':ne['provider_id']=selected[s,rep]['provider']
+  new_schedule.append(ne)
+for ei,e in globals_:
+ ne=copy.deepcopy(e);ne['source_event']=ei
+ if e['kind']=='bank_padding_cover_sweep':ne['families']=[DATA,DATA]
+ else:ne.update(t['cover_final_correction'])
+ new_schedule.append(ne)
+t['execution_schedule']=new_schedule
+cmap={(c['stage'],c['replica']):c for c in t['calls']}
+t['calls']=[dict(cmap[s,rep],time=tm)for tm,(s,rep)in enumerate(call_order)]
+t['loop_order']='Follow the explicit asynchronous execution_schedule. Each local invocation completes before the next, including its entire cover sweep and normalization wrappers. Per-replica source event order is preserved; each idle remainder executes before that replica next touches its family.'
+t['async_schedule']=dict(order=[list(x)for x in call_order],source_plan_sha256=hashlib.sha256(PLAN.read_bytes().replace(b'\r\n',b'\n')).hexdigest(),source_schedule=parent['execution_schedule'],source_call_order=[[c['stage'],c['replica']]for c in parent['calls']],scope='Only independent replica controllers are interleaved. Owner windows are measured on the owner replica timeline; no within-cover or within-invocation interleaving.')
+assert dict(sorted(paid.items()))=={int(k):v for k,v in plan['profile'].items()}
+assert M*M>2*max(paid)**2
+
+assert all(c['local_program_sha256']==registry[c['provider_id']]['local_program_checks'][c['orientation']]['sha256']for c in t['calls'])
+t['provider_dispatch']='For each indivisible local_cover_sweep, execute local_providers[call.provider_id].local_programs[call.orientation] with that provider residual adapters and Clifford recipes. The sweep provider_id must equal its call provider_id.'
+raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+res=dict(status='EMITTED_MIXED_PROVIDER_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE',
+ template_sha256=hashlib.sha256(raw).hexdigest(),
+ parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),
+ live=DATA,physical=physical,global_profile=dict(sorted(paid.items())),
+ rank_mass=sum(r*n for r,n in paid.items()),deficit=2560,maxchild=max(paid),
+ hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering,
+ unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(),
+ cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles),
+ asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(),
+ source_artifacts=source_artifacts,provider_counts=dict(Counter(c['provider_id']for c in t['calls'])),
+ scope='Two actual verified plain/width-seven providers dispatched per complete invocation; independent controller/spectator/normalization and complete finite invoice admission required.')
+(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2))
diff --git a/research/gauge44-leaver8/code/freeze_spec.py b/research/gauge44-leaver8/code/freeze_spec.py
new file mode 100644
index 0000000000..dd0358d396
--- /dev/null
+++ b/research/gauge44-leaver8/code/freeze_spec.py
@@ -0,0 +1,29 @@
+"""Freeze independently recomputed discovery values before strict replay."""
+import argparse
+import json
+from pathlib import Path
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--spec', type=Path, required=True)
+ap.add_argument('--discovery', type=Path, required=True)
+a = ap.parse_args()
+spec = json.loads(a.spec.read_text())
+for line in (a.discovery/'WITNESS-RECORD.jsonl').read_text().splitlines():
+    key, value = json.loads(line)
+    parts = key.split('.')
+    if len(parts)>3 and parts[0]=='providers' and parts[2]=='artifacts':
+        parts = parts[:3] + ['.'.join(parts[3:])]
+    target = spec
+    for part in parts[:-1]:
+        target = target.setdefault(part, {})
+    if parts[-1] in target:
+        assert target[parts[-1]]==value, 'Conflicting independent recomputations: '+key
+    target[parts[-1]] = value
+assembly = json.loads((a.discovery/'ASSEMBLY.json').read_text())
+for key in ('complex_lower','conservative_complex_lower','kappa','kappa_decimal','conservative_kappa_decimal'):
+    spec['expected'][key] = assembly[key]
+spec['expected']['assembly_controls_rejected'] = 69
+spec['expected']['provider_counts'] = {'gauge44':72}
+spec['expected']['mutations_rejected'] = 15
+a.spec.write_text(json.dumps(spec, indent=2)+'\n')
+print('Frozen exact witness for strict replay:', assembly['kappa_decimal'])
diff --git a/research/gauge44-leaver8/code/generated_identity.py b/research/gauge44-leaver8/code/generated_identity.py
new file mode 100644
index 0000000000..74a9b60479
--- /dev/null
+++ b/research/gauge44-leaver8/code/generated_identity.py
@@ -0,0 +1,62 @@
+"""Proof-relevant identities for generated artifacts, independent of gzip streams.
+
+Immutable source archives retain their exact byte hashes. For freshly emitted
+artifacts, gzip identity is the exact decompressed payload and JSON identity
+retains every field. Only CLIFFORD-REVIEW's root timing field is excluded.
+Literal receipt references are checked against actual files before replacing
+the three gzip references (and the phase recipe reference) with content hashes.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+import copy
+import gzip
+import hashlib
+import json
+import math
+
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+
+FILES=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+       'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json',
+       'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json')
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+def json_identity(value):
+    return hashlib.sha256(json.dumps(value,sort_keys=True,separators=(',',':'),allow_nan=False).encode('utf-8')).hexdigest()
+
+def payload_identity(path):
+    return hashlib.sha256(gzip.decompress(Path(path).read_bytes())).hexdigest()
+
+def phase_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'CLIFFORD-REVIEW.json').read_bytes())if value is None else value)
+    assert value['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz'),'stale phase canonical word reference'
+    assert value['recipe_sha256']==sha(directory/'CLIFFORD-RECIPES.json'),'stale phase recipe reference'
+    seconds=value.pop('seconds')
+    assert type(seconds)in(int,float) and math.isfinite(seconds) and seconds>=0,'invalid phase timing metadata'
+    value['canonical_word_sha256']=payload_identity(directory/'CANONICAL-WORD.json.gz')
+    value['recipe_sha256']=json_identity(json.loads((directory/'CLIFFORD-RECIPES.json').read_bytes()))
+    return value
+
+def native_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'INDEPENDENT-LOCAL-REPLAY.json').read_bytes())if value is None else value)
+    for field,name in [('canonical_word_sha256','CANONICAL-WORD.json.gz'),('local_programs_sha256','LOCAL-PROGRAMS.json.gz')]:
+        assert value[field]==sha(directory/name),'stale native artifact reference: '+field
+        value[field]=payload_identity(directory/name)
+    return value
+
+def artifact_identities(directory):
+    directory=Path(directory)
+    result={}
+    for name in FILES:
+        path=directory/name
+        if name.endswith('.gz'):
+            result[name]=payload_identity(path)
+        else:
+            value=phase_value(directory)if name=='CLIFFORD-REVIEW.json'else native_value(directory)if name=='INDEPENDENT-LOCAL-REPLAY.json'else json.loads(path.read_bytes())
+            result[name]=json_identity(value)
+    return result
diff --git a/research/gauge44-leaver8/code/invoice_allcold.py b/research/gauge44-leaver8/code/invoice_allcold.py
new file mode 100644
index 0000000000..b244cd5994
--- /dev/null
+++ b/research/gauge44-leaver8/code/invoice_allcold.py
@@ -0,0 +1,329 @@
+"""Fresh call-specific mixed-provider finite invoice.
+
+Prepared with OpenAI Codex assistance, Apache-2.0. The scalar/Horner recount
+and finite inequalities are adapted from the retained PR558 -> PR552 ->
+PR531 invoice_final.py, whose notices and sources are preserved in the package.
+Every call selects a hash-bound provider. Shared compiler reserves use maxima;
+primitive work, coefficient work, local children and wrappers are also summed
+from actual selected provider/orientation records.
+"""
+import argparse, gzip, hashlib, json
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+from generated_identity import artifact_identities
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+assert __debug__, 'Assertions required'
+
+def read(path):
+    data=path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix=='.gz' else data)
+def filehash(path): return hashlib.sha256(path.read_bytes()).hexdigest()
+def contenthash(path):
+    data=path.read_bytes()
+    return hashlib.sha256(gzip.decompress(data) if path.suffix=='.gz' else data).hexdigest()
+def programhash(events):
+    return hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest()
+
+def recount_provider(local_dir, registry):
+    cp=local_dir/'CANONICAL-WORD.json.gz'; pp=local_dir/'LOCAL-PROGRAMS.json.gz'
+    rp=local_dir/'INDEPENDENT-LOCAL-REPLAY.json'
+    w,programs,replay=read(cp),read(pp),read(rp)
+    checks=read(local_dir/'LOCAL-CHECKS.json')
+    assert set(programs)=={'forward','backward'}
+    assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+    assert replay['canonical_word_sha256']==filehash(cp)==registry['canonical_word_sha256']
+    assert replay['local_programs_sha256']==filehash(pp)==registry['local_programs_sha256']
+    assert programs==registry['local_programs']
+    assert checks==registry['local_program_checks']
+    assert filehash(local_dir/'CLIFFORD-RECIPES.json')==registry['exact_local_clifford_recipe_sha256']
+    assert filehash(local_dir/'RESIDUAL-ADAPTERS.json')==registry['residual_adapter_sha256']
+    v,helpers,h,m=w['v'],w['R'],w['h'],73
+    assert (v,h)==(112,9) and type(helpers) is int and helpers>0
+    assert registry['v']==v and registry['R']==helpers and registry['h']==h
+    assert registry['ports']==w['ports'] and registry['centers']==w['centers']
+    assert replay['v']==v and replay['helpers']==helpers
+    n=2*v+helpers
+    widths = [len(w['frames'][w['final'][r]])-len(w['frames'][w['start'][r]]) for r in range(2*v, 2*v+helpers)]  # HPE: |final|-|start|
+    terminal_codim = sum(h-len(w['frames'][w['final'][r]]) for r in range(2*v, 2*v+helpers))  # HPE: 0 for FULL-ended helpers
+    ends = {r: f for r, f in enumerate(w['final']) if r >= 2*v and f != 1}
+    assert len(widths) == helpers
+    entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0}
+    entering = len(entrances)
+    wrapped = {**entrances, **{r: 0 for r in ends if r not in entrances}}   # COLD-HPE: cold hyperplane-ended helpers carry wrappers too
+    cold_ends = len(wrapped) - len(entrances)
+    assert entering == replay['entering_helpers']
+    local = {}
+    for orientation, events in programs.items():
+        # Endpoint equality and native frames were already independently
+        # replayed on all n columns in the hash-bound receipt above.
+        env = {('L', r): Q(1) for r in range(n)}
+        peak = Q(1)
+        real = macros = workops = 0
+        paid = Counter()
+        wrappers = {'pre': set(), 'post': set()}
+        for event in events:
+            tag = event[0]
+            if tag == 'climb':
+                paid[event[5]] += 1
+            elif tag == 'center':
+                paid[event[4]] += 1
+            elif tag == 'residual_adapter':
+                _, kind, register, frame, *end = event
+                assert kind in wrappers and wrapped.get(register) == frame
+                assert end == ([ends[register]] if register in ends else [])  # HPE: R_{E,U}^-1 and L_{E,U}^-1 name U
+                assert register not in wrappers[kind]
+                wrappers[kind].add(register)
+            elif tag == 'scalar':
+                macros += 1
+                scalar = event[1]
+                op, target = scalar[0], tuple(scalar[1])
+                if op == 'clear':
+                    env[target] = Q(0)
+                    count = 1
+                elif op == 'copy':
+                    env[target] = env[tuple(scalar[2])]
+                    count = 1
+                elif op == 'scale':
+                    q = Q(scalar[2], scalar[3])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert numerator and numerator & (numerator-1) == 0
+                    assert denominator & (denominator-1) == 0
+                    env[target] *= abs(q)
+                    count = abs(numerator.bit_length()-denominator.bit_length()) + int(q < 0)
+                elif op == 'add':
+                    source = tuple(scalar[2])
+                    q = Q(scalar[3], scalar[4])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert source != target and numerator > 0
+                    assert denominator & (denominator-1) == 0
+                    acc, count = 0, 1  # clear coefficient work
+                    for i, bit in enumerate(bin(numerator)[2:]):
+                        if i:
+                            acc *= 2
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                        if bit == '1':
+                            acc += 1
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                    value = Q(acc)
+                    for _ in range(denominator.bit_length()-1):
+                        value /= 2
+                        count += 1
+                        peak = max(peak, value*env[source])
+                    assert value == abs(q)
+                    count += 2  # signed accumulation and work clear
+                    env[target] = env.get(target, Q(0)) + abs(q)*env[source]
+                    workops += count
+                else:
+                    raise AssertionError(op)
+                real += 2*count
+                peak = max(peak, env[target])
+            else:
+                assert tag in ('adapter', 'phase')
+        assert wrappers['pre'] == wrappers['post'] == set(wrapped)
+        assert all(value == 0 for register, value in env.items() if register[0] == 'C')
+        prior = replay['local'][orientation]
+        assert prior['all_exact_columns'] == n and prior['private_work_erased']
+        assert peak == Q(prior['prefix_l1_upper']) and peak < 2**prior['charged_payload_bits']
+        bits = peak.numerator.bit_length()-peak.denominator.bit_length()+1
+        assert bits == prior['prefix_bits_upper']
+        assert real == checks[orientation]['real_component_primitive_bound']
+        assert macros == checks[orientation]['scalar_macros']
+        assert dict(paid) == {int(r): count for r, count in checks[orientation]['paid_profile'].items()}
+        assert dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()}
+        local[orientation] = dict(
+            events=len(events), macros=macros, real_component_primitives=real,
+            prefix_l1=str(peak), prefix_bits=bits,
+            coefficient_work_primitive_count=workops, all_exact_columns=n,
+            dirty_helper_columns=helpers, all_dirty_helper_columns_restored=True,
+            private_centres_and_coefficient_work_cleared=True,
+            pre_wrappers=len(wrappers['pre']), post_wrappers=len(wrappers['post']),
+            endpoint_evidence='Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json')
+
+    centres = len(w['centers'])
+    children = sum(checks['forward']['paid_profile'].values())
+    assert checks['forward']['paid_profile'] == checks['backward']['paid_profile']
+    macro_bound = max(row['macros'] for row in local.values())
+    compiler = 64*(m+1)**3
+    adapters = 16*(macro_bound+children+n+centres)+64*m
+    primitive_bound = max(row['real_component_primitives'] for row in local.values())+adapters*compiler
+
+    assert widths==registry['widths']
+    artifacts={f.name:filehash(f) for f in local_dir.iterdir() if f.is_file()}
+    phase_review=read(local_dir/'CLIFFORD-REVIEW.json')
+    return dict(local=local,helpers=helpers,centres=centres,v=v,h=h,n=n,
+                entering_helpers=entering,entrance_rank=sum(len(w['frames'][f]) for f in w['start'][2*v:]),
+                terminal_codimension=terminal_codim, hyperplane_ended_helpers=len(ends),  # HPE: always reported (0 for FULL-ended words)
+                **({'cold_hyperplane_ended_helpers': cold_ends} if cold_ends else {}),  # COLD-HPE: absent without cold ends
+                width_inventory=dict(sorted(Counter(widths).items())),widths=widths,
+                local_adapters=adapters,local_primitive_bound=primitive_bound,
+                compiler=compiler,children=children,artifacts=artifacts,
+                paid_profile=checks['forward']['paid_profile'],
+                program_hashes={o:programhash(events) for o,events in programs.items()},semantic_artifact_sha256=artifact_identities(local_dir))
+
+
+def run(base, hosted, audit, out, retained_invoice=None):
+    local_dir=base/'split-centres'
+    parent=read(local_dir/'GLOBAL-TEMPLATE.json.gz')
+    template_path=hosted/'GLOBAL-TEMPLATE.json.gz'
+    template=read(template_path); summary=read(hosted/'HOSTED.json')
+    owners=read(audit/'OWNERS-AND-PROFILE.json'); control=read(audit/'ASYNC-AUDIT.json')
+    template_hash=contenthash(template_path)
+    assert template_hash==control['complex_template_sha256']==owners['template_sha256']==summary['template_sha256']
+    assert owners['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE'
+    assert template['recipe']==parent['recipe']
+    assert 'local_programs' not in template
+    assert set(template['local_providers'])==set(PIDS)
+    providers={pid:recount_provider(base/'providers'/pid,registry)
+               for pid,registry in template['local_providers'].items()}
+    for pid,p in providers.items():
+        assert owners['provider_phase_semantic_sha256'][pid]==control['provider_phase_semantic_sha256'][pid]==p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']
+        # The fresh controller admission must cite precisely these provider bytes.
+        for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+                     'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json',
+                     'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json'):
+            path='providers/'+pid+'/'+name
+            assert summary['source_artifacts'][path]==p['artifacts'][name]
+            assert owners['source_artifacts'][path]==p['artifacts'][name]
+    # R is read from the provider words (all must agree); the parent dedicated-bank
+    # envelope keeps its own helper count R0 from the parent split-centres word.
+    assert len({p['helpers'] for p in providers.values()})==1,'providers disagree on helper count R'
+    v,h,m,centres=112,9,73,8
+    helpers=next(iter(providers.values()))['helpers']; n=2*v+helpers
+    assert all((p['v'],p['h'],p['centres'],p['n'])==(v,h,centres,n) for p in providers.values())
+    parent_helpers=read(local_dir/'CANONICAL-WORD.json.gz')['R']
+    stages,replicas,blocks_per_stream=9,8,4
+    call_count=len(template['calls'])
+    assert call_count==stages*replicas==control['complete_invocations']
+    assert control['one_owner_per_complete_invocation']
+    assert len({(c['stage'],c['replica']) for c in template['calls']})==call_count
+    parent_calls={(c['stage'],c['replica']):c for c in parent['calls']}
+    sweeps=[e for e in template['execution_schedule'] if e['kind']=='local_cover_sweep']
+    assert len(sweeps)==call_count
+    selected=[]; selected_paid=Counter(); provider_counts=Counter(); orientation_counts=Counter()
+    scalar=coefficient_work=macros=0; wrapper_factors=0
+    factors_per_wrapper=2*(m-1)
+    for c in template['calls']:
+        pid,orientation=c['provider_id'],c['orientation']; p=providers[pid]
+        old=parent_calls[(c['stage'],c['replica'])]
+        assert orientation==old['orientation'] and c['owners'][:2*v]==old['owners'][:2*v]
+        assert c['local_program_sha256']==p['program_hashes'][orientation]
+        r=p['local'][orientation]
+        scalar+=r['real_component_primitives']; coefficient_work+=r['coefficient_work_primitive_count']; macros+=r['macros']
+        wrapper_factors+=(r['pre_wrappers']+r['post_wrappers'])*factors_per_wrapper
+        provider_counts[pid]+=1; orientation_counts[(pid,orientation)]+=1
+        selected_paid.update({int(k):v for k,v in p['paid_profile'].items()})
+        selected.append(dict(stage=c['stage'],replica=c['replica'],provider_id=pid,orientation=orientation,
+                             program_sha256=c['local_program_sha256'],events=r['events'],macros=r['macros'],
+                             real_component_primitives=r['real_component_primitives'],
+                             coefficient_work_primitive_count=r['coefficient_work_primitive_count'],
+                             entering_helpers=p['entering_helpers'],entrance_rank=p['entrance_rank'],
+                             pre_wrappers=r['pre_wrappers'],post_wrappers=r['post_wrappers']))
+    assert provider_counts==COUNTS
+    # The sweep registry is executable: no hidden use of the historical supplier.
+    by_call={(c['stage'],c['replica']):c for c in template['calls']}
+    for e in sweeps:
+        c=by_call[(e['stage'],e['replica'])]
+        assert e['provider_id']==c['provider_id']
+    assert set(p['compiler'] for p in providers.values())=={64*(m+1)**3}
+    compiler=64*(m+1)**3
+    adapters=max(p['local_adapters'] for p in providers.values())
+    primitive_bound=max(p['local_primitive_bound'] for p in providers.values())
+    bridge_steps=sum(event['kind']=='bridge' for event in parent['recipe'])
+    bridge_sweeps=sum(event['kind']=='bridge' for event in template['execution_schedule'])
+    assert bridge_sweeps==replicas*bridge_steps
+    bridge_additions=2*v*bridge_sweeps
+    shifts=blocks_per_stream*v*replicas; moves=2*shifts
+    parent_live,parent_physical=parent['live'],parent['physical']
+    data_stock=2*v*blocks_per_stream*replicas
+    assert (parent_live-data_stock)%stages==0
+    parent_banks=(parent_live-data_stock)//stages
+    assert parent_banks>=0 and parent_physical==parent_live+parent_helpers+centres+2
+    nonlocal_items=(4*v*replicas*stages+2*v*replicas*stages+2*call_count*helpers
+        +sum(child['replicas'] for child in parent['idle_children'])+stages*parent_banks
+        +bridge_additions+shifts+moves+parent_live+parent_physical+wrapper_factors)
+    outside=8*nonlocal_items+64*m
+    parent_pervertex=(scalar+bridge_additions+shifts+moves+parent_live
+        +(call_count*adapters+outside)*compiler+64*parent_physical)
+    live,physical=template['live'],template['physical']
+    mass,profile=owners['rank_mass'],owners['paid_profile']
+    assert m*live-mass==owners['deficit']==2560
+    assert mass==sum(int(r)*count for r,count in profile.items())
+    assert physical==live+helpers+centres+2
+    assert live==owners['live'] and physical==owners['physical']
+    assert live<=parent_live and physical<=parent_physical
+    assert not template['bank_padding']['families']
+    assert owners['explicit_idle_remainder_children']<=owners['source_idle_children_charged']
+    # The old dedicated-bank geometry is only a conservative reserve envelope.
+    # Its singular program is never used as evidence for a mixed invocation.
+    rebased=parent_pervertex+65*(physical-parent_physical)+(live-parent_live)
+    used=max(rebased,parent_pervertex); retained=None; payload=512
+    if retained_invoice is not None:
+        previous=read(retained_invoice)
+        assert previous['compiler']==compiler and previous['charged_prefix_bits']==payload
+        previous_bound=previous['conservative_pervertex_used']
+        used=max(used,previous_bound+parent_pervertex)
+        retained=dict(sha256=filehash(retained_invoice),previous_pervertex_allowance=previous_bound,
+            added_complete_new_pervertex=parent_pervertex,policy='Retain old allowance and add entire fresh mixed recount.')
+    half=m//2; group=2**(half*half)
+    for i in range(1,half+1): group*=2**(2*i)-1
+    stock,streamed_mass=group*physical,group*mass
+    logical=group*used+64; router=compiler*(logical+1)*(stock+1)**2
+    g_bound,e_bound,c0=2**30000,2**100000,2**210000
+    total_mass=streamed_mass+e_bound
+    literal=2*g_bound*stock**2+8*streamed_mass+4*stock+4+32*m
+    row=2*stock.bit_length()+9909+252+2*payload
+    maxchild=max(map(int,profile))
+    inequalities=dict(local_primitive_bound=primitive_bound<2**48,
+        logical=logical<2**6050,router=router<g_bound,literal=literal<e_bound,
+        mass=total_mass<2**100001,precision=32*m*total_mass*total_mass<c0,
+        tape=2*total_mass+18<c0,row=row<20161,halving=m*m>2*maxchild*maxchild)
+    assert all(inequalities.values())
+    localbits=max(r['prefix_bits'] for p in providers.values() for r in p['local'].values())
+    input_l2_bits=(m+1)//2
+    required_prefix=localbits+input_l2_bits+call_count+bridge_sweeps+4
+    assert required_prefix<payload
+    receipt=dict(status='PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE',
+        template_sha256=template_hash,parent_template_sha256=contenthash(local_dir/'GLOBAL-TEMPLATE.json.gz'),
+        owner_audit_sha256=filehash(audit/'OWNERS-AND-PROFILE.json'),
+        controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'),
+        providers=providers,provider_phase_semantic_sha256={pid:p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']for pid,p in providers.items()},provider_counts=dict(provider_counts),selected_calls=selected,
+        selected_local_paid_profile=dict(sorted(selected_paid.items())),
+        selected_real_component_primitives=scalar,selected_coefficient_work_primitive_count=coefficient_work,
+        selected_scalar_macros=macros,global_prefix_bits=required_prefix,charged_prefix_bits=payload,
+        complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,
+        helpers=helpers,centres=centres,live=live,physical=physical,
+        physical_stock_identity=dict(data_and_owner_families=live,local_helpers=helpers,
+                                     private_centres=centres,coefficient_work=2),
+        local_adapters=adapters,local_primitive_bound=primitive_bound,
+        wrapper_elementary_factors_charged=wrapper_factors,factors_per_wrapper=factors_per_wrapper,
+        compiler=compiler,unhosted_pervertex=parent_pervertex,hosted_rebased_pervertex=rebased,
+        conservative_pervertex_used=used,retained_prior_overcharge=retained,
+        finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),
+                    literal_bits=literal.bit_length(),physical_row_coefficient=row,
+                    retained_row_coefficient=20161,required_C0_bits=(32*m*total_mass*total_mass).bit_length(),
+                    halving_integer_inequality=[m*m,2*maxchild*maxchild],G_exponent=30000,
+                    E_exponent=100000,C0_exponent=210000),strict_checks=inequalities,
+        scope='Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. All three providers use fresh hash-bound independent all-column/frame/phase/normalization admission. Shared compiler uses conservative maxima; parent is geometry/overcharge only. All-size compiler, hosting, precision/tape and analytic transfer remain conditional.')
+    prefix=dict(status='PASS_MIXED_ASYNC_GLOBAL_PREFIX',template_sha256=template_hash,
+        global_prefix_bits=required_prefix,retained_payload_bits=payload,
+        complete_invocation_cover_sweeps=call_count,bridge_factor_two_sweeps=bridge_sweeps,
+        local_scalar_coefficient_work_prefix_bits=localbits,stream_input_sup_to_l2_bits=input_l2_bits,
+        primitive_arithmetic_margin_bits=4,controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'),
+        proof='Each selected normalized provider restores all arbitrary dirty helper columns and gives the same data shear endpoints. Actual whole-owner charts are right-translation bijections. Sum all 72 invocation and 72 bridge sweeps and take maximum local scalar/Horner prefix over all three providers and orientations. Idle children, phases, spectator endpoints and terminal translations are unitary. Retained all-size interfaces are conditional.')
+    out.mkdir(parents=True,exist_ok=True)
+    (out/'PREFIX-AND-INVOICE.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    (out/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix,indent=2)+'\n')
+    print(json.dumps({k:receipt[k] for k in ['status','provider_counts','selected_real_component_primitives',
+          'selected_coefficient_work_primitive_count','global_prefix_bits','finite','strict_checks']},indent=2))
+    return receipt
+
+if __name__=='__main__':
+    parser=argparse.ArgumentParser(description=__doc__)
+    for name in ('base','hosted','audit','out'):parser.add_argument('--'+name,type=Path,required=True)
+    parser.add_argument('--retained-invoice',type=Path)
+    args=parser.parse_args()
+    run(args.base,args.hosted,args.audit,args.out,args.retained_invoice)
diff --git a/research/gauge44-leaver8/code/prepare_global.py b/research/gauge44-leaver8/code/prepare_global.py
new file mode 100644
index 0000000000..655c9470f6
--- /dev/null
+++ b/research/gauge44-leaver8/code/prepare_global.py
@@ -0,0 +1,124 @@
+"""Bind a frozen explicit owner map to exact native local artifacts.
+
+This preparer nominates a witness. The separate serialized controller audit,
+finite invoice, two exact moment engines and strict pinned replay admit it.
+Apache-2.0; prepared with OpenAI assistance. See NOTICE.md.
+"""
+import argparse
+from collections import Counter, defaultdict
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+from generated_identity import artifact_identities, FILES
+
+assert __debug__, 'Assertions required'
+
+
+def read(path):
+    raw = Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def dump(path, value):
+    Path(path).write_text(json.dumps(value, indent=2) + '\n')
+
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--parent', type=Path, required=True)
+ap.add_argument('--owners', type=Path, required=True)
+ap.add_argument('--local', type=Path, required=True)
+ap.add_argument('--data', type=Path, required=True)
+args = ap.parse_args()
+args.data.mkdir(parents=True, exist_ok=True)
+parent_path = args.parent / 'data/PLAN.json'
+assert sha(parent_path) == '258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda'
+plan = read(parent_path)
+word = read(args.local / 'CANONICAL-WORD.json.gz')
+checks = read(args.local / 'LOCAL-CHECKS.json')
+assert (word['v'], word['h'], word['R']) == (112, 9, 492)
+widths = [len(word['frames'][word['final'][224+h]]) -
+          len(word['frames'][word['start'][224+h]]) for h in range(492)]
+profile = {int(k): v for k, v in word['local_profile'].items()}
+assert profile == {1: 2514, 2: 404, 3: 448, 4: 160, 5: 56, 8: 8}
+assert Counter(widths) == {4: 52, 5: 48, 7: 34, 8: 114, 9: 244}
+assert sum(widths) == 3794
+owners = read(args.owners)
+assert len(owners) == 72 * 492
+order = [tuple(x) for x in plan['order']]
+times = {x: i for i, x in enumerate(order)}
+used, call_helpers, call_families = defaultdict(set), defaultdict(set), defaultdict(set)
+for z in owners:
+    key = (z['stage'], z['replica'])
+    h, i, rep, port = z['helper'], z['child'], z['owner_replica'], z['port']
+    assert key in times and 0 <= h < 492 and 0 <= rep < 8 and 0 <= port < 112
+    assert z['time'] == times[key] and h not in call_helpers[key]
+    assert z['family'] not in call_families[key]
+    call_helpers[key].add(h)
+    call_families[key].add(z['family'])
+    cap, allowed = plan['windows'][f'{rep},{i}']
+    assert z['time'] in allowed and z['width'] == widths[h]
+    assert z['copy'] == rep * 112 + port
+    assert z['family'] == rep * 896 + (2*plan['pairs'][str(i)] + plan['sides'][str(i)])*112 + port
+    assert 0 <= z['offset'] and z['offset'] + z['width'] <= cap
+    cells = set(range(z['offset'], z['offset'] + z['width']))
+    group = (i, rep, port)
+    assert not used[group] & cells
+    used[group].update(cells)
+assert set(call_helpers) == set(order)
+assert all(hs == set(range(492)) for hs in call_helpers.values())
+idle = Counter()
+for key, (cap, _) in plan['windows'].items():
+    rep, i = map(int, key.split(','))
+    for port in range(112):
+        cells = used[i, rep, port]
+        assert cells == set(range(len(cells)))
+        left = cap - len(cells)
+        if left:
+            idle[left] += 1
+global_profile = Counter({r: 72*n for r, n in profile.items()}) + idle
+assert sum(r*n for r, n in global_profile.items()) == 520704
+assert 73*7168 - sum(r*n for r, n in global_profile.items()) == 2560
+pid = 'gauge44'
+for c in plan['provider_calls']:
+    c['provider'] = pid
+    c['local_program_sha256'] = checks[c['orientation']]['sha256']
+for c in plan['per_call_widths']:
+    c['widths'] = widths
+artifacts = {name: sha(args.local / name) for name in FILES}
+identities = artifact_identities(args.local)
+plan['provider_registry'] = {pid: dict(
+    directory='providers/' + pid, artifact_sha256=artifacts,
+    ports=word['ports'], centers=word['centers'], widths=widths,
+    actual_paid_profile=word['local_profile'],
+    orientation_program_sha256={k: v['sha256'] for k, v in checks.items()},
+    artifact_semantic_sha256=identities)}
+plan.update(status='FROZEN_EXPLICIT_GAUGE44_WHOLE_OWNER_NOMINATION',
+            mode='gauge44-all72', profile=dict(sorted(global_profile.items())),
+            solver_status='deterministic-capacity-matching', gap=None,
+            source_plan_sha256=sha(parent_path),
+            source_owners_sha256=sha(args.parent / 'data/OWNERS.json.gz'),
+            assignment_sha256=sha(args.owners))
+target_owners = args.data / 'OWNERS.json.gz'
+if args.owners.resolve() != target_owners.resolve():
+    shutil.copyfile(args.owners, target_owners)
+dump(args.data / 'PLAN.json', plan)
+spec = dict(schema='witness-spec/1', name='gauge44-all72',
+            data=dict(plan_sha256=sha(args.data / 'PLAN.json'), owners_sha256=sha(target_owners)),
+            dispatch=[[s, r, pid] for s in range(9) for r in range(8)],
+            call_order=plan['order'], width_spot_helpers=[264, 276, 288, 300],
+            providers={pid: {}}, expected=dict(gain_baseline_kappa='0.001636241501576388'))
+dump(args.data / 'SPEC.json', spec)
+dump(args.data / 'PREPARATION.json', dict(
+    status='PASS_EXPLICIT_MAP_AND_FRESH_PROVIDER_NOMINATION',
+    parent_plan_sha256=sha(parent_path), source_owners_sha256=sha(args.owners),
+    global_profile=dict(sorted(global_profile.items())), idle_profile=dict(sorted(idle.items())),
+    roles=len(owners), rank_mass=520704, deficit=2560,
+    remaining='Independent emitted-controller audit, fresh finite invoice, exact moments and outer assembly.'))
+print('Prepared all72 gauge44 candidate:', dict(sorted(global_profile.items())))
diff --git a/research/gauge44-leaver8/code/restore_parent.py b/research/gauge44-leaver8/code/restore_parent.py
new file mode 100644
index 0000000000..21135f898a
--- /dev/null
+++ b/research/gauge44-leaver8/code/restore_parent.py
@@ -0,0 +1,67 @@
+"""Materialize the omitted generated PR558 parent, then require its reviewed hash.
+
+The integrated review contains the native inputs and INTEGRATION.json but
+omits GLOBAL-TEMPLATE.json.gz. This is only the deterministic template
+binding from the inherited prepare_supplier_base.py; no old circuit or
+phase calculation is rerun. The whole exact payload must match the review.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+assert __debug__, 'Assertions required'
+ap=argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--source',type=Path,required=True)
+ap.add_argument('--baseline',type=Path,required=True)
+ap.add_argument('--out',type=Path,required=True)
+a=ap.parse_args()
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+assert not a.out.exists()
+base=a.out/'complex-global/base'
+shutil.copytree(a.baseline/'complex-global/base',base)
+d=base/'split-centres'
+parent=a.source/'vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz'
+old=read(parent);can=read(d/'CANONICAL-WORD.json.gz')
+checks=read(d/'LOCAL-CHECKS.json');programs=read(d/'LOCAL-PROGRAMS.json.gz')
+v,h,r=can['v'],can['h'],can['R'];c=len(can['centers']);m,t,l,k=73,8,9,4
+assert(v,h,r,c)==(112,9,504,8)
+widths=[h-len(can['frames'][f])for f in can['start'][2*v:]]
+data=2*k*t*v;live=data+l*r;physical=live+r+c+2
+word=copy.deepcopy(old)
+word.update(version='round20-new-supplier-dedicated-bank-parent-v1',live=live,physical=physical,local_programs=programs)
+word['private_namespace']={'centers':[live,live+c],'reserved_tableau':[live+c,live+c+r],'coefficient':[physical-2,physical]}
+for call in word['calls']:
+ s,rep=call['stage'],call['replica'];owners=copy.deepcopy(call['owners'][:2*v])
+ for helper,w in enumerate(widths):
+  route=[2,rep]if w==9 else[2,rep*w,w,list(range(t*w,t*w+9-w))]
+  owners.append([data+s*r+helper,route])
+ call['owners']=owners;call['local_program_sha256']=checks[call['orientation']]['sha256']
+children=[]
+for s in range(l):
+ for helper,w in enumerate(widths):
+  axes=list(range(t*w,m))
+  children.append(dict(family=data+s*r+helper,rank=len(axes),axis_indices=axes,orthogonal_axes=[1<<j for j in axes]))
+word['bank_padding']={'families':list(range(data,live)),'children':children,
+ 'semantics':'Each listed complement frame is applied once after the eight disjoint residual blocks of that dedicated bank. The final hosted derivative has empty families and children.'}
+word['cover_final_correction'].update(families=[0,live],charged_calls_per_cover=live)
+for i,e in enumerate(word['execution_schedule']):
+ if e['kind']=='bank_padding_cover_sweep':word['execution_schedule'][i]={'kind':'bank_padding_cover_sweep','families':[data,live],'children_source':'bank_padding.children'}
+ elif e['kind']=='translate_every_live_family':e.update(word['cover_final_correction'])
+word['exact_data_phase_recipe_sha256']=sha(base/'work/complex-nine-native/DATA-PHASES.json')
+word['exact_local_clifford_recipe_sha256']=sha(d/'CLIFFORD-RECIPES.json')
+word['residual_adapter_sha256']=sha(d/'RESIDUAL-ADAPTERS.json')
+word['supplier_substitution']={'parent_template_sha256':sha(parent),
+ 'old_canonical_word_sha256':sha(a.baseline/'complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz'),
+ 'new_canonical_word_sha256':sha(d/'CANONICAL-WORD.json.gz'),
+ 'exact_same_ports':True,'data_contract':'The same ordered 112 data ports and both complete-invocation identity-shear orientations feed the unchanged nine-stage controller. No old local program or helper profile is reused.'}
+word['route_semantics']['helper']='Dedicated family DATA+stage*R+helper; one helper per bank per complete invocation. Width-nine route[2,replica] uses axes9*replica..9*replica+8. Width-w entering route[2,w*replica,w,spectators] uses the disjoint residual block and paid normalization wrappers; spectator axes start at8*w, beyond all residual blocks.'
+raw=json.dumps(word,sort_keys=True,separators=(',',':')).encode()
+expected=read(d/'INTEGRATION.json')['global_template_sha256']
+assert hashlib.sha256(raw).hexdigest()==expected=='7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3'
+(d/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+print('PASS_EXACT_REVIEWED_PARENT_TEMPLATE_RESTORED',expected)
diff --git a/research/gauge44-leaver8/code/witness.py b/research/gauge44-leaver8/code/witness.py
new file mode 100644
index 0000000000..c5c7fbc114
--- /dev/null
+++ b/research/gauge44-leaver8/code/witness.py
@@ -0,0 +1,55 @@
+"""Spec loader: spec values are EXPECTED values, compared only after independent recomputation.
+WITNESS_DISCOVER=1 runs the same recomputation without comparing pinned values (pin() records only);
+it is used once to produce outputs for generate_spec.py, after which the strict run must pass.
+"""
+import json,os
+from collections import Counter
+from pathlib import Path
+SPEC=json.loads(Path(os.environ['WITNESS_SPEC']).read_text())
+DISCOVER=os.environ.get('WITNESS_DISCOVER')=='1'
+X=SPEC.get('expected',{})
+PROVIDERS=SPEC.get('providers',{})
+DISPATCH={(s,r):p for s,r,p in SPEC['dispatch']}
+CALL_ORDER=[tuple(x)for x in SPEC['call_order']]
+# width-8 spot helpers: PR558's helpers 270, 282, 294, 306, or their images under a K-triangle word's 504 -> R helper map
+# (verify.py checks the spec value against the constructor's HELPER-MAP.json)
+SPOT=tuple(SPEC.get('width_spot_helpers',(270,282,294,306)))
+# A pivot swap moves a kernel family's pivot role p -> x; the old pivot p becomes an ordinary cold helper and its width
+# goes 8 -> 9 (construction/layers, PR641 PROOF-NOTE-PIVOT). Expected spot widths are derived from the package's pinned
+# pivot-swap recipe (path and sha256 in the spec), not from free data: 9 at a swapped-out pivot, 8 otherwise.
+_PKG=Path(os.environ['WITNESS_SPEC']).resolve().parents[1]
+def _old_pivots():
+ ps=SPEC.get('pivot_swap')
+ if not ps:return frozenset()
+ raw=(_PKG/ps['recipe']).read_bytes();import hashlib
+ assert hashlib.sha256(raw).hexdigest()==ps['sha256'],'pivot-swap recipe pin'
+ return frozenset(s['pivot']for s in json.loads(raw)['swaps'])
+OLD_PIVOTS=_old_pivots()
+def spot_widths(v=112):
+ """Expected residual widths at the spot helpers (helper indices) of the gauge44 provider."""
+ return tuple(9 if 2*v+h in OLD_PIVOTS else 8 for h in SPOT)
+PIDS=tuple(sorted(set(DISPATCH.values())))
+COUNTS=dict(Counter(DISPATCH.values()))
+assert DISCOVER or set(PROVIDERS)==set(PIDS),'spec providers differ from dispatch providers'
+def lookup(key):
+ """Dotted spec path; a segment may itself contain dots when it names a file (split at most once per known file suffix)."""
+ v=SPEC;parts=key.split('.')
+ while parts:
+  for n in range(len(parts),0,-1):
+   k='.'.join(parts[:n])
+   if isinstance(v,dict) and k in v:v=v[k];parts=parts[n:];break
+  else:raise KeyError('spec has no key %s'%key)
+ return v
+def pin(key,got):
+ """Strict mode: got must equal the spec value at dotted key; the failure names the key."""
+ if DISCOVER:
+  if os.environ.get('WITNESS_RECORD'):   # discovery bookkeeping only: append (key, value) for the spec writer
+   with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10))
+  return got
+ want=lookup(key)
+ assert got==want,'SPEC MISMATCH %s: expected %s got %s'%(key,json.dumps(want)[:400],json.dumps(got,default=str)[:400])
+ return got
+def partner(pid):
+ """A different provider for substitution controls (next in sorted order)."""
+ assert len(PIDS)>1
+ return PIDS[(PIDS.index(pid)+1)%len(PIDS)]
diff --git a/research/gauge44-leaver8/construction/COLD44-RECIPE.json.gz b/research/gauge44-leaver8/construction/COLD44-RECIPE.json.gz
new file mode 100644
index 0000000000..6f59d88920
Binary files /dev/null and b/research/gauge44-leaver8/construction/COLD44-RECIPE.json.gz differ
diff --git a/research/gauge44-leaver8/construction/COMPLETION-PRIORITY.json b/research/gauge44-leaver8/construction/COMPLETION-PRIORITY.json
new file mode 100644
index 0000000000..e0df30aeef
--- /dev/null
+++ b/research/gauge44-leaver8/construction/COMPLETION-PRIORITY.json
@@ -0,0 +1,746 @@
+{
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+}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/INPUTS.json b/research/gauge44-leaver8/construction/INPUTS.json
new file mode 100644
index 0000000000..2b12294b58
--- /dev/null
+++ b/research/gauge44-leaver8/construction/INPUTS.json
@@ -0,0 +1,65 @@
+{
+  "schema": "gauge44-compact-construction-v1",
+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "commits": {
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+    "pr635": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f"
+  },
+  "files": {
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+      "research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py": "322d29d43dbee8130cde15d4bf05396698b5e3dfe3735813899db91cc0ba7955",
+      "research/complex-k492-owner-repair/vendor/multicold/data/EIGHT-COLD.json": "089617bdc33fd9f27b7fc8e9ae9e01c8e65a86a57c4b6f180f4f378f3f0e6160",
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+      "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
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+      "research/structural-gain/frontier-composition/multicold-eight-word/FULL-WORD.json.gz": "4d4a59db7f74d7505447fbb2aa87735771cca1d04a0afafa455d21bd8dbf1f77"
+    },
+    "pr635": {
+      "research/complex-571-cold14-st2/code/build_cold_end.py": "864b4701dd73afd0c9d99761b7a749f3354c48985730f17054e18c052996a668",
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+      "research/complex-571-cold14-st2/code/hpe_audit_and_transport.py": "c9a05ff291016b870b4fc925b317abd9c3a604c73ffc8920dfdbbeb475e20aa3",
+      "research/complex-571-cold14-st2/code/hpe_audit_local.py": "6bd9a1e279c9c9e4f3767d9f82e537b559292906feb2ddab02f380fb6523a810",
+      "research/complex-571-cold14-st2/code/hpe_emit_local.py": "7e4a6fbc38c8228157b6311457d1496bf460291393043932d2c365f004f77805",
+      "research/complex-571-cold14-st2/data/TRI-SCHEDULE.json": "94da9d5575f5b237097a77ac7dd09aff594322dd9c35138bfd34ffc5e1a7a51e",
+      "research/complex-571-cold14-st2/data/recipes/k492-jp8-frame_regroup.json": "9bd347334de643f29865290be1ed37289f9cae6cd339547ac89b45fa7aaee65a",
+      "research/complex-571-cold14-st2/data/recipes/k492-jp8-hyperplane_end.json": "e4d4dfd83d0c64cb0a8ee8c8bbd95d0510ee68699859e568fe201cd6f8d250c1"
+    },
+    "delta": {
+      "COLD44-RECIPE.json.gz": "22d0e01e990c0f1c588607a095271f7844851a437ba07174505e98e9528aed4c",
+      "COMPLETION-PRIORITY.json": "0274ffca1725e7460aaf7b672bc1248aa6dfdec11e5f0fec91af18b829f8ba47",
+      "build_gauge_cold44.py": "ec730a4d3ff12fb058780718b1d5a7afe61243c532679ef347a5a48e2af0a3bb",
+      "construct_gauge_xcentre.py": "d8d295566ef2399af2da0707a4adc83e07aa26d2344c01a66bd0ca7684cf9217",
+      "reproduce.py": "047bb9b3536b0b16bb08a21cd9fd80404ca9d022345f1aeab34b21dffc281c92"
+    }
+  },
+  "word_content_sha256": {
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+    "shadow-prefix": "6c361b33967bb62d878b3acef44a4ac2c70970e99f36a11906b03811495de533",
+    "raw": "0ac47f92fc2e3f5aa457d78f7b8a5c785bf140c546932b9dfcd9e610ad319180",
+    "port0": "7086d4309f145f0bf85b97f567e2cbeeaca9fc5011f62c86c805bfadeb0300fc",
+    "port1": "8f47545698a11072f8c6a0b50ae9c8acf8e4e2b0e35a0e8c672bbca216b04534",
+    "port2": "4e4919c140e07f6c820bea4aae83565b3b4967ffbfbb907611216ff6e2e6105d",
+    "port3": "9774dca3e4295e2eb9171a9cf34e1973bc72bad38eddec2cc0fc498bd9e041f3",
+    "regroup": "989082402d2292a18328e86927c0a12d34fcab18ef4ff724bd1ce691cf4e7531",
+    "hpe": "42fb8b3aa314593fe976820cf65824f5fce0ee4f95281796992d4809709864cc",
+    "cold44": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290"
+  },
+  "helper_map_sha256": "688d5115b221be68c96970822cc04ff698e2a84432fa7db9cb59057f6fe55def",
+  "canonical_content_sha256": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+  "local_program_sha256": {
+    "forward": "d17399c8c7458bb7110d8596fab5f769cd4cb3733a3042277fa08bf03f42d6c9",
+    "backward": "4772df0663f88cc218fd7254eb202f46daf136c06e9e96c19ed8ea218b545dc4"
+  },
+  "clifford_recipes_sha256": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771"
+}
diff --git a/research/gauge44-leaver8/construction/LICENSE b/research/gauge44-leaver8/construction/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/gauge44-leaver8/construction/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
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+      "Work" shall mean the work of authorship, whether in Source or
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+      (an example is provided in the Appendix below).
+
+      "Derivative Works" shall mean any work, whether in Source or Object
+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
+      the Work and Derivative Works thereof.
+
+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
+      to that Work or Derivative Works thereof, that is intentionally
+      submitted to Licensor for inclusion in the Work by the copyright owner
+      or by an individual or Legal Entity authorized to submit on behalf of
+      the copyright owner. For the purposes of this definition, "submitted"
+      means any form of electronic, verbal, or written communication sent
+      to the Licensor or its representatives, including but not limited to
+      communication on electronic mailing lists, source code control systems,
+      and issue tracking systems that are managed by, or on behalf of, the
+      Licensor for the purpose of discussing and improving the Work, but
+      excluding communication that is conspicuously marked or otherwise
+      designated in writing by the copyright owner as "Not a Contribution."
+
+      "Contributor" shall mean Licensor and any individual or Legal Entity
+      on behalf of whom a Contribution has been received by Licensor and
+      subsequently incorporated within the Work.
+
+   2. Grant of Copyright License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      copyright license to reproduce, prepare Derivative Works of,
+      publicly display, publicly perform, sublicense, and distribute the
+      Work and such Derivative Works in Source or Object form.
+
+   3. Grant of Patent License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      (except as stated in this section) patent license to make, have made,
+      use, offer to sell, sell, import, and otherwise transfer the Work,
+      where such license applies only to those patent claims licensable
+      by such Contributor that are necessarily infringed by their
+      Contribution(s) alone or by combination of their Contribution(s)
+      with the Work to which such Contribution(s) was submitted. If You
+      institute patent litigation against any entity (including a
+      cross-claim or counterclaim in a lawsuit) alleging that the Work
+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
+      granted to You under this License for that Work shall terminate
+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
+      Work or Derivative Works thereof in any medium, with or without
+      modifications, and in Source or Object form, provided that You
+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
+          attribution notices from the Source form of the Work,
+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
+          distribution, then any Derivative Works that You distribute must
+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
+          pertain to any part of the Derivative Works, in at least one
+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
+          documentation, if provided along with the Derivative Works; or,
+          within a display generated by the Derivative Works, if and
+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+      implied, including, without limitation, any warranties or conditions
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+      PARTICULAR PURPOSE. You are solely responsible for determining the
+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
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+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
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+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
+      the Work or Derivative Works thereof, You may choose to offer,
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+      on Your own behalf and on Your sole responsibility, not on behalf
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+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
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+
+   Unless required by applicable law or agreed to in writing, software
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diff --git a/research/gauge44-leaver8/construction/NOTICE.md b/research/gauge44-leaver8/construction/NOTICE.md
new file mode 100644
index 0000000000..16b0507070
--- /dev/null
+++ b/research/gauge44-leaver8/construction/NOTICE.md
@@ -0,0 +1,9 @@
+# Construction delta notice
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+
+`construct_gauge_xcentre.py` modifies PR635's credited `construct_k_triangle.py`, which in turn extends icekylinx's PR531/PR514/PR425 factory lineage. Its original source comments are retained. The K-triangle schedule and the upstream porting, JP8 frame, kernel and HPE procedures are reused from the pinned source checkouts and are not new contributions of this delta.
+
+The new source-copy exchanges, complementary factory basis, carrier assignment, exact cold44 constructor and compact reproduction driver are described in `../CONSTRUCTION.md`.
+
+`UPSTREAM-NOTICE.md` is the complete unmodified notice from the pinned PR635 package. `LICENSE` is that package's Apache-2.0 license. All further notices and source credits of the referenced upstream packages remain applicable and are retained in the source checkouts rather than vendored again here.
diff --git a/research/gauge44-leaver8/construction/REBUILD-CHECKS.json b/research/gauge44-leaver8/construction/REBUILD-CHECKS.json
new file mode 100644
index 0000000000..0801f35da7
--- /dev/null
+++ b/research/gauge44-leaver8/construction/REBUILD-CHECKS.json
@@ -0,0 +1,51 @@
+{
+  "status": "PASS_COMPACT_SCALAR_REPRODUCTION_AND_FROZEN_RECIPE_SPLICE",
+  "steps": [
+    {
+      "step": "shadow-early",
+      "exit_code": 0,
+      "seconds": 0.355
+    },
+    {
+      "step": "shadow-prefix",
+      "exit_code": 0,
+      "seconds": 0.511
+    },
+    {
+      "step": "gauge-forward",
+      "exit_code": 0,
+      "seconds": 0.527
+    },
+    {
+      "step": "port0",
+      "exit_code": 0,
+      "seconds": 0.468
+    },
+    {
+      "step": "port1",
+      "exit_code": 0,
+      "seconds": 0.636
+    },
+    {
+      "step": "port2",
+      "exit_code": 0,
+      "seconds": 0.474
+    },
+    {
+      "step": "port3",
+      "exit_code": 0,
+      "seconds": 0.497
+    },
+    {
+      "step": "cold44-exact",
+      "exit_code": 0,
+      "seconds": 2.754
+    }
+  ],
+  "constructor_seconds": 6.222,
+  "word_content_sha256": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290",
+  "all_step_input_and_output_pins_checked": true,
+  "regenerated_recipe_equals_frozen_recipe": true,
+  "frozen_splice_matches_exact_constructor": true,
+  "scope": "One portable scalar reconstruction from pinned main and PR635 inputs; existing native and independent mathematical receipts accompany the package separately."
+}
diff --git a/research/gauge44-leaver8/construction/UPSTREAM-NOTICE.md b/research/gauge44-leaver8/construction/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..ebc24a0168
--- /dev/null
+++ b/research/gauge44-leaver8/construction/UPSTREAM-NOTICE.md
@@ -0,0 +1,34 @@
+# Attribution and scope
+
+Four verified provider types are offered to every call: PR571's prefix word with twelve multi-cut cold kernels (PR568's unchanged constructor), the same word with forty width-five entrance promotions (PR569's unchanged frame constructor) before those kernels, PR575's plain joint-prefix provider, and PR568's eight-cold provider. A window MILP with an exact per-pattern model chooses the dispatch and a literal owner map. PR583's six source-bound kernel frame coalescences (its unchanged constructor and negative controls) are applied to every PR571-prefix provider word (ck and atm3), followed by two further coalescences that each first move one addition past two commuting additions (package code/build_gate_moves.py, extending PR583's constructor); a final hyperplane_end step (package code/build_hpe.py) then runs 46 single-gate cleanups h -= p right after part B at the dim-8 join U of their registers, so 46 width-8 entering helpers per call end at U with width 7; each such gate commutes with every earlier cleanup gate on its registers (for 8 of them the partner's one earlier gate x -= p only reads p), and the reordered program is replayed exactly. A window MILP (exact windows, RINS around an LP vertex) gives the dispatch ck 45 / atm3 21 / jp8 6 and the literal owner map.
+
+Pinned external sources (unchanged; `verify.py` checks their manifests and every file it uses):
+- PR568 (`research/complex-multicold`, commit `71c99ac935a33bb7b59a1b4a7af8725a939b0b90`).
+- PR571 (`research/structural-gain`, commit `b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3`).
+- PR569 (`research/larger-gain`, commit `897213a855b7fb8a1b8b0e552a2f5c42e6c1b326`).
+- PR575 (`research/complex-joint-prefix`, commit `eac6f7e378ab622dac50a2fd4b7ef6eab014de44`).
+- PR583 (`research/kernel-frame-coalescing`, commit `89be768f0157f5a3d8e4db69cf1748768605eac9`).
+
+Provider construction is described as typed steps in `data/SPEC.json` (`build`); `verify.py` runs only allowlisted step types with their paired omission audits and checks every input and output content hash. `code/` holds the spec-driven global admission scripts adapted from PR571's `frontier-composition/global-code/` (OpenAI Codex assisted, Apache-2.0): every expected value is read from `data/SPEC.json` and compared only after independent recomputation. `code/generated_identity.py` and `code/generated_identity_controls.py`, and the decompressed-content artifact identities in the bind, audit, invoice, assembly and phase-timing scripts, are taken unchanged from PR586 by chafreaky (`research/promoted-kernel-coalescing`, commit `4846fee5b06af770e9b3a10c36200f673d656725`, OpenAI Codex assisted, Apache-2.0), including its proof-content and reference/metadata mutation controls; the normalization of descriptive width metadata after frame changes follows the same PR.
+
+In PR601, the owner map was nominated by a HiGHS window MILP (adapted from PR569's `global/nominate_width7.py`) with lazy cross-time Hall cuts; this package's re-solved map is described below. Neither is an admission dependency.
+
+DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. (The PR601 package this one starts from states: "Prepared by Claude Code (Anthropic) research agents.") Apache-2.0 applies; LICENSE is included. All notices, licenses, source pins and AI disclosures of the pinned sources and their ancestry are retained in those packages and are not replaced by this notice. All inherited conditional assumptions remain conditional.
+
+**This package (complex-571-cold14, DreamingOfClouds).** It starts from PR601 (jeremykothe2, `research/complex-571-hpem46`, commit `529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550`). Everything above is kept unchanged except the following:
+- every provider chain (ck, atm3, jp8) gains the typed step `cold_end` (`code/build_cold_end.py`, `code/cold_end_controls.py`; recipes `data/recipes/*-cold_end.json.gz`);
+- the generalised native chain and the global admission scripts accept cold helpers that end below FULL (with `0:U` wrappers), a refactored exact cleanup, and check the wrapper order;
+- `data/PLAN.json` / `data/OWNERS.json.gz` (dispatch and literal owner map) come from a relocate/swap/ejection-chain/provider-flip annealing search started from PR601's map, refined by an exact pattern-restricted owner model (CP-SAT) with a literal edge-colouring expansion (not an admission dependency);
+- `data/SPEC.json` holds the expected values, recorded by a discovery run and then checked by a strict run.
+
+The cold-end construction (a row-plus-column cone condition for low-frame ends, a rank-0 dirt-spread premix and multi-gate lower-frame cleanup) builds on PR591 / PR592 / PR593 / PR601 (jeremykothe2) and our PR599 (Lean: multi-gate and cold hyperplane-end tails). DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. Build on this at your own risk.
+
+**This package (complex-571-cold14-b3, jeremykothe2).** It is PR604's `complex-571-cold14` (DreamingOfClouds) with ColdBeyond's second cold end per block (two new `cold_end` A-gate primitives, `PROOF-NOTE.md`), ColdSupply's E1 entering pair and reviewed controls, a free dispatch (jp8 ×60, atm3 ×12) and a literal owner map from an exact per-time-Hall window MIP. All other construction, code, controls and proofs are PR604's and earlier contributors', unchanged.
+
+**This package (complex-571-cold14-k492).** It is complex-571-cold14-b3 with these changes:
+- **K-triangle base words.** The leaver-read K-triangle skeleton atom and its read schedule (`data/TRI-SCHEDULE.json`) are by AtomScout, a Claude Code research agent. `code/construct_k_triangle.py` is PR531's `code/construct_504.py` (icekylinx, OpenAI Codex / GPT assisted, Apache-2.0; pinned source `direct_delivery`) extended with that atom.
+- **Ported chains.** The PR604/B3 chains are ported stage by stage onto the K-triangle words by `code/build_port_stage.py` (Port480, a Claude Code research agent). `code/build_frame_regroup.py` extends PR583's `build_frames.py` (chafreaky).
+- **Helper count R.** The generalisation of the global scripts to the provider helper count R is by GlobalR (a Claude Code research agent), with AtomReviewer's fixes (PROOF-NOTE-R.md).
+- **Owner map.** The owner map, the cold_end recipes on the K-triangle words and the package assembly are by Stack492, Port480 and ColdBeyond (Claude Code research agents).
+
+Build on this at your own risk.
diff --git a/research/gauge44-leaver8/construction/barch/LOCAL-PINS-barch-U8.json b/research/gauge44-leaver8/construction/barch/LOCAL-PINS-barch-U8.json
new file mode 100644
index 0000000000..4028b95c0e
--- /dev/null
+++ b/research/gauge44-leaver8/construction/barch/LOCAL-PINS-barch-U8.json
@@ -0,0 +1,50 @@
+{
+ "word": "U8",
+ "barch_controls": [
+  "C0_identity",
+  "recipe",
+  "drop_restore",
+  "restore_full",
+  "drop_preread",
+  "donation_after",
+  "drop_restore@231",
+  "restore_full@231",
+  "drop_preread@231",
+  "donation_after@231",
+  "drop_restore@230",
+  "restore_full@230",
+  "drop_preread@230",
+  "donation_after@230",
+  "drop_restore@232",
+  "restore_full@232",
+  "drop_preread@232",
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+  "drop_restore@236",
+  "restore_full@236",
+  "drop_preread@236",
+  "donation_after@236",
+  "drop_restore@226",
+  "restore_full@226",
+  "drop_preread@226",
+  "donation_after@226",
+  "drop_restore@228",
+  "restore_full@228",
+  "drop_preread@228",
+  "donation_after@228",
+  "drop_restore@62",
+  "restore_full@62",
+  "drop_preread@62",
+  "donation_after@62",
+  "drop_restore@238",
+  "restore_full@238",
+  "drop_preread@238",
+  "donation_after@238"
+ ],
+ "layer_controls": 95,
+ "canonical_sha256": "24db880b7dab31e6af4eec8a1aba1bbbae29cd50d9a7b77cf0e9b571b3e5ae7c",
+ "program_sha256": {
+  "forward": "83d65a63f51bd1ce7f3dd4e4d3597311e065b4775796cd87aea3e3a62689047c",
+  "backward": "e4e483b764e9a85f84a04425e57d73ecdcc72eb2e4d97a64f17d9da58fa5ace0"
+ },
+ "clifford_recipes_sha256": "4629507dcbdd516457c001ff8f9dbe750d1a0cbfa5cfa3c6be003d45804ba0c5"
+}
diff --git a/research/gauge44-leaver8/construction/barch/RECIPE-U8.json b/research/gauge44-leaver8/construction/barch/RECIPE-U8.json
new file mode 100644
index 0000000000..ee215a805a
--- /dev/null
+++ b/research/gauge44-leaver8/construction/barch/RECIPE-U8.json
@@ -0,0 +1,1528 @@
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+   33,
+   18,
+   11,
+   7
+  ],
+  "1391": [
+   256,
+   128,
+   64,
+   32,
+   18,
+   11,
+   7
+  ],
+  "1394": [
+   257,
+   129,
+   65,
+   33,
+   19,
+   10,
+   7
+  ],
+  "1397": [
+   257,
+   129,
+   64,
+   32,
+   19,
+   10,
+   7
+  ],
+  "1400": [
+   257,
+   128,
+   64,
+   33,
+   18,
+   11,
+   7
+  ],
+  "1403": [
+   257,
+   128,
+   65,
+   32,
+   19,
+   10,
+   7
+  ],
+  "1406": [
+   256,
+   129,
+   64,
+   33,
+   18,
+   11,
+   7
+  ],
+  "1409": [
+   256,
+   129,
+   65,
+   32,
+   19,
+   10,
+   7
+  ],
+  "1412": [
+   257,
+   129,
+   64,
+   33,
+   24,
+   4,
+   3
+  ],
+  "1415": [
+   257,
+   129,
+   65,
+   32,
+   24,
+   5,
+   2
+  ],
+  "1418": [
+   256,
+   128,
+   64,
+   33,
+   24,
+   5,
+   2
+  ],
+  "1421": [
+   256,
+   128,
+   65,
+   32,
+   24,
+   4,
+   3
+  ],
+  "1424": [
+   256,
+   129,
+   65,
+   33,
+   24,
+   4,
+   3
+  ],
+  "1427": [
+   256,
+   129,
+   64,
+   32,
+   24,
+   4,
+   3
+  ],
+  "1430": [
+   257,
+   128,
+   65,
+   33,
+   24,
+   4,
+   3
+  ],
+  "1433": [
+   257,
+   128,
+   64,
+   32,
+   24,
+   4,
+   3
+  ]
+ },
+ "tail_insert": [
+  [
+   7,
+   [
+    "add",
+    496,
+    450,
+    -1,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     24,
+     4,
+     2,
+     1
+    ]
+   ]
+  ],
+  [
+   6,
+   [
+    "add",
+    497,
+    451,
+    -1,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     24,
+     4,
+     2,
+     1
+    ]
+   ]
+  ],
+  [
+   5,
+   [
+    "add",
+    520,
+    452,
+    -1,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ],
+  [
+   4,
+   [
+    "add",
+    521,
+    453,
+    -1,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ],
+  [
+   3,
+   [
+    "add",
+    544,
+    454,
+    2,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ],
+  [
+   2,
+   [
+    "add",
+    545,
+    455,
+    2,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ],
+  [
+   1,
+   [
+    "add",
+    568,
+    456,
+    2,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     24,
+     4,
+     2,
+     1
+    ]
+   ]
+  ],
+  [
+   0,
+   [
+    "add",
+    569,
+    457,
+    2,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     24,
+     4,
+     2,
+     1
+    ]
+   ]
+  ]
+ ],
+ "cleanup_prepend": [
+  [
+   "add",
+   484,
+   231,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   485,
+   226,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   508,
+   230,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   509,
+   228,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   532,
+   232,
+   2,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   533,
+   62,
+   2,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   556,
+   236,
+   2,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   557,
+   238,
+   2,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ]
+ ],
+ "local_profile": {
+  "1": 2548,
+  "2": 338,
+  "3": 446,
+  "4": 162,
+  "5": 72,
+  "8": 8
+ },
+ "expect_sha256": "090fd574747fbf9628e70cb9beb792732914cfa52e1df147579fe4dbccc68c5a",
+ "priced": {
+  "dk_ideal": 3.140480230774418e-07,
+  "dP": {
+   "5": 16,
+   "4": -32,
+   "3": 16
+  }
+ },
+ "variants": [
+  {
+   "X": 231,
+   "E": 450,
+   "dsides": [
+    878,
+    886
+   ],
+   "donors": [
+    450,
+    231
+   ],
+   "hold": [
+    496,
+    484
+   ],
+   "kept": {
+    "1215": 450,
+    "1223": 231
+   },
+   "when": "mid"
+  },
+  {
+   "X": 230,
+   "E": 452,
+   "dsides": [
+    894,
+    902
+   ],
+   "donors": [
+    452,
+    230
+   ],
+   "hold": [
+    520,
+    508
+   ],
+   "kept": {
+    "1231": 452,
+    "1239": 230
+   },
+   "when": "mid"
+  },
+  {
+   "X": 232,
+   "E": 454,
+   "dsides": [
+    910,
+    918
+   ],
+   "donors": [
+    454,
+    232
+   ],
+   "hold": [
+    544,
+    532
+   ],
+   "kept": {
+    "1247": 454,
+    "1255": 232
+   },
+   "when": "mid"
+  },
+  {
+   "X": 236,
+   "E": 456,
+   "dsides": [
+    926,
+    934
+   ],
+   "donors": [
+    456,
+    236
+   ],
+   "hold": [
+    568,
+    556
+   ],
+   "kept": {
+    "1263": 456,
+    "1271": 236
+   },
+   "when": "mid"
+  },
+  {
+   "X": 226,
+   "E": 451,
+   "dsides": [
+    880,
+    888
+   ],
+   "donors": [
+    451,
+    226
+   ],
+   "hold": [
+    497,
+    485
+   ],
+   "kept": {
+    "1217": 451,
+    "1225": 226
+   },
+   "when": "mid"
+  },
+  {
+   "X": 228,
+   "E": 453,
+   "dsides": [
+    896,
+    904
+   ],
+   "donors": [
+    453,
+    228
+   ],
+   "hold": [
+    521,
+    509
+   ],
+   "kept": {
+    "1233": 453,
+    "1241": 228
+   },
+   "when": "mid"
+  },
+  {
+   "X": 62,
+   "E": 455,
+   "dsides": [
+    912,
+    920
+   ],
+   "donors": [
+    455,
+    62
+   ],
+   "hold": [
+    545,
+    533
+   ],
+   "kept": {
+    "1249": 455,
+    "1257": 62
+   },
+   "when": "mid"
+  },
+  {
+   "X": 238,
+   "E": 457,
+   "dsides": [
+    928,
+    936
+   ],
+   "donors": [
+    457,
+    238
+   ],
+   "hold": [
+    569,
+    557
+   ],
+   "kept": {
+    "1265": 457,
+    "1273": 238
+   },
+   "when": "mid"
+  }
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/barch/build_tri.py b/research/gauge44-leaver8/construction/barch/build_tri.py
new file mode 100644
index 0000000000..11c4371114
--- /dev/null
+++ b/research/gauge44-leaver8/construction/barch/build_tri.py
@@ -0,0 +1,87 @@
+#!/usr/bin/env python3
+"""build_tri.py BASE_WORD RECIPE OUT_WORD [--control NAME]
+
+Standard library only. Applies a NewBArch triangle-hybrid recipe to the X4 word (1e1d99ba) and writes a FULL-WORD.json.gz.
+Recipe keys (all indices refer to the BASE word):
+  base_sha256      sha256 of the decompressed base JSON (checked)
+  B_delete         list of B indices removed
+  B_insert         list of [pos, gate]: gate (with frame) inserted before base B gate pos (list order kept)
+  B_frames         {index: frame}: explicit re-chosen frame of a kept base B gate
+  tail_insert      list of [early_index, gate]: gates appended to cleanup in list order, then registered as early cleanup at early_index (ascending)
+  cleanup_prepend  list of gates prepended to the full cleanup (early indices are shifted)
+  local_profile    report.local_profile of the result
+  expect_sha256    sha256 of the decompressed result (checked unless a control is requested)
+Controls (each must be REJECTED by audit_local; see controls.json):
+  drop_restore     omit cleanup_prepend (end value of the holder not restored)
+  restore_full     move tail_insert gates into the full cleanup (FULL frame) instead of early cleanup
+  drop_preread     omit the inserted entrance pre-reads (inserted target += E gates at pos < first donation)
+  donation_after   insert each donation after its reading target's read instead of before it
+  NAME@X           the same control restricted to the instance whose packet register is X (recipe 'variants')
+"""
+import sys, json, gzip, hashlib, copy
+
+FULL = [256, 128, 64, 32, 16, 8, 4, 2, 1]
+
+def load(p):
+    raw = gzip.decompress(open(p, 'rb').read()); return json.loads(raw), hashlib.sha256(raw).hexdigest()
+
+def apply(w, rc, control=None):
+    w = copy.deepcopy(w); B = w['B']
+    S = None
+    if control and '@' in control:                     # per-instance control: name@X mutates only instance X's gates
+        control, x = control.split('@'); x = int(x)
+        vv = [s for s in rc['variants'] if s['X'] == x][0]; S = {vv['X'], vv['E'], *vv['hold']}
+    sel = lambda g: S is None or bool({g[1], g[2]} & S)
+    dele = set(rc['B_delete']); fr = {int(k): f for k, f in rc['B_frames'].items()}
+    ins = [list(x) for x in rc['B_insert']]
+    don = [x for x in ins if not (112 <= x[1][1] < 224)]           # donations: destination is not a target
+    first_don = min(p for p, _ in don) if don else 0
+    if control == 'drop_preread':
+        ins = [x for x in ins if not (x[0] < first_don and 112 <= x[1][1] < 224 and sel(x[1]))]
+    if control == 'donation_after':
+        new = []
+        for p, g in ins:
+            if g in [d[1] for d in don] and sel(g):
+                rd = [i for i, e in enumerate(B) if i >= p and e[0] == 'add' and e[2] == g[1] and 112 <= e[1] < 224]
+                p = rd[0] + 1
+            new.append([p, g])
+        ins = new
+    at = {}
+    for p, g in ins: at.setdefault(p, []).append(list(g))
+    out = []
+    for i, e in enumerate(B):
+        out.extend(at.get(i, []))
+        if i in dele: continue
+        e = list(e)
+        if i in fr: e = e[:-1] + [list(fr[i])]
+        out.append(e)
+    out.extend(at.get(len(B), []))
+    w['B'] = out
+    pre = [list(g) for g in rc['cleanup_prepend'] if not (control == 'drop_restore' and sel(g))]
+    tails = [list(x) for x in rc['tail_insert']]
+    if control == 'restore_full':
+        pre = pre + [g[1][:-1] + [FULL] for g in tails if sel(g[1])]; tails = [g for g in tails if not sel(g[1])]
+    C = pre + w['cleanup']; sh = len(pre)
+    early = [[i + sh, U] for i, U in w['early_cleanup']]
+    idx = []
+    for j, g in tails: C.append(list(g)); idx.append((j, len(C) - 1, list(g[-1])))   # appended in recipe order
+    for j, ci, U in sorted(idx): early.insert(j, [ci, U])                               # then registered at their early index
+    w['cleanup'] = C; w['early_cleanup'] = early
+    w['report'] = dict(w['report']); w['report']['local_profile'] = rc['local_profile']
+    return w
+
+def main():
+    a = sys.argv[1:]; control = None
+    if '--control' in a: k = a.index('--control'); control = a[k + 1]; del a[k:k + 2]
+    base, out = a[0], a[2]
+    w, sha = load(base); rc = json.load(open(a[1]))
+    if sha != rc['base_sha256']: raise SystemExit('base sha mismatch ' + sha)
+    w2 = apply(w, rc, control)
+    raw = json.dumps(w2, separators=(',', ':')).encode()
+    open(out, 'wb').write(gzip.compress(raw, mtime=0))
+    s = hashlib.sha256(raw).hexdigest()
+    if control is None and s != rc['expect_sha256']: raise SystemExit('result sha mismatch ' + s)
+    print(json.dumps(dict(control=control, sha256=s)))
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/barch/reproduce_barch.py b/research/gauge44-leaver8/construction/barch/reproduce_barch.py
new file mode 100644
index 0000000000..22f15b491d
--- /dev/null
+++ b/research/gauge44-leaver8/construction/barch/reproduce_barch.py
@@ -0,0 +1,92 @@
+#!/usr/bin/env python3
+"""Rebuild the B0 word (NewBArch's width-neutral triangle-hybrid B-delivery rewrite on X4) and its native locals.
+
+Input: a fresh `construction/jx/reproduce_jx.py` output directory; its X4 word (1e1d99ba...) is pinned there and by
+RECIPE-B0.json (base_sha256). Steps, each checked exactly:
+  1. barch: build_tri.py (standard library only; NewBArch) applies the recipe's explicit B deletes and inserts (with frames),
+     re-chosen B frames, early-cleanup tails and FULL-cleanup restores; it checks the base and result shas (d9ba0942...).
+  2. barch-controls: run_controls.py rebuilds C0 (identity, must reproduce the input), the recipe word (must PASS #645's
+     independent audit_local.py) and four mutants (drop_restore, restore_full, drop_preread, donation_after), globally
+     and for each recipe variant (NAME@X); each mutant must FAIL audit_local with its pinned message. Every outcome is
+     required and the control set is pinned (LOCAL-PINS).
+  3. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant) on the B0 word; count pinned.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs; canonical word, local programs and
+     Clifford recipes pinned (LOCAL-PINS-barch-<id>.json).
+Apache-2.0. Driver by ColdWitness around NewBArch's builder and controls.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+PKG = HERE.parents[1]
+P6 = HERE.parent / 'layers_p6n'
+MUTANTS = ('drop_restore', 'restore_full', 'drop_preread', 'donation_after')
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--jx-dir', type=Path, required=True, help='construction/jx/reproduce_jx.py output')
+    ap.add_argument('--recipe', default='U8', help='RECIPE-<id>.json and LOCAL-PINS-barch-<id>.json')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-barch-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    inp = a.jx_dir.resolve() / 'jx/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['base_sha256'], 'input must be the pinned X4 word'
+    (out / 'barch').mkdir(); word = out / 'barch/FULL-WORD.json.gz'
+    run('barch', HERE / 'build_tri.py', inp, rfile, word, portable=False)
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['expect_sha256']
+    run('barch-controls', HERE / 'run_controls.py', inp, rfile, PKG / 'independent/audit_local.py', out / 'barch-controls', portable=False)
+    res = read(out / 'barch-controls/controls.json')
+    want = ['C0_identity', 'recipe', *MUTANTS] + [m + '@' + str(v['X']) for v in rec.get('variants', []) for m in MUTANTS]
+    assert sorted(res) == sorted(want) == sorted(pins['barch_controls']) and all(x['ok'] for x in res.values()), res
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/barch/run_controls.py b/research/gauge44-leaver8/construction/barch/run_controls.py
new file mode 100644
index 0000000000..f1ce999bfb
--- /dev/null
+++ b/research/gauge44-leaver8/construction/barch/run_controls.py
@@ -0,0 +1,33 @@
+#!/usr/bin/env python3
+"""run_controls.py BASE_WORD RECIPE AUDIT_LOCAL_PY OUTDIR : C0 identity, the recipe word (must PASS) and the four negative
+controls (each must FAIL audit_local with its pinned message prefix). Standard library only; writes OUTDIR/controls.json."""
+import sys, json, subprocess, os, gzip, hashlib
+base, recipe, audit, out = sys.argv[1:5]
+here = os.path.dirname(os.path.abspath(__file__)); os.makedirs(out, exist_ok=True)
+# pinned rejection sites (observed on RECIPE-V1 and RECIPE-B0; the failing rows are recorded in controls.json): the holder 485 is not restored; the low-end restore 497-=451 moved to the
+# FULL cleanup runs after 451's own tail and leaves 497 wrong; without the pre-read (or with the donation after the read)
+# the entering helper's start value reaches a target.
+EXPECT = {None: 'PASS', 'drop_restore': 'all-column endpoint failure (False, ',
+          'restore_full': 'all-column endpoint failure (False, ',
+          'drop_preread': 'nonzero entrance response', 'donation_after': 'nonzero entrance response'}
+res = {}
+ident = os.path.join(out, 'C0.json')
+json.dump(dict(json.load(open(recipe)), B_delete=[], B_insert=[], B_frames={}, tail_insert=[], cleanup_prepend=[],
+               local_profile=json.loads(gzip.decompress(open(base, 'rb').read()))['report']['local_profile'],
+               expect_sha256=hashlib.sha256(gzip.decompress(open(base, 'rb').read())).hexdigest()), open(ident, 'w'))
+r = subprocess.run([sys.executable, '-B', os.path.join(here, 'build_tri.py'), base, ident, os.path.join(out, 'C0.json.gz')], capture_output=True, text=True)
+res['C0_identity'] = dict(ok=r.returncode == 0, out=r.stdout.strip() or r.stderr.strip()[-200:])
+ctls = list(EXPECT) + [c + '@' + str(s['X']) for s in json.load(open(recipe)).get('variants', []) for c in EXPECT if c]
+for ctl in ctls:
+    name = ctl or 'recipe'; wp = os.path.join(out, name + '.json.gz')
+    cmd = [sys.executable, '-B', os.path.join(here, 'build_tri.py'), base, recipe, wp] + (['--control', ctl] if ctl else [])
+    b = subprocess.run(cmd, capture_output=True, text=True)
+    if b.returncode: res[name] = dict(ok=False, build=b.stderr[-300:]); continue
+    a = subprocess.run([sys.executable, '-B', audit, '--word', wp, '--output', os.path.join(out, name + '.audit.json')], capture_output=True, text=True)
+    txt = a.stdout + a.stderr
+    if ctl is None: ok = a.returncode == 0 and 'PASS_INDEPENDENT' in txt
+    else: ok = a.returncode != 0 and EXPECT[ctl.split('@')[0]] in txt
+    res[name] = dict(ok=ok, build=json.loads(b.stdout), audit_tail=txt.strip().splitlines()[-1][:200])
+json.dump(res, open(os.path.join(out, 'controls.json'), 'w'), indent=1)
+print(json.dumps({k: x['ok'] for k, x in res.items()}))
+sys.exit(0 if all(x['ok'] for x in res.values()) else 1)
diff --git a/research/gauge44-leaver8/construction/build_gauge_cold44.py b/research/gauge44-leaver8/construction/build_gauge_cold44.py
new file mode 100644
index 0000000000..72d2945f6b
--- /dev/null
+++ b/research/gauge44-leaver8/construction/build_gauge_cold44.py
@@ -0,0 +1,210 @@
+"""Exact dyadic cold-end realization of the source-branch/factory-completion word.
+Prepared for icekylinx with OpenAI Codex assistance; Apache-2.0.
+This is a constructor: independent endpoint/frame audits remain required.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+import copy,gzip,json,hashlib,time,sys,argparse,importlib.util
+D=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser(description=__doc__)
+for name in ('input','out','hamming','upstream-package'):ap.add_argument('--'+name,type=Path,required=True)
+args=ap.parse_args();WPATH=args.input;OUT=args.out
+assert __debug__, 'Assertions are required'
+OUT.mkdir(exist_ok=False,parents=True)
+def rd(p):return json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+w=rd(WPATH);v=w['report']['v'];n=2*v+w['report']['R'];N=list(range(v))+list(range(2*v,n));ix={x:i for i,x in enumerate(N)}
+F9=[256,128,64,32,16,8,4,2,1];t0=time.monotonic()
+def basis(vs):
+ d={}
+ for a in vs:
+  for k in sorted(d,reverse=True):
+   if a>>k&1:a^=d[k]
+  if a:
+   k=a.bit_length()-1
+   for j in d:
+    if d[j]>>k&1:d[j]^=a
+   d[k]=a
+ return tuple(d[k] for k in sorted(d,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def regs(e):return e[1:3] if e[0]=='add' else e[1:2]
+def inverse(e):
+ e=copy.deepcopy(e)
+ if e[0]=='add':e[3]=-e[3]
+ else:e[2],e[3]=e[3],e[2]
+ return e
+def apply(e,M,mapping=None):
+ t=mapping[e[1]] if mapping is not None else e[1]
+ if e[0]=='add':
+  s=mapping[e[2]] if mapping is not None else e[2];q=Q(e[3],e[4])
+  for j,a in M[s].items():
+   x=M[t].get(j,Q(0))+q*a
+   if x:M[t][j]=x
+   else:M[t].pop(j,None)
+ else:
+  q=Q(e[2],e[3]);M[t]={j:q*a for j,a in M[t].items()}
+def rref(A):
+ a=[list(map(Q,row)) for row in A];nr=len(a);nc=len(a[0]) if nr else 0;row=0;piv=[]
+ for c in range(nc):
+  k=next((i for i in range(row,nr) if a[i][c]),None)
+  if k is None:continue
+  a[row],a[k]=a[k],a[row];q=a[row][c];a[row]=[x/q for x in a[row]]
+  for i in range(nr):
+   if i!=row and a[i][c]:q=a[i][c];a[i]=[x-q*y for x,y in zip(a[i],a[row])]
+  piv.append(c);row+=1
+  if row==nr:break
+ return a,piv
+def rank(A):return len(rref(A)[1])
+def null(A,nc=None):
+ if A:a,piv=rref(A);nc=len(a[0])
+ else:a=[];piv=[];assert nc is not None
+ free=[j for j in range(nc) if j not in piv];out=[[Q(0) for j in free] for i in range(nc)]
+ for k,c in enumerate(free):out[c][k]=Q(1)
+ for i,c in enumerate(piv):
+  for k,j in enumerate(free):out[c][k]=-a[i][j]
+ return out
+def mm(A,B):
+ if not A:return []
+ if not B:return [[] for row in A]
+ bt=list(zip(*B));return [[sum((a*b for a,b in zip(row,col)),Q(0)) for col in bt] for row in A]
+def tr(A):return list(map(list,zip(*A)))
+def inv(A):
+ n0=len(A);a,p=rref([row+[Q(i==j) for j in range(n0)] for i,row in enumerate(A)])
+ assert p[:n0]==list(range(n0))
+ return [row[n0:] for row in a]
+def unit(q):
+ if not q:return False
+ a=abs(q.numerator);b=q.denominator
+ return not a&(a-1) and not b&(b-1)
+def dyadic(q):return not q.denominator&(q.denominator-1)
+def opadd(t,s,q,F):return ['add',t,s,q.numerator,q.denominator,list(F)]
+def opscale(t,q,F):return ['scale',t,q.numerator,q.denominator,list(F)]
+def eliminate(M,ids,F,skip=()):
+ """Return legal dyadic row operations taking an invertible sparse matrix to I."""
+ skip=set(skip);ops=[];dim=len(M)
+ def add(i,j,q):
+  if q:
+   assert dyadic(q);e=opadd(ids[i],ids[j],q,F);ops.append(e)
+   for c,x in M[j].items():
+    z=M[i].get(c,Q(0))+q*x
+    if z:M[i][c]=z
+    else:M[i].pop(c,None)
+ def scale(i,q):
+  if q!=1:
+   assert unit(q);ops.append(opscale(ids[i],q,F));M[i]={c:q*x for c,x in M[i].items()}
+ def swap(i,j):
+  if i!=j:
+   add(i,j,Q(1));add(j,i,Q(-1));add(i,j,Q(1));scale(j,Q(-1))
+ for c in range(dim):
+  if c in skip:
+   assert M[c]=={c:Q(1)} and all(not M[i].get(c) for i in range(dim) if i!=c)
+   continue
+  cand=[i for i in range(c,dim) if i not in skip and M[i].get(c)]
+  k=next((i for i in cand if unit(M[i][c])),None)
+  if k is None:
+   # Elementary Euclidean row additions reduce the pivot-column numerator gcd.
+   assert cand,('singular',c)
+   while k is None:
+    cand.sort(key=lambda i:abs(M[i][c]));a=cand[0]
+    b=next((i for i in cand[1:] if M[i][c]),None)
+    if b is None:raise ValueError(('non-dyadic determinant pivot',c,M[a][c]))
+    rat=M[b][c]/M[a][c];q=rat.numerator//rat.denominator
+    if q==0:q=1 if rat>0 else -1
+    add(b,a,Q(-q));cand=[i for i in cand if M[i].get(c)]
+    k=next((i for i in cand if unit(M[i][c])),None)
+  swap(c,k);scale(c,1/M[c][c])
+  for i in range(dim):
+   if i!=c and M[i].get(c):
+    assert i not in skip
+    add(i,c,-M[i][c])
+ assert all(row=={i:Q(1)} for i,row in enumerate(M))
+ return ops
+def realize(A,ids,F):
+ M=[{j:Q(x) for j,x in enumerate(row) if x} for row in A]
+ return [inverse(e) for e in reversed(eliminate(M,ids,F))]
+# Reconstruct the actual non-target map after the inherited HPE tail.
+inherited_tail=[w['cleanup'][i][:-1]+[list(f)] for i,f in w.get('early_cleanup',[])]
+mainN=[e for e in w['A']+w['B'] if not v<=e[1]<2*v]
+M=[{i:Q(1)} for i in range(len(N))]
+for e in mainN+inherited_tail:apply(e,M,ix)
+MI=[{i:Q(1)} for i in range(len(N))]
+for e in reversed(mainN+inherited_tail):apply(inverse(e),MI,ix)
+cur={x:(w['ports'][x],) if x<v else basis(w.get('start_extra',{}).get(str(x),[])) for x in N}
+for e in w['A']+w['B']+inherited_tail:
+ for x in regs(e):
+  if x in cur:cur[x]=basis(e[-1])
+enter=set(map(int,w.get('start_extra',{})));protected=[ix[x] for x in N if x<v or x in enter]
+mods=rd(args.hamming/'PACKET-PROGRAMS.json.gz');proto=rd(args.hamming/'PROTOTYPE.json')
+plans=[];premix=[];tail=[];ends={};Mafter=copy.deepcopy(M)
+for b,mod in enumerate(mods):
+ ss=mod['receipt']['source_lines'];F=basis([proto['binary_ports'][s] for s in ss]);I=[ix[x] for x in N if inside(cur[x],F)]
+ hs=list(range(224+16*b,224+16*(b+1)));H=[ix[x] for x in hs]
+ C=[[M[i].get(j,Q(0)) for j in protected] for i in I]
+ L=tr(null(tr(C),len(I)))
+ A=[[MI[j].get(i,Q(0)) for i in I] for j in protected];A=[row for row in A if any(row)]
+ K=null(A,len(I));BK=mm(L,K);_,piv=rref(BK);r=len(piv);assert r==len(L)==(2 if b in [0,1,2,11,12,13] else 4),(b,r,len(L))
+ Ksel=[[row[j] for j in piv] for row in K];Bsel=[[row[j] for j in piv] for row in BK];U=mm(Ksel,inv(Bsel));assert mm(L,U)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ q=mm([[MI[i].get(j,Q(0)) for j in I] for i in range(len(N))],U)
+ assert all(not any(q[i]) for i in range(len(N)) if i not in H),('nonlocal premix',b)
+ RR=mm(L,[[M[i].get(j,Q(0)) for j in H] for i in I]);qH=[q[i] for i in H]
+ assert mm(RR,qH)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ # Pick low physical helper destinations with independent U coordinate rows.
+ ih=[]
+ for j in sorted((j for j,i in enumerate(I) if N[i] in hs),key=lambda j:(cur[N[I[j]]]!=F,N[I[j]])):
+  if rank([U[k] for k in ih]+[U[j]])>len(ih):ih.append(j)
+  if len(ih)==r:break
+ assert len(ih)==r
+ endhs=[N[I[j]] for j in ih];endhidx=[hs.index(h) for h in endhs]
+ kerR=null(RR,16);Qmat=[[Q(0) for j in range(16)] for i in range(16)]
+ for j,hj in enumerate(endhidx):
+  for i in range(16):Qmat[i][hj]=qH[i][j]
+ other=[j for j in range(16) if j not in endhidx]
+ for k,j in enumerate(other):
+  for i in range(16):Qmat[i][j]=kerR[i][k]
+ assert rank(Qmat)==16
+ pops=realize(Qmat,hs,());premix+=pops
+ T=[[Q(i==j)-sum((U[i][k]*L[k][j] for k in range(r)),Q(0)) for j in range(len(I))] for i in range(len(I))]
+ for k,i in enumerate(ih):T[i]=L[k]
+ tops=realize(T,[N[i] for i in I],F);tail+=tops
+ # Right-compose this initial helper premix; other blocks have disjoint H sets.
+ for row in Mafter:
+  vals=[row.get(h,Q(0)) for h in H]
+  if any(vals):
+   for hj in H:row.pop(hj,None)
+   for j,hj in enumerate(H):
+    z=sum((vals[i]*Qmat[i][j] for i in range(16)),Q(0))
+    if z:row[hj]=z
+ for e in tops:apply(e,Mafter,ix)
+ ends.update({h:list(F) for h in endhs})
+ plans.append(dict(block=b,frame=list(F),registers=[N[i] for i in I],ends=endhs,pairing_rank=r,premix_gates=len(pops),tail_gates=len(tops),Q=[[str(x) for x in row] for row in Qmat],T=[[str(x) for x in row] for row in T]))
+ print('BLOCK',b,'ends',endhs,'Qops',len(pops),'Tops',len(tops),flush=True)
+# Check actual post-tail isolation before constructing the high-frame inverse.
+allends=set(ends)|set(map(int,w.get('helper_final',{})))
+for h in allends:
+ j=ix[h];assert Mafter[j]=={j:Q(1)},('row not isolated',h,Mafter[j]);assert all(not row.get(j) for i,row in enumerate(Mafter) if i!=j),('column not isolated',h)
+print('EXACT_ISOLATED',len(ends),'new;',len(allends),'total',round(time.monotonic()-t0,3),flush=True)
+fullops=eliminate(copy.deepcopy(Mafter),N,F9,[ix[x] for x in allends])
+print('FULL_INVERSE',len(fullops),round(time.monotonic()-t0,3),flush=True)
+# Cancel new cold-axis target responses inside A, after their wrappers.
+Dirt=[({h:Q(1)} if h in ends else {}) for h in range(n)]
+for e in premix+w['A']+w['cut']+w['B']:apply(e,Dirt)
+for e in w['precondition']:apply(e,Dirt)
+postcomp=[opadd(y,h,-a,()) for y in range(v,2*v) for h,a in sorted(Dirt[y].items()) if a]
+assert all(h in ends for e in postcomp for h in [e[2]])
+new=copy.deepcopy(w);new['A']=postcomp+premix+w['A'];new['cleanup']=inherited_tail+tail+fullops
+new['early_cleanup']=[[i,e[-1]] for i,e in enumerate(inherited_tail+tail)]
+new['helper_final'].update({str(h):f for h,f in ends.items()})
+new['refactored_cleanup']={'kind':'source_branch_gauge_and_retired_completion_cold44','new_cold_ends':len(ends),'exact_non_target_isolation_checked':True,'high_inverse':'dyadic_sparse_Gauss_Jordan'}
+# Derive paid profile by subtracting and adding literal frame-chain counts.
+spec=importlib.util.spec_from_file_location('upstream_cold_end',args.upstream_package/'code/build_cold_end.py')
+profile_module=importlib.util.module_from_spec(spec);spec.loader.exec_module(profile_module)
+oldprof,_=profile_module.chain_profile(w);newprof,_=profile_module.chain_profile(new)
+prof=Counter({int(k):z for k,z in w['report']['local_profile'].items()});prof.subtract(oldprof);prof.update(newprof)
+widths=Counter(len(basis(new['helper_final'].get(str(h),F9)))-len(basis(new.get('start_extra',{}).get(str(h),[]))) for h in range(224,n))
+new['report'].update(local_profile={str(k):z for k,z in sorted(prof.items()) if z},local_rank_mass=sum(k*z for k,z in prof.items()),width_inventory={str(k):z for k,z in sorted(widths.items()) if z},status='EXACT_COLD44_CONSTRUCTED_PENDING_INDEPENDENT_AUDIT')
+raw=json.dumps(new,sort_keys=True,separators=(',',':')).encode();sha=hashlib.sha256(raw).hexdigest();(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+recipe={'premix':postcomp+premix,'cleanup':new['cleanup'],'early_cleanup':new['early_cleanup'],'cold_ends':{str(h):f for h,f in ends.items()},'refactored_cleanup':new['refactored_cleanup'],'output_content_sha256':sha}
+(OUT/'RECIPE.json.gz').write_bytes(gzip.compress(json.dumps(recipe,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+receipt=dict(input_content_sha256=hashlib.sha256(gzip.decompress(WPATH.read_bytes())).hexdigest(),output_content_sha256=sha,blocks=plans,new_cold_ends=len(ends),all_low_ended_helpers=len(allends),premix_gates=len(premix),postwrapper_compensation_gates=len(postcomp),tail_gates=len(tail),inherited_tail_gates=len(inherited_tail),full_inverse_gates=len(fullops),profile=new['report']['local_profile'],width_inventory=new['report']['width_inventory'],rank_mass=new['report']['local_rank_mass'],seconds=time.monotonic()-t0)
+(OUT/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(json.dumps({k:z for k,z in receipt.items() if k!='blocks'},indent=2),flush=True)
diff --git a/research/gauge44-leaver8/construction/construct_gauge_xcentre.py b/research/gauge44-leaver8/construction/construct_gauge_xcentre.py
new file mode 100644
index 0000000000..1010d86746
--- /dev/null
+++ b/research/gauge44-leaver8/construction/construct_gauge_xcentre.py
@@ -0,0 +1,381 @@
+# Round20 early-coordinate-center / own-Y variant, prepared for icekylinx
+# with OpenAI Codex assistance. Apache-2.0. Scalar elementary-operation
+# helpers below are retained from the attributed PR514 construct_partial.py.
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+# AtomScout: leaver-read K-triangles (schedule from atom1.py / rog.py CP-SAT)
+TRI=json.loads(Path(sys.argv[3]).read_text())
+FULLT={(tuple(tr['p']),tr['e']) for tr in TRI['triangles']}
+TRI_COORDS={t+8 for tr in TRI['triangles'] for t,_,_ in tr['reads']}
+COPYL=[]
+NH=504-3*len(FULLT)+len(COPYL)
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+# Helper ids of the unpatched 504 construction: every allocation advances the 504 numbering; a packet copy that the
+# K-triangle schedule never forms advances it without allocating (HELPER-MAP.json).
+shadow=[];skipped=[];nxt=[2*v]
+def alloc():
+    n=len(cur);cur.append(());rows.append({});shadow.append(nxt[0]);nxt[0]+=1;return n
+def skip():
+    skipped.append(nxt[0]);nxt[0]+=1
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# Each source quartet supplies pair partials first. The other two coordinate
+# partitions supply eight early face packets without touching the eight
+# partials later copied into the preconditioned Y coordinates.
+SELECT=(0,0)
+PRIORITY=json.loads((INPUT/"COMPLETION-PRIORITY.json").read_text())
+maps={};early={};own_rows={};pairs=[];tetrads={};block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)});maps[c]=mp
+    for ei,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[:40]):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        if ei==15:
+            for jj in range(4,8):swap(mp[jj],mp[2*jj+9],(P[ids[jj]],))
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in targets:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                t,u=sorted(ts);e2=R[t][q[0]]*R[t][q[1]]
+                pair={'targets':(t,u),'keys':[(c,p,eps),(c,q,e2)],'selected':pi==SELECT[parity],
+                      'matrix':[[R[a][p[0]],R[a][q[0]]] for a in (t,u)]}
+                pairs.append(pair)
+                if not pair['selected']:continue
+                zz=-Q(2*R[u][p[0]],R[t][p[0]])
+                sources=tet[1-parity]
+                for target,sign in ((t,-1),(u,1)):
+                    wanted={s:-Q(G[t][s],4)-sign*Q(G[u][s],2)/zz for s in sources
+                            if -Q(G[t][s],4)-sign*Q(G[u][s],2)/zz}
+                    assert len(wanted)==2
+                    candidates=[]
+                    for r in mp.values():
+                        if set(rows[r])!=set(wanted):continue
+                        s=next(iter(wanted));coef=wanted[s]/rows[r][s]
+                        if all(wanted[s]==coef*rows[r][s] for s in wanted):candidates.append((r,coef))
+                    assert len(candidates)==1
+                    r,coef=candidates[0];assert len(cur[r])==2
+                    own_rows[target]=(r,coef,cur[r])
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    needed={own_rows[t][0] for t in ids}
+    early[c]={j for j,e in enumerate(z['events'][40:]) if not ({mp[e[0]],mp[e[1]]}&needed)}
+    assert len(early[c])==8
+    retired=[]
+    for j in sorted(early[c]):
+        (t,s,a,b),F=z['events'][40+j],z['event_frames'][40+j]
+        add(mp[t],mp[s],Q(a,b),tuple(F));retired.append(mp[s])
+    assert not set(retired)&needed
+    # These eight retired rows already span every source coordinate. Keep
+    # them invertible and place the four coordinate totals in a changed basis.
+    F=basis([P[s] for s in ids]);assert len(F)==4
+    regs=sorted(retired,key=lambda r:(r>=v,r))
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    M=[[Q(R[s][i]) for s in ids] for i in c]
+    def qr_rank(rs):
+        bs={}
+        for r in rs:
+            r=r.copy()
+            for i,b in sorted(bs.items()):
+                if r[i]:q=r[i];r=[x-q*y for x,y in zip(r,b)]
+            i=next((i for i,x in enumerate(r) if x),None)
+            if i is not None:q=r[i];bs[i]=[x/q for x in r]
+        return len(bs)
+    assert qr_rank(M)==4
+    for rr0 in PRIORITY[",".join(map(str,c))]["rows"]:
+        rr=list(map(Q,rr0))
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    for i in range(8):
+        if len(M)==8:break
+        rr=[Q(i==j) for j in range(8)]
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    assert len(M)==8
+    linear(regs,M,F)
+    for i,r in zip(c,regs):
+        assert rows[r]=={s:Q(R[s][i]) for s in ids}
+        block_totals[c,i]=r
+
+# All centers are complete while Y is still at zero. This is the crucial
+# difference from an illegal early-own-Y prefix using the old center order.
+centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+assert all(cur[v+t]==() for t in range(v))
+
+phase=B
+for t,(r,coef,F) in sorted(own_rows.items()):
+    if t in TRI_COORDS:continue
+    assert cur[r]==F
+    add(v+t,r,coef,F)
+# requests are needed for TRI coefficients
+requests=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    requests[key1].append((t,-Q(mat[0][0],2)))
+    requests[key2].append((u,-Q(mat[0][1],2)))
+reqcoef={t:(key,coef) for key,reqs in requests.items() for t,coef in reqs}
+def face_info(c,p,eps):
+    z=blocks[c];keys=[(pp,ee) for pp in it.combinations(c,2) for ee in (-1,1)]
+    r_local,alpha=z['outputs'][keys.index((p,eps))]
+    j=[j for j in range(40,len(z['events'])) if z['events'][j][0]==r_local];assert len(j)==1
+    return j[0],Q(alpha)
+tri_join_counts=Counter()
+lcopy={}
+for s8 in COPYL:
+    r=s8+8;c=alloc();add(c,r,1,cur[r]);lcopy[r]=c
+for tr in TRI['triangles']:
+    p,eps=tuple(tr['p']),tr['e']
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];r0=r;r=lcopy.get(r,r)
+        key,coef=reqcoef[t];assert key[1]==p and key[2]==eps,(key,p,eps)
+        if blk==key[0]:
+            rr,c0,F0=own_rows[t];assert rr==r0;q=c0
+        else:
+            j,alpha=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert loc in ev[:2]
+            q=coef*alpha
+        F=basis(cur[v+t]+cur[r]);assert inside(F,hyper(P[t])),('TRI frame',t)
+        tri_join_counts[len(F)]+=1;add(v+t,r,q,F)
+
+packets={}
+for c,z in sorted(blocks.items()):
+    mp=maps[c]
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    skipev={face_info(c,p,eps)[0] for p,eps in keys if (p,eps) in FULLT}
+    for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]):
+        if j not in early[c] and 40+j not in skipev:
+            t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    for key,(r,alpha) in zip(keys,z['outputs']):
+        if tuple(key) in FULLT:skip();continue
+        a=mp[r];b=alloc();add(b,a,1,cur[a])
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha))
+
+# Both tetrahedra use the same partition. A selected key has exactly two
+# selected Y loads and no ordinary M consumer. Supply its two raw halves in
+# opposite orders and never form that M. Other keys retain the old M path.
+second=[];first_join_counts=Counter()
+for key,reqs in sorted(requests.items()):
+    assert len(reqs)==2
+    c,p,eps=key
+    if (p,eps) in FULLT:continue
+    ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds
+    for j,(target,coef) in enumerate(sorted(reqs)):
+        first_source,second_source=(a,b) if j==0 else (b,a)
+        r,alpha=packets[first_source,p,eps,second_source]
+        F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+        first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F)
+        r,alpha=packets[second_source,p,eps,c]
+        second.append((target,r,coef*alpha))
+
+Ms={}
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for eps in (-1,1):
+            if (c,p,eps) in requests:continue
+            (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,eps]=(a,alpha)
+
+consumers=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    for key in pair['keys']:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    if key in requests:
+        assert all(pairs[i]['selected'] for i in uses)
+        continue
+    assert all(not pairs[i]['selected'] for i in uses)
+    a,alpha=Ms[key]
+    for j,pid in enumerate(uses):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+assert len(cur)-240==NH,len(cur)-240
+
+selected_join_counts=Counter()
+for target,r,coef in second:
+    F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+    selected_join_counts[len(F)]+=1;add(v+target,r,coef,F)
+output_basis=[]
+for pair in pairs:
+    if not pair['selected']:continue
+    (t,u),mat=pair['targets'],pair['matrix']
+    F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u]))
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert rows[v+t]==expected,('side identity',t)
+
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8
+assert sum(r*z for r,z in H.items())==9*NH+240*8+72,sum(r*z for r,z in H.items())
+
+def apply(e,matrix):
+    if e[0]=='add':
+        _,t,s,a,b,*_=e;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    e[-1]=list(FULL);return e
+cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q]
+cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v]
+matrix=[{r:Q(1)} if r<v else {} for r in range(len(cur))]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(len(cur)))
+
+# Restrict the eight isolated axis ports exactly, keeping the stable 112-port
+# label set. This variant changes the local word, not the outer geometry.
+mp={s:s-8 for s in range(8,120)}
+mp.update({120+s:112+s-8 for s in range(8,120)})
+mp.update({240+r:224+r for r in range(NH)})
+def restrict(events,is_cut=False):
+    out=[]
+    for e in events:
+        regs=e[1:3] if e[0]=='add' else e[1:2]
+        if any(r not in mp for r in regs):
+            assert is_cut and e[0]=='add' and e[1]-120==e[2] and e[2]<8 and e[3:5]==[1,1]
+            continue
+        q=copy.deepcopy(e);q[1]=mp[q[1]]
+        if q[0]=='add':q[2]=mp[q[2]]
+        out.append(q)
+    return out
+H.subtract({1:8,8:16});H=+H
+report={'status':'EXACT_CLEAN_OWN_Y_EARLY_CENTER_WORD_NOT_ADMITTED',
+        'h':9,'v':112,'R':NH,'cst':64,'m':73,'local_profile':dict(sorted(H.items())),
+        'centre_ranks':[8]*8,**({'tri_join_counts':dict(tri_join_counts)} if TRI['triangles'] else {}),'selected_load_join_counts':dict(selected_join_counts),'selected_partitions':list(SELECT),'first_load_join_counts':dict(first_join_counts),
+        'source_columns_exact':112,'borrowed_output_pairs':56,'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'local_rank_mass':sum(r*n for r,n in H.items()),'scope':'Clean scalar identity and all literal monotone local frames only; arbitrary-dirt compensation, entrance kernels, exact phase recipes, and global hosting/pricing are not yet certified.'}
+word={'report':report,'ports':P[8:],'root_lines':R[8:],
+      'A':restrict(A),'B':restrict(B),'cut':restrict(cut,True),'cleanup':restrict(cleanup),'precondition':restrict(precondition),
+      'centers':[mp[r] for r in centers[:8]],'center_frames':center_frames[:8],
+      'scatter':[[str(x) for x in row[:8]] for row in scatter[8:]]}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+assert len(shadow)==NH and len(shadow)+len(skipped)==504
+hmap={**{r:r for r in range(224)},**{224+s_-240:224+i for i,s_ in enumerate(shadow)}}
+(OUT/'HELPER-MAP.json').write_text(json.dumps({'map':{str(k):hmap[k] for k in sorted(hmap)},'removed_504_helpers':[224+s_-240 for s_ in skipped]})+'\n')
+(OUT/'DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/gauge44-leaver8/construction/frames/FRAME-RECIPE-sw4.json b/research/gauge44-leaver8/construction/frames/FRAME-RECIPE-sw4.json
new file mode 100644
index 0000000000..7394064c5e
--- /dev/null
+++ b/research/gauge44-leaver8/construction/frames/FRAME-RECIPE-sw4.json
@@ -0,0 +1,167 @@
+{
+  "input_content_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+  "gate_frames": [
+    [
+      "B",
+      856,
+      [
+        272,
+        144,
+        64,
+        6
+      ],
+      [
+        272,
+        144,
+        64,
+        8,
+        6,
+        1
+      ]
+    ],
+    [
+      "B",
+      860,
+      [
+        265,
+        137,
+        88,
+        6
+      ],
+      [
+        256,
+        128,
+        65,
+        16,
+        9,
+        6
+      ]
+    ],
+    [
+      "B",
+      868,
+      [
+        265,
+        200,
+        33,
+        6
+      ],
+      [
+        256,
+        144,
+        81,
+        33,
+        9,
+        6
+      ]
+    ],
+    [
+      "B",
+      873,
+      [
+        320,
+        192,
+        16,
+        6
+      ],
+      [
+        320,
+        192,
+        32,
+        16,
+        6,
+        1
+      ]
+    ],
+    [
+      "B",
+      876,
+      [
+        392,
+        73,
+        33,
+        6
+      ],
+      [
+        273,
+        144,
+        64,
+        33,
+        9,
+        6
+      ]
+    ],
+    [
+      "B",
+      953,
+      [
+        265,
+        137,
+        73,
+        6
+      ],
+      [
+        265,
+        137,
+        73,
+        32,
+        25,
+        6
+      ]
+    ],
+    [
+      "B",
+      961,
+      [
+        265,
+        185,
+        80,
+        6
+      ],
+      [
+        265,
+        128,
+        64,
+        41,
+        16,
+        6
+      ]
+    ],
+    [
+      "B",
+      965,
+      [
+        272,
+        185,
+        73,
+        6
+      ],
+      [
+        257,
+        128,
+        73,
+        40,
+        17,
+        6
+      ]
+    ]
+  ],
+  "expected": {
+    "output_content_sha256": "e78047028c7dcd25fb1b6216c2b53eda76d2f91292b21d43f5d1903cc13a5c6c",
+    "local_profile": {
+      "1": 2556,
+      "2": 334,
+      "3": 430,
+      "4": 194,
+      "5": 56,
+      "8": 8
+    },
+    "width_inventory": {
+      "4": 80,
+      "5": 32,
+      "7": 54,
+      "8": 122,
+      "9": 216
+    }
+  }
+}
diff --git a/research/gauge44-leaver8/construction/frames/LOCAL-PINS-frames-sw4.json b/research/gauge44-leaver8/construction/frames/LOCAL-PINS-frames-sw4.json
new file mode 100644
index 0000000000..834ae13a2f
--- /dev/null
+++ b/research/gauge44-leaver8/construction/frames/LOCAL-PINS-frames-sw4.json
@@ -0,0 +1,12 @@
+{
+ "word": "P6k4sw4f8",
+ "frame_build_controls": 3,
+ "frame_controls": 10,
+ "layer_controls": 95,
+ "canonical_sha256": "b0d27d99423047ce07af847734f5a86f9411038bb3b0bf721918ece1ee579325",
+ "program_sha256": {
+  "forward": "b2cf8298488cc81aeee1385d4d9ebd842efbb21abb9296fca903adb8ad50f8d0",
+  "backward": "6f28cf1413671d5b7c50488a1603fa8f1558da469abbbb45b6a9b66ec640712b"
+ },
+ "clifford_recipes_sha256": "eb7569e004bd2a2937928db9db49dad949ec291f00c2d21df6af722df7cb6c9c"
+}
diff --git a/research/gauge44-leaver8/construction/frames/build_frames.py b/research/gauge44-leaver8/construction/frames/build_frames.py
new file mode 100644
index 0000000000..22021549e6
--- /dev/null
+++ b/research/gauge44-leaver8/construction/frames/build_frames.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Apply the eight pinned B-gate frame raises of FRAME-RECIPE-sw4.json (chafreaky's PR741) to the SW4 word.
+
+usage: build_frames.py INPUT_WORD.json.gz OUT_DIR RECIPE.json
+
+Standard library only. The frames are applied by BlockInvert's `../promo/build_promotion.apply` (no entrances, eight
+'B' gate_frames), which checks each old frame and recomputes the local profile and widths. This builder then checks:
+input sha pin; the scalar program of A, cut, B, precondition and cleanup unchanged (every field but the frame); start
+and end frames unchanged; local profile and width inventory equal to the recipe's; output sha pin. Three pin controls
+(input pin, wrong old frame, output pin) must be rejected at their pinned reasons on every build.
+Adapted from PR741's extras/build_frames.py (chafreaky). Apache-2.0.
+"""
+import copy, gzip, hashlib, importlib.util, json, sys
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+_s = importlib.util.spec_from_file_location('promotion', HERE.parent / 'promo/build_promotion.py')
+B = importlib.util.module_from_spec(_s); _s.loader.exec_module(B)
+
+
+def construct(raw, recipe):
+    assert hashlib.sha256(raw).hexdigest() == recipe['input_content_sha256'], 'input word pin'
+    w = json.loads(raw)
+    assert len(recipe['gate_frames']) == 8 and all(c[0] == 'B' for c in recipe['gate_frames']), 'eight B frames'
+    out = B.apply(w, dict(entrances={}, gate_frames=recipe['gate_frames']))
+    for section in ('A', 'cut', 'B', 'precondition', 'cleanup'):
+        assert [e[:-1] for e in w[section]] == [e[:-1] for e in out[section]], 'scalar program unchanged'
+    assert out['start_extra'] == w['start_extra'] and out['helper_final'] == w['helper_final'], 'endpoint frames unchanged'
+    assert out['report']['local_profile'] == recipe['expected']['local_profile'] and \
+        out['report']['width_inventory'] == recipe['expected']['width_inventory'], 'profile and width pins'
+    data = json.dumps(out, sort_keys=True, separators=(',', ':')).encode()
+    assert hashlib.sha256(data).hexdigest() == recipe['expected']['output_content_sha256'], 'output word pin'
+    return data
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    inp, outd, rfile = map(Path, sys.argv[1:4])
+    raw = gzip.decompress(inp.read_bytes()); recipe = json.loads(rfile.read_text())
+    data = construct(raw, recipe)
+    rejected = []
+    for name, change, reason in [
+            ('input-pin', lambda r: r.__setitem__('input_content_sha256', '0' * 64), 'input word pin'),
+            ('old-frame', lambda r: r['gate_frames'][0].__setitem__(2, []), 'gate frame mismatch'),
+            ('output-pin', lambda r: r['expected'].__setitem__('output_content_sha256', '0' * 64), 'output word pin')]:
+        r = copy.deepcopy(recipe); change(r)
+        try:
+            construct(raw, r)
+        except AssertionError as e:
+            assert reason in str(e), (name, str(e)); rejected.append(dict(name=name, reason=reason))
+        else:
+            raise AssertionError('accepted ' + name)
+    outd.mkdir(parents=True)
+    (outd / 'FULL-WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+    (outd / 'BUILD.json').write_text(json.dumps(dict(
+        status='PASS_EIGHT_FRAME_EXACT_CONSTRUCTION', input_sha256=hashlib.sha256(raw).hexdigest(),
+        output_sha256=hashlib.sha256(data).hexdigest(), scalar_program_unchanged=True, frames=8,
+        rejected_controls=rejected), indent=2) + '\n')
+    print('PASS eight B frames and three pin controls')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/frames/frame_controls.py b/research/gauge44-leaver8/construction/frames/frame_controls.py
new file mode 100644
index 0000000000..cd951a9f0e
--- /dev/null
+++ b/research/gauge44-leaver8/construction/frames/frame_controls.py
@@ -0,0 +1,45 @@
+#!/usr/bin/env python3
+"""Focused native controls for the eight B-frame raises (PR741's extras/frame_controls.py, ported).
+
+usage: frame_controls.py WORD.json.gz ROUTING.json.gz OUT.json RECIPE.json   (env PR635_CODE = PR635's code/ directory)
+
+The positive word must pass PR635's unchanged native audit `hpe_audit_and_transport.run`. Ten mutants must be rejected
+at their pinned reasons: each of the eight raised gates with its frame emptied ('nonmonotone'), a doubled read
+coefficient on the first raised gate ('arbitrary-dirt endpoint') and a tampered paid profile ('paid local profile
+differs'). Apache-2.0; adapted from chafreaky's PR741.
+"""
+import copy, gzip, importlib.util, json, os, sys, tempfile, time
+from pathlib import Path
+
+_s = importlib.util.spec_from_file_location('audit', Path(os.environ['PR635_CODE']) / 'hpe_audit_and_transport.py')
+A = importlib.util.module_from_spec(_s); _s.loader.exec_module(A)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    word, routing, out, rfile = map(Path, sys.argv[1:5])
+    w = json.loads(gzip.decompress(word.read_bytes())); recipe = json.loads(rfile.read_text())
+
+    def trial(z):
+        with tempfile.TemporaryDirectory() as td:
+            d = Path(td); f = d / 'word.json.gz'; f.write_bytes(gzip.compress(json.dumps(z).encode(), mtime=0))
+            try:
+                A.run(f, routing, d / 'native'); return None
+            except AssertionError as e:
+                return str(e)
+
+    start = time.monotonic(); assert trial(w) is None, 'positive word rejected'; records = []
+    for section, i, old, new in recipe['gate_frames']:
+        z = copy.deepcopy(w); z[section][i][-1] = []; error = trial(z)
+        assert error and 'nonmonotone' in error, (i, error); records.append(dict(name='frame-%d-emptied' % i, rejected=error))
+    z = copy.deepcopy(w); i = recipe['gate_frames'][0][1]; z['B'][i][3] *= 2; error = trial(z)
+    assert error and 'arbitrary-dirt endpoint' in error, error; records.append(dict(name='changed-read-coefficient', rejected=error))
+    z = copy.deepcopy(w); z['report']['local_profile']['1'] += 1; error = trial(z)
+    assert error and 'paid local profile differs' in error, error; records.append(dict(name='paid-profile-tampering', rejected=error))
+    out.write_text(json.dumps(dict(status='PASS_FOCUSED_EIGHT_FRAME_NATIVE_CONTROLS', positive=1, rejected=records,
+                                   seconds=time.monotonic() - start), indent=2) + '\n')
+    print('PASS', len(records), 'mutations', flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/frames/reproduce_frames.py b/research/gauge44-leaver8/construction/frames/reproduce_frames.py
new file mode 100644
index 0000000000..eaf9b47cac
--- /dev/null
+++ b/research/gauge44-leaver8/construction/frames/reproduce_frames.py
@@ -0,0 +1,89 @@
+#!/usr/bin/env python3
+"""Rebuild the SW4F8 word (eight B-gate frame raises on the SW4 word, chafreaky's PR741 recipe) and its native locals.
+
+Input: a fresh `construction/sw4/reproduce_sw4.py --recipe P6k4` output directory; its SW4 word (d232183f...) is pinned
+there and by FRAME-RECIPE-<id>.json. Steps, each checked exactly:
+  1. frames: build_frames.py (standard library only) applies the eight 'B' gate_frames with BlockInvert's
+     build_promotion.apply. Scalar program, start and end frames unchanged; profile, widths and output sha pinned;
+     three pin controls must be rejected (count pinned).
+  2. frame-controls: frame_controls.py, PR741's ten focused mutants judged by PR635's unchanged native audit.
+  3. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant) on the SW4F8 word; count pinned.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs, with the canonical word, local
+     programs and Clifford recipes pinned (LOCAL-PINS-frames-<id>.json).
+Apache-2.0.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P6 = HERE.parent / 'layers_p6n'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--sw4-dir', type=Path, required=True, help='construction/sw4/reproduce_sw4.py output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--recipe', default='sw4', help='FRAME-RECIPE-<id>.json and LOCAL-PINS-frames-<id>.json')
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('FRAME-RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-frames-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    inp = a.sw4_dir.resolve() / 'sw4/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['input_content_sha256'], 'input must be the pinned SW4 word'
+    run('frames', HERE / 'build_frames.py', inp, out / 'frames', rfile, portable=False)
+    b = read(out / 'frames/BUILD.json')
+    assert b['status'] == 'PASS_EIGHT_FRAME_EXACT_CONSTRUCTION' and len(b['rejected_controls']) == pins['frame_build_controls'], b
+    word = out / 'frames/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['expected']['output_content_sha256']
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('frame-controls', HERE / 'frame_controls.py', word, routing, out / 'FRAME-CONTROLS.json', rfile, portable=False)
+    fc = read(out / 'FRAME-CONTROLS.json')
+    assert fc['status'] == 'PASS_FOCUSED_EIGHT_FRAME_NATIVE_CONTROLS' and len(fc['rejected']) == pins['frame_controls'], len(fc['rejected'])
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/jx/LOCAL-PINS-jx-X4.json b/research/gauge44-leaver8/construction/jx/LOCAL-PINS-jx-X4.json
new file mode 100644
index 0000000000..417e4ba7a1
--- /dev/null
+++ b/research/gauge44-leaver8/construction/jx/LOCAL-PINS-jx-X4.json
@@ -0,0 +1,11 @@
+{
+ "word": "X4",
+ "jx_controls": 7,
+ "layer_controls": 95,
+ "canonical_sha256": "1c0e9da767d4418f70016af599e4a447a3f7777acabe930318459c0fbbd260aa",
+ "program_sha256": {
+  "forward": "076a2d428f97abb30473df05110998efbe5ac809885bae4ceb1b8bd81329a1e6",
+  "backward": "7915679ee305927463d19725360cc15132dd21ede18897d09a935dca1df0d55d"
+ },
+ "clifford_recipes_sha256": "20dddfce0ded7e41dc507939df7297bd98aec1286e05d7dbf18000d57e69a0b7"
+}
diff --git a/research/gauge44-leaver8/construction/jx/RECIPE-X4.json b/research/gauge44-leaver8/construction/jx/RECIPE-X4.json
new file mode 100644
index 0000000000..30f7fa5948
--- /dev/null
+++ b/research/gauge44-leaver8/construction/jx/RECIPE-X4.json
@@ -0,0 +1,1412 @@
+{
+ "input_content_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+ "input_word": "P6k4sw4 (BRoute w/P6k4sw4, d232183f)",
+ "frames_741_source": {
+  "pr": 741,
+  "commit": "e516b146",
+  "recipe": "scratch/WasteAttack/FRAME-RECIPE-741.json",
+  "frames_only_output_sha": "e78047028c7dcd25fb1b6216c2b53eda76d2f91292b21d43f5d1903cc13a5c6c"
+ },
+ "frames_741": [
+  [
+   856,
+   [
+    272,
+    144,
+    64,
+    8,
+    6,
+    1
+   ]
+  ],
+  [
+   860,
+   [
+    256,
+    128,
+    65,
+    16,
+    9,
+    6
+   ]
+  ],
+  [
+   868,
+   [
+    256,
+    144,
+    81,
+    33,
+    9,
+    6
+   ]
+  ],
+  [
+   873,
+   [
+    320,
+    192,
+    32,
+    16,
+    6,
+    1
+   ]
+  ],
+  [
+   876,
+   [
+    273,
+    144,
+    64,
+    33,
+    9,
+    6
+   ]
+  ],
+  [
+   953,
+   [
+    265,
+    137,
+    73,
+    32,
+    25,
+    6
+   ]
+  ],
+  [
+   961,
+   [
+    265,
+    128,
+    64,
+    41,
+    16,
+    6
+   ]
+  ],
+  [
+   965,
+   [
+    257,
+    128,
+    73,
+    40,
+    17,
+    6
+   ]
+  ]
+ ],
+ "raises": [
+  [
+   855,
+   [
+    280,
+    128,
+    64,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   859,
+   [
+    256,
+    129,
+    65,
+    40,
+    25,
+    6
+   ]
+  ],
+  [
+   862,
+   [
+    280,
+    144,
+    80,
+    56,
+    6,
+    1
+   ]
+  ],
+  [
+   863,
+   [
+    272,
+    136,
+    80,
+    56,
+    6,
+    1
+   ]
+  ],
+  [
+   867,
+   [
+    256,
+    136,
+    64,
+    41,
+    16,
+    6
+   ]
+  ],
+  [
+   870,
+   [
+    256,
+    200,
+    40,
+    16,
+    6,
+    1
+   ]
+  ],
+  [
+   875,
+   [
+    272,
+    144,
+    80,
+    49,
+    8,
+    6
+   ]
+  ],
+  [
+   942,
+   [
+    256,
+    136,
+    72,
+    33,
+    25,
+    6
+   ]
+  ],
+  [
+   943,
+   [
+    320,
+    193,
+    33,
+    16,
+    9,
+    6
+   ]
+  ],
+  [
+   946,
+   [
+    256,
+    129,
+    64,
+    41,
+    16,
+    6
+   ]
+  ],
+  [
+   947,
+   [
+    273,
+    128,
+    81,
+    33,
+    9,
+    6
+   ]
+  ],
+  [
+   950,
+   [
+    257,
+    193,
+    33,
+    16,
+    9,
+    6
+   ]
+  ],
+  [
+   954,
+   [
+    272,
+    129,
+    80,
+    49,
+    8,
+    6
+   ]
+  ],
+  [
+   955,
+   [
+    256,
+    128,
+    64,
+    33,
+    17,
+    6
+   ]
+  ],
+  [
+   958,
+   [
+    257,
+    128,
+    81,
+    33,
+    9,
+    6
+   ]
+  ],
+  [
+   962,
+   [
+    273,
+    128,
+    64,
+    33,
+    8,
+    6
+   ]
+  ]
+ ],
+ "edits": {
+  "replace": [
+   {
+    "h": 448,
+    "i": 862,
+    "old": [
+     "add",
+     140,
+     448,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     140,
+     235,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 448,
+    "i": 1207,
+    "old": [
+     "add",
+     133,
+     448,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     133,
+     235,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 448,
+    "i": 870,
+    "old": [
+     "add",
+     132,
+     235,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     132,
+     448,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 448,
+    "i": 1199,
+    "old": [
+     "add",
+     141,
+     235,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     141,
+     448,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 472,
+    "i": 855,
+    "old": [
+     "add",
+     173,
+     472,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     173,
+     267,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 472,
+    "i": 1198,
+    "old": [
+     "add",
+     140,
+     472,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     140,
+     267,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 472,
+    "i": 863,
+    "old": [
+     "add",
+     141,
+     267,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     141,
+     472,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 472,
+    "i": 1190,
+    "old": [
+     "add",
+     172,
+     267,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     172,
+     472,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 458,
+    "i": 942,
+    "old": [
+     "add",
+     204,
+     458,
+     1,
+     1
+    ],
+    "new": [
+     "add",
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+     58,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 458,
+    "i": 1287,
+    "old": [
+     "add",
+     197,
+     458,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     197,
+     58,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 458,
+    "i": 950,
+    "old": [
+     "add",
+     196,
+     58,
+     1,
+     1
+    ],
+    "new": [
+     "add",
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+     458,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 458,
+    "i": 1279,
+    "old": [
+     "add",
+     205,
+     58,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     205,
+     458,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 592,
+    "i": 859,
+    "old": [
+     "add",
+     174,
+     592,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     174,
+     427,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 592,
+    "i": 1278,
+    "old": [
+     "add",
+     204,
+     592,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     204,
+     427,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 592,
+    "i": 943,
+    "old": [
+     "add",
+     205,
+     427,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     205,
+     592,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 592,
+    "i": 1194,
+    "old": [
+     "add",
+     170,
+     427,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     170,
+     592,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 470,
+    "i": 946,
+    "old": [
+     "add",
+     202,
+     470,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     202,
+     26,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 470,
+    "i": 1295,
+    "old": [
+     "add",
+     165,
+     470,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     165,
+     26,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 470,
+    "i": 958,
+    "old": [
+     "add",
+     164,
+     26,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     164,
+     470,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 470,
+    "i": 1283,
+    "old": [
+     "add",
+     206,
+     26,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     206,
+     470,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 604,
+    "i": 867,
+    "old": [
+     "add",
+     142,
+     604,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     142,
+     443,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 604,
+    "i": 1282,
+    "old": [
+     "add",
+     202,
+     604,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     202,
+     443,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 604,
+    "i": 947,
+    "old": [
+     "add",
+     206,
+     443,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     206,
+     604,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 604,
+    "i": 1202,
+    "old": [
+     "add",
+     138,
+     443,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     138,
+     604,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 482,
+    "i": 954,
+    "old": [
+     "add",
+     194,
+     482,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     194,
+     18,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 482,
+    "i": 1299,
+    "old": [
+     "add",
+     166,
+     482,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     166,
+     18,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 482,
+    "i": 962,
+    "old": [
+     "add",
+     162,
+     18,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     162,
+     482,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 482,
+    "i": 1291,
+    "old": [
+     "add",
+     198,
+     18,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     198,
+     482,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 614,
+    "i": 875,
+    "old": [
+     "add",
+     134,
+     614,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     134,
+     50,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 614,
+    "i": 1290,
+    "old": [
+     "add",
+     194,
+     614,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     194,
+     50,
+     1,
+     1
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 614,
+    "i": 955,
+    "old": [
+     "add",
+     198,
+     50,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     198,
+     614,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 614,
+    "i": 1210,
+    "old": [
+     "add",
+     130,
+     50,
+     1,
+     1
+    ],
+    "new": [
+     "add",
+     130,
+     614,
+     1,
+     1
+    ],
+    "why": "r2h: read of r -> read of h"
+   }
+  ],
+  "delete": [
+   {
+    "h": 448,
+    "i": 1,
+    "old": [
+     "add",
+     140,
+     448,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 448,
+    "i": 0,
+    "old": [
+     "add",
+     133,
+     448,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 472,
+    "i": 33,
+    "old": [
+     "add",
+     173,
+     472,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 472,
+    "i": 32,
+    "old": [
+     "add",
+     140,
+     472,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 458,
+    "i": 21,
+    "old": [
+     "add",
+     204,
+     458,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 458,
+    "i": 20,
+    "old": [
+     "add",
+     197,
+     458,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 592,
+    "i": 64,
+    "old": [
+     "add",
+     174,
+     592,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 592,
+    "i": 65,
+    "old": [
+     "add",
+     204,
+     592,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 470,
+    "i": 29,
+    "old": [
+     "add",
+     202,
+     470,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 470,
+    "i": 28,
+    "old": [
+     "add",
+     165,
+     470,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 604,
+    "i": 72,
+    "old": [
+     "add",
+     142,
+     604,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 604,
+    "i": 73,
+    "old": [
+     "add",
+     202,
+     604,
+     1,
+     2
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 482,
+    "i": 37,
+    "old": [
+     "add",
+     194,
+     482,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 482,
+    "i": 36,
+    "old": [
+     "add",
+     166,
+     482,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 614,
+    "i": 95,
+    "old": [
+     "add",
+     134,
+     614,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   },
+   {
+    "h": 614,
+    "i": 96,
+    "old": [
+     "add",
+     194,
+     614,
+     -1,
+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   }
+  ],
+  "insert": [
+   {
+    "h": 448,
+    "before": 2,
+    "gate": [
+     "add",
+     132,
+     448,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 448,
+    "before": 2,
+    "gate": [
+     "add",
+     141,
+     448,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 472,
+    "before": 34,
+    "gate": [
+     "add",
+     141,
+     472,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 472,
+    "before": 34,
+    "gate": [
+     "add",
+     172,
+     472,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 458,
+    "before": 22,
+    "gate": [
+     "add",
+     196,
+     458,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 458,
+    "before": 22,
+    "gate": [
+     "add",
+     205,
+     458,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 592,
+    "before": 66,
+    "gate": [
+     "add",
+     205,
+     592,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 592,
+    "before": 66,
+    "gate": [
+     "add",
+     170,
+     592,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 470,
+    "before": 30,
+    "gate": [
+     "add",
+     164,
+     470,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 470,
+    "before": 30,
+    "gate": [
+     "add",
+     206,
+     470,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 604,
+    "before": 74,
+    "gate": [
+     "add",
+     206,
+     604,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 604,
+    "before": 74,
+    "gate": [
+     "add",
+     138,
+     604,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 482,
+    "before": 38,
+    "gate": [
+     "add",
+     162,
+     482,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 482,
+    "before": 38,
+    "gate": [
+     "add",
+     198,
+     482,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 614,
+    "before": 97,
+    "gate": [
+     "add",
+     198,
+     614,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 614,
+    "before": 97,
+    "gate": [
+     "add",
+     130,
+     614,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   }
+  ]
+ },
+ "pairs": {
+  "448": 235,
+  "458": 58,
+  "470": 26,
+  "472": 267,
+  "482": 18,
+  "592": 427,
+  "604": 443,
+  "614": 50
+ },
+ "expected": {
+  "output_content_sha256": "1e1d99ba7aab877d6b573c41f7030ee73de9a52fee51d0a822ddaae71251999f",
+  "local_profile": {
+   "1": 2548,
+   "2": 338,
+   "3": 430,
+   "4": 194,
+   "5": 56,
+   "8": 8
+  }
+ },
+ "controls": {
+  "C0_identity": {
+   "mutation": {
+    "kind": "empty"
+   },
+   "expected_sha": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+   "local_profile": {
+    "1": 2548,
+    "2": 342,
+    "3": 438,
+    "4": 186,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "C1_741_only": {
+   "mutation": {
+    "kind": "only_edits_of",
+    "h": [],
+    "raises": []
+   },
+   "expected_sha": "e78047028c7dcd25fb1b6216c2b53eda76d2f91292b21d43f5d1903cc13a5c6c",
+   "local_profile": {
+    "1": 2556,
+    "2": 334,
+    "3": 430,
+    "4": 194,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "M1_one_pair_448": {
+   "mutation": {
+    "kind": "only_edits_of",
+    "h": [
+     448
+    ],
+    "raises": [
+     862,
+     870
+    ]
+   },
+   "expected_sha": "5fb6fb2e5e63d18b865535c1dbd3dbaddab530c39429a4b09f11ac96723257c9",
+   "local_profile": {
+    "1": 2556,
+    "2": 334,
+    "3": 430,
+    "4": 194,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "N1_drop_preread": {
+   "mutation": {
+    "kind": "drop_insert",
+    "k": 0
+   },
+   "rejection_expected": [
+    "exactness rows",
+    [
+     132,
+     135
+    ]
+   ]
+  },
+  "N2_wrong_sign_preread": {
+   "mutation": {
+    "kind": "flip_insert_sign",
+    "k": 0
+   },
+   "rejection_expected": [
+    "exactness rows",
+    [
+     132,
+     135
+    ]
+   ]
+  },
+  "N3_plain_join_moved_reads": {
+   "mutation": {
+    "kind": "drop_raises"
+   },
+   "expected_sha": "7241cd59dd0376e0b2e1b5ba8403c5423d247ddd7cbcc2f02bdc353752806f30",
+   "local_profile": {
+    "1": 2532,
+    "2": 378,
+    "3": 430,
+    "4": 178,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "N4_raise_dim7_at_855": {
+   "mutation": {
+    "kind": "frame",
+    "i": 855,
+    "frame": [
+     280,
+     128,
+     64,
+     40,
+     4,
+     2,
+     1
+    ]
+   },
+   "rejection_expected": [
+    "cap",
+    1302,
+    174
+   ]
+  }
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/jx/build_jx.py b/research/gauge44-leaver8/construction/jx/build_jx.py
new file mode 100644
index 0000000000..f8d74a6324
--- /dev/null
+++ b/research/gauge44-leaver8/construction/jx/build_jx.py
@@ -0,0 +1,167 @@
+#!/usr/bin/env python3
+"""build_jx.py --input WORD --recipe RECIPE.json --out OUT.json.gz [--control NAME] [--no-pin]
+
+Stdlib-only builder: joint read-set exchange (copy pairs, BRoute sw4 rule) + explicit B frame raises on P6k4sw4.
+Steps:
+ 1. input content sha256 must equal recipe.input_content_sha256.
+ 2. explicit B edits: replace (old gate asserted), delete (old gate asserted), insert (before an original index).
+ 3. frames: replaced/inserted gates take the plain join of their operands' current frames; gates listed in
+    frames_741 / raises take base = the listed frame and the resulting frame must EQUAL it (explicit frames);
+    every other gate keeps span(stored frame + operand frames) (monotone repair). Early cleanup likewise.
+ 4. legality: target frames inside u_t^perp at every gate; tails inside helper_final; every end frame contains the
+    final frame; the explicit frame must contain the join (enforced by equality in 3).
+ 5. exactness: the rational linear map of the whole B segment is identical to the input's (Fraction replay).
+ 6. paid profile recomputed (A + centre levels + B + tails + ends) and written to report.local_profile.
+Output: canonical json (sort_keys, compact) gzip mtime=0. Exit 0 and prints output sha; exit 2 with the first
+rejection (site) on failure. --control applies a named mutation from recipe.controls (expected to be rejected
+or to give a pinned sha)."""
+import argparse, gzip, json, hashlib, sys, copy
+from fractions import Fraction as Fr
+from collections import Counter
+
+V, H = 112, 9
+
+def basis(vs):
+    piv = {}
+    for a in vs:
+        while a:
+            b = a.bit_length() - 1
+            if b in piv: a ^= piv[b]
+            else: piv[b] = a; break
+    for k in sorted(piv):
+        for j in sorted(piv):
+            if j > k and (piv[j] >> k) & 1: piv[j] ^= piv[k]
+    return tuple(piv[k] for k in sorted(piv, reverse=True))
+
+def contained(a, b): return basis(list(a) + list(b)) == tuple(b)
+def registers(e): return e[1:3] if e[0] == 'add' else e[1:2]
+def hyper(p): return basis([x for x in range(1, 1 << H) if (x & p).bit_count() % 2 == 0])
+FULL = basis([1 << i for i in range(H)])
+def csha(w): return hashlib.sha256(json.dumps(w, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+
+class Reject(Exception): pass
+
+def symstate(gs):
+    rows = {}
+    for e in gs:
+        for q in registers(e): rows.setdefault(q, {q: Fr(1)})
+        if e[0] == 'add':
+            t, s = e[1], e[2]; c = Fr(e[3], e[4]); d = rows[t]
+            for k, x in list(rows[s].items()):
+                a = d.get(k, 0) + c * x
+                if a: d[k] = a
+                else: d.pop(k, None)
+        else:
+            t = e[1]; c = Fr(e[2], e[3]); rows[t] = {k: c * x for k, x in rows[t].items()}
+    return rows
+
+def build(w, rc, control=None):
+    w = copy.deepcopy(w); B0 = w['B']
+    edits = copy.deepcopy(rc['edits']); explicit = {int(i): f for i, f in rc['frames_741']}
+    for i, f in rc['raises']:
+        if int(i) in explicit: raise Reject(('duplicate frame', i))
+        explicit[int(i)] = f
+    if control:
+        c = rc['controls'][control]['mutation']
+        if c['kind'] == 'drop_insert': edits['insert'] = [x for k, x in enumerate(edits['insert']) if k != c['k']]
+        elif c['kind'] == 'flip_insert_sign': edits['insert'][c['k']]['gate'][3] *= -1
+        elif c['kind'] == 'frame': explicit[c['i']] = c['frame']
+        elif c['kind'] == 'drop_edits': edits = dict(replace=[], delete=[], insert=[])
+        elif c['kind'] == 'drop_raises': explicit = {int(i): f for i, f in rc['frames_741']}
+        elif c['kind'] == 'only_edits_of':
+            hs = set(c['h'])
+            edits = {k: [x for x in v if x['h'] in hs] for k, v in edits.items()}
+            explicit = {i: f for i, f in explicit.items() if i in {int(j) for j, _ in rc['frames_741']} or i in set(c['raises'])}
+        elif c['kind'] == 'empty': edits = dict(replace=[], delete=[], insert=[]); explicit = {}
+        else: raise SystemExit('unknown control')
+    B = [list(e) for e in B0]; tag = set(); dele = set(); ins = {}
+    for x in edits['replace']:
+        i = x['i']
+        if B[i][:-1] != x['old']: raise Reject(('replace old mismatch', i))
+        B[i] = list(x['new']) + [B[i][-1]]; tag.add(i)
+    for x in edits['delete']:
+        i = x['i']
+        if B[i][:-1] != x['old']: raise Reject(('delete old mismatch', i))
+        dele.add(i)
+    for x in edits['insert']: ins.setdefault(x['before'], []).append(list(x['gate']) + [None])
+    NB, nt, key = [], set(), []
+    for i, e in enumerate(B):
+        for g in ins.get(i, []): nt.add(len(NB)); NB.append(g); key.append(None)
+        if i in dele: continue
+        if i in tag: nt.add(len(NB))
+        NB.append(e); key.append(i)
+    # frames + paid
+    R = w['report']['R']; n = 2 * V + R
+    END = [FULL] * V + [hyper(p) for p in w['ports']] + [FULL] * R
+    for q, U in w['helper_final'].items(): END[int(q)] = basis(U)
+    cur = [(p,) for p in w['ports']] + [()] * (V + R)
+    for q, U in w['start_extra'].items(): cur[int(q)] = basis(U)
+    paid = Counter()
+    for e in w['A']:
+        for q in registers(e):
+            U = basis(e[-1]); d = len(U) - len(cur[q])
+            if d: paid[d] += 1
+            cur[q] = U
+    lev = {int(t): basis(U) for t, U in w.get('target_levels', {}).items()}
+    for q, U in zip(w['centers'], w['center_frames']):
+        U = basis(U); served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == q}
+        for T in sorted(served, key=lambda x: -len(x)):
+            if T != U: paid[len(U) - len(T)] += 1
+            U = T
+    used = set()
+    for j, e in enumerate(NB):
+        rs = registers(e); k = key[j]
+        if k is not None and k in explicit: base = list(explicit[k]); used.add(k)
+        elif j in nt or e[-1] is None: base = []
+        else: base = list(e[-1])
+        F = basis(base + [x for q in rs for x in cur[q]])
+        if k is not None and k in explicit and F != basis(explicit[k]): raise Reject(('explicit frame below join', k))
+        for q in rs:
+            if V <= q < 2 * V and not contained(F, END[q]): raise Reject(('cap', j, q))
+            d = len(F) - len(cur[q])
+            if d: paid[d] += 1
+            cur[q] = F
+        NB[j] = list(e[:-1]) + [list(F)]
+    if used != set(explicit): raise Reject(('unused explicit frame', sorted(set(explicit) - used)))
+    newearly = []
+    for i, U in w['early_cleanup']:
+        rs = registers(w['cleanup'][i]); F = basis(list(U) + [x for q in rs for x in cur[q]])
+        for q in rs:
+            if w['helper_final'].get(str(q)) is not None and not contained(F, END[q]): raise Reject(('tailend', i, q))
+            d = len(F) - len(cur[q])
+            if d: paid[d] += 1
+            cur[q] = F
+        newearly.append([i, list(F)])
+    for q in range(n):
+        if not contained(cur[q], END[q]): raise Reject(('end', q))
+        d = len(END[q]) - len(cur[q])
+        if d: paid[d] += 1
+    # exactness of the B segment
+    a, b = symstate([e[:-1] for e in B0]), symstate([e[:-1] for e in NB])
+    bad = sorted(q for q in set(a) | set(b) if a.get(q, {q: Fr(1)}) != b.get(q, {q: Fr(1)}))
+    if bad: raise Reject(('exactness rows', bad))
+    w['B'] = NB; w['early_cleanup'] = newearly
+    w['report'] = dict(w['report']); w['report']['local_profile'] = {str(k): v for k, v in sorted(paid.items())}
+    return w
+
+def main():
+    ap = argparse.ArgumentParser(); ap.add_argument('--input', required=True); ap.add_argument('--recipe', required=True)
+    ap.add_argument('--out'); ap.add_argument('--control'); ap.add_argument('--no-pin', action='store_true')
+    a = ap.parse_args()
+    w = json.loads(gzip.decompress(open(a.input, 'rb').read())); rc = json.load(open(a.recipe))
+    if csha(w) != rc['input_content_sha256']: print('REJECT input pin'); sys.exit(2)
+    pin = rc['controls'][a.control].get('rejection_expected') if a.control else None
+    try: o = build(w, rc, a.control)
+    except Reject as r:
+        got = json.loads(json.dumps(r.args[0])); print('REJECT', json.dumps(got))
+        if pin is not None:
+            print('CONTROL', 'PINNED' if got == pin else 'PIN MISMATCH %s' % json.dumps(pin)); sys.exit(0 if got == pin else 4)
+        sys.exit(2)
+    if pin is not None and not a.no_pin: print('CONTROL NOT REJECTED, pinned', json.dumps(pin)); sys.exit(4)
+    s = csha(o)
+    exp = rc['controls'][a.control].get('expected_sha') if a.control else rc['expected']['output_content_sha256']
+    print('OK', s, o['report']['local_profile'])
+    if a.out: open(a.out, 'wb').write(gzip.compress(json.dumps(o, sort_keys=True, separators=(',', ':')).encode(), mtime=0))
+    if not a.no_pin and exp and s != exp: print('REJECT output pin', exp); sys.exit(3)
+
+if __name__ == '__main__': main()
diff --git a/research/gauge44-leaver8/construction/jx/reproduce_jx.py b/research/gauge44-leaver8/construction/jx/reproduce_jx.py
new file mode 100644
index 0000000000..6829a1b25d
--- /dev/null
+++ b/research/gauge44-leaver8/construction/jx/reproduce_jx.py
@@ -0,0 +1,99 @@
+#!/usr/bin/env python3
+"""Rebuild the X4 word (JointXF: joint read-set exchange on four further copy-pair instances plus explicit B frame
+raises, including chafreaky's PR741 eight frames) and its native locals.
+
+Input: a fresh `construction/sw4/reproduce_sw4.py --recipe P6k4` output directory; its SW4 word (d232183f...) is pinned
+there and by RECIPE-X4.json. Steps, each checked exactly:
+  1. jx: build_jx.py (standard library only; JointXF) applies the recipe's explicit B edits (replace / delete / insert,
+     each old gate asserted), the PR741 frames and the explicit raises, repairs all other frames monotonically, checks
+     target frames inside u_t^perp, tails and ends, and the exactness of the whole B segment (rational replay), and
+     pins the output sha.
+  2. jx-controls: every control in the recipe is rebuilt and must reproduce its pinned outcome exactly: a pinned
+     rejection site (exit 0 with CONTROL PINNED) or a pinned output sha. C1_741_only must reproduce PR741's word
+     e78047028c... (the construction/frames step's output); C0_identity reproduces the input.
+  3. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant) on the X4 word; count pinned.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs; canonical word, local programs
+     and Clifford recipes pinned (LOCAL-PINS-jx-X4.json).
+Apache-2.0. Driver by ColdWitness around JointXF's builder.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P6 = HERE.parent / 'layers_p6n'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--sw4-dir', type=Path, required=True, help='construction/sw4/reproduce_sw4.py output')
+    ap.add_argument('--recipe', default='X4', help='RECIPE-<id>.json and LOCAL-PINS-jx-<id>.json')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-jx-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True, ok=(0,)):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc in ok, (label, rc)
+        print('PASS', label, flush=True)
+        return (out / (label + '.log')).read_text()
+
+    inp = a.sw4_dir.resolve() / 'sw4/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['input_content_sha256'], 'input must be the pinned SW4 word'
+    (out / 'jx').mkdir(); word = out / 'jx/FULL-WORD.json.gz'
+    run('jx', HERE / 'build_jx.py', '--input', inp, '--recipe', rfile, '--out', word, portable=False)
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['expected']['output_content_sha256']
+    assert len(rec['controls']) == pins['jx_controls'], len(rec['controls'])
+    results = {}
+    for name, c in sorted(rec['controls'].items()):
+        log = run('jx-control-' + name, HERE / 'build_jx.py', '--input', inp, '--recipe', rfile, '--control', name, portable=False)
+        if 'rejection_expected' in c:
+            assert 'CONTROL PINNED' in log, (name, log[-300:]); results[name] = dict(rejected=c['rejection_expected'])
+        else:
+            assert ('OK ' + c['expected_sha']) in log, (name, log[-300:]); results[name] = dict(sha=c['expected_sha'])
+    assert rec['controls']['C1_741_only']['expected_sha'] == rec['frames_741_source']['frames_only_output_sha']
+    (out / 'JX-CONTROLS.json').write_text(json.dumps(dict(status='PASS_JX_PINNED_CONTROLS', controls=results), indent=1) + '\n')
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/layers/build_pivot_swap.py b/research/gauge44-leaver8/construction/layers/build_pivot_swap.py
new file mode 100644
index 0000000000..b225601c01
--- /dev/null
+++ b/research/gauge44-leaver8/construction/layers/build_pivot_swap.py
@@ -0,0 +1,160 @@
+"""Cost-neutral pivot-role swaps inside existing entrance-kernel families.  Apache-2.0.  Prepared with Claude Code
+assistance.  The pivot/donor role exchange follows PR266's "pivot role is moved" idea (bit side), applied here to the
+complex supplier's multicut kernel families (PR568 build_multicut_kernels.py shape).
+
+A kernel family on the input word is an entering helper p (start_extra E) together with the gates that read p at frame
+E before any other touch of p:  d += c_d * p @E  (d a helper or, in B, a target).  They cancel p's complete dirty
+response:  col(p) + sum_d c_d * col_{g_d}(d) = 0, where col_{g}(d) is d's suffix response from gate g on.
+
+Swap to the new pivot x (a helper donor of the family with exactly one family gate g_x = x's FIRST touch, and no other
+touch of x up to the family's last gate):
+    g_x :  x += c_x p   ->   p += (1/c_x) x
+    g_d :  d += c_d p   ->   d += (c_d/c_x) x          (d != x, same position and frame E)
+    start_extra: p -> x (same E); cleanup regenerated by the inherited inverse rule.
+Exactness (PROOF-NOTE-PIVOT.md): x holds only its initial dirt at every rewritten gate, and p holds only its initial dirt
+until g_x, so x's new response is col(x) + col(p)/c_x + sum_d (c_d/c_x) col_{g_d}(d) = (c_x col(x) + col(p) +
+sum_d c_d col_{g_d}(d)) / c_x = 0, because col(x) = col_{g_x}(x).  This script checks it by exact rational replay anyway.
+Cost: the frame chains of p and x are exchanged (p now climbs [] -> E at g_x where x did; x starts at E where p did), so
+gk_word.profile and the width multiset are unchanged; both are asserted.
+
+Recipe: {input_content_sha256, output_content_sha256, swaps: [{pivot, new_pivot, entrance, gates: [{part, index,
+before, after}]}]}.  Every expected `after` gate is recomputed from the rule above and must equal the recipe.
+
+Negative controls (--controls): mutated recipes/words that must be rejected at pinned reasons:
+  * nonzero response: another family gate's rescaled coefficient has the wrong sign;
+  * wrong pivot coefficient: g_x's new coefficient doubled;
+  * wrong entrance: the recipe's entrance is not p's start_extra;
+  * non-family gate: a recipe gate whose `before` is not the word's gate;
+  * new pivot touched in the window: x replaced by a family donor that is not a fresh helper (a target donor, or the
+    first other helper donor when the family has no target donor).
+"""
+from pathlib import Path
+from collections import Counter
+from fractions import Fraction as Q
+import argparse, copy, gzip, hashlib, json, sys
+assert __debug__, 'Assertions required'
+ap = argparse.ArgumentParser()
+for k in ('--input', '--recipe', '--gk-dir', '--out'): ap.add_argument(k, type=Path, required=True)
+a = ap.parse_args(); assert not a.out.exists()
+sys.path.insert(0, str(a.gk_dir)); import gk_word as G, gk_common as C
+G.V = C.V = 112; G.DATA = C.DATA = 7168
+V = 112
+raw = json.loads(gzip.decompress(a.input.read_bytes())); recipe = json.loads(a.recipe.read_text())
+enc = lambda x: json.dumps(x, sort_keys=True, separators=(',', ':')).encode(); sha = lambda x: hashlib.sha256(x).hexdigest()
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+inv_rule = lambda w: [G.inverse(e, G.FULL) for e in reversed(w['A'] + w['B']) if not V <= e[1] < 2 * V]
+dy = lambda q: q != 0 and q.denominator & (q.denominator - 1) == 0
+
+
+def response(w, h):
+    rows = {}
+    def get(r): return rows.setdefault(r, {r: Q(1)})
+    for e in w['A'] + w['cut'] + w['B']:
+        if e[0] == 'scale':
+            q = Q(e[2], e[3]); rows[e[1]] = {j: q * x for j, x in get(e[1]).items()}
+        else:
+            t, s = e[1], e[2]; q = Q(e[3], e[4]); src = get(s); tgt = get(t)
+            for j, x in list(src.items()):
+                z = tgt.get(j, Q(0)) + q * x
+                if z: tgt[j] = z
+                else: tgt.pop(j, None)
+    return {r: rows[r][h] for r in range(V, 2 * V) if r in rows and rows[r].get(h)}
+
+
+def build(w0, rec):
+    w = copy.deepcopy(w0); n = 2 * V + w['report']['R']
+    assert w['cleanup'] == inv_rule(w), 'input cleanup is not the inherited inverse rule'
+    P0 = G.profile(w); W0 = Counter(C.widths_of(w))
+    AB = [('A', i) for i in range(len(w['A']))] + [('B', i) for i in range(len(w['B']))]
+    pos = {k: j for j, k in enumerate(AB)}
+    seen = set(); receipts = []; rules = []
+    for s in rec['swaps']:
+        p, x, E = s['pivot'], s['new_pivot'], s['entrance']
+        assert 2 * V <= p < n and w['start_extra'].get(str(p)) == E, 'pivot is not an entering helper at the entrance'
+        assert 2 * V <= x < n and x not in w['centers'], 'new pivot must be a helper'
+        assert str(x) not in w['start_extra'], 'new pivot already entering'
+        assert not {p, x} & seen, 'registers shared between swaps'; seen |= {p, x}
+        gs = s['gates']; ks = [pos[(g['part'], g['index'])] for g in gs]
+        assert ks == sorted(ks) and len(set(ks)) == len(ks)
+        for g in gs:
+            e = w[g['part']][g['index']]
+            assert e == g['before'], 'recipe gate is not the word gate'
+            assert e[0] == 'add' and e[2] == p and e[1] != p and list(e[-1]) == list(E), 'not a family gate (d += c p @E)'
+        touch = lambda r: [j for j, (part, i) in enumerate(AB) if r in regs(w[part][i])]
+        tp = touch(p); assert tp[:len(ks)] == ks, 'family gates must be all touches of the pivot up to its first other touch'
+        gx = [k for k, g in zip(ks, gs) if g['before'][1] == x]; assert len(gx) == 1, 'new pivot must have exactly one family gate'
+        tx = touch(x); assert tx[0] == gx[0], 'new pivot touched before its family gate'
+        assert len(tx) == 1 or tx[1] > ks[-1], 'new pivot touched inside the family window'
+        cx = Q(*[g['before'][3:5] for g in gs if g['before'][1] == x][0])
+        for g in gs:
+            d, f = g['before'][1], g['after']
+            assert f[0] == 'add' and list(f[-1]) == list(E) and (f[1:3] == [p, x] if d == x else f[1:3] == [d, x]), 'after-gate shape'
+            assert dy(Q(f[3], f[4])), 'non-dyadic swapped coefficient'
+            w[g['part']][g['index']] = f
+            q = 1 / cx if d == x else Q(g['before'][3], g['before'][4]) / cx
+            rules.append((f, ['add', p, x, q.numerator, q.denominator, list(E)] if d == x else ['add', d, x, q.numerator, q.denominator, list(E)]))
+        w['start_extra'][str(x)] = w['start_extra'].pop(str(p))
+        receipts.append(dict(pivot=p, new_pivot=x, entrance=E, family_gates=len(gs)))
+    w['cleanup'] = inv_rule(w)
+    for s in rec['swaps']:
+        assert not response(w, s['new_pivot']), 'new pivot dirty response not zero'
+    assert all(f == e for f, e in rules), 'recipe after-gate is not the swap rule'
+    P1 = G.profile(w)
+    assert P1 == P0, 'paid profile not identical (swap is not cost-neutral)'
+    assert Counter(C.widths_of(w)) == W0, 'width multiset changed'
+    w['report']['local_profile'] = {str(k): v for k, v in sorted(P1.items())}
+    w['report']['local_rank_mass'] = sum(k * v for k, v in P1.items())
+    return w, receipts
+
+
+assert sha(enc(raw)) == recipe['input_content_sha256'], 'input content'
+out, receipts = build(raw, recipe)
+o = enc(out); assert sha(o) == recipe['output_content_sha256'], sha(o)
+
+# ---- negative controls -------------------------------------------------------------------------------------------
+WHY = dict(nonzero='new pivot dirty response not zero', coef='new pivot dirty response not zero',
+           entrance='paid profile not identical', nonfamily='recipe gate is not the word gate',
+           window='new pivot')
+controls = []
+
+
+def reject(name, mut, why):
+    r = copy.deepcopy(recipe); w = copy.deepcopy(raw)
+    mut(r, w)
+    try:
+        build(w, r)
+    except AssertionError as ex:
+        msg = str(ex)
+        assert why in msg, ('control rejected for the wrong reason', name, msg)
+        controls.append(dict(control=name, reason=msg)); return
+    raise AssertionError('control accepted: ' + name)
+
+
+for si, s in enumerate(recipe['swaps']):
+    x = s['new_pivot']; tag = '%d->%d' % (s['pivot'], x)
+    def m_other(r, w, si=si):
+        g = [g for g in r['swaps'][si]['gates'] if g['before'][1] != r['swaps'][si]['new_pivot']][0]
+        g['after'] = list(g['after']); g['after'][3] = -g['after'][3]
+    def m_coef(r, w, si=si):
+        g = [g for g in r['swaps'][si]['gates'] if g['before'][1] == r['swaps'][si]['new_pivot']][0]
+        g['after'] = list(g['after']); g['after'][3] *= 2
+    def m_nonfamily(r, w, si=si):
+        g = r['swaps'][si]['gates'][0]; g['before'] = list(g['before']); g['before'][3] = -g['before'][3]
+    def m_window(r, w, si=si):
+        S = r['swaps'][si]; S['new_pivot'] = [g['before'][1] for g in S['gates'] if g['before'][1] != S['new_pivot']][0]
+    def m_entrance(r, w, si=si):
+        S = r['swaps'][si]; S['entrance'] = [1]
+    reject('swap %s: another family gate keeps a wrong (unrescaled-sign) coefficient: new pivot response nonzero' % tag, m_other, WHY['nonzero'])
+    reject('swap %s: wrong pivot coefficient (1/c doubled) on the new pivot gate' % tag, m_coef, WHY['coef'])
+    reject('swap %s: non-family gate in the recipe' % tag, m_nonfamily, WHY['nonfamily'])
+    reject('swap %s: new pivot replaced by another family donor (not a fresh cold helper)' % tag, m_window, WHY['window'])
+    reject('swap %s: wrong entrance frame for the moved entrance' % tag, m_entrance, 'pivot is not an entering helper at the entrance')
+controls_receipt = list(controls)
+
+a.out.mkdir(parents=True); (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(o, mtime=0))
+rc = dict(status='PASS_COST_NEUTRAL_PIVOT_SWAPS', input_content_sha256=recipe['input_content_sha256'],
+          output_content_sha256=recipe['output_content_sha256'], swaps=receipts, local_profile=out['report']['local_profile'],
+          negative_controls_rejected=controls_receipt,
+          scope='Exact family rewrite, exact zero dirty response of every new pivot, identical paid profile and widths, '
+                'regenerated inverse-rule cleanup.  Native all-column audit, HPE/cold steps and global checks remain separate.')
+(a.out / 'PIVOT-SWAP.json').write_text(json.dumps(rc, indent=2, sort_keys=True) + '\n', newline='\n'); print(json.dumps(rc, indent=2))
diff --git a/research/gauge44-leaver8/construction/layers/layer_end_controls.py b/research/gauge44-leaver8/construction/layers/layer_end_controls.py
new file mode 100644
index 0000000000..317da36d95
--- /dev/null
+++ b/research/gauge44-leaver8/construction/layers/layer_end_controls.py
@@ -0,0 +1,201 @@
+"""layer_end_controls.py LAYERED-WORD.json.gz ROUTING OUTDIR (env PR635_CODE): adapted PR635 cold_end_controls.py (LayerReviewer): raw-word negative controls for the cold low-frame ends and the
+refactored cleanup accepted by hpe_audit_and_transport.py.  Every mutation MUST be rejected (AssertionError); the
+unmutated word MUST pass.  Apache-2.0.  DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code."""
+import copy, gzip, json, shutil, sys, tempfile
+from pathlib import Path
+import os
+sys.path.insert(0, os.environ['PR635_CODE'])   # PR635's unchanged hpe_audit_and_transport.py
+import hpe_audit_and_transport as atc
+
+src, routing, outdir = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3])
+word = json.load(gzip.open(src))
+v, R = word['report']['v'], word['report']['R']; n = 2*v + R
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+meta = word['refactored_cleanup']
+cold = [int(h) for h in meta['cold_low_frame_ended_helpers']]
+npre = meta['premix_gates']; nlow = meta['lower_frame_gates']
+early = word['early_cleanup']; eidx = {i for i, _ in early}
+rest = [i for i in range(len(word['cleanup'])) if i not in eidx]
+
+
+def trial(w):
+    """None if the transport audit accepts w, else the AssertionError message."""
+    tmp = Path(tempfile.mkdtemp())
+    p = tmp/'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w).encode(), mtime=0))
+    try:
+        atc.run(p, routing, tmp/'out')
+        return None
+    except AssertionError as e:
+        return repr(e.args[0]) if e.args else 'AssertionError'
+    finally:
+        shutil.rmtree(tmp, ignore_errors=True)
+
+
+# Pinned rejection reasons: each mutant must fail at this assertion of hpe_audit_and_transport.py (message substring).
+ENDPOINT, COLDPRE, CONE = "'arbitrary-dirt endpoint'", 'touches a cold hyperplane-ended helper', 'hpe cone pre-check (row / column)'
+WHY = dict(premix_to_precondition=COLDPRE, premix_dropped=COLDPRE, e_premix_dropped=ENDPOINT, lower_dropped=ENDPOINT,
+           remainder_dropped=ENDPOINT, coefficient=ENDPOINT, into_full='cleanup on non-FULL end', dyadic=ENDPOINT, frame_below="'nonmonotone'",
+           nonmonotone="'nonmonotone'", other_frame=CONE, cone=CONE, extra_end=COLDPRE, marker='cleanup is not the literal reversed inverse',
+           target='refactored cleanup touches a target', profile_pin='paid local profile differs from the reported local_profile',
+           entering_precondition='zero-frame precondition/compensation touches an entering helper')
+assert trial(word) is None, 'unmutated cold-end word must pass'
+results = []
+
+
+def reject(name, mut, why):
+    """the mutation must be rejected, and for the pinned reason (a substring of the audit's assertion message)."""
+    w = copy.deepcopy(word); mut(w)
+    msg = trial(w)
+    assert msg is not None, 'cold-end mutation accepted: ' + name
+    assert why in msg, 'cold-end mutation %r rejected for the wrong reason: %s' % (name, msg[:300])
+    results.append(name); print('rejected', name, '|', why, flush=True)
+
+
+h0 = cold[0]
+i0, U0 = next((i, f) for i, f in early if h0 in regs(word['cleanup'][i]))
+r0 = rest[len(rest)//2]
+
+
+def premix_to_precondition(w):   # premix before the wrappers; compensation then reads the cold ends
+    w['precondition'] = w['precondition'] + w['A'][:npre]; w['A'] = w['A'][npre:]
+
+
+def lower_gate_into_full(w):     # a lower-frame gate on a cold-ended helper executed in the FULL remainder instead
+    w['early_cleanup'] = [x for x in w['early_cleanup'] if x[0] != i0]
+
+
+def drop_cleanup_gate(w, i):   # remove the gate AND its early_cleanup entry: a structurally valid word missing one gate
+    w['cleanup'].pop(i)
+    w['early_cleanup'] = [[j - (j > i), f] for j, f in w['early_cleanup'] if j != i]
+
+
+def other_frame(w):              # a different frame of the same dimension as the cold end (another cold helper's)
+    f = next(w['helper_final'][str(h)] for h in cold if w['helper_final'][str(h)] != w['helper_final'][str(h0)])
+    w['helper_final'][str(h0)] = f
+
+
+def extra_cold_end(w):           # declare a premixed partner of h0 cold-ended at h0's frame: fails the row/column cone
+    p = next(r for e in w['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    w['helper_final'][str(p)] = w['helper_final'][str(h0)]
+
+
+reject('premix placed in the zero-frame precondition (before the cold wrappers)', premix_to_precondition, WHY['premix_to_precondition'])
+reject('one premix gate dropped (the compensation then reads a cold-ended helper)', lambda w: w['A'].pop(npre - 1), WHY['premix_dropped'])
+reject('one lower-frame cleanup gate dropped (gate and its early_cleanup entry)', lambda w: drop_cleanup_gate(w, i0), WHY['lower_dropped'])
+reject('one FULL-remainder gate dropped', lambda w: drop_cleanup_gate(w, r0), WHY['remainder_dropped'])
+reject('lower-frame gate coefficient changed', lambda w: w['cleanup'][i0].__setitem__(3, w['cleanup'][i0][3] * 2), WHY['coefficient'])
+reject('lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)', lower_gate_into_full, WHY['into_full'])
+reject('lower-frame gate frame below its registers\' frames', lambda w: next(x for x in w['early_cleanup'] if x[0] == i0).__setitem__(1, U0[:-1]), WHY['frame_below'])
+reject('cold end at another dim-4 frame', other_frame, WHY['other_frame'])
+# PROFILE-PIN control: without its helper_final entry the cold-ended helper is a valid FULL-ended helper; the word is
+# rejected because its reported paid profile (which counts the low end) no longer matches the frame chains.
+reject('profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)', lambda w: w['helper_final'].pop(str(h0)), WHY['profile_pin'])
+reject('extra cold end on a premixed partner (the compensation reads it before its wrapper)', extra_cold_end, WHY['extra_end'])
+reject('refactored-cleanup marker removed (literal-inverse rule applies)', lambda w: w.pop('refactored_cleanup'), WHY['marker'])
+reject('remainder gate retargeted to a target register', lambda w: w['cleanup'][r0].__setitem__(1, v + 3), WHY['target'])
+reject('non-dyadic remainder coefficient', lambda w: w['cleanup'][r0].__setitem__(4 if w['cleanup'][r0][0] == 'add' else 3, 3 * w['cleanup'][r0][4 if w['cleanup'][r0][0] == 'add' else 3]), WHY['dyadic'])
+reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('5', w['report']['local_profile']['5'] - 1), WHY['profile_pin'])
+ent = [int(h) for h in sys.argv[4].split(',')] if len(sys.argv) > 4 else [int(h) for h in meta.get('entering_low_frame_ended_helpers', [])]
+for e0 in ent:   # ENTERING LOW-FRAME ENDS (ColdSupply extension; every entering end; absent for words without them)
+    j0 = next((i for i, e in enumerate(word['A'][:npre]) if e0 in regs(e)), None)
+    print('entering end', e0, 'premix gate', j0, flush=True)
+    k0, Ue = next((i, f) for i, f in early if e0 in regs(word['cleanup'][i]))
+    def to_pre(w, j0=j0): w['precondition'].append(w['A'][j0]); w['A'].pop(j0)
+    def other_hp(w, e0=e0, Ue=Ue): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Ue) and sorted(f) != sorted(Ue))
+    if j0 is not None: reject('entering end %d: premix gate dropped' % e0, lambda w, j0=j0: w['A'].pop(j0), WHY['e_premix_dropped'])
+    if j0 is not None: reject('entering end %d: premix gate at frame [] instead of its entrance E' % e0, lambda w, j0=j0: w['A'][j0].__setitem__(-1, []), WHY['nonmonotone'])
+    if j0 is not None: reject('entering end %d: premix gate moved into the zero-frame precondition' % e0, to_pre, WHY['entering_precondition'])
+    reject('entering end %d: lower-frame gate dropped (gate and its early_cleanup entry)' % e0, lambda w, k0=k0: drop_cleanup_gate(w, k0), WHY['lower_dropped'])
+    reject('entering end %d: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)' % e0, lambda w, e0=e0: w['helper_final'].pop(str(e0)), WHY['profile_pin'])
+    reject('entering end %d: end at another hyperplane' % e0, other_hp, WHY['cone'])
+# Pinned rejection reasons of the COLD-BEYOND mutants (substrings of hpe_audit_and_transport.py assertion messages).
+MYWHY = dict(tw_precondition=COLDPRE, tw_dropped=COLDPRE, tw_coefficient=COLDPRE, tw_other_block=COLDPRE,
+             tw_entering='zero-frame compensation reads an entering helper',
+             ab_dropped=ENDPOINT, ab_coefficient=ENDPOINT, ab_early=ENDPOINT, ab_live=ENDPOINT, ab_centre=ENDPOINT,
+             ab_lower="'nonmonotone'", ab_higher="'nonmonotone'",
+             sh_dropped=ENDPOINT, sh_coefficient=ENDPOINT, rel_dropped=ENDPOINT, rel_coefficient=ENDPOINT, rel_live=ENDPOINT,
+             h8_other=CONE, h8_lower=ENDPOINT)
+# COLD-BEYOND primitives (present only when the word carries them): frame-[] target writes in the premix (explicit
+# post-wrapper compensation of an ended helper's dirt) and forward absorptions into dead registers.
+nw = meta.get('premix_target_writes', 0)
+if nw:
+    wi = [i for i in range(npre) if v <= word['A'][i][1] < 2*v]
+    assert len(wi) == nw
+
+    def writes_to_precondition(w):   # the target writes run before the cold wrappers (inside the zero-frame precondition)
+        g = [w['A'][i] for i in wi]; w['precondition'] = w['precondition'] + g
+        w['A'] = [e for i, e in enumerate(w['A']) if i not in set(wi)]
+    reject('premix target writes placed in the zero-frame precondition (before the cold wrappers)', writes_to_precondition, MYWHY['tw_precondition'])
+    reject('one premix target write dropped (compensation must read an ended helper)', lambda w: w['A'].pop(wi[0]), MYWHY['tw_dropped'])
+    reject('premix target write coefficient changed', lambda w: w['A'][wi[0]].__setitem__(3, w['A'][wi[0]][3] * 2), MYWHY['tw_coefficient'])
+    # (reading another register that carries the SAME weight of the ended helper's dirt is a valid variant, so the mutant reads
+    #  the same factory slot of the next block, which carries none of it)
+    entering_regs = sorted(int(r) for r in word.get('start_extra', {}))
+    reject('premix target write reads an entering helper', lambda w: w['A'][wi[0]].__setitem__(2, entering_regs[0]), MYWHY['tw_entering'])
+    reject('premix target write reads a cold helper of another block', lambda w: w['A'][wi[0]].__setitem__(2, 2*v + (w['A'][wi[0]][2] - 2*v + 16) % 224), MYWHY['tw_other_block'])
+ab = meta.get('forward_absorption_A_indices', [])
+if any(len(word['helper_final'][str(h)]) == 8 for h in cold):
+    # with dim-8 cold ends, the centre-retargeted absorption first leaks an ended helper's dirt into the cut's targets
+    MYWHY['ab_centre'] = COLDPRE
+if ab:
+    # the ColdBeyond U_b absorption (q += -1/2 g); ColdThird's extra absorptions have their own controls below
+    a0 = next(a for a in ab if word['A'][a][3] * 2 == -word['A'][a][4]); g0 = word['A'][a0]
+
+    def absorption_moved_early(w):   # absorbed before the absorbed register's last kernel write
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[2] == w['A'][i][1] and w['A'][i][-1] == g0[-1])
+        w['A'].insert(j, e)
+
+    def absorption_into_live(w):     # q += a g moved right after g's previous frame-mate gate, while q is still live
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[1] in regs(w['A'][i]))
+        w['A'].insert(j, e)
+    reject('forward absorption dropped', lambda w: w['A'].pop(a0), MYWHY['ab_dropped'])
+    reject('forward absorption into a centre (a live register read by the cut)', lambda w: w['A'][a0].__setitem__(1, next(c for c in word['centers'] if c not in g0[1:3] and c not in cold)), MYWHY['ab_centre'])
+    reject('forward absorption coefficient changed', lambda w: w['A'][a0].__setitem__(3, w['A'][a0][3] * 2), MYWHY['ab_coefficient'])
+    reject('forward absorption placed before the absorbed register\'s last kernel write', absorption_moved_early, MYWHY['ab_early'])
+    reject('forward absorption placed while the absorbing register is still live', absorption_into_live, MYWHY['ab_live'])
+    reject('forward absorption at a lower frame than its registers', lambda w: w['A'][a0].__setitem__(-1, w['A'][a0][-1][:-1]), MYWHY['ab_lower'])
+    reject('forward absorption at a higher frame (FULL) than its registers', lambda w: w['A'][a0].__setitem__(-1, [256, 128, 64, 32, 16, 8, 4, 2, 1]), MYWHY['ab_higher'])
+# COLD-THIRD primitives (present only when the word carries them): several absorptions after one input gate, dirt-release
+# absorptions (a dead port takes a live helper's value so that a hyperplane unit's column has no dirt on it), and cold ends at
+# a dim-8 frame with lifted partners.
+hyper = [h for h in cold if len(word['helper_final'][str(h)]) == 8]
+if hyper and ab:
+    sh = next(a for a, b in zip(ab, ab[1:]) if b == a + 1)              # two absorptions sharing one input anchor
+    rel = next(a for a in ab if a - 1 not in ab and a + 1 not in ab and word['A'][a][2] in hyper and word['A'][a][3] * 2 != -word['A'][a][4])
+    hh = hyper[0]; ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+    reject('second absorption sharing an input anchor dropped', lambda w: w['A'].pop(sh + 1), MYWHY['sh_dropped'])
+    reject('shared-anchor absorption coefficient changed', lambda w: w['A'][sh + 1].__setitem__(3, w['A'][sh + 1][3] * 2), MYWHY['sh_coefficient'])
+    reject('dirt-release absorption dropped', lambda w: w['A'].pop(rel), MYWHY['rel_dropped'])
+    reject('dirt-release absorption coefficient changed', lambda w: w['A'][rel].__setitem__(3, w['A'][rel][3] * 2), MYWHY['rel_coefficient'])
+    jr = max(i for i in range(npre, rel) if word['A'][i][0] == 'add' and word['A'][i][2] == word['A'][rel][1])
+
+    def release_while_read(w):   # the release runs before a kernel gate that still READS the port (port live)
+        e = w['A'].pop(rel); w['A'].insert(jr, e)
+    reject('dirt-release absorption moved before a kernel gate that still reads the port', release_while_read, MYWHY['rel_live'])
+if hyper:
+    # dim-8 cold-end controls once PER DISTINCT dim-8 terminal frame (each family of dim-8 cold ends keeps its own controls)
+    fams = []
+    for h in hyper:
+        if sorted(word['helper_final'][str(h)]) not in [sorted(word['helper_final'][str(x)]) for x in fams]: fams.append(h)
+    for hh in fams:
+        ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+        Uh = word['helper_final'][str(hh)]
+        reject('dim-8 cold end %d (frame %s) at another dim-8 frame' % (hh, Uh), lambda w, hh=hh: w['helper_final'].__setitem__(str(hh), next(f for h, f in w['helper_final'].items() if len(f) == 8 and sorted(f) != sorted(w['helper_final'][str(hh)]))), MYWHY['h8_other'])
+        reject('dim-8 cold end %d (frame %s): one lower-frame gate dropped (gate and its early_cleanup entry)' % (hh, Uh), lambda w, ih=ih: drop_cleanup_gate(w, ih), MYWHY['h8_lower'])
+        reject('dim-8 cold end %d (frame %s): profile pin (end dropped)' % (hh, Uh), lambda w, hh=hh: w['helper_final'].pop(str(hh)), WHY['profile_pin'])
+# FACTORED ACCUMULATOR (CarrierBypass; present only when the word carries one): a lower-frame tail gate a += x*g on two
+# non-ended registers whose accumulator a is afterwards read by a dim-8 cold end's tail gate (h += y*a at its U).
+ended_all = {int(h) for h in word['helper_final']}
+tailg = [(i, word['cleanup'][i]) for i, _ in early]
+accs = []   # EVERY factored accumulator gate (one per accumulator register a), each controlled on its own
+for k, (i, e) in enumerate(tailg):
+    if e[0] == 'add' and e[1] not in ended_all and e[2] not in ended_all and len(next(f for j, f in early if j == i)) < 8:
+        if e[1] not in [word['cleanup'][j][1] for j in accs] and any(t[0] == 'add' and t[2] == e[1] and t[1] in hyper for _, t in tailg[k + 1:]):
+            accs.append(i)
+for acc in accs:
+    a = word['cleanup'][acc][1]
+    reject('factored accumulator %d (gate %d) zeroed' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, 0), ENDPOINT)
+    reject('factored accumulator %d (gate %d) coefficient doubled' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, w['cleanup'][acc][3] * 2), ENDPOINT)
+outdir.mkdir(parents=True, exist_ok=True)
+(outdir/'COLD-END-CONTROLS.json').write_text(json.dumps(dict(status='PASS_COLD_END_RAW_WORD_CONTROLS', word=str(src), rejected=results), indent=1) + '\n')
+print('PASS', len(results), 'cold-end raw-word mutations rejected')
diff --git a/research/gauge44-leaver8/construction/layers/reproduce_layers.py b/research/gauge44-leaver8/construction/layers/reproduce_layers.py
new file mode 100644
index 0000000000..ed517ba1dd
--- /dev/null
+++ b/research/gauge44-leaver8/construction/layers/reproduce_layers.py
@@ -0,0 +1,105 @@
+#!/usr/bin/env python3
+"""Rebuild the layered gauge44 word (pivot swaps + entering ends + factored dim-8 cold ends) and its native locals.
+
+Input: a fresh `construction/reproduce.py --until word` output directory (its regroup/ and cold44/ words are pinned
+by reproduce.py itself). Steps, each checked exactly:
+  1. pivot-swap: construction/layers/build_pivot_swap.py on regroup/FULL-WORD (six cost-neutral pivot-role swaps,
+     exact zero-response replay, unchanged profile and width multiset, 30 negative controls);
+  2. hpe: the inherited jp8 hyperplane-end changes (HYPERPLANE-END-S6.json) applied with PR635's build_hpe.apply;
+  3. cold44-exact: #645's build_gauge_cold44.py on the swapped HPE word; its 44 rank-four cold ends, premix and tail
+     must equal the unswapped cold44 construction's (the swaps touch no factory block);
+  4. layers: PR635's unchanged build_cold_end.apply(HPE, COLD-LAYERS-RECIPE) - the cold44 recipe plus 8 entering ends
+     (560/561/572/573 at U24, 597/599/537/549 at U30) and 10 factored dim-8 cold ends; output sha pinned;
+  5. layer-end-controls: raw-word negative controls on the layered word (PR635 cold_end_controls adapted by
+     LayerReviewer: lower->FULL pinned at 'cleanup on non-FULL end', entering ends from the recipe); 59 rejected;
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs (as in reproduce.py).
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+LAYERED_SHA = '0be48b1d8a6105059addf3f0d5e420c27ae3398b3a1186b6b11e9c4aa9e3f3d4'
+LAYER_CONTROLS = 59
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--word-dir', type=Path, required=True, help='construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    env.pop('PYTHONOPTIMIZE', None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    wd = a.word_dir.resolve()
+    run('pivot-swap', HERE / 'build_pivot_swap.py', '--input', wd / 'regroup/FULL-WORD.json.gz',
+        '--recipe', HERE / 'PIVOT-SWAP-S6.json', '--gk-dir', gk, '--out', out / 'swap')
+    hpe = load('upstream_hpe', up / 'code/build_hpe.py')
+    w = hpe.apply(read(out / 'swap/FULL-WORD.json.gz'), read(HERE / 'HYPERPLANE-END-S6.json')['changes'])
+    (out / 'hpe').mkdir(); (out / 'hpe/FULL-WORD.json.gz').write_bytes(gzip.compress(enc(w), mtime=0))
+    run('cold44-exact', HERE.parent / 'build_gauge_cold44.py', '--input', out / 'hpe/FULL-WORD.json.gz',
+        '--out', out / 'cold44', '--hamming', wd / 'hamming', '--upstream-package', up)
+    new, old = read(out / 'cold44/RECIPE.json.gz'), read(wd / 'cold44/RECIPE.json.gz')
+    # The swaps touch no factory block: the 44 ends, their premix and their low tails are identical; only the FULL
+    # inverse (rebuilt from the whole word) differs.
+    for key in ('premix', 'early_cleanup', 'cold_ends'):
+        assert new[key] == old[key], ('swapped cold44 differs from the pinned cold44 construction', key)
+    tail = len(new['early_cleanup']); assert new['cleanup'][:tail] == old['cleanup'][:tail], 'low tails'
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    layered = bce.apply(w, read(HERE / 'COLD-LAYERS-RECIPE.json.gz'))
+    raw = enc(layered); assert hashlib.sha256(raw).hexdigest() == LAYERED_SHA, 'layered word'
+    rep = layered['report']
+    assert rep['local_profile'] == {'1': 2542, '2': 414, '3': 434, '4': 154, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 52, '5': 48, '7': 42, '8': 116, '9': 234}, rep['width_inventory']
+    (out / 'layers').mkdir(); word = out / 'layers/FULL-WORD.json.gz'; word.write_bytes(gzip.compress(raw, mtime=0))
+    print('PASS layered scalar word', word, flush=True)
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', HERE / 'layer_end_controls.py', word, routing, out / 'controls')
+    ctl = json.loads((out / 'controls/COLD-END-CONTROLS.json').read_text())
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == LAYER_CONTROLS, len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word,
+        '--routing', routing, '--out', local)
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz b/research/gauge44-leaver8/construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz
new file mode 100644
index 0000000000..f9155e3079
Binary files /dev/null and b/research/gauge44-leaver8/construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz differ
diff --git a/research/gauge44-leaver8/construction/layers_np/HPE-RECIPE-NP.json b/research/gauge44-leaver8/construction/layers_np/HPE-RECIPE-NP.json
new file mode 100644
index 0000000000..2605d199ed
--- /dev/null
+++ b/research/gauge44-leaver8/construction/layers_np/HPE-RECIPE-NP.json
@@ -0,0 +1 @@
+{"changes": [{"helper": 448, "cleanup_index": 674, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 449, "cleanup_index": 673, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 450, "cleanup_index": 672, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 451, "cleanup_index": 671, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 452, "cleanup_index": 670, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 453, "cleanup_index": 669, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 454, "cleanup_index": 668, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 455, "cleanup_index": 667, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 456, "cleanup_index": 666, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 457, "cleanup_index": 665, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 458, "cleanup_index": 664, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 459, "cleanup_index": 663, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 460, "cleanup_index": 658, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 461, "cleanup_index": 657, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 470, "cleanup_index": 648, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 471, "cleanup_index": 647, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 472, "cleanup_index": 642, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 473, "cleanup_index": 641, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 482, "cleanup_index": 632, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 483, "cleanup_index": 631, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 496, "cleanup_index": 609, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 497, "cleanup_index": 608, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 520, "cleanup_index": 573, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 521, "cleanup_index": 572, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 544, "cleanup_index": 539, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 545, "cleanup_index": 538, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 568, "cleanup_index": 507, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 569, "cleanup_index": 506, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 580, "cleanup_index": 491, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 581, "cleanup_index": 490, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 590, "cleanup_index": 481, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 591, "cleanup_index": 480, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 592, "cleanup_index": 475, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 593, "cleanup_index": 474, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 602, "cleanup_index": 465, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 603, "cleanup_index": 464, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 604, "cleanup_index": 459, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 605, "cleanup_index": 458, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 606, "cleanup_index": 457, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 607, "cleanup_index": 456, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 609, "cleanup_index": 454, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 611, "cleanup_index": 452, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 612, "cleanup_index": 451, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 613, "cleanup_index": 450, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 614, "cleanup_index": 449, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 615, "cleanup_index": 448, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}]}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/layers_np/PIVOT-SWAP-NP.json b/research/gauge44-leaver8/construction/layers_np/PIVOT-SWAP-NP.json
new file mode 100644
index 0000000000..4e0d846426
--- /dev/null
+++ b/research/gauge44-leaver8/construction/layers_np/PIVOT-SWAP-NP.json
@@ -0,0 +1,588 @@
+{
+ "input_content_sha256": "864ff4a19987bcb27016367801a98ca50dae69eafe01d3614f8bae69f5713d6d",
+ "output_content_sha256": "beb3579fce83cb3b70f4e85761cbb3b8c91d711d4b9cf473074269b8447fc4e4",
+ "swaps": [
+  {
+   "pivot": 494,
+   "new_pivot": 566,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 379,
+     "before": [
+      "add",
+      566,
+      494,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      494,
+      566,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 380,
+     "before": [
+      "add",
+      640,
+      494,
+      2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      640,
+      566,
+      -2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 381,
+     "before": [
+      "add",
+      642,
+      494,
+      -2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      642,
+      566,
+      2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 382,
+     "before": [
+      "add",
+      688,
+      494,
+      1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      688,
+      566,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 383,
+     "before": [
+      "add",
+      690,
+      494,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      690,
+      566,
+      1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 495,
+   "new_pivot": 567,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 516,
+     "before": [
+      "add",
+      123,
+      495,
+      1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      123,
+      567,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 584,
+     "before": [
+      "add",
+      187,
+      495,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      187,
+      567,
+      1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 686,
+     "before": [
+      "add",
+      567,
+      495,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      495,
+      567,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 506,
+   "new_pivot": 578,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 176,
+     "before": [
+      "add",
+      652,
+      506,
+      2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      652,
+      578,
+      -2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 178,
+     "before": [
+      "add",
+      652,
+      506,
+      -2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      652,
+      578,
+      2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 278,
+     "before": [
+      "add",
+      700,
+      506,
+      -2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      700,
+      578,
+      2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 280,
+     "before": [
+      "add",
+      700,
+      506,
+      2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      700,
+      578,
+      -2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 702,
+     "before": [
+      "add",
+      578,
+      506,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      506,
+      578,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 507,
+   "new_pivot": 579,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 93,
+     "before": [
+      "add",
+      211,
+      507,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      211,
+      579,
+      1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 541,
+     "before": [
+      "add",
+      147,
+      507,
+      1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      147,
+      579,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 704,
+     "before": [
+      "add",
+      579,
+      507,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      507,
+      579,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 519,
+   "new_pivot": 543,
+   "entrance": [
+    30
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 507,
+     "before": [
+      "add",
+      115,
+      519,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      115,
+      543,
+      1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 575,
+     "before": [
+      "add",
+      179,
+      519,
+      1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      179,
+      543,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 722,
+     "before": [
+      "add",
+      543,
+      519,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      519,
+      543,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 531,
+   "new_pivot": 555,
+   "entrance": [
+    30
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 550,
+     "before": [
+      "add",
+      155,
+      531,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      155,
+      555,
+      1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 617,
+     "before": [
+      "add",
+      219,
+      531,
+      1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      219,
+      555,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 740,
+     "before": [
+      "add",
+      555,
+      531,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      531,
+      555,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    }
+   ]
+  }
+ ]
+}
diff --git a/research/gauge44-leaver8/construction/layers_np/reproduce_np.py b/research/gauge44-leaver8/construction/layers_np/reproduce_np.py
new file mode 100644
index 0000000000..79cb6fa912
--- /dev/null
+++ b/research/gauge44-leaver8/construction/layers_np/reproduce_np.py
@@ -0,0 +1,149 @@
+#!/usr/bin/env python3
+"""Rebuild the layered no-triangle word (NP) and its native locals.
+
+Input: a fresh `construction/notri/reproduce_notri.py --word-only` output directory. That driver pins the
+no-triangle word (3e99ba77...) and writes its regroup/ and cold44/ words. Steps, each checked exactly:
+  1. pivot-swap: ../layers/build_pivot_swap.py (PR641's constructor, signed, unchanged) on the no-triangle regroup word, with PIVOT-SWAP-NP.json:
+     the six pivot-role swaps of research/gauge44-layered, mapped through the 504-helper map (494->566, 495->567,
+     506->578, 507->579, 519->543, 531->555). Exact zero-response replay, unchanged profile and width multiset,
+     30 negative controls.
+  2. hpe: PR635's build_hpe.candidates, greedy with disjoint registers. Must equal HPE-RECIPE-NP.json (46 changes,
+     the same helpers as the unswapped word); applied with build_hpe.apply.
+  3. cold44-exact: notri/cold44x.py on the swapped HPE word, pairing ranks pinned [4]*14. Its 56 cold ends, premix
+     and low tails must equal the unswapped no-triangle construction's.
+  4. layers: PR635's unchanged build_cold_end.apply(HPE, COLD-LAYERS-RECIPE-NP): cold44 plus the entering ends
+     566/567/578/579 at U24 (s4) and 608/610/543/555 at U30 (x30), BlockCombine's b6 and the q4 dim-8 cold ends.
+     The output word sha and its profile and widths are pinned.
+  5. layer-end-controls: ../layers/layer_end_controls.py (LayerReviewer's signed adaptation of PR635's
+     cold_end_controls.py, unchanged) on the layered word; exactly 59 rejections at pinned reasons.
+../layers/reproduce_layers.py is research/gauge44-layered's driver for the 492-helper word, shipped unchanged as
+signed; it is not used for this word.
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs, with pins.
+Apache-2.0. Driver by ColdWitness after G44Stack's NP chain (NP/chain.py, seq.py).
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NOTRI = HERE.parent / 'notri'
+LAYERS = HERE.parent / 'layers'   # the signed research/gauge44-layered files, unchanged
+REGROUP_SHA = '864ff4a1'   # prefix; full value checked against PIVOT-SWAP-NP.json's input_content_sha256
+SWAP_SHA = 'beb3579f'
+NP_SHA = 'a9de804f194eeb39f52a4c6e54c14d93e881bec4b632694249733ed410b58113'
+LAYER_CONTROLS = 59
+CANONICAL_SHA = '1ae812a336178760071efe347e876e0102b5b71f799d957db15c5f3004c19d7a'
+PROGRAM_SHA = {'forward': 'a3882a428bdafab888072211d4ed8d34572746873d77c6ef900495853cc3fa11',
+               'backward': 'f67a3dc20c27fb39295b8030e951e9779109ef1537f6f8de9d08510b9ad6792a'}
+CLIFFORD_SHA = '890b60fc4ae183c773c51405e0f4ef6a945dc2aae55ba2480f134602e8296cda'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def dump(p, v):
+    p.parent.mkdir(parents=True, exist_ok=True); p.write_bytes(gzip.compress(enc(v), mtime=0))
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--notri-dir', type=Path, required=True, help='construction/notri/reproduce_notri.py --word-only output')
+    ap.add_argument('--hamming', type=Path, required=True, help='hamming/ of the construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    nd = a.notri_dir.resolve()
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    # the input must be the pinned no-triangle construction
+    nr = load('notri_driver', NOTRI / 'reproduce_notri.py')
+    assert hashlib.sha256(enc(read(nd / 'cold44/FULL-WORD.json.gz'))).hexdigest() == nr.NOTRI_SHA, 'notri word'
+    # 1. pivot swaps on the regroup word
+    rg = hashlib.sha256(enc(read(nd / 'regroup/FULL-WORD.json.gz'))).hexdigest()
+    assert rg.startswith(REGROUP_SHA) and rg == read(HERE / 'PIVOT-SWAP-NP.json')['input_content_sha256'], ('regroup word', rg)
+    run('pivot-swap', LAYERS / 'build_pivot_swap.py', '--input', nd / 'regroup/FULL-WORD.json.gz',
+        '--recipe', HERE / 'PIVOT-SWAP-NP.json', '--gk-dir', gk, '--out', out / 'swap')
+    w = read(out / 'swap/FULL-WORD.json.gz')
+    sw = hashlib.sha256(enc(w)).hexdigest(); assert sw.startswith(SWAP_SHA) and sw == read(HERE / 'PIVOT-SWAP-NP.json')['output_content_sha256'], ('swap word', sw)
+    # 2. HPE (greedy, must equal the pinned recipe)
+    h = load('upstream_hpe', up / 'code/build_hpe.py')
+    used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    assert ch == read(HERE / 'HPE-RECIPE-NP.json')['changes'], 'HPE recipe'
+    w = h.apply(w, ch); dump(out / 'hpe/FULL-WORD.json.gz', w)
+    # 3. cold44 on the swapped word: same ends, premix and tails as the unswapped no-triangle construction
+    hm = set(read(nd / 'raw/HELPER-MAP.json')['map'].values())
+    env['EXTRAH'] = json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm))
+    env['PAIRING_RANKS'] = json.dumps([4] * 14)
+    run('cold44-exact', NOTRI / 'cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', a.hamming.resolve(), '--upstream-package', up)
+    for k in ('EXTRAH', 'PAIRING_RANKS'): env.pop(k)
+    new, old = read(out / 'cold44/RECIPE.json.gz'), read(nd / 'cold44/RECIPE.json.gz')
+    for key in ('premix', 'early_cleanup', 'cold_ends'):
+        assert new[key] == old[key], ('swapped cold44 differs from the pinned no-triangle construction', key)
+    tail = len(new['early_cleanup']); assert new['cleanup'][:tail] == old['cleanup'][:tail], 'low tails'
+    # 4. layers
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    layered = bce.apply(w, read(HERE / 'COLD-LAYERS-RECIPE-NP.json.gz'))
+    raw = enc(layered); assert hashlib.sha256(raw).hexdigest() == NP_SHA, ('layered word', hashlib.sha256(raw).hexdigest())
+    rep = layered['report']
+    assert rep['local_profile'] == {'1': 2534, '2': 346, '3': 458, '4': 178, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 64, '5': 48, '7': 54, '8': 116, '9': 222}, rep['width_inventory']
+    (out / 'layers').mkdir(); word = out / 'layers/FULL-WORD.json.gz'; word.write_bytes(gzip.compress(raw, mtime=0))
+    print('PASS layered no-triangle word', NP_SHA, flush=True)
+    # 5. layer-end controls
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', LAYERS / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = json.loads((out / 'controls/COLD-END-CONTROLS.json').read_text())
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == LAYER_CONTROLS, len(ctl['rejected'])
+    # 6. native locals
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == CANONICAL_SHA, 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in PROGRAM_SHA.items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == CLIFFORD_SHA, 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz b/research/gauge44-leaver8/construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz
new file mode 100644
index 0000000000..a408c95816
Binary files /dev/null and b/research/gauge44-leaver8/construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz differ
diff --git a/research/gauge44-leaver8/construction/layers_p6n/P6N-SPEC.json b/research/gauge44-leaver8/construction/layers_p6n/P6N-SPEC.json
new file mode 100644
index 0000000000..43c3ec265c
--- /dev/null
+++ b/research/gauge44-leaver8/construction/layers_p6n/P6N-SPEC.json
@@ -0,0 +1 @@
+{"ends":[{"U":[256,128,66,34,16,8,6,1],"labels":[512,513]},{"U":[256,128,72,40,24,4,2,1],"labels":[311,510]},{"U":[256,128,66,34,18,10,6,1],"labels":[522,327]}]}
diff --git a/research/gauge44-leaver8/construction/layers_p6n/layer_end_controls.py b/research/gauge44-leaver8/construction/layers_p6n/layer_end_controls.py
new file mode 100644
index 0000000000..dd321fe255
--- /dev/null
+++ b/research/gauge44-leaver8/construction/layers_p6n/layer_end_controls.py
@@ -0,0 +1,199 @@
+"""layer_end_controls.py LAYERED-WORD.json.gz ROUTING OUTDIR (env PR635_CODE): adapted PR635 cold_end_controls.py (LayerReviewer): raw-word negative controls for the cold low-frame ends and the
+refactored cleanup accepted by hpe_audit_and_transport.py.  Every mutation MUST be rejected (AssertionError); the
+unmutated word MUST pass.  Apache-2.0.  DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code."""
+import copy, gzip, json, shutil, sys, tempfile
+from pathlib import Path
+import os
+sys.path.insert(0, os.environ['PR635_CODE'])   # PR635's unchanged hpe_audit_and_transport.py
+import hpe_audit_and_transport as atc
+
+src, routing, outdir = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3])
+word = json.load(gzip.open(src))
+v, R = word['report']['v'], word['report']['R']; n = 2*v + R
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+meta = word['refactored_cleanup']
+cold = [int(h) for h in meta['cold_low_frame_ended_helpers']]
+npre = meta['premix_gates']; nlow = meta['lower_frame_gates']
+early = word['early_cleanup']; eidx = {i for i, _ in early}
+rest = [i for i in range(len(word['cleanup'])) if i not in eidx]
+
+
+def trial(w):
+    """None if the transport audit accepts w, else the AssertionError message."""
+    tmp = Path(tempfile.mkdtemp())
+    p = tmp/'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w).encode(), mtime=0))
+    try:
+        atc.run(p, routing, tmp/'out')
+        return None
+    except AssertionError as e:
+        return repr(e.args[0]) if e.args else 'AssertionError'
+    finally:
+        shutil.rmtree(tmp, ignore_errors=True)
+
+
+# Pinned rejection reasons: each mutant must fail at this assertion of hpe_audit_and_transport.py (message substring).
+ENDPOINT, COLDPRE, CONE = "'arbitrary-dirt endpoint'", 'touches a cold hyperplane-ended helper', 'hpe cone pre-check (row / column)'
+WHY = dict(premix_to_precondition=COLDPRE, premix_dropped=COLDPRE, e_premix_dropped=ENDPOINT, lower_dropped=ENDPOINT,
+           remainder_dropped=ENDPOINT, coefficient=ENDPOINT, into_full='cleanup on non-FULL end', dyadic=ENDPOINT, frame_below="'nonmonotone'",
+           nonmonotone="'nonmonotone'", other_frame=CONE, cone=CONE, extra_end=COLDPRE, marker='cleanup is not the literal reversed inverse',
+           target='refactored cleanup touches a target', profile_pin='paid local profile differs from the reported local_profile',
+           entering_precondition='zero-frame precondition/compensation touches an entering helper')
+assert trial(word) is None, 'unmutated cold-end word must pass'
+results = []
+
+
+def reject(name, mut, why):
+    """the mutation must be rejected, and for the pinned reason (a substring of the audit's assertion message)."""
+    w = copy.deepcopy(word); mut(w)
+    msg = trial(w)
+    assert msg is not None, 'cold-end mutation accepted: ' + name
+    assert why in msg, 'cold-end mutation %r rejected for the wrong reason: %s' % (name, msg[:300])
+    results.append(name); print('rejected', name, '|', why, flush=True)
+
+
+h0 = cold[0]
+i0, U0 = next((i, f) for i, f in early if h0 in regs(word['cleanup'][i]))
+r0 = rest[len(rest)//2]
+
+
+def premix_to_precondition(w):   # premix before the wrappers; compensation then reads the cold ends
+    w['precondition'] = w['precondition'] + w['A'][:npre]; w['A'] = w['A'][npre:]
+
+
+def lower_gate_into_full(w):     # a lower-frame gate on a cold-ended helper executed in the FULL remainder instead
+    w['early_cleanup'] = [x for x in w['early_cleanup'] if x[0] != i0]
+
+
+def drop_cleanup_gate(w, i):   # remove the gate AND its early_cleanup entry: a structurally valid word missing one gate
+    w['cleanup'].pop(i)
+    w['early_cleanup'] = [[j - (j > i), f] for j, f in w['early_cleanup'] if j != i]
+
+
+def other_frame(w):              # a different frame of the same dimension as the cold end (another cold helper's)
+    f = next(w['helper_final'][str(h)] for h in cold if w['helper_final'][str(h)] != w['helper_final'][str(h0)])
+    w['helper_final'][str(h0)] = f
+
+
+def extra_cold_end(w):           # declare a premixed partner of h0 cold-ended at h0's frame: fails the row/column cone
+    p = next(r for e in w['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    w['helper_final'][str(p)] = w['helper_final'][str(h0)]
+
+
+reject('premix placed in the zero-frame precondition (before the cold wrappers)', premix_to_precondition, WHY['premix_to_precondition'])
+reject('one premix gate dropped (the compensation then reads a cold-ended helper)', lambda w: w['A'].pop(npre - 1), WHY['premix_dropped'])
+reject('one lower-frame cleanup gate dropped (gate and its early_cleanup entry)', lambda w: drop_cleanup_gate(w, i0), WHY['lower_dropped'])
+reject('one FULL-remainder gate dropped', lambda w: drop_cleanup_gate(w, r0), WHY['remainder_dropped'])
+reject('lower-frame gate coefficient changed', lambda w: w['cleanup'][i0].__setitem__(3, w['cleanup'][i0][3] * 2), WHY['coefficient'])
+reject('lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)', lower_gate_into_full, WHY['into_full'])
+reject('lower-frame gate frame below its registers\' frames', lambda w: next(x for x in w['early_cleanup'] if x[0] == i0).__setitem__(1, U0[:-1]), WHY['frame_below'])
+reject('cold end at another dim-4 frame', other_frame, WHY['other_frame'])
+# PROFILE-PIN control: without its helper_final entry the cold-ended helper is a valid FULL-ended helper; the word is
+# rejected because its reported paid profile (which counts the low end) no longer matches the frame chains.
+reject('profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)', lambda w: w['helper_final'].pop(str(h0)), WHY['profile_pin'])
+reject('extra cold end on a premixed partner (the compensation reads it before its wrapper)', extra_cold_end, WHY['extra_end'])
+reject('refactored-cleanup marker removed (literal-inverse rule applies)', lambda w: w.pop('refactored_cleanup'), WHY['marker'])
+reject('remainder gate retargeted to a target register', lambda w: w['cleanup'][r0].__setitem__(1, v + 3), WHY['target'])
+reject('non-dyadic remainder coefficient', lambda w: w['cleanup'][r0].__setitem__(4 if w['cleanup'][r0][0] == 'add' else 3, 3 * w['cleanup'][r0][4 if w['cleanup'][r0][0] == 'add' else 3]), WHY['dyadic'])
+reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('5', w['report']['local_profile']['5'] - 1), WHY['profile_pin'])
+ent = [int(h) for h in sys.argv[4].split(',')] if len(sys.argv) > 4 else [int(h) for h in meta.get('entering_low_frame_ended_helpers', [])]
+for e0 in ent:   # ENTERING LOW-FRAME ENDS (ColdSupply extension; every entering end; absent for words without them)
+    j0 = next((i for i, e in enumerate(word['A'][:npre]) if e0 in regs(e)), None)
+    print('entering end', e0, 'premix gate', j0, flush=True)
+    k0, Ue = next((i, f) for i, f in early if e0 in regs(word['cleanup'][i]))
+    def to_pre(w, j0=j0): w['precondition'].append(w['A'][j0]); w['A'].pop(j0)
+    def other_hp(w, e0=e0, Ue=Ue): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Ue) and sorted(f) != sorted(Ue))
+    if j0 is not None: reject('entering end %d: premix gate dropped' % e0, lambda w, j0=j0: w['A'].pop(j0), WHY['e_premix_dropped'])
+    if j0 is not None: reject('entering end %d: premix gate at frame [] instead of its entrance E' % e0, lambda w, j0=j0: w['A'][j0].__setitem__(-1, []), WHY['nonmonotone'])
+    if j0 is not None: reject('entering end %d: premix gate moved into the zero-frame precondition' % e0, to_pre, WHY['entering_precondition'])
+    reject('entering end %d: lower-frame gate dropped (gate and its early_cleanup entry)' % e0, lambda w, k0=k0: drop_cleanup_gate(w, k0), WHY['lower_dropped'])
+    reject('entering end %d: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)' % e0, lambda w, e0=e0: w['helper_final'].pop(str(e0)), WHY['profile_pin'])
+    reject('entering end %d: end at another hyperplane' % e0, other_hp, WHY['cone'])
+# Pinned rejection reasons of the COLD-BEYOND mutants (substrings of hpe_audit_and_transport.py assertion messages).
+MYWHY = dict(tw_precondition=COLDPRE, tw_dropped=COLDPRE, tw_coefficient=COLDPRE, tw_other_block=COLDPRE,
+             tw_entering='zero-frame compensation reads an entering helper',
+             ab_dropped=ENDPOINT, ab_coefficient=ENDPOINT, ab_early=ENDPOINT, ab_live=ENDPOINT, ab_centre=ENDPOINT,
+             ab_lower="'nonmonotone'", ab_higher="'nonmonotone'",
+             sh_dropped=ENDPOINT, sh_coefficient=ENDPOINT, rel_dropped=ENDPOINT, rel_coefficient=ENDPOINT, rel_live=ENDPOINT,
+             h8_other=CONE, h8_lower=ENDPOINT)
+# COLD-BEYOND primitives (present only when the word carries them): frame-[] target writes in the premix (explicit
+# post-wrapper compensation of an ended helper's dirt) and forward absorptions into dead registers.
+nw = meta.get('premix_target_writes', 0)
+if nw:
+    wi = [i for i in range(npre) if v <= word['A'][i][1] < 2*v]
+    assert len(wi) == nw
+
+    def writes_to_precondition(w):   # the target writes run before the cold wrappers (inside the zero-frame precondition)
+        g = [w['A'][i] for i in wi]; w['precondition'] = w['precondition'] + g
+        w['A'] = [e for i, e in enumerate(w['A']) if i not in set(wi)]
+    reject('premix target writes placed in the zero-frame precondition (before the cold wrappers)', writes_to_precondition, MYWHY['tw_precondition'])
+    reject('one premix target write dropped (compensation must read an ended helper)', lambda w: w['A'].pop(wi[0]), MYWHY['tw_dropped'])
+    reject('premix target write coefficient changed', lambda w: w['A'][wi[0]].__setitem__(3, w['A'][wi[0]][3] * 2), MYWHY['tw_coefficient'])
+    # (reading another register that carries the SAME weight of the ended helper's dirt is a valid variant, so the mutant reads
+    #  the same factory slot of the next block, which carries none of it)
+    entering_regs = sorted(int(r) for r in word.get('start_extra', {}))
+    reject('premix target write reads an entering helper', lambda w: w['A'][wi[0]].__setitem__(2, entering_regs[0]), MYWHY['tw_entering'])
+    reject('premix target write reads a cold helper of another block', lambda w: w['A'][wi[0]].__setitem__(2, 2*v + (w['A'][wi[0]][2] - 2*v + 16) % 224), MYWHY['tw_other_block'])
+ab = meta.get('forward_absorption_A_indices', [])
+if any(len(word['helper_final'][str(h)]) == 8 for h in cold):
+    # with dim-8 cold ends, the centre-retargeted absorption first leaks an ended helper's dirt into the cut's targets
+    MYWHY['ab_centre'] = COLDPRE
+if ab:
+    # the ColdBeyond U_b absorption (q += -1/2 g); ColdThird's extra absorptions have their own controls below
+    a0 = next(a for a in ab if word['A'][a][3] * 2 == -word['A'][a][4]); g0 = word['A'][a0]
+
+    def absorption_moved_early(w):   # absorbed before the absorbed register's last kernel write
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[2] == w['A'][i][1] and w['A'][i][-1] == g0[-1])
+        w['A'].insert(j, e)
+
+    def absorption_into_live(w):     # q += a g moved right after g's previous frame-mate gate, while q is still live
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[1] in regs(w['A'][i]))
+        w['A'].insert(j, e)
+    reject('forward absorption dropped', lambda w: w['A'].pop(a0), MYWHY['ab_dropped'])
+    reject('forward absorption into a centre (a live register read by the cut)', lambda w: w['A'][a0].__setitem__(1, next(c for c in word['centers'] if c not in g0[1:3] and c not in cold)), MYWHY['ab_centre'])
+    reject('forward absorption coefficient changed', lambda w: w['A'][a0].__setitem__(3, w['A'][a0][3] * 2), MYWHY['ab_coefficient'])
+    reject('forward absorption placed before the absorbed register\'s last kernel write', absorption_moved_early, MYWHY['ab_early'])
+    reject('forward absorption placed while the absorbing register is still live', absorption_into_live, MYWHY['ab_live'])
+    reject('forward absorption at a lower frame than its registers', lambda w: w['A'][a0].__setitem__(-1, w['A'][a0][-1][:-1]), MYWHY['ab_lower'])
+    reject('forward absorption at a higher frame (FULL) than its registers', lambda w: w['A'][a0].__setitem__(-1, [256, 128, 64, 32, 16, 8, 4, 2, 1]), MYWHY['ab_higher'])
+# COLD-THIRD primitives (present only when the word carries them): several absorptions after one input gate, dirt-release
+# absorptions (a dead port takes a live helper's value so that a hyperplane unit's column has no dirt on it), and cold ends at
+# a dim-8 frame with lifted partners.
+hyper = [h for h in cold if len(word['helper_final'][str(h)]) == 8]
+if hyper and ab:
+    sh = next(a for a, b in zip(ab, ab[1:]) if b == a + 1)              # two absorptions sharing one input anchor
+    rel = next(a for a in ab if a - 1 not in ab and a + 1 not in ab and word['A'][a][2] in hyper and word['A'][a][3] * 2 != -word['A'][a][4])
+    hh = hyper[0]; ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+    reject('second absorption sharing an input anchor dropped', lambda w: w['A'].pop(sh + 1), MYWHY['sh_dropped'])
+    reject('shared-anchor absorption coefficient changed', lambda w: w['A'][sh + 1].__setitem__(3, w['A'][sh + 1][3] * 2), MYWHY['sh_coefficient'])
+    reject('dirt-release absorption dropped', lambda w: w['A'].pop(rel), MYWHY['rel_dropped'])
+    reject('dirt-release absorption coefficient changed', lambda w: w['A'][rel].__setitem__(3, w['A'][rel][3] * 2), MYWHY['rel_coefficient'])
+    jr = max(i for i in range(npre, rel) if word['A'][i][0] == 'add' and word['A'][i][2] == word['A'][rel][1])
+
+    def release_while_read(w):   # the release runs before a kernel gate that still READS the port (port live)
+        e = w['A'].pop(rel); w['A'].insert(jr, e)
+    reject('dirt-release absorption moved before a kernel gate that still reads the port', release_while_read, MYWHY['rel_live'])
+if hyper:
+    # dim-8 cold-end controls for EVERY dim-8 cold end of the word (read from the word's helper_final and the recipe meta's
+    # cold_low_frame_ended_helpers), not one representative per terminal frame
+    for hh in hyper:
+        ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+        Uh = word['helper_final'][str(hh)]
+        reject('dim-8 cold end %d (frame %s) at another dim-8 frame' % (hh, Uh), lambda w, hh=hh: w['helper_final'].__setitem__(str(hh), next(f for h, f in w['helper_final'].items() if len(f) == 8 and sorted(f) != sorted(w['helper_final'][str(hh)]))), MYWHY['h8_other'])
+        reject('dim-8 cold end %d (frame %s): one lower-frame gate dropped (gate and its early_cleanup entry)' % (hh, Uh), lambda w, ih=ih: drop_cleanup_gate(w, ih), MYWHY['h8_lower'])
+        reject('dim-8 cold end %d (frame %s): profile pin (end dropped)' % (hh, Uh), lambda w, hh=hh: w['helper_final'].pop(str(hh)), WHY['profile_pin'])
+# FACTORED ACCUMULATOR (CarrierBypass; present only when the word carries one): a lower-frame tail gate a += x*g on two
+# non-ended registers whose accumulator a is afterwards read by a dim-8 cold end's tail gate (h += y*a at its U).
+ended_all = {int(h) for h in word['helper_final']}
+tailg = [(i, word['cleanup'][i]) for i, _ in early]
+accs = []   # EVERY factored accumulator gate (one per accumulator register a), each controlled on its own
+for k, (i, e) in enumerate(tailg):
+    if e[0] == 'add' and e[1] not in ended_all and e[2] not in ended_all and len(next(f for j, f in early if j == i)) < 8:
+        if e[1] not in [word['cleanup'][j][1] for j in accs] and any(t[0] == 'add' and t[2] == e[1] and t[1] in hyper for _, t in tailg[k + 1:]):
+            accs.append(i)
+for acc in accs:
+    a = word['cleanup'][acc][1]
+    reject('factored accumulator %d (gate %d) zeroed' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, 0), ENDPOINT)
+    reject('factored accumulator %d (gate %d) coefficient doubled' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, w['cleanup'][acc][3] * 2), ENDPOINT)
+outdir.mkdir(parents=True, exist_ok=True)
+(outdir/'COLD-END-CONTROLS.json').write_text(json.dumps(dict(status='PASS_COLD_END_RAW_WORD_CONTROLS', word=str(src), rejected=results), indent=1) + '\n')
+print('PASS', len(results), 'cold-end raw-word mutations rejected')
diff --git a/research/gauge44-leaver8/construction/layers_p6n/reproduce_p6n.py b/research/gauge44-leaver8/construction/layers_p6n/reproduce_p6n.py
new file mode 100644
index 0000000000..f9eb173bc1
--- /dev/null
+++ b/research/gauge44-leaver8/construction/layers_p6n/reproduce_p6n.py
@@ -0,0 +1,78 @@
+#!/usr/bin/env python3
+"""Rebuild the p6n word (NoTriReopen): the layered no-triangle word with p123's lane rebuilt as three factored dim-8 pairs.
+
+Input: a fresh `construction/layers_np/reproduce_np.py` output directory. Its swapped HPE word (hpe/) and its
+layered word a9de804f... are pinned there. Steps, each checked exactly:
+  1. layers: PR635's unchanged build_cold_end.apply(swapped HPE word, COLD-LAYERS-RECIPE-P6N.json.gz). The recipe is
+     NP's cold-layer recipe (cold44, s4, x30, b6, q4) plus the six cold ends of P6N-SPEC.json, built by NoTriReopen
+     with JP8Ends' stackJ/stackE (the CarrierBypass premix-only factored construction): [512,513] at
+     U(256,128,66,34,16,8,6,1), [311,510] at U(256,128,72,40,24,4,2,1), [522,327] at U(256,128,66,34,18,10,6,1).
+     The output word sha (34b683fa...), profile and widths are pinned.
+  2. layer-end-controls: layer_end_controls.py (Q6Reviewer-signed variant fc58c569..., which controls every dim-8
+     cold end individually) on the p6n word; exactly 95 rejections at pinned reasons.
+The promotion step (construction/promo/reproduce_promo.py --base p6n) builds the final word and its native locals.
+Apache-2.0. Driver by ColdWitness after NoTriReopen's runspec.py.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NP_SHA = 'a9de804f194eeb39f52a4c6e54c14d93e881bec4b632694249733ed410b58113'
+P6N_SHA = '34b683fa08f0'   # prefix; full value is the recipe's output_content_sha256 (asserted equal below)
+LAYER_CONTROLS = 95
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--np-dir', type=Path, required=True, help='construction/layers_np/reproduce_np.py output')
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    parent = src / 'vendor/pr558/vendor/pr552'
+    npd = a.np_dir.resolve()
+    assert hashlib.sha256(enc(read(npd / 'layers/FULL-WORD.json.gz'))).hexdigest() == NP_SHA, 'np-dir must hold the pinned NP word'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src), PR635_CODE=str(up / 'code'))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    rec = read(HERE / 'COLD-LAYERS-RECIPE-P6N.json.gz')
+    w = bce.apply(read(npd / 'hpe/FULL-WORD.json.gz'), rec)
+    raw = enc(w); got = hashlib.sha256(raw).hexdigest()
+    assert got == rec['output_content_sha256'] and got.startswith(P6N_SHA), ('p6n word', got)
+    rep = w['report']
+    assert rep['local_profile'] == {'1': 2540, '2': 358, '3': 446, '4': 178, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 64, '5': 48, '7': 54, '8': 122, '9': 216}, rep['width_inventory']
+    (out / 'p6n').mkdir(); word = out / 'p6n/FULL-WORD.json.gz'; word.write_bytes(gzip.compress(raw, mtime=0))
+    print('PASS p6n word', got, flush=True)
+    t = time.monotonic()
+    with (out / 'layer-end-controls.log').open('w') as f:
+        rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(HERE / 'layer_end_controls.py'), str(word),
+                              str(parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'), str(out / 'controls')],
+                             env=env, stdout=f, stderr=subprocess.STDOUT)
+    (out / 'STEPS.json').write_text(json.dumps([dict(step='layer-end-controls', exit_code=rc, seconds=round(time.monotonic() - t, 3))], indent=2) + '\n')
+    assert rc == 0, 'layer-end-controls'
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == LAYER_CONTROLS, len(ctl['rejected'])
+    print('PASS layer-end-controls', LAYER_CONTROLS, flush=True)
+    print('DONE', word, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/leaver/CHAIN-PINS-k8.json b/research/gauge44-leaver8/construction/leaver/CHAIN-PINS-k8.json
new file mode 100644
index 0000000000..afd0467911
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/CHAIN-PINS-k8.json
@@ -0,0 +1,89 @@
+{
+ "np_profile": {
+  "1": 2422,
+  "2": 408,
+  "3": 494,
+  "4": 136,
+  "5": 56,
+  "8": 8
+ },
+ "p6n_profile": {
+  "1": 2428,
+  "2": 420,
+  "3": 482,
+  "4": 136,
+  "5": 56,
+  "8": 8
+ },
+ "lec-p6n_pins_sha256": "d87ed7b5869bed4a3d266f0ce5fc784cbe88340a625d22ab9f580fa00872df19",
+ "lec-p6n": 95,
+ "lec-p6n_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)"
+ },
+ "promo_controls": 11,
+ "lec-promo_pins_sha256": "d87ed7b5869bed4a3d266f0ce5fc784cbe88340a625d22ab9f580fa00872df19",
+ "lec-promo": 95,
+ "lec-promo_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)"
+ },
+ "jx_controls": [
+  "C0_identity",
+  "C1_741_only",
+  "N3_plain_join_moved_reads"
+ ],
+ "lec-jx_pins_sha256": "d87ed7b5869bed4a3d266f0ce5fc784cbe88340a625d22ab9f580fa00872df19",
+ "lec-jx": 95,
+ "lec-jx_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)"
+ },
+ "hybrid_controls": [
+  "C0_identity",
+  "donation_after",
+  "donation_after@226",
+  "donation_after@228",
+  "donation_after@230",
+  "donation_after@231",
+  "donation_after@232",
+  "donation_after@62",
+  "drop_preread",
+  "drop_preread@226",
+  "drop_preread@228",
+  "drop_preread@230",
+  "drop_preread@231",
+  "drop_preread@232",
+  "drop_preread@62",
+  "drop_restore",
+  "drop_restore@226",
+  "drop_restore@228",
+  "drop_restore@230",
+  "drop_restore@231",
+  "drop_restore@232",
+  "drop_restore@62",
+  "recipe",
+  "restore_full",
+  "restore_full@226",
+  "restore_full@228",
+  "restore_full@230",
+  "restore_full@231",
+  "restore_full@232",
+  "restore_full@62"
+ ],
+ "lec-hyb_pins_sha256": "d87ed7b5869bed4a3d266f0ce5fc784cbe88340a625d22ab9f580fa00872df19",
+ "lec-hyb": 95,
+ "lec-hyb_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)"
+ },
+ "frame_build_controls": 3,
+ "lec-frames_pins_sha256": "b07279e41ec9d8f89e8509081e1e7f2c8e8b062fd951b22608a03ac461982914",
+ "lec-frames": 95,
+ "lec-frames_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)",
+  "other_hp:554": "tail frame dim 5; no other helper_final frame of that dim"
+ },
+ "canonical_sha256": "d1bf3c6f250a61be7421ce566668092f362c465274fb472d4bb01fc80cba9b23",
+ "program_sha256": {
+  "forward": "683f83231d4d4890a7fc3d18f30d4ac7bfbd7bbdf4e7ff57ad0eb09e8a5f571c",
+  "backward": "2d184e4d9d48aa4d5e3679368ee0eca7e0388b1966eb05e0fd17d22d00d36293"
+ },
+ "clifford_recipes_sha256": "e3bfdfa2c044f14c00a8706950c8ae838ceeedd9ca78a83bffefe7886219516a"
+}
diff --git a/research/gauge44-leaver8/construction/leaver/CODED-CELLS-k8.json b/research/gauge44-leaver8/construction/leaver/CODED-CELLS-k8.json
new file mode 100644
index 0000000000..cd23561e0b
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/CODED-CELLS-k8.json
@@ -0,0 +1,2826 @@
+[
+ {
+  "cell": "01+",
+  "bindings": {
+   "x0": [
+    "source",
+    [
+     0,
+     1,
+     2,
+     3
+    ],
+    1
+   ],
+   "x1": [
+    "source",
+    [
+     0,
+     1,
+     2,
+     3
+    ],
+    0
+   ],
+   "x2": [
+    "source",
+    [
+     0,
+     1,
+     4,
+     5
+    ],
+    1
+   ],
+   "x3": [
+    "source",
+    [
+     0,
+     1,
+     4,
+     5
+    ],
+    0
+   ],
+   "x4": [
+    "source",
+    [
+     0,
+     1,
+     6,
+     7
+    ],
+    1
+   ],
+   "x5": [
+    "source",
+    [
+     0,
+     1,
+     6,
+     7
+    ],
+    0
+   ],
+   "y0": [
+    "target",
+    65
+   ],
+   "y1": [
+    "target",
+    64
+   ],
+   "y2": [
+    "target",
+    33
+   ],
+   "y3": [
+    "target",
+    32
+   ],
+   "y4": [
+    "target",
+    25
+   ],
+   "y5": [
+    "target",
+    24
+   ]
+  },
+  "scaled": [
+   [
+    "y1",
+    "x0",
+    "-1/2"
+   ],
+   [
+    "y0",
+    "x1",
+    "-1/2"
+   ],
+   [
+    "y2",
+    "x5",
+    "-1/2"
+   ],
+   [
+    "y3",
+    "x4",
+    "-1/2"
+   ],
+   [
+    "y4",
+    "x3",
+    "-1/2"
+   ],
+   [
+    "y5",
+    "x2",
+    "-1/2"
+   ],
+   [
+    "x0",
+    "x1",
+    "1"
+   ],
+   [
+    "x2",
+    "x5",
+    "1"
+   ],
+   [
+    "x4",
+    "x3",
+    "1"
+   ],
+   [
+    "y1",
+    "x2",
+    "-1/2"
+   ],
+   [
+    "y3",
+    "x0",
+    "-1/2"
+   ],
+   [
+    "y5",
+    "x4",
+    "-1/2"
+   ],
+   [
+    "y0",
+    "y5",
+    "1"
+   ],
+   [
+    "y2",
+    "y3",
+    "1"
+   ],
+   [
+    "y4",
+    "y1",
+    "1"
+   ],
+   [
+    "y1",
+    "x4",
+    "-1/2"
+   ],
+   [
+    "y0",
+    "x5",
+    "-1/2"
+   ],
+   [
+    "y2",
+    "x3",
+    "-1/2"
+   ],
+   [
+    "y3",
+    "x2",
+    "-1/2"
+   ],
+   [
+    "y4",
+    "x1",
+    "-1/2"
+   ],
+   [
+    "y5",
+    "x0",
+    "-1/2"
+   ]
+  ],
+  "unit": [
+   [
+    "y1",
+    "x0",
+    1
+   ],
+   [
+    "y0",
+    "x1",
+    1
+   ],
+   [
+    "y2",
+    "x5",
+    1
+   ],
+   [
+    "y3",
+    "x4",
+    1
+   ],
+   [
+    "y4",
+    "x3",
+    1
+   ],
+   [
+    "y5",
+    "x2",
+    1
+   ],
+   [
+    "x0",
+    "x1",
+    1
+   ],
+   [
+    "x2",
+    "x5",
+    1
+   ],
+   [
+    "x4",
+    "x3",
+    1
+   ],
+   [
+    "y1",
+    "x2",
+    1
+   ],
+   [
+    "y3",
+    "x0",
+    1
+   ],
+   [
+    "y5",
+    "x4",
+    1
+   ],
+   [
+    "y0",
+    "y5",
+    1
+   ],
+   [
+    "y2",
+    "y3",
+    1
+   ],
+   [
+    "y4",
+    "y1",
+    1
+   ],
+   [
+    "y1",
+    "x4",
+    1
+   ],
+   [
+    "y0",
+    "x5",
+    1
+   ],
+   [
+    "y2",
+    "x3",
+    1
+   ],
+   [
+    "y3",
+    "x2",
+    1
+   ],
+   [
+    "y4",
+    "x1",
+    1
+   ],
+   [
+    "y5",
+    "x0",
+    1
+   ]
+  ],
+  "coefficients": [
+   [
+    "0",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2"
+   ],
+   [
+    "-1/2",
+    "0",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2"
+   ],
+   [
+    "-1/2",
+    "-1/2",
+    "0",
+    "-1/2",
+    "-1/2",
+    "-1/2"
+   ],
+   [
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "0",
+    "-1/2",
+    "-1/2"
+   ],
+   [
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "0",
+    "-1/2"
+   ],
+   [
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "0"
+   ]
+  ]
+ },
+ {
+  "cell": "23+",
+  "bindings": {
+   "x0": [
+    "source",
+    [
+     0,
+     1,
+     2,
+     3
+    ],
+    23
+   ],
+   "x1": [
+    "source",
+    [
+     0,
+     1,
+     2,
+     3
+    ],
+    3
+   ],
+   "x2": [
+    "source",
+    [
+     2,
+     3,
+     4,
+     5
+    ],
+    1
+   ],
+   "x3": [
+    "source",
+    [
+     2,
+     3,
+     4,
+     5
+    ],
+    0
+   ],
+   "x4": [
+    "source",
+    [
+     2,
+     3,
+     6,
+     7
+    ],
+    1
+   ],
+   "x5": [
+    "source",
+    [
+     2,
+     3,
+     6,
+     7
+    ],
+    0
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new file mode 100644
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+ }
+}
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diff --git a/research/gauge44-leaver8/construction/leaver/REGROUP-LEAVER-k8.json b/research/gauge44-leaver8/construction/leaver/REGROUP-LEAVER-k8.json
new file mode 100644
index 0000000000..d482da23a8
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/REGROUP-LEAVER-k8.json
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diff --git a/research/gauge44-leaver8/construction/leaver/TRI-LEAVER-k8.json b/research/gauge44-leaver8/construction/leaver/TRI-LEAVER-k8.json
new file mode 100644
index 0000000000..e3bb24cc49
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/TRI-LEAVER-k8.json
@@ -0,0 +1,590 @@
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+     26,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     21
+    ],
+    [
+     30,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     2
+    ],
+    [
+     90,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     21
+    ],
+    [
+     94,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     2
+    ],
+    [
+     53,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     17
+    ],
+    [
+     52,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     19
+    ]
+   ],
+   "coded": true,
+   "cell": 7
+  }
+ ]
+}
diff --git a/research/gauge44-leaver8/construction/leaver/build_frames_lv.py b/research/gauge44-leaver8/construction/leaver/build_frames_lv.py
new file mode 100644
index 0000000000..5f8aa7a24b
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/build_frames_lv.py
@@ -0,0 +1,64 @@
+#!/usr/bin/env python3
+"""Apply the pinned gate/tail frame re-optimisation of FRAME-RECIPE-LV-k5.json (exact global frame optimum, gopt2) to the
+leaver U8 word.
+
+usage: build_frames_lv.py INPUT_WORD.json.gz OUT_DIR RECIPE.json
+
+Standard library only. The frames are applied by BlockInvert's `../promo/build_promotion.apply` (no entrances; 'B' gate
+frames and 'T' tail frames), which checks each old frame and recomputes the local profile and widths. This builder then checks:
+input sha pin; the scalar program of A, cut, B, precondition and cleanup unchanged (every field but the frame); start
+and end frames unchanged; local profile and width inventory equal to the recipe's; output sha pin. Three pin controls
+(input pin, wrong old frame, output pin) must be rejected at their pinned reasons on every build.
+Adapted from ../frames/build_frames.py (from PR741's extras/build_frames.py, chafreaky). Apache-2.0.
+"""
+import copy, gzip, hashlib, importlib.util, json, sys
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+_s = importlib.util.spec_from_file_location('promotion', HERE.parent / 'promo/build_promotion.py')
+B = importlib.util.module_from_spec(_s); _s.loader.exec_module(B)
+
+
+def construct(raw, recipe):
+    assert hashlib.sha256(raw).hexdigest() == recipe['input_content_sha256'], 'input word pin'
+    w = json.loads(raw)
+    assert recipe['gate_frames'] and all(c[0] in ('B', 'T') for c in recipe['gate_frames']), 'B and T frames only'
+    out = B.apply(w, dict(entrances={}, gate_frames=recipe['gate_frames']))
+    for section in ('A', 'cut', 'B', 'precondition', 'cleanup'):
+        assert [e[:-1] for e in w[section]] == [e[:-1] for e in out[section]], 'scalar program unchanged'
+    assert out['start_extra'] == w['start_extra'] and out['helper_final'] == w['helper_final'], 'endpoint frames unchanged'
+    assert out['report']['local_profile'] == recipe['expected']['local_profile'] and \
+        out['report']['width_inventory'] == recipe['expected']['width_inventory'], 'profile and width pins'
+    data = json.dumps(out, sort_keys=True, separators=(',', ':')).encode()
+    assert hashlib.sha256(data).hexdigest() == recipe['expected']['output_content_sha256'], 'output word pin'
+    return data
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    inp, outd, rfile = map(Path, sys.argv[1:4])
+    raw = gzip.decompress(inp.read_bytes()); recipe = json.loads(rfile.read_text())
+    data = construct(raw, recipe)
+    rejected = []
+    for name, change, reason in [
+            ('input-pin', lambda r: r.__setitem__('input_content_sha256', '0' * 64), 'input word pin'),
+            ('old-frame', lambda r: r['gate_frames'][0].__setitem__(2, []), 'gate frame mismatch'),
+            ('output-pin', lambda r: r['expected'].__setitem__('output_content_sha256', '0' * 64), 'output word pin')]:
+        r = copy.deepcopy(recipe); change(r)
+        try:
+            construct(raw, r)
+        except AssertionError as e:
+            assert reason in str(e), (name, str(e)); rejected.append(dict(name=name, reason=reason))
+        else:
+            raise AssertionError('accepted ' + name)
+    outd.mkdir(parents=True)
+    (outd / 'FULL-WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+    (outd / 'BUILD.json').write_text(json.dumps(dict(
+        status='PASS_FRAME_REOPT_EXACT_CONSTRUCTION', input_sha256=hashlib.sha256(raw).hexdigest(),
+        output_sha256=hashlib.sha256(data).hexdigest(), scalar_program_unchanged=True, frames=len(recipe['gate_frames']),
+        rejected_controls=rejected), indent=2) + '\n')
+    print('PASS', len(recipe['gate_frames']), 'frames and three pin controls')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-01+.json b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-01+.json
new file mode 100644
index 0000000000..bfef820f29
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-01+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x0",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x0",
+   "-1/2"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-01-.json b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-01-.json
new file mode 100644
index 0000000000..3afa894b20
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-01-.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "x1",
+   "x0",
+   1
+  ],
+  [
+   "x3",
+   "x4",
+   1
+  ],
+  [
+   "x5",
+   "x2",
+   1
+  ],
+  [
+   "y0",
+   "x3",
+   1
+  ],
+  [
+   "y2",
+   "x1",
+   1
+  ],
+  [
+   "y4",
+   "x5",
+   1
+  ],
+  [
+   "y1",
+   "y4",
+   1
+  ],
+  [
+   "y3",
+   "y2",
+   1
+  ],
+  [
+   "y5",
+   "y0",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y0",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y1",
+   "x0",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "x1",
+   "x0",
+   "1"
+  ],
+  [
+   "x3",
+   "x4",
+   "1"
+  ],
+  [
+   "x5",
+   "x2",
+   "1"
+  ],
+  [
+   "y0",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y1",
+   "y4",
+   "1"
+  ],
+  [
+   "y3",
+   "y2",
+   "1"
+  ],
+  [
+   "y5",
+   "y0",
+   "1"
+  ],
+  [
+   "y0",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y1",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x0",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x1",
+   "-1/2"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-23+.json b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-23+.json
new file mode 100644
index 0000000000..98ff8050e7
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-23+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y5",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-23-.json b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-23-.json
new file mode 100644
index 0000000000..517b89d382
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-23-.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x3",
+   "x4",
+   1
+  ],
+  [
+   "x5",
+   "x2",
+   1
+  ],
+  [
+   "y1",
+   "x3",
+   1
+  ],
+  [
+   "y2",
+   "x0",
+   1
+  ],
+  [
+   "y4",
+   "x5",
+   1
+  ],
+  [
+   "y0",
+   "y4",
+   1
+  ],
+  [
+   "y3",
+   "y2",
+   1
+  ],
+  [
+   "y5",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x5",
+   1
+  ],
+  [
+   "y0",
+   "x4",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x1",
+   1
+  ],
+  [
+   "y4",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x3",
+   "x4",
+   "1"
+  ],
+  [
+   "x5",
+   "x2",
+   "1"
+  ],
+  [
+   "y1",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x0",
+   "1"
+  ],
+  [
+   "y4",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y4",
+   "1"
+  ],
+  [
+   "y3",
+   "y2",
+   "1"
+  ],
+  [
+   "y5",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x1",
+   "1"
+  ],
+  [
+   "y4",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-45+.json b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-45+.json
new file mode 100644
index 0000000000..2bc89e1de1
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-45+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "1"
+  ],
+  [
+   "y5",
+   "x2",
+   "1"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "x4",
+   "x3",
+   "-2"
+  ],
+  [
+   "y1",
+   "x2",
+   "1"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y5",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "1"
+  ],
+  [
+   "y3",
+   "x2",
+   "1"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-45-.json b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-45-.json
new file mode 100644
index 0000000000..b9c1904b83
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-45-.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x4",
+   1
+  ],
+  [
+   "y3",
+   "x5",
+   1
+  ],
+  [
+   "y5",
+   "x3",
+   1
+  ],
+  [
+   "y4",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x4",
+   1
+  ],
+  [
+   "x5",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y4",
+   "x5",
+   1
+  ],
+  [
+   "y0",
+   "y4",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y5",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x5",
+   1
+  ],
+  [
+   "y0",
+   "x4",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y5",
+   "x1",
+   1
+  ],
+  [
+   "y4",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x3",
+   "1"
+  ],
+  [
+   "y4",
+   "x2",
+   "1"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "x5",
+   "x3",
+   "-2"
+  ],
+  [
+   "y1",
+   "x2",
+   "1"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y4",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y4",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y5",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "1"
+  ],
+  [
+   "y3",
+   "x2",
+   "1"
+  ],
+  [
+   "y5",
+   "x1",
+   "1"
+  ],
+  [
+   "y4",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-67+.json b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-67+.json
new file mode 100644
index 0000000000..7d756cb19d
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-67+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x5",
+   "1"
+  ],
+  [
+   "y3",
+   "x4",
+   "1"
+  ],
+  [
+   "y4",
+   "x3",
+   "1"
+  ],
+  [
+   "y5",
+   "x2",
+   "1"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "1"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y5",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "x5",
+   "1"
+  ],
+  [
+   "y2",
+   "x3",
+   "1"
+  ],
+  [
+   "y3",
+   "x2",
+   "1"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-67-.json b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-67-.json
new file mode 100644
index 0000000000..7d756cb19d
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/cells-k8/CORE-67-.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x5",
+   "1"
+  ],
+  [
+   "y3",
+   "x4",
+   "1"
+  ],
+  [
+   "y4",
+   "x3",
+   "1"
+  ],
+  [
+   "y5",
+   "x2",
+   "1"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "1"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y5",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "x5",
+   "1"
+  ],
+  [
+   "y2",
+   "x3",
+   "1"
+  ],
+  [
+   "y3",
+   "x2",
+   "1"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/leaver/cgx_leaver.py b/research/gauge44-leaver8/construction/leaver/cgx_leaver.py
new file mode 100644
index 0000000000..e686c66306
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/cgx_leaver.py
@@ -0,0 +1,491 @@
+# LeaverSAT: no-helper mutable-leaver all-K cells (coded triangles) on the no-triangle word. Generated by
+# LeaverSAT/mkpkg.py from construction/notri/cgx.py with the leaver edits (lv.leaver_source); Apache-2.0.
+import json as _lj, os as _lo, sys as _ls
+from fractions import Fraction as _lF
+CODED_CELLS=[(c['bindings'],[[t,s,_lF(q)] for t,s,q in c['scaled']]) for c in _lj.load(open(_lo.path.join(_lo.path.dirname(_lo.path.abspath(_ls.argv[3])),'CODED-CELLS.json')))]
+# Round20 early-coordinate-center / own-Y variant, prepared for icekylinx
+# with OpenAI Codex assistance. Apache-2.0. Scalar elementary-operation
+# helpers below are retained from the attributed PR514 construct_partial.py.
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+# AtomScout: leaver-read K-triangles (schedule from atom1.py / rog.py CP-SAT)
+TRI=json.loads(Path(sys.argv[3]).read_text())
+FULLT={(tuple(tr['p']),tr['e']) for tr in TRI['triangles']}
+TRI_COORDS={t+8 for tr in TRI['triangles'] for t,_,_ in tr['reads']}
+import os as _o
+COPYL=json.loads(open(_o.environ['XPARAM']).read()).get('copyl',[]) if _o.environ.get('XPARAM') else []
+NH=504-3*len(FULLT)+len(COPYL)
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+# Helper ids of the unpatched 504 construction: every allocation advances the 504 numbering; a packet copy that the
+# K-triangle schedule never forms advances it without allocating (HELPER-MAP.json).
+shadow=[];skipped=[];nxt=[2*v]
+def alloc():
+    n=len(cur);cur.append(());rows.append({});shadow.append(nxt[0]);nxt[0]+=1;return n
+def skip():
+    skipped.append(nxt[0]);nxt[0]+=1
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# Each source quartet supplies pair partials first. The other two coordinate
+# partitions supply eight early face packets without touching the eight
+# partials later copied into the preconditioned Y coordinates.
+SELECT=(0,0)
+PRIORITY=json.loads((INPUT/"COMPLETION-PRIORITY.json").read_text())
+import os
+XP=json.loads(open(os.environ['XPARAM']).read()) if os.environ.get('XPARAM') else {}
+XCH=XP.get('exch',{});PRIO=XP.get('prio',{})
+maps={};early={};own_rows={};pairs=[];tetrads={};block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)});maps[c]=mp
+    for ei,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[:40]):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        if ei==15:
+            for jj,cl in XCH.get(str(len(maps)-1),[[4,17],[5,19],[6,21],[7,23]]):swap(mp[jj],mp[cl],(P[ids[jj]],))
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in targets:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                t,u=sorted(ts);e2=R[t][q[0]]*R[t][q[1]]
+                pair={'targets':(t,u),'keys':[(c,p,eps),(c,q,e2)],'selected':pi==SELECT[parity],
+                      'matrix':[[R[a][p[0]],R[a][q[0]]] for a in (t,u)]}
+                pairs.append(pair)
+                if not pair['selected']:continue
+                zz=-Q(2*R[u][p[0]],R[t][p[0]])
+                sources=tet[1-parity]
+                for target,sign in ((t,-1),(u,1)):
+                    wanted={s:-Q(G[t][s],4)-sign*Q(G[u][s],2)/zz for s in sources
+                            if -Q(G[t][s],4)-sign*Q(G[u][s],2)/zz}
+                    assert len(wanted)==2
+                    candidates=[]
+                    for r in mp.values():
+                        if set(rows[r])!=set(wanted):continue
+                        s=next(iter(wanted));coef=wanted[s]/rows[r][s]
+                        if all(wanted[s]==coef*rows[r][s] for s in wanted):candidates.append((r,coef))
+                    assert len(candidates)==1
+                    r,coef=candidates[0];assert len(cur[r])==2
+                    own_rows[target]=(r,coef,cur[r])
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    needed={own_rows[t][0] for t in ids}
+    early[c]={j for j,e in enumerate(z['events'][40:]) if not ({mp[e[0]],mp[e[1]]}&needed)}
+    assert len(early[c])==8
+    retired=[]
+    for j in sorted(early[c]):
+        (t,s,a,b),F=z['events'][40+j],z['event_frames'][40+j]
+        add(mp[t],mp[s],Q(a,b),tuple(F));retired.append(mp[s])
+    assert not set(retired)&needed
+    # These eight retired rows already span every source coordinate. Keep
+    # them invertible and place the four coordinate totals in a changed basis.
+    F=basis([P[s] for s in ids]);assert len(F)==4
+    regs=sorted(retired,key=lambda r:(r>=v,r))
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    M=[[Q(R[s][i]) for s in ids] for i in c]
+    def qr_rank(rs):
+        bs={}
+        for r in rs:
+            r=r.copy()
+            for i,b in sorted(bs.items()):
+                if r[i]:q=r[i];r=[x-q*y for x,y in zip(r,b)]
+            i=next((i for i,x in enumerate(r) if x),None)
+            if i is not None:q=r[i];bs[i]=[x/q for x in r]
+        return len(bs)
+    assert qr_rank(M)==4
+    for rr0 in PRIO.get(",".join(map(str,c)),[])+PRIORITY[",".join(map(str,c))]["rows"]:
+        rr=list(map(Q,rr0))
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    for i in range(8):
+        if len(M)==8:break
+        rr=[Q(i==j) for j in range(8)]
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    assert len(M)==8
+    linear(regs,M,F)
+    for i,r in zip(c,regs):
+        assert rows[r]=={s:Q(R[s][i]) for s in ids}
+        block_totals[c,i]=r
+
+# All centers are complete while Y is still at zero. This is the crucial
+# difference from an illegal early-own-Y prefix using the old center order.
+centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+assert all(cur[v+t]==() for t in range(v))
+
+phase=B
+for t,(r,coef,F) in sorted(own_rows.items()):
+    if t in TRI_COORDS:continue
+    assert cur[r]==F
+    add(v+t,r,coef,F)
+# requests are needed for TRI coefficients
+requests=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    requests[key1].append((t,-Q(mat[0][0],2)))
+    requests[key2].append((u,-Q(mat[0][1],2)))
+reqcoef={t:(key,coef) for key,reqs in requests.items() for t,coef in reqs}
+def face_info(c,p,eps):
+    z=blocks[c];keys=[(pp,ee) for pp in it.combinations(c,2) for ee in (-1,1)]
+    r_local,alpha=z['outputs'][keys.index((p,eps))]
+    j=[j for j in range(40,len(z['events'])) if z['events'][j][0]==r_local];assert len(j)==1
+    return j[0],Q(alpha)
+tri_join_counts=Counter()
+coded_shadow_slot={}
+coded_target_edges=[];TRILOG=[]
+lcopy={}
+for s8 in COPYL:
+    r=s8+8;c=len(cur);cur.append(());rows.append({});shadow.append(None);add(c,r,1,cur[r]);lcopy[r]=c
+BF={c:basis([P[x] for x in z['receipt']['source_lines']]) for c,z in blocks.items()}
+HYB={(tuple(map(int,h[0])),tuple(map(int,h[1])),int(h[2])) for h in XP.get('hyb',[])}
+HYBLOG=[]
+def triread(t,blk,r,q):
+    F=basis(cur[v+t]+cur[r]);assert inside(F,hyper(P[t])),('TRI frame',t,blk,r,cur[v+t],cur[r],hyper(P[t]),[x for x in TRILOG if x[2]==r],HYBLOG)
+    tri_join_counts[len(F)]+=1;add(v+t,r,q,F);TRILOG.append([t,list(blk),r,str(q),list(F),list(cur[r])])
+for tr in TRI['triangles']:
+    if tr.get('coded'):
+        bindings={}
+        for name,binding in CODED_CELLS[tr['cell']][0].items():
+            bindings[name]=maps[tuple(binding[1])][binding[2]] if binding[0]=='source' else v+binding[1]
+        for tn,sn,q in CODED_CELLS[tr['cell']][1]:
+            target,source=bindings[tn],bindings[sn]
+            F=basis(cur[target]+cur[source])
+            for register in (target,source):
+                if v<=register<2*v:assert inside(F,hyper(P[register-v])),('coded frame',register,F)
+            add(target,source,q,F)
+            if sn.startswith('y'):coded_target_edges.append((target,source,Q(q)))
+        continue
+    p,eps=tuple(tr['p']),tr['e']
+    hb={blk for _,blk,_ in map(lambda x:(x[0],tuple(x[1]),x[2]),tr['reads']) if (blk,p,eps) in HYB}
+    own=[];rest=[]
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];r0=r;r=lcopy.get(r,r)
+        key,coef=reqcoef[t];assert key[1]==p and key[2]==eps,(key,p,eps)
+        if blk==key[0]:
+            rr,c0,F0=own_rows[t];assert rr==r0;own.append((t,blk,r,c0))
+        else:
+            j,alpha=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert loc in ev[:2]
+            rest.append((t,blk,loc,r,coef*alpha))
+    if not hb:
+        # original interleaved order
+        for t8,blk,loc in tr['reads']:
+            t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+            if blk==key[0]:q=own_rows[t][1]
+            else:j,alpha=face_info(blk,p,eps);q=coef*alpha
+            triread(t,blk,r,q)
+        continue
+    items=[]  # (kind, t, reg, q, blk)
+    for t,blk,r,q in own:items.append(('r',t,r,q,blk,blk in hb))
+    for blk in sorted(hb):items.append(('e',None,None,None,blk,True))
+    done=set()
+    for t,blk,loc,r,q in rest:
+        if blk in hb:
+            j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j]
+            ws=[x for x in rest if x[0]==t and x[1]==blk];assert len(ws)==2 and ws[0][4]==ws[1][4] and {ws[0][2],ws[1][2]}==set(ev[:2])
+            if (t,blk) in done:continue
+            done.add((t,blk));items.append(('m',t,maps[blk][ev[0]],q,blk,True))
+        else:items.append(('r',t,r,q,blk,False))
+    # Original read order with the two half reads collapsed into one M read at the first half's slot; the face event goes
+    # just before the first M read of its block; own reads of the M register are hoisted ahead of that event.
+    def evinfo(blk):
+        j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert ev[2]==ev[3]==1,ev
+        mpb=maps[blk];return mpb[ev[0]],mpb[ev[1]],tuple(blocks[blk]['event_frames'][j])
+    items=[]
+    seen=set()
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+        if blk==key[0]:items.append(('r',t,r,own_rows[t][1],blk,blk in hb))
+        else:
+            j,alpha=face_info(blk,p,eps);q=coef*alpha
+            if blk in hb:
+                if (t,blk) not in seen:seen.add((t,blk));continue
+                items.append(('m',t,evinfo(blk)[0],q,blk,True))
+            else:items.append(('r',t,r,q,blk,False))
+    for blk in sorted(hb):
+        k0=min(i for i,x in enumerate(items) if x[0]=='m' and x[4]==blk)
+        items.insert(k0,('e',None,None,None,blk,True))
+    n=len(items)
+    def step(it,st):
+        k,t,r,q,blk,h=it;g=lambda x:st.get(x,cur[x])
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(g(a_))+list(g(b_)))
+            return {a_:FF,b_:FF} if inside(FF,BF[blk]) else None
+        F=basis(list(g(v+t))+list(g(r)))
+        if not inside(F,hyper(P[t])):return None
+        if h and k=='r' and r==evinfo(blk)[1] and not inside(F,BF[blk]):return None
+        return {v+t:F,r:F}
+    def allowed(i,used):
+        k,t,r,q,blk,h=items[i]
+        evi=[j for j,x in enumerate(items) if x[0]=='e' and x[4]==blk] if h else []
+        if k=='e':return all(j in used for j,x in enumerate(items) if x[0]=='r' and x[4]==blk and x[5] and x[2]==evinfo(blk)[0])
+        if k=='m':return evi[0] in used
+        if k=='r' and h and r==evinfo(blk)[0]:return evi[0] not in used
+        return True
+    budget=[int(os.environ.get('HYBBUDGET','300000'))];memo=set()
+    def dfs(st,used,order):
+        if len(order)==n:return order
+        budget[0]-=1
+        if budget[0]<0:return None
+        sig=(used,tuple(sorted(st.items())))
+        if sig in memo:return None
+        memo.add(sig)
+        for i in range(n):
+            if i in used or not allowed(i,used):continue
+            d=step(items[i],st)
+            if d is None:continue
+            ns=dict(st);ns.update(d);res=dfs(ns,used|{i},order+[i])
+            if res:return res
+        return None
+    import sys as _s;_s.setrecursionlimit(20000)
+    order=dfs({},frozenset(),[])
+    assert order,('no feasible hybrid order',p,eps,sorted(hb),budget)
+    for i in order:
+        k,t,r,q,blk,h=items[i]
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(cur[a_])+list(cur[b_]));add(a_,b_,1,FF);HYBLOG.append([list(blk),list(p),eps,list(FF)])
+        else:triread(t,blk,r,q)
+
+packets={}
+for c,z in sorted(blocks.items()):
+    mp=maps[c]
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    skipev={face_info(c,p,eps)[0] for p,eps in keys if (p,eps) in FULLT}
+    for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]):
+        if j not in early[c] and 40+j not in skipev:
+            t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    for key,(r,alpha) in zip(keys,z['outputs']):
+        if tuple(key) in FULLT:skip();continue
+        a=mp[r];b=alloc();add(b,a,1,cur[a])
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha))
+
+# Both tetrahedra use the same partition. A selected key has exactly two
+# selected Y loads and no ordinary M consumer. Supply its two raw halves in
+# opposite orders and never form that M. Other keys retain the old M path.
+second=[];first_join_counts=Counter()
+for key,reqs in sorted(requests.items()):
+    assert len(reqs)==2
+    c,p,eps=key
+    if (p,eps) in FULLT:continue
+    ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds
+    for j,(target,coef) in enumerate(sorted(reqs)):
+        first_source,second_source=(a,b) if j==0 else (b,a)
+        r,alpha=packets[first_source,p,eps,second_source]
+        F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+        first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F)
+        r,alpha=packets[second_source,p,eps,c]
+        second.append((target,r,coef*alpha))
+
+Ms={}
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for eps in (-1,1):
+            if (c,p,eps) in requests:continue
+            (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,eps]=(a,alpha)
+
+consumers=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    for key in pair['keys']:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    if key in requests:
+        assert all(pairs[i]['selected'] for i in uses)
+        continue
+    assert all(not pairs[i]['selected'] for i in uses)
+    a,alpha=Ms[key]
+    for j,pid in enumerate(uses):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+assert len(cur)-240==NH,len(cur)-240
+
+selected_join_counts=Counter()
+for target,r,coef in second:
+    F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+    selected_join_counts[len(F)]+=1;add(v+target,r,coef,F)
+output_basis=[]
+for pair in pairs:
+    if not pair['selected']:continue
+    (t,u),mat=pair['targets'],pair['matrix']
+    F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u]))
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert rows[v+t]==expected,('side identity',t)
+
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+for target,source,q in reversed(coded_target_edges):
+    scatter[target-v]=[a-q*b for a,b in zip(scatter[target-v],scatter[source-v])]
+    precondition.append(['add',target,source,-q.numerator,q.denominator,[]])
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8
+assert sum(r*z for r,z in H.items())==9*NH+240*8+72,sum(r*z for r,z in H.items())
+
+def apply(e,matrix):
+    if e[0]=='add':
+        _,t,s,a,b,*_=e;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    e[-1]=list(FULL);return e
+cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q]
+cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v]
+matrix=[{r:Q(1)} if r<v else {} for r in range(len(cur))]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(len(cur)))
+
+# Restrict the eight isolated axis ports exactly, keeping the stable 112-port
+# label set. This variant changes the local word, not the outer geometry.
+mp={s:s-8 for s in range(8,120)}
+mp.update({120+s:112+s-8 for s in range(8,120)})
+mp.update({240+r:224+r for r in range(NH)})
+def restrict(events,is_cut=False):
+    out=[]
+    for e in events:
+        regs=e[1:3] if e[0]=='add' else e[1:2]
+        if any(r not in mp for r in regs):
+            assert is_cut and e[0]=='add' and e[1]-120==e[2] and e[2]<8 and e[3:5]==[1,1]
+            continue
+        q=copy.deepcopy(e);q[1]=mp[q[1]]
+        if q[0]=='add':q[2]=mp[q[2]]
+        out.append(q)
+    return out
+H.subtract({1:8,8:16});H=+H
+report={'status':'EXACT_CLEAN_OWN_Y_EARLY_CENTER_WORD_NOT_ADMITTED',
+        'h':9,'v':112,'R':NH,'cst':64,'m':73,'local_profile':dict(sorted(H.items())),
+        'centre_ranks':[8]*8,**({'tri_join_counts':dict(tri_join_counts)} if TRI['triangles'] else {}),'selected_load_join_counts':dict(selected_join_counts),'selected_partitions':list(SELECT),'first_load_join_counts':dict(first_join_counts),
+        'source_columns_exact':112,'borrowed_output_pairs':56,'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'local_rank_mass':sum(r*n for r,n in H.items()),'scope':'Clean scalar identity and all literal monotone local frames only; arbitrary-dirt compensation, entrance kernels, exact phase recipes, and global hosting/pricing are not yet certified.'}
+word={'report':report,'ports':P[8:],'root_lines':R[8:],
+      'A':restrict(A),'B':restrict(B),'cut':restrict(cut,True),'cleanup':restrict(cleanup),'precondition':restrict(precondition),
+      'centers':[mp[r] for r in centers[:8]],'center_frames':center_frames[:8],
+      'scatter':[[str(x) for x in row[:8]] for row in scatter[8:]]}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+assert len(shadow)==NH and len([x for x in shadow if x is not None])+len(skipped)==504
+hmap={**{r:r for r in range(224)},**{224+s_-240:224+i for i,s_ in enumerate(shadow) if s_ is not None}}
+(OUT/'HELPER-MAP.json').write_text(json.dumps({'map':{str(k):hmap[k] for k in sorted(hmap)},'removed_504_helpers':[224+s_-240 for s_ in skipped]})+'\n')
+(OUT/'TRILOG.json').write_text(json.dumps(dict(reads=TRILOG,hyb=HYBLOG)));(OUT/'DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/gauge44-leaver8/construction/leaver/layer_end_controls_leaver.py b/research/gauge44-leaver8/construction/leaver/layer_end_controls_leaver.py
new file mode 100644
index 0000000000..84b1c52ed2
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/layer_end_controls_leaver.py
@@ -0,0 +1,242 @@
+"""layer_end_controls_leaver.py LAYERED-WORD.json.gz ROUTING OUTDIR [ENTERING] (env PR635_CODE, optional env LEC_REASON_PINS
+= JSON file {mutant key: expected reason key or literal message substring}).  LeaverSAT variant of the signed
+layers_p6n/layer_end_controls.py (fc58c569...): IDENTICAL mutations and checks; the only change is that the expected
+rejection reason of a named mutant can be re-pinned per word (on the leaver words, with fewer cold ends, the premix-drop
+and into-full mutants are caught by the arbitrary-dirt endpoint replay before the pinned site is reached).  Every
+mutation is still REQUIRED to be rejected at its (re-)pinned reason; the unmutated word MUST pass.
+NOT-APPLICABLE SITES (Q6Reviewer, k8 / fo_hyb): two mutant constructions can be vacuous on a word:
+  extra_end      - h0's first premixed partner is already cold-ended at h0's frame, so the mutant is the identity;
+  other_hp:<e>   - entering end e's tail frame has a dimension that no helper_final frame has, so the mutant cannot be built.
+Such a site is never skipped silently: the pins file MUST declare it under "not_applicable" ({site: reason}), the
+declared set MUST equal the detected set, an identity is PROVEN by byte equality of the mutated and honest words (both
+sha256 recorded), and a substitute mutant of the same class is built and MUST be rejected at the class's pinned reason:
+  extra_end      -> the first premixed partner of h0 that is not yet ended, cold-ended at h0's frame;
+  other_hp:<e>   -> e's end moved to another helper_final frame of the dimension of e's own end frame.
+Original docstring: layer_end_controls.py LAYERED-WORD.json.gz ROUTING OUTDIR (env PR635_CODE): adapted PR635 cold_end_controls.py (LayerReviewer): raw-word negative controls for the cold low-frame ends and the
+refactored cleanup accepted by hpe_audit_and_transport.py.  Every mutation MUST be rejected (AssertionError); the
+unmutated word MUST pass.  Apache-2.0.  DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code."""
+import copy, gzip, hashlib, json, shutil, sys, tempfile
+from pathlib import Path
+import os
+sys.path.insert(0, os.environ['PR635_CODE'])   # PR635's unchanged hpe_audit_and_transport.py
+import hpe_audit_and_transport as atc
+
+src, routing, outdir = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3])
+word = json.load(gzip.open(src))
+v, R = word['report']['v'], word['report']['R']; n = 2*v + R
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+meta = word['refactored_cleanup']
+cold = [int(h) for h in meta['cold_low_frame_ended_helpers']]
+npre = meta['premix_gates']; nlow = meta['lower_frame_gates']
+early = word['early_cleanup']; eidx = {i for i, _ in early}
+rest = [i for i in range(len(word['cleanup'])) if i not in eidx]
+
+
+def trial(w):
+    """None if the transport audit accepts w, else the AssertionError message."""
+    tmp = Path(tempfile.mkdtemp())
+    p = tmp/'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w).encode(), mtime=0))
+    try:
+        atc.run(p, routing, tmp/'out')
+        return None
+    except AssertionError as e:
+        return repr(e.args[0]) if e.args else 'AssertionError'
+    finally:
+        shutil.rmtree(tmp, ignore_errors=True)
+
+
+# Pinned rejection reasons: each mutant must fail at this assertion of hpe_audit_and_transport.py (message substring).
+ENDPOINT, COLDPRE, CONE = "'arbitrary-dirt endpoint'", 'touches a cold hyperplane-ended helper', 'hpe cone pre-check (row / column)'
+WHY = dict(premix_to_precondition=COLDPRE, premix_dropped=COLDPRE, e_premix_dropped=ENDPOINT, lower_dropped=ENDPOINT,
+           remainder_dropped=ENDPOINT, coefficient=ENDPOINT, into_full='cleanup on non-FULL end', dyadic=ENDPOINT, frame_below="'nonmonotone'",
+           nonmonotone="'nonmonotone'", other_frame=CONE, cone=CONE, extra_end=COLDPRE, marker='cleanup is not the literal reversed inverse',
+           target='refactored cleanup touches a target', profile_pin='paid local profile differs from the reported local_profile',
+           entering_precondition='zero-frame precondition/compensation touches an entering helper')
+_REASONS = dict(ENDPOINT=ENDPOINT, COLDPRE=COLDPRE, CONE=CONE)
+NA_DECLARED = {}
+if os.environ.get('LEC_REASON_PINS'):
+    for _k, _v in json.loads(Path(os.environ['LEC_REASON_PINS']).read_text()).items():
+        if _k == 'not_applicable': NA_DECLARED = dict(_v); continue
+        assert _k in WHY, ('unknown mutant key', _k); WHY[_k] = _REASONS.get(_v, _v)
+assert trial(word) is None, 'unmutated cold-end word must pass'
+results = []
+
+
+def reject(name, mut, why):
+    """the mutation must be rejected, and for the pinned reason (a substring of the audit's assertion message)."""
+    w = copy.deepcopy(word); mut(w)
+    msg = trial(w)
+    assert msg is not None, 'cold-end mutation accepted: ' + name
+    assert why in msg, 'cold-end mutation %r rejected for the wrong reason: %s' % (name, msg[:300])
+    results.append(name); print('rejected', name, '|', why, flush=True)
+
+
+h0 = cold[0]
+i0, U0 = next((i, f) for i, f in early if h0 in regs(word['cleanup'][i]))
+r0 = rest[len(rest)//2]
+
+
+def premix_to_precondition(w):   # premix before the wrappers; compensation then reads the cold ends
+    w['precondition'] = w['precondition'] + w['A'][:npre]; w['A'] = w['A'][npre:]
+
+
+def lower_gate_into_full(w):     # a lower-frame gate on a cold-ended helper executed in the FULL remainder instead
+    w['early_cleanup'] = [x for x in w['early_cleanup'] if x[0] != i0]
+
+
+def drop_cleanup_gate(w, i):   # remove the gate AND its early_cleanup entry: a structurally valid word missing one gate
+    w['cleanup'].pop(i)
+    w['early_cleanup'] = [[j - (j > i), f] for j, f in w['early_cleanup'] if j != i]
+
+
+def other_frame(w):              # a different frame of the same dimension as the cold end (another cold helper's)
+    f = next(w['helper_final'][str(h)] for h in cold if w['helper_final'][str(h)] != w['helper_final'][str(h0)])
+    w['helper_final'][str(h0)] = f
+
+
+NA = []   # detected not-applicable sites: dict(site, reason, ...)
+wsha = lambda w: hashlib.sha256(json.dumps(w, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+HONEST_SHA = wsha(word)
+
+
+def extra_cold_end(w):           # declare a premixed partner of h0 cold-ended at h0's frame: fails the row/column cone
+    p = next(r for e in w['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    w['helper_final'][str(p)] = w['helper_final'][str(h0)]
+
+
+_m = copy.deepcopy(word); extra_cold_end(_m)
+if wsha(_m) == HONEST_SHA:   # identity: the first partner is already ended at h0's frame
+    _p = next(r for e in word['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    _q = next(r for e in word['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e) and str(r) not in word['helper_final'] and not v <= r < 2*v)
+    NA.append(dict(site='extra_end', reason='partner %d already cold-ended at h0 %d frame (identity)' % (_p, h0),
+                   honest_sha256=HONEST_SHA, mutated_sha256=wsha(_m), substitute='partner %d' % _q))
+
+    def extra_cold_end(w, q=_q): w['helper_final'][str(q)] = w['helper_final'][str(h0)]
+    assert wsha((lambda x: (extra_cold_end(x), x)[1])(copy.deepcopy(word))) != HONEST_SHA
+
+
+reject('premix placed in the zero-frame precondition (before the cold wrappers)', premix_to_precondition, WHY['premix_to_precondition'])
+reject('one premix gate dropped (the compensation then reads a cold-ended helper)', lambda w: w['A'].pop(npre - 1), WHY['premix_dropped'])
+reject('one lower-frame cleanup gate dropped (gate and its early_cleanup entry)', lambda w: drop_cleanup_gate(w, i0), WHY['lower_dropped'])
+reject('one FULL-remainder gate dropped', lambda w: drop_cleanup_gate(w, r0), WHY['remainder_dropped'])
+reject('lower-frame gate coefficient changed', lambda w: w['cleanup'][i0].__setitem__(3, w['cleanup'][i0][3] * 2), WHY['coefficient'])
+reject('lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)', lower_gate_into_full, WHY['into_full'])
+reject('lower-frame gate frame below its registers\' frames', lambda w: next(x for x in w['early_cleanup'] if x[0] == i0).__setitem__(1, U0[:-1]), WHY['frame_below'])
+reject('cold end at another dim-4 frame', other_frame, WHY['other_frame'])
+# PROFILE-PIN control: without its helper_final entry the cold-ended helper is a valid FULL-ended helper; the word is
+# rejected because its reported paid profile (which counts the low end) no longer matches the frame chains.
+reject('profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)', lambda w: w['helper_final'].pop(str(h0)), WHY['profile_pin'])
+reject('extra cold end on a premixed partner (the compensation reads it before its wrapper)', extra_cold_end, WHY['extra_end'])
+reject('refactored-cleanup marker removed (literal-inverse rule applies)', lambda w: w.pop('refactored_cleanup'), WHY['marker'])
+reject('remainder gate retargeted to a target register', lambda w: w['cleanup'][r0].__setitem__(1, v + 3), WHY['target'])
+reject('non-dyadic remainder coefficient', lambda w: w['cleanup'][r0].__setitem__(4 if w['cleanup'][r0][0] == 'add' else 3, 3 * w['cleanup'][r0][4 if w['cleanup'][r0][0] == 'add' else 3]), WHY['dyadic'])
+reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('5', w['report']['local_profile']['5'] - 1), WHY['profile_pin'])
+ent = [int(h) for h in sys.argv[4].split(',')] if len(sys.argv) > 4 else [int(h) for h in meta.get('entering_low_frame_ended_helpers', [])]
+for e0 in ent:   # ENTERING LOW-FRAME ENDS (ColdSupply extension; every entering end; absent for words without them)
+    j0 = next((i for i, e in enumerate(word['A'][:npre]) if e0 in regs(e)), None)
+    print('entering end', e0, 'premix gate', j0, flush=True)
+    k0, Ue = next((i, f) for i, f in early if e0 in regs(word['cleanup'][i]))
+    def to_pre(w, j0=j0): w['precondition'].append(w['A'][j0]); w['A'].pop(j0)
+    def other_hp(w, e0=e0, Ue=Ue): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Ue) and sorted(f) != sorted(Ue))
+    if not any(len(f) == len(Ue) and sorted(f) != sorted(Ue) for f in word['helper_final'].values()):   # unbuildable
+        Uh = word['helper_final'][str(e0)]
+        NA.append(dict(site='other_hp:%d' % e0, reason='tail frame dim %d; no other helper_final frame of that dim' % len(Ue),
+                       dims_available=sorted({len(f) for f in word['helper_final'].values()}), substitute='end-frame dim %d' % len(Uh)))
+
+        def other_hp(w, e0=e0, Uh=Uh): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Uh) and sorted(f) != sorted(Uh))
+    if j0 is not None: reject('entering end %d: premix gate dropped' % e0, lambda w, j0=j0: w['A'].pop(j0), WHY['e_premix_dropped'])
+    if j0 is not None: reject('entering end %d: premix gate at frame [] instead of its entrance E' % e0, lambda w, j0=j0: w['A'][j0].__setitem__(-1, []), WHY['nonmonotone'])
+    if j0 is not None: reject('entering end %d: premix gate moved into the zero-frame precondition' % e0, to_pre, WHY['entering_precondition'])
+    reject('entering end %d: lower-frame gate dropped (gate and its early_cleanup entry)' % e0, lambda w, k0=k0: drop_cleanup_gate(w, k0), WHY['lower_dropped'])
+    reject('entering end %d: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)' % e0, lambda w, e0=e0: w['helper_final'].pop(str(e0)), WHY['profile_pin'])
+    reject('entering end %d: end at another hyperplane' % e0, other_hp, WHY['cone'])
+# Pinned rejection reasons of the COLD-BEYOND mutants (substrings of hpe_audit_and_transport.py assertion messages).
+MYWHY = dict(tw_precondition=COLDPRE, tw_dropped=COLDPRE, tw_coefficient=COLDPRE, tw_other_block=COLDPRE,
+             tw_entering='zero-frame compensation reads an entering helper',
+             ab_dropped=ENDPOINT, ab_coefficient=ENDPOINT, ab_early=ENDPOINT, ab_live=ENDPOINT, ab_centre=ENDPOINT,
+             ab_lower="'nonmonotone'", ab_higher="'nonmonotone'",
+             sh_dropped=ENDPOINT, sh_coefficient=ENDPOINT, rel_dropped=ENDPOINT, rel_coefficient=ENDPOINT, rel_live=ENDPOINT,
+             h8_other=CONE, h8_lower=ENDPOINT)
+# COLD-BEYOND primitives (present only when the word carries them): frame-[] target writes in the premix (explicit
+# post-wrapper compensation of an ended helper's dirt) and forward absorptions into dead registers.
+nw = meta.get('premix_target_writes', 0)
+if nw:
+    wi = [i for i in range(npre) if v <= word['A'][i][1] < 2*v]
+    assert len(wi) == nw
+
+    def writes_to_precondition(w):   # the target writes run before the cold wrappers (inside the zero-frame precondition)
+        g = [w['A'][i] for i in wi]; w['precondition'] = w['precondition'] + g
+        w['A'] = [e for i, e in enumerate(w['A']) if i not in set(wi)]
+    reject('premix target writes placed in the zero-frame precondition (before the cold wrappers)', writes_to_precondition, MYWHY['tw_precondition'])
+    reject('one premix target write dropped (compensation must read an ended helper)', lambda w: w['A'].pop(wi[0]), MYWHY['tw_dropped'])
+    reject('premix target write coefficient changed', lambda w: w['A'][wi[0]].__setitem__(3, w['A'][wi[0]][3] * 2), MYWHY['tw_coefficient'])
+    # (reading another register that carries the SAME weight of the ended helper's dirt is a valid variant, so the mutant reads
+    #  the same factory slot of the next block, which carries none of it)
+    entering_regs = sorted(int(r) for r in word.get('start_extra', {}))
+    reject('premix target write reads an entering helper', lambda w: w['A'][wi[0]].__setitem__(2, entering_regs[0]), MYWHY['tw_entering'])
+    reject('premix target write reads a cold helper of another block', lambda w: w['A'][wi[0]].__setitem__(2, 2*v + (w['A'][wi[0]][2] - 2*v + 16) % 224), MYWHY['tw_other_block'])
+ab = meta.get('forward_absorption_A_indices', [])
+if any(len(word['helper_final'][str(h)]) == 8 for h in cold):
+    # with dim-8 cold ends, the centre-retargeted absorption first leaks an ended helper's dirt into the cut's targets
+    MYWHY['ab_centre'] = COLDPRE
+if ab:
+    # the ColdBeyond U_b absorption (q += -1/2 g); ColdThird's extra absorptions have their own controls below
+    a0 = next(a for a in ab if word['A'][a][3] * 2 == -word['A'][a][4]); g0 = word['A'][a0]
+
+    def absorption_moved_early(w):   # absorbed before the absorbed register's last kernel write
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[2] == w['A'][i][1] and w['A'][i][-1] == g0[-1])
+        w['A'].insert(j, e)
+
+    def absorption_into_live(w):     # q += a g moved right after g's previous frame-mate gate, while q is still live
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[1] in regs(w['A'][i]))
+        w['A'].insert(j, e)
+    reject('forward absorption dropped', lambda w: w['A'].pop(a0), MYWHY['ab_dropped'])
+    reject('forward absorption into a centre (a live register read by the cut)', lambda w: w['A'][a0].__setitem__(1, next(c for c in word['centers'] if c not in g0[1:3] and c not in cold)), MYWHY['ab_centre'])
+    reject('forward absorption coefficient changed', lambda w: w['A'][a0].__setitem__(3, w['A'][a0][3] * 2), MYWHY['ab_coefficient'])
+    reject('forward absorption placed before the absorbed register\'s last kernel write', absorption_moved_early, MYWHY['ab_early'])
+    reject('forward absorption placed while the absorbing register is still live', absorption_into_live, MYWHY['ab_live'])
+    reject('forward absorption at a lower frame than its registers', lambda w: w['A'][a0].__setitem__(-1, w['A'][a0][-1][:-1]), MYWHY['ab_lower'])
+    reject('forward absorption at a higher frame (FULL) than its registers', lambda w: w['A'][a0].__setitem__(-1, [256, 128, 64, 32, 16, 8, 4, 2, 1]), MYWHY['ab_higher'])
+# COLD-THIRD primitives (present only when the word carries them): several absorptions after one input gate, dirt-release
+# absorptions (a dead port takes a live helper's value so that a hyperplane unit's column has no dirt on it), and cold ends at
+# a dim-8 frame with lifted partners.
+hyper = [h for h in cold if len(word['helper_final'][str(h)]) == 8]
+if hyper and ab:
+    sh = next(a for a, b in zip(ab, ab[1:]) if b == a + 1)              # two absorptions sharing one input anchor
+    rel = next(a for a in ab if a - 1 not in ab and a + 1 not in ab and word['A'][a][2] in hyper and word['A'][a][3] * 2 != -word['A'][a][4])
+    hh = hyper[0]; ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+    reject('second absorption sharing an input anchor dropped', lambda w: w['A'].pop(sh + 1), MYWHY['sh_dropped'])
+    reject('shared-anchor absorption coefficient changed', lambda w: w['A'][sh + 1].__setitem__(3, w['A'][sh + 1][3] * 2), MYWHY['sh_coefficient'])
+    reject('dirt-release absorption dropped', lambda w: w['A'].pop(rel), MYWHY['rel_dropped'])
+    reject('dirt-release absorption coefficient changed', lambda w: w['A'][rel].__setitem__(3, w['A'][rel][3] * 2), MYWHY['rel_coefficient'])
+    jr = max(i for i in range(npre, rel) if word['A'][i][0] == 'add' and word['A'][i][2] == word['A'][rel][1])
+
+    def release_while_read(w):   # the release runs before a kernel gate that still READS the port (port live)
+        e = w['A'].pop(rel); w['A'].insert(jr, e)
+    reject('dirt-release absorption moved before a kernel gate that still reads the port', release_while_read, MYWHY['rel_live'])
+if hyper:
+    # dim-8 cold-end controls for EVERY dim-8 cold end of the word (read from the word's helper_final and the recipe meta's
+    # cold_low_frame_ended_helpers), not one representative per terminal frame
+    for hh in hyper:
+        ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+        Uh = word['helper_final'][str(hh)]
+        reject('dim-8 cold end %d (frame %s) at another dim-8 frame' % (hh, Uh), lambda w, hh=hh: w['helper_final'].__setitem__(str(hh), next(f for h, f in w['helper_final'].items() if len(f) == 8 and sorted(f) != sorted(w['helper_final'][str(hh)]))), MYWHY['h8_other'])
+        reject('dim-8 cold end %d (frame %s): one lower-frame gate dropped (gate and its early_cleanup entry)' % (hh, Uh), lambda w, ih=ih: drop_cleanup_gate(w, ih), MYWHY['h8_lower'])
+        reject('dim-8 cold end %d (frame %s): profile pin (end dropped)' % (hh, Uh), lambda w, hh=hh: w['helper_final'].pop(str(hh)), WHY['profile_pin'])
+# FACTORED ACCUMULATOR (CarrierBypass; present only when the word carries one): a lower-frame tail gate a += x*g on two
+# non-ended registers whose accumulator a is afterwards read by a dim-8 cold end's tail gate (h += y*a at its U).
+ended_all = {int(h) for h in word['helper_final']}
+tailg = [(i, word['cleanup'][i]) for i, _ in early]
+accs = []   # EVERY factored accumulator gate (one per accumulator register a), each controlled on its own
+for k, (i, e) in enumerate(tailg):
+    if e[0] == 'add' and e[1] not in ended_all and e[2] not in ended_all and len(next(f for j, f in early if j == i)) < 8:
+        if e[1] not in [word['cleanup'][j][1] for j in accs] and any(t[0] == 'add' and t[2] == e[1] and t[1] in hyper for _, t in tailg[k + 1:]):
+            accs.append(i)
+for acc in accs:
+    a = word['cleanup'][acc][1]
+    reject('factored accumulator %d (gate %d) zeroed' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, 0), ENDPOINT)
+    reject('factored accumulator %d (gate %d) coefficient doubled' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, w['cleanup'][acc][3] * 2), ENDPOINT)
+assert {x['site']: x['reason'] for x in NA} == NA_DECLARED, ('not-applicable sites differ from the pins file', NA, NA_DECLARED)
+outdir.mkdir(parents=True, exist_ok=True)
+(outdir/'COLD-END-CONTROLS.json').write_text(json.dumps(dict(status='PASS_COLD_END_RAW_WORD_CONTROLS', word=str(src), rejected=results, not_applicable=NA), indent=1) + '\n')
+print('PASS', len(results), 'cold-end raw-word mutations rejected')
diff --git a/research/gauge44-leaver8/construction/leaver/reproduce_leaver.py b/research/gauge44-leaver8/construction/leaver/reproduce_leaver.py
new file mode 100644
index 0000000000..bc4360ef93
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/reproduce_leaver.py
@@ -0,0 +1,177 @@
+#!/usr/bin/env python3
+"""Rebuild the leaver word: the no-triangle word with no-helper mutable-leaver all-K cells, and its native locals.
+
+Each cell (pair p, sign e) replaces the three face events of the blocks containing p and their three packet copies
+by a 21-gate circuit on the cell's six leaver sources x_j (the face-event operands, which have no later reads and are
+restored by the inherited cleanup at FULL) and its six targets y_i: 3 leaver gates x_k += c x_m, 3 target gates
+y_a += c y_b (inverted at frame zero in the precondition and scatter, #781's recipe) and 15 reads y_i += c x_j.
+Unit circuit (LeaverSAT, layered CP-SAT on the exact set model), relabelled per cell so that no y += y source carries
+port-stage entering-helper dirt at the gate; coefficients rescaled exactly to the cell (C_ij = r_i c_j).
+Input: a fresh `construction/reproduce.py --until word` output directory (hamming/, shadow-early/, shadow-prefix/).
+Steps, each checked exactly (pins in LEAVER-PINS.json):
+  0. cells: CODED-CELLS.json's scaled gates are re-derived from the unit circuits and the cell coefficients, and the
+     clean map Y_i = sum_j C_ij X_j is checked in exact rationals.
+  1. gauge-forward: cgx_leaver.py (notri/cgx.py + the leaver edits) with TRI-LEAVER.json, XPARAM = notri/PRIO6.json.
+  2. port0-3: notri/port_stage_x.py.
+  3. regroup: REGROUP-LEAVER.json's changes where their `before` gate occurs (count pinned).
+  4. hpe: PR635's build_hpe.candidates greedy with disjoint registers, build_hpe.apply (recipe pinned).
+  5. cold44: notri/cold44x.py with EXTRAH and pinned pairing ranks; output sha, profile and widths pinned.
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs (pins).
+Apache-2.0. LeaverSAT (Claude Code research agent), driver after construction/notri/reproduce_notri.py.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, shutil, subprocess, sys, time
+from fractions import Fraction
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NOTRI = HERE.parent / 'notri'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def dump(p, v):
+    p.parent.mkdir(parents=True, exist_ok=True); p.write_bytes(gzip.compress(enc(v), mtime=0))
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def check_cells(cells):
+    for c in cells:
+        C = [[Fraction(q) for q in r] for r in c['coefficients']]
+        col = [None] * 6; row = [Fraction(1)] + [None] * 5
+        for j in range(1, 6): col[j] = C[0][j]
+        col[0] = C[1][0] / (C[1][2] / col[2])
+        for i in range(1, 6): row[i] = C[i][(i + 1) % 6] / col[(i + 1) % 6]
+        assert all(C[i][j] == row[i] * col[j] for i in range(6) for j in range(6) if i != j), ('rank-one cell', c['cell'])
+        idx = lambda s: int(s[1:])
+        scaled = []
+        for t, s, q in c['unit']:
+            assert Fraction(q) == 1
+            if t[0] == 'x': assert s[0] == 'x'; q = col[idx(s)] / col[idx(t)]
+            elif s[0] == 'y': q = row[idx(t)] / row[idx(s)]
+            else: q = row[idx(t)] * col[idx(s)]
+            scaled.append([t, s, str(q)])
+        assert scaled == c['scaled'], ('scaled gates', c['cell'])
+        R = {f'x{j}': {j: Fraction(1)} for j in range(6)}; R.update({f'y{i}': {} for i in range(6)})
+        for t, s, q in scaled:
+            for k, x in list(R[s].items()): R[t][k] = R[t].get(k, 0) + Fraction(q) * x
+        for i in range(6):
+            assert {k: x for k, x in R[f'y{i}'].items() if x} == {j: C[i][j] for j in range(6) if j != i}, ('clean map', c['cell'], i)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--word-dir', type=Path, required=True, help='construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    ap.add_argument('--word-only', action='store_true', help='stop after the pinned scalar word (input to the layers)')
+    ap.add_argument('--id', default='k5', help='cell set: TRI-LEAVER-<id>, CODED-CELLS-<id>, REGROUP-LEAVER-<id>, LEAVER-PINS-<id>')
+    ap.add_argument('--record-pins', action='store_true', help='write LEAVER-PINS.json from this run instead of checking')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    pins = {} if a.record_pins else read(HERE / ('LEAVER-PINS-%s.json' % a.id)); got = {}
+    def pin(k, v):
+        got[k] = v
+        if not a.record_pins: assert pins[k] == v, ('pin', k, v, pins[k])
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    structural = a.main.resolve() / 'research/structural-gain/frontier-composition'
+    wd = a.word_dir.resolve()
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    # 0. cells
+    cells = read(HERE / ('CODED-CELLS-%s.json' % a.id)); check_cells(cells); print('PASS cells', [c['cell'] for c in cells], flush=True)
+    # 1. gauge-forward
+    shutil.copy(HERE / ('TRI-LEAVER-%s.json' % a.id), out / 'TRI.json'); shutil.copy(HERE / ('CODED-CELLS-%s.json' % a.id), out / 'CODED-CELLS.json')
+    env['XPARAM'] = str(NOTRI / 'PRIO6.json')
+    raw = out / 'raw'
+    run('gauge-forward', HERE / 'cgx_leaver.py', wd / 'hamming', raw, out / 'TRI.json')
+    word = raw / 'FULL-WORD.json.gz'; pin('raw_sha256', hashlib.sha256(enc(read(word))).hexdigest())
+    # 2. port stages
+    chain = [parent / 'complex-local/static44/inputs/RAW504.json.gz', structural / 'global-replay/base/split-centres/FULL-WORD.json.gz',
+             wd / 'shadow-early/FULL-WORD.json.gz', structural / 'multicold-eight-word/FULL-WORD.json.gz',
+             wd / 'shadow-prefix/FULL-WORD.json.gz']
+    for i, (b, c) in enumerate(zip(chain, chain[1:])):
+        t = out / ('port%d' % i)
+        run('port%d' % i, NOTRI / 'port_stage_x.py', '--shadow-input', b, '--shadow-output', c, '--input', word,
+            '--map', raw / 'HELPER-MAP.json', '--gk-dir', gk, '--out', t)
+        word = t / 'FULL-WORD.json.gz'
+    # 3. regroup
+    w = read(word); rg = {json.dumps(c['before']): c['after'] for c in read(HERE / ('REGROUP-LEAVER-%s.json' % a.id))['changes']}
+    n = 0
+    for part in ('A', 'B'):
+        for i, e in enumerate(w[part]):
+            k = json.dumps(e)
+            if k in rg: w[part][i] = rg[k]; n += 1
+    sys.path.insert(0, str(gk)); import gk_word as GW, gk_common as GC
+    GW.V = GC.V = 112; GW.DATA = GC.DATA = 7168
+    H = GW.profile(w)
+    w['report'].update(local_profile={str(k): z for k, z in sorted(H.items()) if z}, local_rank_mass=sum(r * z for r, z in H.items()))
+    pin('regroup_count', n); dump(out / 'regroup/FULL-WORD.json.gz', w); pin('regroup_sha256', hashlib.sha256(enc(w)).hexdigest())
+    # 4. HPE
+    h = load('upstream_hpe', up / 'code/build_hpe.py')
+    used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    (out / 'HPE-RECIPE.json').write_text(json.dumps(dict(changes=ch)))
+    pin('hpe_recipe_sha256', hashlib.sha256(enc(dict(changes=ch))).hexdigest())
+    w = h.apply(w, ch); dump(out / 'hpe/FULL-WORD.json.gz', w)
+    # 5. cold44
+    hm = set(read(raw / 'HELPER-MAP.json')['map'].values())
+    env['EXTRAH'] = json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm))
+    if not a.record_pins: env['PAIRING_RANKS'] = json.dumps(pins['pairing_ranks'])
+    run('cold44', NOTRI / 'cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', wd / 'hamming', '--upstream-package', up)
+    pin('pairing_ranks', [b['pairing_rank'] for b in read(out / 'cold44/CONSTRUCTION.json')['blocks']])
+    word = out / 'cold44/FULL-WORD.json.gz'; w = read(word)
+    pin('cold44_sha256', hashlib.sha256(enc(w)).hexdigest()); rep = w['report']
+    pin('R', rep['R']); pin('local_profile', rep['local_profile']); pin('width_inventory', rep['width_inventory'])
+    print('PASS leaver scalar word', got['cold44_sha256'], flush=True)
+    if not a.word_only:
+        for k in ('XPARAM', 'EXTRAH', 'PAIRING_RANKS'): env.pop(k, None)
+        local = out / 'local'
+        run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word,
+            '--routing', parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz', '--out', local)
+        pin('canonical_sha256', hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest())
+        run('ledgers', up / 'code/hpe_emit_local.py', local)
+        run('local-replay', up / 'code/hpe_audit_local.py', local)
+        run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+            local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+        checks = read(local / 'LOCAL-CHECKS.json')
+        pin('program_sha256', {o: checks[o]['sha256'] for o in ('forward', 'backward')})
+        if not a.skip_phases:
+            run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+            pin('clifford_recipes_sha256', hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest())
+    if a.record_pins: (HERE / ('LEAVER-PINS-%s.json' % a.id)).write_text(json.dumps(got, indent=1) + '\n')
+    print('DONE', out, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/leaver/reproduce_leaver_chain.py b/research/gauge44-leaver8/construction/leaver/reproduce_leaver_chain.py
new file mode 100644
index 0000000000..19fcd28f4d
--- /dev/null
+++ b/research/gauge44-leaver8/construction/leaver/reproduce_leaver_chain.py
@@ -0,0 +1,187 @@
+#!/usr/bin/env python3
+"""Rebuild the leaver stack on top of the leaver cell word: layers (NP, p6n), promotions, joint exchange and U8-style
+hybrids, and the final word's native locals.
+
+Input: a fresh `construction/leaver/reproduce_leaver.py --word-only` output directory (raw/HELPER-MAP.json, regroup/,
+cold44/; the cell word and its regroup word are pinned there by LEAVER-PINS.json). Each step uses an unchanged signed
+builder with a LeaverSAT recipe (data only), and every intermediate word is pinned:
+  1. pivot-swap: ../layers/build_pivot_swap.py with PIVOT-SWAP-<id>.json on the regroup word (its own 30 controls).
+  2. hpe: PR635's build_hpe.candidates (greedy, disjoint registers) must equal HPE-RECIPE-<id>.json; build_hpe.apply.
+     The swapped HPE word is pinned by the cold-layer recipes' input_content_sha256.
+  3. cold44-exact: ../notri/cold44x.py on the swapped HPE word (pairing ranks pinned to LEAVER-PINS); its cold ends,
+     premix and low tails must equal the unswapped leaver construction's.
+  4. layers: PR635's build_cold_end.apply(HPE, COLD-LAYERS-RECIPE-NP-<id>) -> NP word and (.., -P6N-<id>) -> p6n word;
+     output shas pinned by the recipes.
+  5. promotion: ../promo/build_promotion.py with PROMO-RECIPE-<id>.json on the p6n word; ../promo/promo_controls.py.
+  6. jx: ../jx/build_jx.py with RECIPE-X4-<id>.json on the promoted word; all recipe controls rerun at their pins.
+  7. hybrids: ../barch/build_tri.py with RECIPE-U8-<id>.json on the jx word; ../barch/run_controls.py (all outcomes).
+  8. frames: build_frames_lv.py (LeaverSAT2) applies FRAME-RECIPE-LV-<id>.json (B/T frame changes, exact global frame
+     optimum) with ../promo/build_promotion.apply; scalar program unchanged; 3 pin controls; output pinned.
+  8b. layer-end-controls: layer_end_controls_leaver.py (v2: the signed per-end controls with per-word reason re-pins
+     and declared not-applicable sites, each replaced by a same-class substitute mutant) on the p6n, promoted, jx and
+     hybrid words with LEC-REASON-PINS-STACK-<id>.json, and on the re-framed final word with LEC-REASON-PINS-<id>.json;
+     counts, not-applicable sites and the sha256 of each pins file pinned.
+  9. native, ledgers, local-replay, wrappers, phases on the final word; canonical, programs, Clifford pinned.
+All counts and native pins are in CHAIN-PINS-<id>.json (--record-pins writes it from a run instead of checking;
+a checking run requires its pins to equal the file exactly).
+Apache-2.0. Driver by ColdWitness over LeaverSAT's frozen recipes and the signed builders.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+C = HERE.parent
+MUTANTS = ('drop_restore', 'restore_full', 'drop_preread', 'donation_after')
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def csha(p): return hashlib.sha256(gzip.decompress(Path(p).read_bytes())).hexdigest()
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--leaver-dir', type=Path, required=True, help='construction/leaver/reproduce_leaver.py --word-only output')
+    ap.add_argument('--hamming', type=Path, required=True, help='hamming/ of the construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    ap.add_argument('--id', default='k5', help='recipe set id: every recipe and pin file below is <NAME>-<id>')
+    ap.add_argument('--record-pins', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    lp = read(HERE / ('LEAVER-PINS-%s.json' % a.id))
+    pins = {} if a.record_pins else read(HERE / ('CHAIN-PINS-%s.json' % a.id)); got = {}
+
+    def pin(key, value):
+        got[key] = value
+        if not a.record_pins: assert pins[key] == value, (key, value, pins.get(key))
+
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE', 'LEC_REASON_PINS', 'SW4_PIN'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True, extra=None):
+        t = time.monotonic(); e = dict(env, **(extra or {}))
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=e, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+        return (out / (label + '.log')).read_text()
+
+    def lec(label, word, pins_name):
+        pf = HERE / ('%s-%s.json' % (pins_name, a.id)); pin(label + '_pins_sha256', hashlib.sha256(pf.read_bytes()).hexdigest())
+        run(label, HERE / 'layer_end_controls_leaver.py', word, routing, out / label,
+            extra=dict(PR635_CODE=str(up / 'code'), LEC_REASON_PINS=str(pf)))
+        c = read(out / label / 'COLD-END-CONTROLS.json'); assert c['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS'
+        pin(label, len(c['rejected'])); pin(label + '_not_applicable', {x['site']: x['reason'] for x in c['not_applicable']})
+
+    ld = a.leaver_dir.resolve()
+    assert hashlib.sha256(enc(read(ld / 'cold44/FULL-WORD.json.gz'))).hexdigest() == lp['cold44_sha256'], 'leaver cell word'
+    rg = ld / 'regroup/FULL-WORD.json.gz'
+    sw = read(HERE / ('PIVOT-SWAP-%s.json' % a.id))
+    assert hashlib.sha256(enc(read(rg))).hexdigest() == lp['regroup_sha256'] == sw['input_content_sha256'], 'regroup word'
+    # 1. pivot swaps
+    run('pivot-swap', C / 'layers/build_pivot_swap.py', '--input', rg, '--recipe', HERE / ('PIVOT-SWAP-%s.json' % a.id), '--gk-dir', gk, '--out', out / 'swap')
+    w = read(out / 'swap/FULL-WORD.json.gz'); assert hashlib.sha256(enc(w)).hexdigest() == sw['output_content_sha256'], 'swap word'
+    # 2. HPE
+    h = load('upstream_hpe', up / 'code/build_hpe.py'); used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    assert ch == read(HERE / ('HPE-RECIPE-%s.json' % a.id))['changes'], 'HPE recipe'
+    w = h.apply(w, ch); (out / 'hpe').mkdir(); (out / 'hpe/FULL-WORD.json.gz').write_bytes(gzip.compress(enc(w), mtime=0))
+    rnp, rp6 = read(HERE / ('COLD-LAYERS-RECIPE-NP-%s.json.gz' % a.id)), read(HERE / ('COLD-LAYERS-RECIPE-P6N-%s.json.gz' % a.id))
+    assert hashlib.sha256(enc(w)).hexdigest() == rnp['input_content_sha256'] == rp6['input_content_sha256'], 'swapped HPE word'
+    # 3. cold44 on the swapped word: same ends, premix and tails
+    hm = set(read(ld / 'raw/HELPER-MAP.json')['map'].values())
+    run('cold44-exact', C / 'notri/cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', a.hamming.resolve(), '--upstream-package', up,
+        extra=dict(EXTRAH=json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm)), PAIRING_RANKS=json.dumps(lp['pairing_ranks'])))
+    new, old = read(out / 'cold44/RECIPE.json.gz'), read(ld / 'cold44/RECIPE.json.gz')
+    for key in ('premix', 'early_cleanup', 'cold_ends'): assert new[key] == old[key], ('swapped cold44 differs', key)
+    tail = len(new['early_cleanup']); assert new['cleanup'][:tail] == old['cleanup'][:tail], 'low tails'
+    # 4. NP and p6n layers
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    for name, r in (('np', rnp), ('p6n', rp6)):
+        lw = bce.apply(w, r); raw = enc(lw); assert hashlib.sha256(raw).hexdigest() == r['output_content_sha256'], (name, 'word')
+        (out / name).mkdir(); (out / name / 'FULL-WORD.json.gz').write_bytes(gzip.compress(raw, mtime=0))
+        pin(name + '_profile', lw['report']['local_profile'])
+    p6n = out / 'p6n/FULL-WORD.json.gz'; lec('lec-p6n', p6n, 'LEC-REASON-PINS-STACK')
+    # 5. promotion
+    pr = HERE / ('PROMO-RECIPE-%s.json' % a.id)
+    run('promotion', C / 'promo/build_promotion.py', '--input', p6n, '--recipe', pr, '--out', out / 'promo', portable=False)
+    assert csha(out / 'promo/FULL-WORD.json.gz') == read(pr)['expected']['output_content_sha256']
+    run('promo-controls', C / 'promo/promo_controls.py', '--input', p6n, '--recipe', pr, '--audit', C.parent / 'independent/audit_local.py',
+        '--out', out / 'PROMO-CONTROLS.json', portable=False)
+    pc = read(out / 'PROMO-CONTROLS.json'); assert pc['honest'] == 'PASS'; pin('promo_controls', pc['rejected'])
+    lec('lec-promo', out / 'promo/FULL-WORD.json.gz', 'LEC-REASON-PINS-STACK')
+    # 6. jx
+    xr = HERE / ('RECIPE-X4-%s.json' % a.id); rec = read(xr); inp = out / 'promo/FULL-WORD.json.gz'
+    (out / 'jx').mkdir(); jw = out / 'jx/FULL-WORD.json.gz'
+    run('jx', C / 'jx/build_jx.py', '--input', inp, '--recipe', xr, '--out', jw, portable=False)
+    assert csha(jw) == rec['expected']['output_content_sha256']
+    for name, cc in sorted(rec['controls'].items()):
+        log = run('jx-control-' + name, C / 'jx/build_jx.py', '--input', inp, '--recipe', xr, '--control', name, portable=False)
+        if 'rejection_expected' in cc: assert 'CONTROL PINNED' in log, (name, log[-300:])
+        else: assert ('OK ' + cc['expected_sha']) in log, (name, log[-300:])
+    pin('jx_controls', sorted(rec['controls']))
+    lec('lec-jx', jw, 'LEC-REASON-PINS-STACK')
+    # 7. hybrids
+    ur = HERE / ('RECIPE-U8-%s.json' % a.id); u = read(ur); (out / 'hyb').mkdir(); fw = out / 'hyb/FULL-WORD.json.gz'
+    run('hybrids', C / 'barch/build_tri.py', jw, ur, fw, portable=False)
+    assert csha(fw) == u['expect_sha256']
+    run('hybrid-controls', C / 'barch/run_controls.py', jw, ur, C.parent / 'independent/audit_local.py', out / 'hybrid-controls', portable=False)
+    res = read(out / 'hybrid-controls/controls.json')
+    want = ['C0_identity', 'recipe', *MUTANTS] + [m + '@' + str(v['X']) for v in u.get('variants', []) for m in MUTANTS]
+    assert sorted(res) == sorted(want) and all(x['ok'] for x in res.values()), res
+    pin('hybrid_controls', sorted(want))
+    lec('lec-hyb', fw, 'LEC-REASON-PINS-STACK')
+    # 8. frame re-optimisation (LeaverSAT2): exact global frame optimum of the hybrid word; scalar program unchanged
+    fr = HERE / ('FRAME-RECIPE-LV-%s.json' % a.id); frec = read(fr)
+    run('frames', HERE / 'build_frames_lv.py', fw, out / 'frames', fr, portable=False)
+    fw = out / 'frames/FULL-WORD.json.gz'; assert csha(fw) == frec['expected']['output_content_sha256']
+    pin('frame_build_controls', len(read(out / 'frames/BUILD.json')['rejected_controls']))
+    # 8b. layer-end controls on the re-framed final word (v2, not-applicable sites declared in LEC-REASON-PINS-<id>):
+    # the frame re-optimisation lowers an entering-end tail frame to a dimension no helper_final frame has, so that
+    # site's 'end at another hyperplane' mutant is replaced by its same-class substitute.
+    lec('lec-frames', fw, 'LEC-REASON-PINS')
+    # 9. native locals of the final word
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', fw, '--routing', routing, '--out', local)
+    pin('canonical_sha256', hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest())
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz', local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json'); pin('program_sha256', {o: checks[o]['sha256'] for o in ('forward', 'backward')})
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        pin('clifford_recipes_sha256', hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest())
+    if a.record_pins: (out / ('CHAIN-PINS-%s.json' % a.id)).write_bytes((json.dumps(got, indent=1) + '\n').encode())
+    else: assert got == pins, ('chain pins differ', sorted(set(got) ^ set(pins)))
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/notri/PRIO6.json b/research/gauge44-leaver8/construction/notri/PRIO6.json
new file mode 100644
index 0000000000..069a7bf5a5
--- /dev/null
+++ b/research/gauge44-leaver8/construction/notri/PRIO6.json
@@ -0,0 +1 @@
+{"prio": {"0,1,2,3": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "0,1,4,5": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "0,1,6,7": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "2,3,4,5": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "2,3,6,7": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "4,5,6,7": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]]}}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/notri/cgx.py b/research/gauge44-leaver8/construction/notri/cgx.py
new file mode 100644
index 0000000000..08e80804eb
--- /dev/null
+++ b/research/gauge44-leaver8/construction/notri/cgx.py
@@ -0,0 +1,469 @@
+# Round20 early-coordinate-center / own-Y variant, prepared for icekylinx
+# with OpenAI Codex assistance. Apache-2.0. Scalar elementary-operation
+# helpers below are retained from the attributed PR514 construct_partial.py.
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+# AtomScout: leaver-read K-triangles (schedule from atom1.py / rog.py CP-SAT)
+TRI=json.loads(Path(sys.argv[3]).read_text())
+FULLT={(tuple(tr['p']),tr['e']) for tr in TRI['triangles']}
+TRI_COORDS={t+8 for tr in TRI['triangles'] for t,_,_ in tr['reads']}
+import os as _o
+COPYL=json.loads(open(_o.environ['XPARAM']).read()).get('copyl',[]) if _o.environ.get('XPARAM') else []
+NH=504-3*len(FULLT)+len(COPYL)
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+# Helper ids of the unpatched 504 construction: every allocation advances the 504 numbering; a packet copy that the
+# K-triangle schedule never forms advances it without allocating (HELPER-MAP.json).
+shadow=[];skipped=[];nxt=[2*v]
+def alloc():
+    n=len(cur);cur.append(());rows.append({});shadow.append(nxt[0]);nxt[0]+=1;return n
+def skip():
+    skipped.append(nxt[0]);nxt[0]+=1
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# Each source quartet supplies pair partials first. The other two coordinate
+# partitions supply eight early face packets without touching the eight
+# partials later copied into the preconditioned Y coordinates.
+SELECT=(0,0)
+PRIORITY=json.loads((INPUT/"COMPLETION-PRIORITY.json").read_text())
+import os
+XP=json.loads(open(os.environ['XPARAM']).read()) if os.environ.get('XPARAM') else {}
+XCH=XP.get('exch',{});PRIO=XP.get('prio',{})
+maps={};early={};own_rows={};pairs=[];tetrads={};block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)});maps[c]=mp
+    for ei,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[:40]):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        if ei==15:
+            for jj,cl in XCH.get(str(len(maps)-1),[[4,17],[5,19],[6,21],[7,23]]):swap(mp[jj],mp[cl],(P[ids[jj]],))
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in targets:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                t,u=sorted(ts);e2=R[t][q[0]]*R[t][q[1]]
+                pair={'targets':(t,u),'keys':[(c,p,eps),(c,q,e2)],'selected':pi==SELECT[parity],
+                      'matrix':[[R[a][p[0]],R[a][q[0]]] for a in (t,u)]}
+                pairs.append(pair)
+                if not pair['selected']:continue
+                zz=-Q(2*R[u][p[0]],R[t][p[0]])
+                sources=tet[1-parity]
+                for target,sign in ((t,-1),(u,1)):
+                    wanted={s:-Q(G[t][s],4)-sign*Q(G[u][s],2)/zz for s in sources
+                            if -Q(G[t][s],4)-sign*Q(G[u][s],2)/zz}
+                    assert len(wanted)==2
+                    candidates=[]
+                    for r in mp.values():
+                        if set(rows[r])!=set(wanted):continue
+                        s=next(iter(wanted));coef=wanted[s]/rows[r][s]
+                        if all(wanted[s]==coef*rows[r][s] for s in wanted):candidates.append((r,coef))
+                    assert len(candidates)==1
+                    r,coef=candidates[0];assert len(cur[r])==2
+                    own_rows[target]=(r,coef,cur[r])
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    needed={own_rows[t][0] for t in ids}
+    early[c]={j for j,e in enumerate(z['events'][40:]) if not ({mp[e[0]],mp[e[1]]}&needed)}
+    assert len(early[c])==8
+    retired=[]
+    for j in sorted(early[c]):
+        (t,s,a,b),F=z['events'][40+j],z['event_frames'][40+j]
+        add(mp[t],mp[s],Q(a,b),tuple(F));retired.append(mp[s])
+    assert not set(retired)&needed
+    # These eight retired rows already span every source coordinate. Keep
+    # them invertible and place the four coordinate totals in a changed basis.
+    F=basis([P[s] for s in ids]);assert len(F)==4
+    regs=sorted(retired,key=lambda r:(r>=v,r))
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    M=[[Q(R[s][i]) for s in ids] for i in c]
+    def qr_rank(rs):
+        bs={}
+        for r in rs:
+            r=r.copy()
+            for i,b in sorted(bs.items()):
+                if r[i]:q=r[i];r=[x-q*y for x,y in zip(r,b)]
+            i=next((i for i,x in enumerate(r) if x),None)
+            if i is not None:q=r[i];bs[i]=[x/q for x in r]
+        return len(bs)
+    assert qr_rank(M)==4
+    for rr0 in PRIO.get(",".join(map(str,c)),[])+PRIORITY[",".join(map(str,c))]["rows"]:
+        rr=list(map(Q,rr0))
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    for i in range(8):
+        if len(M)==8:break
+        rr=[Q(i==j) for j in range(8)]
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    assert len(M)==8
+    linear(regs,M,F)
+    for i,r in zip(c,regs):
+        assert rows[r]=={s:Q(R[s][i]) for s in ids}
+        block_totals[c,i]=r
+
+# All centers are complete while Y is still at zero. This is the crucial
+# difference from an illegal early-own-Y prefix using the old center order.
+centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+assert all(cur[v+t]==() for t in range(v))
+
+phase=B
+for t,(r,coef,F) in sorted(own_rows.items()):
+    if t in TRI_COORDS:continue
+    assert cur[r]==F
+    add(v+t,r,coef,F)
+# requests are needed for TRI coefficients
+requests=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    requests[key1].append((t,-Q(mat[0][0],2)))
+    requests[key2].append((u,-Q(mat[0][1],2)))
+reqcoef={t:(key,coef) for key,reqs in requests.items() for t,coef in reqs}
+def face_info(c,p,eps):
+    z=blocks[c];keys=[(pp,ee) for pp in it.combinations(c,2) for ee in (-1,1)]
+    r_local,alpha=z['outputs'][keys.index((p,eps))]
+    j=[j for j in range(40,len(z['events'])) if z['events'][j][0]==r_local];assert len(j)==1
+    return j[0],Q(alpha)
+tri_join_counts=Counter();TRILOG=[]
+lcopy={}
+for s8 in COPYL:
+    r=s8+8;c=len(cur);cur.append(());rows.append({});shadow.append(None);add(c,r,1,cur[r]);lcopy[r]=c
+BF={c:basis([P[x] for x in z['receipt']['source_lines']]) for c,z in blocks.items()}
+HYB={(tuple(map(int,h[0])),tuple(map(int,h[1])),int(h[2])) for h in XP.get('hyb',[])}
+HYBLOG=[]
+def triread(t,blk,r,q):
+    F=basis(cur[v+t]+cur[r]);assert inside(F,hyper(P[t])),('TRI frame',t,blk,r,cur[v+t],cur[r],hyper(P[t]),[x for x in TRILOG if x[2]==r],HYBLOG)
+    tri_join_counts[len(F)]+=1;add(v+t,r,q,F);TRILOG.append([t,list(blk),r,str(q),list(F),list(cur[r])])
+for tr in TRI['triangles']:
+    p,eps=tuple(tr['p']),tr['e']
+    hb={blk for _,blk,_ in map(lambda x:(x[0],tuple(x[1]),x[2]),tr['reads']) if (blk,p,eps) in HYB}
+    own=[];rest=[]
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];r0=r;r=lcopy.get(r,r)
+        key,coef=reqcoef[t];assert key[1]==p and key[2]==eps,(key,p,eps)
+        if blk==key[0]:
+            rr,c0,F0=own_rows[t];assert rr==r0;own.append((t,blk,r,c0))
+        else:
+            j,alpha=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert loc in ev[:2]
+            rest.append((t,blk,loc,r,coef*alpha))
+    if not hb:
+        # original interleaved order
+        for t8,blk,loc in tr['reads']:
+            t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+            if blk==key[0]:q=own_rows[t][1]
+            else:j,alpha=face_info(blk,p,eps);q=coef*alpha
+            triread(t,blk,r,q)
+        continue
+    items=[]  # (kind, t, reg, q, blk)
+    for t,blk,r,q in own:items.append(('r',t,r,q,blk,blk in hb))
+    for blk in sorted(hb):items.append(('e',None,None,None,blk,True))
+    done=set()
+    for t,blk,loc,r,q in rest:
+        if blk in hb:
+            j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j]
+            ws=[x for x in rest if x[0]==t and x[1]==blk];assert len(ws)==2 and ws[0][4]==ws[1][4] and {ws[0][2],ws[1][2]}==set(ev[:2])
+            if (t,blk) in done:continue
+            done.add((t,blk));items.append(('m',t,maps[blk][ev[0]],q,blk,True))
+        else:items.append(('r',t,r,q,blk,False))
+    # Original read order with the two half reads collapsed into one M read at the first half's slot; the face event goes
+    # just before the first M read of its block; own reads of the M register are hoisted ahead of that event.
+    def evinfo(blk):
+        j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert ev[2]==ev[3]==1,ev
+        mpb=maps[blk];return mpb[ev[0]],mpb[ev[1]],tuple(blocks[blk]['event_frames'][j])
+    items=[]
+    seen=set()
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+        if blk==key[0]:items.append(('r',t,r,own_rows[t][1],blk,blk in hb))
+        else:
+            j,alpha=face_info(blk,p,eps);q=coef*alpha
+            if blk in hb:
+                if (t,blk) not in seen:seen.add((t,blk));continue
+                items.append(('m',t,evinfo(blk)[0],q,blk,True))
+            else:items.append(('r',t,r,q,blk,False))
+    for blk in sorted(hb):
+        k0=min(i for i,x in enumerate(items) if x[0]=='m' and x[4]==blk)
+        items.insert(k0,('e',None,None,None,blk,True))
+    n=len(items)
+    def step(it,st):
+        k,t,r,q,blk,h=it;g=lambda x:st.get(x,cur[x])
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(g(a_))+list(g(b_)))
+            return {a_:FF,b_:FF} if inside(FF,BF[blk]) else None
+        F=basis(list(g(v+t))+list(g(r)))
+        if not inside(F,hyper(P[t])):return None
+        if h and k=='r' and r==evinfo(blk)[1] and not inside(F,BF[blk]):return None
+        return {v+t:F,r:F}
+    def allowed(i,used):
+        k,t,r,q,blk,h=items[i]
+        evi=[j for j,x in enumerate(items) if x[0]=='e' and x[4]==blk] if h else []
+        if k=='e':return all(j in used for j,x in enumerate(items) if x[0]=='r' and x[4]==blk and x[5] and x[2]==evinfo(blk)[0])
+        if k=='m':return evi[0] in used
+        if k=='r' and h and r==evinfo(blk)[0]:return evi[0] not in used
+        return True
+    budget=[int(os.environ.get('HYBBUDGET','300000'))];memo=set()
+    def dfs(st,used,order):
+        if len(order)==n:return order
+        budget[0]-=1
+        if budget[0]<0:return None
+        sig=(used,tuple(sorted(st.items())))
+        if sig in memo:return None
+        memo.add(sig)
+        for i in range(n):
+            if i in used or not allowed(i,used):continue
+            d=step(items[i],st)
+            if d is None:continue
+            ns=dict(st);ns.update(d);res=dfs(ns,used|{i},order+[i])
+            if res:return res
+        return None
+    import sys as _s;_s.setrecursionlimit(20000)
+    order=dfs({},frozenset(),[])
+    assert order,('no feasible hybrid order',p,eps,sorted(hb),budget)
+    for i in order:
+        k,t,r,q,blk,h=items[i]
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(cur[a_])+list(cur[b_]));add(a_,b_,1,FF);HYBLOG.append([list(blk),list(p),eps,list(FF)])
+        else:triread(t,blk,r,q)
+
+packets={}
+for c,z in sorted(blocks.items()):
+    mp=maps[c]
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    skipev={face_info(c,p,eps)[0] for p,eps in keys if (p,eps) in FULLT}
+    for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]):
+        if j not in early[c] and 40+j not in skipev:
+            t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    for key,(r,alpha) in zip(keys,z['outputs']):
+        if tuple(key) in FULLT:skip();continue
+        a=mp[r];b=alloc();add(b,a,1,cur[a])
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha))
+
+# Both tetrahedra use the same partition. A selected key has exactly two
+# selected Y loads and no ordinary M consumer. Supply its two raw halves in
+# opposite orders and never form that M. Other keys retain the old M path.
+second=[];first_join_counts=Counter()
+for key,reqs in sorted(requests.items()):
+    assert len(reqs)==2
+    c,p,eps=key
+    if (p,eps) in FULLT:continue
+    ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds
+    for j,(target,coef) in enumerate(sorted(reqs)):
+        first_source,second_source=(a,b) if j==0 else (b,a)
+        r,alpha=packets[first_source,p,eps,second_source]
+        F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+        first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F)
+        r,alpha=packets[second_source,p,eps,c]
+        second.append((target,r,coef*alpha))
+
+Ms={}
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for eps in (-1,1):
+            if (c,p,eps) in requests:continue
+            (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,eps]=(a,alpha)
+
+consumers=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    for key in pair['keys']:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    if key in requests:
+        assert all(pairs[i]['selected'] for i in uses)
+        continue
+    assert all(not pairs[i]['selected'] for i in uses)
+    a,alpha=Ms[key]
+    for j,pid in enumerate(uses):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+assert len(cur)-240==NH,len(cur)-240
+
+selected_join_counts=Counter()
+for target,r,coef in second:
+    F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+    selected_join_counts[len(F)]+=1;add(v+target,r,coef,F)
+output_basis=[]
+for pair in pairs:
+    if not pair['selected']:continue
+    (t,u),mat=pair['targets'],pair['matrix']
+    F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u]))
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert rows[v+t]==expected,('side identity',t)
+
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8
+assert sum(r*z for r,z in H.items())==9*NH+240*8+72,sum(r*z for r,z in H.items())
+
+def apply(e,matrix):
+    if e[0]=='add':
+        _,t,s,a,b,*_=e;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    e[-1]=list(FULL);return e
+cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q]
+cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v]
+matrix=[{r:Q(1)} if r<v else {} for r in range(len(cur))]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(len(cur)))
+
+# Restrict the eight isolated axis ports exactly, keeping the stable 112-port
+# label set. This variant changes the local word, not the outer geometry.
+mp={s:s-8 for s in range(8,120)}
+mp.update({120+s:112+s-8 for s in range(8,120)})
+mp.update({240+r:224+r for r in range(NH)})
+def restrict(events,is_cut=False):
+    out=[]
+    for e in events:
+        regs=e[1:3] if e[0]=='add' else e[1:2]
+        if any(r not in mp for r in regs):
+            assert is_cut and e[0]=='add' and e[1]-120==e[2] and e[2]<8 and e[3:5]==[1,1]
+            continue
+        q=copy.deepcopy(e);q[1]=mp[q[1]]
+        if q[0]=='add':q[2]=mp[q[2]]
+        out.append(q)
+    return out
+H.subtract({1:8,8:16});H=+H
+report={'status':'EXACT_CLEAN_OWN_Y_EARLY_CENTER_WORD_NOT_ADMITTED',
+        'h':9,'v':112,'R':NH,'cst':64,'m':73,'local_profile':dict(sorted(H.items())),
+        'centre_ranks':[8]*8,**({'tri_join_counts':dict(tri_join_counts)} if TRI['triangles'] else {}),'selected_load_join_counts':dict(selected_join_counts),'selected_partitions':list(SELECT),'first_load_join_counts':dict(first_join_counts),
+        'source_columns_exact':112,'borrowed_output_pairs':56,'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'local_rank_mass':sum(r*n for r,n in H.items()),'scope':'Clean scalar identity and all literal monotone local frames only; arbitrary-dirt compensation, entrance kernels, exact phase recipes, and global hosting/pricing are not yet certified.'}
+word={'report':report,'ports':P[8:],'root_lines':R[8:],
+      'A':restrict(A),'B':restrict(B),'cut':restrict(cut,True),'cleanup':restrict(cleanup),'precondition':restrict(precondition),
+      'centers':[mp[r] for r in centers[:8]],'center_frames':center_frames[:8],
+      'scatter':[[str(x) for x in row[:8]] for row in scatter[8:]]}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+assert len(shadow)==NH and len([x for x in shadow if x is not None])+len(skipped)==504
+hmap={**{r:r for r in range(224)},**{224+s_-240:224+i for i,s_ in enumerate(shadow) if s_ is not None}}
+(OUT/'HELPER-MAP.json').write_text(json.dumps({'map':{str(k):hmap[k] for k in sorted(hmap)},'removed_504_helpers':[224+s_-240 for s_ in skipped]})+'\n')
+(OUT/'TRILOG.json').write_text(json.dumps(dict(reads=TRILOG,hyb=HYBLOG)));(OUT/'DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/gauge44-leaver8/construction/notri/cold44x.py b/research/gauge44-leaver8/construction/notri/cold44x.py
new file mode 100644
index 0000000000..8fa6f3a6a6
--- /dev/null
+++ b/research/gauge44-leaver8/construction/notri/cold44x.py
@@ -0,0 +1,217 @@
+"""Exact dyadic cold-end realization of the source-branch/factory-completion word.
+Prepared for icekylinx with OpenAI Codex assistance; Apache-2.0.
+This is a constructor: independent endpoint/frame audits remain required.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+import copy,gzip,json,hashlib,time,sys,argparse,importlib.util,os
+D=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser(description=__doc__)
+for name in ('input','out','hamming','upstream-package'):ap.add_argument('--'+name,type=Path,required=True)
+args=ap.parse_args();WPATH=args.input;OUT=args.out
+assert __debug__, 'Assertions are required'
+OUT.mkdir(exist_ok=False,parents=True)
+def rd(p):return json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+w=rd(WPATH);v=w['report']['v'];n=2*v+w['report']['R'];N=list(range(v))+list(range(2*v,n));ix={x:i for i,x in enumerate(N)}
+F9=[256,128,64,32,16,8,4,2,1];t0=time.monotonic()
+def basis(vs):
+ d={}
+ for a in vs:
+  for k in sorted(d,reverse=True):
+   if a>>k&1:a^=d[k]
+  if a:
+   k=a.bit_length()-1
+   for j in d:
+    if d[j]>>k&1:d[j]^=a
+   d[k]=a
+ return tuple(d[k] for k in sorted(d,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def regs(e):return e[1:3] if e[0]=='add' else e[1:2]
+def inverse(e):
+ e=copy.deepcopy(e)
+ if e[0]=='add':e[3]=-e[3]
+ else:e[2],e[3]=e[3],e[2]
+ return e
+def apply(e,M,mapping=None):
+ t=mapping[e[1]] if mapping is not None else e[1]
+ if e[0]=='add':
+  s=mapping[e[2]] if mapping is not None else e[2];q=Q(e[3],e[4])
+  for j,a in M[s].items():
+   x=M[t].get(j,Q(0))+q*a
+   if x:M[t][j]=x
+   else:M[t].pop(j,None)
+ else:
+  q=Q(e[2],e[3]);M[t]={j:q*a for j,a in M[t].items()}
+def rref(A):
+ a=[list(map(Q,row)) for row in A];nr=len(a);nc=len(a[0]) if nr else 0;row=0;piv=[]
+ for c in range(nc):
+  k=next((i for i in range(row,nr) if a[i][c]),None)
+  if k is None:continue
+  a[row],a[k]=a[k],a[row];q=a[row][c];a[row]=[x/q for x in a[row]]
+  for i in range(nr):
+   if i!=row and a[i][c]:q=a[i][c];a[i]=[x-q*y for x,y in zip(a[i],a[row])]
+  piv.append(c);row+=1
+  if row==nr:break
+ return a,piv
+def rank(A):return len(rref(A)[1])
+def null(A,nc=None):
+ if A:a,piv=rref(A);nc=len(a[0])
+ else:a=[];piv=[];assert nc is not None
+ free=[j for j in range(nc) if j not in piv];out=[[Q(0) for j in free] for i in range(nc)]
+ for k,c in enumerate(free):out[c][k]=Q(1)
+ for i,c in enumerate(piv):
+  for k,j in enumerate(free):out[c][k]=-a[i][j]
+ return out
+def mm(A,B):
+ if not A:return []
+ if not B:return [[] for row in A]
+ bt=list(zip(*B));return [[sum((a*b for a,b in zip(row,col)),Q(0)) for col in bt] for row in A]
+def tr(A):return list(map(list,zip(*A)))
+def inv(A):
+ n0=len(A);a,p=rref([row+[Q(i==j) for j in range(n0)] for i,row in enumerate(A)])
+ assert p[:n0]==list(range(n0))
+ return [row[n0:] for row in a]
+def unit(q):
+ if not q:return False
+ a=abs(q.numerator);b=q.denominator
+ return not a&(a-1) and not b&(b-1)
+def dyadic(q):return not q.denominator&(q.denominator-1)
+def opadd(t,s,q,F):return ['add',t,s,q.numerator,q.denominator,list(F)]
+def opscale(t,q,F):return ['scale',t,q.numerator,q.denominator,list(F)]
+def eliminate(M,ids,F,skip=()):
+ """Return legal dyadic row operations taking an invertible sparse matrix to I."""
+ skip=set(skip);ops=[];dim=len(M)
+ def add(i,j,q):
+  if q:
+   assert dyadic(q);e=opadd(ids[i],ids[j],q,F);ops.append(e)
+   for c,x in M[j].items():
+    z=M[i].get(c,Q(0))+q*x
+    if z:M[i][c]=z
+    else:M[i].pop(c,None)
+ def scale(i,q):
+  if q!=1:
+   assert unit(q);ops.append(opscale(ids[i],q,F));M[i]={c:q*x for c,x in M[i].items()}
+ def swap(i,j):
+  if i!=j:
+   add(i,j,Q(1));add(j,i,Q(-1));add(i,j,Q(1));scale(j,Q(-1))
+ for c in range(dim):
+  if c in skip:
+   assert M[c]=={c:Q(1)} and all(not M[i].get(c) for i in range(dim) if i!=c)
+   continue
+  cand=[i for i in range(c,dim) if i not in skip and M[i].get(c)]
+  k=next((i for i in cand if unit(M[i][c])),None)
+  if k is None:
+   # Elementary Euclidean row additions reduce the pivot-column numerator gcd.
+   assert cand,('singular',c)
+   while k is None:
+    cand.sort(key=lambda i:abs(M[i][c]));a=cand[0]
+    b=next((i for i in cand[1:] if M[i][c]),None)
+    if b is None:raise ValueError(('non-dyadic determinant pivot',c,M[a][c]))
+    rat=M[b][c]/M[a][c];q=rat.numerator//rat.denominator
+    if q==0:q=1 if rat>0 else -1
+    add(b,a,Q(-q));cand=[i for i in cand if M[i].get(c)]
+    k=next((i for i in cand if unit(M[i][c])),None)
+  swap(c,k);scale(c,1/M[c][c])
+  for i in range(dim):
+   if i!=c and M[i].get(c):
+    assert i not in skip
+    add(i,c,-M[i][c])
+ assert all(row=={i:Q(1)} for i,row in enumerate(M))
+ return ops
+def realize(A,ids,F):
+ M=[{j:Q(x) for j,x in enumerate(row) if x} for row in A]
+ return [inverse(e) for e in reversed(eliminate(M,ids,F))]
+# Reconstruct the actual non-target map after the inherited HPE tail.
+inherited_tail=[w['cleanup'][i][:-1]+[list(f)] for i,f in w.get('early_cleanup',[])]
+mainN=[e for e in w['A']+w['B'] if not v<=e[1]<2*v]
+M=[{i:Q(1)} for i in range(len(N))]
+for e in mainN+inherited_tail:apply(e,M,ix)
+MI=[{i:Q(1)} for i in range(len(N))]
+for e in reversed(mainN+inherited_tail):apply(inverse(e),MI,ix)
+cur={x:(w['ports'][x],) if x<v else basis(w.get('start_extra',{}).get(str(x),[])) for x in N}
+for e in w['A']+w['B']+inherited_tail:
+ for x in regs(e):
+  if x in cur:cur[x]=basis(e[-1])
+enter=set(map(int,w.get('start_extra',{})));protected=[ix[x] for x in N if x<v or x in enter]
+EXTRAH=json.loads(os.environ.get('EXTRAH','[]'))
+PAIRING_RANKS=json.loads(os.environ['PAIRING_RANKS']) if os.environ.get('PAIRING_RANKS') else None   # per-block pin, set by the driver
+mods=rd(args.hamming/'PACKET-PROGRAMS.json.gz');proto=rd(args.hamming/'PROTOTYPE.json')
+plans=[];premix=[];tail=[];ends={};Mafter=copy.deepcopy(M)
+for b,mod in enumerate(mods):
+ ss=mod['receipt']['source_lines'];F=basis([proto['binary_ports'][s] for s in ss]);I=[ix[x] for x in N if inside(cur[x],F)]
+ hs=list(range(224+16*b,224+16*(b+1)))+[x for x in EXTRAH if ix[x] in I];H=[ix[x] for x in hs];NB=len(hs)
+ C=[[M[i].get(j,Q(0)) for j in protected] for i in I]
+ L=tr(null(tr(C),len(I)))
+ A=[[MI[j].get(i,Q(0)) for i in I] for j in protected];A=[row for row in A if any(row)]
+ K=null(A,len(I));BK=mm(L,K);_,piv=rref(BK);r=len(piv);print('PAIR',b,'I',len(I),'L',len(L),'K',len(K),'r',r,flush=True);assert r==len(L),(b,r,len(L))
+ if PAIRING_RANKS is not None: assert r==PAIRING_RANKS[b],('pinned pairing rank',b,r,PAIRING_RANKS[b])
+ if os.environ.get('DIAG'):
+  print(' regs',[(N[i],cur[N[i]],rank([C[k]]) ) for k,i in enumerate(I)],'rankC',rank(C) if C else 0,flush=True)
+  for row in L: print('  Lrow',{N[I[k]]:str(x) for k,x in enumerate(row) if x})
+ if r==0:plans.append(dict(block=b,frame=list(F),registers=[N[i] for i in I],ends=[],pairing_rank=0));continue
+ Ksel=[[row[j] for j in piv] for row in K];Bsel=[[row[j] for j in piv] for row in BK];U=mm(Ksel,inv(Bsel));assert mm(L,U)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ q=mm([[MI[i].get(j,Q(0)) for j in I] for i in range(len(N))],U)
+ assert all(not any(q[i]) for i in range(len(N)) if i not in H),('nonlocal premix',b)
+ RR=mm(L,[[M[i].get(j,Q(0)) for j in H] for i in I]);qH=[q[i] for i in H]
+ assert mm(RR,qH)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ # Pick low physical helper destinations with independent U coordinate rows.
+ ih=[]
+ for j in sorted((j for j,i in enumerate(I) if N[i] in hs),key=lambda j:(cur[N[I[j]]]!=F,N[I[j]])):
+  if rank([U[k] for k in ih]+[U[j]])>len(ih):ih.append(j)
+  if len(ih)==r:break
+ assert len(ih)==r
+ endhs=[N[I[j]] for j in ih];endhidx=[hs.index(h) for h in endhs]
+ kerR=null(RR,NB);Qmat=[[Q(0) for j in range(NB)] for i in range(NB)]
+ for j,hj in enumerate(endhidx):
+  for i in range(NB):Qmat[i][hj]=qH[i][j]
+ other=[j for j in range(NB) if j not in endhidx]
+ for k,j in enumerate(other):
+  for i in range(NB):Qmat[i][j]=kerR[i][k]
+ assert rank(Qmat)==NB
+ pops=realize(Qmat,hs,());premix+=pops
+ T=[[Q(i==j)-sum((U[i][k]*L[k][j] for k in range(r)),Q(0)) for j in range(len(I))] for i in range(len(I))]
+ for k,i in enumerate(ih):T[i]=L[k]
+ tops=realize(T,[N[i] for i in I],F);tail+=tops
+ # Right-compose this initial helper premix; other blocks have disjoint H sets.
+ for row in Mafter:
+  vals=[row.get(h,Q(0)) for h in H]
+  if any(vals):
+   for hj in H:row.pop(hj,None)
+   for j,hj in enumerate(H):
+    z=sum((vals[i]*Qmat[i][j] for i in range(NB)),Q(0))
+    if z:row[hj]=z
+ for e in tops:apply(e,Mafter,ix)
+ ends.update({h:list(F) for h in endhs})
+ plans.append(dict(block=b,frame=list(F),registers=[N[i] for i in I],ends=endhs,pairing_rank=r,premix_gates=len(pops),tail_gates=len(tops),Q=[[str(x) for x in row] for row in Qmat],T=[[str(x) for x in row] for row in T]))
+ print('BLOCK',b,'ends',endhs,'Qops',len(pops),'Tops',len(tops),flush=True)
+# Check actual post-tail isolation before constructing the high-frame inverse.
+allends=set(ends)|set(map(int,w.get('helper_final',{})))
+for h in allends:
+ j=ix[h];assert Mafter[j]=={j:Q(1)},('row not isolated',h,Mafter[j]);assert all(not row.get(j) for i,row in enumerate(Mafter) if i!=j),('column not isolated',h)
+print('EXACT_ISOLATED',len(ends),'new;',len(allends),'total',round(time.monotonic()-t0,3),flush=True)
+fullops=eliminate(copy.deepcopy(Mafter),N,F9,[ix[x] for x in allends])
+print('FULL_INVERSE',len(fullops),round(time.monotonic()-t0,3),flush=True)
+# Cancel new cold-axis target responses inside A, after their wrappers.
+Dirt=[({h:Q(1)} if h in ends else {}) for h in range(n)]
+for e in premix+w['A']+w['cut']+w['B']:apply(e,Dirt)
+for e in w['precondition']:apply(e,Dirt)
+postcomp=[opadd(y,h,-a,()) for y in range(v,2*v) for h,a in sorted(Dirt[y].items()) if a]
+assert all(h in ends for e in postcomp for h in [e[2]])
+new=copy.deepcopy(w);new['A']=postcomp+premix+w['A'];new['cleanup']=inherited_tail+tail+fullops
+new['early_cleanup']=[[i,e[-1]] for i,e in enumerate(inherited_tail+tail)]
+new['helper_final'].update({str(h):f for h,f in ends.items()})
+new['refactored_cleanup']={'kind':'source_branch_gauge_and_retired_completion_cold44','new_cold_ends':len(ends),'exact_non_target_isolation_checked':True,'high_inverse':'dyadic_sparse_Gauss_Jordan'}
+# Derive paid profile by subtracting and adding literal frame-chain counts.
+spec=importlib.util.spec_from_file_location('upstream_cold_end',args.upstream_package/'code/build_cold_end.py')
+profile_module=importlib.util.module_from_spec(spec);spec.loader.exec_module(profile_module)
+oldprof,_=profile_module.chain_profile(w);newprof,_=profile_module.chain_profile(new)
+prof=Counter({int(k):z for k,z in w['report']['local_profile'].items()});prof.subtract(oldprof);prof.update(newprof)
+widths=Counter(len(basis(new['helper_final'].get(str(h),F9)))-len(basis(new.get('start_extra',{}).get(str(h),[]))) for h in range(224,n))
+new['report'].update(local_profile={str(k):z for k,z in sorted(prof.items()) if z},local_rank_mass=sum(k*z for k,z in prof.items()),width_inventory={str(k):z for k,z in sorted(widths.items()) if z},status='EXACT_COLD44_CONSTRUCTED_PENDING_INDEPENDENT_AUDIT')
+raw=json.dumps(new,sort_keys=True,separators=(',',':')).encode();sha=hashlib.sha256(raw).hexdigest();(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+recipe={'premix':postcomp+premix,'cleanup':new['cleanup'],'early_cleanup':new['early_cleanup'],'cold_ends':{str(h):f for h,f in ends.items()},'refactored_cleanup':new['refactored_cleanup'],'output_content_sha256':sha}
+(OUT/'RECIPE.json.gz').write_bytes(gzip.compress(json.dumps(recipe,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+receipt=dict(input_content_sha256=hashlib.sha256(gzip.decompress(WPATH.read_bytes())).hexdigest(),output_content_sha256=sha,blocks=plans,new_cold_ends=len(ends),all_low_ended_helpers=len(allends),premix_gates=len(premix),postwrapper_compensation_gates=len(postcomp),tail_gates=len(tail),inherited_tail_gates=len(inherited_tail),full_inverse_gates=len(fullops),profile=new['report']['local_profile'],width_inventory=new['report']['width_inventory'],rank_mass=new['report']['local_rank_mass'],seconds=time.monotonic()-t0)
+(OUT/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(json.dumps({k:z for k,z in receipt.items() if k!='blocks'},indent=2),flush=True)
diff --git a/research/gauge44-leaver8/construction/notri/port_stage_x.py b/research/gauge44-leaver8/construction/notri/port_stage_x.py
new file mode 100644
index 0000000000..81ac65ceff
--- /dev/null
+++ b/research/gauge44-leaver8/construction/notri/port_stage_x.py
@@ -0,0 +1,125 @@
+"""Port one 504-helper construction stage onto the K-triangle word.  Apache-2.0.  Prepared with Claude Code assistance.
+
+usage: build_port_stage.py --shadow-input I4 --shadow-output O4 --input I8 --map HELPER-MAP.json --gk-dir GK --out DIR
+
+The shadow pair (I4 -> O4) is one stage of a 504-helper chain, rebuilt in the same run from pinned sources.  I8 is the
+K-triangle word at the matching point of its own chain, and HELPER-MAP.json is the 504 -> R register map written by
+construct_k_triangle.py.  Registers below 448 keep their ids; the removed packet copies have no image.
+
+The port does the following:
+* It renumbers I4 and O4 through the map and drops their gates that touch a removed register.
+* It matches gates by scalar operation (the gate without its frame), aligning I4 with O4 and I4 with I8 separately.
+* It builds O8 in O4 gate order:
+  * each matched gate is taken from I8, with O4's frame wherever the stage changed that frame;
+  * each gate the stage introduced is taken from O4;
+  * each I8-only gate (the K-triangle reads) stays after the O4 image of its I8 predecessor.
+* It replays the stage's entrance (start_extra) and target_levels changes.
+* It rebuilds the cleanup with the inherited inverse rule.
+
+The constructor is a search transfer only.  The verifier certifies the output independently: the generalised native
+audit (exact forward and inverse replay of every column, native frame chains) runs on every ported word, and every
+input and output is pinned by content hash."""
+import argparse, copy, difflib, gzip, hashlib, json, sys
+from collections import Counter
+from pathlib import Path
+
+assert __debug__, 'Assertions required'
+FULL = [256, 128, 64, 32, 16, 8, 4, 2, 1]
+
+
+def regs(g): return (g[1], g[2]) if g[0] == 'add' else (g[1],)
+
+
+def key(g): return json.dumps(g[:-1])
+
+
+def inverse(e):
+    e = copy.deepcopy(e)
+    if e[0] == 'add': e[3] *= -1
+    else: e[2], e[3] = e[3], e[2]
+    e[-1] = list(FULL); return e
+
+
+def align(xs, ys):
+    """index map xs -> ys over runs of equal scalar operations"""
+    sm = difflib.SequenceMatcher(None, [key(g) for g in xs], [key(g) for g in ys], autojunk=False)
+    return {i1 + k: j1 + k for tag, i1, i2, j1, j2 in sm.get_opcodes() if tag == 'equal' for k in range(i2 - i1)}
+
+
+def transfer_section(I4, O4, I8, stats):
+    a, b = align(I4, O4), align(I4, I8)
+    o2i = {j: i for i, j in a.items()}; i8from4 = {j: i for i, j in b.items()}
+    anchor = {j8: a[i4] for j8, i4 in i8from4.items() if i4 in a}
+    pending, last = {}, -1
+    for j8, g in enumerate(I8):
+        if j8 in anchor: last = anchor[j8]
+        elif j8 not in i8from4: pending.setdefault(last, []).append(copy.deepcopy(g)); stats['kept_own'] += 1
+        else: stats['dropped_by_stage'] += 1
+    out = list(pending.get(-1, []))
+    for k, g in enumerate(O4):
+        if k in o2i:
+            i4 = o2i[k]
+            if i4 in b:
+                g8 = copy.deepcopy(I8[b[i4]])
+                if I4[i4][-1] != g[-1]: g8[-1] = copy.deepcopy(g[-1]); stats['frames_changed'] += 1
+                out.append(g8)
+        else:
+            out.append(copy.deepcopy(g)); stats['introduced'] += 1
+        out.extend(pending.get(k, []))
+    return out
+
+
+def main():
+    ap = argparse.ArgumentParser()
+    for k in ('--shadow-input', '--shadow-output', '--input', '--map', '--gk-dir', '--out'): ap.add_argument(k, type=Path, required=True)
+    a = ap.parse_args(); assert not a.out.exists()
+    sys.path.insert(0, str(a.gk_dir)); import gk_word as G, gk_common as C
+    G.V = C.V = 112
+    rd = lambda p: json.loads(gzip.decompress(p.read_bytes()))
+    enc = lambda x: json.dumps(x, sort_keys=True, separators=(',', ':')).encode(); sha = lambda x: hashlib.sha256(x).hexdigest()
+    I4, O4, I8 = rd(a.shadow_input), rd(a.shadow_output), rd(a.input)
+    fm = {int(k): int(v) for k, v in json.loads(a.map.read_text())['map'].items()}
+    assert all(fm[k] == k for k in fm if k < 448), 'only ids >= 448 may move'
+    R = I8['report']['R']; EXTRA = set(range(224 + R)) - set(fm.values()); assert len(set(fm.values())) == len(fm) and set(fm.values()) <= set(range(224 + R)), 'map is not injective into the K-triangle registers'
+    assert I4['report'].get('R', 504) == 504 and len(fm) + len(set(range(728)) - set(fm)) == 728
+    rem = set(range(728)) - set(fm)
+    rn = lambda r: fm[r]
+    touches = lambda g: any(r in rem for r in regs(g))
+    def rg(g):
+        g = copy.deepcopy(g); g[1] = rn(g[1])
+        if g[0] == 'add': g[2] = rn(g[2])
+        return g
+    def rn_word(w):
+        w = copy.deepcopy(w)
+        for s in ('A', 'B', 'cut', 'precondition', 'cleanup'):
+            if s in w: w[s] = [rg(g) for g in w[s] if not touches(g)]
+        for k in ('start_extra', 'helper_final'):
+            if k in w: w[k] = {str(rn(int(r))): f for r, f in w[k].items() if int(r) not in rem}
+        return w
+    I4r, O4r = rn_word(I4), rn_word(O4)
+    O8 = copy.deepcopy(I8); stats = {s: Counter() for s in ('A', 'B')}
+    for s in ('A', 'B'): O8[s] = transfer_section(I4r[s], O4r[s], I8[s], stats[s])
+    for k in ('start_extra', 'target_levels'):
+        x, y = I4r.get(k, {}), O4r.get(k, {}); d = dict(I8.get(k, {}))
+        for r in set(x) | set(y):
+            if x.get(r) != y.get(r):
+                if r in y: d[r] = y[r]
+                else: d.pop(r, None)
+        if k in O4 or k in I8: O8[k] = dict(sorted(d.items(), key=lambda kv: int(kv[0])))
+    for k in O4:
+        if k not in ('A', 'B', 'cleanup', 'report', 'start_extra', 'target_levels', 'cut', 'precondition'):
+            assert O4r[k] == I4r[k], 'stage changed an unported field: ' + k
+    O8['cleanup'] = [inverse(e) for e in reversed(O8['A'] + O8['B']) if not 112 <= e[1] < 224]
+    H = G.profile(O8)
+    ws = [9 - len(G.basis(O8['start_extra'].get(str(224 + h), []))) for h in range(R)]
+    O8['report'] = dict(I8['report'], local_profile={str(k): v for k, v in sorted(H.items())}, local_rank_mass=sum(k * v for k, v in H.items()),
+                        width_inventory={str(k): v for k, v in sorted(Counter(ws).items())})
+    a.out.mkdir(parents=True); (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(enc(O8), mtime=0))
+    receipt = dict(status='PORTED_STAGE_PENDING_NATIVE_AUDIT', R=R, removed_504_helpers=sorted(rem),
+                   shadow_input_content_sha256=sha(enc(I4)), shadow_output_content_sha256=sha(enc(O4)), input_content_sha256=sha(enc(I8)),
+                   output_content_sha256=sha(enc(O8)), sections={s: dict(v) for s, v in stats.items()}, local_profile=O8['report']['local_profile'],
+                   scope='Transfer construction only; exactness, frame chains and profile are certified by the native audit run on the output.')
+    (a.out / 'PORT-STAGE.json').write_text(json.dumps(receipt, indent=2, sort_keys=True) + '\n', newline='\n'); print(json.dumps(receipt, indent=2))
+
+
+main()
diff --git a/research/gauge44-leaver8/construction/notri/reproduce_notri.py b/research/gauge44-leaver8/construction/notri/reproduce_notri.py
new file mode 100644
index 0000000000..a85f2acf15
--- /dev/null
+++ b/research/gauge44-leaver8/construction/notri/reproduce_notri.py
@@ -0,0 +1,166 @@
+#!/usr/bin/env python3
+"""Rebuild the no-triangle gauge44 word (R = 504) and its native locals.
+
+The no-triangle word is #645's gauge44 chain with none of the four (p,-1) K-triangles. In the six K-blocks
+{0,1,2,11,12,13}, the completion priority is extended by the 6-row list PRIO6.json, the list blocks 3-10 already use.
+Each block then pairs at rank 4, giving 56 rank-four cold ends instead of 44 (PartialK).
+
+Input: a fresh `construction/reproduce.py --until word` output directory. Its shadow-early and shadow-prefix words and
+its hamming inputs are pinned by reproduce.py itself. Steps, each checked exactly:
+  1. gauge-forward: cgx.py, #645's construct_gauge_xcentre.py generalised by PartialK. The extra rows come from XPARAM,
+     and the K-triangle schedule comes from the TRI file. Run on the triangle set {} with XPARAM = PRIO6.json.
+  2. port0-3: port_stage_x.py, PR635's build_port_stage.py with the helper map allowed to be injective rather than onto.
+     With R = 504 and no triangles, the map is onto again.
+  3. regroup: PR635's k492 frame-regroup changes, applied where their `before` gate occurs. For this word none occurs,
+     and that count (0) is pinned.
+  4. hpe: PR635's build_hpe.candidates, taken greedily with disjoint registers, and build_hpe.apply. 46 changes, pinned.
+  5. cold44: cold44x.py, #645's build_gauge_cold44.py generalised by PartialK to blocks whose helper list includes the
+     helpers outside the 224+16b ranges (EXTRAH). 56 cold ends; the 14 pairing ranks are pinned to [4]*14 inside cold44x (PAIRING_RANKS) and rechecked here. The output word content sha256 is pinned (3e99ba77...).
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs, as in reproduce.py.
+--control-g44 instead runs steps 1-5 with #645's four triangles and no XPARAM. It must reproduce #645's pinned gauge44
+cold44 word (78c7aada...), the same word #645's own reproduce.py builds. This shows the generalised scripts reduce to
+#645's constructors.
+Apache-2.0. Driver by ColdWitness from PartialK's variant.py; constructors credited above.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NOTRI_SHA = '3e99ba778ab8a97853f50912776247802b529439937176363f6c42786163b1f9'
+G44_SHA = '78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290'
+# native-local pins (the strict locals the SPEC was frozen against: PartialK runs/none_p6/local)
+CANONICAL_SHA = '4265a3bb7f9b46967dfadfca5f2cc1f5b3e6e8681f16c02590f1b9430c013637'
+PROGRAM_SHA = {'forward': '0afda28699e15cf5a5a17aee5475ac608c9fb68b15766d463b93ec8e2df4ae85',
+               'backward': '5be6cb4ea7a1da36d7bbe7eb2392873c058dd3cbb3cc2eeadd55ecca9310ca8a'}
+CLIFFORD_SHA = '4b5789e43e04d71f02c2d480450ec0b354007d9cf523bda76c7345730806344b'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def dump(p, v):
+    p.parent.mkdir(parents=True, exist_ok=True); p.write_bytes(gzip.compress(enc(v), mtime=0))
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--word-dir', type=Path, required=True, help='construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--control-g44', action='store_true', help='rebuild #645 gauge44 (4 triangles) instead; word only')
+    ap.add_argument('--skip-phases', action='store_true')
+    ap.add_argument('--word-only', action='store_true', help='stop after the pinned scalar word (input to construction/layers_np)')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    structural = a.main.resolve() / 'research/structural-gain/frontier-composition'
+    wd = a.word_dir.resolve()
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    # 1. gauge-forward on the chosen K-triangle set
+    tri = read(up / 'data/TRI-SCHEDULE.json')
+    if not a.control_g44:
+        tri = dict(full_pairs=tri['full_pairs'], triangles=[])
+        env['XPARAM'] = str(HERE / 'PRIO6.json')
+    (out / 'TRI.json').write_text(json.dumps(tri))
+    raw = out / 'raw'
+    run('gauge-forward', HERE / 'cgx.py', wd / 'hamming', raw, out / 'TRI.json')
+    word = raw / 'FULL-WORD.json.gz'
+    # 2. port stages (same chain as reproduce.py)
+    chain = [parent / 'complex-local/static44/inputs/RAW504.json.gz', structural / 'global-replay/base/split-centres/FULL-WORD.json.gz',
+             wd / 'shadow-early/FULL-WORD.json.gz', structural / 'multicold-eight-word/FULL-WORD.json.gz',
+             wd / 'shadow-prefix/FULL-WORD.json.gz']
+    for i, (b, c) in enumerate(zip(chain, chain[1:])):
+        t = out / ('port%d' % i)
+        run('port%d' % i, HERE / 'port_stage_x.py', '--shadow-input', b, '--shadow-output', c, '--input', word,
+            '--map', raw / 'HELPER-MAP.json', '--gk-dir', gk, '--out', t)
+        word = t / 'FULL-WORD.json.gz'
+    # 3. PR635 frame regroup where its `before` gate occurs
+    w = read(word); rg = {json.dumps(c['before']): c['after'] for c in read(up / 'data/recipes/k492-jp8-frame_regroup.json')['changes']}
+    n = 0
+    for part in ('A', 'B'):
+        for i, e in enumerate(w[part]):
+            k = json.dumps(e)
+            if k in rg: w[part][i] = rg[k]; n += 1
+    sys.path.insert(0, str(gk)); import gk_word as GW, gk_common as GC
+    GW.V = GC.V = 112; GW.DATA = GC.DATA = 7168
+    H = GW.profile(w)
+    w['report'].update(local_profile={str(k): z for k, z in sorted(H.items()) if z}, local_rank_mass=sum(r * z for r, z in H.items()))
+    assert n == (24 if a.control_g44 else 0), ('regroup count', n)
+    dump(out / 'regroup/FULL-WORD.json.gz', w)
+    # 4. HPE: PR635's candidates, greedy with disjoint registers
+    h = load('upstream_hpe', up / 'code/build_hpe.py')
+    used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    assert len(ch) == (34 if a.control_g44 else 46), ('hpe count', len(ch))
+    (out / 'HPE-RECIPE.json').write_text(json.dumps(dict(changes=ch)))
+    w = h.apply(w, ch); dump(out / 'hpe/FULL-WORD.json.gz', w)
+    # 5. cold44 (generalised): helpers outside the 224+16b ranges join their blocks
+    hm = set(read(raw / 'HELPER-MAP.json')['map'].values())
+    env['EXTRAH'] = json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm))
+    ranks = [2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2] if a.control_g44 else [4] * 14
+    env['PAIRING_RANKS'] = json.dumps(ranks)   # cold44x asserts every block's pairing rank
+    run('cold44', HERE / 'cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', wd / 'hamming', '--upstream-package', up)
+    assert [b['pairing_rank'] for b in read(out / 'cold44/CONSTRUCTION.json')['blocks']] == ranks, 'pairing ranks'
+    word = out / 'cold44/FULL-WORD.json.gz'; w = read(word)
+    got = hashlib.sha256(enc(w)).hexdigest()
+    assert got == (G44_SHA if a.control_g44 else NOTRI_SHA), ('word', got)
+    rep = w['report']
+    if a.control_g44:
+        print('PASS control: #645 gauge44 word reproduced', got, flush=True); return
+    assert rep['R'] == 504 and rep['local_rank_mass'] == 5674
+    assert rep['local_profile'] == {'1': 2506, '2': 336, '3': 472, '4': 184, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 64, '5': 48, '7': 46, '8': 114, '9': 232}, rep['width_inventory']
+    print('PASS no-triangle scalar word', got, flush=True)
+    if a.word_only:
+        return
+    # 6. native locals (PR635, as in reproduce.py)
+    for k in ('XPARAM', 'EXTRAH', 'PAIRING_RANKS'): env.pop(k, None)
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word,
+        '--routing', parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz', '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == CANONICAL_SHA, 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in PROGRAM_SHA.items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == CLIFFORD_SHA, 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/promo/LOCAL-PINS-p6n-k4.json b/research/gauge44-leaver8/construction/promo/LOCAL-PINS-p6n-k4.json
new file mode 100644
index 0000000000..c43b391a43
--- /dev/null
+++ b/research/gauge44-leaver8/construction/promo/LOCAL-PINS-p6n-k4.json
@@ -0,0 +1,11 @@
+{
+ "word": "P6k4",
+ "layer_controls": 95,
+ "promo_controls": 11,
+ "canonical_sha256": "c0c5734a2eb6984ccd1e314dbcea2a6971b9708e5f611aa8912fcf47f02de61d",
+ "program_sha256": {
+  "forward": "6cfedac02e899df7fa50a3e38845982a4e9dbc866e9decc4052e011532bdb30f",
+  "backward": "207d9352aeea7d56a6da865745a1ad756e28531fbf9bcb0cd54950aac7270381"
+ },
+ "clifford_recipes_sha256": "1c1d037d602b503b35f01a65d0ccc07ac63fde9df501b0a61e3e189a44a779de"
+}
diff --git a/research/gauge44-leaver8/construction/promo/PROMO-RECIPE-p6n-k4.json b/research/gauge44-leaver8/construction/promo/PROMO-RECIPE-p6n-k4.json
new file mode 100644
index 0000000000..3f336c07ea
--- /dev/null
+++ b/research/gauge44-leaver8/construction/promo/PROMO-RECIPE-p6n-k4.json
@@ -0,0 +1,971 @@
+{
+ "input_content_sha256": "34b683fa08f054fe725704ec15b1c8da42f846430999d14d0cae0fcd42296fe2",
+ "groups": [
+  627,
+  629,
+  630,
+  631,
+  635,
+  637,
+  638,
+  639,
+  651,
+  653,
+  654,
+  655,
+  659,
+  661,
+  662,
+  663
+ ],
+ "entrances": {
+  "627": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "629": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "630": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "631": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "635": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "637": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "638": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "639": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "651": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "653": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "654": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "655": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "659": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ],
+  "661": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ],
+  "662": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ],
+  "663": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ]
+ },
+ "gate_frames": [
+  [
+   "B",
+   420,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   421,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   422,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   423,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   424,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   425,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   426,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   427,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   428,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   429,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   430,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   431,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   432,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   433,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   434,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   435,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   436,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   437,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   438,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   439,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   440,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   441,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   442,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   443,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   444,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   445,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   446,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   447,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   448,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   449,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   450,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   451,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   452,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   453,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   454,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   455,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   456,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   457,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   458,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   459,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   460,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   461,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   462,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   463,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   464,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   465,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   466,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   467,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ]
+ ],
+ "expected": {
+  "output_content_sha256": "0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073",
+  "local_profile": {
+   "1": 2572,
+   "2": 326,
+   "3": 430,
+   "4": 194,
+   "5": 56,
+   "8": 8
+  },
+  "width_inventory": {
+   "4": 80,
+   "5": 32,
+   "7": 54,
+   "8": 122,
+   "9": 216
+  }
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/construction/promo/build_promotion.py b/research/gauge44-leaver8/construction/promo/build_promotion.py
new file mode 100644
index 0000000000..f1daad34c2
--- /dev/null
+++ b/research/gauge44-leaver8/construction/promo/build_promotion.py
@@ -0,0 +1,109 @@
+"""Entrance promotions E4 -> E5 of whole kernel groups: deterministic constructor.  Apache-2.0.
+BlockInvert (Claude Code research agent) for the gauge44 lineage.
+
+usage: build_promotion.py --input FULL-WORD.json.gz --recipe PROMO-RECIPE.json --out DIR
+
+The recipe is data only:
+  input_content_sha256   sha256 of the decompressed input word (pinned);
+  entrances              {helper: frame vectors}: new start frames (each strictly contains the old one);
+  gate_frames            [[section, index, old frame, new frame], ...]: section 'A' / 'B' (main gates) or 'T'
+                         (early_cleanup entry index); the old frame must match the input exactly (as a span);
+  expected               output_content_sha256, local_profile, width_inventory.
+The scalar program is unchanged (only frame annotations and start frames move), so the endpoint, the
+zero-target-response entrance condition and every cone are those of the input; the independent audit
+(audit_local.py) re-checks all of them, plus monotone chains and the recomputed profile/widths."""
+import argparse, gzip, hashlib, json
+from collections import Counter
+from pathlib import Path
+
+
+def span(vs):
+    p = {}
+    for x in vs:
+        for k in sorted(p, reverse=True):
+            if x >> k & 1: x ^= p[k]
+        if x:
+            k = x.bit_length() - 1
+            for j in list(p):
+                if p[j] >> k & 1: p[j] ^= x
+            p[k] = x
+    return tuple(p[k] for k in sorted(p, reverse=True))
+
+
+def regs(e): return [e[1]] + ([e[2]] if e[0] == 'add' else [])
+
+
+def chain_profile(w):
+    """paid climbs of the A, B, early-tail and final chains, target ends included (centre descents unchanged, not counted)."""
+    v, R = w['report']['v'], w['report']['R']; n = 2*v + R
+    cur = [() for _ in range(n)]
+    for i, p in enumerate(w['ports']): cur[i] = span([p])
+    for r, f in w.get('start_extra', {}).items(): cur[int(r)] = span(f)
+    prof = Counter()
+
+    def climb(r, F):
+        assert span(list(cur[r]) + list(F)) == F, ('nonmonotone', r)
+        if len(F) > len(cur[r]): prof[len(F) - len(cur[r])] += 1
+        cur[r] = F
+    for part in ('A', 'B'):
+        for e in w[part]:
+            for r in regs(e): climb(r, span(e[-1]))
+    for i, f in w.get('early_cleanup', []):
+        for r in regs(w['cleanup'][i]): climb(r, span(f))
+    full = span([1 << i for i in range(9)])
+    final = {int(r): span(f) for r, f in w.get('helper_final', {}).items()}
+    for r in range(n):
+        if v <= r < 2*v:     # targets end at their port hyperplane (as in the independent audit); counted on both sides
+            climb(r, span([x for x in range(1, 512) if (x & w['ports'][r - v]).bit_count() % 2 == 0])); continue
+        climb(r, final.get(r, full))
+    return prof
+
+
+def widths(w):
+    v, R = w['report']['v'], w['report']['R']; full = [1 << i for i in range(9)]
+    return Counter(len(span(w['helper_final'].get(str(r), full))) - len(span(w['start_extra'].get(str(r), [])))
+                   for r in range(2*v, 2*v + R))
+
+
+def apply(w, r):
+    nw = json.loads(json.dumps(w))
+    for h, F in r['entrances'].items():
+        assert h in nw['start_extra'], ('not an entering helper', h)
+        old, new = span(nw['start_extra'][h]), span(F)
+        assert len(new) > len(old) and span(list(old) + list(new)) == new, ('not a promotion', h)
+        nw['start_extra'][h] = list(new)
+    for sec, i, old, new in r['gate_frames']:
+        if sec in ('A', 'B'):
+            assert span(nw[sec][i][-1]) == span(old), ('gate frame mismatch', sec, i)
+            nw[sec][i][-1] = list(span(new))
+        else:
+            assert sec == 'T' and span(nw['early_cleanup'][i][1]) == span(old), ('tail frame mismatch', i)
+            nw['early_cleanup'][i][1] = list(span(new))
+    old_prof, new_prof = chain_profile(w), chain_profile(nw)
+    lp = Counter({int(k): c for k, c in w['report']['local_profile'].items()}); lp.subtract(old_prof); lp.update(new_prof)
+    assert min(lp.values()) >= 0
+    inv = widths(nw)
+    rep = dict(w['report'])
+    rep['local_profile'] = {str(k): c for k, c in sorted(lp.items()) if c}
+    rep['local_rank_mass'] = sum(k*c for k, c in lp.items())
+    rep['width_inventory'] = {str(k): c for k, c in sorted(inv.items()) if c}
+    nw['report'] = rep
+    return nw
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(); ap.add_argument('--input', type=Path, required=True)
+    ap.add_argument('--recipe', type=Path, required=True); ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    raw = gzip.decompress(a.input.read_bytes()); r = json.loads(a.recipe.read_text())
+    assert hashlib.sha256(raw).hexdigest() == r['input_content_sha256'], 'input word pin'
+    nw = apply(json.loads(raw), r)
+    data = json.dumps(nw, separators=(',', ':')).encode()
+    x = r['expected']
+    assert nw['report']['local_profile'] == x['local_profile'], 'profile pin'
+    assert nw['report']['width_inventory'] == x['width_inventory'], 'width pin'
+    assert hashlib.sha256(data).hexdigest() == x['output_content_sha256'], 'output word pin'
+    a.out.mkdir(parents=True, exist_ok=True)
+    (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+    print('PASS', len(r['entrances']), 'promoted entrances;', len(r['gate_frames']), 'gate frames;',
+          'profile', x['local_profile'], 'sha', x['output_content_sha256'])
diff --git a/research/gauge44-leaver8/construction/promo/make_recipe.py b/research/gauge44-leaver8/construction/promo/make_recipe.py
new file mode 100644
index 0000000000..618d609453
--- /dev/null
+++ b/research/gauge44-leaver8/construction/promo/make_recipe.py
@@ -0,0 +1,12 @@
+"""make_recipe.py BASEWORD SOLUTION.json BUILTWORD OUT: discovery-side recipe writer (CP-SAT solution -> data recipe)."""
+import sys, json, gzip, hashlib
+base = gzip.decompress(open(sys.argv[1], 'rb').read()); s = json.load(open(sys.argv[2]))
+built = gzip.decompress(open(sys.argv[3], 'rb').read()); bw = json.loads(built)
+key = {'A': 0, 'B': 1, 'T': 2}
+r = dict(input_content_sha256=hashlib.sha256(base).hexdigest(),
+         groups=sorted(int(h) for h in s['newstarts']),
+         entrances={h: s['newstarts'][h] for h in sorted(s['newstarts'], key=int)},
+         gate_frames=sorted(s['changed'], key=lambda c: (key[c[0]], c[1])),
+         expected=dict(output_content_sha256=hashlib.sha256(built).hexdigest(),
+                       local_profile=bw['report']['local_profile'], width_inventory=bw['report']['width_inventory']))
+json.dump(r, open(sys.argv[4], 'w'), indent=1)
diff --git a/research/gauge44-leaver8/construction/promo/promo_controls.py b/research/gauge44-leaver8/construction/promo/promo_controls.py
new file mode 100644
index 0000000000..20ee51f7db
--- /dev/null
+++ b/research/gauge44-leaver8/construction/promo/promo_controls.py
@@ -0,0 +1,115 @@
+"""Promotion controls: mutate the promoted word / recipe and require rejection at a pinned site.  Apache-2.0.
+BlockInvert (Claude Code research agent).
+
+usage: promo_controls.py --input BASE-FULL-WORD.json.gz --recipe PROMO-RECIPE.json --audit audit_local.py --out CONTROLS.json
+
+Word-level mutants are checked by the independent audit (audit_local.py, imported from the given path; it shares no
+code with the constructor); recipe-level mutants by build_promotion.apply / its pins.  Each mutant must raise with the
+pinned message prefix; the honest word must pass both."""
+import argparse, gzip, hashlib, importlib.util, json, sys, tempfile
+from pathlib import Path
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+import build_promotion as B
+
+ap = argparse.ArgumentParser()
+for k in ('input', 'recipe', 'audit', 'out'): ap.add_argument('--' + k, type=Path, required=True)
+a = ap.parse_args()
+s = importlib.util.spec_from_file_location('audit_local', a.audit); AL = importlib.util.module_from_spec(s); s.loader.exec_module(AL)
+raw = gzip.decompress(a.input.read_bytes()); base = json.loads(raw); r = json.loads(a.recipe.read_text())
+assert hashlib.sha256(raw).hexdigest() == r['input_content_sha256']
+honest = B.apply(base, r)
+v = base['report']['v']
+tmp = Path(tempfile.mkdtemp())
+
+
+def audit(w):
+    p = tmp / 'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w, separators=(',', ':')).encode(), mtime=0))
+    import io, contextlib
+    with contextlib.redirect_stdout(io.StringIO()):
+        AL.run(p, tmp / 'r.json')
+
+
+def first_gate(w, h):
+    for sec in ('A', 'B'):
+        for i, e in enumerate(w[sec]):
+            if h in B.regs(e): return sec, i
+    raise AssertionError(h)
+
+
+results = []
+
+
+def expect(name, fn, prefix):
+    try:
+        fn(); got = 'ACCEPTED'
+    except (RuntimeError, AssertionError) as e:
+        got = str(e.args[0]) if e.args else type(e).__name__
+    ok = got.startswith(prefix)
+    results.append(dict(control=name, expected=prefix, got=got[:160], rejected_at_pinned_site=ok))
+    print(('OK  ' if ok else 'BAD ') + name + ': ' + got[:120], flush=True)
+
+
+# honest
+audit(honest); print('honest word: audit PASS', flush=True)
+H = sorted(int(h) for h in r['entrances'])
+h0 = str(H[0]); E5 = B.span(r['entrances'][h0]); sec, i = first_gate(honest, int(h0)); F1 = B.span(honest[sec][i][-1])
+full = B.span([1 << k for k in range(9)])
+
+
+def mut(f):
+    w = json.loads(json.dumps(honest)); f(w); return w
+
+
+# 1. promoted entrance moved to a dim-5 frame NOT inside its first gate frame
+def bad_entrance(w):
+    for x in range(1, 512):
+        G = B.span(list(B.span(base['start_extra'][h0])) + [x])
+        if len(G) == 5 and B.span(list(G) + list(F1)) != F1:
+            w['start_extra'][h0] = list(G); return
+    raise AssertionError('no frame')
+expect('entrance_outside_first_gate_frame', lambda: audit(mut(bad_entrance)), 'frame not monotone')
+# 2. a raised gauge gate of a promoted helper left at its old (E4) frame
+old_of = {(c[0], c[1]): c[2] for c in r['gate_frames']}
+assert (sec, i) in old_of, 'first gate of a promoted helper is a raised gate'
+expect('raised_gate_missing', lambda: audit(mut(lambda w: w[sec][i].__setitem__(-1, list(B.span(old_of[(sec, i)]))))), 'frame not monotone')
+# 2b. per promoted group: its first helper's raised entry gate left at the old frame
+for hg in H[4::4]:
+    sg, ig = first_gate(honest, hg)
+    if (sg, ig) in old_of:
+        expect('raised_gate_missing_group_%d' % hg, lambda sg=sg, ig=ig: audit(mut(lambda w: w[sg][ig].__setitem__(-1, list(B.span(old_of[(sg, ig)]))))), 'frame not monotone')
+# 3. every raised gate kept but one entrance reverted to E4 (report kept): the paid profile no longer matches
+expect('entrance_reverted_profile', lambda: audit(mut(lambda w: w['start_extra'].__setitem__(h0, list(B.span(base['start_extra'][h0]))))), 'paid profile mismatch')
+# 4. an E4 helper outside the promoted groups promoted alone (no raised gates)
+others = sorted(int(h) for h, f in base['start_extra'].items() if len(B.span(f)) == 4 and h not in r['entrances'])
+if others:
+    h1 = str(others[0])
+    expect('ungrouped_promotion', lambda: audit(mut(lambda w: w['start_extra'].__setitem__(h1, list(E5)))), 'frame not monotone')
+# 5. recipe-level: wrong old frame for a raised gate; non-promotion entrance; input pin
+def r_bad_old():
+    q = json.loads(json.dumps(r)); q['gate_frames'][0][2] = list(full); B.apply(base, q)
+expect('recipe_gate_old_frame', r_bad_old, "('gate frame mismatch'" if r['gate_frames'][0][0] != 'T' else "('tail frame mismatch'")
+def r_demote():
+    q = json.loads(json.dumps(r)); q['entrances'][h0] = base['start_extra'][h0]; B.apply(base, q)
+expect('recipe_not_a_promotion', r_demote, "('not a promotion'")
+def r_pin():   # the driver's own __main__ path on a tampered input word (one gate scalar changed)
+    import subprocess
+    t = json.loads(raw); e = t['B'][0]
+    if e[0] == 'add': e[3] += e[4]
+    else: e[2] = -e[2]
+    p = tmp / 'tampered.json.gz'; p.write_bytes(gzip.compress(json.dumps(t, separators=(',', ':')).encode(), mtime=0))
+    q = subprocess.run([sys.executable, '-B', str(Path(B.__file__)), '--input', str(p), '--recipe', str(a.recipe), '--out', str(tmp / 'o')],
+                       capture_output=True, text=True)
+    assert q.returncode == 0, q.stderr.strip().splitlines()[-1].split('AssertionError: ', 1)[-1]
+expect('recipe_input_pin', r_pin, 'input word pin')
+# 6. scalar tamper inside a promoted group's raised gate (frames intact): exactness must fail
+def scal(w):
+    e = w[sec][i]
+    if e[0] == 'add': e[3] = e[3] + e[4]
+    else: e[2] = -e[2]
+expect('raised_gate_scalar_tamper', lambda: audit(mut(scal)), '')
+results[-1]['rejected_at_pinned_site'] = results[-1]['got'] != 'ACCEPTED'
+bad = [x for x in results if not x['rejected_at_pinned_site']]
+a.out.write_text(json.dumps(dict(recipe=r['expected']['output_content_sha256'], honest='PASS', controls=results,
+                                 rejected=len(results) - len(bad)), indent=1))
+assert not bad, bad
+print('PASS', len(results), 'controls rejected at pinned sites')
diff --git a/research/gauge44-leaver8/construction/promo/reproduce_promo.py b/research/gauge44-leaver8/construction/promo/reproduce_promo.py
new file mode 100644
index 0000000000..6e04aa71b1
--- /dev/null
+++ b/research/gauge44-leaver8/construction/promo/reproduce_promo.py
@@ -0,0 +1,99 @@
+#!/usr/bin/env python3
+"""Rebuild a promoted no-triangle layered word (entrance promotions E4 -> E5) and its native locals.
+
+Input (--base): `np` = a fresh `construction/layers_np/reproduce_np.py` output (word a9de804f...), or `p6n` = a fresh
+`construction/layers_p6n/reproduce_p6n.py` output (word 34b683fa...). Recipe k: PROMO-RECIPE-<k>.json (BlockInvert;
+data only; it pins its input word) and LOCAL-PINS-<k>.json. Steps, each
+checked exactly:
+  1. promotion: BlockInvert's build_promotion.py. It pins the input word and the recipe's output sha, profile and
+     widths; every old frame must match the input; only frame annotations and start frames move (no scalar change).
+  2. promo-controls: BlockInvert's promo_controls.py. The honest word must pass #645's independent audit_local.py,
+     and its recipe- and word-level mutants must be rejected at their pinned sites (count pinned in LOCAL-PINS).
+  3. layer-end-controls on the promoted word, pinned count: ../layers/layer_end_controls.py (LayerReviewer-signed) for
+     base np; ../layers_p6n/layer_end_controls.py (Q6Reviewer-signed per-end variant) for base p6n.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs; the canonical word, local
+     programs and Clifford recipes are pinned (LOCAL-PINS).
+Moving to another recipe k is a recipe and pins swap; this driver does not change.
+Apache-2.0. Driver by ColdWitness around BlockInvert's constructor and controls.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+PKG = HERE.parents[1]
+LAYERS = HERE.parent / 'layers'
+BASES = {'np': ('layers/FULL-WORD.json.gz', 'a9de804f194eeb39f52a4c6e54c14d93e881bec4b632694249733ed410b58113'),
+         'p6n': ('p6n/FULL-WORD.json.gz', '34b683fa08f0')}   # p6n: prefix; full pin is the p6n recipe's output sha
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--base', choices=sorted(BASES), default='p6n')
+    ap.add_argument('--base-dir', type=Path, required=True, help='reproduce_np.py (np) or reproduce_p6n.py (p6n) output')
+    ap.add_argument('--k', default='p6n-k4', help='recipe id (PROMO-RECIPE-<k>.json)')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    recipe = HERE / ('PROMO-RECIPE-%s.json' % a.k); pins = read(HERE / ('LOCAL-PINS-%s.json' % a.k))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    rel, pin = BASES[a.base]; inp = a.base_dir.resolve() / rel
+    got = hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest()
+    assert got.startswith(pin) and got == read(recipe)['input_content_sha256'], ('input must be the pinned base word', a.base, got)
+    if a.base == 'p6n':
+        assert got == read(HERE.parent / 'layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz')['output_content_sha256']
+    run('promotion', HERE / 'build_promotion.py', '--input', inp, '--recipe', recipe, '--out', out / 'promo', portable=False)
+    word = out / 'promo/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == read(recipe)['expected']['output_content_sha256']
+    run('promo-controls', HERE / 'promo_controls.py', '--input', inp, '--recipe', recipe,
+        '--audit', PKG / 'independent/audit_local.py', '--out', out / 'PROMO-CONTROLS.json', portable=False)
+    pc = read(out / 'PROMO-CONTROLS.json'); assert pc['honest'] == 'PASS' and pc['rejected'] == pins['promo_controls'], pc['rejected']
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    ctlpy = (HERE.parent / 'layers_p6n/layer_end_controls.py') if a.base == 'p6n' else (LAYERS / 'layer_end_controls.py')
+    run('layer-end-controls', ctlpy, word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/reproduce.py b/research/gauge44-leaver8/construction/reproduce.py
new file mode 100644
index 0000000000..8b51efa646
--- /dev/null
+++ b/research/gauge44-leaver8/construction/reproduce.py
@@ -0,0 +1,194 @@
+#!/usr/bin/env python3
+"""Rebuild the frozen gauge44 delta from two pinned upstream checkouts.
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+This driver calls the credited upstream constructors unchanged; it runs no
+search or optimizer. See ../CONSTRUCTION.md and INPUTS.json.
+"""
+import argparse
+import gzip
+import hashlib
+import importlib.util
+import json
+import os
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import time
+
+HERE = Path(__file__).resolve().parent
+
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw)
+
+
+def sha(path, content=False):
+    raw = path.read_bytes()
+    if content and path.suffix == '.gz':
+        raw = gzip.decompress(raw)
+    return hashlib.sha256(raw).hexdigest()
+
+
+def dump(path, value):
+    path.parent.mkdir(parents=True, exist_ok=True)
+    raw = json.dumps(value, sort_keys=True, separators=(',', ':')).encode()
+    path.write_bytes(gzip.compress(raw, mtime=0) if path.suffix == '.gz' else raw)
+
+
+def load_module(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def main():
+    assert __debug__, 'Assertions are required; do not use python -O.'
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--main', type=Path, required=True,
+                        help='integer-mult-bounds checkout at the pinned main commit')
+    parser.add_argument('--pr635', type=Path, required=True,
+                        help='integer-mult-bounds checkout at the pinned PR635 commit')
+    parser.add_argument('--out', type=Path, required=True,
+                        help='new output directory outside both checkouts')
+    parser.add_argument('--until', choices=('word', 'local', 'phases'), default='word',
+                        help='default: scalar constructor only; local adds exact native replay and wrappers')
+    parser.add_argument('--frozen-cold', action='store_true',
+                        help='splice the pinned cold recipe instead of deriving its exact Q/T matrices again')
+    args = parser.parse_args()
+    roots = {'main': args.main.resolve(), 'pr635': args.pr635.resolve(), 'delta': HERE}
+    out = args.out.resolve()
+    assert not out.exists(), 'Use a new output directory.'
+    assert not any(out.is_relative_to(root) for root in roots.values())
+    pins = read(HERE / 'INPUTS.json')
+    for family, files in pins['files'].items():
+        for relative, expected in files.items():
+            path = roots[family] / relative
+            assert sha(path) == expected, ('input pin', family, relative)
+    out.mkdir(parents=True)
+    upstream = roots['pr635'] / 'research/complex-571-cold14-st2'
+    source = roots['main'] / 'research/complex-k492-owner-repair/vendor/multicold'
+    joint = source.parent / 'joint_prefix'
+    base = source / 'vendor/pr558'
+    parent = base / 'vendor/pr552'
+    gk = parent / 'complex-local/static44/gk'
+    hamming = source.parent / 'direct_delivery/inputs/hamming'
+    structural = roots['main'] / 'research/structural-gain/frontier-composition'
+    runner = source / 'code/run_portable.py'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1',
+               PYTHONINTMAXSTRDIGITS='0', MULTICOLD_SOURCE=str(source),
+               GAIN_PR564_SOURCE=str(source))
+    env.pop('PYTHONOPTIMIZE', None)
+    records = []
+
+    def run(label, script, *arguments):
+        start = time.monotonic()
+        log = out / (label + '.log')
+        print('RUN', label, flush=True)
+        with log.open('w', encoding='utf-8') as stream:
+            result = subprocess.run([sys.executable, '-B', str(runner), str(script),
+                                     *map(str, arguments)], env=env, stdout=stream,
+                                    stderr=subprocess.STDOUT)
+        records.append({'step': label, 'exit_code': result.returncode,
+                        'seconds': round(time.monotonic() - start, 3)})
+        (out / 'STEPS.json').write_text(json.dumps(records, indent=2) + '\n')
+        if result.returncode:
+            raise RuntimeError(label + '\n' + log.read_text()[-6000:])
+        print('PASS', label, flush=True)
+
+    def check_word(label, path):
+        assert sha(path, content=True) == pins['word_content_sha256'][label], ('step pin', label)
+        return path
+
+    raw504 = parent / 'complex-local/static44/inputs/RAW504.json.gz'
+    promoted = structural / 'global-replay/base/split-centres/FULL-WORD.json.gz'
+    multi = structural / 'multicold-eight-word/FULL-WORD.json.gz'
+    early = out / 'shadow-early'
+    run('shadow-early', source / 'code/build_cold_kernel.py', '--input', promoted,
+        '--recipe', source / 'data/EIGHT-COLD.json', '--gk-dir', gk, '--out', early)
+    early_word = check_word('shadow-early', early / 'FULL-WORD.json.gz')
+    prefix = out / 'shadow-prefix'
+    run('shadow-prefix', joint / 'code/build_joint_prefix.py', '--input', multi,
+        '--recipe', joint / 'data/JOINT-PREFIX.json', '--variant', 'eightcold',
+        '--gk-dir', gk, '--out', prefix)
+    prefix_word = check_word('shadow-prefix', prefix / 'FULL-WORD.json.gz')
+
+    inputs = out / 'hamming'
+    inputs.mkdir()
+    for name in ('PROTOTYPE.json', 'PACKET-PROGRAMS.json.gz'):
+        shutil.copyfile(hamming / name, inputs / name)
+    shutil.copyfile(HERE / 'COMPLETION-PRIORITY.json', inputs / 'COMPLETION-PRIORITY.json')
+    raw = out / 'raw'
+    run('gauge-forward', HERE / 'construct_gauge_xcentre.py', inputs, raw,
+        upstream / 'data/TRI-SCHEDULE.json')
+    word = check_word('raw', raw / 'FULL-WORD.json.gz')
+    assert sha(raw / 'HELPER-MAP.json') == pins['helper_map_sha256']
+    chain = [raw504, promoted, early_word, multi, prefix_word]
+    for i, (before, after) in enumerate(zip(chain, chain[1:])):
+        target = out / ('port' + str(i))
+        run('port' + str(i), upstream / 'code/build_port_stage.py',
+            '--shadow-input', before, '--shadow-output', after, '--input', word,
+            '--map', raw / 'HELPER-MAP.json', '--gk-dir', gk, '--out', target)
+        word = check_word('port' + str(i), target / 'FULL-WORD.json.gz')
+
+    changed = read(word)
+    regroup = read(upstream / 'data/recipes/k492-jp8-frame_regroup.json')
+    # The inherited changes are B-only and are checked against the actual new gates.
+    for edit in regroup['changes']:
+        assert changed[edit['section']][edit['index']] == edit['before']
+        changed[edit['section']][edit['index']] = edit['after']
+    changed['report'].update(local_profile=regroup['after'],
+                             local_rank_mass=sum(int(r)*n for r, n in regroup['after'].items()))
+    word = out / 'regroup/FULL-WORD.json.gz'
+    dump(word, changed)
+    check_word('regroup', word)
+    hpe = load_module('upstream_hpe', upstream / 'code/build_hpe.py')
+    changed = hpe.apply(changed, read(upstream / 'data/recipes/k492-jp8-hyperplane_end.json')['changes'])
+    word = out / 'hpe/FULL-WORD.json.gz'
+    dump(word, changed)
+    check_word('hpe', word)
+
+    target = out / 'cold44'
+    if args.frozen_cold:
+        cold = load_module('upstream_cold', upstream / 'code/build_cold_end.py')
+        changed = cold.apply(changed, read(HERE / 'COLD44-RECIPE.json.gz'))
+        # Match the exact constructor's descriptive status; this is not an audit assertion.
+        changed['report']['status'] = 'EXACT_COLD44_CONSTRUCTED_PENDING_INDEPENDENT_AUDIT'
+        dump(target / 'FULL-WORD.json.gz', changed)
+    else:
+        run('cold44-exact', HERE / 'build_gauge_cold44.py', '--input', word,
+            '--out', target, '--hamming', inputs, '--upstream-package', upstream)
+        assert read(target / 'RECIPE.json.gz') == read(HERE / 'COLD44-RECIPE.json.gz')
+    word = check_word('cold44', target / 'FULL-WORD.json.gz')
+    report = read(word)['report']
+    assert report['local_rank_mass'] == 5650
+    assert report['local_profile'] == {'1': 2514, '2': 404, '3': 448, '4': 160, '5': 56, '8': 8}
+    assert report['width_inventory'] == {'4': 52, '5': 48, '7': 34, '8': 114, '9': 244}
+    print('PASS exact frozen scalar word', word, flush=True)
+    if args.until == 'word':
+        return
+
+    local = out / 'local'
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    run('native', upstream / 'code/hpe_audit_and_transport.py', '--raw', word,
+        '--routing', routing, '--out', local)
+    assert sha(local / 'CANONICAL-WORD.json.gz', content=True) == pins['canonical_content_sha256']
+    run('ledgers', upstream / 'code/hpe_emit_local.py', local)
+    run('local-replay', upstream / 'code/hpe_audit_local.py', local)
+    run('wrappers', upstream / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for orientation, expected in pins['local_program_sha256'].items():
+        assert checks[orientation]['sha256'] == expected
+    if args.until == 'phases':
+        clifford = parent / 'complex-global/vendor531/vendor/clifford'
+        run('phases', base / 'code/phases_full.py', local, clifford)
+        assert sha(local / 'CLIFFORD-RECIPES.json') == pins['clifford_recipes_sha256']
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/sw4/LOCAL-PINS-sw4-P6k4.json b/research/gauge44-leaver8/construction/sw4/LOCAL-PINS-sw4-P6k4.json
new file mode 100644
index 0000000000..ae26a0f2f1
--- /dev/null
+++ b/research/gauge44-leaver8/construction/sw4/LOCAL-PINS-sw4-P6k4.json
@@ -0,0 +1,11 @@
+{
+ "word": "P6k4sw4",
+ "sw4_controls": 4,
+ "layer_controls": 95,
+ "canonical_sha256": "5f5f163e43e8c21c16e2f10aef0078131d127a1ccacc39e0238d111fbd29f195",
+ "program_sha256": {
+  "forward": "36e75fc972766fa42f1b371a055e74976a165c894b816911c3510a88b431ea09",
+  "backward": "3176ccde98d90e754105e60096598fee348e2455e046290d3674b79dd6b402df"
+ },
+ "clifford_recipes_sha256": "202eeaf5fac0c801b98811c1e140fd0af443090d7f7e05c7b55a4ddc6f6acdab"
+}
diff --git a/research/gauge44-leaver8/construction/sw4/NOTES.md b/research/gauge44-leaver8/construction/sw4/NOTES.md
new file mode 100644
index 0000000000..2a53ffb3b8
--- /dev/null
+++ b/research/gauge44-leaver8/construction/sw4/NOTES.md
@@ -0,0 +1,21 @@
+# SW4: read-set exchange on 4 entering-copy pairs
+
+- **Input.** P6k3, sha a38bb414.
+- **Output.** sha f35a852b. Strict PASS at κ 0.001659645685315104, which is +3.267e-7 over P6k3 and equal to the ideal.
+- **Width.** W 3782 is unchanged, as are start_extra, helper_final, cleanup and the helper numbering.
+- **Rebuild.** `python build_sw4.py INPUT OUT [SW4-RECIPE.json]`. It is a deterministic apply of the 16 explicit moves, with 4 pinned controls: C0 (identity), N1 (keeping the pre-read is rejected), N2 (a partial exchange is rejected) and N3 (a wrong-sign pre-read is rejected).
+
+## Move
+For each pair (h,r) in {(461,25), (581,89), (591,415), (603,431)}, where h = E_h + r after h's copy gate:
+- every post-copy target read of h becomes a read of r, and that target's entrance pre-read of h is deleted;
+- every target read of r becomes a read of h, with the pre-read add(t,h,−c) inserted after h's last pre-read, while h = E_h.
+
+The B-end state of every register is unchanged (checked mod p).
+
+## How exhaustive the search was
+These 4 are the only positives within an exactly defined family.
+- **Copy pair.** h is an entering helper whose first B write is add(h,r,1/1) from a non-target r, and whose only earlier B gates are single target pre-reads. NP has 107 such pairs.
+- **Candidates.** Every nonempty subset of one pair's movable reads (target reads of h or r between the copy and the next write of h or r), with all other pairs left unchanged. That is 602 candidates over the 54 pairs that have reads.
+- **Outcome.** 564 are frame-illegal. The 38 legal ones are all full single-pair exchanges, and only these 4 are positive. Their gains are additive.
+
+**What is not covered.** Cross-pair combinations of partial moves were not enumerated. Without a decomposition proof (moves can shrink as well as grow target frames), the result is exhaustive only within this single-pair family.
diff --git a/research/gauge44-leaver8/construction/sw4/SW4-RECIPE-P6k4.json b/research/gauge44-leaver8/construction/sw4/SW4-RECIPE-P6k4.json
new file mode 100644
index 0000000000..b9dea4152a
--- /dev/null
+++ b/research/gauge44-leaver8/construction/sw4/SW4-RECIPE-P6k4.json
@@ -0,0 +1,314 @@
+{
+ "name": "SW4",
+ "description": "BRoute read-set exchange on entering-copy pairs (h,r); indices refer to the input word B section",
+ "input_sha256": "0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073",
+ "output_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+ "pairs": {
+  "461": 25,
+  "581": 89,
+  "591": 415,
+  "603": 431
+ },
+ "moves": [
+  {
+   "kind": "h2r",
+   "h": 461,
+   "r": 25,
+   "read_index": 856,
+   "target": 168,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 27
+  },
+  {
+   "kind": "h2r",
+   "h": 461,
+   "r": 25,
+   "read_index": 1208,
+   "target": 128,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 26
+  },
+  {
+   "kind": "r2h",
+   "h": 461,
+   "r": 25,
+   "read_index": 873,
+   "target": 129,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 28,
+   "preread": [
+    "add",
+    129,
+    461,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 461,
+   "r": 25,
+   "read_index": 1193,
+   "target": 169,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 28,
+   "preread": [
+    "add",
+    169,
+    461,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 581,
+   "r": 89,
+   "read_index": 860,
+   "target": 171,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 58
+  },
+  {
+   "kind": "h2r",
+   "h": 581,
+   "r": 89,
+   "read_index": 1288,
+   "target": 192,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 59
+  },
+  {
+   "kind": "r2h",
+   "h": 581,
+   "r": 89,
+   "read_index": 953,
+   "target": 193,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 60,
+   "preread": [
+    "add",
+    193,
+    581,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 581,
+   "r": 89,
+   "read_index": 1197,
+   "target": 175,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 60,
+   "preread": [
+    "add",
+    175,
+    581,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 591,
+   "r": 415,
+   "read_index": 868,
+   "target": 139,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 62
+  },
+  {
+   "kind": "h2r",
+   "h": 591,
+   "r": 415,
+   "read_index": 1296,
+   "target": 160,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 63
+  },
+  {
+   "kind": "r2h",
+   "h": 591,
+   "r": 415,
+   "read_index": 961,
+   "target": 161,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 64,
+   "preread": [
+    "add",
+    161,
+    591,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 591,
+   "r": 415,
+   "read_index": 1205,
+   "target": 143,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 64,
+   "preread": [
+    "add",
+    143,
+    591,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 603,
+   "r": 431,
+   "read_index": 876,
+   "target": 131,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 70
+  },
+  {
+   "kind": "h2r",
+   "h": 603,
+   "r": 431,
+   "read_index": 1300,
+   "target": 163,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 71
+  },
+  {
+   "kind": "r2h",
+   "h": 603,
+   "r": 431,
+   "read_index": 965,
+   "target": 167,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 72,
+   "preread": [
+    "add",
+    167,
+    603,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 603,
+   "r": 431,
+   "read_index": 1213,
+   "target": 135,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 72,
+   "preread": [
+    "add",
+    135,
+    603,
+    -1,
+    1
+   ]
+  }
+ ],
+ "kappa_ideal_in": 0.0016603565408383088,
+ "kappa_ideal_out": 0.0016606836036204419,
+ "W": 3778,
+ "profile_in": {
+  "1": 2572,
+  "2": 326,
+  "3": 430,
+  "4": 194,
+  "5": 56,
+  "8": 8
+ },
+ "profile_out": {
+  "1": 2548,
+  "2": 342,
+  "3": 438,
+  "4": 186,
+  "5": 56,
+  "8": 8
+ },
+ "width_inventory": {
+  "4": 80,
+  "5": 32,
+  "7": 54,
+  "8": 122,
+  "9": 216
+ },
+ "rejection_expected": {
+  "N1": {
+   "changed_registers": [
+    168,
+    171
+   ],
+   "n": 2
+  },
+  "N2": {
+   "first": [
+    "cap",
+    1192,
+    169
+   ],
+   "n": 10
+  },
+  "N3": {
+   "changed_registers": [
+    129,
+    130,
+    169,
+    170
+   ],
+   "n": 4
+  }
+ }
+}
diff --git a/research/gauge44-leaver8/construction/sw4/build_sw4.py b/research/gauge44-leaver8/construction/sw4/build_sw4.py
new file mode 100644
index 0000000000..617e0ed06d
--- /dev/null
+++ b/research/gauge44-leaver8/construction/sw4/build_sw4.py
@@ -0,0 +1,203 @@
+#!/usr/bin/env python3
+"""build_sw4.py INPUT_WORD OUT_DIR [RECIPE] : deterministic, standard-library-only rebuild of the BRoute SW4 word.
+
+SW4 exchanges the B-phase target read sets of four entering packet copies h and their face registers r
+(h = E_h + r after h's copy gate; E_h = h's entering content):
+  h2r: a post-copy read add(t,h,c) becomes add(t,r,c), and t's entrance pre-read add(t,h,-c) (taken while h = E_h) is deleted;
+  r2h: a read add(t,r,c) becomes add(t,h,c), and a pre-read add(t,h,-c) is inserted before index insert_preread_before
+       (right after h's last existing pre-read, still before h's copy gate).
+Every register holds the same value at the end of B (checked mod p). Frames: a moved or inserted gate gets the plain join of
+its operands' current frames; every other B gate and every early-cleanup tail keeps span(old frame + current operand frames).
+Targets must stay inside u_t^perp, and tails and ends must contain the current frame.
+
+Controls (run on every build; the count is pinned to 4 and all must hold, else exit 1):
+  C0 the identity recipe (no moves) reproduces the input B and early_cleanup byte for byte;
+  N1 h2r without deleting the pre-read is rejected by exactness;
+  N2 a partial exchange (one read only) is rejected by the frame cap;
+  N3 an inserted pre-read with the wrong sign is rejected by exactness.
+Rejection sites are pinned: the recipe's 'rejection_expected' gives, for N1/N3, the exact set of target rows whose B-end
+state changes (the mutated target plus its butterfly partner(s)) and, for N2, the first cap violation (kind, B index,
+register) and the violation count. Each control must reproduce its pinned site exactly. BUILD.json records the observed
+sites under 'rejection'.
+Writes OUT_DIR/FULL-WORD.json.gz (sha checked against the recipe) and OUT_DIR/BUILD.json."""
+import sys, json, gzip, hashlib, os
+from collections import Counter, defaultdict
+
+PR = 2147483629
+HERE = os.path.dirname(os.path.abspath(__file__))
+V, HH = 112, 9
+
+
+def basis(vs):
+    piv = {}
+    for a in vs:
+        while a:
+            bit = a.bit_length() - 1
+            if bit in piv: a ^= piv[bit]
+            else:
+                piv[bit] = a; break
+    for k in sorted(piv):
+        for j in piv:
+            if j > k and piv[j] >> k & 1: piv[j] ^= piv[k]
+    return tuple(piv[k] for k in sorted(piv, reverse=True))
+
+
+def contained(a, b): return basis(list(a) + list(b)) == tuple(b)
+def registers(e): return e[1:3] if e[0] == 'add' else e[1:2]
+def hyper(p): return basis([x for x in range(1, 1 << HH) if (x & p).bit_count() % 2 == 0])
+FULL = basis([1 << i for i in range(HH)])
+
+
+def coef(e):
+    a, b = (e[3], e[4]) if e[0] == 'add' else (e[2], e[3])
+    return a % PR * pow(b % PR, PR - 2, PR) % PR
+
+
+def bend_state(w):
+    """sparse rows mod p of every register after A + cut + B (identity start)."""
+    n = 2 * V + w['report']['R']; rows = [{i: 1} for i in range(n)]
+    for e in w['A'] + w['cut'] + w['B']:
+        q = coef(e); t = e[1]
+        if e[0] == 'scale': rows[t] = {k: x * q % PR for k, x in rows[t].items()}
+        else:
+            d = rows[t]
+            for k, x in rows[e[2]].items():
+                y = (d.get(k, 0) + q * x) % PR
+                if y: d[k] = y
+                else: d.pop(k, None)
+    return rows
+
+
+def apply_recipe(w, moves, drop_delete=False, wrong_sign=False):
+    B = [list(e[:-1]) + [list(e[-1]) if e[-1] is not None else None] for e in w['B']]
+    tag = {}; dele = set(); ins = defaultdict(list)
+    for m in moves:
+        i = m['read_index']; e = B[i]; t = m['target']; a, b = m['coef']
+        assert e[0] == 'add' and e[1] == t and [e[3], e[4]] == [a, b], ('recipe/word mismatch', m)
+        if m['kind'] == 'h2r':
+            assert e[2] == m['h']
+            pi = m['delete_preread_index']; g = B[pi]
+            assert g[:5] == ['add', t, m['h'], -a, b], ('pre-read mismatch', m)
+            B[i] = ['add', t, m['r'], a, b, e[-1]]
+            if not drop_delete: dele.add(pi)
+        else:
+            assert e[2] == m['r']
+            B[i] = ['add', t, m['h'], a, b, e[-1]]
+            g = list(m['preread'])
+            if wrong_sign: g[3] = -g[3]
+            ins[m['insert_preread_before']].append(g + [None])
+        tag[i] = 1
+    NB, nt = [], []
+    for i, e in enumerate(B):
+        for g in ins.get(i, []): NB.append(g); nt.append(1)
+        if i in dele: continue
+        NB.append(e); nt.append(tag.get(i, 0))
+    w2 = dict(w); w2['B'] = NB; w2['early_cleanup'] = [list(x) for x in w.get('early_cleanup', [])]
+    return w2, nt
+
+
+def refit(w, nt):
+    n = 2 * V + w['report']['R']
+    cur = [(p,) for p in w['ports']] + [()] * (n - V)
+    for q, U in w['start_extra'].items(): cur[int(q)] = basis(U)
+    for e in w['A']:
+        for q in registers(e): cur[q] = basis(e[-1])
+    prob = []
+    for i, e in enumerate(w['B']):
+        rs = registers(e)
+        base = [] if nt[i] or e[-1] is None else list(e[-1])
+        F = basis(base + [x for q in rs for x in cur[q]])
+        for q in rs:
+            if V <= q < 2 * V and not contained(F, hyper(w['ports'][q - V])): prob.append(('cap', i, q))
+        e[-1] = list(F)
+        for q in rs: cur[q] = F
+    ne = []
+    for i, U in w.get('early_cleanup', []):
+        rs = registers(w['cleanup'][i]); F = basis(list(U) + [x for q in rs for x in cur[q]])
+        for q in rs:
+            fin = w['helper_final'].get(str(q))
+            if fin is not None and not contained(F, basis(fin)): prob.append(('tail', i, q))
+        ne.append([i, list(F)])
+        for q in rs: cur[q] = F
+    w['early_cleanup'] = ne
+    for q in range(2 * V, n):
+        fin = w['helper_final'].get(str(q))
+        if fin is not None and not contained(cur[q], basis(fin)): prob.append(('end', q))
+    return prob
+
+
+def profile(w):
+    n = 2 * V + w['report']['R']
+    tail = [w['cleanup'][i][:-1] + [U] for i, U in w.get('early_cleanup', [])]
+    end = [FULL] * V + [hyper(p) for p in w['ports']] + [FULL] * (n - 2 * V)
+    for q, U in w['helper_final'].items(): end[int(q)] = basis(U)
+    start = [(p,) for p in w['ports']] + [()] * (n - V)
+    for q, U in w['start_extra'].items(): start[int(q)] = basis(U)
+    cur = list(start); paid = Counter()
+    def climb(q, U):
+        U = basis(U); assert contained(cur[q], U), ('monotone', q)
+        d = len(U) - len(cur[q])
+        if d: paid[d] += 1
+        cur[q] = U
+    for sec in ('A', 'B'):
+        if sec == 'B':
+            lev = {int(t): basis(U) for t, U in w.get('target_levels', {}).items()}
+            for q, U in zip(w['centers'], w['center_frames']):
+                U = basis(U); served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == q}
+                for T in sorted(served, key=lambda x: -len(x)):
+                    if T != U: paid[len(U) - len(T)] += 1
+                    U = T
+        for e in w[sec]:
+            for q in registers(e): climb(q, e[-1])
+    for e in tail:
+        for q in registers(e): climb(q, e[-1])
+    for q, U in enumerate(end): climb(q, U)
+    widths = Counter(len(end[q]) - len(start[q]) for q in range(2 * V, n))
+    return paid, widths
+
+
+def enc(w): return json.dumps(w, sort_keys=True, separators=(',', ':')).encode()
+
+
+def main():
+    src, out = sys.argv[1], sys.argv[2]
+    rec = json.load(open(sys.argv[3] if len(sys.argv) > 3 else os.path.join(HERE, 'SW4-RECIPE.json')))
+    raw = gzip.decompress(open(src, 'rb').read())
+    assert hashlib.sha256(raw).hexdigest() == rec['input_sha256'], 'input sha mismatch'
+    w = json.loads(raw); S0 = bend_state(w); moves = rec['moves']
+    h0 = moves[0]['h']; one = [m for m in moves if m['h'] == h0]
+    ctl = {}; why = {}; EXP = rec.get('rejection_expected', {})
+    if os.environ.get('SW4_PIN') != '1' and set(EXP) != {'N1', 'N2', 'N3'}: raise SystemExit('recipe rejection_expected must pin exactly N1, N2, N3 (set SW4_PIN=1 to record)')
+    def diff(S):
+        d = [q for q in range(len(S0)) if S[q] != S0[q]]
+        return dict(changed_registers=d[:8], n=len(d))
+    w0, nt0 = apply_recipe(w, []); p0 = refit(w0, nt0)
+    ctl['C0_identity'] = not p0 and w0['B'] == w['B'] and w0['early_cleanup'] == w['early_cleanup']
+    m1 = [m for m in one if m['kind'] == 'h2r'][:1]
+    w1, nt1 = apply_recipe(w, m1, drop_delete=True); d1 = diff(bend_state(w1))
+    ctl['N1_keep_preread_rejected'] = d1['n'] > 0 and d1 == EXP.get('N1', d1); why['N1'] = d1
+    w2, nt2 = apply_recipe(w, m1); p2 = refit(w2, nt2)
+    why['N2'] = dict(first=list(p2[0]) if p2 else None, n=len(p2)); ctl['N2_partial_rejected'] = bool(p2) and p2[0][0] == 'cap' and why['N2'] == EXP.get('N2', why['N2'])
+    w3, nt3 = apply_recipe(w, one, wrong_sign=True); d3 = diff(bend_state(w3))
+    ctl['N3_wrong_sign_rejected'] = d3['n'] > 0 and d3 == EXP.get('N3', d3); why['N3'] = d3
+    assert len(ctl) == 4
+    wn, nt = apply_recipe(w, moves); pr = refit(wn, nt)
+    assert not pr, ('illegal', pr[:5])
+    assert bend_state(wn) == S0, 'B-end state changed'
+    paid, widths = profile(wn)
+    wn['report'] = dict(wn['report'], local_profile={str(k): v for k, v in sorted(paid.items())},
+                        local_rank_mass=sum(k * v for k, v in paid.items()))
+    data = enc(wn); sha = hashlib.sha256(data).hexdigest()
+    os.makedirs(out, exist_ok=True)
+    with open(os.path.join(out, 'FULL-WORD.json.gz'), 'wb') as f: f.write(gzip.compress(data, mtime=0))
+    rep = dict(recipe=rec['name'], input_sha256=rec['input_sha256'], output_sha256=sha, expected_output_sha256=rec['output_sha256'],
+               moves=len(moves), controls=ctl, rejection=why, profile=wn['report']['local_profile'],
+               widths={str(k): v for k, v in sorted(widths.items()) if k}, W=sum(k * v for k, v in widths.items()))
+    with open(os.path.join(out, 'BUILD.json'), 'w', newline='\n') as f: f.write(json.dumps(rep, indent=1) + '\n')
+    print(json.dumps(rep, indent=1))
+    ok = all(ctl.values()) and sha == rec['output_sha256'] and rep['profile'] == rec['profile_out'] and rep['W'] == rec['W']
+    sys.exit(0 if ok else 1)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/construction/sw4/reproduce_sw4.py b/research/gauge44-leaver8/construction/sw4/reproduce_sw4.py
new file mode 100644
index 0000000000..cb038e064b
--- /dev/null
+++ b/research/gauge44-leaver8/construction/sw4/reproduce_sw4.py
@@ -0,0 +1,87 @@
+#!/usr/bin/env python3
+"""Rebuild the SW4 word (BRoute read-set exchange on four entering-copy pairs) and its native locals.
+
+Input: a fresh `construction/promo/reproduce_promo.py --base p6n --k <promo recipe>` output directory; its promoted
+word is pinned there and by SW4-RECIPE-<id>.json (this package: --k p6n-k4, P6k4 0390ec65..., recipe P6k4). Steps, each checked exactly:
+  1. sw4: BRoute's build_sw4.py (standard library only). It applies the 16 explicit moves of SW4-RECIPE-<id>.json:
+     every listed read of h becomes a read of its face register r and vice versa, with the entrance pre-reads deleted
+     or inserted. It checks the B-end state of every register mod p, the frame caps, tails and ends, and the output sha
+     and profile. Its controls C0, N1, N2 and N3 run on every build and must all hold (count pinned to 4).
+  2. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant, Q6Reviewer-signed) on the SW4 word;
+     the count is pinned in LOCAL-PINS-sw4-<id>.json.
+  3. native, ledgers, local-replay, wrappers, phases: PR635's native local programs. The canonical word, local
+     programs and Clifford recipes are pinned (LOCAL-PINS-sw4-<id>.json).
+Apache-2.0. Driver by ColdWitness around BRoute's constructor.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P6 = HERE.parent / 'layers_p6n'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--promo-dir', type=Path, required=True, help='construction/promo/reproduce_promo.py output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--recipe', default='P6k4', help='SW4-RECIPE-<id>.json and LOCAL-PINS-sw4-<id>.json')
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('SW4-RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-sw4-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    inp = a.promo_dir.resolve() / 'promo/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['input_sha256'], 'input must be the pinned promoted word'
+    run('sw4', HERE / 'build_sw4.py', inp, out / 'sw4', rfile, portable=False)
+    b = read(out / 'sw4/BUILD.json')
+    assert len(b['controls']) == pins['sw4_controls'] and all(b['controls'].values()), b['controls']
+    word = out / 'sw4/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['output_sha256']
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/data/FRONTIER.json b/research/gauge44-leaver8/data/FRONTIER.json
new file mode 100644
index 0000000000..70285d4d85
--- /dev/null
+++ b/research/gauge44-leaver8/data/FRONTIER.json
@@ -0,0 +1,36 @@
+{
+  "checked_at_utc": "2026-10-13 00:54:29 UTC",
+  "construction_base": {
+    "pr": 635,
+    "commit": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f",
+    "kappa": "0.001636241501576388"
+  },
+  "latest_pr": 642,
+  "strongest_reported_pr": 641,
+  "comparisons": [
+    {
+      "number": 641,
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/641",
+      "title": "Conditional κ = 0.001636523543003976: cost-neutral pivot swaps with four entering ends (s4) on PR635",
+      "head_sha": "ff580ea5407aa427d64233523e46ee0afe24a766",
+      "head_repo": "jeremykothe2/integer-mult-bounds",
+      "created_at": "2026-10-13T00:36:30Z",
+      "updated_at": "2026-10-13T00:36:30Z",
+      "reported_kappa": "0.001636523543003976"
+    },
+    {
+      "number": 642,
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/642",
+      "title": "Conditional κ = 0.001636472098484378: selective helper-249 dispatch",
+      "head_sha": "d1154e23e13d85fdbf64d4b41fa20bb0f56a428f",
+      "head_repo": "vectorsss/integer-mult-bounds",
+      "created_at": "2026-10-13T00:40:40Z",
+      "updated_at": "2026-10-13T00:46:54Z",
+      "reported_kappa": "0.001636472098484378"
+    }
+  ],
+  "new_kappa": "0.001649483702558979",
+  "gain_over_641_percent": "0.791932362379189601995955118466917211009518325743405547289975",
+  "gain_over_642_percent": "0.795100881136422911010672021375626721886288268207407873093008",
+  "scope": "PR641/642 values are their public reported conditional witnesses, not independently replayed here. This delta retains the pinned PR635 construction ancestry and replaces its local supplier and whole-owner dispatch; it does not claim to compose the later pivot swaps or helper249 end."
+}
diff --git a/research/gauge44-leaver8/data/OWNERS.json.gz b/research/gauge44-leaver8/data/OWNERS.json.gz
new file mode 100644
index 0000000000..8eda84ea0c
Binary files /dev/null and b/research/gauge44-leaver8/data/OWNERS.json.gz differ
diff --git a/research/gauge44-leaver8/data/PLAN.json b/research/gauge44-leaver8/data/PLAN.json
new file mode 100644
index 0000000000..4f17b4ccf3
--- /dev/null
+++ b/research/gauge44-leaver8/data/PLAN.json
@@ -0,0 +1,40249 @@
+{
+  "status": "FROZEN_EXPLICIT_GAUGE44_WHOLE_OWNER_NOMINATION",
+  "mode": "gauge44-all72",
+  "K": 4,
+  "T": 8,
+  "M": 73,
+  "L": 9,
+  "live": 7168,
+  "deficit": 2560,
+  "profile": {
+    "1": 174763,
+    "2": 30105,
+    "3": 30275,
+    "4": 12240,
+    "5": 4896,
+    "7": 54,
+    "8": 576,
+    "16": 23,
+    "48": 2419
+  },
+  "order": [
+    [
+      0,
+      0
+    ],
+    [
+      0,
+      1
+    ],
+    [
+      1,
+      0
+    ],
+    [
+      0,
+      2
+    ],
+    [
+      1,
+      1
+    ],
+    [
+      2,
+      0
+    ],
+    [
+      0,
+      3
+    ],
+    [
+      1,
+      2
+    ],
+    [
+      2,
+      1
+    ],
+    [
+      3,
+      0
+    ],
+    [
+      0,
+      4
+    ],
+    [
+      1,
+      3
+    ],
+    [
+      2,
+      2
+    ],
+    [
+      3,
+      1
+    ],
+    [
+      4,
+      0
+    ],
+    [
+      0,
+      5
+    ],
+    [
+      1,
+      4
+    ],
+    [
+      2,
+      3
+    ],
+    [
+      3,
+      2
+    ],
+    [
+      4,
+      1
+    ],
+    [
+      5,
+      0
+    ],
+    [
+      0,
+      6
+    ],
+    [
+      1,
+      5
+    ],
+    [
+      2,
+      4
+    ],
+    [
+      3,
+      3
+    ],
+    [
+      4,
+      2
+    ],
+    [
+      5,
+      1
+    ],
+    [
+      0,
+      7
+    ],
+    [
+      6,
+      0
+    ],
+    [
+      1,
+      6
+    ],
+    [
+      2,
+      5
+    ],
+    [
+      3,
+      4
+    ],
+    [
+      4,
+      3
+    ],
+    [
+      5,
+      2
+    ],
+    [
+      6,
+      1
+    ],
+    [
+      1,
+      7
+    ],
+    [
+      7,
+      0
+    ],
+    [
+      2,
+      6
+    ],
+    [
+      3,
+      5
+    ],
+    [
+      4,
+      4
+    ],
+    [
+      5,
+      3
+    ],
+    [
+      6,
+      2
+    ],
+    [
+      7,
+      1
+    ],
+    [
+      2,
+      7
+    ],
+    [
+      8,
+      0
+    ],
+    [
+      3,
+      6
+    ],
+    [
+      4,
+      5
+    ],
+    [
+      5,
+      4
+    ],
+    [
+      6,
+      3
+    ],
+    [
+      7,
+      2
+    ],
+    [
+      8,
+      1
+    ],
+    [
+      3,
+      7
+    ],
+    [
+      4,
+      6
+    ],
+    [
+      5,
+      5
+    ],
+    [
+      6,
+      4
+    ],
+    [
+      7,
+      3
+    ],
+    [
+      8,
+      2
+    ],
+    [
+      4,
+      7
+    ],
+    [
+      5,
+      6
+    ],
+    [
+      6,
+      5
+    ],
+    [
+      7,
+      4
+    ],
+    [
+      8,
+      3
+    ],
+    [
+      5,
+      7
+    ],
+    [
+      6,
+      6
+    ],
+    [
+      7,
+      5
+    ],
+    [
+      8,
+      4
+    ],
+    [
+      6,
+      7
+    ],
+    [
+      7,
+      6
+    ],
+    [
+      8,
+      5
+    ],
+    [
+      7,
+      7
+    ],
+    [
+      8,
+      6
+    ],
+    [
+      8,
+      7
+    ]
+  ],
+  "windows": {
+    "0,0": [
+      16,
+      [
+        0,
+        1,
+        2
+      ]
+    ],
+    "0,2": [
+      16,
+      [
+        0,
+        1,
+        2
+      ]
+    ],
+    "0,1": [
+      8,
+      [
+        3,
+        4,
+        5
+      ]
+    ],
+    "0,3": [
+      8,
+      [
+        3,
+        4,
+        5
+      ]
+    ],
+    "0,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9
+      ]
+    ],
+    "0,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9
+      ]
+    ],
+    "0,5": [
+      8,
+      [
+        10,
+        11,
+        12,
+        13,
+        14
+      ]
+    ],
+    "0,7": [
+      8,
+      [
+        10,
+        11,
+        12,
+        13,
+        14
+      ]
+    ],
+    "0,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20
+      ]
+    ],
+    "0,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20
+      ]
+    ],
+    "0,9": [
+      8,
+      [
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28
+      ]
+    ],
+    "0,11": [
+      8,
+      [
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28
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diff --git a/research/gauge44-leaver8/data/PREPARATION.json b/research/gauge44-leaver8/data/PREPARATION.json
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index 0000000000..8c7796820f
--- /dev/null
+++ b/research/gauge44-leaver8/data/PREPARATION.json
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new file mode 100644
index 0000000000..db24c49da4
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+        ],
+        "local_adapters": 386832,
+        "local_primitive_bound": 10032231262226,
+        "compiler": 25934336,
+        "children": 3494,
+        "paid_profile": {
+          "1": 2412,
+          "2": 418,
+          "3": 418,
+          "4": 170,
+          "5": 68,
+          "8": 8
+        },
+        "program_hashes": {
+          "backward": "2d184e4d9d48aa4d5e3679368ee0eca7e0388b1966eb05e0fd17d22d00d36293",
+          "forward": "683f83231d4d4890a7fc3d18f30d4ac7bfbd7bbdf4e7ff57ad0eb09e8a5f571c"
+        },
+        "semantic_artifact_sha256": {
+          "CANONICAL-WORD.json.gz": "d1bf3c6f250a61be7421ce566668092f362c465274fb472d4bb01fc80cba9b23",
+          "LOCAL-PROGRAMS.json.gz": "ad9ce1708474b8b4790b8a1908b47fde0e182d319b3baac4180dd6d928bcfab5",
+          "LOCAL-CHECKS.json": "d51d68565b29e8552c94b6a682f8b79d4819d49339437a599da4e32ddffe2c34",
+          "INDEPENDENT-LOCAL-REPLAY.json": "837cb8512af6a4c6338d1cf246c124ea7e269005374fb9ba07a44aff1891fa59",
+          "CLIFFORD-RECIPES.json": "e3bfdfa2c044f14c00a8706950c8ae838ceeedd9ca78a83bffefe7886219516a",
+          "CLIFFORD-REVIEW.json": "b5ead2492b255dc030c5796c66d885fdc4fb4129c3d4bd6e632a627ebd4244d1",
+          "RESIDUAL-ADAPTERS.json": "c682e9ff1b347f89771c6800f46ad98c2bb92b91c5c88452d53a9e7f0180c35f"
+        }
+      },
+      "semantic_phase_sha256": "b5ead2492b255dc030c5796c66d885fdc4fb4129c3d4bd6e632a627ebd4244d1",
+      "expected_local": {
+        "forward": {
+          "events": 24753,
+          "macros": 19679,
+          "real_component_primitives": 198626,
+          "prefix_l1": "11061380959509307613/4096",
+          "coefficient_work_primitive_count": 98263
+        },
+        "backward": {
+          "events": 24753,
+          "macros": 19679,
+          "real_component_primitives": 198674,
+          "prefix_l1": "14824955600738971847565/64",
+          "coefficient_work_primitive_count": 98295
+        }
+      },
+      "wrappers": 240
+    }
+  },
+  "expected": {
+    "gain_baseline_kappa": "0.001636241501576388",
+    "hosted_residuals": 34560,
+    "rank_mass": 520704,
+    "actual_73column_sigmas": 8899,
+    "cross_replica_helper_roles": 27858,
+    "idle_remainders": 3783,
+    "idle_remainder_profile": {
+      "1": 1099,
+      "2": 9,
+      "3": 179,
+      "7": 54,
+      "16": 23,
+      "48": 2419
+    },
+    "global_profile": {
+      "1": 174763,
+      "2": 30105,
+      "3": 30275,
+      "4": 12240,
+      "5": 4896,
+      "7": 54,
+      "8": 576,
+      "16": 23,
+      "48": 2419
+    },
+    "live": 7168,
+    "physical": 7658,
+    "conservative_kappa_decimal": "0.001671387261540186",
+    "kappa_decimal": "0.001671387264390146",
+    "complex_lower": "837092738337043214923/500000000000000000000000",
+    "conservative_complex_lower": "1674185473814575474867/1000000000000000000000000",
+    "kappa": "835693632195073/500000000000000000",
+    "assembly_controls_rejected": 69,
+    "provider_counts": {
+      "gauge44": 72
+    },
+    "mutations_rejected": 15
+  },
+  "pivot_swap": {
+    "recipe": "construction/leaver/PIVOT-SWAP-k8.json",
+    "sha256": "3ef7acf0cf67442a532f25b53d5fbeda76d3a84524118df8e003ca69b5cac0bb"
+  }
+}
diff --git a/research/gauge44-leaver8/data/UPSTREAM-PINS.json b/research/gauge44-leaver8/data/UPSTREAM-PINS.json
new file mode 100644
index 0000000000..68486b84e3
--- /dev/null
+++ b/research/gauge44-leaver8/data/UPSTREAM-PINS.json
@@ -0,0 +1,23 @@
+{
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-RECIPES.json": "534ace870cabe515987e00f50f71550030965006ea18978e0924590ac6944345",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-REVIEW.json": "ee9b86428278392d2c933f76d60e51f5af90d4ab67e4d3937ed2fa416e7755ab",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-LOCAL-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INTEGRATION.json": "5c14538134dfffbc58fa4b4d2f26b270ec5f56d17d4bf23752c82964f45171db",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-CHECKS.json": "79177449e404403964ce1b2f4a9a8bd49e1916daba3123d7fd7f5cfd1f1ac0ea",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-PROGRAMS.json.gz": "99a18eede965accf65943e490b8d2b2ffb9f1c9bc6babdb825413a80cbea2cde",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/RESIDUAL-ADAPTERS.json": "baafef737acc16dafbe1150896feb16744f3d669fa123bb2bff19ecc4e71b275",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/SCALAR-FRAME-AUDIT.json": "73b3601a6239502475a272ea0c46945fd42034486aaf43e66a212eb4f012ca44",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/WRAPPER-CHECKS.json": "9a09146e686c4f535b04fdef3753fe01dad8f5e8881a69408a91394acb5b48f5",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+  "research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py": "322d29d43dbee8130cde15d4bf05396698b5e3dfe3735813899db91cc0ba7955",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+  "research/complex-k492-owner-repair/vendor/multicold/inputs/PR543-EXPECTED.json": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz": "025448abdf2012d327e50a009084e1501690d05e650300d2982836aa0350ae00",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz": "de2be0f4b6d24ace368fd5b834b7a00f9625d0a1824c4ff969f2db5f115db667",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/prepare_supplier_base.py": "f5eae94aca965d0008bc07cff8245ccb7509042ccad457d3bcb7d51c1e9409f0"
+}
diff --git a/research/gauge44-leaver8/evidence/ADMISSION-CONTROLS.json b/research/gauge44-leaver8/evidence/ADMISSION-CONTROLS.json
new file mode 100644
index 0000000000..2e15a10065
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/ADMISSION-CONTROLS.json
@@ -0,0 +1,102 @@
+{
+  "status": "PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS",
+  "valid_receipt_kappa": "1649483702558979/1000000000000000000",
+  "input_sha256": {
+    "owner_audit": "a32ecc0d5387d65648e1ff284209122860ee37aaba43ce2dd12024c4bc394313",
+    "fresh_invoice": "14b0f41c88209e800236ce4ebbf91d83537e22e18807153d90013f7eee57a582",
+    "inputs/PR543-EXPECTED.json": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d",
+    "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+  },
+  "assembler_sha256": "7ac28118d69416e4fb67b61216285fb0823310b7635ce1b9025aa3f10119ef6a",
+  "rejected_controls": [
+    "empty_certification_maps",
+    "failed_invoice_status",
+    "nonboolean_precision_check",
+    "wrong_owner_role_count",
+    "understated_physical_stock",
+    "changed_profile_same_rank_mass",
+    "insufficient_finite_C0",
+    "missing_finite_check",
+    "wrong_reflected_orientation_selfconsistent_totals",
+    "missing_selected_call",
+    "wrong_selected_primitive_sum",
+    "wrong_selected_coefficient_work_sum",
+    "unpaid_wrapper_factors",
+    "wrong_global_compiler",
+    "wrong_global_adapter_maximum",
+    "understated_exact_prefix_and_global_sum",
+    "wrong_global_prefix_sum",
+    "wrong_row_prefix_reserve",
+    "wrong_parent_geometry_charge",
+    "wrong_rebased_geometry_charge",
+    "wrong_complete_pervertex_envelope",
+    "wrong_prior_added_complete_invoice",
+    "wrong_finite_router_bits",
+    "wrong_finite_literal_bits",
+    "wrong_finite_physical_stock_bits",
+    "wrong_finite_row_coefficient",
+    "reordered_complete_calls",
+    "understated_explicit_idle_remainders",
+    "understated_actual_chart_types",
+    "wrong_cross_replica_role_count",
+    "old_no_cold_wrapper_counts_selfconsistent",
+    "gauge44:missing_provider",
+    "gauge44:missing_backward_orientation",
+    "gauge44:unpaid_scalar_primitive",
+    "gauge44:wrong_local_artifact_binding",
+    "gauge44:false_dirty_restoration",
+    "gauge44:wrong_declared_provider_count",
+    "gauge44:wrong_local_compiler",
+    "gauge44:wrong_local_adapter_charge",
+    "gauge44:wrong_local_primitive_bound",
+    "gauge44:forged_provider_and_call_program_hash",
+    "gauge44:provider_at_wrong_call",
+    "gauge44:synchronized_forged_source_recipe_hash",
+    "gauge44:synchronized_forged_phase_review_semantics",
+    "gauge44:width_order_swap_4_5",
+    "gauge44:width_inventory_shift_4_5",
+    "gauge44:width_order_swap_4_7",
+    "gauge44:width_inventory_shift_4_7",
+    "gauge44:width_order_swap_4_8",
+    "gauge44:width_inventory_shift_4_8",
+    "gauge44:width_order_swap_4_9",
+    "gauge44:width_inventory_shift_4_9",
+    "gauge44:width_order_swap_5_7",
+    "gauge44:width_inventory_shift_5_7",
+    "gauge44:width_order_swap_5_8",
+    "gauge44:width_inventory_shift_5_8",
+    "gauge44:width_order_swap_5_9",
+    "gauge44:width_inventory_shift_5_9",
+    "gauge44:width_order_swap_7_8",
+    "gauge44:width_inventory_shift_7_8",
+    "gauge44:width_order_swap_7_9",
+    "gauge44:width_inventory_shift_7_9",
+    "gauge44:width_order_swap_8_9",
+    "gauge44:width_inventory_shift_8_9",
+    "gauge44:cold_helper_width_swap_264",
+    "gauge44:cold_helper_width_swap_276",
+    "gauge44:cold_helper_width_swap_288",
+    "gauge44:cold_helper_width_swap_300",
+    "wrong_owner_receipt_hash"
+  ],
+  "discovery_accepted_controls": [],
+  "exact_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "conservative_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "recurrence_model_controls": [
+    "native_complex_endpoint_rejected_with_old_surcharge",
+    "omitting_bit_surcharge_would_fail_next_endpoint_rejection"
+  ],
+  "scope": "Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay."
+}
diff --git a/research/gauge44-leaver8/evidence/ASSEMBLY.json b/research/gauge44-leaver8/evidence/ASSEMBLY.json
new file mode 100644
index 0000000000..6feaaf28f5
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/ASSEMBLY.json
@@ -0,0 +1,336 @@
+{
+  "status": "PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY",
+  "kappa": "1649483702558979/1000000000000000000",
+  "kappa_decimal": "0.001649483702558979",
+  "complex_lower": "1652208994368411824947/1000000000000000000000000",
+  "complex_decimal": "0.001652208994368411824947",
+  "bit_lower": "413456747036699736067/250000000000000000000000",
+  "bit_decimal": "0.001653826988146798944268",
+  "binding": "complex",
+  "gain_over_pr635_percent": "0.8093060205252829126484020359439672024956960385078942889840023844750830",
+  "complex_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "surcharge_model": {
+    "complex": false,
+    "bit": true
+  },
+  "conservative_complex_lower": "826104495740783435531/500000000000000000000000",
+  "conservative_complex_decimal": "0.001652208991481566871062",
+  "conservative_kappa": "32989673993633/20000000000000000",
+  "conservative_kappa_decimal": "0.00164948369968165",
+  "conservative_moments": [
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "826104495740783435531/500000000000000000000000",
+      "accept": true,
+      "mercator": [
+        "-21470727653278306311183666306239229019733127/13479973333575319897333507543509815336818572211270286240551805124608",
+        "-10735363826639153155591833153119614509866563/6739986666787659948666753771754907668409286105635143120275902562304"
+      ],
+      "base_two": [
+        "-497746012127833654257/312500000000000000000000000000000000000000000",
+        "-15927862388090676936081/10000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "1652208991481566871063/1000000000000000000000000",
+      "accept": false,
+      "mercator": [
+        "18565857384700607217299861034814026061253869/13479973333575319897333507543509815336818572211270286240551805124608",
+        "9282928692350303608649930517407013030626935/6739986666787659948666753771754907668409286105635143120275902562304"
+      ],
+      "base_two": [
+        "3443229403069298452661/2500000000000000000000000000000000000000000000",
+        "6886463806138596905393/5000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "conservative_bootstrap": [
+    {
+      "exponent": "412385685180656454166549264744655866734211385357236332091088842586409092836277952888766748039/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "666562689735263598950072203096262874070849142763667908911157413590907163722047111233251961/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "5064079519162"
+    },
+    {
+      "exponent": "206525573284761175512531267070234734086162997564863775372380915312260537579589712487639916151798780772051965162106786567177267184954922826291/125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "550650434683370218401403641330717978119685136224627619084687739462420410287512360083848201219227948034837893213432822732815045077173709/125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1855113791006194394"
+    },
+    {
+      "exponent": "103263061512703129767826074285021991628452086339263045204373010454992865610677336738873844192820011712987227316937414267052501172258472295234559238219891652401488082322583795324180689654479/62500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "454894799673548759951916040773618472285736954795626989545007134389322663261126155807179988287012772683062585732947498827741527704765440761780108347598511917677416204675819310345521/62500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "679580003544484094184219"
+    },
+    {
+      "exponent": "51631530983423174081587995422763705511463803560275446891594962002253805557680841136478473308373535599630472737022595278769657751046420516932624996624821336420775380353032156988877311591948170858471939709729324917119896056841137038106651/31250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "375790639099421695705310689571475752224553108405037997746194442319158863521526691626464400369527262977404721230342248953579483067375003375178663579224619646967843011122688408051829141528060290270675082880103943158862961893349/31250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "248949139107542177224284717390"
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+    "small_field_exposure": "1/1000000000000000000000000",
+    "artificial_boundary": "28052870687819789178396573746942554881945552217657432084634864074395589440468656236697540052712284541524031824211862034164560265703537066127970590931564509850315985626323347506810242717329863369746611861037020660989119250383041371050571010532356065357152905568552022376148940123930219891520143226253589408420900672815173496482569881827632815204222224070568991954864544636207549131231883796360430421207861560214076773241672626630634083/4006608835977473647299571030558030173799116810039786953171693612465848209443568599664054422252400750023225868773931711189284875874229534487947361868717007126780069080757830842241571271850494760695005752555974214631697998719485520320030065455700818193760348194659684561042764682974955861767304104402104161601556563759516793211688660155490175673178096210915179205756083399302683754754960204728644460337681690888000000000000000000000000",
+    "literal_scalar_guard": "1",
+    "row_product_gap": "23971789/25",
+    "balanced_prefix_above_kappa": "384836754948704936518390080286389004763190679571631416083335375425490380659422846922349219607884635917039474482556378074796393103615265478935526743142995785277965991920542575867329404082937294587671597128436387521101370842739834550650414154320702290281170117836140043954928114189095044806439229775952058740929618067139100165877377039970533655513737284898865861249271614750592100633440385821327668139841639581/500826104497184205912446378819753771724889601254973369146461701558231026180446074958006802781550093752903233596741463898660609484278691810993420233589625890847508635094728855280196408981311845086875719069496776828962249839935690040003758181962602274220043524332460570130345585371869482720913013050263020200194570469939599151461082519436271959147262026364397400719510424912835469344370025591080557542210211361000000000000000000",
+    "coordinate_movement_above_kappa": "2725291809432824892760943925532186602852295468626143987776322166643298144437891566249896386783794682250325982720570888808333058035587427982244795917897766192126153947302396188350346875998068356230515694247409920636392332411468502336205197989213263024053337331536239117696791845640104898504335919624091669350736887870142170348377574017694034808393425549949474408919442457789788639/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_phase_layer_above_kappa": "384836254122600439334184167840010185009418954682030161109966228963788822428396666476274261601081854366945721579322781333332494443005781200243715749722762195652075144411907481138474123886528313275826510252717318024324541880489994614960374150562520327678895897792615711494357983843509672936956508862939008477909417872568630226278225578888014219241778137636839496851870895240167187797971041451302077059284097370788639/500826104497184205912446378819753771724889601254973369146461701558231026180446074958006802781550093752903233596741463898660609484278691810993420233589625890847508635094728855280196408981311845086875719069496776828962249839935690040003758181962602274220043524332460570130345585371869482720913013050263020200194570469939599151461082519436271959147262026364397400719510424912835469344370025591080557542210211361000000000000000000000000",
+    "bulk_exposure_above_kappa": "2725291809432824892760943925532186602852295468626143987776322166643298144437891566249896386783794682250325982720570888808333058035587427982244795917897766192126153947302396188350346875998068356230515694247409920636392332411468502336205197989213263024053337331536239117696791845640104898504335919624091669350736887870142170348377574017694034808393425549949474408919442457789788639/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "Gaussian_arithmetic_above_kappa": "615738307091823401245218216011843587867333362425009010759967454219083050824050374629683793365812635917169406268856608178210330305174940487605031795608559666818854739564233026658871766336290690028429468529779150536985364386133895345350622643154941701847597968494299737867314852356966699820820046728510243722467188712852090325804651802870334412550020508576159013601433864090522448178035272944098677943189081119388639/801321767195494729459914206111606034759823362007957390634338722493169641888713719932810884450480150004645173754786342237856975174845906897589472373743401425356013816151566168448314254370098952139001150511194842926339599743897104064006013091140163638752069638931936912208552936594991172353460820880420832320311312751903358642337732031098035134635619242183035841151216679860536750950992040945728892067536338177600000000000000000000000",
+    "scalar_work_above_kappa": "3078693538763534994962914729844733218351753711683450073693313856942221487044356594932718798856274305786222042957217427856907246168312639552792402951723732692597837087855705512209779952467089375389527690151772030672034137779668836469513273230807436359647086722645596019178854783167174986582031117294603419664416744342542331387419864858681749807837939131928900525596772198494311892232053742200595754038175574437788639/4006608835977473647299571030558030173799116810039786953171693612465848209443568599664054422252400750023225868773931711189284875874229534487947361868717007126780069080757830842241571271850494760695005752555974214631697998719485520320030065455700818193760348194659684561042764682974955861767304104402104161601556563759516793211688660155490175673178096210915179205756083399302683754754960204728644460337681690888000000000000000000000000",
+    "dimension_above_kappa": "499173895502815794472389376128951164793500479031415635616728978013400389902889300467483577877872753169445986011143172018378864998277686263802972870025639588088018108048266929997769582939230730780453685013440517758709347288500697481097612660777232276430370629988241720150824532464270561234015101138832024606244659306012459589468535547702828206730115013606136254794226859986030391904901589159511543091230174460327668139841639581/500826104497184205912446378819753771724889601254973369146461701558231026180446074958006802781550093752903233596741463898660609484278691810993420233589625890847508635094728855280196408981311845086875719069496776828962249839935690040003758181962602274220043524332460570130345585371869482720913013050263020200194570469939599151461082519436271959147262026364397400719510424912835469344370025591080557542210211361000000000000000000"
+  },
+  "controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the same cited unchanged PR543 bit supplier as PR635. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/gauge44-leaver8/evidence/BINDING.json b/research/gauge44-leaver8/evidence/BINDING.json
new file mode 100644
index 0000000000..b03160c67a
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/BINDING.json
@@ -0,0 +1,25 @@
+{
+  "status": "PASS_FROZEN_048_ALLCOLD_DISPATCH_FRESH_PROVIDER_BINDING",
+  "source_plan_sha256": "8c4804859aee83082196348c33127070d2885d3a366ce9acc8dc5166202f4687",
+  "runtime_plan_sha256": "609adb126d7d3de2abdd9275f9015589c0b137d0d19821c2c3e7c1a8541c18d2",
+  "providers": {
+    "gauge44": {
+      "artifact_sha256": {
+        "CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+        "LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+        "LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+        "INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+        "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+        "CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12",
+        "RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94"
+      },
+      "canonical_content_sha256": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+      "all_phase_edges": 3019
+    }
+  },
+  "only_rebound_fields": [
+    "provider_registry.directory",
+    "provider_registry.artifact_sha256",
+    "runtime_source_plan_sha256"
+  ]
+}
diff --git a/research/gauge44-leaver8/evidence/CENTER-COMPATIBILITY.json b/research/gauge44-leaver8/evidence/CENTER-COMPATIBILITY.json
new file mode 100644
index 0000000000..5a3ae37422
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/CENTER-COMPATIBILITY.json
@@ -0,0 +1,112 @@
+{
+  "status": "PASS_IDENTICAL_PORT_ORDER_AND_ORDERED_CENTER_FRAMES",
+  "new_canonical_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+  "comparison_canonical": "pr635/research/community-k492-audit/pr626/replay/mixed-global/base/split-centres/CANONICAL-WORD.json.gz",
+  "comparison_canonical_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+  "new_centers": [
+    92,
+    57,
+    81,
+    224,
+    11,
+    240,
+    9,
+    256
+  ],
+  "old_centers": [
+    229,
+    224,
+    227,
+    225,
+    243,
+    241,
+    259,
+    257
+  ],
+  "ordered_center_frames": [
+    [
+      256,
+      128,
+      64,
+      34,
+      16,
+      10,
+      4,
+      1
+    ],
+    [
+      256,
+      128,
+      64,
+      32,
+      16,
+      8,
+      5,
+      3
+    ],
+    [
+      256,
+      128,
+      64,
+      32,
+      17,
+      9,
+      4,
+      2
+    ],
+    [
+      256,
+      128,
+      64,
+      36,
+      20,
+      8,
+      2,
+      1
+    ],
+    [
+      256,
+      128,
+      66,
+      32,
+      18,
+      8,
+      4,
+      1
+    ],
+    [
+      256,
+      128,
+      65,
+      33,
+      17,
+      9,
+      5,
+      3
+    ],
+    [
+      256,
+      128,
+      65,
+      33,
+      16,
+      8,
+      4,
+      2
+    ],
+    [
+      256,
+      128,
+      68,
+      32,
+      16,
+      12,
+      2,
+      1
+    ]
+  ],
+  "v": 112,
+  "h": 9,
+  "center_count": 8,
+  "scope": "Carrier register identity changes; native cut center channels retain exact ordered frames and ports. Full endpoint and exact center clearing are independently checked by local ledger replay."
+}
diff --git a/research/gauge44-leaver8/evidence/LOCAL-STAGES.json b/research/gauge44-leaver8/evidence/LOCAL-STAGES.json
new file mode 100644
index 0000000000..b2753eb57a
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/LOCAL-STAGES.json
@@ -0,0 +1,27 @@
+[
+  {
+    "tag": "44-native",
+    "seconds": 4.460461161999774,
+    "exit": 0
+  },
+  {
+    "tag": "44-emitted-ledgers",
+    "seconds": 3.058037757999955,
+    "exit": 0
+  },
+  {
+    "tag": "44-local-replay",
+    "seconds": 28.33760359400003,
+    "exit": 0
+  },
+  {
+    "tag": "44-wrappers",
+    "seconds": 5.294312295000054,
+    "exit": 0
+  },
+  {
+    "tag": "44-phase",
+    "seconds": 198.39076561599995,
+    "exit": 0
+  }
+]
diff --git a/research/gauge44-leaver8/evidence/REPLAY.json b/research/gauge44-leaver8/evidence/REPLAY.json
new file mode 100644
index 0000000000..c6f4e0f983
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/REPLAY.json
@@ -0,0 +1,54 @@
+{
+  "status": "PASS_GAUGE44_STRICT_GLOBAL_REPLAY",
+  "kappa": "1649483702558979/1000000000000000000",
+  "kappa_decimal": "0.001649483702558979",
+  "complex_lower": "1652208994368411824947/1000000000000000000000000",
+  "bit_lower": "413456747036699736067/250000000000000000000000",
+  "gain_over_pr635_percent": "0.8093060205252829126484020359439672024956960385078942889840023844750830",
+  "spec_sha256": "fee57674a7f36b30b1e7eb96a8f567a90a522217bc644c1a6a1f8bff85196fbf",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 2.152,
+      "exit_code": 0,
+      "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.686,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "emit",
+      "seconds": 5.456,
+      "exit_code": 0,
+      "log_sha256": "60866eb6ced5b9eb259bfc1d59ea7b80fb439164b629e868586ad5bef845a88e"
+    },
+    {
+      "name": "audit",
+      "seconds": 26.943,
+      "exit_code": 0,
+      "log_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662"
+    },
+    {
+      "name": "invoice",
+      "seconds": 1.897,
+      "exit_code": 0,
+      "log_sha256": "5d10712d494304287749dd7a6c3369f9b707bba30e9f567b68230669dcf5418a"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.724,
+      "exit_code": 0,
+      "log_sha256": "768d3215f1918117dc6c33b4cfeaf0b5f5da9ba5c77178db4bb1d08d000e226f"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 0.816,
+      "exit_code": 0,
+      "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+    }
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the same cited unchanged PR543 bit supplier as PR635. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/gauge44-leaver8/evidence/STAGES.json b/research/gauge44-leaver8/evidence/STAGES.json
new file mode 100644
index 0000000000..9464e2dfea
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/STAGES.json
@@ -0,0 +1,44 @@
+[
+  {
+    "name": "restore-parent",
+    "seconds": 2.152,
+    "exit_code": 0,
+    "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+  },
+  {
+    "name": "bind",
+    "seconds": 0.686,
+    "exit_code": 0,
+    "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+  },
+  {
+    "name": "emit",
+    "seconds": 5.456,
+    "exit_code": 0,
+    "log_sha256": "60866eb6ced5b9eb259bfc1d59ea7b80fb439164b629e868586ad5bef845a88e"
+  },
+  {
+    "name": "audit",
+    "seconds": 26.943,
+    "exit_code": 0,
+    "log_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662"
+  },
+  {
+    "name": "invoice",
+    "seconds": 1.897,
+    "exit_code": 0,
+    "log_sha256": "5d10712d494304287749dd7a6c3369f9b707bba30e9f567b68230669dcf5418a"
+  },
+  {
+    "name": "assembly",
+    "seconds": 0.724,
+    "exit_code": 0,
+    "log_sha256": "768d3215f1918117dc6c33b4cfeaf0b5f5da9ba5c77178db4bb1d08d000e226f"
+  },
+  {
+    "name": "admission-controls",
+    "seconds": 0.816,
+    "exit_code": 0,
+    "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+  }
+]
diff --git a/research/gauge44-leaver8/evidence/audit/ASYNC-AUDIT.json b/research/gauge44-leaver8/evidence/audit/ASYNC-AUDIT.json
new file mode 100644
index 0000000000..05975382b5
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/audit/ASYNC-AUDIT.json
@@ -0,0 +1,84 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "complex_template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "complex_live": 7168,
+  "complex_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "complex_hosted_residuals": 35424,
+  "physical": 7670,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "entering_helper_roles": 17856,
+  "cross_replica_helper_roles": 25937,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 35424,
+  "complete_invocations": 72,
+  "actual_orthogonal_73column_maps": 7870,
+  "actual_sigma_stream_sha256": "f4e9802acb2ed53fc1f0486e7d0f55a6faa30ed7f5d2ad48a06450234b00ba76",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 2759,
+  "mutations_rejected": [
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit idle remainder",
+    "understate physical reserve",
+    "gauge44: wrong provider at its invocation",
+    "gauge44: stale per-call local program hash",
+    "gauge44: stale serialized provider program",
+    "gauge44: unbound residual adapter hash",
+    "gauge44: wrong provider width registry",
+    "gauge44: wrong per-call residual width",
+    "gauge44: wrong sweep provider",
+    "gauge44: entering helper width silently restored to nine"
+  ],
+  "mutation_controls_run": true,
+  "provider_phase_semantic_sha256": {
+    "gauge44": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152"
+  },
+  "provider_artifact_semantic_sha256": {
+    "gauge44": {
+      "CANONICAL-WORD.json.gz": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+      "LOCAL-PROGRAMS.json.gz": "39b230dba9e6b022c691cd0167f331c1b3fa6795d49256e3a2b859c68d4acfda",
+      "LOCAL-CHECKS.json": "bd53e0cca4488f365ca5b7c7174d8dfb35ced5e0229835f27334c11c3d839717",
+      "INDEPENDENT-LOCAL-REPLAY.json": "adb5c8ce0b5025dcd96f41b9fa0e26b9a176e067ab36a5bfadad00bc19522b38",
+      "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+      "CLIFFORD-REVIEW.json": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152",
+      "RESIDUAL-ADAPTERS.json": "c233611dd4c08c389dfb6c7d1c84dd86a3efa560223fcd6549a2848692541cd9"
+    }
+  },
+  "widths_by_provider": {
+    "gauge44": {
+      "4": 52,
+      "5": 48,
+      "7": 34,
+      "8": 114,
+      "9": 244
+    }
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "all_provider_program_phase_and_wrapper_bindings": true,
+  "scope": "Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations."
+}
diff --git a/research/gauge44-leaver8/evidence/audit/GLOBAL-PREFIX.json b/research/gauge44-leaver8/evidence/audit/GLOBAL-PREFIX.json
new file mode 100644
index 0000000000..a557ebbe60
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/audit/GLOBAL-PREFIX.json
@@ -0,0 +1,13 @@
+{
+  "status": "PASS_MIXED_ASYNC_GLOBAL_PREFIX",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "global_prefix_bits": 360,
+  "retained_payload_bits": 512,
+  "complete_invocation_cover_sweeps": 72,
+  "bridge_factor_two_sweeps": 72,
+  "local_scalar_coefficient_work_prefix_bits": 175,
+  "stream_input_sup_to_l2_bits": 37,
+  "primitive_arithmetic_margin_bits": 4,
+  "controller_audit_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662",
+  "proof": "Each selected normalized provider restores all arbitrary dirty helper columns and gives the same data shear endpoints. Actual whole-owner charts are right-translation bijections. Sum all 72 invocation and 72 bridge sweeps and take maximum local scalar/Horner prefix over all three providers and orientations. Idle children, phases, spectator endpoints and terminal translations are unitary. Retained all-size interfaces are conditional."
+}
diff --git a/research/gauge44-leaver8/evidence/audit/IDLE-REMAINDER-FRAMES.json b/research/gauge44-leaver8/evidence/audit/IDLE-REMAINDER-FRAMES.json
new file mode 100644
index 0000000000..1c86a8a01d
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/audit/IDLE-REMAINDER-FRAMES.json
@@ -0,0 +1,25 @@
+{
+  "status": "PASS_LITERAL_IDLE_REMAINDER_FRAMES",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "uncompressed_frames_sha256": "38eba7dfe023d0b2a8aea1c5184e50bdfff5727b350c2de4d27800acbdd3708c",
+  "children": 2759,
+  "rank_profile": {
+    "1": 85,
+    "2": 76,
+    "3": 173,
+    "7": 7,
+    "8": 6,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "source_data_phase_sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+  "scope": "Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child."
+}
diff --git a/research/gauge44-leaver8/evidence/audit/OWNERS-AND-PROFILE.json b/research/gauge44-leaver8/evidence/audit/OWNERS-AND-PROFILE.json
new file mode 100644
index 0000000000..bdb9441b7e
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/audit/OWNERS-AND-PROFILE.json
@@ -0,0 +1,61 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "paid_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "live": 7168,
+  "physical": 7670,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "hosted_residuals": 35424,
+  "banked_residuals": 0,
+  "all_live_owners_per_call_distinct": true,
+  "owners_per_call": 716,
+  "actual_helper_owner_charts": 35424,
+  "actual_73column_sigmas": 7870,
+  "cross_replica_helper_roles": 25937,
+  "explicit_idle_remainder_children": 2759,
+  "source_idle_children_charged": 16128,
+  "source_artifacts": {
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "providers/gauge44/CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+    "providers/gauge44/LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+    "providers/gauge44/LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+    "providers/gauge44/INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+    "providers/gauge44/RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94",
+    "providers/gauge44/CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+    "providers/gauge44/CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12"
+  },
+  "provider_phase_semantic_sha256": {
+    "gauge44": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152"
+  },
+  "provider_artifact_semantic_sha256": {
+    "gauge44": {
+      "CANONICAL-WORD.json.gz": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+      "LOCAL-PROGRAMS.json.gz": "39b230dba9e6b022c691cd0167f331c1b3fa6795d49256e3a2b859c68d4acfda",
+      "LOCAL-CHECKS.json": "bd53e0cca4488f365ca5b7c7174d8dfb35ced5e0229835f27334c11c3d839717",
+      "INDEPENDENT-LOCAL-REPLAY.json": "adb5c8ce0b5025dcd96f41b9fa0e26b9a176e067ab36a5bfadad00bc19522b38",
+      "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+      "CLIFFORD-REVIEW.json": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152",
+      "RESIDUAL-ADAPTERS.json": "c233611dd4c08c389dfb6c7d1c84dd86a3efa560223fcd6549a2848692541cd9"
+    }
+  },
+  "controller_audit_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662"
+}
diff --git a/research/gauge44-leaver8/evidence/audit/PREFIX-AND-INVOICE.json b/research/gauge44-leaver8/evidence/audit/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..6c96ec6706
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/audit/PREFIX-AND-INVOICE.json
@@ -0,0 +1,1746 @@
+{
+  "status": "PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "parent_template_sha256": "7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3",
+  "owner_audit_sha256": "a32ecc0d5387d65648e1ff284209122860ee37aaba43ce2dd12024c4bc394313",
+  "controller_audit_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662",
+  "providers": {
+    "gauge44": {
+      "local": {
+        "backward": {
+          "events": 46772,
+          "macros": 41570,
+          "real_component_primitives": 420100,
+          "prefix_l1": "600338326363508935771850050281004728884643/32",
+          "prefix_bits": 134,
+          "coefficient_work_primitive_count": 208744,
+          "all_exact_columns": 716,
+          "dirty_helper_columns": 492,
+          "all_dirty_helper_columns_restored": true,
+          "private_centres_and_coefficient_work_cleared": true,
+          "pre_wrappers": 248,
+          "post_wrappers": 248,
+          "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+        },
+        "forward": {
+          "events": 46772,
+          "macros": 41570,
+          "real_component_primitives": 420052,
+          "prefix_l1": "2323449462751823289130723296176889733365478515961323543/64",
+          "prefix_bits": 175,
+          "coefficient_work_primitive_count": 208712,
+          "all_exact_columns": 716,
+          "dirty_helper_columns": 492,
+          "all_dirty_helper_columns_restored": true,
+          "private_centres_and_coefficient_work_cleared": true,
+          "pre_wrappers": 248,
+          "post_wrappers": 248,
+          "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+        }
+      },
+      "helpers": 492,
+      "centres": 8,
+      "v": 112,
+      "h": 9,
+      "n": 716,
+      "entering_helpers": 204,
+      "entrance_rank": 380,
+      "terminal_codimension": 254,
+      "hyperplane_ended_helpers": 78,
+      "cold_hyperplane_ended_helpers": 44,
+      "width_inventory": {
+        "4": 52,
+        "5": 48,
+        "7": 34,
+        "8": 114,
+        "9": 244
+      },
+      "widths": [
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+      "local_adapters": 738816,
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+      "compiler": 25934336,
+      "children": 3590,
+      "artifacts": {
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+        "RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94",
+        "LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+        "INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+        "CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+        "SCALAR-FRAME-AUDIT.json": "cfc73040079b43ea82a42f3cf4c910edda1362deb09ec21c816c329347313bcb",
+        "FULL-WORD.json.gz": "0ad202612f010df4ab66432a628247b37ad8b497dd6b27595b1685cbd7eb119e",
+        "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+        "CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12",
+        "LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c"
+      },
+      "paid_profile": {
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+        "2": 404,
+        "3": 448,
+        "4": 160,
+        "5": 56,
+        "8": 8
+      },
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+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. All three providers use fresh hash-bound independent all-column/frame/phase/normalization admission. Shared compiler uses conservative maxima; parent is geometry/overcharge only. All-size compiler, hosting, precision/tape and analytic transfer remain conditional."
+}
diff --git a/research/gauge44-leaver8/evidence/global/ACTUAL-SIGMAS.json.gz b/research/gauge44-leaver8/evidence/global/ACTUAL-SIGMAS.json.gz
new file mode 100644
index 0000000000..dbb57066e2
Binary files /dev/null and b/research/gauge44-leaver8/evidence/global/ACTUAL-SIGMAS.json.gz differ
diff --git a/research/gauge44-leaver8/evidence/global/GLOBAL-TEMPLATE.json.gz b/research/gauge44-leaver8/evidence/global/GLOBAL-TEMPLATE.json.gz
new file mode 100644
index 0000000000..424c2df489
Binary files /dev/null and b/research/gauge44-leaver8/evidence/global/GLOBAL-TEMPLATE.json.gz differ
diff --git a/research/gauge44-leaver8/evidence/global/HOSTED.json b/research/gauge44-leaver8/evidence/global/HOSTED.json
new file mode 100644
index 0000000000..498e849ab7
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/global/HOSTED.json
@@ -0,0 +1,60 @@
+{
+  "status": "EMITTED_MIXED_PROVIDER_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "parent_template_sha256": "7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3",
+  "live": 7168,
+  "physical": 7670,
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "hosted_residuals": 35424,
+  "banks_per_stage": [
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0
+  ],
+  "entering_helper_roles": 17856,
+  "unique_actual_73column_sigmas": 7870,
+  "sigma_stream_sha256": "f4e9802acb2ed53fc1f0486e7d0f55a6faa30ed7f5d2ad48a06450234b00ba76",
+  "cross_replica_helper_roles": 25937,
+  "asynchronous_order_sha256": "2acd6b2004be3d3ef6645f3c968feb22b5167c400bb49eb446821e5cb7af6eee",
+  "source_artifacts": {
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "providers/gauge44/CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+    "providers/gauge44/LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+    "providers/gauge44/LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+    "providers/gauge44/INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+    "providers/gauge44/RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94",
+    "providers/gauge44/CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+    "providers/gauge44/CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12"
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "scope": "Two actual verified plain/width-seven providers dispatched per complete invocation; independent controller/spectator/normalization and complete finite invoice admission required."
+}
diff --git a/research/gauge44-leaver8/evidence/global/IDLE-REMAINDER-FRAMES.json.gz b/research/gauge44-leaver8/evidence/global/IDLE-REMAINDER-FRAMES.json.gz
new file mode 100644
index 0000000000..3562e60f05
Binary files /dev/null and b/research/gauge44-leaver8/evidence/global/IDLE-REMAINDER-FRAMES.json.gz differ
diff --git a/research/gauge44-leaver8/evidence/layers/LOCAL-AUDIT-LAYERED.json b/research/gauge44-leaver8/evidence/layers/LOCAL-AUDIT-LAYERED.json
new file mode 100644
index 0000000000..0780787674
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/layers/LOCAL-AUDIT-LAYERED.json
@@ -0,0 +1,137 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+  "input_file": "FULL-WORD.json.gz",
+  "content_sha256": "db2c7cfb3f8eee2b76c2e0154fc530520fb4d90cd9511a002cab527b16033b83",
+  "compressed_sha256": "3b268a3adb543e930454e9d9405e5f7a664c75c487f6c5cbe29c199f24a89789",
+  "parent_center_interface": {
+    "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+    "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "transport_tau": 43,
+    "ordered_frame_bases_match": true,
+    "all_ports_match": true,
+    "transported_centers": [
+      92,
+      57,
+      81,
+      224,
+      11,
+      240,
+      9,
+      256
+    ],
+    "source_centers": [
+      92,
+      57,
+      81,
+      11,
+      9
+    ],
+    "ordered_frame_bases": [
+      [
+        256,
+        128,
+        64,
+        34,
+        16,
+        10,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        16,
+        8,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        17,
+        9,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ],
+      [
+        256,
+        128,
+        66,
+        32,
+        18,
+        8,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        17,
+        9,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        16,
+        8,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        68,
+        32,
+        16,
+        12,
+        2,
+        1
+      ]
+    ]
+  },
+  "v": 112,
+  "h": 9,
+  "R": 480,
+  "entering": 192,
+  "lowends": 78,
+  "coldends": 48,
+  "compensation_gates": 7208,
+  "local_profile": {
+    "1": 2412,
+    "2": 418,
+    "3": 418,
+    "4": 170,
+    "5": 68,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 56,
+    "5": 32,
+    "7": 30,
+    "8": 122,
+    "9": 240
+  },
+  "checked_columns": 704,
+  "elapsed_seconds": 0.8600000000005821,
+  "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+}
diff --git a/research/gauge44-leaver8/evidence/leaver/CELL-MUTANTS-LV.json b/research/gauge44-leaver8/evidence/leaver/CELL-MUTANTS-LV.json
new file mode 100644
index 0000000000..4d4ef7403c
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/leaver/CELL-MUTANTS-LV.json
@@ -0,0 +1,261 @@
+{
+ "c01m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_233": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [233])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [172, 175])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [132, 135, 173, 174])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_233": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [233])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c01p": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_57": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [57, 58, 224, 225, 226])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [169, 170])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [129, 130, 168, 171])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_57": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [57, 58, 224, 225, 226])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c23m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_58": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [58])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [169, 170])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [173, 174, 196, 199])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_58": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [58])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c23p": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_239": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [60, 63, 231, 232, 238, 239])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [172, 175])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [168, 171, 193, 194])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_239": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [60, 63, 231, 232, 238, 239])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c45m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_441": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [52, 55, 439, 440, 446, 447])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [137, 138])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [141, 142, 164, 167])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_441": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [52, 55, 439, 440, 446, 447])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c45p": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_255": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [28, 31, 247, 248, 254, 255])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [140, 143])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [136, 139, 161, 162])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_255": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [28, 31, 247, 248, 254, 255])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c67m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_18": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [18])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [129, 130])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [133, 134, 161, 162])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_18": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [18])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-leaver8/evidence/leaver/FRAME-CONTROLS-LV-k8.json b/research/gauge44-leaver8/evidence/leaver/FRAME-CONTROLS-LV-k8.json
new file mode 100644
index 0000000000..9f56e21000
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/leaver/FRAME-CONTROLS-LV-k8.json
@@ -0,0 +1,54 @@
+{
+ "base": "c836d892",
+ "recipe": "FRAME-RECIPE-LV-k8.json",
+ "controls": {
+  "shrink_raised_B": {
+   "builder": "profile and width pins",
+   "stage": "native_atc",
+   "native": "PASS",
+   "rc": 0,
+   "reason": "}",
+   "frame": [
+    "B",
+    539
+   ]
+  },
+  "shrink_lowered_B": {
+   "builder": "('nonmonotone', 174)",
+   "stage": "apply",
+   "reason": "('nonmonotone', 174)"
+  },
+  "shrink_T": {
+   "builder": "('nonmonotone', 554)",
+   "stage": "apply",
+   "reason": "('nonmonotone', 554)"
+  },
+  "empty_B": {
+   "builder": "('nonmonotone', 169)",
+   "stage": "apply",
+   "reason": "('nonmonotone', 169)"
+  },
+  "drop_one_lowering": {
+   "builder": "output word pin",
+   "stage": "native_atc",
+   "native": "PASS",
+   "rc": 0,
+   "reason": "}",
+   "frame": [
+    "B",
+    1232
+   ]
+  },
+  "drop_one_raise": {
+   "builder": "profile and width pins",
+   "stage": "native_atc",
+   "native": "PASS",
+   "rc": 0,
+   "reason": "}",
+   "frame": [
+    "B",
+    539
+   ]
+  }
+ }
+}
diff --git a/research/gauge44-leaver8/evidence/local/CANONICAL-WORD.json.gz b/research/gauge44-leaver8/evidence/local/CANONICAL-WORD.json.gz
new file mode 100644
index 0000000000..5062a1f62f
Binary files /dev/null and b/research/gauge44-leaver8/evidence/local/CANONICAL-WORD.json.gz differ
diff --git a/research/gauge44-leaver8/evidence/local/CLIFFORD-RECIPES.json b/research/gauge44-leaver8/evidence/local/CLIFFORD-RECIPES.json
new file mode 100644
index 0000000000..3ba8326d3a
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/local/CLIFFORD-RECIPES.json
@@ -0,0 +1 @@
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new file mode 100644
index 0000000000..6b12ae0e4b
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/local/CLIFFORD-REVIEW.json
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+{
+  "status": "PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES",
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+  "directed_edges": 3019,
+  "ranks": {
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+    "8": 16,
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+    "5": 14
+  },
+  "endpoint_adapters": 224,
+  "all_child_equalities_include_global_phase": true,
+  "recipe_sha256": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+  "seconds": 198.28347681800005,
+  "scope": "Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations."
+}
diff --git a/research/gauge44-leaver8/evidence/local/FULL-WORD.json.gz b/research/gauge44-leaver8/evidence/local/FULL-WORD.json.gz
new file mode 100644
index 0000000000..447d45d08b
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diff --git a/research/gauge44-leaver8/evidence/local/INDEPENDENT-LOCAL-REPLAY.json b/research/gauge44-leaver8/evidence/local/INDEPENDENT-LOCAL-REPLAY.json
new file mode 100644
index 0000000000..aa15edfba5
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/local/INDEPENDENT-LOCAL-REPLAY.json
@@ -0,0 +1,71 @@
+{
+  "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY",
+  "canonical_word_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+  "local_programs_sha256": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+  "v": 112,
+  "helpers": 492,
+  "local": {
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+      "prefix_l1_upper": "2323449462751823289130723296176889733365478515961323543/64",
+      "prefix_bits_upper": 175,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    },
+    "backward": {
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+      "prefix_l1_upper": "600338326363508935771850050281004728884643/32",
+      "prefix_bits_upper": 134,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    }
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+      "5": 56
+    },
+    "backward": {
+      "1": 2514,
+      "4": 160,
+      "8": 8,
+      "3": 448,
+      "2": 404,
+      "5": 56
+    }
+  },
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+  "cold_hyperplane_ended_helpers": 44,
+  "negative_controls_rejected": [
+    "wrong_scale",
+    "missing_center",
+    "wrong_common_frame",
+    "wrong_child_rank",
+    "missing_pre_wrapper",
+    "missing_post_wrapper",
+    "wrapper_with_wrong_frame",
+    "wrapper_in_wrong_phase",
+    "wrapper_on_a_data_register",
+    "wrapper_on_a_target_register",
+    "wrapper_on_a_centre_register",
+    "hpe_pre_wrapper_resolved_to_full_recipe",
+    "hpe_post_wrapper_without_terminal_frame",
+    "hpe_post_wrapper_wrong_terminal_frame",
+    "hpe_tail_gate_at_full_frame",
+    "hpe_tail_climb_dropped",
+    "hpe_helper_exit_adapter_to_full",
+    "hpe_tail_gate_moved_into_full_cleanup",
+    "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter",
+    "cold_hpe_pre_wrapper_dropped",
+    "cold_hpe_post_wrapper_replaced_by_exit_adapter",
+    "cold_hpe_pre_wrapper_resolved_to_cold_full_convention",
+    "cold_hpe_wrapper_with_nonzero_entrance",
+    "cold_hpe_post_wrapper_wrong_terminal_frame",
+    "cold_hpe_premix_gate_before_pre_wrapper"
+  ],
+  "scope": "Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate."
+}
diff --git a/research/gauge44-leaver8/evidence/local/LOCAL-CHECKS.json b/research/gauge44-leaver8/evidence/local/LOCAL-CHECKS.json
new file mode 100644
index 0000000000..3872f0e596
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/local/LOCAL-CHECKS.json
@@ -0,0 +1,36 @@
+{
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+    "sha256": "d17399c8c7458bb7110d8596fab5f769cd4cb3733a3042277fa08bf03f42d6c9",
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+    "scalar_macros": 41570,
+    "real_component_primitive_bound": 420052,
+    "paid_profile": {
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+    "private_centers_cleared": true,
+    "private_coefficient_stream_cleared_after_each_macro": true
+  },
+  "backward": {
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diff --git a/research/gauge44-leaver8/evidence/local/LOCAL-PROGRAMS.json.gz b/research/gauge44-leaver8/evidence/local/LOCAL-PROGRAMS.json.gz
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+  "refactored_cleanup": {
+    "exact_non_target_isolation_checked": true,
+    "high_inverse": "dyadic_sparse_Gauss_Jordan",
+    "kind": "source_branch_gauge_and_retired_completion_cold44",
+    "new_cold_ends": 44
+  }
+}
diff --git a/research/gauge44-leaver8/evidence/local/WRAPPER-CHECKS.json b/research/gauge44-leaver8/evidence/local/WRAPPER-CHECKS.json
new file mode 100644
index 0000000000..a18afd4fad
--- /dev/null
+++ b/research/gauge44-leaver8/evidence/local/WRAPPER-CHECKS.json
@@ -0,0 +1,413 @@
+{
+ "status": "PASS_RESIDUAL_WRAPPERS_ARE_EXACT",
+ "frames": 22,
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+   "residual_width": 4
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+  "wrong quadratic form",
+  "sides swapped",
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+  "hpe: width misreported as 9 - dim E",
+  "hpe: wrong terminal hyperplane",
+  "hpe: pre wrapper resolved to the FULL recipe R_{E,FULL}",
+  "hpe: wrong global phase",
+  "cold hpe: identity pre wrapper instead of R_{0,U}",
+  "cold hpe: identity post wrapper instead of L_{0,U}",
+  "cold hpe: no wrappers (cold FULL convention L = R = I)",
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+  "cold hpe: wrong terminal hyperplane",
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+ ]
+}
diff --git a/research/gauge44-leaver8/hosting/PROOF.md b/research/gauge44-leaver8/hosting/PROOF.md
new file mode 100644
index 0000000000..b551b6d3e5
--- /dev/null
+++ b/research/gauge44-leaver8/hosting/PROOF.md
@@ -0,0 +1,237 @@
+# Exact owner reuse and concave-cost matching
+
+## 1. Objects and interface assumptions
+
+The parent controller has 72 ordered calls, 112 source ports, 112 target ports,
+and 492 helper roles per call. The ambient dimension is 73. A pending-child
+group is a triple
+
+$$
+g=(\text{owner replica},\text{child},\text{port}).
+$$
+
+The parent window catalogue gives group capacity $C_g$, together with the call
+times at which its physical stream is idle. The map from a group to its
+physical family is
+
+$$
+F(g)=896\,\text{owner replica}
+  +112(2\,\text{pair(child)}+\text{side(child)})+\text{port}.
+$$
+
+At every call in this particular parent geometry, at most one pending child of
+a physical family is eligible. Both the matcher and the independent frozen
+audit check this condition. They also exclude both active data families of the
+call. Consequently, injective assignment to eligible groups is equivalent to
+assignment to distinct idle physical families at that call.
+
+Helper $h$ requests an integer width $w_h$, read afresh from the new local
+word as the final-frame dimension minus the start-frame dimension. Native
+program profiles are also recomputed from their paid edges. The finite local
+compiler supplies the normalized helper chart and verifies its warm-start
+semantics. A hosted width is a reservation in the pending child's address
+coordinates on an existing physical stream; it is not a new physical stream.
+
+This proof concerns the discrete assignment and its moment contribution. It
+uses the parent windows as input. Independent global admission must verify
+those windows against the actual controller and construct the actual
+73-column charts for the fresh native local word.
+
+## 2. Feasible shrinking on the original families
+
+For one call, sort the old slot widths and the new helper widths increasingly,
+breaking ties by the old or new helper number. Suppose the new width in each
+position is no larger than its matched old width. Assign that helper to the
+matched old slot.
+
+This operation preserves the call time, stage, replica, pending child, port,
+owner replica, and physical family. It preserves the set of 492 distinct
+helper-owner families at the call, so the old window and active-data
+exclusions still hold. In each pending-child group, the sum of new widths is
+no larger than the old sum, hence remains within capacity.
+
+Now order the assignments in each group consistently and replace their
+offsets by consecutive prefix sums. The occupied sets become pairwise
+disjoint intervals whose union is exactly a prefix of length
+$U_g=\sum w_h\le C_g$. The idle child retains rank $C_g-U_g$, with pending
+offset $U_g$. Thus the shrinking operation has a direct capacity proof; it
+requires neither an owner solver nor any change to the controller.
+
+The seed constructor applies this termwise argument to the 71 former `jp8`
+calls. It keeps the remaining `ck` call provisionally unchanged. Two optional
+fixed-family assignment passes redistribute the available capacity before
+freezing the seed. Their result is audited using the same integer constraints.
+
+## 3. One call with all other calls fixed
+
+Fix one call $t$. Remove its existing assignments while keeping every other
+call fixed. For each eligible group, define the available capacity
+
+$$
+c_g=C_g-\sum_{\substack{\text{assignments in }g\\\text{from calls other than }t}}w.
+$$
+
+The call must assign each of its 492 widths to a distinct eligible group with
+$w\le c_g$. Unused groups can be viewed as receiving a dummy width zero.
+After the assignment, group $g$'s idle rank is $c_g-w_g$. For any function
+$\phi$, the portion of the idle objective affected by the call is exactly
+
+$$
+\sum_{g\text{ eligible at }t}\phi(c_g-w_g).
+$$
+
+All other idle contributions, and all local paid-edge contributions, are
+constant in this single-call problem.
+
+### Greedy rule
+
+Sort eligible capacities increasingly. At each capacity, assign the largest
+remaining helper width that fits; assign zero if none fits. Continue through
+the remaining capacities.
+
+This rule has no floating parameter. Equal-capacity tie choices are used only
+to limit changes to physical owners and make the artifact deterministic.
+
+### Exchange lemma
+
+Take two capacities $c_1\le c_2$ and two widths $w_1\le w_2\le c_1$. The
+assignment of $w_1$ to $c_1$ and $w_2$ to $c_2$ has residual pair
+
+$$
+(c_1-w_1,\ c_2-w_2).
+$$
+
+Exchange the widths. Feasibility is preserved, and the new pair is
+
+$$
+(c_1-w_2,\ c_2-w_1).
+$$
+
+The total is unchanged. The first new component is no larger than either old
+component, and the second is no smaller than either old component. Therefore
+the new pair majorizes the old pair. Every concave $\phi$ has weakly smaller
+sum on the new pair.
+
+### Consequence: feasibility and optimality
+
+Start from any feasible complete assignment. At the smallest remaining
+capacity, its assigned width is no larger than the largest remaining width
+that fits. The greedy width occurs at some later capacity. If the two differ,
+the exchange lemma moves that width to the current capacity while preserving
+feasibility and weakly decreasing every concave objective. Fix this first
+position and repeat on the suffix. Dummy zero widths cover unused groups.
+
+Thus the greedy procedure succeeds whenever a feasible assignment exists, and
+its remainder vector majorizes that of every feasible assignment. It
+simultaneously minimizes every concave remainder objective for this call.
+This proof depends on the absence of any eligibility restriction beyond the
+capacity and the already fixed call window; that property is explicitly
+checked for the present geometry.
+
+## 4. Exact majorization receipts
+
+Let $a_r$ and $b_r$ be the old and new remainder histograms for one update,
+including zero remainders. When the helper-width multiset is unchanged, their
+total numbers of groups and total ranks agree. Every remainder lies between
+0 and 48. The implementation checks, with integers, that for each
+$k=0,1,\ldots,48$,
+
+$$
+\sum_r b_r\max(r-k,0)
+\;\ge\;
+\sum_r a_r\max(r-k,0).
+$$
+
+These are the stored stop-loss margins. Between integer breakpoints the
+difference is linear, so checking all integer breakpoints checks every real
+threshold. With equal sums and equal lengths, the inequalities are the
+standard majorization criterion: the new vector majorizes the old one.
+
+The transcript contains 288 such equal-width updates: four passes through 72
+calls. A single preceding update replaces the seed's last `ck` width multiset.
+That bootstrap has different total width, so it is checked for exact
+feasibility and is not represented as an equal-sum majorization step.
+
+`reproduce.py` reruns every update and compares the full transcript's semantic
+hash. Independently, `audit_frozen.py` removes each final call in turn, computes
+all available capacities directly from the frozen owner map, runs a separate
+histogram-only greedy calculation, and verifies that it returns exactly the
+existing remainder histogram. This checks all 72 final coordinate optima
+without relying on the transcript or the discovery seed.
+
+## 5. Relation to the global moment
+
+For ambient dimension $M=73$, define
+
+$$
+\phi_b(r)=r\bigl((73/r)^b-1\bigr)
+          =73^b r^{1-b}-r,\qquad \phi_b(0)=0.
+$$
+
+For $0<b<1$, this function is continuous at zero and strictly concave on
+positive ranks, because
+
+$$
+\phi_b''(r)=-b(1-b)73^b r^{-b-1}<0.
+$$
+
+Once all calls use the new provider, the local paid profile is fixed and every
+accepted owner update preserves the global paid rank mass. The exchange and
+majorization arguments therefore weakly decrease the global moment pressure
+for every $b\in(0,1)$ simultaneously. A strict histogram majorization strictly
+decreases that pressure. No estimated root, derivative, or floating cost is
+needed to establish the improvement of these updates.
+
+For the frozen map, the exact paid rank mass is 520704, so
+
+$$
+73\cdot7168-520704=2560.
+$$
+
+The final profile is recomputed from 72 copies of the new local paid profile
+and from the actual remaining rank in every pending-child group. Numerical
+roots printed by the matcher are screens only. Exact moment bounds and their
+combination with the bit supplier are performed by the package's admitted
+global pipeline.
+
+## 6. Determinism and fixed-point scope
+
+The implementation keeps the parent call order, alternating a forward pass
+and a reverse pass. Within equal-capacity groups, it first prefers the old
+assigned width, then other previously used owners, and finally physical-family
+order. It retains an old helper number when possible and otherwise takes the
+smallest unassigned helper number of the required width. These tie rules
+affect the frozen map, but not the single-call optimum remainder histogram.
+
+The recorded run has three passes with strict improvements. Its fourth pass
+has zero strict changes and zero changed helper owners. Hence the recorded map
+is a fixed point of the implemented call update. The separate final audit
+also establishes the stronger cost-level statement that every individual call
+already minimizes every concave remainder objective with the other calls
+fixed.
+
+Calls share capacities. Simultaneously changing two or more calls could
+possibly improve on a coordinate fixed point. The argument makes **no claim
+of joint global optimality**, and the frozen artifact does not depend on such
+a claim.
+
+## 7. Fields to regenerate for actual global admission
+
+| Field or object | Required action |
+| --- | --- |
+| Call `stage`, `replica`, `time` and parent windows | Preserve the parent controller |
+| Helper number and width | Read the new local signature and use the nominated assignment |
+| `owner_replica`, `child`, `port` | Use the final legal group selected by the matcher |
+| `copy`, `family` | Recompute from the selected group, then check uniqueness and active-data exclusion |
+| Helper `offset` | Compact all widths in each group into a disjoint prefix |
+| Idle `rank`, `hosted`, `pending_offset` | Recompute from the actual occupied prefix |
+| Per-call width lists and global paid profile | Recompute from the fresh local programs and actual cells |
+| Provider bindings, center carriers and program hashes | Bind the freshly checked provider; do not retain stale parent IDs or hashes |
+| Actual 73-column owner charts and their digests | Generate afresh from the selected child, port, offset, width and spectator coordinates |
+
+The new construction uses different center carrier registers, including source
+registers. Its ordered center frames and checked operator, rather than old
+carrier numbers, are the semantic interface. The hosting proof does not waive
+that interface check. The signature-only intermediate PLAN produced during
+replay is explicitly marked as such and is never a substitute for fresh
+provider binding or global phase admission.
diff --git a/research/gauge44-leaver8/hosting/README.md b/research/gauge44-leaver8/hosting/README.md
new file mode 100644
index 0000000000..b9505ebbea
--- /dev/null
+++ b/research/gauge44-leaver8/hosting/README.md
@@ -0,0 +1,162 @@
+# Cold44 hosting: frozen owner map and exact callwise matching
+
+This directory contains the owner assignment used to turn the new cold44 local
+word into a global improvement. All 72 calls use the new local signature. The
+assignment is frozen; no search, tuning, or optimization is needed to consume
+it in the global verifier.
+
+The local word reduces the helper width sum from 3894 for the previous `jp8`
+provider to 3794. Simply shrinking the old allocations leaves many small idle
+remainders. The matcher below moves helpers to other physical families that are
+already idle at the same call, concentrating those remainders while respecting
+every parent capacity and window. This recovers a substantial part of the local
+saving in the global moment calculation.
+
+## Frozen result
+
+The exact finite data are in [frozen/MANIFEST.json](frozen/MANIFEST.json) and
+[frozen/MATCHING-RECEIPT.json](frozen/MATCHING-RECEIPT.json).
+
+| Quantity | Frozen value |
+| --- | ---: |
+| Calls | 72 |
+| Helpers per call | 492 |
+| Owner roles | 35,424 |
+| Ambient dimension | 73 |
+| Live streams | 7,168 |
+| New local width sum | 3,794 |
+| New local paid rank mass | 5,650 |
+| Global paid rank mass | 520,704 |
+| Global deficit | 2,560 |
+| Maximum child rank | 48 |
+| Equal-width updates with exact majorization receipts | 288 |
+| Final callwise optima independently checked | 72 |
+
+The new local width inventory is `{4:52, 5:48, 7:34, 8:114, 9:244}` and its paid
+profile is `{1:2514, 2:404, 3:448, 4:160, 5:56, 8:8}`. The final global paid
+profile, including all idle remainders, is:
+
+```json
+{"1":181093,"2":29164,"3":32429,"4":11520,"5":4032,"7":7,
+ "8":582,"12":13,"16":33,"19":1,"20":2,"28":4,"32":62,
+ "36":1,"40":1,"44":6,"48":2289}
+```
+
+Its floating moment screen is `b = 0.0016522089943684115`, giving the analytic
+screen `b/(1+b) = 0.0016494837025589793`. Relative to PR #635's reported
+`0.001636241501576388`, that is approximately **0.8093%**. These decimal screens
+are diagnostic values; the package's exact moment and outer assembly determine
+the admitted exponent. The owner replay never uses the floating root to choose
+an expanded-matching move.
+
+The frozen owner file has byte SHA-256:
+
+```text
+90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57
+```
+
+Its semantic SHA-256, computed from sorted-key compact uncompressed JSON, is:
+
+```text
+c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d
+```
+
+Semantic hashes are the portable replay criterion. The gzip byte hash is also
+reported, but compressor implementations need not produce identical streams.
+
+## Reproduce with the Python standard library
+
+Supply the PR #635 parent `PLAN.json` and `OWNERS.json.gz`, plus either the new
+verified native provider directory or the new raw word. The expected parent
+hashes are pinned in the manifest. The command below is run from the package
+root; replace the example input paths with actual paths.
+
+```sh
+python hosting/reproduce.py \
+  --parent-plan /path/to/pr635/research/complex-571-cold14-st2/data/PLAN.json \
+  --parent-owners /path/to/pr635/research/complex-571-cold14-st2/data/OWNERS.json.gz \
+  --local44 /path/to/verified/local44 \
+  --out /path/to/new/hosting-replay
+```
+
+For the raw provider, replace `--local44 ...` with
+`--raw-word /path/to/FULL-WORD.json.gz`. Reading a raw word here only extracts a
+nomination signature; it does not replace independent local verification.
+
+The default replay copies the frozen mixed-provider seed, checks its semantic
+hash, derives its profile afresh, and runs the exact expanded matcher. It then
+compares the final owner and majorization transcript with the frozen semantic
+hashes and independently checks the final map's 72 callwise fixed points.
+Outputs include `all72/OWNERS.json.gz`, `all72/PROFILE.json`, recomputed
+remainders, `FROZEN-AUDIT.json`, and `REPRODUCTION.json`.
+
+The seed has 71 cold44 calls and one inherited `ck` call. Expanded matching first
+replaces that last call using newly available legal families. This changed-width
+bootstrap is checked for feasibility and is explicitly excluded from the
+equal-width majorization count. The following four passes use cold44 at all 72
+calls:
+
+| Pass | Calls with strict majorization | Changed helper owners |
+| --- | ---: | ---: |
+| 1 | 70 | 1,245 |
+| 2 | 41 | 169 |
+| 3 | 8 | 13 |
+| 4 | 0 | 0 |
+
+Pass 4 changes neither the map nor its remainder histogram. The independent
+audit additionally recomputes the optimal remainder histogram for each call
+with all other calls fixed.
+
+## Optional: reproduce seed discovery
+
+Add `--rebuild-seed` to the same command to rebuild the mixed seed from the
+original PR #635 owners. This step first matches sorted new helper widths to
+sorted old owner slots, then performs two fixed-family Hungarian passes.
+Discovery used Python 3.12.14, NumPy 2.3.5, and SciPy 1.17.0. Equal-cost matching
+tie choices may vary across SciPy versions, so the script compares the rebuilt
+seed with the frozen semantic hash and fails if it differs. Default frozen-seed
+replay has no NumPy or SciPy dependency.
+
+The two discovery passes are an optional way to recover the recorded seed.
+Their floating costs are not needed for feasibility, for the final fixed-point
+proof, or for the package's admitted exponent.
+
+## Audit without regenerating the assignment
+
+```sh
+python hosting/audit_frozen.py \
+  --parent-plan /path/to/pr635/research/complex-571-cold14-st2/data/PLAN.json \
+  --parent-owners /path/to/pr635/research/complex-571-cold14-st2/data/OWNERS.json.gz \
+  --local44 /path/to/verified/local44 \
+  --out /path/to/FROZEN-AUDIT.json
+```
+
+This integer audit checks helper coverage, capacity, allowed call times, active
+data exclusion, physical-family uniqueness within each call, disjoint compacted
+coordinate prefixes, the exact global profile and rank mass, and callwise
+optimality of the frozen remainder histograms. It reads the explicit parent
+window catalogue. The package's separate global verifier must also derive
+those windows and all 73-column charts from the actual program.
+
+## Files and scope
+
+| File | Purpose |
+| --- | --- |
+| `frozen/OWNERS.json.gz` | The final all-cold44 map consumed by global assembly |
+| `frozen/SEED-OWNERS.json.gz` | Pinned feasible mixed seed for dependency-free replay |
+| `frozen/MAJORIZATION.json.gz` | Integer stop-loss margins for every expanded update |
+| `frozen/MANIFEST.json` | Parent, provider, artifact, profile, and parameter bindings |
+| `frozen/SEED-RECEIPT.json` | Recorded sorted matching and two seed discovery passes |
+| `frozen/MATCHING-RECEIPT.json` | Recorded expanded passes and exact finite totals |
+| `reproduce.py` | End-to-end parameterized hosting replay |
+| `reuse_owners.py` | Optional original-family seed constructor |
+| `expand_owners.py` | Exact greedy matching over all eligible physical families |
+| `audit_frozen.py` | Independent feasibility and final callwise fixed-point audit |
+| `PROOF.md` | Capacity, exchange, majorization, and integration arguments |
+
+The expanded matcher is individually optimal for each call when other calls
+are fixed, for every concave remainder cost simultaneously. The frozen map is
+a verified coordinate fixed point. **No joint global optimality claim is
+made.** New local algebra, changed center carriers, phase compatibility,
+actual owner charts, the finite invoice, and exact exponent admission remain
+the responsibility of the package's global verification pipeline.
diff --git a/research/gauge44-leaver8/hosting/audit_frozen.py b/research/gauge44-leaver8/hosting/audit_frozen.py
new file mode 100644
index 0000000000..26a07408ea
--- /dev/null
+++ b/research/gauge44-leaver8/hosting/audit_frozen.py
@@ -0,0 +1,169 @@
+"""Audit the frozen owner map and its callwise fixed point using integers.
+
+The parent window catalogue is an explicit input. The package's independent
+global verifier must additionally derive the windows from the actual program.
+This audit does not certify local algebra, phase charts, or an exponent.
+"""
+from collections import Counter, defaultdict
+from pathlib import Path
+import argparse
+import hashlib
+import json
+
+from reuse_owners import packed, read, sha, signature
+
+
+HERE = Path(__file__).resolve().parent
+
+
+def semantic_sha(path):
+    return hashlib.sha256(packed(read(path))).hexdigest()
+
+
+def add_inputs(parser):
+    parser.add_argument('--parent-plan', type=Path, required=True)
+    parser.add_argument('--parent-owners', type=Path, required=True)
+    provider = parser.add_mutually_exclusive_group(required=True)
+    provider.add_argument('--local44', type=Path, help='Independently checked native provider directory')
+    provider.add_argument('--raw-word', type=Path, help='New FULL-WORD.json.gz; nomination signature only')
+
+
+def bound_inputs(args, manifest):
+    assert sha(args.parent_plan) == manifest['parent_plan_sha256'], 'Wrong parent PLAN'
+    assert sha(args.parent_owners) == manifest['parent_owners_sha256'], 'Wrong parent OWNERS'
+    plan = read(args.parent_plan)
+    assert (plan['K'], plan['T'], plan['M'], plan['L'], plan['live']) == (4, 8, 73, 9, 7168)
+    provider_path = args.local44 if args.local44 is not None else args.raw_word
+    sig = signature(provider_path)
+    expected = manifest['new_provider']
+    assert len(sig['widths']) == expected['R']
+    assert hashlib.sha256(packed(sig['widths'])).hexdigest() == expected['width_vector_sha256']
+    assert sig['profile'] == {int(r): n for r, n in expected['profile'].items()}
+    assert Counter(sig['widths']) == {int(w): n for w, n in expected['width_histogram'].items()}
+    assert sum(sig['widths']) == expected['width_sum']
+    assert sum(r*n for r, n in sig['profile'].items()) == expected['rank_mass']
+    return plan, sig, provider_path
+
+
+def audit(plan, sig, owners):
+    V, R = 112, 492
+    order = [tuple(c) for c in plan['order']]
+    assert len(order) == 72 and len(set(order)) == 72
+    assert len(owners) == 72*R
+    bycall = defaultdict(dict)
+    cells = defaultdict(set)
+    caps, family, eligible = {}, {}, defaultdict(list)
+    for key, (cap, times) in plan['windows'].items():
+        rep, child = map(int, key.split(','))
+        assert 0 <= cap <= 48 and len(times) == len(set(times))
+        for port in range(V):
+            g = (rep, child, port)
+            caps[g] = cap
+            family[g] = rep*8*V + (2*plan['pairs'][str(child)] + plan['sides'][str(child)])*V + port
+            for t in times:
+                assert 0 <= t < len(order)
+                eligible[t].append(g)
+    for t, gs in eligible.items():
+        assert len({family[g] for g in gs}) == len(gs), 'Multiple eligible children on one family'
+        stage, rep = order[t]
+        pair = max(0, (stage-1)//2)
+        assert all(g[0] != rep or plan['pairs'][str(g[1])] != pair for g in gs)
+    for z in owners:
+        t, h = z['time'], z['helper']
+        assert 0 <= t < len(order) and 0 <= h < R
+        assert (z['stage'], z['replica']) == order[t]
+        assert h not in bycall[t]
+        assert z['width'] == sig['widths'][h]
+        g = (z['owner_replica'], z['child'], z['port'])
+        assert g in caps and t in plan['windows'][f'{g[0]},{g[1]}'][1]
+        assert z['copy'] == g[0]*V + g[2] and z['family'] == family[g]
+        off, width = z['offset'], z['width']
+        assert 0 <= off and off+width <= caps[g]
+        occupied = set(range(off, off+width))
+        assert not cells[g] & occupied, 'Overlapping hosted coordinates'
+        cells[g] |= occupied
+        bycall[t][h] = (g, width)
+    for t in range(72):
+        assert set(bycall[t]) == set(range(R))
+        assert len({family[g] for g, w in bycall[t].values()}) == R
+    for occupied in cells.values():
+        assert occupied == set(range(len(occupied))), 'Uncompacted hosted coordinates'
+    used = {g: len(cells[g]) for g in caps}
+    idle = Counter(caps[g]-used[g] for g in caps if caps[g] > used[g])
+    paid = Counter({r: 72*n for r, n in sig['profile'].items()})
+    paid.update(idle)
+
+    # Independent cost-level fixed-point check. No helper-ID or family-ID
+    # tie-breaking is needed: equal capacities give the same histogram.
+    for t in range(72):
+        old = {g: w for g, w in bycall[t].values()}
+        assert len(old) == R
+        before = Counter(caps[g]-used[g] for g in eligible[t])
+        available = sorted(caps[g]-used[g]+old.get(g, 0) for g in eligible[t])
+        want = Counter(sig['widths'])
+        after = Counter()
+        for cap in available:
+            width = next((w for w in sorted(want, reverse=True) if want[w] and w <= cap), 0)
+            if width:
+                want[width] -= 1
+            after[cap-width] += 1
+        assert not any(want.values()), 'Greedy assignment unexpectedly infeasible'
+        assert after == before, ('Frozen map is not callwise optimal', t)
+    mass = sum(r*n for r, n in paid.items())
+    assert 73*7168-mass == 2560 and max(paid) == 48
+    return {
+        'roles': len(owners), 'calls': 72, 'fixed_point_calls_checked': 72,
+        'remainder_profile': dict(sorted(idle.items())),
+        'global_profile': dict(sorted(paid.items())),
+        'rank_mass': mass, 'deficit': 2560, 'maxchild': 48,
+        'all_footprints_disjoint_compacted_prefixes': True,
+        'all_helper_families_idle_and_outside_active_data': True,
+        'one_helper_per_physical_family_per_call': True,
+        'every_call_optimal_for_every_concave_remainder_cost': True,
+        'global_optimality_claimed': False,
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    add_inputs(parser)
+    parser.add_argument('--owners', type=Path, default=HERE/'frozen/OWNERS.json.gz')
+    parser.add_argument('--majorization', type=Path, default=HERE/'frozen/MAJORIZATION.json.gz')
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    manifest = read(HERE/'frozen/MANIFEST.json')
+    plan, sig, provider_path = bound_inputs(args, manifest)
+    assert semantic_sha(args.owners) == manifest['artifacts']['OWNERS.json.gz']['semantic_sha256']
+    assert semantic_sha(args.majorization) == manifest['artifacts']['MAJORIZATION.json.gz']['semantic_sha256']
+    result = audit(plan, sig, read(args.owners))
+    for key in ('remainder_profile', 'global_profile'):
+        assert result[key] == {int(r): n for r, n in manifest[key].items()}
+    moves = read(args.majorization)
+    checked = 0
+    for move in moves:
+        if move['equal_width_multiset']:
+            margins = move['integer_stoploss_margins']
+            assert len(margins) == 49 and all(type(x) is int and x >= 0 for x in margins)
+            assert margins[0] == margins[-1] == 0
+            assert move['strict_majorization'] == bool(any(margins))
+            checked += 1
+        else:
+            assert move['bootstrap'] and move['integer_stoploss_margins'] is None
+    assert checked == 288 and len(moves) == 289
+    result.update({
+        'status': 'PASS_FROZEN_HOSTING_AND_ALL_72_CALLWISE_FIXED_POINTS',
+        'parent_plan_sha256': sha(args.parent_plan),
+        'parent_owners_sha256': sha(args.parent_owners),
+        'owners_semantic_sha256': semantic_sha(args.owners),
+        'majorization_semantic_sha256': semantic_sha(args.majorization),
+        'stored_integer_majorization_steps': checked,
+        'majorization_replay': 'reproduce.py re-executes every step; this audit separately checks the final fixed point.',
+        'remaining_scope': 'The package global verifier checks fresh local algebra, phases, windows, invoice, moment, and outer assembly.',
+    })
+    args.out.parent.mkdir(parents=True, exist_ok=True)
+    args.out.write_text(json.dumps(result, indent=2)+'\n')
+    print(json.dumps(result, indent=2))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/hosting/expand_owners.py b/research/gauge44-leaver8/hosting/expand_owners.py
new file mode 100644
index 0000000000..ee6c4c24e6
--- /dev/null
+++ b/research/gauge44-leaver8/hosting/expand_owners.py
@@ -0,0 +1,186 @@
+"""Exact callwise concave-cost owner matching over every legal idle family.
+
+This is a finite integer nomination algorithm, not a MILP. Each greedy
+matching is optimal for every concave remainder cost. Its majorization
+receipt is checked with integers, independently of floating root screens.
+"""
+from collections import Counter, defaultdict, deque
+from pathlib import Path
+import argparse
+import gzip
+import hashlib
+import json
+import time
+
+from reuse_owners import read, packed, sha, signature, audit_roles, rate
+
+
+def stoploss(hist,k):return sum(n*max(r-k,0) for r,n in hist.items())
+
+
+def main():
+    ap=argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--plan',type=Path,required=True)
+    ap.add_argument('--owners',type=Path,required=True)
+    ap.add_argument('--signature',action='append',required=True,help='Existing PID=verified native directory or raw/signature JSON')
+    ap.add_argument('--max-passes',type=int,default=8)
+    ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args();assert 1<=a.max_passes<=12
+    a.out.mkdir(parents=True,exist_ok=False);beg=time.monotonic()
+    plan,oldroles=read(a.plan),read(a.owners);V,M=112,73
+    assert (plan['K'],plan['T'],plan['M'],plan['L'])==(4,8,73,9)
+    sig={pid:{'widths':desc['widths'],'profile':{int(r):n for r,n in desc['actual_paid_profile'].items()},'source':'input PLAN'} for pid,desc in plan['provider_registry'].items()}
+    for spec in a.signature:
+        pid,path=spec.split('=',1);assert pid in sig;sig[pid]=signature(path)
+    R=len(next(iter(sig.values()))['widths'])
+    for s in sig.values():
+        assert len(s['widths'])==R and all(type(w) is int and 0<w<=9 for w in s['widths'])
+        assert sum(r*n for r,n in s['profile'].items())==16*V+64+sum(s['widths'])
+    calls={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+    order=[tuple(c) for c in plan['order']]
+    oldwidths={k:plan['provider_registry'][c['provider']]['widths'] for k,c in calls.items()}
+    widths={k:sig[c['provider']]['widths'] for k,c in calls.items()}
+    audit_roles(oldroles,plan,oldwidths,V,R)
+    caps={};families={};eligible=defaultdict(list)
+    for key,(cap,window) in plan['windows'].items():
+        rep,ch=map(int,key.split(','))
+        for port in range(V):
+            g=(rep,ch,port);caps[g]=cap
+            families[g]=rep*(8*V)+(2*plan['pairs'][str(ch)]+plan['sides'][str(ch)])*V+port
+            for t in window:eligible[t].append(g)
+    for t,gs in eligible.items():
+        assert len({families[g] for g in gs})==len(gs), 'current geometry requires one eligible child per family'
+        s,rep=order[t];active_pair=max(0,(s-1)//2)
+        assert all(not (g[0]==rep and plan['pairs'][str(g[1])]==active_pair) for g in gs), 'active data family in idle window'
+    current=defaultdict(dict);used={g:0 for g in caps}
+    for z in oldroles:
+        c=(z['stage'],z['replica']);g=(z['owner_replica'],z['child'],z['port'])
+        current[c][z['helper']]=(g,z['width']);used[g]+=z['width']
+    assert all(0<=used[g]<=caps[g] for g in caps)
+    moves=[]
+
+    def idle_profile():return Counter(caps[g]-used[g] for g in caps if caps[g]>used[g])
+
+    def total_profile():
+        p=Counter()
+        for c in plan['provider_calls']:p.update(sig[c['provider']]['profile'])
+        p.update(idle_profile());assert M*plan['live']-sum(r*n for r,n in p.items())==2560
+        return p
+
+    def update(call,bootstrap=False):
+        t=calls[call]['time'];gs=eligible[t]
+        old=current[call]
+        old_by_group={g:(h,w) for h,(g,w) in old.items()}
+        assert len(old_by_group)==R and set(old_by_group)<=set(gs)
+        oldhist=Counter(caps[g]-used[g] for g in gs)
+        for g,(h,w) in old_by_group.items():used[g]-=w
+        want=defaultdict(set)
+        for h,w in enumerate(widths[call]):want[w].add(h)
+        # Equal-capacity opportunities have identical costs. Preserve old
+        # matching widths first, then old owners, and finally family order.
+        buckets=defaultdict(lambda:defaultdict(deque))
+        for g in sorted(gs,key=lambda g:(families[g],g[1])):
+            available=caps[g]-used[g];oldw=old_by_group.get(g,(None,0))[1]
+            buckets[available][oldw].append(g)
+        result={};unassigned=R
+        for c in sorted(buckets):
+            bucket=buckets[c]
+            while unassigned and any(bucket.values()):
+                w=next((w for w in sorted(want,reverse=True) if w<=c and want[w]),None)
+                if w is None:break
+                if bucket.get(w):q=w
+                else:q=next(q for q in sorted(bucket,reverse=True) if bucket[q])
+                g=bucket[q].popleft()
+                h0=old_by_group.get(g,(None,0))[0]
+                h=h0 if h0 in want[w] else min(want[w])
+                want[w].remove(h);result[h]=(g,w);used[g]+=w;unassigned-=1
+                assert used[g]<=caps[g]
+        assert unassigned==0,('no legal family matching',call,{w:len(h) for w,h in want.items() if h})
+        assert set(result)==set(range(R)) and len({families[g] for g,w in result.values()})==R
+        newhist=Counter(caps[g]-used[g] for g in gs)
+        equal_widths=Counter(w for g,w in old.values())==Counter(widths[call])
+        strict=False
+        if equal_widths:
+            assert sum(oldhist.values())==sum(newhist.values())
+            assert stoploss(oldhist,0)==stoploss(newhist,0)
+            margins=[stoploss(newhist,k)-stoploss(oldhist,k) for k in range(49)]
+            assert min(margins)>=0,('greedy did not majorize old assignment',call,margins)
+            strict=any(margins)
+        else:
+            assert bootstrap
+            margins=None
+        changed=sum(result[h]!=old[h] for h in result)
+        current[call]=result
+        moves.append({'stage':call[0],'replica':call[1],'time':t,'bootstrap':bootstrap,
+                      'equal_width_multiset':equal_widths,'integer_stoploss_margins':margins,
+                      'strict_majorization':strict,'changed_helper_owners':changed})
+        return strict,changed
+
+    changed_calls=[c for c in order if any(current[c][h][1]!=widths[c][h] for h in range(R))]
+    for c in changed_calls:update(c,bootstrap=True)
+    p=total_profile();baseline_b=rate(p,2560,M)
+    rounds=[{'pass':'bootstrap','changed_provider_calls':[list(c) for c in changed_calls],
+             'floating_b':baseline_b,'remainder_profile':dict(sorted(idle_profile().items()))}]
+    print(json.dumps({'checkpoint':'all_goal_signatures_feasible','bootstrap_calls':len(changed_calls),'floating_b':baseline_b}),flush=True)
+    quiet=0
+    for passno in range(a.max_passes):
+        strict=changed=0
+        for c in (order if passno%2==0 else list(reversed(order))):
+            s,z=update(c);strict+=bool(s);changed+=z
+        p=total_profile();r={'pass':passno+1,'strictly_improved_calls':strict,'changed_helper_owners':changed,
+                             'floating_b':rate(p,2560,M),'remainder_profile':dict(sorted(idle_profile().items()))}
+        rounds.append(r);print(json.dumps({k:r[k] for k in ('pass','strictly_improved_calls','changed_helper_owners','floating_b')}),flush=True)
+        quiet=quiet+1 if not strict else 0
+        if quiet>=2 or (not strict and not changed):break
+
+    groups=defaultdict(list);roles=[]
+    for call in order:
+        s,rep=call;t=calls[call]['time']
+        for h,(g,w) in current[call].items():
+            orp,ch,port=g
+            z={'child':ch,'copy':orp*V+port,'family':families[g],'helper':h,'offset':0,
+               'owner_replica':orp,'port':port,'replica':rep,'stage':s,'time':t,'width':w}
+            roles.append(z);groups[g].append(z)
+    for g,zs in groups.items():
+        off=0
+        for z in sorted(zs,key=lambda z:(z['time'],z['helper'])):z['offset']=off;off+=z['width']
+        assert off==used[g]<=caps[g]
+    roles.sort(key=lambda z:(z['time'],z['helper']))
+    cells,_=audit_roles(roles,plan,widths,V,R)
+    for z in roles:
+        active=max(0,(z['stage']-1)//2)
+        assert not (z['owner_replica']==z['replica'] and plan['pairs'][str(z['child'])]==active)
+    for g in caps:assert len(cells[g])==used[g]
+    remainder=[]
+    for g in caps:
+        left=caps[g]-used[g]
+        if left:
+            rep,ch,port=g
+            remainder.append({'child':ch,'port':port,'replica':rep,'replicas':1,'family':families[g],
+                              'rank':left,'hosted':used[g],'pending_offset':used[g]})
+    profile=dict(sorted(total_profile().items()));assert M*M>2*max(profile)**2
+    raw=packed(roles);compressed=bytearray(gzip.compress(raw,mtime=0));compressed[9]=255
+    (a.out/'OWNERS.json.gz').write_bytes(bytes(compressed))
+    (a.out/'MAJORIZATION.json.gz').write_bytes(gzip.compress(packed(moves),mtime=0))
+    (a.out/'REMAINDERS.json').write_text(json.dumps(remainder,indent=2)+'\n')
+    (a.out/'PROFILE.json').write_text(json.dumps(profile,indent=2)+'\n')
+    fields={'profile':profile,'per_call_widths':[{'stage':s,'replica':r,'widths':widths[s,r]} for s,r in order],
+            'assignment_sha256':hashlib.sha256(raw).hexdigest(),'assignment_sha256_semantics':'SHA256 sorted-key compact uncompressed OWNERS array',
+            'source_owners_sha256':sha(a.owners),'provider_signatures':sig}
+    (a.out/'PLAN-OWNER-FIELDS.json').write_text(json.dumps(fields,indent=2)+'\n')
+    receipt={'status':'PASS_EXPANDED_OWNER_MATCHING_EXACT_COMBINATORICS_PENDING_GLOBAL_ADMISSION',
+             'source_plan':str(a.plan),'source_plan_sha256':sha(a.plan),'source_owners':str(a.owners),'source_owners_sha256':sha(a.owners),
+             'owners_sha256':sha(a.out/'OWNERS.json.gz'),'source_signatures':sig,
+             'roles':len(roles),'calls':len(order),'unchanged_call_order_and_windows':True,
+             'all_families_idle_and_outside_active_data':True,'one_helper_per_family_per_call':True,
+             'all_footprints_disjoint_compacted_prefixes':True,'integer_majorization_steps':sum(z['equal_width_multiset'] for z in moves),
+             'majorization_sha256':sha(a.out/'MAJORIZATION.json.gz'),'matching_rounds':rounds,
+             'global_profile':profile,'rank_mass':sum(r*n for r,n in profile.items()),'deficit':2560,
+             'remainder_profile':dict(sorted(idle_profile().items())),'maxchild':max(profile),
+             'candidate_floating_screen_b':rate(profile,2560,M),'seconds':time.monotonic()-beg,
+             'remaining_admission':'Fresh native-provider bindings, actual 73-column owner charts, independent full controller audit, finite invoice, exact moment and outer assembly.'}
+    (a.out/'EXPANDED-OWNER-REUSE.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    print(json.dumps({k:receipt[k] for k in ('status','roles','remainder_profile','rank_mass','candidate_floating_screen_b','seconds')},indent=2),flush=True)
+
+
+if __name__=='__main__':main()
diff --git a/research/gauge44-leaver8/hosting/frozen/FROZEN-AUDIT.json b/research/gauge44-leaver8/hosting/frozen/FROZEN-AUDIT.json
new file mode 100644
index 0000000000..5f95552366
--- /dev/null
+++ b/research/gauge44-leaver8/hosting/frozen/FROZEN-AUDIT.json
@@ -0,0 +1,57 @@
+{
+  "roles": 35424,
+  "calls": 72,
+  "fixed_point_calls_checked": 72,
+  "remainder_profile": {
+    "1": 85,
+    "2": 76,
+    "3": 173,
+    "7": 7,
+    "8": 6,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "all_footprints_disjoint_compacted_prefixes": true,
+  "all_helper_families_idle_and_outside_active_data": true,
+  "one_helper_per_physical_family_per_call": true,
+  "every_call_optimal_for_every_concave_remainder_cost": true,
+  "global_optimality_claimed": false,
+  "status": "PASS_FROZEN_HOSTING_AND_ALL_72_CALLWISE_FIXED_POINTS",
+  "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+  "owners_semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d",
+  "majorization_semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc",
+  "stored_integer_majorization_steps": 288,
+  "majorization_replay": "reproduce.py re-executes every step; this audit separately checks the final fixed point.",
+  "remaining_scope": "The package global verifier checks fresh local algebra, phases, windows, invoice, moment, and outer assembly."
+}
diff --git a/research/gauge44-leaver8/hosting/frozen/MAJORIZATION.json.gz b/research/gauge44-leaver8/hosting/frozen/MAJORIZATION.json.gz
new file mode 100644
index 0000000000..047b1cfb67
Binary files /dev/null and b/research/gauge44-leaver8/hosting/frozen/MAJORIZATION.json.gz differ
diff --git a/research/gauge44-leaver8/hosting/frozen/MANIFEST.json b/research/gauge44-leaver8/hosting/frozen/MANIFEST.json
new file mode 100644
index 0000000000..291005722c
--- /dev/null
+++ b/research/gauge44-leaver8/hosting/frozen/MANIFEST.json
@@ -0,0 +1,114 @@
+{
+  "schema": "gauge44-hosting-frozen-v1",
+  "parent_pr": 635,
+  "parent_paths": {
+    "plan": "research/complex-571-cold14-st2/data/PLAN.json",
+    "owners": "research/complex-571-cold14-st2/data/OWNERS.json.gz"
+  },
+  "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+  "artifacts": {
+    "OWNERS.json.gz": {
+      "sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+      "semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d"
+    },
+    "SEED-OWNERS.json.gz": {
+      "sha256": "eb3be5eebbb84349d7e7f1bde2fc77772a12ad5bccc6dab7c4efd8d903e2a048",
+      "semantic_sha256": "beea695aa2e1ab973ad53f475b3e3e9cf6d0f8a9bca2033a445b64f3b3484e34"
+    },
+    "MAJORIZATION.json.gz": {
+      "sha256": "ec5f94b13d190d72bc0608dc9fe2498cc43ba9deb05028159a812ec1e4dcacdf",
+      "semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc"
+    }
+  },
+  "new_provider": {
+    "R": 492,
+    "h": 9,
+    "v": 112,
+    "width_histogram": {
+      "4": 52,
+      "5": 48,
+      "7": 34,
+      "8": 114,
+      "9": 244
+    },
+    "width_sum": 3794,
+    "profile": {
+      "1": 2514,
+      "2": 404,
+      "3": 448,
+      "4": 160,
+      "5": 56,
+      "8": 8
+    },
+    "rank_mass": 5650,
+    "raw_word_sha256": "3ef4e74e81e2f4621fc95272918ac7b8bb8858df0baa16cc6d91424d55aead9e",
+    "canonical_word_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+    "local_programs_sha256": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+    "width_vector_sha256": "b7fbefdb3af3942194ac9314c767c7812bd68adb734d4e00b70b2916bdb55de8"
+  },
+  "seed_discovery": {
+    "provider_replaced": "jp8",
+    "unchanged_provider": "ck",
+    "passes": 2,
+    "price_b": 0.001638923,
+    "python": "3.12.14",
+    "numpy": "2.3.5",
+    "scipy": "1.17.0",
+    "note": "Only seed discovery uses floating-point Hungarian costs. Frozen seed and the expanded exact replay require the Python standard library."
+  },
+  "expanded_replay": {
+    "providers_replaced": [
+      "jp8",
+      "ck"
+    ],
+    "max_passes": 8,
+    "actual_passes": 4,
+    "integer_majorization_steps": 288,
+    "changed_width_bootstrap_calls": 1
+  },
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "remainder_profile": {
+    "1": 85,
+    "2": 76,
+    "3": 173,
+    "7": 7,
+    "8": 6,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "live": 7168,
+  "roles": 35424,
+  "calls": 72,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "candidate_floating_screen_b": 0.0016522089943684115,
+  "screening_only": "The floating rate here is not a certified exponent. Exact supplier and outer admission belong to the package verifier."
+}
diff --git a/research/gauge44-leaver8/hosting/frozen/MATCHING-RECEIPT.json b/research/gauge44-leaver8/hosting/frozen/MATCHING-RECEIPT.json
new file mode 100644
index 0000000000..993331090c
--- /dev/null
+++ b/research/gauge44-leaver8/hosting/frozen/MATCHING-RECEIPT.json
@@ -0,0 +1,1205 @@
+{
+  "status": "PASS_EXPANDED_OWNER_MATCHING_EXACT_COMBINATORICS_PENDING_GLOBAL_ADMISSION",
+  "source_plan": "explicit parent PLAN, with a temporary signature-only seed view for expanded replay",
+  "source_plan_sha256": "0d2b6a12d3450cfb78e556e80d34cabb8cd1a7f8aa85c1a712a5177236672a37",
+  "source_owners": "frozen/SEED-OWNERS.json.gz",
+  "source_owners_sha256": "eb3be5eebbb84349d7e7f1bde2fc77772a12ad5bccc6dab7c4efd8d903e2a048",
+  "owners_sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+  "source_signatures": {
+    "ck": {
+      "widths": [
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
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+}
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diff --git a/research/gauge44-leaver8/hosting/frozen/REPRODUCTION.json b/research/gauge44-leaver8/hosting/frozen/REPRODUCTION.json
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diff --git a/research/gauge44-leaver8/hosting/frozen/SEED-OWNERS.json.gz b/research/gauge44-leaver8/hosting/frozen/SEED-OWNERS.json.gz
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index 0000000000..d61916a156
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diff --git a/research/gauge44-leaver8/hosting/frozen/SEED-RECEIPT.json b/research/gauge44-leaver8/hosting/frozen/SEED-RECEIPT.json
new file mode 100644
index 0000000000..82911f647b
--- /dev/null
+++ b/research/gauge44-leaver8/hosting/frozen/SEED-RECEIPT.json
@@ -0,0 +1,1537 @@
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+    },
+    "(0, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(0, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(0, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    }
+  },
+  "matching_passes": [
+    {
+      "pass": "sorted",
+      "touched_group_idle_pressure": 44.06409529228022,
+      "calls_awaiting_capacity_matching": 0
+    },
+    {
+      "pass": 1,
+      "accepted_calls": 71,
+      "touched_group_idle_pressure": 24.92521223381306,
+      "decrease": 19.13888305846716
+    },
+    {
+      "pass": 2,
+      "accepted_calls": 58,
+      "touched_group_idle_pressure": 23.047886627886065,
+      "decrease": 1.8773256059269947
+    }
+  ],
+  "roles": 35424,
+  "calls": 72,
+  "remainder_children": 3197,
+  "remainder_profile": {
+    "1": 83,
+    "2": 99,
+    "3": 197,
+    "4": 168,
+    "5": 6,
+    "6": 13,
+    "7": 16,
+    "8": 145,
+    "10": 4,
+    "11": 24,
+    "12": 19,
+    "13": 1,
+    "14": 3,
+    "15": 9,
+    "16": 107,
+    "18": 1,
+    "19": 10,
+    "20": 15,
+    "23": 2,
+    "24": 52,
+    "32": 1,
+    "44": 1,
+    "48": 2221
+  },
+  "global_profile": {
+    "1": 181177,
+    "2": 29335,
+    "3": 32309,
+    "4": 11692,
+    "5": 4052,
+    "6": 17,
+    "7": 16,
+    "8": 721,
+    "10": 4,
+    "11": 24,
+    "12": 19,
+    "13": 1,
+    "14": 3,
+    "15": 9,
+    "16": 107,
+    "18": 1,
+    "19": 10,
+    "20": 15,
+    "23": 2,
+    "24": 52,
+    "32": 1,
+    "44": 1,
+    "48": 2221
+  },
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "source_floating_screen_b": 0.001638923175694355,
+  "candidate_floating_screen_b": 0.0016446065186552388,
+  "remaining_admission": "Bind freshly verified provider artifacts and their hashes; regenerate the global template, actual 73-column sigmas and remainder axes with the existing emitter; run independent owner/frame audit, finite invoice, and exact moment/outer assembly.",
+  "provenance_note": "Absolute discovery paths and wall time removed; original artifact hashes and all exact combinatorial fields preserved."
+}
diff --git a/research/gauge44-leaver8/hosting/frozen/SEED-REPRODUCTION.json b/research/gauge44-leaver8/hosting/frozen/SEED-REPRODUCTION.json
new file mode 100644
index 0000000000..91ee98cf70
--- /dev/null
+++ b/research/gauge44-leaver8/hosting/frozen/SEED-REPRODUCTION.json
@@ -0,0 +1,29 @@
+{
+  "status": "PASS_FROZEN_OWNER_AND_INTEGER_MAJORIZATION_REPLAY",
+  "seed_mode": "two_pass_hungarian_discovery_rebuilt",
+  "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+  "owners_semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d",
+  "owners_gzip_sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+  "majorization_semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc",
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "scope": "Exact hosting nomination and callwise fixed-point replay; full supplier admission is separate."
+}
diff --git a/research/gauge44-leaver8/hosting/reproduce.py b/research/gauge44-leaver8/hosting/reproduce.py
new file mode 100644
index 0000000000..2f29a5ff13
--- /dev/null
+++ b/research/gauge44-leaver8/hosting/reproduce.py
@@ -0,0 +1,100 @@
+"""Reproduce the frozen all-cold44 owner nomination from explicit inputs.
+
+By default, replay the exact integer optimizer from the included frozen seed.
+--rebuild-seed additionally repeats the original two floating-cost Hungarian
+discovery passes; that optional route requires NumPy and SciPy.
+"""
+from pathlib import Path
+from collections import Counter
+import argparse
+import copy
+import json
+import shutil
+import subprocess
+import sys
+
+from audit_frozen import HERE, add_inputs, bound_inputs, semantic_sha
+from reuse_owners import audit_roles, read, sha
+
+
+def run(name, *args):
+    subprocess.run([sys.executable, str(HERE/name), *map(str, args)], check=True)
+
+
+def seed_plan(parent, seed_owners, new_signature):
+    """Build a signature-only resizer input; never an admitted provider PLAN."""
+    plan = copy.deepcopy(parent)
+    plan['provider_registry']['jp8']['widths'] = new_signature['widths']
+    plan['provider_registry']['jp8']['actual_paid_profile'] = new_signature['profile']
+    call_widths = {
+        (c['stage'], c['replica']): plan['provider_registry'][c['provider']]['widths']
+        for c in plan['provider_calls']
+    }
+    used, families = audit_roles(seed_owners, plan, call_widths, 112, 492)
+    profile = Counter()
+    for c in plan['provider_calls']:
+        profile.update({int(r): n for r, n in plan['provider_registry'][c['provider']]['actual_paid_profile'].items()})
+    for key, (cap, times) in plan['windows'].items():
+        rep, child = map(int, key.split(','))
+        for port in range(112):
+            left = cap-len(used[rep, child, port])
+            if left:
+                profile[left] += 1
+    assert 73*7168-sum(r*n for r, n in profile.items()) == 2560
+    plan['profile'] = dict(sorted(profile.items()))
+    plan['per_call_widths'] = [
+        {'stage': s, 'replica': r, 'widths': call_widths[s, r]}
+        for s, r in plan['order']
+    ]
+    plan['status'] = 'INTERMEDIATE_SIGNATURE_ONLY_OWNER_SEED_NOT_PROVIDER_ADMISSION'
+    return plan
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    add_inputs(parser)
+    parser.add_argument('--rebuild-seed', action='store_true')
+    parser.add_argument('--out', type=Path, required=True, help='New output directory')
+    args = parser.parse_args()
+    manifest = read(HERE/'frozen/MANIFEST.json')
+    parent, sig, provider = bound_inputs(args, manifest)
+    args.out.mkdir(parents=True, exist_ok=False)
+    seed_dir = args.out/'seed'
+    if args.rebuild_seed:
+        run('reuse_owners.py', '--plan', args.parent_plan, '--owners', args.parent_owners,
+            '--signature', f'jp8={provider}', '--passes', '2', '--price-b', '0.001638923', '--out', seed_dir)
+    else:
+        seed_dir.mkdir()
+        shutil.copyfile(HERE/'frozen/SEED-OWNERS.json.gz', seed_dir/'OWNERS.json.gz')
+    assert semantic_sha(seed_dir/'OWNERS.json.gz') == manifest['artifacts']['SEED-OWNERS.json.gz']['semantic_sha256'], (
+        'Seed differs; use the default frozen-seed replay, or the recorded NumPy/SciPy versions for discovery replay.'
+    )
+    plan = seed_plan(parent, read(seed_dir/'OWNERS.json.gz'), sig)
+    plan_path = seed_dir/'PLAN-FOR-RESIZER.json'
+    plan_path.write_text(json.dumps(plan, indent=2)+'\n')
+    final_dir = args.out/'all72'
+    run('expand_owners.py', '--plan', plan_path, '--owners', seed_dir/'OWNERS.json.gz',
+        '--signature', f'jp8={provider}', '--signature', f'ck={provider}',
+        '--max-passes', '8', '--out', final_dir)
+    for name in ('OWNERS.json.gz', 'MAJORIZATION.json.gz'):
+        assert semantic_sha(final_dir/name) == manifest['artifacts'][name]['semantic_sha256'], (name, 'Frozen semantic digest mismatch')
+    kwargs = ('--local44', args.local44) if args.local44 is not None else ('--raw-word', args.raw_word)
+    run('audit_frozen.py', '--parent-plan', args.parent_plan, '--parent-owners', args.parent_owners,
+        *kwargs, '--owners', final_dir/'OWNERS.json.gz', '--majorization', final_dir/'MAJORIZATION.json.gz',
+        '--out', args.out/'FROZEN-AUDIT.json')
+    receipt = {
+        'status': 'PASS_FROZEN_OWNER_AND_INTEGER_MAJORIZATION_REPLAY',
+        'seed_mode': 'two_pass_hungarian_discovery_rebuilt' if args.rebuild_seed else 'included_frozen_seed',
+        'parent_plan_sha256': sha(args.parent_plan), 'parent_owners_sha256': sha(args.parent_owners),
+        'owners_semantic_sha256': semantic_sha(final_dir/'OWNERS.json.gz'),
+        'owners_gzip_sha256': sha(final_dir/'OWNERS.json.gz'),
+        'majorization_semantic_sha256': semantic_sha(final_dir/'MAJORIZATION.json.gz'),
+        'global_profile': read(final_dir/'PROFILE.json'),
+        'scope': 'Exact hosting nomination and callwise fixed-point replay; full supplier admission is separate.',
+    }
+    (args.out/'REPRODUCTION.json').write_text(json.dumps(receipt, indent=2)+'\n')
+    print(json.dumps(receipt, indent=2))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/hosting/reuse_owners.py b/research/gauge44-leaver8/hosting/reuse_owners.py
new file mode 100644
index 0000000000..234b831790
--- /dev/null
+++ b/research/gauge44-leaver8/hosting/reuse_owners.py
@@ -0,0 +1,230 @@
+"""Deterministic existing-family owner reuse and optional callwise matching.
+
+The output is a nomination, requiring the ordinary independent owner, phase,
+finite-invoice, and exact-moment admission. No MILP or new owner family is used.
+"""
+from collections import Counter, defaultdict
+from pathlib import Path
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+import math
+import time
+
+
+def read(path):
+    raw=Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def packed(obj):return json.dumps(obj,sort_keys=True,separators=(',',':')).encode()
+def sha(path):return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def signature(path):
+    path=Path(path)
+    if path.is_dir():
+        w=read(path/'CANONICAL-WORD.json.gz');V,R=w['v'],w['R']
+        widths=[len(w['frames'][w['final'][2*V+h]])-len(w['frames'][w['start'][2*V+h]]) for h in range(R)]
+        programs=read(path/'LOCAL-PROGRAMS.json.gz')
+        profiles=[Counter(e[-1] for e in programs[o] if e[0] in ('climb','center')) for o in ('forward','backward')]
+        assert profiles[0]==profiles[1]
+        assert profiles[0]=={int(r):n for r,n in w['local_profile'].items()}
+        return {'widths':widths,'profile':dict(profiles[0]),'source':str(path),
+                'canonical_sha256':sha(path/'CANONICAL-WORD.json.gz'),
+                'program_sha256':sha(path/'LOCAL-PROGRAMS.json.gz')}
+    w=read(path)
+    if 'report' in w:
+        V,R=w['report']['v'],w['report']['R']
+        widths=[len(w.get('helper_final',{}).get(str(2*V+h),range(9)))-len(w.get('start_extra',{}).get(str(2*V+h),[])) for h in range(R)]
+        profile={int(r):n for r,n in w['report']['local_profile'].items()}
+    else:
+        widths=w['widths'];profile={int(r):n for r,n in w['profile'].items()}
+    return {'widths':widths,'profile':profile,'source':str(path),'source_sha256':sha(path)}
+
+
+def phi(rank,b,M):return rank*math.expm1(b*math.log(M/rank)) if rank else 0.
+
+
+def rate(profile,deficit,M):
+    lo,hi=0.,.02
+    for _ in range(58):
+        mid=(lo+hi)/2
+        if sum(n*phi(r,mid,M) for r,n in profile.items())<deficit:lo=mid
+        else:hi=mid
+    return lo
+
+
+def audit_roles(roles,plan,widths_by_call,V,R):
+    used=defaultdict(set);families=defaultdict(set);helpers=defaultdict(set)
+    for z in roles:
+        s,rep,h=z['stage'],z['replica'],z['helper'];call=(s,rep)
+        assert z['time']==plan['order'].index([s,rep])
+        assert 0<=h<R and z['width']==widths_by_call[call][h]
+        assert h not in helpers[call] and z['family'] not in families[call]
+        helpers[call].add(h);families[call].add(z['family'])
+        orp,ch,port=z['owner_replica'],z['child'],z['port']
+        assert z['copy']==orp*V+port
+        assert z['family']==orp*(8*V)+(2*plan['pairs'][str(ch)]+plan['sides'][str(ch)])*V+port
+        cap,window=plan['windows'][f'{orp},{ch}']
+        assert z['time'] in window and 0<=z['offset'] and z['offset']+z['width']<=cap
+        cells=set(range(z['offset'],z['offset']+z['width']))
+        key=(orp,ch,port);assert not used[key]&cells;used[key]|=cells
+    assert len(roles)==len(plan['order'])*R
+    assert all(helpers[tuple(c)]==set(range(R)) for c in plan['order'])
+    for cells in used.values():assert cells==set(range(len(cells)))
+    return used,families
+
+
+def main():
+    ap=argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--plan',type=Path,required=True)
+    ap.add_argument('--owners',type=Path,required=True)
+    ap.add_argument('--signature',action='append',default=[],help='Existing PID=raw-word, signature JSON, or verified native directory')
+    ap.add_argument('--passes',type=int,default=2)
+    ap.add_argument('--price-b',type=float,default=0.001638923)
+    ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args();assert 0<=a.passes<=2
+    a.out.mkdir(parents=True,exist_ok=False);beg=time.monotonic()
+    plan,oldroles=read(a.plan),read(a.owners)
+    assert (plan['K'],plan['T'],plan['M'],plan['L'])==(4,8,73,9)
+    M,V=73,112;R=len(next(iter(plan['provider_registry'].values()))['widths'])
+    signatures={pid:{'widths':desc['widths'],'profile':{int(r):n for r,n in desc['actual_paid_profile'].items()},'source':'inherited PLAN'} for pid,desc in plan['provider_registry'].items()}
+    for spec in a.signature:
+        pid,path=spec.split('=',1);assert pid in signatures
+        signatures[pid]=signature(path)
+    for sig in signatures.values():
+        assert len(sig['widths'])==R and all(type(w) is int and 0<w<=9 for w in sig['widths'])
+        assert sum(int(r)*n for r,n in sig['profile'].items())==16*V+64+sum(sig['widths'])
+    calls={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+    oldwidths={k:plan['provider_registry'][c['provider']]['widths'] for k,c in calls.items()}
+    newwidths={k:signatures[c['provider']]['widths'] for k,c in calls.items()}
+    oldused,oldfamilies=audit_roles(oldroles,plan,oldwidths,V,R)
+
+    # A slot is an old immutable owner-family opportunity. Only the helper
+    # assigned to the opportunity and its footprint width may change.
+    bycall=defaultdict(list);groups=defaultdict(list)
+    for i,z in enumerate(oldroles):
+        bycall[z['stage'],z['replica']].append(i)
+        groups[z['owner_replica'],z['child'],z['port']].append(i)
+    group_of={i:g for g,ids in groups.items() for i in ids}
+    cap={g:plan['windows'][f'{g[0]},{g[1]}'][0] for g in groups}
+    assigned_h={};assigned_w={};dominance={};pending=[]
+    for call,ids in bycall.items():
+        slots=sorted(ids,key=lambda i:(oldroles[i]['width'],oldroles[i]['helper']))
+        helpers=sorted(range(R),key=lambda h:(newwidths[call][h],h))
+        failures=[(h,newwidths[call][h],oldroles[i]['width']) for h,i in zip(helpers,slots) if newwidths[call][h]>oldroles[i]['width']]
+        if failures:
+            # Keep this call's old widths provisionally; shrunk calls leave
+            # slack on their original owner families. A subsequent exact
+            # bipartite matching may use that slack for this call.
+            pending.append(call)
+            for i in ids:assigned_h[i]=oldroles[i]['helper'];assigned_w[i]=oldroles[i]['width']
+        else:
+            for h,i in zip(helpers,slots):assigned_h[i]=h;assigned_w[i]=newwidths[call][h]
+        dominance[str(call)]={'old_total':sum(oldwidths[call]),'new_total':sum(newwidths[call]),'sorted_termwise_dominance':not failures,'failed_positions':failures}
+    used={g:sum(assigned_w[i] for i in ids) for g,ids in groups.items()}
+    assert all(used[g]<=cap[g] for g in groups)
+    cost_cache=[phi(r,a.price_b,M) for r in range(49)]
+    def current_cost():return sum(cost_cache[cap[g]-used[g]] for g in groups)
+    passes=[{'pass':'sorted','touched_group_idle_pressure':current_cost(),'calls_awaiting_capacity_matching':len(pending)}]
+
+    if a.passes or pending:
+        import numpy as np
+        from scipy.optimize import linear_sum_assignment
+        def match_call(call,force=False):
+            ids=sorted(bycall[call],key=lambda i:oldroles[i]['helper'])
+            gs=[group_of[i] for i in ids]
+            assert len(set(gs))==R, 'one owner family per complete call is essential'
+            available=np.array([cap[g]-used[g]+assigned_w[i] for i,g in zip(ids,gs)],dtype=np.int64)
+            ws=np.array(newwidths[call],dtype=np.int64)
+            left=available[None,:]-ws[:,None]
+            matrix=np.full((R,R),np.inf)
+            valid=left>=0
+            matrix[valid]=np.asarray(cost_cache)[left[valid]]
+            ri,ci=linear_sum_assignment(matrix)
+            assert len(ri)==R and np.all(np.isfinite(matrix[ri,ci]))
+            oldcost=sum(cost_cache[cap[g]-used[g]] for g in gs)
+            newcost=float(matrix[ri,ci].sum())
+            if not force:
+                assert newcost<=oldcost+1e-10
+                if oldcost-newcost<=1e-10:return False
+            for h,col in zip(ri,ci):
+                i=ids[int(col)];g=group_of[i];h=int(h);ww=int(ws[h])
+                used[g]+=ww-assigned_w[i];assigned_w[i]=ww;assigned_h[i]=h
+                assert used[g]<=cap[g]
+            return True
+        for call in pending:
+            match_call(call,force=True)
+            dominance[str(call)]['capacity_matching_feasible']=True
+        if pending:passes.append({'pass':'capacity_bootstrap','touched_group_idle_pressure':current_cost(),'resolved_calls':[list(c) for c in pending]})
+        for p in range(a.passes):
+            accepted=0;startcost=current_cost()
+            order=[tuple(k) for k in plan['order']]
+            if p%2:order.reverse()
+            for call in order:
+                accepted+=match_call(call)
+            finalcost=current_cost();assert finalcost<=startcost+1e-9
+            passes.append({'pass':p+1,'accepted_calls':accepted,'touched_group_idle_pressure':finalcost,'decrease':startcost-finalcost})
+
+    # The inherited compiler requires each used coordinate set to be a
+    # prefix. Stable left compaction preserves every immutable owner field.
+    roles=copy.deepcopy(oldroles);matching=[]
+    for g,ids in groups.items():
+        off=0
+        for i in sorted(ids,key=lambda i:(oldroles[i]['offset'],oldroles[i]['time'],oldroles[i]['helper'])):
+            z=roles[i];z['helper']=assigned_h[i];z['width']=assigned_w[i];z['offset']=off;off+=z['width']
+            matching.append({'stage':z['stage'],'replica':z['replica'],'old_helper':oldroles[i]['helper'],
+                             'new_helper':z['helper'],'old_width':oldroles[i]['width'],'new_width':z['width'],
+                             'family':z['family'],'child':z['child'],'old_offset':oldroles[i]['offset'],'new_offset':z['offset']})
+        assert off==used[g]<=cap[g]
+    roles.sort(key=lambda z:(z['time'],z['helper']))
+    newused,newfamilies=audit_roles(roles,plan,newwidths,V,R)
+    assert newfamilies==oldfamilies
+    paid=Counter();remainders=[]
+    for c in plan['provider_calls']:paid.update(signatures[c['provider']]['profile'])
+    idle=Counter()
+    for key,(capacity,window) in plan['windows'].items():
+        rep,ch=map(int,key.split(','))
+        for port in range(V):
+            occupied=len(newused[rep,ch,port]);left=capacity-occupied
+            if left:
+                family=rep*(8*V)+(2*plan['pairs'][str(ch)]+plan['sides'][str(ch)])*V+port
+                remainders.append({'child':ch,'port':port,'replica':rep,'replicas':1,'family':family,
+                                   'rank':left,'hosted':occupied,'pending_offset':occupied})
+                idle[left]+=1
+    paid.update(idle);mass=sum(r*n for r,n in paid.items())
+    assert M*plan['live']-mass==plan['deficit']==2560
+    assert M*M>2*max(paid)**2
+    oldprofile={int(r):n for r,n in plan['profile'].items()}
+    ownerraw=packed(roles);gz=bytearray(gzip.compress(ownerraw,mtime=0));gz[9]=255
+    (a.out/'OWNERS.json.gz').write_bytes(bytes(gz))
+    (a.out/'MATCHING.json.gz').write_bytes(gzip.compress(packed(matching),mtime=0))
+    (a.out/'REMAINDERS.json').write_text(json.dumps(remainders,indent=2)+'\n')
+    profile=dict(sorted(paid.items()))
+    (a.out/'PROFILE.json').write_text(json.dumps(profile,indent=2)+'\n')
+    owner_fields={'profile':profile,
+                  'per_call_widths':[{'stage':s,'replica':r,'widths':newwidths[s,r]} for s,r in plan['order']],
+                  'assignment_sha256':hashlib.sha256(ownerraw).hexdigest(),
+                  'assignment_sha256_semantics':'SHA256 of sorted-key compact uncompressed OWNERS array',
+                  'source_owners_sha256':sha(a.owners),
+                  'provider_signatures':signatures}
+    (a.out/'PLAN-OWNER-FIELDS.json').write_text(json.dumps(owner_fields,indent=2)+'\n')
+    rec={'status':'PASS_OWNER_REUSE_NOMINATION_COMBINATORICS_NOT_FULL_SUPPLIER_ADMISSION',
+         'source_plan':str(a.plan),'source_plan_sha256':sha(a.plan),'source_owners_sha256':sha(a.owners),
+         'owners_sha256':sha(a.out/'OWNERS.json.gz'),'unchanged_owner_family_sets':True,
+         'unchanged_call_order_and_windows':True,'all_footprints_are_disjoint_compacted_prefixes':True,
+         'local_signatures':signatures,'sorted_initial_dominance':dominance,'matching_passes':passes,
+         'roles':len(roles),'calls':len(calls),'remainder_children':len(remainders),'remainder_profile':dict(sorted(idle.items())),
+         'global_profile':profile,'rank_mass':mass,'deficit':2560,'maxchild':max(paid),
+         'source_floating_screen_b':rate(oldprofile,2560,M),
+         'candidate_floating_screen_b':rate(profile,2560,M),
+         'seconds':time.monotonic()-beg,
+         'remaining_admission':'Bind freshly verified provider artifacts and their hashes; regenerate the global template, actual 73-column sigmas and remainder axes with the existing emitter; run independent owner/frame audit, finite invoice, and exact moment/outer assembly.'}
+    (a.out/'OWNER-REUSE.json').write_text(json.dumps(rec,indent=2)+'\n')
+    print(json.dumps({k:rec[k] for k in ('status','roles','matching_passes','remainder_profile','rank_mass','source_floating_screen_b','candidate_floating_screen_b','seconds')},indent=2),flush=True)
+
+
+if __name__=='__main__':main()
diff --git a/research/gauge44-leaver8/independent/CENTRE-GUARD-REVIEW.md b/research/gauge44-leaver8/independent/CENTRE-GUARD-REVIEW.md
new file mode 100644
index 0000000000..6c62bd070e
--- /dev/null
+++ b/research/gauge44-leaver8/independent/CENTRE-GUARD-REVIEW.md
@@ -0,0 +1,79 @@
+# Independent review of the centre and admission interfaces
+
+**Finding:** the replacement of old local centre-carrier IDs by equality of the
+eight ordered centre-frame bases preserves the inherited global contract. It
+must be used together with the complete local scalar, frame, phase and wrapper
+admission. No mathematical admission guard was found to have been removed.
+
+## Why source carriers may supply centres
+
+The transported gauge44 centre carriers are
+`[92, 57, 81, 224, 11, 240, 9, 256]`. Five are source registers and three are
+helper registers. All 112 transported port labels and all eight ordered
+rank-eight centre-frame bases agree exactly with the retained parent. The
+optional `--main` check in `audit_local.py` independently verifies that boundary
+against a byte-pinned parent canonical word.
+
+The actual forward local program copies the current row of `L_r` into private
+`C_k` at their common frame `F_k`. It then descends `C_k` from `F_k` to frame
+zero, scatters to the targets, and clears `C_k`. The backward program performs
+the corresponding reversed ascent and scatter. This construction depends on
+the copied row, its frame and the exact local program, rather than on a
+requirement that `r` be in the helper-ID interval. The source itself is not
+cleared or treated as private work.
+
+The independently checked local contract retains every required obligation:
+all 716 input columns in both orientations; the forward and backward shear
+identities; arbitrary initial helper dirt; scalar/COPY common-frame legality;
+centre lifetimes and nested steps; exact native phase identities; endpoint
+and row/column cone conditions; and residual wrappers before and after every
+relevant touch. Its finite invoice recounts the actual operations.
+
+The global controller addresses private centres by `k`, while the source or
+helper `L_r` is mapped through the complete invocation's ordinary owner array.
+The owner audit retains pairwise distinct owners for all active source, target
+and helper roles. A helper therefore cannot borrow the family of an active
+source centre. The private-centre namespace is disjoint from those owners and
+the local program clears it. Each whole invocation finishes before another
+begins, so no new interleaving or family lifetime assumption is introduced.
+
+## Admission guards and single-provider controls
+
+An AST comparison with PR635 found all **91 assertions in `code/assemble.py`
+identical, in the same traversal order**, including constants. This includes
+the unchanged PR543 bit input, deficit and surcharge, every finite-invoice
+guard, both conservative and native complex moment checks, and the strict
+outer assembly and its controls. The following files retain the reviewed PR635 code (the packaged
+`bind_providers_portable.py` only trims trailing whitespace): `invoice_allcold.py` (67 assertions),
+`bind_providers_portable.py` (22), `generated_identity.py` (4), and `witness.py`
+(3). `review_guards.py` reproduces the assertion comparison and records the
+file hashes.
+
+The controller still checks the complete serialized provider registry,
+per-call program and dispatch, native phase and wrapper bindings, helper
+widths, owner uniqueness, actual busy-family windows, spectator orthogonality,
+and literal idle remainders. The single-provider branch replaces partner
+substitutions by direct invalid-ID, program, width and hash mutations. Only
+four assembly mutation scenarios requiring a second registered provider are
+inapplicable. Their removal does not remove any admission predicate. Direct
+forged program/phase tests, width-order and width-inventory tests, and
+selected-call/order tests remain.
+
+## Price and bit headroom
+
+The frozen all72 profile gives the native complex root bracket
+`(0.001652208994368411824947, 0.001652208994368411824948)` and
+`kappa = 0.001649483702558979`. Both independent rational engines certify the
+two signs. The seven-step outer driver passes all 47 strict constraints and
+rejects its four standard mutations. The conservative complex price passes
+separately at `kappa = 0.001649483699681650`.
+
+The achieved complex rate is below PR543's retained bit rate
+`0.001653826988146798944268`. Using eumemic's independently reviewed PR555 bit
+rate `0.001733052823330162099157` gives exactly the same attained kappa. PR543
+therefore remains the cited supplier for this delta; no bit improvement is
+claimed here and no PR555 implementation is bundled.
+
+These receipts supplement the package's complete native, owner, phase and
+finite-invoice replay. The inherited all-size realization and analytic
+transfer assumptions remain conditional.
diff --git a/research/gauge44-leaver8/independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json b/research/gauge44-leaver8/independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json
new file mode 100644
index 0000000000..771faa86a7
--- /dev/null
+++ b/research/gauge44-leaver8/independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json
@@ -0,0 +1,137 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+  "input_file": "FULL-WORD.json.gz",
+  "content_sha256": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290",
+  "compressed_sha256": "3ef4e74e81e2f4621fc95272918ac7b8bb8858df0baa16cc6d91424d55aead9e",
+  "parent_center_interface": {
+    "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+    "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "transport_tau": 43,
+    "ordered_frame_bases_match": true,
+    "all_ports_match": true,
+    "transported_centers": [
+      92,
+      57,
+      81,
+      224,
+      11,
+      240,
+      9,
+      256
+    ],
+    "source_centers": [
+      92,
+      57,
+      81,
+      11,
+      9
+    ],
+    "ordered_frame_bases": [
+      [
+        256,
+        128,
+        64,
+        34,
+        16,
+        10,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        16,
+        8,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        17,
+        9,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ],
+      [
+        256,
+        128,
+        66,
+        32,
+        18,
+        8,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        17,
+        9,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        16,
+        8,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        68,
+        32,
+        16,
+        12,
+        2,
+        1
+      ]
+    ]
+  },
+  "v": 112,
+  "h": 9,
+  "R": 492,
+  "entering": 204,
+  "lowends": 78,
+  "coldends": 44,
+  "compensation_gates": 7348,
+  "local_profile": {
+    "1": 2514,
+    "2": 404,
+    "3": 448,
+    "4": 160,
+    "5": 56,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 52,
+    "5": 48,
+    "7": 34,
+    "8": 114,
+    "9": 244
+  },
+  "checked_columns": 716,
+  "elapsed_seconds": 3.147683588000291,
+  "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+}
diff --git a/research/gauge44-leaver8/independent/GAUGE44-GLOBAL-GUARD-REVIEW.json b/research/gauge44-leaver8/independent/GAUGE44-GLOBAL-GUARD-REVIEW.json
new file mode 100644
index 0000000000..e2df1dcca8
--- /dev/null
+++ b/research/gauge44-leaver8/independent/GAUGE44-GLOBAL-GUARD-REVIEW.json
@@ -0,0 +1,47 @@
+{
+  "status": "PASS_PR635_ADMISSION_ASSERTION_PRESERVATION",
+  "files": [
+    {
+      "file": "code/assemble.py",
+      "baseline_sha256": "1b1a9024ac910dc9b9d9e30150684e1fa9cb228a4c1c275b75ab04b57fdef1dd",
+      "new_sha256": "7ac28118d69416e4fb67b61216285fb0823310b7635ce1b9025aa3f10119ef6a",
+      "byte_identical": false,
+      "assert_count": 91,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/invoice_allcold.py",
+      "baseline_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+      "new_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+      "byte_identical": true,
+      "assert_count": 67,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/bind_providers_portable.py",
+      "baseline_sha256": "2eb5c262bf481b3bec9ceaec654fa46ff6fc3a89b13d4906a29a55a89e35feea",
+      "new_sha256": "2eb5c262bf481b3bec9ceaec654fa46ff6fc3a89b13d4906a29a55a89e35feea",
+      "byte_identical": true,
+      "assert_count": 22,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/generated_identity.py",
+      "baseline_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+      "new_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+      "byte_identical": true,
+      "assert_count": 4,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/witness.py",
+      "baseline_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+      "new_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+      "byte_identical": true,
+      "assert_count": 3,
+      "all_assertions_identical_in_order": true
+    }
+  ],
+  "centre_interface_review": "CENTRE-GUARD-REVIEW.md",
+  "scope": "Exact syntax preservation for all admission assertions in these five files. The changed emitter/controller centre boundary and single-provider controls require the separate semantic review; assertion counts alone do not prove them."
+}
diff --git a/research/gauge44-leaver8/independent/GAUGE44-INDEPENDENT-PRICE.json b/research/gauge44-leaver8/independent/GAUGE44-INDEPENDENT-PRICE.json
new file mode 100644
index 0000000000..7aa86180dd
--- /dev/null
+++ b/research/gauge44-leaver8/independent/GAUGE44-INDEPENDENT-PRICE.json
@@ -0,0 +1,156 @@
+{
+  "status": "PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK",
+  "profile_input_file": "PLAN.json",
+  "profile_input_sha256": "7b3122026e82b9d9e964d2a50c7bffdc976ae3dfea64bb98b2fdad5cfbdbaa20",
+  "global_profile": {
+    "1": 174763,
+    "2": 30105,
+    "3": 30275,
+    "4": 12240,
+    "5": 4896,
+    "7": 54,
+    "8": 576,
+    "16": 23,
+    "48": 2419
+  },
+  "live": 7168,
+  "m": 73,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "prices": {
+    "native": {
+      "root": {
+        "lower": "0.001674185476674086429846",
+        "upper": "0.001674185476674086429847",
+        "lower_endpoint_residual_upper": "-9.258737006004892346173061244464039982798397391664878463422077941068021E-25",
+        "upper_endpoint_residual_lower": "2.005290772036567694936493754533147163786510359586083088453102073919377E-24",
+        "strict_rational_signs": true
+      },
+      "exact_moments": [
+        {
+          "endpoint": "837092738337043214923/500000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-24961505588706589063536270371864708160498115/26959946667150639794667015087019630673637144422540572481103610249216",
+            "-24961505588706589063536270371864708160498113/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "-462937/500000000000000000000000000000",
+            "-925873/1000000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "1674185476674086429847/1000000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "54062532266235196619370246291034158858524675/26959946667150639794667015087019630673637144422540572481103610249216",
+            "54062532266235196619370246291034158858524677/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "200529/100000000000000000000000000000",
+            "2005291/1000000000000000000000000000000"
+          ]
+        }
+      ],
+      "outer_with_bit": {
+        "complex_b": "837092738337043214923/500000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "835693632195073/500000000000000000",
+        "kappa_decimal": "0.001671387264390146",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    },
+    "conservative": {
+      "root": {
+        "lower": "0.001674185473814575474867",
+        "upper": "0.001674185473814575474868",
+        "lower_endpoint_residual_upper": "-4.932703074050864500363221905991238131757959051186123070698964701314504E-25",
+        "upper_endpoint_residual_lower": "2.437894165237372647986425295760776771093048289170590753978317997095726E-24",
+        "strict_rational_signs": true
+      },
+      "exact_moments": [
+        {
+          "endpoint": "1674185473814575474867/1000000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-6649270590065065997663222052892326679295837/13479973333575319897333507543509815336818572211270286240551805124608",
+            "-1662317647516266499415805513223081669823959/3369993333393829974333376885877453834204643052817571560137951281152"
+          ],
+          "base_two_residual": [
+            "-246635539906040992121/500000000000000000000000000000000000000000000",
+            "-2466350399060409921139/5000000000000000000000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "418546368453643868717/250000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "65725496674957295861389862879254608557678601/26959946667150639794667015087019630673637144422540572481103610249216",
+            "65725496674957295861389862879254608557678603/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "12189469601119396732213/5000000000000000000000000000000000000000000000",
+            "24378949202238793464567/10000000000000000000000000000000000000000000000"
+          ]
+        }
+      ],
+      "outer_with_bit": {
+        "complex_b": "1674185473814575474867/1000000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "835693630770093/500000000000000000",
+        "kappa_decimal": "0.001671387261540186",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    }
+  },
+  "bit_supplier_pr": 589,
+  "bit_deficit": 10272,
+  "bit_moments_with_surcharge": [
+    {
+      "endpoint": "1733427039589844234749/1000000000000000000000000",
+      "accept": true,
+      "mercator_residual": [
+        "-43100600330766044577088869872467188970742291/26959946667150639794667015087019630673637144422540572481103610249216",
+        "-43100600330766044577088869872467188970742289/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two_residual": [
+        "-799345163337715793503/500000000000000000000000000000000000000000000",
+        "-3197378653350863173989/2000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "endpoint": "6933708158359376939/4000000000000000000000",
+      "accept": false,
+      "mercator_residual": [
+        "22502934905675809315035333485365686073718547/13479973333575319897333507543509815336818572211270286240551805124608",
+        "5625733726418952328758833371341421518429637/3369993333393829974333376885877453834204643052817571560137951281152"
+      ],
+      "base_two_residual": [
+        "8346798366759439729359/5000000000000000000000000000000000000000000000",
+        "16693606733518879458833/10000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "gain_over_pr635_percent": "2.14795693544613460937516788041147829054201996498013663108098185775358537919",
+  "input_sha256": {
+    "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "package:inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4"
+  },
+  "scope": "Independent arithmetic for the exact nominated all72 profile. Complete local, controller and finite invoice admission are separately replayed by the package driver; this receipt does not replace them. The cited PR589 bit supplier is unchanged and its exceptional-residue surcharge is retained. Any alternative c is only a headroom comparison."
+}
diff --git a/research/gauge44-leaver8/independent/README.md b/research/gauge44-leaver8/independent/README.md
new file mode 100644
index 0000000000..f97dcf81b1
--- /dev/null
+++ b/research/gauge44-leaver8/independent/README.md
@@ -0,0 +1,43 @@
+# Independent checks
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0, under the
+package license. The scalar/frame audit imports no generator or supplier
+checker. Pricing uses the pinned inherited rational engines and the retained
+PR635 outer formula, with their original notices preserved in the main
+dependency tree.
+
+From the delta package directory, using the pinned checkouts and a rebuilt
+word:
+
+```sh
+python independent/audit_local.py \
+  --word /path/to/rebuild/cold44/FULL-WORD.json.gz \
+  --main /path/to/main \
+  --output /path/to/output/LOCAL-AUDIT.json
+
+python independent/price_profile.py \
+  --main /path/to/main \
+  --output /path/to/output/PRICE.json
+
+python independent/review_guards.py \
+  --pr635 /path/to/pr635 \
+  --output /path/to/output/GUARD-REVIEW.json
+```
+
+`audit_local.py` can run without `--main`; including it also verifies the
+transported centre-frame and port boundary against the pinned parent. Its
+receipt authenticates the supplied word by its content SHA256, independent
+of its location. `price_profile.py` defaults to the package's `data/PLAN.json`;
+`--profile` accepts another explicit profile for arithmetic only. The bit side is the cited merged PR589 supplier
+(`inputs/PR589-EXPECTED.json`, git blob `e293ddc5…`); its rank-mass deficit
+`T(2Kv - L*cst) = 32*(8*111 - 9*63) = 10272` is re-derived independently of
+`code/assemble.py`, and the outer receipt key is `outer_with_bit`. The retained
+`GAUGE44-INDEPENDENT-PRICE.json` is #645/PR543 historical evidence unless regenerated. The optional
+`--headroom-c 0.001733052823330162099157` reproduces the unchanged-kappa
+comparison with the reviewed PR555 rate without importing a second supplier.
+
+The retained receipts are `GAUGE-COLD44-INDEPENDENT-AUDIT.json`,
+`GAUGE44-INDEPENDENT-PRICE.json`, and `GAUGE44-GLOBAL-GUARD-REVIEW.json`.
+[CENTRE-GUARD-REVIEW.md](CENTRE-GUARD-REVIEW.md) gives the semantic argument
+behind the changed centre boundary and the single-provider control branch.
+The main package driver performs the separate complete global admission.
diff --git a/research/gauge44-leaver8/independent/audit_local.py b/research/gauge44-leaver8/independent/audit_local.py
new file mode 100644
index 0000000000..4744d8783c
--- /dev/null
+++ b/research/gauge44-leaver8/independent/audit_local.py
@@ -0,0 +1,171 @@
+"""Independent exact scalar/frame audit of the changed forward supplier.
+
+This does not import a generator, builder, stored compensation, or price.
+All claimed endpoint matrices are derived from the input word's gates.
+Optional --main checks the transported boundary against the pinned parent.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse,gzip,json,hashlib,time
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+
+def require(x,label):
+    if not x:raise RuntimeError(label)
+
+def basis(vs):
+    piv={}
+    for a in vs:
+        while a:
+            bit=a.bit_length()-1
+            if bit in piv:a^=piv[bit]
+            else:
+                piv[bit]=a;break
+    for k in sorted(piv):
+        for j in piv:
+            if j>k and piv[j]>>k&1:piv[j]^=piv[k]
+    return tuple(piv[k] for k in sorted(piv,reverse=True))
+
+def contained(a,b):return basis(a+b)==b
+
+def registers(e):return e[1:3] if e[0]=='add' else e[1:2]
+
+def apply(e,rows,dual=False):
+    if e[0]=='add':
+        t,s=e[1:3];q=F(e[3],e[4]);require(t!=s,'self add')
+        if dual:t,s,q=s,t,-q
+        dst=rows[t]
+        for k,x in list(rows[s].items()):
+            a=dst.get(k,F(0))+q*x
+            if a:dst[k]=a
+            else:dst.pop(k,None)
+    elif e[0]=='scale':
+        t=e[1];q=F(e[2],e[3]);require(q!=0,'zero scale')
+        if dual:q=1/q
+        rows[t]={k:q*x for k,x in rows[t].items()}
+    else:raise RuntimeError('unknown scalar primitive')
+
+def invert(e):
+    r=list(e)
+    if r[0]=='add':r[3]=-r[3]
+    else:r[2],r[3]=r[3],r[2]
+    return r
+
+def check_parent_interface(word,main):
+    # Read only the retained boundary data. No builder or local checker is imported.
+    relative="research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz"
+    path=main/relative;raw=path.read_bytes()
+    require(hashlib.sha256(raw).hexdigest()=="66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",'parent canonical input pin')
+    parent=json.loads(gzip.decompress(raw))
+    tau=lambda x:x^(43 if (x&43).bit_count()%2 else 0)
+    ports=parent['ports'];v=word['report']['v']
+    require(len(ports)==len(set(ports))==v,'parent port count')
+    require(set(map(tau,word['ports']))==set(ports),'transported source/target ports')
+    moved={i:ports.index(tau(p)) for i,p in enumerate(word['ports'])}
+    centers=[moved.get(r,r) for r in word['centers']]
+    actual=[list(basis([tau(x) for x in frame])) for frame in word['center_frames']]
+    expected=[parent['frames'][f] for f in parent['center_frames']]
+    require(len(centers)==len(set(centers))==len(actual)==8,'eight distinct centre carriers')
+    require(actual==expected and all(len(f)==8 for f in actual),'ordered centre frame interface')
+    return dict(parent_path=relative,parent_file_sha256=hashlib.sha256(raw).hexdigest(),
+                transport_tau=43,ordered_frame_bases_match=True,all_ports_match=True,
+                transported_centers=centers,source_centers=[r for r in centers if r<v],
+                ordered_frame_bases=actual)
+
+
+def run(path,out,main=None):
+    begin=time.monotonic();data=gzip.decompress(path.read_bytes());w=json.loads(data)
+    v,h,R=w['report']['v'],w['report']['h'],w['report']['R'];n=2*v+R
+    require((v,h)==(112,9),'wrong source geometry')
+    center_interface=check_parent_interface(w,main) if main is not None else None
+    ident=lambda:[{k:F(1)} for k in range(n)]
+    main=w['A']+w['cut']+w['B']
+    for e in main+w['precondition']+w['cleanup']:
+        require(all(0<=k<n for k in registers(e)),'register out of range')
+        q=F(e[3],e[4]) if e[0]=='add' else F(e[2],e[3])
+        require(q.denominator&(q.denominator-1)==0,'non-dyadic scalar')
+        if e[0]=='scale':require(abs(q.numerator)&(abs(q.numerator)-1)==0,'non-unit scale')
+    require(all(not(v<=e[2]<2*v) for e in w['A']+w['B'] if e[0]=='add' and not(v<=e[1]<2*v)), 'non-target reads target')
+    raw=ident()
+    for e in main:apply(e,raw)
+    dirt=[{} for _ in range(n)]
+    for y in range(v,2*v):dirt[y]={k:a for k,a in raw[y].items() if k>=2*v}
+    for e in w['precondition']:apply(e,dirt)
+    compensation=[['add',y,k,-a.numerator,a.denominator,[]] for y in range(v,2*v) for k,a in sorted(dirt[y].items())]
+    entering=set(map(int,w.get('start_extra',{})));lowends=set(map(int,w.get('helper_final',{})))
+    coldends=lowends-entering
+    require(not any(e[2] in entering for e in compensation),'nonzero entrance response')
+    require(not any(r in entering|coldends for e in w['precondition']+compensation for r in registers(e)), 'pre-wrapper touch of residual helper')
+    require(all(e[-1]==[] for e in w['precondition']+compensation),'nonzero frame precondition')
+    early=w.get('early_cleanup',[]);earlyids={i for i,U in early}
+    require(len(earlyids)==len(early),'duplicate early cleanup gate')
+    tail=[w['cleanup'][i][:-1]+[U] for i,U in early]
+    cleanup=[e for i,e in enumerate(w['cleanup']) if i not in earlyids]
+    prefix=w['precondition']+compensation+main
+    program=prefix+tail+cleanup
+    for dual in (False,True):
+        actual=ident()
+        for e in program:apply(e,actual,dual)
+        expected=ident()
+        for t in range(v):expected[t if dual else v+t][v+t if dual else t]=F(-1 if dual else 1)
+        bad=[i for i in range(n) if actual[i]!=expected[i]]
+        require(not bad,'all-column endpoint failure '+str((dual,bad[:8])))
+        print('endpoint', 'dual' if dual else 'forward','PASS',flush=True)
+    full=basis([1<<i for i in range(h)])
+    end=[full]*v+[basis([x for x in range(1,1<<h) if (x&p).bit_count()%2==0]) for p in w['ports']]+[full]*R
+    for q,U in w.get('helper_final',{}).items():end[int(q)]=basis(U)
+    start=[(p,) for p in w['ports']]+[()]*(v+R)
+    for q,U in w.get('start_extra',{}).items():
+        require(2*v<=int(q)<n,'non-helper entrance');start[int(q)]=basis(U)
+    cur=start.copy();paid=Counter()
+    def climb(q,U):
+        U=basis(U);require(contained(cur[q],U),'frame not monotone '+str((q,cur[q],U)))
+        d=len(U)-len(cur[q])
+        if d:paid[d]+=1
+        cur[q]=U
+    for section in ('A','B'):
+        if section=='B':
+            lev={int(t):basis(U) for t,U in w.get('target_levels',{}).items()}
+            require(all(cur[v+t]==lev.get(t,()) for t in range(v)),'target centre levels')
+            for q,U in zip(w['centers'],w['center_frames']):
+                U=basis(U);require(cur[q]==U,'center frame')
+                served={lev.get(e[1]-v,()) for e in w['cut'] if e[2]==q}
+                for T in sorted(served,key=lambda x:-len(x)):
+                    require(contained(T,U),'center path not nested')
+                    if T!=U:paid[len(U)-len(T)]+=1
+                    U=T
+        for e in w[section]:
+            for q in registers(e):climb(q,e[-1])
+    endB=cur.copy()
+    for e in tail:
+        for q in registers(e):climb(q,e[-1])
+    for q,U in enumerate(end):climb(q,U)
+    require(all(all(end[q]==full for q in registers(e)) for e in cleanup),'full cleanup reads a low end')
+    require(dict(paid)=={int(k):a for k,a in w['report']['local_profile'].items()},'paid profile mismatch')
+    inventory=Counter(len(end[q])-len(start[q]) for q in range(2*v,n))
+    require(dict(inventory)=={int(k):a for k,a in w['report']['width_inventory'].items()},'width inventory mismatch')
+    p=ident();pinv=ident()
+    for e in prefix:apply(e,p)
+    for e in reversed(prefix):apply(invert(e),pinv)
+    for q in lowends:
+        U=end[q]
+        require(all(contained(endB[k],U) for k in pinv[q]),'inverse-row cone '+str(q))
+        require(all(k==q or not p[k].get(q) or contained(endB[k],U) for k in range(n)),'dirt-column cone '+str(q))
+    report=dict(status='PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES',
+                input_file=path.name,content_sha256=hashlib.sha256(data).hexdigest(),
+                compressed_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),
+                parent_center_interface=center_interface,v=v,h=h,R=R,
+                entering=len(entering),lowends=len(lowends),coldends=len(coldends),
+                compensation_gates=len(compensation),local_profile=dict(sorted(paid.items())),
+                width_inventory=dict(sorted(inventory.items())),checked_columns=n,
+                elapsed_seconds=time.monotonic()-begin,
+                scope='Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing.')
+    out.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2),flush=True)
+
+if __name__=='__main__':
+    parser=argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--word',type=Path,required=True,help='FULL-WORD.json.gz to check')
+    parser.add_argument('--output',type=Path,required=True,help='JSON receipt output path')
+    parser.add_argument('--main',type=Path,help='Optional pinned main checkout: also verify the transported centre/port interface')
+    args=parser.parse_args()
+    run(args.word,args.output,args.main)
diff --git a/research/gauge44-leaver8/independent/price_profile.py b/research/gauge44-leaver8/independent/price_profile.py
new file mode 100644
index 0000000000..0e36ebd468
--- /dev/null
+++ b/research/gauge44-leaver8/independent/price_profile.py
@@ -0,0 +1,161 @@
+"""Independent arithmetic for the frozen gauge44 profile.
+
+The two rational moment engines and outer.assembly are imported unchanged from
+the pinned main dependencies; no constructor, owner emitter or invoice is run.
+The outer driver is the seven-step formula retained in PR635.
+The bit side is the cited merged PR589 supplier (package inputs/PR589-EXPECTED.json,
+pinned by git blob), with its rank-mass deficit T(2Kv - L*cst) re-derived here
+independently of code/assemble.py.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse
+from decimal import Decimal, localcontext
+from fractions import Fraction as Q
+import hashlib
+import importlib.util
+import json
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+SOURCE = Path('research/complex-k492-owner-repair/vendor/multicold')
+BIT_PATH = HERE.parent/'inputs/PR589-EXPECTED.json'
+BIT_BLOB = 'e293ddc557742637f9f679f083a1a282d87b1b13'
+
+
+def pr589_deficit(word, live):
+    # Nine stages, 32 replicas, four pairs: deficit = 32*(2*4*v - 9*cst), cst = sum of the nine COPY ranks.
+    v, cst, ranks = word['v'], word['decoder_constant'], word['copy_ranks']
+    require(len(ranks) == word['retained_totals'] == 9 and cst == sum(ranks), 'bit decoder constant')
+    require(live == 2*4*v*32, 'bit live wires')
+    return 32*(2*4*v-9*cst)
+
+
+def require(condition, message):
+    if not condition:
+        raise RuntimeError(message)
+
+
+def decimal(q):
+    with localcontext() as ctx:
+        ctx.prec = 75
+        return str(Decimal(q.numerator) / Decimal(q.denominator))
+
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def load(path, name):
+    spec = importlib.util.spec_from_file_location('independent_' + name, path / (name + '.py'))
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def moment_checks(M, B, H, m, W, lower, deficit, bad):
+    require(m*W-sum(r*n for r, n in H.items()) == deficit, 'rank deficit')
+    require(m*m > 2*max(H)**2, 'halving guard')
+    rows = []
+    for z, accept in [(lower, True), (lower+Q(1, 10**24), False)]:
+        l, u = M.moment(H, m, W, z, bad)
+        ll, uu = B.moment(m, W, list(H.items()), z)
+        if bad:
+            fl, fu = B.moment(m, W, [(1, 32*m*m*sum(H.values()))], z)
+            ll, uu = ll+fl/10**16, uu+fu/10**16
+        require((u < 1 and uu < 1) if accept else (l > 1 and ll > 1), 'two exact moment signs')
+        rows.append(dict(endpoint=str(z), accept=accept,
+                         mercator_residual=[str(l-1), str(u-1)],
+                         base_two_residual=[str(ll-1), str(uu-1)]))
+    return rows
+
+
+def outer47(c, b, engine):
+    eta = beta = Q(1, 10**24)
+    s = min(c, (1-beta)*b)-Q(1, 10**27)
+    require(0 < s < c and s < (1-beta)*b, 'strict common saving')
+    a = Q(384599, 10**10)
+    for _ in range(7):
+        old = a
+        a = (1-s)*s+s*old
+        gap = min(s-a, 1-a-s, 1-a-s*(1-old), 1-s)
+        require(old < a < s < 1-a and gap > 0, 'bootstrap gap')
+        ceil = lambda x: -(-x.numerator//x.denominator)
+        cut = max(ceil(36/gap**2), ceil(2*(4+512)/gap))
+        require(cut*gap**2 >= 36 and cut*gap >= 2*(4+512), 'finite bootstrap cutoff')
+    q = a*(1-2*eta)
+    margin = (1-eta)*q/(1+q)
+    ticks = margin*10**18
+    k = Q((ticks.numerator-1)//ticks.denominator, 10**18)
+    bridge = {'semantic': {'C0': {'base': 2, 'exponent': 210000}, 'strict_literal_gap': 1},
+              'rows': {'degree_gap': Q(10**6)-Q(51*20161, 25)}}
+    result = engine.assembly(a, b, bridge, k, eta=eta, beta=beta)
+    require(len(result['strict_constraints']) == 47, '47 outer constraints')
+    require(all(x > 0 for x in result['strict_constraints'].values()), 'strict outer constraints')
+    rejected = []
+    for name, kk, ee, be in [('next_grid', k+Q(1, 10**18), eta, beta),
+                             ('zero_eta', k, Q(0), beta), ('zero_beta', k, eta, Q(0)),
+                             ('unit_beta', k, eta, Q(1))]:
+        try:
+            engine.assembly(a, b, bridge, kk, eta=ee, beta=be)
+        except AssertionError:
+            rejected.append(name)
+        else:
+            raise RuntimeError('accepted negative control: '+name)
+    return dict(complex_b=str(b), bit_c=str(c), kappa=str(k), kappa_decimal=decimal(k),
+                binding='bit' if c < (1-beta)*b else 'complex',
+                strict_constraints_passed=47, controls_rejected=rejected)
+
+
+def main():
+    require(__debug__, 'Do not use python -O: the retained outer engine requires assertions')
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--main', type=Path, required=True, help='Pinned main checkout')
+    parser.add_argument('--profile', type=Path, default=HERE.parent/'data/PLAN.json',
+                        help='Raw profile or a JSON object containing profile/global_profile')
+    parser.add_argument('--output', type=Path, required=True)
+    parser.add_argument('--headroom-c', help='Optional alternative bit saving, for comparison only')
+    args = parser.parse_args()
+    inputs = json.loads((HERE.parent/'data/UPSTREAM-PINS.json').read_text())
+    selected = [SOURCE/'engines'/(n+'.py') for n in ('moment', 'base_two_moment', 'outer')]
+    for relative in selected:
+        require(sha(args.main/relative) == inputs[relative.as_posix()], 'pinned input '+str(relative))
+    M, B, A = [load(args.main/SOURCE/'engines', n) for n in ('moment', 'base_two_moment', 'outer')]
+    supplied = json.loads(args.profile.read_text())
+    H = {int(r): n for r, n in supplied.get('profile', supplied.get('global_profile', supplied)).items()}
+    bit_data = BIT_PATH.read_bytes()
+    require(hashlib.sha1(b'blob '+str(len(bit_data)).encode()+b'\0'+bit_data).hexdigest() == BIT_BLOB, 'PR589 blob pin')
+    record = json.loads(bit_data)
+    bit = record['nine']
+    require('nine-stage' in bit['pipeline'] and '32 replicas' in bit['pipeline'], 'nine-stage bit record')
+    bit_deficit = pr589_deficit(record['word'], bit['bit']['live'])
+    require(sum(int(r)*n for r, n in bit['profile'].items()) == bit['bit']['rank_mass'], 'bit rank mass')
+    c = Q(bit['bit_lower'])
+    bit_checks = moment_checks(M, B, {int(r): n for r, n in bit['profile'].items()},
+                               64, bit['bit']['live'], c, bit_deficit, True)
+    prices = {}
+    for mode, bad in [('native', False), ('conservative', True)]:
+        root = M.certify(H, 73, 7168, bad)
+        root = {key: root[key] for key in ('lower', 'upper', 'lower_endpoint_residual_upper',
+                                          'upper_endpoint_residual_lower', 'strict_rational_signs')}
+        b = Q(root['lower'])
+        row = dict(root=root, exact_moments=moment_checks(M, B, H, 73, 7168, b, 2560, bad),
+                   outer_with_bit=outer47(c, b, A))
+        if args.headroom_c:
+            alternate = outer47(Q(args.headroom_c), b, A)
+            require(alternate['kappa'] == row['outer_with_bit']['kappa'], 'headroom comparison changed kappa')
+            row.update(outer_with_alternative_bit_rate=alternate, same_kappa_with_either_bit_rate=True)
+        prices[mode] = row
+    native_k = Q(prices['native']['outer_with_bit']['kappa'])
+    result = dict(status='PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK',
+                  profile_input_file=args.profile.name, profile_input_sha256=sha(args.profile),
+                  global_profile=H, live=7168, m=73, rank_mass=sum(r*n for r, n in H.items()), deficit=2560,
+                  prices=prices, bit_supplier_pr=589, bit_deficit=bit_deficit, bit_moments_with_surcharge=bit_checks,
+                  gain_over_pr635_percent=decimal(100*(native_k/Q('0.001636241501576388')-1)),
+                  input_sha256={**{relative.as_posix(): sha(args.main/relative) for relative in selected}, 'package:inputs/PR589-EXPECTED.json': sha(BIT_PATH)},
+                  scope='Independent arithmetic for the exact nominated all72 profile. Complete local, controller and finite invoice admission are separately replayed by the package driver; this receipt does not replace them. The cited PR589 bit supplier is unchanged and its exceptional-residue surcharge is retained. Any alternative c is only a headroom comparison.')
+    args.output.write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], prices['native']['outer_with_bit']['kappa_decimal'], result['gain_over_pr635_percent'])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/independent/review_guards.py b/research/gauge44-leaver8/independent/review_guards.py
new file mode 100644
index 0000000000..086dcf3d11
--- /dev/null
+++ b/research/gauge44-leaver8/independent/review_guards.py
@@ -0,0 +1,46 @@
+"""Reproduce the assertion-preservation part of the independent guard review.
+
+This compares complete assertion ASTs in their traversal order. It supplements
+the semantic centre-interface argument in CENTRE-GUARD-REVIEW.md.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse
+import ast
+import hashlib
+import json
+from pathlib import Path
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--pr635', type=Path, required=True, help='Pinned PR635 checkout or supplier directory')
+    parser.add_argument('--delta', type=Path, default=Path(__file__).resolve().parents[1])
+    parser.add_argument('--output', type=Path, required=True)
+    args = parser.parse_args()
+    old = args.pr635
+    if not (old/'code/assemble.py').exists():
+        old = old/'research/complex-571-cold14-st2'
+    names = ['assemble.py', 'invoice_allcold.py', 'bind_providers_portable.py',
+             'generated_identity.py', 'witness.py']
+    records = []
+    for name in names:
+        a, b = (old/'code'/name).read_bytes(), (args.delta/'code'/name).read_bytes()
+        assertions = lambda data: [ast.dump(n, include_attributes=False) for n in ast.walk(ast.parse(data))
+                                   if isinstance(n, ast.Assert)]
+        aa, bb = assertions(a), assertions(b)
+        if aa != bb:
+            raise RuntimeError('Assertion sequence changed: '+name)
+        records.append(dict(file='code/'+name, baseline_sha256=hashlib.sha256(a).hexdigest(),
+                            new_sha256=hashlib.sha256(b).hexdigest(), byte_identical=a == b,
+                            assert_count=len(aa), all_assertions_identical_in_order=True))
+    if records[0]['assert_count'] != 91:
+        raise RuntimeError('The expected PR635 assembly has 91 assertions')
+    result = dict(status='PASS_PR635_ADMISSION_ASSERTION_PRESERVATION', files=records,
+                  centre_interface_review='CENTRE-GUARD-REVIEW.md',
+                  scope='Exact syntax preservation for all admission assertions in these five files. The changed emitter/controller centre boundary and single-provider controls require the separate semantic review; assertion counts alone do not prove them.')
+    args.output.write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], [r['assert_count'] for r in records])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-leaver8/inputs/PR589-EXPECTED.json b/research/gauge44-leaver8/inputs/PR589-EXPECTED.json
new file mode 100644
index 0000000000..e293ddc557
--- /dev/null
+++ b/research/gauge44-leaver8/inputs/PR589-EXPECTED.json
@@ -0,0 +1,222 @@
+{
+ "word": {
+  "file": "tune/bitE8mut-p111-tuned.json.gz",
+  "file_sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f",
+  "content_sha256": "5642fd0e35a1acc11acff8d0c08350c1617e95f310d4d35ad63a651f9eeeba0b",
+  "v": 111,
+  "R": 439,
+  "punctured": [
+   10,
+   15,
+   51,
+   53,
+   56,
+   66,
+   72,
+   89,
+   111
+  ],
+  "retained_totals": 9,
+  "copy_ranks": [
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7
+  ],
+  "decoder_constant": 63,
+  "gates": {
+   "D": 111,
+   "A": 2075,
+   "B": 712,
+   "C": 2574
+  },
+  "local_histogram": {
+   "1": 1323,
+   "2": 1342,
+   "3": 79,
+   "4": 44,
+   "5": 102,
+   "6": 11,
+   "7": 19
+  },
+  "legality": {
+   "records": 27234,
+   "common_frame_ADDs": 24305,
+   "rank_mass": 5129
+  },
+  "five_stage_columns": 883,
+  "five_stage_payload_bits": 93,
+  "nine_stage_columns": 1327,
+  "nine_stage_payload_bits": 93,
+  "eleven_stage_columns": 1549,
+  "eleven_stage_payload_bits": 93,
+  "base_content_sha256": "d0df3c89ae84989f4045ba1681a5e2e9fcdfa38ed0301c8abf5185537155cbe3"
+ },
+ "interface": {
+  "hypotheses": {
+   "H1_no_target_feeds_z": true,
+   "H2_D_frame0_targets_from_helpers": true,
+   "H3_A_z_only_scatter_targets_B_split": true,
+   "H4_C_literal_reverse_at_full": true,
+   "H5_V_identity": true
+  },
+  "conclusion": {
+   "U_block_form": true,
+   "J_identity": true,
+   "K_equals_D": true,
+   "C_is_U_inverse": true
+  },
+  "interleaving": {
+   "z_gates_A": 2075,
+   "source_writes_A": 0,
+   "z_gates_B": 499,
+   "source_writes_B": 483,
+   "helper_writes_B": 16,
+   "sources_rewritten_B": 108,
+   "B_z_write_frame_dims": {
+    "4": 388,
+    "6": 111
+   },
+   "B_z_operand_kinds": {
+    "helper<-helper": 3,
+    "helper<-source": 13,
+    "source<-helper": 108,
+    "source<-source": 375
+   },
+   "B_z_operand_kinds_by_dim": {
+    "dim4:helper<-source": 13,
+    "dim4:source<-source": 375,
+    "dim6:helper<-helper": 3,
+    "dim6:source<-helper": 108
+   },
+   "B_z_writes_after_a_target_read_of_the_same_register": 454,
+   "B_target_reads_of_registers_rewritten_earlier_in_B": 111,
+   "target_reads_of_targets": 0,
+   "cleanup_gates": 2574
+  }
+ },
+ "nine": {
+  "pipeline": "PR #510 (PR #463 nine-stage template, 32 replicas, PR #442 hosting, PR #493 outer assembly), parameterised for v <= 120 by code/adapt9p.py",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_lower_decimal": "0.001733427039589844234749",
+  "profile": {
+   "1": 381024,
+   "2": 400416,
+   "3": 22752,
+   "4": 26880,
+   "5": 29376,
+   "6": 17376,
+   "7": 26784,
+   "42": 288
+  },
+  "bit": {
+   "live": 28416,
+   "physical": 28425,
+   "maxchild": 42,
+   "rank_mass": 1808352,
+   "hosted_residuals": 126432,
+   "bank_assignments": 0,
+   "prefix_bits": 177,
+   "charged_prefix_bits": 192,
+   "coefficient_bits": 177,
+   "two_level_coefficient_bits": 393,
+   "charged_two_level_coefficient_bits": 512,
+   "row_coefficient": 18355,
+   "halving_depth": 2
+  },
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "eleven": {
+  "pipeline": "PR #493 (PR #445 geometry, PR #472 emitter, audit and invoice, PR #442 hosting), parameterised by PR #545's code/adapt.py",
+  "bit_lower": "855475950388791987811/500000000000000000000000",
+  "bit_lower_decimal": "0.001710951900777583975622",
+  "profile": {
+   "1": 116424,
+   "2": 121648,
+   "3": 6952,
+   "4": 7424,
+   "5": 8976,
+   "6": 4520,
+   "7": 8776,
+   "56": 2600
+  },
+  "bit": {
+   "live": 8880,
+   "physical": 8889,
+   "maxchild": 56,
+   "rank_mass": 689304,
+   "hosted_residuals": 38632,
+   "prefix_bits": 4304,
+   "charged_prefix_bits": 4352,
+   "coefficient_bits": 4304,
+   "three_level_coefficient_bits": 12966,
+   "charged_three_level_coefficient_bits": 12992,
+   "row_coefficient": 19431,
+   "halving_depth": 3
+  },
+  "emitted_program_sha256": "793b6f40c9aa4b8db57fec0ac0973e16884dae28707e482ee8f7a2349a5d5a4b",
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "base": {
+  "nine_bit_lower": "1733052823330162099157/1000000000000000000000000",
+  "nine_bit_lower_decimal": "0.001733052823330162099157",
+  "eleven_bit_lower": "427652201524503168379/250000000000000000000000",
+  "eleven_bit_lower_decimal": "0.001710608806098012673516",
+  "note": "PR #555's EXPECTED.json (untuned word); the tune/ pipeline is the same, with the same frozen hosting selections"
+ }
+}
diff --git a/research/gauge44-leaver8/verify_global.py b/research/gauge44-leaver8/verify_global.py
new file mode 100644
index 0000000000..7ab79e3062
--- /dev/null
+++ b/research/gauge44-leaver8/verify_global.py
@@ -0,0 +1,112 @@
+"""Replay the changed global admission against pinned upstream dependencies.
+
+The local directory must contain the fresh canonical/native/phase/wrapper
+artifacts produced by construction/reproduce.py. Frozen evidence may be used
+for a short admission-only replay. No optimizer runs during this verifier.
+"""
+import argparse
+import hashlib
+import json
+import os
+from pathlib import Path
+import subprocess
+import sys
+import time
+
+assert __debug__, 'Assertions required'
+PACKAGE = Path(__file__).resolve().parent
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def dump(path, value):
+    Path(path).write_text(json.dumps(value, indent=2) + '\n')
+
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--main', type=Path, required=True, help='Pinned CrocSwap main checkout')
+ap.add_argument('--local', type=Path, required=True, help='Rebuilt or frozen native gauge44 directory')
+ap.add_argument('--work', type=Path, required=True, help='New output directory')
+ap.add_argument('--discover', action='store_true', help=argparse.SUPPRESS)
+args = ap.parse_args()
+main, local, work = args.main.resolve(), args.local.resolve(), args.work.resolve()
+assert not work.exists(), 'Output directory must be new'
+source = main/'research/complex-k492-owner-repair/vendor/multicold'
+baseline = main/'research/community-k492-audit/pr622/replay/baseline558'
+vendor = source/'vendor/pr558/vendor/pr552/complex-global/vendor531'
+pins = PACKAGE/'data/UPSTREAM-PINS.json'
+if pins.exists():
+    for rel, expected in json.loads(pins.read_text()).items():
+        assert sha(main/rel) == expected, 'Upstream dependency changed: ' + rel
+else:
+    assert args.discover, 'Missing upstream pins'
+    paths = list((baseline/'complex-global/base').rglob('*'))
+    paths += [source/'code/run_portable.py', source/'inputs/PR543-EXPECTED.json',
+              vendor/'evidence/audit/PREFIX-AND-INVOICE.json']
+    paths += [source/'vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz',
+              baseline/'complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz',
+              vendor/'code/prepare_supplier_base.py']
+    paths += [source/'engines'/name for name in ('moment.py', 'base_two_moment.py', 'outer.py')]
+    dump(pins, {p.relative_to(main).as_posix(): sha(p) for p in sorted(paths) if p.is_file()})
+work.mkdir(parents=True)
+env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1',
+           PYTHONINTMAXSTRDIGITS='0', MULTICOLD_SOURCE=str(source),
+           GAIN_PR564_SOURCE=str(source), WITNESS_SPEC=str(PACKAGE/'data/SPEC.json'))
+env.pop('PYTHONOPTIMIZE', None)
+env.pop('WITNESS_DISCOVER', None)
+env.pop('WITNESS_RECORD', None)
+if args.discover:
+    env.update(WITNESS_DISCOVER='1', WITNESS_RECORD=str(work/'WITNESS-RECORD.jsonl'))
+stages = []
+
+
+def run(name, script, *arguments):
+    started = time.monotonic()
+    log = work/(name + '.log')
+    with log.open('w') as stream:
+        result = subprocess.run([sys.executable, '-B', str(source/'code/run_portable.py'),
+                                 str(script), *map(str, arguments)], env=env,
+                                stdout=stream, stderr=subprocess.STDOUT)
+    stages.append(dict(name=name, seconds=round(time.monotonic()-started, 3),
+                       exit_code=result.returncode, log_sha256=sha(log)))
+    dump(work/'STAGES.json', stages)
+    if result.returncode:
+        raise RuntimeError(name + ' failed:\n' + log.read_text()[-7000:])
+    print('PASS', name, stages[-1]['seconds'], flush=True)
+
+
+code = PACKAGE/'code'
+global_dir = work/'global'
+run('restore-parent', code/'restore_parent.py', '--source', source,
+    '--baseline', baseline, '--out', work/'parent558')
+run('bind', code/'bind_providers_portable.py', '--baseline', work/'parent558',
+    '--provider', 'gauge44='+str(local), '--plan', PACKAGE/'data/PLAN.json', '--out', global_dir)
+run('emit', code/'emit_allcold.py', '--base', global_dir/'base',
+    '--owners', PACKAGE/'data/OWNERS.json.gz', '--plan', global_dir/'PLAN.json', '--out', global_dir/'hosted')
+run('audit', code/'audit_allcold.py', global_dir/'base', global_dir/'hosted',
+    global_dir/'audit/ASYNC-AUDIT.json', '--mutation-controls')
+run('invoice', code/'invoice_allcold.py', '--base', global_dir/'base',
+    '--hosted', global_dir/'hosted', '--audit', global_dir/'audit', '--out', global_dir/'audit',
+    '--retained-invoice', vendor/'evidence/audit/PREFIX-AND-INVOICE.json')
+run('assembly', code/'assemble.py', source, global_dir, work/'ASSEMBLY.json')
+if not args.discover:
+    run('admission-controls', code/'assembly_controls.py', '--source-package', source,
+        '--owner', global_dir/'audit/OWNERS-AND-PROFILE.json',
+        '--invoice', global_dir/'audit/PREFIX-AND-INVOICE.json', '--out', work/'ADMISSION-CONTROLS.json')
+    run('bit-supplier-controls', code/'bit_supplier_controls.py', '--source-package', source,
+        '--owner', global_dir/'audit/OWNERS-AND-PROFILE.json',
+        '--invoice', global_dir/'audit/PREFIX-AND-INVOICE.json', '--out', work/'BIT-SUPPLIER-CONTROLS.json')
+    bit_controls = json.loads((work/'BIT-SUPPLIER-CONTROLS.json').read_text())
+    assert bit_controls['status'] == 'PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS'
+    assert len(bit_controls['rejected_controls']) == 12 and bit_controls['derived_deficit'] == 10272
+result = json.loads((work/'ASSEMBLY.json').read_text())
+dump(work/'REPLAY.json', dict(status='PASS_GAUGE44_DISCOVERY' if args.discover else 'PASS_GAUGE44_STRICT_GLOBAL_REPLAY',
+                            kappa=result['kappa'], kappa_decimal=result['kappa_decimal'],
+                            complex_lower=result['complex_lower'], bit_lower=result['bit_lower'],
+                            bit_supplier=result['bit_supplier'],
+                            gain_over_pr635_percent=result['gain_over_pr635_percent'],
+                            spec_sha256=sha(PACKAGE/'data/SPEC.json'), stages=stages,
+                            scope=result['scope']))
+print(result['status'], result['kappa_decimal'], result['gain_over_pr635_percent'], flush=True)
diff --git a/research/gauge44-leaver8/verify_manifest.py b/research/gauge44-leaver8/verify_manifest.py
new file mode 100644
index 0000000000..8c2441d392
--- /dev/null
+++ b/research/gauge44-leaver8/verify_manifest.py
@@ -0,0 +1,19 @@
+"""Verify the submitted package's exact file inventory and SHA256 bindings."""
+from hashlib import sha256
+import json
+from pathlib import Path
+
+root = Path(__file__).resolve().parent
+expected = json.loads((root / 'MANIFEST.json').read_text())
+actual = {
+    p.relative_to(root).as_posix(): sha256(p.read_bytes()).hexdigest()
+    for p in root.rglob('*')
+    if p.is_file() and '__pycache__' not in p.parts
+    and p != root / 'MANIFEST.json'
+}
+if actual != expected:
+    missing = sorted(expected.keys() - actual.keys())
+    extra = sorted(actual.keys() - expected.keys())
+    changed = sorted(k for k in expected.keys() & actual.keys() if expected[k] != actual[k])
+    raise SystemExit(f'Manifest mismatch: missing={missing}, extra={extra}, changed={changed}')
+print(f'PASS package manifest: {len(actual)} files')
diff --git a/research/gauge44-slots-t16/CONSTRUCTION.md b/research/gauge44-slots-t16/CONSTRUCTION.md
new file mode 100644
index 0000000000..fa15676366
--- /dev/null
+++ b/research/gauge44-slots-t16/CONSTRUCTION.md
@@ -0,0 +1,210 @@
+# Gauge44: a changed factory forward map with 44 rank-four cold ends
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0. This note describes the new complex local construction. The package's global evidence supplies the resulting global bound and retains the upstream conditional assumptions.
+
+## 1. Exact result and comparison
+
+The final word has 112 source ports, 112 target ports and 492 helper registers. It implements the same arbitrary-dirt scalar endpoint as the upstream word,
+
+$$
+(X,Y,H)\longmapsto(X,Y+X,H),
+$$
+
+and its inverse-transpose orientation is checked separately. All 204 nonzero entrance frames remain valid. The new ending set consists of **44 cold helpers at rank-four frames**, together with the 34 entering-helper ends inherited from the JP8 HPE stage.
+
+The precise comparison is with the JP8 provider reconstructed from PR635, commit `a6895a69f8ad98ab45777b03e9e6f48888c39f6f`:
+
+| Local quantity | PR635 JP8 | Gauge44 |
+|---|---:|---:|
+| Helpers | 492 | 492 |
+| Nonzero entrance frames | 204 | 204 |
+| Rank-four cold ends | 22 | 44 |
+| Rank-seven cold ends | 2 | 0 |
+| Rank-eight cold ends | 4 | 0 |
+| Entering helpers ending below FULL | 36 | 34 |
+| Total residual helper width | 3894 | **3794** |
+| Local paid rank mass | 5750 | **5650** |
+
+Thus the new word saves **100 units of residual width per invocation** against the complete PR635 provider. It replaces that provider's cold-end construction; the old six higher-rank cold ends and two additional entering ends are not added to the new count.
+
+The exact paid-child profiles are:
+
+| Child rank | PR635 count | Gauge44 count |
+|---:|---:|---:|
+| 1 | 2518 | 2514 |
+| 2 | 402 | 404 |
+| 3 | 448 | 448 |
+| 4 | 164 | 160 |
+| 5 | 68 | 56 |
+| 6 | 4 | 0 |
+| 8 | 8 | 8 |
+
+The final residual-width inventory is `{4:52, 5:48, 7:34, 8:114, 9:244}`. Both the profile and the inventory are recomputed from the literal native frame chains. They are not inferred from the nominal number of ended helpers.
+
+## 2. What changes in the forward factory
+
+The inherited K-triangle schedule and its 492-helper allocation remain the starting construction. Within each of the fourteen eight-source packet factories, three changes alter the arbitrary-dirt forward map while retaining the required clean packet values.
+
+### A. Exchange a source with an equal clean copy
+
+After the sixteen initial copy gates, local source position `j` and its two helper copies have clean values `(x_j,x_j,x_j)`. For positions `j = 4,5,6,7`, exchange the original source register with its second helper copy. The exact register pair in the constructor is `mp[j]` and `mp[2*j+9]`.
+
+For arbitrary helper dirt the triple is instead
+
+$$
+(x_j,\;x_j+h_{j,1},\;x_j+h_{j,2}).
+$$
+
+The exchange changes where the second dirty direction enters the subsequent factory. It does not change any clean operand. Both exchanged registers already have the same rank-one frame, so the exchange adds no frame climb. Each exchange is emitted as three additions and one sign change; these scalar operations remain part of the finite implementation invoice.
+
+This is a change of the forward map, not an output relabeling. In particular, the inverse recovery functional for the original source changes from the original branch to a different combination of the three equal-clean branches. That changes which cold input directions can have their entire final support inside a low frame.
+
+### B. Change the complement to the four coordinate totals
+
+Eight retired factory rows already span the eight source coordinates. The first four rows of their replacement basis are the four required coordinate totals. The remaining four rows are chosen by exact row-rank extension, first using the ordered clean linear forms recorded in `construction/COMPLETION-PRIORITY.json`, then using coordinate rows if an extension is still needed.
+
+These candidate forms are the future low-frame leaver forms used during discovery. The frozen priority data are the complete input to the final constructor: no discovery search is run in reproduction. Every accepted row must increase the rational rank; the resulting eight-by-eight basis is explicitly applied by elementary operations.
+
+All eight retired registers are already at the block's rank-four frame. Consequently this basis replacement also adds no frame climb. It gives the low final rows more independent linear combinations that annihilate the original source data.
+
+### C. Place coordinate totals on the available source carriers
+
+The retired registers are ordered with source registers first. Three available source carriers and one helper carry the four coordinate totals, leaving the four complementary rows on physical helper registers. This lets the new cold directions end on helper wires under the unchanged native endpoint interface.
+
+A carrier permutation alone does not increase the available cold space. Its role here is to realize the independent directions created jointly by the source-copy exchange and the new complementary basis.
+
+## 3. Exact cold-space calculation
+
+Let `P` be the non-target forward matrix after parts A and B and the 34 inherited HPE tail gates. It has 604 rows and columns: 112 original sources and 492 helpers. Let `J` be the 316 protected initial columns consisting of the 112 original sources and all 204 entering helpers.
+
+For a block frame `F`, let `I` be every non-target output register whose current frame is contained in `F`. Source output rows are included in this set. Define
+
+$$
+L=\operatorname{leftker} P[I,J],\qquad
+K=\ker P^{-1}[J,I].
+$$
+
+Rows of `L` are low output linear forms with no protected initial dependence. Columns of `K` are low-supported output directions whose inverse images have no protected component. The rank of the pairing `LK` counts the simultaneously usable cold directions in this fixed forward word.
+
+The changed forward map has the following exact block data:
+
+| Block indices | Number of blocks | Low registers `|I|` | `dim L` | `dim K` | `rank(LK)` |
+|---|---:|---:|---:|---:|---:|
+| 0, 1, 2, 11, 12, 13 | 6 | 6 | 2 | 4 | **2** |
+| 3 through 10 | 8 | 8 | 4 | 4 | **4** |
+
+The count is therefore `6*2 + 8*4 = 44`. The fixed upstream rank-four cold construction supplied one and two directions respectively, for `6*1 + 8*2 = 22`.
+
+The complement change by itself improves the available low annihilating rows but leaves the inverse-support obstruction. The source-copy exchanges remove that obstruction: `K` has dimension four in every block and pairs with all the available rows of `L`.
+
+## 4. Realizing the directions with legal dyadic operations
+
+`construction/build_gauge_cold44.py` recomputes these spaces over exact rational numbers. It selects columns of `K` and normalizes them to a matrix `U` satisfying
+
+$$
+LU=I_r,
+\qquad q=P^{-1}[:,I]U.
+$$
+
+The constructor checks that `q` is supported entirely on that block's sixteen initially cold factory helpers, denoted `H_b`. Put
+
+$$
+R_b=LP[I,H_b].
+$$
+
+Then `R_b q[H_b,:] = I_r`. A sixteen-by-sixteen input basis `Q_b` places the columns `q[H_b,:]` at the designated ended-helper positions and fills the other columns with a basis of `ker R_b`. The resulting input basis is explicitly invertible.
+
+For the low-frame output transformation, the ended-helper rows are replaced by the rows of `L`; each remaining low row `i` becomes
+
+$$
+e_i-U_iL.
+$$
+
+The actual chosen helper positions give an invertible tail matrix. Its nonsingularity and dyadic implementation are checked by exact elimination, rather than assumed from a dimension count. The construction receipt records every `Q_b`, tail matrix and selected endpoint.
+
+Every `Q_b` is emitted at frame zero, at the head of A **after** the entry normalization wrappers. Every low tail is emitted at its block frame. The remaining cleanup is rebuilt as an exact dyadic Gauss-Jordan inverse on the non-ended registers at FULL. It is not obtained by blindly reversing a changed partial schedule.
+
+Before forming the FULL inverse, the constructor verifies both the row and the column identity of each of the 78 ended helpers. Thus no protected data or other helper dirt remains in an ended helper, and its initial dirt remains nowhere else. The FULL inverse skips these isolated rows and columns entirely.
+
+The realized word has:
+
+| Construction component | Scalar gates |
+|---|---:|
+| Frame-zero helper premix | 1489 |
+| New rank-four tail | 60 |
+| Inherited HPE tail | 34 |
+| Refactored FULL inverse | 28056 |
+| Additional target compensation after wrappers | **0** |
+
+All selected new cold directions have zero target response. The independent scalar auditor nevertheless recomputes the complete existing dirty-response compensation, obtaining 7348 additions, and checks both orientations on all 716 input columns.
+
+Relative to the HPE-stage word before any cold-end construction, the aggregate chain delta is `N_1 += 44, N_6 -= 44`, reducing rank mass and residual width by 220. PR635 had already saved 120 units through its complete cold/extra-HPE construction. The net new saving is therefore 100. There is no omitted cost for lifting the low tails: their rank-one increments are included explicitly.
+
+## 5. Native interface and validation
+
+The transport preserves the exact ordered list of 112 ports and the exact ordered eight center frames. The center carriers change because some totals now reside on sources. In native coordinates they are
+
+```
+[92, 57, 81, 224, 11, 240, 9, 256]
+```
+
+A global interface check must compare the ordered center frames and port geometry, and use the provider's actual center carriers. Equality of carrier numbers with an old provider is not a mathematical requirement. The local event ledgers explicitly clear all private center channels in both orientations.
+
+Completed checks for the frozen word include exact forward and inverse-transpose scalar replay on all 716 columns; every literal native frame chain; the 204 zero-response entrance conditions; the 44 cold and 34 entering endpoint cones; wrapper placement and normalized wrapper identities; both emitted local ledgers; and exact phase lowering for 3019 directed edges and 224 endpoint adapters. The independent audit does not import the new constructor.
+
+This local result does not by itself certify a global exponent. Physical whole-family owners, actual residual/spectator routing, idle remainders, global scalar assembly and the complete finite invoice are the separate global checks reported elsewhere in the package.
+
+## 6. Compact reproduction
+
+Only Python's standard library is needed for this construction and the retained local pipeline. Do not use `python -O`. The reproduction driver checks byte hashes of every named upstream input and the changed code, then checks the content hash after each construction step. Its two source checkouts are:
+
+| Argument | Repository commit |
+|---|---|
+| `--main` | `17ce0c79b7b51c2634b439ea5a2b754f09909693` |
+| `--pr635` | `a6895a69f8ad98ab45777b03e9e6f48888c39f6f` |
+
+Starting from a clone of `https://github.com/CrocSwap/integer-mult-bounds` containing those commits, prepare detached worktrees:
+
+```bash
+git -C integer-mult-bounds fetch origin main refs/pull/635/head
+git -C integer-mult-bounds worktree add --detach ../integer-main 17ce0c79b7b51c2634b439ea5a2b754f09909693
+git -C integer-mult-bounds worktree add --detach ../integer-pr635 a6895a69f8ad98ab45777b03e9e6f48888c39f6f
+```
+
+From the directory containing those worktrees and this delta package, run:
+
+```bash
+python -B research/gauge44-global/construction/reproduce.py \
+  --main integer-main \
+  --pr635 integer-pr635 \
+  --out gauge44-reproduction
+```
+
+The default stops after regenerating the exact final scalar word and comparing the newly derived cold recipe with the frozen recipe. It rebuilds only the two short shadow steps needed by the four port transfers. It does not rerun the ancestor admission stack, search for a basis, optimize owners, or replay global assembly.
+
+Use `--frozen-cold` to splice the included recipe instead of re-deriving its small exact linear systems. Use `--until local` to add native transport, emitted ledgers, independent local replay and wrappers. Use `--until phases` to add the complete phase lowering. Every invocation needs a fresh output directory; these are alternatives, not resumable increments. On the research machine, exact cold derivation took about 2.6 seconds, native transport/ledgers/replay/wrappers about 41 seconds, and complete phase lowering about 198 seconds.
+
+The exact dependency chain is:
+
+1. Construct the changed raw R492 factory from the pinned Hamming inputs, frozen priority and pinned K-triangle schedule.
+2. Apply the four inherited port stages.
+3. Apply the inherited B-frame regroup and 34-HPE construction.
+4. Derive the exact block premixes, cold44 tails and FULL inverse.
+5. Optionally emit and check the native ledgers, wrappers and complete phase lowering.
+
+`construction/INPUTS.json` gives the input hashes and every intermediate content hash. The key decompressed content identities are:
+
+| Word | SHA-256 |
+|---|---|
+| Changed raw factory | `0ac47f92fc2e3f5aa457d78f7b8a5c785bf140c546932b9dfcd9e610ad319180` |
+| Changed HPE forward | `42fb8b3aa314593fe976820cf65824f5fce0ee4f95281796992d4809709864cc` |
+| Final cold44 word | `78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290` |
+| Native canonical word | `e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f` |
+
+## 7. Attribution
+
+The original 504-helper factory and borrowed-register construction are icekylinx's PR531 lineage, prepared with OpenAI Codex/GPT assistance and retaining the earlier PR425/PR514 credits. The inherited K-triangle atom and frozen read schedule are credited in PR635 to AtomScout, a Claude Code research agent. The porting routine is credited there to Port480. This package does not claim those as new work.
+
+The reused JP8 ancestry includes the PR558/PR552 supplier, the earlier-cut and multicold kernels, and the joint prefix adapted from Dominik Scholz's PR571 work. Native HPE and cold-end transport, frame and wrapper machinery come from the credited PR635 lineage, including DreamingOfClouds, jeremykothe2, chafreaky and their disclosed assistants. The retained `construction/UPSTREAM-NOTICE.md` and `construction/LICENSE` preserve the upstream notice and Apache-2.0 license.
+
+The new contribution here is the combination of source-copy exchange, changed retired-row completion, source-carried coordinate totals, and the explicit exact cold44 realization. Those changes were developed for icekylinx with OpenAI GPT-6 Astra assistance. The upstream notices, proof scope and conditional assumptions continue to apply.
diff --git a/research/gauge44-slots-t16/LICENSE b/research/gauge44-slots-t16/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/gauge44-slots-t16/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/gauge44-slots-t16/LOCAL-VALIDATION.json b/research/gauge44-slots-t16/LOCAL-VALIDATION.json
new file mode 100644
index 0000000000..5973645e1a
--- /dev/null
+++ b/research/gauge44-slots-t16/LOCAL-VALIDATION.json
@@ -0,0 +1,356 @@
+{
+  "status": "PASS_LOCAL_INCREMENTAL_GAUGE44",
+  "python": "3.14.8",
+  "upstream_main": "17ce0c79b7b51c2634b439ea5a2b754f09909693",
+  "pr635": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f",
+  "construction_steps": [
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+      "step": "shadow-early",
+      "exit_code": 0,
+      "seconds": 0.322
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+    {
+      "step": "shadow-prefix",
+      "exit_code": 0,
+      "seconds": 0.429
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+    {
+      "step": "gauge-forward",
+      "exit_code": 0,
+      "seconds": 0.474
+    },
+    {
+      "step": "port0",
+      "exit_code": 0,
+      "seconds": 0.388
+    },
+    {
+      "step": "port1",
+      "exit_code": 0,
+      "seconds": 0.407
+    },
+    {
+      "step": "port2",
+      "exit_code": 0,
+      "seconds": 0.403
+    },
+    {
+      "step": "port3",
+      "exit_code": 0,
+      "seconds": 0.389
+    },
+    {
+      "step": "cold44-exact",
+      "exit_code": 0,
+      "seconds": 2.544
+    },
+    {
+      "step": "native",
+      "exit_code": 0,
+      "seconds": 3.63
+    },
+    {
+      "step": "ledgers",
+      "exit_code": 0,
+      "seconds": 2.759
+    },
+    {
+      "step": "local-replay",
+      "exit_code": 0,
+      "seconds": 15.924
+    },
+    {
+      "step": "wrappers",
+      "exit_code": 0,
+      "seconds": 2.706
+    },
+    {
+      "step": "phases",
+      "exit_code": 0,
+      "seconds": 186.772
+    }
+  ],
+  "five_mathematical_local_artifacts_match_frozen_evidence": true,
+  "phase_edges": 3019,
+  "endpoint_adapters": 224,
+  "independent_scalar_audit": {
+    "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+    "input_file": "FULL-WORD.json.gz",
+    "content_sha256": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290",
+    "compressed_sha256": "0ad202612f010df4ab66432a628247b37ad8b497dd6b27595b1685cbd7eb119e",
+    "parent_center_interface": {
+      "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+      "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+      "transport_tau": 43,
+      "ordered_frame_bases_match": true,
+      "all_ports_match": true,
+      "transported_centers": [
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+        57,
+        81,
+        224,
+        11,
+        240,
+        9,
+        256
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+      "source_centers": [
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+        57,
+        81,
+        11,
+        9
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+      "ordered_frame_bases": [
+        [
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+          128,
+          64,
+          34,
+          16,
+          10,
+          4,
+          1
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+        [
+          256,
+          128,
+          64,
+          32,
+          16,
+          8,
+          5,
+          3
+        ],
+        [
+          256,
+          128,
+          64,
+          32,
+          17,
+          9,
+          4,
+          2
+        ],
+        [
+          256,
+          128,
+          64,
+          36,
+          20,
+          8,
+          2,
+          1
+        ],
+        [
+          256,
+          128,
+          66,
+          32,
+          18,
+          8,
+          4,
+          1
+        ],
+        [
+          256,
+          128,
+          65,
+          33,
+          17,
+          9,
+          5,
+          3
+        ],
+        [
+          256,
+          128,
+          65,
+          33,
+          16,
+          8,
+          4,
+          2
+        ],
+        [
+          256,
+          128,
+          68,
+          32,
+          16,
+          12,
+          2,
+          1
+        ]
+      ]
+    },
+    "v": 112,
+    "h": 9,
+    "R": 492,
+    "entering": 204,
+    "lowends": 78,
+    "coldends": 44,
+    "compensation_gates": 7348,
+    "local_profile": {
+      "1": 2514,
+      "2": 404,
+      "3": 448,
+      "4": 160,
+      "5": 56,
+      "8": 8
+    },
+    "width_inventory": {
+      "4": 52,
+      "5": 48,
+      "7": 34,
+      "8": 114,
+      "9": 244
+    },
+    "checked_columns": 716,
+    "elapsed_seconds": 2.443164045999765,
+    "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+  },
+  "independent_guard_review": {
+    "status": "PASS_PR635_ADMISSION_ASSERTION_PRESERVATION",
+    "files": [
+      {
+        "file": "code/assemble.py",
+        "baseline_sha256": "1b1a9024ac910dc9b9d9e30150684e1fa9cb228a4c1c275b75ab04b57fdef1dd",
+        "new_sha256": "7ac28118d69416e4fb67b61216285fb0823310b7635ce1b9025aa3f10119ef6a",
+        "byte_identical": false,
+        "assert_count": 91,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/invoice_allcold.py",
+        "baseline_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+        "new_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+        "byte_identical": true,
+        "assert_count": 67,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/bind_providers_portable.py",
+        "baseline_sha256": "2eb5c262bf481b3bec9ceaec654fa46ff6fc3a89b13d4906a29a55a89e35feea",
+        "new_sha256": "7c9aba6c7f138d270852d859d902f905a15598b6263567700b5b08a153823cb6",
+        "byte_identical": false,
+        "assert_count": 22,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/generated_identity.py",
+        "baseline_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+        "new_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+        "byte_identical": true,
+        "assert_count": 4,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/witness.py",
+        "baseline_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+        "new_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+        "byte_identical": true,
+        "assert_count": 3,
+        "all_assertions_identical_in_order": true
+      }
+    ],
+    "centre_interface_review": "CENTRE-GUARD-REVIEW.md",
+    "scope": "Exact syntax preservation for all admission assertions in these five files. The changed emitter/controller centre boundary and single-provider controls require the separate semantic review; assertion counts alone do not prove them."
+  },
+  "owner_replay": {
+    "status": "PASS_FROZEN_OWNER_AND_INTEGER_MAJORIZATION_REPLAY",
+    "seed_mode": "included_frozen_seed",
+    "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+    "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+    "owners_semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d",
+    "owners_gzip_sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+    "majorization_semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc",
+    "global_profile": {
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+      "3": 32429,
+      "4": 11520,
+      "5": 4032,
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+      "8": 582,
+      "12": 13,
+      "16": 33,
+      "19": 1,
+      "20": 2,
+      "28": 4,
+      "32": 62,
+      "36": 1,
+      "40": 1,
+      "44": 6,
+      "48": 2289
+    },
+    "scope": "Exact hosting nomination and callwise fixed-point replay; full supplier admission is separate."
+  },
+  "global_replay": {
+    "status": "PASS_GAUGE44_STRICT_GLOBAL_REPLAY",
+    "kappa": "1649483702558979/1000000000000000000",
+    "kappa_decimal": "0.001649483702558979",
+    "complex_lower": "1652208994368411824947/1000000000000000000000000",
+    "bit_lower": "413456747036699736067/250000000000000000000000",
+    "gain_over_pr635_percent": "0.8093060205252829126484020359439672024956960385078942889840023844750830",
+    "spec_sha256": "fee57674a7f36b30b1e7eb96a8f567a90a522217bc644c1a6a1f8bff85196fbf",
+    "stages": [
+      {
+        "name": "restore-parent",
+        "seconds": 2.089,
+        "exit_code": 0,
+        "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+      },
+      {
+        "name": "bind",
+        "seconds": 0.962,
+        "exit_code": 0,
+        "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+      },
+      {
+        "name": "emit",
+        "seconds": 4.817,
+        "exit_code": 0,
+        "log_sha256": "90ce07d06a8eaffdb66201e8346021183e5a803395fb9f6d8ceb0e5ff068ef2c"
+      },
+      {
+        "name": "audit",
+        "seconds": 19.625,
+        "exit_code": 0,
+        "log_sha256": "66b4abb2a88a4eaba8a8baa3585ef4aa819be5f8acb7947bae734b3478280456"
+      },
+      {
+        "name": "invoice",
+        "seconds": 1.804,
+        "exit_code": 0,
+        "log_sha256": "5d10712d494304287749dd7a6c3369f9b707bba30e9f567b68230669dcf5418a"
+      },
+      {
+        "name": "assembly",
+        "seconds": 0.808,
+        "exit_code": 0,
+        "log_sha256": "768d3215f1918117dc6c33b4cfeaf0b5f5da9ba5c77178db4bb1d08d000e226f"
+      },
+      {
+        "name": "admission-controls",
+        "seconds": 0.885,
+        "exit_code": 0,
+        "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+      }
+    ],
+    "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the same cited unchanged PR543 bit supplier as PR635. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+  },
+  "admission_mutations_rejected": 69,
+  "controller_mutations_rejected": 15,
+  "frozen_template_content_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "fresh_template_content_sha256": "a1692259fb5a06bbebdc1049a7f757c6d2fc79ff8c31ed0c25b38fe9f98ed051",
+  "template_comparison": {
+    "sole_changed_field": "async_schedule.source_plan_sha256",
+    "frozen_plan_sha256": "609adb126d7d3de2abdd9275f9015589c0b137d0d19821c2c3e7c1a8541c18d2",
+    "fresh_plan_sha256": "b2e4b1f063250c40e0087f77e896882c60f36ed8764e86ba1610dec9bdff7394",
+    "explanation": "Fresh phase review differs only in its measured seconds. Runtime provider binding consequently changes the plan byte hash. All remaining serialized template fields match exactly; each runtime hash is checked against its own file."
+  },
+  "assembly_matches_frozen_rates_and_profile": true,
+  "post_replay_packaging": "Four files received trailing-whitespace cleanup only; complete parsed ASTs were checked unchanged. Constructor input pin refreshed. Admission assertion comparison rerun.",
+  "scope": "Changed construction and exact recipe, fresh native ledgers/wrappers/phases, independent scalar and guard audits, integer owner reproduction, strict global admission and independent pricing. No predecessor full replay, seed-discovery optimizer or PDF generation. Local Python 3.14; Python 3.11 is covered by CI."
+}
diff --git a/research/gauge44-slots-t16/MANIFEST.json b/research/gauge44-slots-t16/MANIFEST.json
new file mode 100644
index 0000000000..438842145b
--- /dev/null
+++ b/research/gauge44-slots-t16/MANIFEST.json
@@ -0,0 +1,181 @@
+{
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+  "code/assembly_controls.py": "da7e981ae1b9f099d4e1524cb4f3ba1116011936ebe378692889b5dbfa99029d",
+  "code/audit_allcold.py": "1467a2acb654e62552c69fb9a7c4c85f70a02120881d222313865058ab71a6cc",
+  "code/bind_providers_portable.py": "1d39bcc7b63ac158e021454beaae897d123e174360573762aecade3cd43193f6",
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+  "data/PREPARATION.json": "1d576298bfafc509992113fdd58b5482655a88e321cbfafe9386588eb6fbb6e9",
+  "data/SPEC-T8.json": "8e95ae8087124189cbd366d0e9d1c5ebededff536ff3501927b4b2a2e8dac70e",
+  "data/SPEC.json": "2a8728207fc2d1f65bcc0229a61c52a4fbd02f9d4acebe1b479d3fb0fe0690f6",
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+  "evidence/BINDING.json": "f80ad585c9cf94989d459971189fbb176084aedbe27edf5b5cccc5c2a44de43b",
+  "evidence/CENTER-COMPATIBILITY.json": "c66c7da1099ac8618381e2a7cb48b09b43ccf8d125ff124e129aba8ddb922cf3",
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+  "evidence/layers/LOCAL-AUDIT-LAYERED.json": "a596d7262374a023ae079e0da41d20189bd3ca4594101e5e6f402ce5799df9ff",
+  "evidence/leaver/CELL-MUTANTS-LV.json": "308975b8288cb9c853ee6b69e68b25e6f3727d259dccfb7509042f103bb03220",
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+  "evidence/local/CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+  "evidence/local/CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12",
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+  "evidence/local/SCALAR-FRAME-AUDIT.json": "cfc73040079b43ea82a42f3cf4c910edda1362deb09ec21c816c329347313bcb",
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+  "evidence/STAGES.json": "09d7c6daf1e93c58863267141dedc3873264d3baede0cddefda0d56ecb560458",
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+  "hosting/reuse_owners.py": "2106fe79bd89071e62a3a25c1e444531e14fb89f88b4bdeb72d7b40c91266402",
+  "independent/audit_local.py": "03afcfc9da428b3f6edac81c1fee7f277ab81b64998efae78380b63498dec6cd",
+  "independent/CENTRE-GUARD-REVIEW.md": "7b82518d7ddf042d6e71174bc286311fa72127e0dc6dc9e500025fcf7abbf897",
+  "independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json": "9fb5265c4d2ddf3d615e46600954c79cd1a42481500a0973a5695fcb9f2558c9",
+  "independent/GAUGE44-GLOBAL-GUARD-REVIEW.json": "631107a9a9acb02441ce80298f815e0c624f811b0d58c6fd78f8dc58d564bb5b",
+  "independent/GAUGE44-INDEPENDENT-PRICE.json": "6e222b252f3453446d0e41b08f00a9bf9449ce3588b6ddc00c9accc1c00e7683",
+  "independent/price_profile.py": "d2f548ad6b99f64a8ca5fbaf822a89560bb99359957ce3420b497f6a46fc0acf",
+  "independent/README.md": "25668a62d8c91f6860f8412cf2fc750ba41bf1085dad3709ad5067c7956eac89",
+  "independent/review_guards.py": "b83164d6c0122a055b3281f3381b305683a875760a2d727dd0188bb2aa59d67d",
+  "inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "LOCAL-VALIDATION.json": "f81fbd98eb608b8119f03f89a5692bcd610845fc97022337931586d8582b706e",
+  "NOTICE.md": "7a8d17b04da1e6c9d0ec217fb5bda72faa09d9a21695128722dd1e2827870fcf",
+  "PROOF-NOTE-BARCH.md": "c24f211b09358b25d6cf47dd18e4bbd8bcf4ecf279e6f1c6c90613cfa230818d",
+  "PROOF-NOTE-BIT.md": "dd771adb12f6f0bef0e2931c28b21b243b04d5f512370cbad1207275c342aaf7",
+  "PROOF-NOTE-FRAMES-X4.md": "39c50420ebb6e8813706a49b2cf759f277c4afac9f6780fc0a7ac6a5fb86e036",
+  "PROOF-NOTE-LAYERS.md": "92bb85b056803770882afa916277c5b49a7027159c113a106e7b2b33e57c097f",
+  "PROOF-NOTE-LEAVER.md": "e4f9482ef551d6d4300d8ed8bb7c34dc9327fbcfa30a502bf3476b78468e60c3",
+  "PROOF-NOTE-NOTRI.md": "774d1ff7b77844990da7bc1feff7f9ffff8b1f4f9b03232a620f1f9a29935414",
+  "PROOF-NOTE-P6N.md": "cef8fad3d6644b4376ed15c4c5c46c68324009ab8f42d10bfa2da4b505b2c26d",
+  "PROOF-NOTE-PROMO.md": "c170e5196d3081f86ac377c6fe614ca17f6281972837580275ce5af41cbc64ae",
+  "PROOF-NOTE-SW4.md": "d7bb225f1a7f9fd363e819a67e92a5fe14c0942f6c3616d73609cc48042daf3d",
+  "README.md": "d0fbd05569504afbdde71899ca5c0c6da0f818d7aac50a22d241d106589af95c",
+  "RESULT.json": "7204341041ea90fe0394e8843f083fcc1b1c262214e6bc5d3118d35787c24101",
+  "SOURCES.json": "abb903d9b46388f99325a3939eb68171ac163c66b4b62b7961ea46daa20a88f0",
+  "t16/build_parent.py": "82e274d0c7a94f9bf0468dd37f0505d0c42017559ebb4ba8c079a1f4e403d91e",
+  "t16/indep16.py": "1beb512a1d072f81d3e8e492c8827636029686897093bd433e4d4c92d0c830c7",
+  "t16/lift16.py": "072fe6ac032543d5106631f9b4aa36103269b64ab72061d97ec604f648830689",
+  "t16/NOTICE.md": "902370e6bfcd39dbea2ece474f15fccbcce3b8e966b2b94066bd03e5174591b5",
+  "UPSTREAM-NOTICE.md": "a75967ebc34e3bf2ff2c25c08e6c7f1a61b0c0d171cfd1b62196ae2caaf2c610",
+  "verify_manifest.py": "723d726dbbe5b65a49caecae0f1aab664a1413fb639abfd3e826a5a538e14e5b",
+  "verify_t16.py": "050e2dfba59911b8f29fd94422833d421367a0ad01c5e4ae916a75a235ee5e46"
+}
diff --git a/research/gauge44-slots-t16/NOTICE.md b/research/gauge44-slots-t16/NOTICE.md
new file mode 100644
index 0000000000..30d0c8cd3c
--- /dev/null
+++ b/research/gauge44-slots-t16/NOTICE.md
@@ -0,0 +1,24 @@
+# Gauge44 attribution and scope
+
+New contributions by icekylinx, with OpenAI GPT-6 Astra assistance.
+Local review and packaging used OpenAI Codex. Apache-2.0 applies;
+the license is included. The full original PR635 notice is preserved as
+UPSTREAM-NOTICE.md and construction/UPSTREAM-NOTICE.md.
+
+The new contribution is the changed source-branch gauge and retired-row
+completion, source-carried coordinate totals, exact 44-cold-end realization,
+and explicit all72 whole-family assignment using concave capacity matching
+with integer majorization certificates. The center-carrier generalization
+retains the exact ordered common frames and complete native local contract.
+Independent local, price, interface and owner fixed-point checks are included.
+
+The construction retains the credited PR635 K-triangle and porting machinery,
+earlier joint-prefix/HPE/frame ancestry and icekylinx's prior factory work.
+#645 used the same cited PR543 bit supplier as PR635. This package (research/gauge44-leaver8) cites the merged PR589 bit supplier instead, with a derived rank-mass deficit (PROOF-NOTE-BIT.md); #645's retained PR543-based evidence is historical. It builds #645's word without K-triangles (PartialK) and stacks earlier community jp8 layers on it (G44Stack), adds the p6n ends (NoTriReopen), entrance promotions (BlockInvert) a read-set exchange (BRoute), chafreaky's #741 frames, JointXF's joint exchange, NewBArch's triangle-hybrid B rewrite and LeaverSAT's eight k8 leaver cells (with LeaverSAT2's frame re-optimisation); see README. All-size, realization,
+hosting, precision/tape, analytic-transfer and bit H1-H5 assumptions remain
+conditional. No upstream license, credit, source pin or AI disclosure is
+replaced by this notice.
+
+PR641 and PR642 were checked as concurrent reported frontier comparisons.
+Their endpoints and owner maps are not included here. See CONSTRUCTION.md,
+hosting/PROOF.md, independent/ and README.md for the exact contribution scope.
diff --git a/research/gauge44-slots-t16/PROOF-NOTE-BARCH.md b/research/gauge44-slots-t16/PROOF-NOTE-BARCH.md
new file mode 100644
index 0000000000..8cea5a6846
--- /dev/null
+++ b/research/gauge44-slots-t16/PROOF-NOTE-BARCH.md
@@ -0,0 +1,43 @@
+# PROOF-NOTE-BARCH: width-neutral triangle-hybrid B-delivery rewrite (U8)
+
+Construction by NewBArch (`construction/barch/`, builder `build_tri.py`, controls `run_controls.py`, recipe
+`RECIPE-U8.json`). Driver: `construction/barch/reproduce_barch.py`, chained after `construction/jx`.
+
+## The move
+On research/gauge44-frames-x's X4 word (`1e1d99ba…`), eight disjoint slots are rewritten. In each slot X an entering
+copy E donates into a halves-copy X: 231 (E 450), 230 (E 452), 232 (E 454), 236 (E 456), 226 (E 451), 228 (E 453), 62 (E 455), 238 (E 457). That way, so that one target
+read takes X + H in a single gate. A holder pair (for example 496/484) carries the value. Each holder is restored by a
+low-end tail at its frame (early cleanup) and a FULL-cleanup restore. Entrance pre-reads keep the entering helper's
+start value away from every target.
+
+The recipe is explicit, with every index referring to the X4 word:
+- 40 B deletions;
+- 40 B insertions, each with its frame;
+- 32 explicit re-chosen B frames;
+- 8 early-cleanup tails;
+- 8 FULL-cleanup restores.
+
+The A section and X4's tail frames are untouched. The width is unchanged at 3778. The profile goes
+{1:2548, 2:338, 3:430, 4:194, 5:56, 8:8} → {1:2548, 2:338, 3:446, 4:162, 5:72, 8:8}, a delta of {3:+16, 4:−32, 5:+16}.
+The eight slots are additive (8 × 3.925e-8 ideal = 3.140e-7). Output word `090fd574…`. U8 contains B0's four slots
+(231, 230, 226, 228) plus 232, 236, 62 and 238.
+
+## Checks rerun on every rebuild
+- `build_tri.py` (standard library only) checks the base sha (`1e1d99ba…`) and the result sha (`090fd574…`).
+- `run_controls.py` produces 38 outcomes, all required. The control set is pinned in `LOCAL-PINS-barch-U8.json`.
+  - C0 identity reproduces the input.
+  - The recipe word PASSes #645's independent `audit_local.py`.
+  - Four mutants must each FAIL `audit_local` with a pinned message, both globally and for each of the eight slots
+    (NAME@X):
+    - drop_restore: the holder is not restored, giving "all-column endpoint failure";
+    - restore_full: the low-end restore is moved into the FULL cleanup, giving "all-column endpoint failure";
+    - drop_preread: the inserted entrance pre-reads are omitted, giving "nonzero entrance response";
+    - donation_after: the donation is placed after the target read, giving "nonzero entrance response".
+- The per-end layer-end controls (`../layers_p6n/layer_end_controls.py`) reject 95.
+- PR635's native chain runs, with the canonical word, local programs and Clifford recipes pinned.
+
+## Strict
+NewBArch's strict replay: the #741 map (`G44Pack/m741`, byte-identical OWNERS) is rebound to the U8 locals with
+`rewidth.py` and admitted with this package's own code (NEWWORD `admit645.py` on research/gauge44-frames-x's tree).
+The result is κ 0.001661948695165034, +3.1404e-7 over research/gauge44-frames-x. The four-slot subset B0 strict-passes
+at 0.001661791659578416 and the single slot V1 at 0.001661673902364948.
diff --git a/research/gauge44-slots-t16/PROOF-NOTE-BIT.md b/research/gauge44-slots-t16/PROOF-NOTE-BIT.md
new file mode 100644
index 0000000000..da06360da0
--- /dev/null
+++ b/research/gauge44-slots-t16/PROOF-NOTE-BIT.md
@@ -0,0 +1,112 @@
+# PROOF-NOTE-BIT: citing the PR589 bit supplier with a derived rank-mass deficit (gauge44)
+
+This note is BitCap's `PROOF-NOTE-BIT.md` from `complex-571-cold14-k492-bit589`, adapted to the gauge44 package. It
+covers the only verifier change relative to #645's package (`research/gauge44-global`): the bit supplier changes from
+PR543 to PR589. The complex side is #645's construction, unchanged: supplier word, recipes and every complex check in
+`code/assemble.py`. The only complex-side change is the repacked owner map (`data/PLAN.json`, `data/OWNERS.json.gz`),
+with expected values re-derived in `data/SPEC.json`.
+
+## Changed sites
+
+The changes are in `code/assemble.py`, plus one new stage in `verify_global.py` and a new file
+`code/bit_supplier_controls.py`. The independent (non-verifier) `independent/price_profile.py` is ported to PR589 as well. Every other `.py` file equals #645's.
+
+| # | site | before (#645) | after |
+|---|---|---|---|
+| S1 | bit input | `inputs/PR543-EXPECTED.json` from the multicold source, blob pin `b61d8598…` | `inputs/PR589-EXPECTED.json`, shipped in this package, blob pin `e293ddc5…`, through `load_bit` |
+| S2 | bit deficit | literal `9984` | `bit_deficit(word, live)` = T(2Kv − L·cst), with L = 9, T = 32, K = (L−1)/2 = 4 |
+| S3 | profile binding | (none) | Σ r·n of the bit profile = `bit.rank_mass`; moment width `BIT_M = 1 + 7L` asserted = 64 |
+| S4 | pipeline binding | (none) | the record's `nine.pipeline` names the nine-stage template with 32 replicas |
+| S5 | citation / receipt | input hash names the PR543 file | `bit_supplier` cites PR589 (head `a5afc8c6`, merged as `b3eb785a`, path `research/e8-bit-p111-tuned/tune/EXPECTED.json`) and records v = 111, cst = 63, COPY ranks [7×9] and the derived deficit 10272 |
+| S6 | `verify_global.py` | (none) | stage `bit-supplier-controls` runs `code/bit_supplier_controls.py`; it requires status `PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS`, exactly 12 rejected controls and derived deficit 10272 |
+
+The shipped `inputs/PR589-EXPECTED.json` has git blob `e293ddc557742637f9f679f083a1a282d87b1b13`, which equals
+`origin/main:research/e8-bit-p111-tuned/tune/EXPECTED.json`.
+
+## Why the derived deficit is correct
+
+**The identity.** The rank-mass identity of #545 and #555 is M·live − mass = T(2Kv − L·cst). Its source is
+#555's README, "Rank-mass identity", and `code/adapt9p.py`, whose audit carries `DEFICIT=T*(2*K*V-L*CST)`.
+
+**The parameters.** The bit word has v live ports and decoder constant cst, the sum of the nine retained totals' COPY
+ranks. The nine-stage chain is #463/#510 with 32 replicas, so L = 9, T = 32, K = 4 and M = 1 + 7L = 64. The live data
+wires number 2KvT.
+
+**The constraints checked.** The verifier asserts all of:
+1. cst = Σ copy_ranks, with exactly `retained_totals` = 9 entries, each in (0, 8].
+2. live = 2KvT. For #589: 2·4·111·32 = 28416.
+3. Σ r·n over the priced profile = the record's `rank_mass` = 1808352.
+4. M·live − Σ r·n = T(2Kv − L·cst). For #589: 64·28416 − 1808352 = 10272 = 32·(888 − 567).
+
+Check (4) is #645's `check_moment` guard, unchanged. So v, cst, the profile and live must all agree.
+
+**PR543 consistency.** The same formula reproduces #645's constant: PR543 has live = 30720, so v = 120; its nine
+totals have COPY rank 8, so cst = 72; 32·(960 − 648) = 9984.
+
+**The deficit does not raise c.** `check_moment` uses the deficit only as an equality guard. The moment engines
+compute from (profile, m = 64, live, z) and never read it. The bit value c is established only by the unchanged
+acceptance tests at the same exact endpoints, with the bit bad-residue surcharge retained: accept at c and reject at
+c + 10⁻²⁴, by both engines.
+
+## Effect on the outer chain (differs from the k492 package)
+
+In the k492 package the complex side bound under either supplier, so κ did not move. Here it does. With the
+gm3 map the complex side certifies b = 0.001654663299688920102557, with research/gauge44-bit589's dz1 map
+b = 0.00165526410310589140991, and with research/gauge44-bit589b's L1g4 map b = 0.001655496738330440231813. PR543's c = 0.001653826988146798944268 is
+below b, so under PR543 the bit side would bind. BitCap's table gives the PR543 bit-side κ cap as
+0.001651096360425895, which is exactly the κ of `research/gauge44-repack`. PR589's c = 0.001733427039589844234749
+exceeds b, so the complex side binds again (`binding = complex` in `ASSEMBLY.json`): κ = 0.001651929911890057 for gm3
+(conservative 0.001651929909011672) κ = 0.001652528731617094 for dz1 (conservative 0.001652528728737236), and
+κ = 0.001652760598550299 for L1g4 (conservative 0.001652760595670246).
+Bit589Reviewer recomputed both suppliers with the outer engine and confirmed this. The gain over gauge44-repack therefore depends on this change and on the
+assumptions below.
+
+## Negative controls (all must be rejected; the verifier requires exactly these 12)
+
+Each control runs the real `assemble()` on the fresh owner/invoice receipts with one input mutated. The strict run's
+`BIT-SUPPLIER-CONTROLS.json` lists all 12 as rejected.
+
+| control | site | rejected at |
+|---|---|---|
+| `revert_hardcoded_9984` | S2 | `check_moment` deficit guard (10272 ≠ 9984) |
+| `ports_112` | S2 | `bit_deficit`: live ≠ 2KvT |
+| `decoder_constant_64_copy_ranks_unchanged` | S2 | `bit_deficit`: cst ≠ Σ COPY ranks |
+| `decoder_constant_64_with_one_copy_rank_8` (derives exactly 9984) | S2 | `check_moment` deficit guard |
+| `eight_retained_totals` | S2 | `bit_deficit`: totals count ≠ 9 |
+| `live_minus_one` | S2 | `bit_deficit`: live ≠ 2KvT |
+| `profile_rank_mass_plus_one` | S2/S3 | `check_moment` deficit guard |
+| `profile_rank_mass_receipt_mismatch` | S3 | profile mass ≠ `rank_mass` |
+| `bit_lower_next_grid` | endpoint | `check_moment` reject-side moment test |
+| `not_nine_stage_record` | S4 | pipeline binding |
+| `tampered_bytes_next_grid` | S1 | blob pin |
+| `pr543_file_under_pr589_pin` | S1 | blob pin |
+
+Bit589Reviewer re-traced all 12 rejection sites on the gauge44 word (b589gm3), and they match the table: `code/assemble.py` L191 (`revert_hardcoded_9984`, `decoder_constant_64_with_one_copy_rank_8`, `profile_rank_mass_plus_one`), L48 (`ports_112`, `live_minus_one`), L47 (`decoder_constant_64_copy_ranks_unchanged`, `eight_retained_totals`), L201 (`profile_rank_mass_receipt_mismatch`), L197 (`bit_lower_next_grid`), L179 (`not_nine_stage_record`) and L39 (both blob controls). dz1 and L1g4 run the same code.
+
+The ported `independent/price_profile.py` re-derives the deficit separately (`pr589_deficit`) and checks the same blob pin. Its regenerated receipt on this package's PLAN gives the same κ.
+
+## Inherited assumptions
+
+**PR merge status (`gh pr view`, 2026-10-13):** #589 MERGED 2026-10-12T17:00:38Z. #555 was merged 2026-10-12. #645
+is OPEN. Main's review replayed #589 freshly as "supplier-only headroom", and main's *selected* composition still
+cites #543.
+
+**Unmerged assumptions:**
+1. **#645 itself (open):** the gauge44 factory, its construction steps and all of its retained interfaces and notes.
+   These are unchanged here.
+2. **This verifier change (S1–S6):** under review (Bit589Reviewer). The PR589 record replaces PR543 as an *input of
+   the gauge44 assembly*, a composition main has not selected.
+
+**Assumptions carried by #555/#589 (merged, stated there as review points, not theorems):**
+3. #545's punctured unit: a 111-port unit with decoder constant 63 is an admissible bit supplier on the same hypotheses
+   as v = 120.
+4. #510's nine-stage chain as re-parameterised for v ≤ 120 by #555's `code/adapt9p.py`, including the rank-mass
+   identity used in S2.
+5. #543's interleaved scalar-interface lemma (H1–H5) for phase-B source rewrites. This is not new: #645 already
+   inherits it through PR543.
+6. #589's two A-section transports.
+7. The same bit bad-residue surcharge model as PR543 (`surcharge_model = {'complex': False, 'bit': True}`).
+
+## Result
+
+The bit-supplier change is the same as in research/gauge44-bit589 and gauge44-bit589b: the code is byte-identical and was signed by Bit589Reviewer. For this package (k8 leaver word db2c7cfb, K8c8 map), the complex side certifies b = 0.001674185476674086429846 and binds under PR589. Under PR543 the bit side would cap κ at 0.001651096360425895. κ is given in the README and `RESULT.json`.
diff --git a/research/gauge44-slots-t16/PROOF-NOTE-FRAMES-X4.md b/research/gauge44-slots-t16/PROOF-NOTE-FRAMES-X4.md
new file mode 100644
index 0000000000..a456a8127b
--- /dev/null
+++ b/research/gauge44-slots-t16/PROOF-NOTE-FRAMES-X4.md
@@ -0,0 +1,58 @@
+# PROOF-NOTE-FRAMES-X4: chafreaky's #741 frames and JointXF's joint exchange (X4)
+
+Two construction steps on top of research/gauge44-promo-p6k4sw's SW4 word P6k4sw4 (`d232183f…`).
+
+## 1. #741's eight B frames (`construction/frames/`)
+The eight B-gate frame raises are by **chafreaky**, [#741](https://github.com/CrocSwap/integer-mult-bounds/pull/741)
+(`research/complex-sw4-frame8`, commit e516b146). `FRAME-RECIPE-sw4.json` is byte-identical to #741's
+`data/FRAME-RECIPE.json` (a2c7ca4d…). CompetitorMine ported #741's builder and controls; only package paths are adapted.
+The step applies the frames with BlockInvert's `build_promotion.apply` and checks:
+- the scalar program of A, cut, B, precondition and cleanup is unchanged;
+- start and end frames are unchanged;
+- the profile, the widths and the output word `e7804702…` are pinned;
+- 3 pin controls are rejected;
+- #741's 10 focused native controls are rejected (8 frames emptied, a changed read coefficient, paid-profile tampering);
+- the per-end layer-end controls reject 95;
+- the native chain matches its pins.
+
+The rebuilt locals equal G44Pack's F741 locals except the `seconds` field in CLIFFORD-REVIEW.
+This step reproduces #741's word. The final word is built by step 2, which contains these frames.
+
+## 2. Joint exchange X4 (`construction/jx/`, JointXF)
+There are four disjoint instances of BRoute's sw4 read-set exchange rule. Each one exchanges *two* copy pairs that
+share targets: (448, 472), (458, 592), (470, 604) and (482, 614), with face registers 235, 267, 58, 427, 26, 443, 18
+and 50. #741's eight frames sit on top. The 16 moved reads keep their original stored dim-6 frames: they are
+monotone-repaired rather than refitted to the plain join. The recipe `RECIPE-X4.json` is explicit:
+- 32 replaced gates, 16 deleted gates and 16 inserted gates, each with its old gate asserted;
+- #741's 8 frames, listed with their source;
+- 16 explicit frames at the moved reads, each asserted equal to the recomputed frame.
+
+The builder `build_jx.py` uses only the standard library. It checks:
+- target frames lie inside u_t^⊥;
+- tails and ends;
+- exactness of the whole B segment's rational linear map against the input (a Fraction replay);
+- the recomputed paid profile and the output sha `1e1d99ba…`.
+
+Effect against #741's word: the profile goes {1:2556, 2:334, 3:430, 4:194, 5:56, 8:8} → {1:2548, 2:338, 3:430,
+4:194, 5:56, 8:8}. The width inventory is unchanged, and each instance gives +1.0798e-7 at ideal, exactly additive.
+
+**Controls**, each pinned in the recipe and rerun by `reproduce_jx.py`:
+
+| control | outcome |
+|---|---|
+| C0 identity | returns the input `d232183f` |
+| C1 #741 only | `e7804702`, #741's word (ties step 1 to step 2) |
+| M1 one pair (448) with frames retained | `5fb6fb2e`, neutral (profile = #741) |
+| N1 pre-read dropped | rejected: exactness rows [132, 135] |
+| N2 pre-read with wrong sign | rejected: exactness rows [132, 135] |
+| N3 plain-join refit of the moved reads | `7241cd59`, strictly worse |
+| N4 a raise made dim-7 at B855 | rejected: cap at (1302, 174) |
+
+N3 and M1 are pinned-outcome controls (a specific different word), not rejections. They show the gain needs both the
+target-sharing pair and the retained frames.
+
+**Other checks (JointXF):**
+- `audit_local` PASS;
+- native chain PASS;
+- FrameCoal's global frame optimiser reaches the same profile on this move set, so X4 is frame-optimal for these moves;
+- SW4Extend found the same word independently.
diff --git a/research/gauge44-slots-t16/PROOF-NOTE-LAYERS.md b/research/gauge44-slots-t16/PROOF-NOTE-LAYERS.md
new file mode 100644
index 0000000000..c4b4e85b6a
--- /dev/null
+++ b/research/gauge44-slots-t16/PROOF-NOTE-LAYERS.md
@@ -0,0 +1,129 @@
+# PROOF-NOTE-LAYERS: earlier jp8 layers, here stacked on the no-triangle gauge44 word
+
+> In this package the layers sit on the no-triangle word (R = 504), not on #645's 492-helper word. The mapping, the
+> NP chain (regroup `864ff4a1` → swap `beb3579f` → layered `a9de804f`), the per-layer status on this base and the
+> checks are in `PROOF-NOTE-NOTRI.md` ("Layers on this word"). The text below is research/gauge44-layered's note. It
+> describes the same layers and controls on the 492-helper word; its word shas, helper numbers, counts and result
+> table refer to that word.
+
+
+This note covers the second change of research/gauge44-layered relative to research/gauge44-bit589. The first change,
+the PR589 bit supplier, is covered unchanged by `PROOF-NOTE-BIT.md`. Here the community jp8 layers that were reviewed
+on the k492 words (#629/#637/#641 lineage) are re-applied to #645's gauge44 provider word. The layers, their
+construction code and their recipes were all reviewed earlier, on k492 words. This note says what carries over
+unchanged, what is re-checked on the gauge44 word, and what is new. Sources: G44Stack's report (porting and checks on
+gauge44); PivotReviewer's report (sections 1-4, Addenda 3-5); H4aReviewer's report (Addenda 7-8); JP8Ends' report.
+
+## What the layered word is
+
+`construction/layers/reproduce_layers.py` builds the layered word from a fresh `construction/reproduce.py --until word`
+output. Each step is checked exactly:
+
+1. **Pivot swaps** (`build_pivot_swap.py`, PR641's constructor, LF sha256 `8e8bced8…`, the file PivotReviewer signed for
+   st2s4). It reads `PIVOT-SWAP-S6.json` and runs on #645's `regroup/FULL-WORD`. There are six pivot-role swaps: 488→560,
+   489→561, 500→572, 501→573 (s4) and 513→537, 525→549 (s6). The `swaps` list is identical, gate for gate, to S6Ship's
+   s6/s6j3 recipe (`k492-jp8-pivot_swap.json`); only `input_content_sha256` differs, because the base word is #645's
+   regroup word. The constructor replays the zero response exactly, keeps the profile and width multiset unchanged, and
+   rejects its 30 negative controls.
+2. **HPE.** PR635's `build_hpe.apply` applies the inherited jp8 hyperplane-end changes (`HYPERPLANE-END-S6.json`). Its
+   LF sha256 `23c9d7ce…` equals the k492 jp8 hyperplane_end recipe committed in s6j3 and earlier.
+3. **cold44, exactly.** #645's `build_gauge_cold44.py` runs on the swapped HPE word. Its 44 rank-four cold ends, premix
+   and low tails must equal the unswapped (pinned) cold44 construction; only the FULL inverse differs. Consequently the
+   swaps touch no factory block.
+4. **Layers.** PR635's unchanged `build_cold_end.apply(HPE, COLD-LAYERS-RECIPE)` applies the cold44 recipe plus:
+   - 8 entering ends: 560/561/572/573 at U24 (s4) and 597/599/537/549 at U30 (x30: #629's E1 pair, which #645 dropped,
+     plus s6's two ends);
+   - 10 factored dim-8 cold ends: p123 (310/506, 311/504, 516/327) and q4 (579, 592, 589, 518).
+   The output word's sha256 is pinned (`0be48b1d…`), as are its local profile `{1:2542, 2:414, 3:434, 4:154, 5:56,
+   8:8}` and width inventory `{4:52, 5:48, 7:42, 8:116, 9:234}`. The recipe's `refactored_cleanup` meta lists the 8
+   entering ends in `entering_low_frame_ended_helpers` (LayerReviewer's fix). That meta is copied into the word, which
+   is why the pinned word sha moved from `b25f0ed9…` to `0be48b1d…`; gates, frames and report are unchanged.
+5. **Layer-end controls** (`layer_end_controls.py`, LayerReviewer's adaptation of PR635's `cold_end_controls.py`
+   d966e29a). These are raw-word negative controls on the layered word, judged by PR635's unchanged
+   `hpe_audit_and_transport.py`. Each mutant must be rejected at its pinned reason. The adaptation has three parts: the
+   lower→FULL mutant is pinned at "cleanup on non-FULL end", where gauge44 rejects it; entering ends come from the
+   recipe meta; and the premix-gate controls are skipped for entering ends that have no premix gate. `reproduce_layers.py`
+   requires exactly 59 rejections.
+6. **Native locals.** PR635's native audit and transport, ledgers, local replay (the 192-bit payload bound), wrappers and
+   phases all pass. The result is the `--local` that `verify_global.py` consumes.
+
+G44Stack's run of this driver (`rlayers2`, all steps exit 0, 59 controls rejected) reproduces `locs/pq/local`, the
+local G44Pack's strict runs used. Every SPEC-pinned artifact is byte-identical: CANONICAL-WORD, LOCAL-PROGRAMS,
+LOCAL-CHECKS, INDEPENDENT-LOCAL-REPLAY, CLIFFORD-RECIPES, RESIDUAL-ADAPTERS and WRAPPER-CHECKS. CLIFFORD-REVIEW differs
+only in a seconds field; its semantic hash is what SPEC pins. The two unpinned files that embed the word,
+FULL-WORD and SCALAR-FRAME-AUDIT, differ because of the meta.
+
+## Per-layer status on gauge44 (G44Stack, ideal Δκ at ×72)
+
+| layer | prior review (k492 words) | on gauge44 | per-call Δ profile | ideal Δκ |
+|---|---|---|---|---|
+| pivot swaps (6) | PivotReviewer §1-2 (s4), Addenda 4-5 (s6): exact; omitting any rewritten gate is rejected; cost-neutral | all 6 recipe `before` gates match the regroup word; 30 controls rejected; cold44 rebuilds the same 44 ends | neutral | 0 |
+| s4 ends 560/561/572/573 @U24 | PivotReviewer §3: (N) exact for ([24], U24) and its canonical pair; climbs paid | positive | {1:+8, 2:−4, 3:+4, 4:−4}, w −4 | +7.0e-8 |
+| x30: E1 597/599 + 537/549 @U30 | #629 (E1); PivotReviewer Addenda 4-5 (537/549 end monotonically at the E1 hyperplane, whose (N) is exact) | positive | {1:+10, 2:−6, 3:+2, 4:−2}, w −4 | +2.0e-7 |
+| p123 | H4aReviewer Addendum 7: 0 bad rows, dyadic, exact in all 3 orientations; (N) for (0,1039)-(0,1041); Δ recomputed | positive | {1:+6, 2:+12, 3:−12}, w −6 | +2.0e-8 |
+| q4 (after p123) | H4aReviewer Addendum 8 (n_q4): exact; (N) for the 310/311/327 frames and 518's (0,1042); independent of u4 | positive | {1:+4, 2:+8, 3:−8}, w −4 | +1.4e-8 |
+| **stack T_pq** | — | built and audited | {1:+28, 2:+10, 3:−14, 4:−6}, w 3794→3776 | **+3.08e-7** |
+
+These layers were left out because they are negative or dead on gauge44: u4 (−1.2e-6), the 249 end (−3.2e-7), a joint
+p123+q4 (−2.6e-7, worse than sequential), and #627's dim-7 ends 581/590 (no dyadic basis). j3 is dead: its st2 partner
+403 is one of #645's 44 ends, and cold44's block premix uses up the row space.
+
+**Payload.** H4aReviewer's Addendum 8 correction found that the k492 word n_q4 broke the 192-bit local payload bound
+(backward prefix 280 bits). On gauge44 the layered word passes PR635's `hpe_audit_local.py` local-replay stage
+(`prefix < 2**192`), both in G44Stack's `localchain.py` and as step 5 of `reproduce_layers.py`. So the q4 layer here
+does not repeat that failure.
+
+## Verifier changes (spot widths)
+
+A swapped-out pivot p becomes an ordinary cold helper, and its width goes from 8 to 9. #645's global code checks the
+spot helpers' widths as all 8, so the five global files gain the spot-width rule PivotReviewer signed as SOUND for
+S4Ship (Addendum 3), ported to gauge44:
+
+- `code/witness.py`: `spot_widths(v)` gives 9 at a spot helper h with 2v+h among the swapped-out pivots and 8
+  elsewhere. The swapped-out pivots are read from the recipe that SPEC key `pivot_swap` names (path and sha256; the
+  sha256 is asserted). Without `pivot_swap` the tuple is all 8, the same as #645.
+- `code/bind_providers_portable.py`, `code/audit_allcold.py`, `code/assemble.py`: the `all(... == 8)` spot checks become
+  tuple equality with `spot_widths()`, which pins every spot width exactly.
+- `code/assembly_controls.py`: the `cold_swap` control picks a swap partner whose width differs, so the mutant can
+  never be the identity.
+
+Here the spot helpers 264 and 276 (pivots 488 and 500) expect width 9 and the other spot helpers expect 8. The k492
+spot-width review (PivotReviewer Addendum 3) covered the same rule on k492 code. Its gauge44 port is part of this
+package's review (LayerReviewer).
+
+## Controls and what is not re-run
+
+- The pivot-swap constructor's 30 controls run inside `reproduce_layers.py` (step 1).
+- `verify_global.py`'s strict controls are unchanged, including the 12 bit-supplier controls and #645's admission
+  controls. They run on the layered locals.
+- Layer-end controls: 59 raw-word mutants, all rejected at pinned reasons, run as step 5 of `reproduce_layers.py`
+  (see above). They cover the cold low-frame ends, the refactored cleanup, every entering end (its lower-frame gate,
+  profile pin and hyperplane, plus its premix gate where it has one) and each distinct dim-8 frame. LayerReviewer ran
+  them on the layered word (59 rejected). The k492 version (d966e29a) rejected 103-112 on the p123/q4 words; the
+  k492-only primitives (absorptions, factored accumulators, target writes) are absent from this word.
+- #645's independent audit `independent/audit_local.py` on the layered word: PASS, with 204 entering helpers, 96 low ends,
+  54 cold ends and 716 columns. Its receipt is `evidence/layers/LOCAL-AUDIT-LAYERED.json` (word `0be48b1d…`, run with
+  `--main`). The README's clean-clone command reruns it; only `elapsed_seconds` varies. The other `independent/`
+  receipts are #645's own.
+- The prior (N), exactness and pricing checks for each layer were done on k492 words. On gauge44 they are covered by
+  the native chain (native audit, local replay, wrappers, phases) on the layered word, together with the pinned
+  profile and width inventory.
+
+## Inherited assumptions
+
+These are the same as `PROOF-NOTE-BIT.md` (#645 open; PR589 citation; #545/#555/#589 review points; H1-H5). In
+addition:
+
+1. **(N) for the entering-end pairs outside #599's three Lean-covered pairs** (U24, U30, the dim-8 frames). As on
+   k492, these are covered by the tool check (clifford_exact / `nchk.py`) and by the native wrappers, not by a Lean
+   proof (PivotReviewer §3).
+2. **The reviews of PR641's pivot-swap constructor and PR635's `build_cold_end.apply` / `build_hpe.apply`**, which this
+   package uses unchanged.
+
+## Result
+
+| | gauge44-bit589b (L1g4 map) | this package (layered, LN5c map) |
+|---|---|---|
+| κ | 0.001652760598550299 | 0.00165395497190225 |
+| per-call width | 3794 | 3776 |
+| local profile | #645's {1:2514, 2:404, 3:448, 4:160, 5:56, 8:8} | {1:2542, 2:414, 3:434, 4:154, 5:56, 8:8} |
diff --git a/research/gauge44-slots-t16/PROOF-NOTE-LEAVER.md b/research/gauge44-slots-t16/PROOF-NOTE-LEAVER.md
new file mode 100644
index 0000000000..b34a289c48
--- /dev/null
+++ b/research/gauge44-slots-t16/PROOF-NOTE-LEAVER.md
@@ -0,0 +1,82 @@
+# PROOF-NOTE-LEAVER: no-helper mutable-leaver all-K cells, re-stacked layers, hybrids and a frame re-optimisation (k8)
+
+Construction: LeaverSAT (cells, layer re-indexing, frozen recipes) and LeaverSAT2 (frame re-optimisation).
+Drivers: `construction/leaver/reproduce_leaver.py` (cell word) and `construction/leaver/reproduce_leaver_chain.py`
+(everything after it). Reviews: PromoReviewer (leaver chain, k8 cells and frames, k8 clean rebuild), SW4Reviewer (hybrid structure), Q6Reviewer
+(`layer_end_controls_leaver.py` v2, `LEC-REASON-PINS-k8.json`), LecReviewer (`LEC-REASON-PINS-STACK-k8.json`).
+
+## 1. The cell (set model, LeaverSAT)
+In #781's all-K cell, a pair p with sign e replaces three face events and three packet copies. Direct delivery uses
+15 reads y_i += c x_j. LeaverSAT's 21-gate circuit uses the six leaver sources x_j (face-event operands with no later
+reads, restored at FULL by the inherited cleanup) as mutable intermediates. It has 3 leaver gates x_k += c x_m,
+3 target gates y_a += c y_b (inverted at frame zero in the precondition and scatter, #781's recipe) and 15 reads.
+Coefficients are rescaled exactly per cell, C_ij = r_i c_j. The driver re-derives the scaled gates from the unit
+circuit and checks the clean map Y_i = Σ_j C_ij X_j in exact rationals.
+
+Native legality needs one relabelling: the plain circuit fails the native audit, because a y += y source carries
+port-stage entering-helper dirt. Each cell is therefore relabelled by S6 so that y–y sources avoid targets carrying
+entering dirt at that time.
+
+**Set k8:** all eight cells (01±, 23±, 45±, 67±), R = 480. The cores are in `construction/leaver/cells-k8/` (documentary;
+the driver re-derives every scaled gate from `CODED-CELLS-k8.json`). The regroup word is `00aeefe0…` and the cell word is
+cold44 `58e14a02…`. Its pairing ranks are pinned to [0,0,0,4,4,4,4,4,4,4,4,0,0,0] in `cold44x.py` and checked again in
+the driver.
+
+## 2. Re-stacked layers (LeaverSAT; signed builders unchanged, recipes re-indexed)
+| step | recipe (data) | word |
+|---|---|---|
+| pivot swaps (6), mapped through the leaver helper map | `PIVOT-SWAP-k8.json` | `377ab10c…` |
+| HPE, greedy (22) | `HPE-RECIPE-k8.json` | `598543fa…` |
+| cold44, exact (same ends, premix and tails as the unswapped cell word) | — | — |
+| NP layers (s4, x30, b6, q4) | `COLD-LAYERS-RECIPE-NP-k8` | `2c1740f6…` |
+| p6n ends | `COLD-LAYERS-RECIPE-P6N-k8` | `25c40614…` |
+| promotions (16, minimal) | `PROMO-RECIPE-k8.json` | `84d4da2e…` |
+| joint exchange (re-indexed X4) | `RECIPE-X4-k8.json` | `84d4da2e…` (identity) |
+| U8-style hybrids ×6 (NewBArch's builder; instances 62, 226, 228, 230, 231, 232) | `RECIPE-U8-k8.json` | `c836d892…` |
+| frame re-optimisation (exact global frame optimum, gopt2; 137 B and 2 T frames) | `FRAME-RECIPE-LV-k8.json` | **`db2c7cfb…`** |
+
+Three steps don't apply to k8. The sw4 exchanges use copy helpers 461, 581, 591 and 603, which the cells drop. Of
+#741's eight frames, none survives. All four X4 exchange groups use dropped helpers, so the joint exchange is the
+identity (0 raises, 0 frames); it is still run, with its three remaining controls (C0, C1, N3) at their pins.
+
+The two cold-layer recipes are LeaverSAT's frozen k8 recipes (`fea82fb8…`, `76aedf23…` as .gz) with one key added,
+`input_content_sha256` = the swapped HPE word `598543fa…`, as in the k5 package. Removing the key gives the frozen
+recipe content exactly.
+
+## 3. Controls rerun on every rebuild
+- **Cell stage:** the exact clean-map check; native audit, ledgers, local replay, wrappers and phases on the cell word.
+- **Pivot swaps:** the swap constructor's 30 controls.
+- **Promotions:** BlockInvert's `promo_controls.py`, 11 mutants rejected at pinned sites.
+- **Joint exchange:** the 3 `RECIPE-X4-k8` controls reproduce their pinned outcomes.
+- **Hybrids:** `run_controls.py` gives 30 outcomes, all required. These are C0, the recipe word passing audit_local,
+  and 4 mutants, each run both globally and per instance.
+- **Frames:** `build_frames_lv.py`'s 3 pin controls. LeaverSAT2's 6 frame-recipe mutants are rejected by the builder;
+  that receipt was reviewed by PromoReviewer and is not rerun.
+- **Layer-end controls:** `layer_end_controls_leaver.py` v2 (`4ba676f1…`), Q6Reviewer-signed. It is the signed
+  per-end controls with per-word reason re-pins and **declared not-applicable sites**. A vacuous mutant site is never
+  skipped silently: the pins file must declare it, the declared set must equal the detected set, an identity is proven by
+  sha equality of the mutated and honest words, and a same-class substitute mutant is built and must be rejected at the
+  class's pinned reason. The count stays 95 on every word. The controls run on all five words:
+  - p6n, promoted, jx and hybrid words, with `LEC-REASON-PINS-STACK-k8.json`: `extra_end` only. h0 273's first
+    premixed partner 282 is already cold-ended at h0's frame, so the mutant is the identity (sha-proven per word); the
+    substitute is partner 281, cold-ended at h0's frame.
+  - the re-framed final word, with `LEC-REASON-PINS-k8.json`: `extra_end` as above, and `other_hp:554`. The frame
+    re-optimisation lowers entering end 554's tail frame to dimension 5, and no helper_final frame has dimension 5, so
+    the 'end at another hyperplane' mutant cannot be built; the substitute moves 554's end to another dim-8 frame and
+    must be rejected at the cone pre-check. This replaces the interim skip of research/gauge44-leaver.
+  No reason re-pins are needed on the k8 words. The receipts (`COLD-END-CONTROLS.json`) carry the not-applicable list;
+  the counts, the not-applicable sites with their reasons and the sha256 of each pins file (`LEC-REASON-PINS-STACK-k8.json`
+  d87ed7b5…, signed by LecReviewer; `LEC-REASON-PINS-k8.json` b07279e4…, signed by Q6Reviewer) are pinned in
+  `CHAIN-PINS-k8.json`.
+- **Native chain on the final word:** the canonical word, local programs and Clifford recipes are pinned in
+  `CHAIN-PINS-k8.json`, which also pins every count above.
+
+## 4. Cell mutants (evidence, not rerun)
+LeaverSAT2's `CELL-MUTANTS-LV.json` (in `evidence/leaver/`) records PromoReviewer's cell mutants M1–M6, generalised
+to every cell sign. All 42 are rejected by both audit_local and the native audit, on single-cell builds.
+
+## 5. Strict
+The owner map is G44Pack3's K8c8: its pattern-flow LNS on the R = 480 k8 word. Admitted on this package's own code,
+with SPEC `width_spot_helpers` [258,270,282,294] and `pivot_swap` → `construction/leaver/PIVOT-SWAP-k8.json` (NEWWORD
+discovery, freeze, strict), it gives κ 0.001671387264390146. That is +7.154e-6 over research/gauge44-leaver (k5,
+0.001664233607446043).
diff --git a/research/gauge44-slots-t16/PROOF-NOTE-NOTRI.md b/research/gauge44-slots-t16/PROOF-NOTE-NOTRI.md
new file mode 100644
index 0000000000..54bd84e01d
--- /dev/null
+++ b/research/gauge44-slots-t16/PROOF-NOTE-NOTRI.md
@@ -0,0 +1,53 @@
+# PROOF-NOTE-NOTRI: #645's gauge44 word without K-triangles (R = 504)
+
+Construction by PartialK; review by NotriReviewer (scratch/NotriReviewer/FINAL-REPORT.md). Drivers:
+`construction/notri/reproduce_notri.py` (this word) and `construction/layers_np/reproduce_np.py` (layers on it).
+
+## Why the triangles were the blocker
+- In #645's gauge44, a K-block has I = 6 low registers with rank C = 4, so L = 2. Only the 2-row priority completion
+  fits there. The (p,−) triangle reads climb copies loc17/19/21 and source loc2.
+- Without the triangles, I = 8. With the 2-row completion, rank C stays 6 (L = 2), which is why the plain removal sweep
+  restored nothing. With the 6-row completion (`PRIO6.json`, the list blocks 3–10 already use), rank C = 4, so L = 4,
+  the cap. All 14 blocks then pair at rank 4: 56 rank-four cold ends, R = 504, width 3818, profile
+  {1:2506, 2:336, 3:472, 4:184, 5:56, 8:8}, rank mass 5674.
+
+## Constructor changes (NotriReviewer §1)
+- **`cgx.py`** is #645's `construct_gauge_xcentre.py`, parameterised by XPARAM. On this path the only change that takes
+  effect is the K-block priority: `PRIO[c]` is placed in front of the inherited rows. The prepended rows equal the
+  shared 6-row list of blocks 3–10 (all 8 lists identical). Every completion assert is kept (`qr_rank(M)==4`,
+  `len(M)==8`, the exact block-total rows). An empty TRI schedule is an input #645 already supports (`NH = 504 − 3·0`).
+  `HELPER-MAP` is the identity on 728. The `exch`, `COPYL` and `hyb` branches are inert here (defaults, empty, not
+  reached).
+- **`port_stage_x.py`** is PR635's `build_port_stage.py`. The helper map only has to be injective rather than onto;
+  with no triangles it is onto again.
+- **`cold44x.py`** is #645's `build_gauge_cold44.py`. Its per-block pin `r == len(L) == (2 if K-block else 4)` is
+  replaced by `r == len(L)` together with the explicit per-block pin `PAIRING_RANKS` (set by the driver to [4]*14,
+  and to #645's pattern in `--control-g44`). Helpers outside the 224+16b ranges join their blocks (EXTRAH, empty here).
+  Every other assert is kept (U, nonlocal premix, `rank(Qmat) == NB`).
+- **Control.** `reproduce_notri.py --control-g44` runs the same scripts with #645's four triangles and no XPARAM. It
+  reproduces #645's gauge44 word `78c7aada…` exactly, with ranks [2,2,2,4,4,4,4,4,4,4,4,2,2,2].
+
+## Exactness and locals (NotriReviewer §2)
+- Replay: 0 bad rows over 27,932 gates, all dyadic; forward, inverse and adjoint are exact. None of the 6,448
+  compensation additions reads an ended helper, and the precondition never touches one.
+- 0 FULL-remainder gates touch an ended helper; E⊂U holds for every entering end. The delta against gauge44
+  ({1:−8, 2:−68, 3:+24, 4:+24}, width +24) matches the reported profiles.
+- (N): all 17 pairs pass (14 cold dim-4 pairs with 4 helpers each, plus 3 dim-8 entering pairs).
+- `audit_local.py --main`: PASS. Payload: prefix bits 66 forward and 72 backward, against 192.
+- Native locals: 25 controls rejected, Lemma A on 22 frames, 17 wrapper mutants rejected. The rebuilt locals equal
+  the strict locals (`PartialK/runs/none_p6/local`): byte-identical except CLIFFORD-REVIEW and SCALAR-FRAME-AUDIT,
+  which differ only in their `seconds` field.
+
+## Layers on this word (G44Stack)
+The layers are research/gauge44-layered's (see `PROOF-NOTE-LAYERS.md`), mapped to the 504 numbering:
+- the 6 pivot swaps 494→566, 495→567, 506→578, 507→579, 519→543, 531→555, which are neutral (same 46 HPE helpers,
+  same 56 cold ends);
+- s4 566/567/578/579 at U24;
+- x30 608/610/543/555 at U30;
+- BlockCombine's b6;
+- q4.
+
+p123 is negative on this base and dropped; j3 is dead (L = 0 at U24 and U30). The chain is regroup `864ff4a1` → swap
+`beb3579f` → layered `a9de804f`, with profile {1:2534, 2:346, 3:458, 4:178, 5:56, 8:8} and width 3800. On that word
+the signed `layer_end_controls.py` rejects 59/59 and `audit_local.py` passes with 216 entering helpers, 120 low ends,
+66 cold ends and 728 columns. NotriReviewer independently reproduced a9de804f from the packaged recipes.
diff --git a/research/gauge44-slots-t16/PROOF-NOTE-P6N.md b/research/gauge44-slots-t16/PROOF-NOTE-P6N.md
new file mode 100644
index 0000000000..bef9ad2de0
--- /dev/null
+++ b/research/gauge44-slots-t16/PROOF-NOTE-P6N.md
@@ -0,0 +1,34 @@
+# PROOF-NOTE-P6N: six b-type dim-8 cold ends on the layered no-triangle word (p6n)
+
+Construction by NoTriReopen. Driver: `construction/layers_p6n/reproduce_p6n.py`. Review: Q6Reviewer.
+
+## What p6n adds
+On research/gauge44-notri-layered's word NP (`a9de804f…`), p123's lane is rebuilt as three factored dim-8 pairs
+(`P6N-SPEC.json`):
+- [512, 513] at U = (256,128,66,34,16,8,6,1). The old pair [310,512] split a rank-3 end; [512,513] replaces it;
+- [311, 510] at U = (256,128,72,40,24,4,2,1);
+- [522, 327] at U = (256,128,66,34,18,10,6,1).
+
+They are built with the same premix-only factored construction as p123/q4/b6 (JP8Ends' stackJ/stackE, CarrierBypass
+pattern; PR635's unchanged `build_cold_end.apply`). The cold-layer recipe `COLD-LAYERS-RECIPE-P6N.json.gz` is NP's
+recipe plus these six ends; its meta lists 72 cold ends and the 8 entering ends. Applied to NP's swapped HPE word, it
+gives p6n `34b683fa…`:
+- profile {1:2540, 2:358, 3:446, 4:178, 5:56, 8:8};
+- widths {4:64, 5:48, 7:54, 8:122, 9:216};
+- width 3794 (NP 3800);
+- Δ per call {1:+6, 2:+12, 3:−12}, w −6, every end b-type.
+
+## Checks
+- **NoTriReopen:** native chain including phases PASS; audit_local PASS; 95/95 layer-end controls rejected.
+- **Q6Reviewer:**
+  - exact;
+  - (N) passes on all 21 pairs;
+  - payload 55/72 bits, against 192;
+  - the per-end control variant `layer_end_controls.py` (fc58c569…, which Q6Reviewer signed for research/gauge44-pq6) rejects 95/95;
+  - 165 further mutants on the six ends are all rejected.
+  The LayerReviewer-signed `../layers/layer_end_controls.py` controls one end per dim-8 frame family, so it would not
+  control each new end. This package therefore uses the per-end variant for p6n and for the promoted word built on it.
+- **Rebuild:** `reproduce_p6n.py` pins the input NP word, the output sha, profile and widths, and 95 controls.
+
+## Remaining capacity (NoTriReopen)
+After p6n, the only residual cold capacity on the word is 2 a-type units, and every end there prices about −9e-7.
diff --git a/research/gauge44-slots-t16/PROOF-NOTE-PROMO.md b/research/gauge44-slots-t16/PROOF-NOTE-PROMO.md
new file mode 100644
index 0000000000..8233bbd6b8
--- /dev/null
+++ b/research/gauge44-slots-t16/PROOF-NOTE-PROMO.md
@@ -0,0 +1,46 @@
+# PROOF-NOTE-PROMO: entrance promotions E4 → E5 on the p6n word
+
+Construction by BlockInvert (`construction/promo/`); driver `construction/promo/reproduce_promo.py`.
+
+## What a promotion is
+An entering helper h starts at an entrance frame E (its `start_extra`) and climbs to its final frame. Promotion
+enlarges E to E′ ⊃ E (here dim 4 → dim 5). That removes one paid climb from h's chain (width −1 per helper) at the
+cost of re-choosing the frames of the gates on h's early chain. It is the time-reverse dual of end deepening. Two
+conditions make it legal:
+1. **Zero target response for h's dirt.** This condition does not depend on E, so it is inherited unchanged from the
+   input word.
+2. **Monotone frames.** Every gate's frame must contain its registers' current frames.
+Only frame annotations and start frames change. The scalar program (every gate's registers and coefficients) is
+untouched, so the endpoint, every cone and the compensation are those of the input word.
+
+## The recipe (`PROMO-RECIPE-p6n-k4.json`, data only, minimal)
+- Input: the p6n word `34b683fa…` (`PROOF-NOTE-P6N.md`), pinned.
+- `entrances`: the 16 entering helpers 627, 629–631, 635, 637–639, 651, 653–655, 659 and 661–663 (four E4 kernel groups) go E4 → E5.
+- `gate_frames`: 48 frame re-choices, the promotion's own entry-gate raises (12 per group); each records the old frame,
+  which must equal the input's exactly. This is BlockInvert's **minimal** recipe: the deterministic rule
+  E′ = E + ⟨smallest x⟩ on each group's entry gates (PromoReviewer). Unlike research/gauge44-promo's k3 recipe, it
+  carries none of the 72 price-neutral CP-SAT re-choices.
+- `expected`: output `0390ec65…`, profile {1:2572, 2:326, 3:430, 4:194, 5:56, 8:8}, widths
+  {4:80, 5:32, 7:54, 8:122, 9:216} (width 3778). Against p6n the delta is {1:+32, 2:−32, 3:−16, 4:+16}, width −16.
+
+## Checks rerun on every rebuild (`reproduce_promo.py`)
+- `build_promotion.py`: input pin; each old frame matches; each new entrance strictly contains the old one; the
+  profile and widths are recomputed from the chains, including target end climbs; output pins.
+- `promo_controls.py`: the honest word passes #645's independent `audit_local.py` (exact forward and dual endpoint
+  frames, entrances, cones). For p6n-k4, 11 mutants are rejected at pinned sites (the count is pinned in `LOCAL-PINS-p6n-k4.json`):
+  - entrance outside the first gate frame;
+  - raised gate missing, once per promoted group;
+  - entrance reverted, so the profile does not match;
+  - ungrouped promotion;
+  - a recipe gate whose old frame is wrong;
+  - a recipe entry that is not a promotion;
+  - a tampered input word (the constructor's own `__main__` must refuse it at the input pin);
+  - a scalar tamper on a raised gate.
+- The per-end layer-end controls (`../layers_p6n/layer_end_controls.py`, Q6Reviewer-signed): 95 rejected.
+- PR635's native chain: transport audit (all columns, native frames), ledgers, local replay (192-bit payload),
+  wrappers and phases, with the canonical word, local programs and Clifford recipes pinned (`LOCAL-PINS-p6n-k4.json`).
+
+## Search (not run by the rebuild)
+`make_recipe.py` writes the recipe from BlockInvert's CP-SAT solution (`prom.py` with `exactframe2.py`, using MinCutSel's
+chain model). These promotions were priced negative before (MinCutSel #3, under a fixed-window arc-flow packer). Under
+near-ideal packing (G44Pack's dissolve/gapmerge) they price positive; the strict replay confirms the gain.
diff --git a/research/gauge44-slots-t16/PROOF-NOTE-SW4.md b/research/gauge44-slots-t16/PROOF-NOTE-SW4.md
new file mode 100644
index 0000000000..a064cc54cc
--- /dev/null
+++ b/research/gauge44-slots-t16/PROOF-NOTE-SW4.md
@@ -0,0 +1,44 @@
+# PROOF-NOTE-SW4: read-set exchange on four entering-copy pairs
+
+Construction by BRoute (`construction/sw4/`, with the author's notes in `construction/sw4/NOTES.md`). Driver:
+`construction/sw4/reproduce_sw4.py`.
+
+## The move
+In P6k4 (`0390ec65…`; research/gauge44-promo-p6sw applied the same exchange to P6k3 `a38bb414…`), each of four entering packet copies h is written first as h = E_h + r: copy gate add(h, r, 1)
+from a non-target face register r, with E_h being h's entering content. The pairs are (h, r) =
+(461, 25), (581, 89), (591, 415), (603, 431). For each pair the read sets of h and r are exchanged in phase B:
+- every post-copy target read add(t, h, c) becomes add(t, r, c), and t's entrance pre-read add(t, h, −c) (taken
+  while h = E_h) is deleted;
+- every target read add(t, r, c) becomes add(t, h, c), with a pre-read add(t, h, −c) inserted after h's last existing
+  pre-read and before h's copy gate.
+
+Since h − r = E_h after the copy, each target's value is unchanged at the end of B. The builder checks this for every
+register mod p (p = 2147483629). Moved and inserted gates take the plain join of their operands' current frames.
+Every other B gate and every early-cleanup tail keeps span(old frame + current operand frames). Targets must stay
+inside u_t^⊥, and tails and ends must contain the current frame. start_extra, helper_final, cleanup and the helper
+numbering are unchanged.
+
+## Effect
+Output `d232183f…`. Width 3778 is unchanged. The profile goes from {1:2572, 2:326, 3:430, 4:194, 5:56, 8:8} to
+{1:2548, 2:342, 3:438, 4:186, 5:56, 8:8}, a delta of {1:−24, 2:+16, 3:+8, 4:−8}, the same as on P6k3. The four
+exchanges are additive. The fourth promotion group (659, 661–663; gates B420–431) commutes exactly with the exchange:
+there is no index or register overlap, and SW4Reviewer checked that applying the k3→k4 frame and start differences
+to f35a852b gives d232183f. Ideal κ +3.271e-7 over P6k4.
+
+## Checks rerun on every rebuild
+- `build_sw4.py` (standard library only): the input sha pin; the 16 explicit moves of `SW4-RECIPE-P6k4.json`; B-end
+  state exactness mod p; frame caps, tails and ends; the output sha, profile and W. It also runs 4 controls, all of
+  which must hold, each at the exact site pinned in the recipe's `rejection_expected` (all three keys N1, N2 and N3 are required):
+  - C0: the identity recipe reproduces the input B and early_cleanup byte for byte;
+  - N1: h2r without deleting the pre-read is rejected by exactness, with changed B-end rows exactly {168, 171};
+  - N2: a partial exchange (one read only) is rejected by the frame cap, first at ('cap', B1192, register 169), 10 violations;
+  - N3: an inserted pre-read with the wrong sign is rejected by exactness, with changed rows exactly {129, 130, 169, 170}.
+- The per-end layer-end controls (`../layers_p6n/layer_end_controls.py`, Q6Reviewer-signed): 95 rejected.
+- PR635's native chain, with the canonical word, local programs and Clifford recipes pinned (`LOCAL-PINS-sw4-P6k4.json`).
+  The native transport audit re-checks every column and native frame of the exchanged word.
+
+## Scope of the search (BRoute)
+The search was exhaustive within the single-pair family only. NP has 107 copy pairs, and 54 of them have movable
+reads. Over those, every nonempty subset of one pair's movable reads gives 602 candidates: 564 are frame-illegal, and
+the 38 legal ones are all full single-pair exchanges, of which exactly these 4 are positive. Cross-pair combinations
+of partial moves were not enumerated.
diff --git a/research/gauge44-slots-t16/README.md b/research/gauge44-slots-t16/README.md
new file mode 100644
index 0000000000..a584e0a8ad
--- /dev/null
+++ b/research/gauge44-slots-t16/README.md
@@ -0,0 +1,305 @@
+# Sixteen replicas on the seven-slot k8 word (#1018): conditional κ = 0.001672654541898561
+
+This package runs the two-bank T16 whole-owner controller on [research/gauge44-slots](../gauge44-slots) (#1018).
+The local word (`c2b29430…`), its 480 helper widths and the PR589 bit supplier are unchanged. The only new
+object is a 16-replica owner map.
+
+- **κ = 0.001672654541898561** (conservative 0.001672654539046638). That is +9.89×10⁻⁷ over #1018's T8
+  κ 0.00167166528321877. The complex side binds.
+- **Change:** T16 on #1018. `data/OWNERS.json.gz` (`d7e11f5f…`, 69,120 whole-helper roles, 144 calls) is an exact
+  pattern-flow LNS repack (integer pattern counts + König edge colouring) on the actual T16 window geometry. It is
+  frozen data. The verifier runs no constructor and no optimizer: `t16/lift16.py` checks every role inside its
+  owner's actual bridge-aware window, the controller audit re-derives the profile, and `t16/indep16.py` independently
+  rechecks windows, whole widths, charts, prefix and row. Idle profile `{1:2280, 3:378, 7:6, 48:4866}`.
+  Prefix 397 < 512; physical row coefficient 16469 < 20161.
+- **Code:** `code/` is byte-identical to the signed research/gauge44-barch-t16 code (the #870 T16 adaptation of
+  #858's source edits). `t16/` holds #858's `build_parent.py` and the generic-R `lift16.py`/`indep16.py` (R taken from the
+  word; the parent namespace stays at 504). The T8 package's `data/` moves to `data/T8/` and `data/SPEC-T8.json`;
+  the `bind8` stage replays #1018's T8 admission.
+- **Controls:** 69 admission, 12 bit-supplier, 15 controller mutations and 6 independent T16 controls.
+- **Credit:** the T16 two-bank controller, parent lift, actual-window reconstruction and independent checker are
+  Hao Yan's (@FanPUYen) [#858](https://github.com/CrocSwap/integer-mult-bounds/pull/858). The T16 code adaptation is
+  from #870. The word and T8 package are #1018's (rohanarun's #987 slots on the #1005 leaver word).
+
+## Verification
+
+```sh
+# 1. #1018's own replay (research/gauge44-slots README): it writes the new word's locals to /tmp/slots/local
+python -B research/gauge44-slots/construction/slots/verify_slots.py \
+  --main . --pr635 /tmp/gauge44-pr635 --baseline /tmp/lvc --work /tmp/slots
+# 2. this package (about 2 minutes)
+python -B research/gauge44-slots-t16/verify_manifest.py
+python -B research/gauge44-slots-t16/verify_t16.py --main . --local /tmp/slots/local --work /tmp/slots-t16
+# PASS_GAUGE44_T16_STRICT_GLOBAL_REPLAY 0.001672654541898561
+```
+
+Step 1 must use research/gauge44-slots itself: this package's inherited `verify_global.py` is removed, and the T8
+admission runs inside `verify_t16.py` as `bind8`. Everything below is #1018's README, unchanged.
+
+---
+
+# Seven triangle-hybrid slots on the k8 leaver word: conditional κ = 0.00167166528321877
+
+This package adds one construction layer to [research/gauge44-leaver8](../gauge44-leaver8) (#1005): seven
+additional triangle-hybrid B-delivery slots on #1005's final word `db2c7cfb…`. **Credit:** the slot search and
+the first two slots (X = 444, 446) are **rohanarun's #987**; the other five (X = 236, 238, 434, 436, 439) were found by
+running #987's search on the k8 word. The mechanism is NewBArch's #869 triangle-hybrid delivery.
+
+- **κ = 0.00167166528321877**. That is +2.78×10⁻⁷ over #1005 (0.001671387264390146). The complex side binds; the bit
+  supplier is PR589's, unchanged.
+- **Construction:** #1005's reviewed `construction/barch/build_tri.py` and `run_controls.py`, both **unchanged**,
+  with the new recipe `construction/slots/RECIPE-SLOTS-k8.json`. The output word is `c2b29430…`, profile
+  `{1:2412, 2:418, 3:432, 4:142, 5:82, 8:8}`, and widths are unchanged.
+- **Controls:** 34. These are C0 identity, the recipe, and the four mutants (`drop_restore`, `restore_full`, `drop_preread`,
+  `donation_after`) applied globally and to each of the seven slots. Every mutant is rejected and pinned in
+  `construction/slots/SLOT-PINS-k8.json`.
+- **Frames:** the exact global frame optimiser (gopt2) finds no gain on the slot word, so there is no frame step.
+- **Owners:** #1005's K8c8 owner map is rebound to the new word (widths and idle counts are unchanged). The admitted
+  data in `data/` passes the strict replay.
+
+## Verification (explicit reuse of a completed #1005 replay, as research/complex-t37-owners does for #799)
+
+```sh
+# Completed #1005 chain (the README commands of research/gauge44-leaver8), or any completed run of it:
+python -B research/gauge44-leaver8/construction/leaver/reproduce_leaver_chain.py \
+  --main . --pr635 /tmp/gauge44-pr635 --leaver-dir /tmp/lv --hamming /tmp/notri-base/hamming --id k8 --out /tmp/lvc
+# This package (about 3 minutes):
+python -B research/gauge44-slots/verify_manifest.py
+python -B research/gauge44-slots/construction/slots/verify_slots.py \
+  --main . --pr635 /tmp/gauge44-pr635 --baseline /tmp/lvc --work /tmp/slots
+# PASS_SLOTS_ON_CHECKED_K8_BASELINE 0.00167166528321877
+```
+
+`verify_slots.py` rechecks the baseline: its complete step receipt (every chain step exited 0), the final word against
+#1005's frame-recipe pin, its canonical, program and Clifford locals against `CHAIN-PINS-k8`, and all five
+layer-end control counts. It then rebuilds only the slot layer and its controls, the native locals of the new word, the
+independent `audit_local`, and the strict global replay of this package's data. Everything below is #1005's README,
+unchanged; this package differs from it only in `construction/slots/`, `data/`, this section, `RESULT.json` and `MANIFEST.json`.
+
+---
+
+# Gauge44 without K-triangles, with earlier jp8 layers, the p6n ends, entrance promotions, a read-set exchange, #741's frames, a joint exchange, a triangle-hybrid B rewrite, no-helper mutable-leaver cells and PR589's bit supplier: conditional κ = 0.001671387264390146
+
+Under the retained all-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1–H5 interfaces (as in #645), and the PR589 bit supplier,
+
+$$
+T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad
+\kappa=\frac{1671387264390146}{10^{18}}=0.001671387264390146.
+$$
+
+**The construction is icekylinx's [#645](https://github.com/CrocSwap/integer-mult-bounds/pull/645) (`research/gauge44-global`).** This package builds the research/gauge44-barch construction (items 1–8) and then rebuilds its word around **no-helper mutable-leaver cells** (item 9):
+1. **No-triangle word (PartialK).** #645's gauge44 chain is run with **none** of the four (p,−1) K-triangles, so there are R = 504 helpers. In the six K-blocks {0,1,2,11,12,13}, the completion priority is extended by the 6-row list `construction/notri/PRIO6.json`. Every block then pairs at rank 4, giving **56** rank-four cold ends instead of 44. `construction/notri/reproduce_notri.py` rebuilds this word from a #645 `reproduce.py --until word` output. It uses PartialK's generalisations of #645's and PR635's constructors (`cgx.py`, `port_stage_x.py`, `cold44x.py`; each differs from its original only in the documented parameters). It pins:
+   - the pairing ranks [4]*14, inside `cold44x.py` and again in the driver;
+   - the word (`3e99ba77…`);
+   - the canonical word, the local programs and the Clifford recipes.
+   `--control-g44` instead rebuilds #645's own gauge44 word (`78c7aada…`) with the same scripts.
+2. **Layers on the no-triangle word (G44Stack).** `construction/layers_np/reproduce_np.py` applies to the no-triangle regroup word (`864ff4a1…`):
+   - research/gauge44-layered's six pivot swaps, mapped to the 504-helper numbering (`PIVOT-SWAP-NP.json`, swap word `beb3579f…`);
+   - the greedy HPE (46, `HPE-RECIPE-NP.json`);
+   - the exact cold44 (same 56 ends);
+   - the entering ends s4 (566/567/578/579 at U24) and x30 (608/610/543/555 at U30), plus BlockCombine's b6 and q4 dim-8 cold ends (`COLD-LAYERS-RECIPE-NP.json.gz`). p123 is negative on this base and dropped; j3 is dead.
+   The layered word is pinned (`a9de804f…`): profile `{1:2534, 2:346, 3:458, 4:178, 5:56, 8:8}`, width 3800. The signed research/gauge44-layered files `construction/layers/build_pivot_swap.py` and `construction/layers/layer_end_controls.py` are used unchanged, and the latter must reject exactly 59 controls. The global code is research/gauge44-layered's (spot-width rule): SPEC `width_spot_helpers` [270,282,294,306] and `pivot_swap` → `construction/layers_np/PIVOT-SWAP-NP.json`, giving spot widths [9,9,8,8].
+3. **p6n ends (NoTriReopen).** `construction/layers_p6n/reproduce_p6n.py` applies `COLD-LAYERS-RECIPE-P6N.json.gz` to the NP swapped HPE word with PR635's unchanged `build_cold_end.apply`. That is NP's cold-layer recipe plus six b-type dim-8 cold ends: [512,513], [311,510] and [522,327], which rebuild p123's lane as clean pairs. The result is the p6n word (`34b683fa…`): profile `{1:2540, 2:358, 3:446, 4:178, 5:56, 8:8}`, width 3794. The per-end layer-end controls (`construction/layers_p6n/layer_end_controls.py`, the variant Q6Reviewer signed for research/gauge44-pq6) must reject exactly 95 mutants. See `PROOF-NOTE-P6N.md`.
+4. **Entrance promotions (BlockInvert).** `construction/promo/reproduce_promo.py --base p6n --k p6n-k4` applies the minimal recipe `PROMO-RECIPE-p6n-k4.json` to the p6n word with BlockInvert's deterministic constructor `build_promotion.py`. The recipe promotes the 16 entering helpers 627, 629–631, 635, 637–639, 651, 653–655, 659 and 661–663 (four E4 kernel groups) from E4 to E5, the time-reverse dual of end deepening. It re-chooses the frames of the gates affected. Only frame annotations and start frames move; the scalar program is unchanged. The promoted word is pinned (`0390ec65…`): profile `{1:2572, 2:326, 3:430, 4:194, 5:56, 8:8}`, widths `{4:80, 5:32, 7:54, 8:122, 9:216}`, width 3778. BlockInvert's `promo_controls.py` runs #645's independent `audit_local.py` on the honest word and must reject 11 recipe- and word-level mutants at pinned sites. The per-end layer-end controls (95) and the native chain then run with pins. The recipe is minimal: 48 entry-gate frame raises and no other frame re-choices. See `PROOF-NOTE-PROMO.md`.
+5. **Read-set exchange (BRoute).** `construction/sw4/reproduce_sw4.py` runs BRoute's standard-library builder `build_sw4.py` with `SW4-RECIPE-P6k4.json`, 16 explicit moves, on the promoted word (`0390ec65…`). For the entering-copy pairs (h, r) = (461,25), (581,89), (591,415) and (603,431), the phase-B target read sets of h and its face register r are exchanged. The entrance pre-reads are deleted or inserted so that every register's value at the end of B is unchanged; the builder checks this mod p. Frames are repaired monotonically, and the width is unchanged. The SW4 word is pinned (`d232183f…`): profile `{1:2548, 2:342, 3:438, 4:186, 5:56, 8:8}`, width 3778. Four controls (C0 identity, N1 kept pre-read, N2 partial exchange, N3 wrong sign) must all hold, each at its exact rejection site pinned in the recipe. The per-end layer-end controls (95) and the native chain then run with pins. See `PROOF-NOTE-SW4.md` and `construction/sw4/NOTES.md`.
+6. **#741's eight B frames (chafreaky).** `construction/frames/reproduce_frames.py` applies chafreaky's [#741](https://github.com/CrocSwap/integer-mult-bounds/pull/741) frame recipe, `FRAME-RECIPE-sw4.json`, byte-identical to #741's. Ported by CompetitorMine, it raises eight B-gate frames with the scalar program unchanged, giving #741's word `e7804702…`. It runs 3 pin controls, #741's 10 focused native controls, 95 layer-end controls and the native chain with pins.
+7. **Joint exchange X4 (JointXF).** `construction/jx/reproduce_jx.py` runs JointXF's standard-library builder `build_jx.py` with `RECIPE-X4.json` on #741's word (step 6's output). It makes four disjoint instances of the read-set exchange, each over two target-sharing copy pairs: (448,472), (458,592), (470,604) and (482,614). The moved reads keep their stored frames, and #741's frames are included. All edits are explicit, and B-segment exactness is checked by Fraction replay. The final word is pinned (`1e1d99ba…`): profile `{1:2548, 2:338, 3:430, 4:194, 5:56, 8:8}`, width 3778. All seven pinned controls are rerun; C1 reproduces #741's word. See `PROOF-NOTE-FRAMES-X4.md`.
+8. **Triangle-hybrid B rewrite (NewBArch).** `construction/barch/reproduce_barch.py` runs NewBArch's standard-library builder `build_tri.py` with `RECIPE-U8.json` on the X4 word (step 7's output). Eight disjoint slots receive a width-neutral B-delivery rewrite: an entering copy donates into a halves-copy so that one target read gets X+H, with holder restores and entrance pre-reads. The U8 word is pinned (`090fd574…`): profile `{1:2548, 2:338, 3:446, 4:162, 5:72, 8:8}`, width 3778. All 38 pinned controls are rerun (identity, the recipe word passing audit_local, and four audit_local-rejected mutants, globally and per slot). See `PROOF-NOTE-BARCH.md`.
+9. **Leaver cells, re-stacked (LeaverSAT, LeaverSAT2).** `construction/leaver/reproduce_leaver.py --id k8` replaces the no-triangle word's construction with all eight all-K cells (01±, 23±, 45±, 67±). Each cell is LeaverSAT's 21-gate circuit, which uses the face-event leaver sources as mutable intermediates (R = 480, cell word `58e14a02…`). `construction/leaver/reproduce_leaver_chain.py --id k8` then re-applies items 2–8 with the signed builders unchanged and LeaverSAT's re-indexed recipes: swap, HPE, cold44, NP, p6n, 16 promotions, the re-indexed X4 exchange (the identity on this word) and 6 U8-style hybrids (`c836d892…`). It adds LeaverSAT2's exact global frame re-optimisation (`FRAME-RECIPE-LV-k8.json`), which gives the final word **`db2c7cfb…`**. Every intermediate word, control count and native pin is pinned (`LEAVER-PINS-k8.json`, `CHAIN-PINS-k8.json`). The per-word layer-end controls are the Q6Reviewer-signed `layer_end_controls_leaver.py` v2 (95 each), on the p6n, promoted, jx and hybrid words (`LEC-REASON-PINS-STACK-k8.json`) and on the re-framed final word (`LEC-REASON-PINS-k8.json`); its declared not-applicable sites are sha-proven identities or unbuildable mutants, each replaced by a same-class substitute that must be rejected. Items 5 and 6 don't apply on this word: the sw4 copies are dropped, and none of #741's frames survive. Items 1–8 remain in the package as the construction record of research/gauge44-barch. See `PROOF-NOTE-LEAVER.md`.
+10. **Owner map (chafreaky's [#685](https://github.com/CrocSwap/integer-mult-bounds/pull/685), adapted by G44Pack).** The map is G44Pack3's K8c8, from its pattern-flow LNS (`pflns`) on the R = 480 k8 word. Its lineage is the #685/#741 map (chafreaky) via G44Pack's relabel and rewidth, followed by G44Pack3's LNS. It was admitted with this package's own code (NEWWORD discovery, `freeze_spec.py`, strict) at κ 0.001671387264390146. Only PLAN and OWNERS change. These are search inputs only; no verifier reads them.
+11. **Expected values.** `data/SPEC.json` is re-derived by #645's discovery → `code/freeze_spec.py` → strict chain.
+
+- **κ = 0.001671387264390146** (conservative 0.001671387261540186). That is +0.4298% over research/gauge44-leaver (k5 cells, κ 0.001664233607446043; same chain on five cells, FO_c1 map) and +0.5672% over [#942](https://github.com/CrocSwap/integer-mult-bounds/pull/942) (κ 0.001661960547713947) and +1.3279% over #645, +0.9174% over research/gauge44-notri-layered (0.001656193765416678) and +0.7701% over research/gauge44-promo (0.00165861362787227) and +0.7273% over research/gauge44-promo-p6 (0.001659319032684569) and +0.7075% over research/gauge44-promo-p6sw (0.001659645685315104) and +0.5869% over research/gauge44-frames-x (0.001661634653669567) and +0.5679% over research/gauge44-barch (0.001661948695165034) and +0.6131% over [#741](https://github.com/CrocSwap/integer-mult-bounds/pull/741) (chafreaky, κ 0.001661202643272239) and +0.6654% over [#685](https://github.com/CrocSwap/integer-mult-bounds/pull/685) (chafreaky, κ 0.001660339298410333). The complex side certifies 0.001674185476674086429846 and PR589's bit supplier gives 0.001733427039589844234749, so **the complex side binds**. Under PR543 the bit side would cap κ at 0.001651096360425895 (`PROOF-NOTE-BIT.md`).
+- **Evidence.** This package's own code admitted G44Pack3's K8c8 map (NEWWORD discovery → `freeze_spec.py` → strict): `verify_global.py` passes (`PASS_GAUGE44_STRICT_GLOBAL_REPLAY`, κ 0.001671387264390146) against G44Pack3's k8 locals, with SPEC `width_spot_helpers` [258,270,282,294] and `pivot_swap` → `construction/leaver/PIVOT-SWAP-k8.json`. It equals G44Pack3's own strict κ for K8c8. `RESULT.json` is that replay's `REPLAY.json`, converted to LF. The locals rebuilt by `reproduce_leaver_chain.py --id k8` match G44Pack3's strict locals byte for byte in every file except CLIFFORD-REVIEW and SCALAR-FRAME-AUDIT. Those two differ only in their `seconds` field, and the comparison normalises only that field (canonical `d1bf3c6f…`, programs `683f8323…`/`2d184e4d…`, Clifford `e3bfdfa2…`, pinned in `CHAIN-PINS-k8.json`). For this package, `data/SPEC.json` and a fresh `verify_global.py` replay on locals rebuilt by the two drivers are the binding record.
+- **Independent price.** `independent/GAUGE44-INDEPENDENT-PRICE.json` is regenerated on this package's `data/PLAN.json` with the ported `independent/price_profile.py`: `PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK`, κ equal to the strict replay.
+- **Independent local audit.** `evidence/layers/LOCAL-AUDIT-LAYERED.json` is #645's `independent/audit_local.py`, run with `--main` on the final leaver word (content `db2c7cfb…`): `PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES`, 192 entering helpers, 78 low ends, 48 cold ends, 704 checked columns. Rerunning it reproduces the receipt except `elapsed_seconds` and, across zlib versions, `compressed_sha256`.
+- **Historical #645 files (PR543-based, 492 helpers).** These are #645's files, retained unchanged and **not** updated for this package: `LOCAL-VALIDATION.json`, `CONSTRUCTION.md`, `hosting/`, `evidence/` (except `evidence/layers/`), the rest of `independent/`, `construction/reproduce.py` and its inputs, and `code/prepare_global.py`. They describe #645's word, owner map, PR543 supplier and κ 0.001649483702558979. `code/prepare_global.py` is #645's one-shot owner-map preparer, hard-wired to #645's parent plan and R = 492. No verifier imports it. This package's PLAN/OWNERS are frozen search output, and the strict replay checks them. `construction/reproduce.py` is still used for its `--until word` shadow and hamming inputs; its 492-word output is then superseded by `construction/notri/`. `construction/layers/reproduce_layers.py` is research/gauge44-layered's driver for the 492-helper layered word, shipped unchanged as signed; it is not used here.
+- **Construction and code files** by committed LF SHA-256:
+  - `construction/notri/reproduce_notri.py` 90148c2a0422b4f92164298a283de73d413ab3d4cb7151a0e6b643a37ea025a8 (no-triangle driver)
+  - `construction/notri/cgx.py` 3da039d4184097c14802f9dbf972520d5b807671196f5e47a2247bc9f29bb418 (PartialK's generalised construct_gauge_xcentre.py)
+  - `construction/notri/port_stage_x.py` 38310744d054e393ea35e996047cddeb2d212141aaaaa4b07f7a4663b11db8e7 (PartialK's generalised build_port_stage.py)
+  - `construction/notri/cold44x.py` f0bc3500efb2c839a0f8cb03dbb9ea0a54f1dfc71ef81e5373b3d638ac5b8296 (PartialK's generalised build_gauge_cold44.py plus the PAIRING_RANKS pin)
+  - `construction/notri/PRIO6.json` de0412511b0dd1af13e9717bc791126ac0e91c569b5391fd6c70268083045d15 (completion priority)
+  - `construction/layers_np/reproduce_np.py` 1a304144a250d00d14154692ba522365b036777cf2b6fac466095e8ba733c16c (NP layer driver)
+  - `construction/layers_np/PIVOT-SWAP-NP.json` d49b8d316da1cbdaf995dd0e8314d3c67cc9cd4d5902e9d85ccb907be645bef5 (layer input)
+  - `construction/layers_np/HPE-RECIPE-NP.json` 43900139f618bdc06b8319098fb8dccaf4fc315b43ef7c067ca2cd778cdba2c1 (layer input)
+  - `construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz` 3164cfb71baaeba4ac43427bc14075a225fc3a32ecd9341e58aa52c03a4ee2c0 (layer input)
+  - `construction/layers/build_pivot_swap.py` 8e8bced88be2e592ded40929499bac385ca92fcc1fa59183c22229dbf34093b8 (signed, unchanged)
+  - `construction/layers/layer_end_controls.py` 7829187bfc8f909948d5250e0ec00f02c89f5fe98306a3ed88daee36cb3c92ef (signed, unchanged)
+  - `construction/layers/reproduce_layers.py` 435699f6f79c6c7fb8d6cc5a8382576d6ac88747583a975ff671e45440b93c4e (signed, unchanged, unused here)
+  - `construction/promo/reproduce_promo.py` f979be666c3f5cf57e342a8427863c0b35b67ca4d3be495ac386f6870deb2026 (promotion driver)
+  - `construction/promo/build_promotion.py` 9c9e2001b8d68bbe934d136026276fe97bd9bf6f94d4d78441fc28e14aca4daf (BlockInvert's constructor)
+  - `construction/promo/promo_controls.py` 786c51f84b53698c2c833083506c4432c30eb0ed3b71e7dbe458a70c7413c372 (BlockInvert's controls)
+  - `construction/promo/make_recipe.py` ba9e4fdc0c1be7f6a150a5a50909911257a1a8c7cc5d03d61f541178fc07c122 (discovery-side recipe writer (search, not run))
+  - `construction/promo/PROMO-RECIPE-p6n-k4.json` fa6065d142646f7ab1f268912ce0cf5a1a6cd33c3994ff96bd6e204cf16b3e90 (minimal recipe)
+  - `construction/promo/LOCAL-PINS-p6n-k4.json` a92bb02266596956bd53e9c86e8bbcc6639c92b4a4a248a1521f8eb79228271f (native pins)
+  - `construction/layers_p6n/reproduce_p6n.py` aa7d6bcbed05aa1c689437c07a26e5c95be3c700c0c1fb7bcf91c432a88436ca (p6n driver)
+  - `construction/layers_p6n/layer_end_controls.py` fc58c5699ba6191c1163a3041241f6f0b619626c4462cd99bcf88210bac9e81e (per-end controls (Q6Reviewer-signed variant))
+  - `construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz` 17e218a17e47c58fe2cde775ab2314d3d84030a61327b7f13da61cae3b374ad4 (p6n recipe)
+  - `construction/layers_p6n/P6N-SPEC.json` 132a59635077d6afe80f99964a6935fce1dc2ece6587d74209c6f9c60025c8f1 (p6n end spec)
+  - `construction/sw4/reproduce_sw4.py` 3d082e0cc576fb1b4fb9e5dd11d63bab697c8a8626e2837813cd00d100b1aeac (SW4 driver)
+  - `construction/sw4/build_sw4.py` 9a295f3d534594a6b1326d8a6647e947670d1c6fbc92f37f5169661fde4c8f66 (BRoute's builder (stdlib))
+  - `construction/sw4/SW4-RECIPE-P6k4.json` fa58d0ffc95d10b7453daefe4b34404a52895f94126ef973e92e92106cd615fa (16-move recipe with pinned rejection sites)
+  - `construction/sw4/LOCAL-PINS-sw4-P6k4.json` 3c06bf68b28ff125a6a2372bb70cefd76fb9fe1333438cd34dfb5b617cd70327 (native pins)
+  - `construction/frames/reproduce_frames.py` dc39ada9a2eb387310be181f3cea5dbd4b538632a888cd7372ece5e38a771832 (#741 frames driver)
+  - `construction/frames/build_frames.py` 200847a7e8b3125cbeea0765dad67650e0bf83d32b66d72ba4977e99b8ee8eeb (#741's builder (chafreaky; ported))
+  - `construction/frames/frame_controls.py` 477de854ec9184a2c73d6ac3857a9d0cbd6bc04b71d10a105e7344434b492a77 (#741's controls (chafreaky; ported))
+  - `construction/frames/FRAME-RECIPE-sw4.json` a2c7ca4d44671386d05974e2627645b42bbb7da7a35cefff6e9fa158b6ac8473 (#741's recipe, byte-identical)
+  - `construction/frames/LOCAL-PINS-frames-sw4.json` bc416b8f6443d59c715fb358c4d70fa27eae2d306388ffe0e2a303f60d929f7f (native pins)
+  - `construction/jx/reproduce_jx.py` 5c7afebb4eb7fcdeb7e971cfbc457cf071850e2da21c3c71295efdd453c2399c (X4 driver)
+  - `construction/jx/build_jx.py` 3cc7550b0c24bb54e245c6f7f16de489fd7844721fbb64aac628f38f43887916 (JointXF's builder (stdlib))
+  - `construction/jx/RECIPE-X4.json` 9d42c6b38e8124f5ffe15da56c260a7fba7260626bf3c5f8cbd93aa4a71ceadd (explicit recipe with pinned controls)
+  - `construction/jx/LOCAL-PINS-jx-X4.json` 95c5114c8e937c2737a1b9f9da97303f2e5e129d39e6dfcc4010e99bfdb9c974 (native pins)
+  - `construction/barch/reproduce_barch.py` 19bc970aa6af25ab0e7fa96fb65c64dd0c5243976d8f2cb733cba839155482c1 (U8 driver)
+  - `construction/barch/build_tri.py` 0fba65b31c2fd71864c291358bb0ad8d5f7e1be07e21df23f0ae73d7b966002e (NewBArch's builder (stdlib))
+  - `construction/barch/run_controls.py` 42639bf62bf57795e3ea615c1944c67efed00f28591333daeb3139bf63d04476 (NewBArch's controls (38 outcomes))
+  - `construction/barch/RECIPE-U8.json` 292f0e9f82824c4111728cf4de929bf6e43320fbbdc77658aae9681906b0d652 (explicit recipe)
+  - `construction/barch/LOCAL-PINS-barch-U8.json` 2d16f99e1f71fd66378f5f767cf4cfa2a58264919a95074c7b31029f39a3c9f5 (control set and native pins)
+  - `construction/leaver/reproduce_leaver.py` 831bfdf2247b5d864b74c3b2b6a475718053d48570851d48bd1c5471d410ee30 (cell driver)
+  - `construction/leaver/cgx_leaver.py` 3af491c63dd96204a7c36006c7e419c2e5ce77e5bc453ccd2495c1e41f83f87c (cell constructor)
+  - `construction/leaver/reproduce_leaver_chain.py` 2bc3fc3f32e0f957a0731b79254c553ca48fc6d4d47c4f99d6cd31e1901d85b5 (chain driver)
+  - `construction/leaver/layer_end_controls_leaver.py` 4ba676f1ea326b739a64c3477f64eeb295f8151514f78fa7e62b71e4373a6206 (per-word reason re-pins and declared not-applicable sites, v2 (Q6Reviewer-signed))
+  - `construction/leaver/build_frames_lv.py` 2eb80d612aa59a7bd8b04a122045e3bd2b83a21954e3164943cd20cf6050a21b (LeaverSAT2's frame builder)
+  The global code is research/gauge44-layered's, unchanged: assemble 4c270a99, assembly_controls e4c0f782, audit_allcold a87d7f48, bind 1d39bcc7, witness 779c5172. The bit-supplier code is research/gauge44-bit589's, unchanged: verify_global 16bd5e54, bit_supplier_controls e6d33fb6, price_profile d2f548ad.
+- **Line endings.** These files had CRLF in the admitted trees and are committed as LF only (`crlf.replace(b'\r\n', b'\n') == lf`, no lone `\r`):
+  - `construction/jx/build_jx.py`: CRLF 775c2ae60eec9abc…, committed (LF) 3cc7550b0c24bb54…
+  - `construction/jx/RECIPE-X4.json`: CRLF 228079b304358500…, committed (LF) 9d42c6b38e8124f5…
+  - `construction/barch/build_tri.py`: CRLF 2432372f148a4d34…, committed (LF) 0fba65b31c2fd718…
+  - `construction/barch/run_controls.py`: CRLF 18e1f5953403784f…, committed (LF) 42639bf62bf57795…
+  - `construction/barch/RECIPE-U8.json`: CRLF 3e97088ad641eb6e…, committed (LF) 292f0e9f82824c41…
+  - `data/SPEC.json`: CRLF b2515d29d54e5027…, committed (LF) 1208c7c3ae84c158…
+  - `RESULT.json`: CRLF 454c25d5b0cd7df7…, committed (LF) 72bf797ce995ff61…
+  - `independent/GAUGE44-INDEPENDENT-PRICE.json`: CRLF 0b8482888e64327f…, committed (LF) 6e222b252f345344…
+  - `evidence/layers/LOCAL-AUDIT-LAYERED.json`: CRLF 6b63fc2bbea96cb5…, committed (LF) a596d7262374a023…
+
+
+Clean-clone verification, from the repository root (Python 3.11+, assertions on; prepare the pinned #635 supplier as in the #645 section below):
+
+```sh
+python -B research/gauge44-leaver8/verify_manifest.py
+python -B research/gauge44-leaver8/construction/reproduce.py \
+  --main . --pr635 /tmp/gauge44-pr635 --out /tmp/notri-base --until word
+python -B research/gauge44-leaver8/construction/notri/reproduce_notri.py \
+  --main . --pr635 /tmp/gauge44-pr635 --word-dir /tmp/notri-base --out /tmp/notri-word --word-only
+python -B research/gauge44-leaver8/construction/layers_np/reproduce_np.py \
+  --main . --pr635 /tmp/gauge44-pr635 --notri-dir /tmp/notri-word --hamming /tmp/notri-base/hamming --out /tmp/notri-np
+python -B research/gauge44-leaver8/construction/layers_p6n/reproduce_p6n.py \
+  --main . --pr635 /tmp/gauge44-pr635 --np-dir /tmp/notri-np --out /tmp/p6n
+python -B research/gauge44-leaver8/construction/promo/reproduce_promo.py \
+  --main . --pr635 /tmp/gauge44-pr635 --base p6n --base-dir /tmp/p6n --k p6n-k4 --out /tmp/promo
+python -B research/gauge44-leaver8/construction/sw4/reproduce_sw4.py \
+  --main . --pr635 /tmp/gauge44-pr635 --promo-dir /tmp/promo --recipe P6k4 --out /tmp/sw4
+python -B research/gauge44-leaver8/construction/frames/reproduce_frames.py \
+  --main . --pr635 /tmp/gauge44-pr635 --sw4-dir /tmp/sw4 --out /tmp/frames
+python -B research/gauge44-leaver8/construction/jx/reproduce_jx.py \
+  --main . --pr635 /tmp/gauge44-pr635 --frames-dir /tmp/frames --out /tmp/x4
+python -B research/gauge44-leaver8/construction/leaver/reproduce_leaver.py \
+  --main . --pr635 /tmp/gauge44-pr635 --word-dir /tmp/notri-base --id k8 --out /tmp/lv --word-only
+python -B research/gauge44-leaver8/construction/leaver/reproduce_leaver_chain.py \
+  --main . --pr635 /tmp/gauge44-pr635 --leaver-dir /tmp/lv --hamming /tmp/notri-base/hamming --id k8 --out /tmp/lvc
+python -B research/gauge44-leaver8/independent/audit_local.py \
+  --word /tmp/lvc/frames/FULL-WORD.json.gz --main . --output /tmp/lvc-audit.json
+python -B research/gauge44-leaver8/verify_global.py \
+  --main . --local /tmp/lvc/local --work /tmp/lvc-global
+# kappa 0.001671387264390146
+```
+
+Optional control: `reproduce_notri.py ... --control-g44 --out /tmp/notri-ctl` rebuilds #645's gauge44 word `78c7aada…`.
+
+## Predecessor: #645's README (unchanged below; paths read `research/gauge44-global`)
+
+### Gauge44: conditional κ = 0.001649483702558979
+
+New contributions by **icekylinx**, with **OpenAI GPT-6 Astra** assistance.
+Local review and packaging used OpenAI Codex. Original notices and Apache-2.0 licenses are retained.
+
+Under the retained all-size compiler, common-label/mutable-source realization,
+whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit
+H1–H5 interfaces,
+
+$$
+T(n)=O\!\left(n(\log n)^{1-\kappa_{645}}\right),\qquad
+\kappa_{645}=\frac{1649483702558979}{10^{18}}=0.001649483702558979
+$$
+
+(This is #645's own κ. **This package's κ is the one at the top of this README.**)
+
+The certified complex saving is `0.001652208994368411824947`. The unchanged
+[#543](https://github.com/CrocSwap/integer-mult-bounds/pull/543) bit supplier gives
+`0.001653826988146798944268`, so the complex side binds. The conservative complex
+model separately certifies κ `0.001649483699681650`.
+
+### Construction
+
+This replaces the local supplier and all 72 owner assignments of pinned
+[#635](https://github.com/CrocSwap/integer-mult-bounds/pull/635). Source/copy exchanges
+at equal rank-one frames alter the factory's arbitrary-helper-input propagation.
+An invertible completion of the retired rows and source-carried coordinate totals
+then expose 44 rank-four cold endpoints. Exact input premixes, low-frame tails
+and a recomputed full inverse realize them.
+
+| Per-invocation quantity | Complete #635 JP8 | Gauge44 |
+| --- | ---: | ---: |
+| Source / target ports | 112 / 112 | 112 / 112 |
+| Helpers | 492 | 492 |
+| Rank-four cold endpoints | 22 | 44 |
+| Helper residual width | 3,894 | 3,794 |
+| Paid local rank mass | 5,750 | 5,650 |
+
+The new paid local profile is `{1:2514, 2:404, 3:448, 4:160, 5:56, 8:8}`.
+The explicit whole-family assignment covers 35,424 helper roles on 7,168 live
+and 7,670 physical families. It retains the rank deficit 2,560 and charges every
+idle remainder. Exact integer majorization certificates justify the owner
+updates; the resulting map is a coordinate fixed point, with no claim of joint
+optimality.
+
+The assembled κ is 0.809306% above #635. `data/FRONTIER.json` records Pro's dated
+comparison snapshot; it is not a live ranking of community results.
+
+### Proof and evidence
+
+- `CONSTRUCTION.md`: exact cold-space calculation, dyadic realization and attribution.
+- `hosting/PROOF.md`: capacity, exchange and majorization arguments.
+- `independent/CENTRE-GUARD-REVIEW.md`: ordered center-frame interface and source carriers.
+- `data/SPEC.json`, `evidence/ASSEMBLY.json`: strict component moments and outer parameters.
+- `evidence/audit/`: actual controller, physical charts and finite invoice.
+- `construction/INPUTS.json`, `data/UPSTREAM-PINS.json`: inherited input hashes.
+- `MANIFEST.json`, `SOURCES.json`, `LOCAL-VALIDATION.json`: submitted bytes, provenance and local checks.
+
+Original Pro run receipts are retained as evidence; their raw logs remain in
+the original archive outside the submission. Fresh replay writes new logs to
+the selected output directory.
+
+### Incremental reproduction
+
+Use Python 3.11 or newer with assertions enabled. The required replay uses only
+the standard library. The optional historical seed-discovery optimizer is not
+part of admission.
+
+Prepare the pinned #635 supplier in a separate directory (the main dependencies
+are already present in this repository):
+
+```sh
+git fetch https://github.com/CrocSwap/integer-mult-bounds.git a6895a69f8ad98ab45777b03e9e6f48888c39f6f
+mkdir -p /tmp/gauge44-pr635
+git archive FETCH_HEAD research/complex-571-cold14-st2 | tar -x -C /tmp/gauge44-pr635
+```
+
+From the repository root, with fresh output directories:
+
+```sh
+python -B research/gauge44-global/verify_manifest.py
+python -B research/gauge44-global/construction/reproduce.py \
+  --main . --pr635 /tmp/gauge44-pr635 \
+  --out /tmp/gauge44-local --until phases
+python -B research/gauge44-global/verify_global.py \
+  --main . --local /tmp/gauge44-local/local --work /tmp/gauge44-global
+```
+
+The dedicated workflow also runs the independent literal-word audit, exact owner
+reproduction, preserved-assertion comparison and independent pricing on Python
+3.11 and 3.14. `hosting/README.md` and `independent/README.md` give those commands.
+No ancestral full replay, optimizer search or PDF generation is required.
+
+The result remains a finite conditional witness. It does not establish an
+unconditional multiplication theorem or a complete Lean formalization.
diff --git a/research/gauge44-slots-t16/RESULT.json b/research/gauge44-slots-t16/RESULT.json
new file mode 100644
index 0000000000..b6d957f694
--- /dev/null
+++ b/research/gauge44-slots-t16/RESULT.json
@@ -0,0 +1,108 @@
+{
+  "status": "PASS_GAUGE44_T16_STRICT_GLOBAL_REPLAY",
+  "kappa": "1672654541898561/1000000000000000000",
+  "kappa_decimal": "0.001672654541898561",
+  "conservative_kappa_decimal": "0.001672654539046638",
+  "complex_lower": "837728501331911376831/500000000000000000000000",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "complex_profile": {
+    "1": 349608,
+    "2": 60192,
+    "3": 62586,
+    "4": 20448,
+    "5": 11808,
+    "7": 6,
+    "8": 1152,
+    "48": 4866
+  },
+  "idle_remainder_profile": {
+    "1": 2280,
+    "3": 378,
+    "7": 6,
+    "48": 4866
+  },
+  "complete_invocations": 144,
+  "roles": 69120,
+  "prefix_bits": 397,
+  "charged_prefix_bits": 512,
+  "physical_row_coefficient": 16469,
+  "retained_row_coefficient": 20161,
+  "actual_73_axis_charts": 9997,
+  "controls": {
+    "admission": 69,
+    "bit_supplier": 12,
+    "independent_t16": 6,
+    "controller_mutations": 15
+  },
+  "t8_kappa": "167166528321877/100000000000000000",
+  "spec_sha256": "2a8728207fc2d1f65bcc0229a61c52a4fbd02f9d4acebe1b479d3fb0fe0690f6",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 2.828,
+      "exit_code": 0,
+      "log_sha256": "3aea2a4b68e7aaeadd9ffef649be0d25e2dff1535d9a61bffeaf6d92e55ba6a8"
+    },
+    {
+      "name": "bind8",
+      "seconds": 1.172,
+      "exit_code": 0,
+      "log_sha256": "78a081673d6b4fde10a86e6f767d53648b868d1f0cac2441d12951434ad7341b"
+    },
+    {
+      "name": "lift16",
+      "seconds": 4.984,
+      "exit_code": 0,
+      "log_sha256": "eb855e248709c72d340c20e7e901dca27b8c639cf8f38fac151c25a48e9c03bf"
+    },
+    {
+      "name": "bind",
+      "seconds": 1.468,
+      "exit_code": 0,
+      "log_sha256": "78a081673d6b4fde10a86e6f767d53648b868d1f0cac2441d12951434ad7341b"
+    },
+    {
+      "name": "emit",
+      "seconds": 8.593,
+      "exit_code": 0,
+      "log_sha256": "3dcd31605a40e540a61847b02894d9fdab7a8b7804626f601ed1ff80990f1e0b"
+    },
+    {
+      "name": "audit",
+      "seconds": 37.016,
+      "exit_code": 0,
+      "log_sha256": "45dd8137ec65a3918029a2763ae0dcd3e1882be891d008aa9da4ff842da0132b"
+    },
+    {
+      "name": "invoice",
+      "seconds": 3.609,
+      "exit_code": 0,
+      "log_sha256": "caa1229b78eca961462d35e8ee458be536111111a985294a153e4dd74b9171a8"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.922,
+      "exit_code": 0,
+      "log_sha256": "4e4deb2b4e3d935d740f462aadc14940ad4f9bfac2e2a18636721cd29ea63f71"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 1.218,
+      "exit_code": 0,
+      "log_sha256": "34527ddfe1e53bec71dc5759eb9a26417be6d4e93e76cbf80575d9bafebd876b"
+    },
+    {
+      "name": "bit-supplier-controls",
+      "seconds": 1.484,
+      "exit_code": 0,
+      "log_sha256": "c648542cd6dddbb154af7d02a41aaed1025603d9a4ab54f7c249d2b683e22249"
+    },
+    {
+      "name": "independent-t16",
+      "seconds": 2.5,
+      "exit_code": 0,
+      "log_sha256": "d2c13b333d463a5c2de42078e9c47a89209075e1d1beac24cf3fc1f573f18c05"
+    }
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/gauge44-slots-t16/SOURCES.json b/research/gauge44-slots-t16/SOURCES.json
new file mode 100644
index 0000000000..0d69845db9
--- /dev/null
+++ b/research/gauge44-slots-t16/SOURCES.json
@@ -0,0 +1,36 @@
+{
+  "contributor": "icekylinx",
+  "research_assistance": "OpenAI GPT-6 Astra",
+  "local_review_and_packaging": "OpenAI Codex",
+  "original_archive": {
+    "filename": "integer_mult_round23_gauge44_delta.zip",
+    "sha256": "40a20a120f51cbed3c9ae4017603be74a9e9332ad4068bd914bf3e81bf8be6b4",
+    "manifest_sha256": "ffa23eb668ad558ebb5601470fc1997a9fb8cea0e188aa3c5d61318be9000603"
+  },
+  "upstream_main": "17ce0c79b7b51c2634b439ea5a2b754f09909693",
+  "construction_parent": {
+    "pr": 635,
+    "commit": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f"
+  },
+  "bit_supplier_pr": 589,
+  "packaging_changes": [
+    "Omit original run logs; retain their original receipts as historical evidence.",
+    "Use repository paths and dollar-delimited Markdown mathematics.",
+    "Add manifest verification, incremental CI and local validation record.",
+    "Trim trailing whitespace in four Python files; complete ASTs are unchanged. Refresh the corresponding constructor input hash.",
+    "research/gauge44-bit589: PR589 bit supplier (G44Stack port, Bit589Reviewer SOUND-WITH-FIXES), G44Pack dz1 owner map, re-derived SPEC, LF line endings, regenerated MANIFEST.",
+    "research/gauge44-leaver: research/gauge44-barch tree plus construction/leaver (k5 cells, chain, frames); G44Pack3 FO_c1 owner map, re-derived SPEC, regenerated independent price receipt, RESULT.json = strict REPLAY, LF, regenerated MANIFEST.",
+    "research/gauge44-leaver8: research/gauge44-leaver tree with the k8 cell set (all eight cells, R = 480) and its chain recipes (LeaverSAT/LeaverSAT2 pkg_k8), layer_end_controls_leaver v2 with declared not-applicable sites on all five stack words (replacing the final-word interim skip), CHAIN-PINS-k8; G44Pack3 K8c8 owner map, re-derived SPEC, regenerated independent price receipt and local audit, RESULT.json = strict REPLAY, LF, regenerated MANIFEST."
+  ],
+  "attribution": "Original notices and licenses retained. See NOTICE.md, UPSTREAM-NOTICE.md and CONSTRUCTION.md.",
+  "whitespace_only_python_files": [
+    "code/audit_allcold.py",
+    "code/bind_providers_portable.py",
+    "construction/construct_gauge_xcentre.py",
+    "independent/audit_local.py"
+  ],
+  "historical_bit_supplier_pr": 543,
+  "bit_supplier_note": "This package cites PR589 (inputs/PR589-EXPECTED.json, git blob e293ddc5…). PR543 is the supplier of #645's retained historical evidence (LOCAL-VALIDATION.json, independent/ audit files, hosting/, evidence/). RESULT.json is this package's strict replay.",
+  "owner_map": "G44Pack/G44Pack3: The map is G44Pack3's K8c8, from its pattern-flow LNS (`pflns`) on the R = 480 k8 word. Its lineage is the #685/#741 map (chafreaky) via G44Pack's relabel and rewidth, followed by G44Pack3's LNS. It was admitted with this package's own code (NEWWORD discovery, `freeze_spec.py`, strict) at κ 0.001671387264390146.",
+  "construction_changes": "PartialK: no-triangle gauge44 word (R=504, PRIO6, ranks [4]*14); G44Stack: layers on it (pivot swaps, s4, x30, b6, q4); LeaverSAT: no-helper mutable-leaver cells and re-stacked recipes, LeaverSAT2: frame re-optimisation (construction/leaver); NewBArch: triangle-hybrid B rewrite U8 (construction/barch); chafreaky #741: eight B frames (construction/frames, ported by CompetitorMine) and the owner map; JointXF: joint exchange X4 (construction/jx); BRoute: read-set exchange SW4 (construction/sw4); NoTriReopen: p6n ends (construction/layers_p6n); BlockInvert: entrance promotions E4->E5 (construction/promo, minimal recipe p6n-k4); drivers construction/notri/reproduce_notri.py, construction/layers_np/reproduce_np.py, construction/promo/reproduce_promo.py"
+}
diff --git a/research/gauge44-slots-t16/UPSTREAM-NOTICE.md b/research/gauge44-slots-t16/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..ebc24a0168
--- /dev/null
+++ b/research/gauge44-slots-t16/UPSTREAM-NOTICE.md
@@ -0,0 +1,34 @@
+# Attribution and scope
+
+Four verified provider types are offered to every call: PR571's prefix word with twelve multi-cut cold kernels (PR568's unchanged constructor), the same word with forty width-five entrance promotions (PR569's unchanged frame constructor) before those kernels, PR575's plain joint-prefix provider, and PR568's eight-cold provider. A window MILP with an exact per-pattern model chooses the dispatch and a literal owner map. PR583's six source-bound kernel frame coalescences (its unchanged constructor and negative controls) are applied to every PR571-prefix provider word (ck and atm3), followed by two further coalescences that each first move one addition past two commuting additions (package code/build_gate_moves.py, extending PR583's constructor); a final hyperplane_end step (package code/build_hpe.py) then runs 46 single-gate cleanups h -= p right after part B at the dim-8 join U of their registers, so 46 width-8 entering helpers per call end at U with width 7; each such gate commutes with every earlier cleanup gate on its registers (for 8 of them the partner's one earlier gate x -= p only reads p), and the reordered program is replayed exactly. A window MILP (exact windows, RINS around an LP vertex) gives the dispatch ck 45 / atm3 21 / jp8 6 and the literal owner map.
+
+Pinned external sources (unchanged; `verify.py` checks their manifests and every file it uses):
+- PR568 (`research/complex-multicold`, commit `71c99ac935a33bb7b59a1b4a7af8725a939b0b90`).
+- PR571 (`research/structural-gain`, commit `b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3`).
+- PR569 (`research/larger-gain`, commit `897213a855b7fb8a1b8b0e552a2f5c42e6c1b326`).
+- PR575 (`research/complex-joint-prefix`, commit `eac6f7e378ab622dac50a2fd4b7ef6eab014de44`).
+- PR583 (`research/kernel-frame-coalescing`, commit `89be768f0157f5a3d8e4db69cf1748768605eac9`).
+
+Provider construction is described as typed steps in `data/SPEC.json` (`build`); `verify.py` runs only allowlisted step types with their paired omission audits and checks every input and output content hash. `code/` holds the spec-driven global admission scripts adapted from PR571's `frontier-composition/global-code/` (OpenAI Codex assisted, Apache-2.0): every expected value is read from `data/SPEC.json` and compared only after independent recomputation. `code/generated_identity.py` and `code/generated_identity_controls.py`, and the decompressed-content artifact identities in the bind, audit, invoice, assembly and phase-timing scripts, are taken unchanged from PR586 by chafreaky (`research/promoted-kernel-coalescing`, commit `4846fee5b06af770e9b3a10c36200f673d656725`, OpenAI Codex assisted, Apache-2.0), including its proof-content and reference/metadata mutation controls; the normalization of descriptive width metadata after frame changes follows the same PR.
+
+In PR601, the owner map was nominated by a HiGHS window MILP (adapted from PR569's `global/nominate_width7.py`) with lazy cross-time Hall cuts; this package's re-solved map is described below. Neither is an admission dependency.
+
+DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. (The PR601 package this one starts from states: "Prepared by Claude Code (Anthropic) research agents.") Apache-2.0 applies; LICENSE is included. All notices, licenses, source pins and AI disclosures of the pinned sources and their ancestry are retained in those packages and are not replaced by this notice. All inherited conditional assumptions remain conditional.
+
+**This package (complex-571-cold14, DreamingOfClouds).** It starts from PR601 (jeremykothe2, `research/complex-571-hpem46`, commit `529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550`). Everything above is kept unchanged except the following:
+- every provider chain (ck, atm3, jp8) gains the typed step `cold_end` (`code/build_cold_end.py`, `code/cold_end_controls.py`; recipes `data/recipes/*-cold_end.json.gz`);
+- the generalised native chain and the global admission scripts accept cold helpers that end below FULL (with `0:U` wrappers), a refactored exact cleanup, and check the wrapper order;
+- `data/PLAN.json` / `data/OWNERS.json.gz` (dispatch and literal owner map) come from a relocate/swap/ejection-chain/provider-flip annealing search started from PR601's map, refined by an exact pattern-restricted owner model (CP-SAT) with a literal edge-colouring expansion (not an admission dependency);
+- `data/SPEC.json` holds the expected values, recorded by a discovery run and then checked by a strict run.
+
+The cold-end construction (a row-plus-column cone condition for low-frame ends, a rank-0 dirt-spread premix and multi-gate lower-frame cleanup) builds on PR591 / PR592 / PR593 / PR601 (jeremykothe2) and our PR599 (Lean: multi-gate and cold hyperplane-end tails). DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. Build on this at your own risk.
+
+**This package (complex-571-cold14-b3, jeremykothe2).** It is PR604's `complex-571-cold14` (DreamingOfClouds) with ColdBeyond's second cold end per block (two new `cold_end` A-gate primitives, `PROOF-NOTE.md`), ColdSupply's E1 entering pair and reviewed controls, a free dispatch (jp8 ×60, atm3 ×12) and a literal owner map from an exact per-time-Hall window MIP. All other construction, code, controls and proofs are PR604's and earlier contributors', unchanged.
+
+**This package (complex-571-cold14-k492).** It is complex-571-cold14-b3 with these changes:
+- **K-triangle base words.** The leaver-read K-triangle skeleton atom and its read schedule (`data/TRI-SCHEDULE.json`) are by AtomScout, a Claude Code research agent. `code/construct_k_triangle.py` is PR531's `code/construct_504.py` (icekylinx, OpenAI Codex / GPT assisted, Apache-2.0; pinned source `direct_delivery`) extended with that atom.
+- **Ported chains.** The PR604/B3 chains are ported stage by stage onto the K-triangle words by `code/build_port_stage.py` (Port480, a Claude Code research agent). `code/build_frame_regroup.py` extends PR583's `build_frames.py` (chafreaky).
+- **Helper count R.** The generalisation of the global scripts to the provider helper count R is by GlobalR (a Claude Code research agent), with AtomReviewer's fixes (PROOF-NOTE-R.md).
+- **Owner map.** The owner map, the cold_end recipes on the K-triangle words and the package assembly are by Stack492, Port480 and ColdBeyond (Claude Code research agents).
+
+Build on this at your own risk.
diff --git a/research/gauge44-slots-t16/code/assemble.py b/research/gauge44-slots-t16/code/assemble.py
new file mode 100644
index 0000000000..581dd9cb29
--- /dev/null
+++ b/research/gauge44-slots-t16/code/assemble.py
@@ -0,0 +1,241 @@
+"""Gauge44 complete global admission with the retained native exact-complex moment.
+
+Prepared with OpenAI Codex assistance. The rational engines and outer
+constraints are retained from PR547/PR548 and their preserved ancestry.
+The bit operator is the cited unchanged PR589 supplier (PR555's punctured
+R439 word, v = 111, decoder constant 63, two A-section transports), shipped
+as inputs/PR589-EXPECTED.json and pinned by git blob id. Its rank-mass
+deficit is derived from the word's parameters, T(2Kv - L*cst) at nine
+stages (PR545/PR555 rank-mass identity), not hard-coded. The complex owner
+and invoice inputs must be freshly emitted by the packaged physical replay.
+All conservative admission guards and conservative moment/outer witnesses run
+before the PR559 native-complex correction. The bit surcharge is retained.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from decimal import Decimal, localcontext
+import argparse,json,hashlib,importlib.util,os,sys
+from collections import Counter
+assert __debug__, 'Assertions required'
+P=Path(sys.argv[1] if __name__=='__main__' else os.environ['GAIN_PR564_SOURCE']).resolve()
+read=lambda p:json.loads(p.read_text())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+hash_ok=lambda x:isinstance(x,str) and len(x)==64 and all(t in '0123456789abcdef'for t in x)
+digest=lambda x:hashlib.sha256(json.dumps(x,separators=(',',':')).encode()).hexdigest()
+def load(n):
+ s=importlib.util.spec_from_file_location(n,P/'engines'/(n+'.py'));m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,B,A=[load(n)for n in ('moment','base_two_moment','outer')]
+def dec(x):
+ with localcontext()as ctx:ctx.prec=70;return str(Decimal(x.numerator)/Decimal(x.denominator))
+from witness import DISPATCH,CALL_ORDER,COUNTS,PIDS,X,DISCOVER,pin,SPOT,spot_widths
+# Cited bit supplier: PR589's tune/EXPECTED.json (merged on main as research/e8-bit-p111-tuned/tune/EXPECTED.json).
+BIT_PATH=Path(__file__).resolve().parents[1]/'inputs/PR589-EXPECTED.json'
+BIT_BLOB='e293ddc557742637f9f679f083a1a282d87b1b13'
+# Nine-stage bit template (PR463/PR510 chain, 32 replicas): L stages, T replicas, K=(L-1)//2 pairs, moment width M=1+7L.
+BIT_L,BIT_T=9,32;BIT_K=(BIT_L-1)//2;BIT_M=1+7*BIT_L
+def git_blob(data):return hashlib.sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest()
+def load_bit(data):
+ """The pinned supplier record: its full record (word parameters) and its nine-stage price."""
+ assert git_blob(data)==BIT_BLOB,'bit supplier blob pin'
+ return json.loads(data)
+def bit_deficit(word,live):
+ """Rank-mass deficit M*live - mass = T(2Kv - L*cst) of a v-port bit word with decoder constant cst (PR545/PR555).
+ cst is the sum of the retained totals' COPY ranks and live = 2KvT data wires; both are cross-checked here, and the
+ caller checks the result against the priced profile, so neither v nor cst is free."""
+ v,cst,ranks=word['v'],word['decoder_constant'],word['copy_ranks']
+ assert type(v)is int and type(cst)is int and all(type(r)is int and 0<r<=8 for r in ranks)
+ assert len(ranks)==word['retained_totals']==BIT_L and cst==sum(ranks)
+ assert live==2*BIT_K*v*BIT_T
+ d=BIT_T*(2*BIT_K*v-BIT_L*cst);assert d>0;return d
+
+
+def assemble(owner,invoice,owner_sha,invoice_sha):
+ # These are admission receipts, not optional collections of successful rows.
+ # Require both orientations and every finite check before pricing anything.
+ assert owner['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE'
+ assert invoice['status']=='PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE'
+ assert all(hash_ok(x)for x in (owner_sha,invoice_sha,owner['template_sha256'],owner['controller_audit_sha256'],invoice['parent_template_sha256']))
+ checks={'local_primitive_bound','logical','router','literal','mass','precision','tape','row','halving'}
+ assert set(invoice['strict_checks'])==checks
+ assert all(invoice['strict_checks'][name] is True for name in checks)
+ assert set(invoice['providers'])==set(PIDS)
+ assert invoice['provider_counts']==COUNTS
+ assert owner['all_live_owners_per_call_distinct'] is True
+ # R (helpers per provider word) is read from the invoice and must be shared by every provider; n=2v+R.
+ R=invoice['helpers'];assert type(R) is int and R>0 and all(p['helpers']==R for p in invoice['providers'].values())
+ assert owner['owners_per_call']==2*112+R and owner['actual_helper_owner_charts']==owner['hosted_residuals']==144*R==pin('expected.hosted_residuals',owner['hosted_residuals'])
+ pin('expected.rank_mass',owner['rank_mass'])
+ pin('expected.actual_73column_sigmas',owner['actual_73column_sigmas']);pin('expected.cross_replica_helper_roles',owner['cross_replica_helper_roles'])
+ pin('expected.idle_remainders',owner['explicit_idle_remainder_children'])
+ assert invoice['complete_invocation_sweeps']==invoice['bridge_sweeps']==144
+ assert invoice['live']==owner['live'] and invoice['physical']==owner['physical']
+ assert invoice['centres']==8
+ assert invoice['physical_stock_identity']==dict(data_and_owner_families=14336,local_helpers=R,private_centres=8,coefficient_work=2)
+ assert sum(invoice['physical_stock_identity'].values())==invoice['physical']
+ assert invoice['controller_audit_sha256']==owner['controller_audit_sha256']
+ for pid,p in invoice['providers'].items():
+  assert set(p['local'])=={'forward','backward'}
+  assert p['helpers']==R and p['centres']==8 and p['n']==2*112+R and p['v']==112 and p['h']==9
+  K='providers.'+pid+'.';pin(K+'entering',p['entering_helpers']);pin(K+'entrance',p['entrance_rank'])
+  pin(K+'inventory',p['width_inventory'])
+  assert all(type(w) is int and 0<w<=9 for w in p['widths'])
+  assert Counter(p['widths'])==Counter({int(r):n for r,n in p['width_inventory'].items()})
+  assert sum(p['widths'])==9*R-p['entrance_rank']-p['terminal_codimension'] and len(p['widths'])==R   # HPE: widths |final|-|start|
+  pin(K+'width_digest',digest(p['widths']));assert tuple(p['widths'][h]for h in SPOT)==spot_widths()
+  pin(K+'expected_profile',p['paid_profile'])
+  assert p['children']==sum(p['paid_profile'].values())
+  pin(K+'program_hashes',p['program_hashes'])
+  for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json'):
+   assert hash_ok(p['artifacts'][name]) and p['artifacts'][name]==owner['source_artifacts']['providers/'+pid+'/'+name]
+   if name in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):pin(K+'artifacts.'+name,p['artifacts'][name])
+  pin(K+'artifact_semantic_sha256',p['semantic_artifact_sha256'])
+  pin(K+'complete_contract',{k:v for k,v in p.items()if k!='artifacts'})
+  assert owner['provider_artifact_semantic_sha256'][pid]==p['semantic_artifact_sha256']
+  pin(K+'semantic_phase_sha256',p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'])
+  assert owner['provider_phase_semantic_sha256'][pid]==invoice['provider_phase_semantic_sha256'][pid]==p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']
+  for name in ('forward','backward'):
+   z=p['local'][name];pinned=pin(K+'expected_local.'+name,{k:z[k]for k in('events','macros','real_component_primitives','prefix_l1','coefficient_work_primitive_count')});primitives=pinned['real_component_primitives'];coefficient_work=pinned['coefficient_work_primitive_count']
+   assert z['all_dirty_helper_columns_restored'] is True and z['private_centres_and_coefficient_work_cleared'] is True
+   assert z['all_exact_columns']==2*112+R and z['dirty_helper_columns']==R
+   assert z['events']==pinned['events'] and z['macros']==pinned['macros']
+   assert z['real_component_primitives']==primitives and z['coefficient_work_primitive_count']==coefficient_work
+   assert z['pre_wrappers']==z['post_wrappers']==p['entering_helpers']+p.get('cold_hyperplane_ended_helpers',0);pin(K+'wrappers',z['pre_wrappers'])   # COLD-HPE
+   assert 0<z['prefix_bits']<=192 and 0<Q(z['prefix_l1'])<2**192
+   peak=Q(z['prefix_l1']);assert z['prefix_bits']==peak.numerator.bit_length()-peak.denominator.bit_length()+1
+   assert peak==Q(pinned['prefix_l1'])
+  assert p['compiler']==64*74**3
+  assert p['local_adapters']==16*(max(z['macros']for z in p['local'].values())+p['children']+2*112+R+8)+64*73
+  assert p['local_primitive_bound']==max(z['real_component_primitives']for z in p['local'].values())+p['local_adapters']*p['compiler']
+ calls=invoice['selected_calls'];assert len(calls)==144
+ assert [(c['stage'],c['replica'])for c in calls]==CALL_ORDER
+ assert {(c['stage'],c['replica']) for c in calls}=={(s,r) for s in range(9) for r in range(16)}
+ for c in calls:
+  pid=DISPATCH[c['stage'],c['replica']]
+  assert c['provider_id']==pid
+  # The retained nine-stage recipe alternates its two reflected shears.
+  assert c['orientation']==('forward' if c['stage']%2==0 else 'backward')
+  p=invoice['providers'][pid];z=p['local'][c['orientation']]
+  assert c['program_sha256']==p['program_hashes'][c['orientation']]
+  for name in ('events','macros','real_component_primitives','coefficient_work_primitive_count','pre_wrappers','post_wrappers'):
+   assert c[name]==z[name]
+  assert c['entering_helpers']==p['entering_helpers'] and c['entrance_rank']==p['entrance_rank']
+ assert invoice['selected_real_component_primitives']==sum(c['real_component_primitives'] for c in calls)
+ assert invoice['selected_coefficient_work_primitive_count']==sum(c['coefficient_work_primitive_count'] for c in calls)
+ assert invoice['selected_scalar_macros']==sum(c['macros'] for c in calls)==sum(invoice['providers'][c['provider_id']]['local'][c['orientation']]['macros'] for c in calls)
+ assert invoice['factors_per_wrapper']==144
+ assert invoice['wrapper_elementary_factors_charged']==sum(c['pre_wrappers']+c['post_wrappers'] for c in calls)*144
+ paid=Counter()
+ for c in calls:paid.update({int(r):n for r,n in invoice['providers'][c['provider_id']]['paid_profile'].items()})
+ assert dict(paid)=={int(r):n for r,n in invoice['selected_local_paid_profile'].items()}
+ idle=Counter({int(r):n for r,n in owner['paid_profile'].items()});idle.subtract(paid);assert all(n>=0 for n in idle.values())
+ idle=+idle;assert sum(idle.values())==owner['explicit_idle_remainder_children']
+ pin('expected.idle_remainder_profile',{str(r):n for r,n in sorted(idle.items())})
+ paid.update(idle)
+ assert dict(paid)=={int(r):n for r,n in owner['paid_profile'].items()}
+ assert invoice['compiler']==64*74**3
+ assert invoice['local_adapters']==max(p['local_adapters']for p in invoice['providers'].values())
+ assert invoice['local_primitive_bound']==max(p['local_primitive_bound']for p in invoice['providers'].values())
+ # Recount the retained dedicated-bank envelope independently. Its geometry
+ # stays fixed, while every local primitive and wrapper comes from the actual
+ # selected provider/orientation sums above.
+ parent_live,parent_physical,parent_idle=23408,23922,32256
+ parent_banks,rem=divmod(parent_live-2*112*4*16,9);assert rem==0 and parent_physical==parent_live+504+8+2   # two independent bank groups, each with R0=504 helpers; restored private workspace is shared
+ assert owner['source_idle_children_charged']==parent_idle
+ bridges,shifts=2*112*144,4*112*16;moves=2*shifts
+ nonlocal_items=(4*112*16*9+2*112*16*9+2*144*R+parent_idle+9*parent_banks+bridges+shifts+moves+parent_live+parent_physical+invoice['wrapper_elementary_factors_charged'])
+ outside=8*nonlocal_items+64*73
+ pervertex=(invoice['selected_real_component_primitives']+bridges+shifts+moves+parent_live+(144*invoice['local_adapters']+outside)*invoice['compiler']+64*parent_physical)
+ rebased=pervertex+65*(invoice['physical']-parent_physical)+(invoice['live']-parent_live)
+ assert invoice['unhosted_pervertex']==pervertex and invoice['hosted_rebased_pervertex']==rebased
+ used=max(pervertex,rebased)
+ prior=invoice['retained_prior_overcharge']
+ if prior is not None:
+  assert hash_ok(prior['sha256']) and type(prior['previous_pervertex_allowance']) is int and prior['previous_pervertex_allowance']>0
+  assert prior['added_complete_new_pervertex']==pervertex
+  assert prior['policy']=='Retain old allowance and add entire fresh mixed recount.'
+  used=max(used,prior['previous_pervertex_allowance']+pervertex)
+ assert invoice['conservative_pervertex_used']==used
+ finite=invoice['finite']
+ assert 0<finite['physical_row_coefficient']<finite['retained_row_coefficient']==20161
+ assert 0<finite['required_C0_bits']<finite['C0_exponent']==210000
+ assert finite['G_exponent']==30000 and finite['E_exponent']==100000
+ assert finite['halving_integer_inequality']==[5329,4608]
+ assert 0<invoice['global_prefix_bits']<=invoice['charged_prefix_bits']==512
+ assert invoice['row_prefix_extra']==1024
+ assert invoice['global_prefix_bits']==max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())+37+144+144+4
+ group=2**(36*36)
+ for j in range(1,37):group*=2**(2*j)-1
+ stock=group*invoice['physical'];streamed_mass=group*owner['rank_mass']
+ logical=group*used+64;router=invoice['compiler']*(logical+1)*(stock+1)**2
+ literal=2*2**30000*stock**2+8*streamed_mass+4*stock+4+32*73
+ total_mass=streamed_mass+2**100000
+ assert finite['physical_stock_bits']==stock.bit_length() and finite['router_bits']==router.bit_length() and finite['literal_bits']==literal.bit_length()
+ assert finite['physical_row_coefficient']==2*stock.bit_length()+9909+252+1024
+ assert finite['required_C0_bits']==(32*73*total_mass*total_mass).bit_length()
+ actual_checks=dict(local_primitive_bound=invoice['local_primitive_bound']<2**48,logical=logical<2**6050,router=router<2**30000,literal=literal<2**100000,mass=total_mass<2**100001,precision=32*73*total_mass*total_mass<2**210000,tape=2*total_mass+18<2**210000,row=finite['physical_row_coefficient']<20161,halving=73*73>2*48*48)
+ assert actual_checks==invoice['strict_checks'] and all(actual_checks.values())
+ bit_record=load_bit(BIT_PATH.read_bytes())
+ bit=bit_record['nine']
+ assert 'nine-stage' in bit['pipeline'] and '32 replicas' in bit['pipeline']
+ c=Q(bit['bit_lower'])
+ bit_D=bit_deficit(bit_record['word'],bit['bit']['live'])
+ H={int(r):n for r,n in owner['paid_profile'].items()};pin('expected.global_profile',owner['paid_profile'])
+ # Claimed lower endpoints come from the spec; discovery derives them with the same certified moment engine.
+ # Either way they are verified below (accepted at b, rejected at b+1e-24).
+ if DISCOVER:b=Q(M.certify(H,73,owner['live'],False)['lower']);conservative_b=Q(M.certify(H,73,owner['live'],True)['lower'])
+ else:b=Q(X['complex_lower']);conservative_b=Q(X['conservative_complex_lower'])
+ assert owner['template_sha256']==invoice['template_sha256'] and owner_sha==invoice['owner_audit_sha256']
+ pin('expected.live',owner['live']);pin('expected.physical',owner['physical']);assert owner['deficit']==5120
+ assert owner['banked_residuals']==0
+ def check_moment(side,h,m,W,lower,deficit,bad):
+  assert m*W-sum(r*n for r,n in h.items())==deficit and m*m>2*max(h)**2
+  rows=[]
+  for z,accept in [(lower,True),(lower+Q(1,10**24),False)]:
+   l,u=M.moment(h,m,W,z,bad);ll,uu=B.moment(m,W,list(h.items()),z)
+   if bad:
+    fl,fu=B.moment(m,W,[(1,32*m*m*sum(h.values()))],z);ll+=fl/10**16;uu+=fu/10**16
+   assert (u<1 and uu<1)if accept else(l>1 and ll>1)
+   rows.append(dict(side=side,surcharge=bad,endpoint=str(z),accept=accept,mercator=[str(l-1),str(u-1)],base_two=[str(ll-1),str(uu-1)]))
+  return rows
+ bitH={int(r):n for r,n in bit['profile'].items()}
+ assert BIT_M==64 and sum(r*n for r,n in bitH.items())==bit['bit']['rank_mass']
+ bit_moments=check_moment('bit',bitH,BIT_M,bit['bit']['live'],c,bit_D,True)
+ conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,5120,True)
+ assert bit['bit']['two_level_coefficient_bits']<bit['bit']['charged_two_level_coefficient_bits']==512 and bit['bit']['row_coefficient']<20161
+ def outer_witness(bb):
+  eta=beta=Q(1,10**24);s=min(c,(1-beta)*bb)-Q(1,10**27);assert 0<s<c and s<(1-beta)*bb
+  chain=[Q(384599,10**10)];cuts=[]
+  for _ in range(7):
+   old=chain[-1];a=(1-s)*s+s*old;gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+   ceil=lambda x:-(-x.numerator//x.denominator);cut=max(ceil(36/gap**2),ceil(2*(4+512)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+512)
+   cuts.append(dict(exponent=str(a),gap=str(gap),cutoff_log2=str(cut)));chain.append(a)
+  q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin*10**18;k=Q((ticks.numerator-1)//ticks.denominator,10**18)
+  bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}
+  outer=A.assembly(chain[-1],bb,bridge,k,eta=eta,beta=beta);assert len(outer['strict_constraints'])==47 and all(v>0 for v in outer['strict_constraints'].values())
+  controls=[]
+  for name,kk,ee,be in [('next_grid',k+Q(1,10**18),eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]:
+   try:A.assembly(chain[-1],bb,bridge,kk,eta=ee,beta=be)
+   except AssertionError:controls.append(name)
+   else:raise AssertionError(name)
+  return k,cuts,outer,controls
+ conservative_k,conservative_cuts,conservative_outer,conservative_controls=outer_witness(conservative_b)
+ pin('expected.conservative_kappa_decimal',dec(conservative_k))
+ # Only after every conservative supplier/admission/outer check succeeds is
+ # the reviewed native exact-complex recurrence selected. Bit charge stays.
+ native_moments=check_moment('complex',H,73,owner['live'],b,5120,False)
+ k,cuts,outer,controls=outer_witness(b)
+ pin('expected.kappa_decimal',dec(k))
+ assert M.moment(H,73,owner['live'],b,True)[0]>1
+ assert M.moment(bitH,64,bit['bit']['live'],c+Q(1,10**24),False)[1]<1
+ model_controls=['native_complex_endpoint_rejected_with_old_surcharge','omitting_bit_surcharge_would_fail_next_endpoint_rejection']
+ moments=bit_moments+native_moments
+ input_hashes={'owner_audit':owner_sha,'fresh_invoice':invoice_sha,'package:inputs/PR589-EXPECTED.json':sha(BIT_PATH)}
+ input_hashes.update({'engines/'+name+'.py':sha(P/'engines'/(name+'.py'))for name in ('moment','base_two_moment','outer')})
+ return dict(status='PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY',kappa=str(k),kappa_decimal=dec(k),complex_lower=str(b),complex_decimal=dec(b),bit_lower=str(c),bit_decimal=dec(c),binding='complex',gain_over_pr635_percent=dec(100*(k/Q(X['gain_baseline_kappa'])-1)),complex_profile=H,provider_counts=invoice['provider_counts'],surcharge_model={'complex':False,'bit':True},conservative_complex_lower=str(conservative_b),conservative_complex_decimal=dec(conservative_b),conservative_kappa=str(conservative_k),conservative_kappa_decimal=dec(conservative_k),conservative_moments=conservative_moments,conservative_bootstrap=conservative_cuts,conservative_outer={n:str(v)for n,v in conservative_outer['strict_constraints'].items()},conservative_controls=conservative_controls,model_controls=model_controls,native_correction_gain=dec(k-conservative_k),template_sha256=owner['template_sha256'],input_sha256=input_hashes,bit_supplier=dict(pr=589,repository='CrocSwap/integer-mult-bounds',commit='a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46',merged_as='b3eb785ac5b4b1ca2beea0f80db078a505626a90',path='research/e8-bit-p111-tuned/tune/EXPECTED.json',git_blob_sha1=BIT_BLOB,word=dict(v=bit_record['word']['v'],decoder_constant=bit_record['word']['decoder_constant'],copy_ranks=bit_record['word']['copy_ranks']),derived_deficit=bit_D,deficit_formula='T(2Kv-L*cst), L=%d T=%d K=%d M=%d'%(BIT_L,BIT_T,BIT_K,BIT_M),replay_scope='Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit.'),moments=moments,bootstrap=cuts,outer={n:str(v)for n,v in outer['strict_constraints'].items()},controls=controls,scope='Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification.')
+if __name__=='__main__':
+ import sys
+ package,C,out=map(Path,sys.argv[1:4]);assert package.resolve()==P and not out.exists()
+ owner_path=C/'audit/OWNERS-AND-PROFILE.json';invoice_path=C/'audit/PREFIX-AND-INVOICE.json'
+ owner,invoice=read(owner_path),read(invoice_path)
+ assert owner['template_sha256']==read(C/'hosted/HOSTED.json')['template_sha256']
+ r=assemble(owner,invoice,sha(owner_path),sha(invoice_path));out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],r['kappa_decimal'])
diff --git a/research/gauge44-slots-t16/code/assembly_controls.py b/research/gauge44-slots-t16/code/assembly_controls.py
new file mode 100644
index 0000000000..096ba9cdfe
--- /dev/null
+++ b/research/gauge44-slots-t16/code/assembly_controls.py
@@ -0,0 +1,260 @@
+"""Independent admission controls for the N-provider native-complex assembly (per-provider controls).
+
+Prepared with OpenAI Codex assistance; Apache-2.0. Mutation receipts are
+rebound to their new owner digest, so unrelated stale hashes cannot conceal
+an incomplete width, provider, orientation, paid-profile or finite check.
+The fresh physical replay remains a separate prerequisite.
+"""
+import argparse
+import copy
+import itertools
+import math
+import hashlib
+import json
+import os
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+
+assert __debug__, 'Assertions required'
+P = Path(__file__).resolve().parent
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+digest = lambda x: hashlib.sha256(json.dumps(x, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+
+
+def verify(owner_path, invoice_path, source_package):
+    os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve())
+    from assemble import assemble
+    owner = json.loads(owner_path.read_text())
+    invoice = json.loads(invoice_path.read_text())
+    baseline = assemble(owner, invoice, sha(owner_path), sha(invoice_path))
+
+    def empty_maps(o, i):
+        i['strict_checks'] = {}
+        i['providers'] = {}
+
+    def understated_stock(o, i):
+        o['physical'] -= 1
+        i['physical'] -= 1
+        i['physical_stock_identity']['coefficient_work'] -= 1
+
+    def changed_profile(o, i):
+        o['paid_profile']['1'] += 2
+        o['paid_profile']['2'] -= 1
+
+    def wrong_orientation(o, i):
+        c = next(c for c in i['selected_calls'] if c['stage'] == 0)
+        c['orientation'] = 'backward'
+        p = i['providers'][c['provider_id']]
+        z = p['local']['backward']
+        c['program_sha256'] = p['program_hashes']['backward']
+        for name in ('events', 'macros', 'real_component_primitives',
+                     'coefficient_work_primitive_count', 'pre_wrappers', 'post_wrappers'):
+            c[name] = z[name]
+        i['selected_real_component_primitives'] = sum(c['real_component_primitives'] for c in i['selected_calls'])
+        i['selected_coefficient_work_primitive_count'] = sum(c['coefficient_work_primitive_count'] for c in i['selected_calls'])
+
+    def understated_prefix(o, i):
+        for p in i['providers'].values():
+            for z in p['local'].values():
+                z['prefix_bits'], z['prefix_l1'] = 1, '1'
+        i['global_prefix_bits'] = 1 + 37 + 144 + 144 + 4
+
+    def reordered_calls(o, i):
+        i['selected_calls'][0], i['selected_calls'][1] = i['selected_calls'][1], i['selected_calls'][0]
+
+    def no_cold_wrappers(o, i):
+        for p in i['providers'].values():
+            p['entering_helpers'] -= 4
+            for z in p['local'].values():z['pre_wrappers'] = z['post_wrappers'] = p['entering_helpers']
+        for c in i['selected_calls']:
+            c['entering_helpers'] = c['pre_wrappers'] = c['post_wrappers'] = i['providers'][c['provider_id']]['entering_helpers']
+        i['wrapper_elementary_factors_charged'] = sum(2*c['pre_wrappers'] for c in i['selected_calls'])*i['factors_per_wrapper']
+
+    controls = [
+        ('empty_certification_maps', empty_maps),
+        ('failed_invoice_status', lambda o, i: i.__setitem__('status', 'FAIL')),
+        ('nonboolean_precision_check', lambda o, i: i['strict_checks'].__setitem__('precision', 'true')),
+        ('wrong_owner_role_count', lambda o, i: o.__setitem__('actual_helper_owner_charts', o['actual_helper_owner_charts'] - 1)),
+        ('understated_physical_stock', understated_stock),
+        ('changed_profile_same_rank_mass', changed_profile),
+        ('insufficient_finite_C0', lambda o, i: i['finite'].__setitem__('required_C0_bits', 210001)),
+        ('missing_finite_check', lambda o, i: i['strict_checks'].pop('halving')),
+        ('wrong_reflected_orientation_selfconsistent_totals', wrong_orientation),
+        ('missing_selected_call', lambda o, i: i['selected_calls'].pop()),
+        ('wrong_selected_primitive_sum', lambda o, i: i.__setitem__('selected_real_component_primitives', i['selected_real_component_primitives'] - 1)),
+        ('wrong_selected_coefficient_work_sum', lambda o, i: i.__setitem__('selected_coefficient_work_primitive_count', i['selected_coefficient_work_primitive_count'] - 1)),
+        ('unpaid_wrapper_factors', lambda o, i: i.__setitem__('wrapper_elementary_factors_charged', i['wrapper_elementary_factors_charged'] - 144)),
+        ('wrong_global_compiler', lambda o, i: i.__setitem__('compiler', 1)),
+        ('wrong_global_adapter_maximum', lambda o, i: i.__setitem__('local_adapters', 1)),
+        ('understated_exact_prefix_and_global_sum', understated_prefix),
+        ('wrong_global_prefix_sum', lambda o, i: i.__setitem__('global_prefix_bits', 224)),
+        ('wrong_row_prefix_reserve', lambda o, i: i.__setitem__('row_prefix_extra', 0)),
+        ('wrong_parent_geometry_charge', lambda o, i: i.__setitem__('unhosted_pervertex', 1)),
+        ('wrong_rebased_geometry_charge', lambda o, i: i.__setitem__('hosted_rebased_pervertex', 1)),
+        ('wrong_complete_pervertex_envelope', lambda o, i: i.__setitem__('conservative_pervertex_used', 1)),
+        ('wrong_prior_added_complete_invoice', lambda o, i: i['retained_prior_overcharge'].__setitem__('added_complete_new_pervertex', 1)),
+        ('wrong_finite_router_bits', lambda o, i: i['finite'].__setitem__('router_bits', 1)),
+        ('wrong_finite_literal_bits', lambda o, i: i['finite'].__setitem__('literal_bits', 1)),
+        ('wrong_finite_physical_stock_bits', lambda o, i: i['finite'].__setitem__('physical_stock_bits', 1)),
+        ('wrong_finite_row_coefficient', lambda o, i: i['finite'].__setitem__('physical_row_coefficient', 1)),
+        ('reordered_complete_calls', reordered_calls),
+        ('understated_explicit_idle_remainders', lambda o, i: o.__setitem__('explicit_idle_remainder_children', o['explicit_idle_remainder_children']-1)),
+        ('understated_actual_chart_types', lambda o, i: o.__setitem__('actual_73column_sigmas', o['actual_73column_sigmas']-1)),
+        ('wrong_cross_replica_role_count', lambda o, i: o.__setitem__('cross_replica_helper_roles', o['cross_replica_helper_roles']-1)),
+        ('old_no_cold_wrapper_counts_selfconsistent', no_cold_wrappers),
+    ]
+
+    def resync(i, c):
+        p = i['providers'][c['provider_id']]
+        c['program_sha256'] = p['program_hashes'][c['orientation']]
+        c['entering_helpers'], c['entrance_rank'] = p['entering_helpers'], p['entrance_rank']
+        for name in ('events','macros','real_component_primitives','coefficient_work_primitive_count','pre_wrappers','post_wrappers'):
+            c[name] = p['local'][c['orientation']][name]
+
+    # Every provider gets the full per-provider control set, substituting a partner provider where needed.
+    for P in PIDS:
+        Qp = partner(P) if len(PIDS)>1 else '__unregistered__'
+        widths = invoice['providers'][P]['widths']
+
+        def forged_program_hash(o, i, P=P):
+            i['providers'][P]['program_hashes']['forward'] = '0' * 64
+            for c in i['selected_calls']:
+                if c['provider_id'] == P:
+                    c['program_sha256'] = '0' * 64
+
+        def wrong_selected_call(o, i, P=P):
+            c = next(c for c in i['selected_calls'] if c['provider_id'] == P)
+            d = next(d for d in i['selected_calls'] if d is not c and (d['provider_id'] != P or len(PIDS)==1) and (d['stage'] - c['stage']) % 2 == 0)
+            c['stage'], d['stage'], c['replica'], d['replica'] = d['stage'], c['stage'], d['replica'], c['replica']
+
+        def stale_program(o, i, P=P, Qp=Qp):
+            p = i['providers'][P]
+            p['program_hashes'] = copy.deepcopy(i['providers'][Qp]['program_hashes'])
+            for c in i['selected_calls']:
+                if c['provider_id'] == P:
+                    c['program_sha256'] = p['program_hashes'][c['orientation']]
+
+        def stale_profile(o, i, P=P, Qp=Qp):
+            p = i['providers'][P]
+            p['paid_profile'] = copy.deepcopy(i['providers'][Qp]['paid_profile'])
+            p['children'] = sum(p['paid_profile'].values())
+
+        def moved(o, i, P=P):
+            a = next(c for c in i['selected_calls'] if c['provider_id'] == P)
+            b = next(c for c in i['selected_calls'] if c['provider_id'] != P and c['orientation'] == a['orientation'])
+            a['provider_id'], b['provider_id'] = b['provider_id'], a['provider_id']
+            resync(i, a); resync(i, b)
+
+        def compensating(o, i, P=P, Qp=Qp):
+            # Two dishonest profiles that cancel exactly in the dispatch-weighted aggregate.
+            g = math.gcd(COUNTS[P], COUNTS[Qp]); dp, dq = COUNTS[Qp] // g, COUNTS[P] // g
+            p, q = i['providers'][P], i['providers'][Qp]
+            p['paid_profile']['1'] += dp; q['paid_profile']['1'] -= dq
+            p['children'] += dp; q['children'] -= dq
+
+        def forged_recipe(o, i, P=P):
+            name = 'CLIFFORD-RECIPES.json'
+            i['providers'][P]['artifacts'][name] = '0'*64
+            o['source_artifacts']['providers/'+P+'/'+name] = '0'*64
+
+        def forged_phase(o, i, P=P):
+            i['providers'][P]['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'] = '0'*64
+            o['provider_phase_semantic_sha256'][P] = i['provider_phase_semantic_sha256'][P] = '0'*64
+
+        controls += [
+            (P + ':missing_provider', lambda o, i, P=P: i['providers'].pop(P)),
+            (P + ':missing_backward_orientation', lambda o, i, P=P: i['providers'][P]['local'].pop('backward')),
+            (P + ':unpaid_scalar_primitive', lambda o, i, P=P: i['providers'][P]['local']['forward'].__setitem__('real_component_primitives', i['providers'][P]['local']['forward']['real_component_primitives'] - 1)),
+            (P + ':wrong_local_artifact_binding', lambda o, i, P=P: i['providers'][P]['artifacts'].__setitem__('LOCAL-PROGRAMS.json.gz', '0' * 64)),
+            (P + ':false_dirty_restoration', lambda o, i, P=P: i['providers'][P]['local']['backward'].__setitem__('all_dirty_helper_columns_restored', False)),
+            (P + ':wrong_declared_provider_count', lambda o, i, P=P: i['provider_counts'].__setitem__(P, i['provider_counts'][P] + 1)),
+            (P + ':wrong_local_compiler', lambda o, i, P=P: i['providers'][P].__setitem__('compiler', 1)),
+            (P + ':wrong_local_adapter_charge', lambda o, i, P=P: i['providers'][P].__setitem__('local_adapters', 1)),
+            (P + ':wrong_local_primitive_bound', lambda o, i, P=P: i['providers'][P].__setitem__('local_primitive_bound', 1)),
+            (P + ':forged_provider_and_call_program_hash', forged_program_hash),
+            (P + ':provider_at_wrong_call', wrong_selected_call),
+            (P + ':stale_partner_program_consistent_call_hashes', stale_program),
+            (P + ':stale_partner_profile_consistent_child_total', stale_profile),
+            (P + ':relocated_against_partner_same_counts', moved),
+            (P + ':compensating_false_profiles_with_' + Qp, compensating),
+            (P + ':synchronized_forged_source_recipe_hash', forged_recipe),
+            (P + ':synchronized_forged_phase_review_semantics', forged_phase),
+        ]
+        if len(PIDS)==1:
+            # Cross-provider substitutions require a second actual supplier.
+            # All single-provider program, phase, profile and dispatch bindings
+            # retain their direct mutations above and in the controller audit.
+            partner_only = {P+':stale_partner_program_consistent_call_hashes',
+                            P+':stale_partner_profile_consistent_child_total',
+                            P+':relocated_against_partner_same_counts',
+                            P+':compensating_false_profiles_with_'+Qp}
+            controls = [(name, fn) for name, fn in controls if name not in partner_only]
+        # Width order and inventory: swap the first helper of every pair of distinct widths (same inventory),
+        # and shift one unit between them (same total).
+        first = {}
+        for h, w in enumerate(widths):
+            first.setdefault(w, h)
+        for wa, wb in itertools.combinations(sorted(first), 2):
+            def swap(o, i, P=P, a=first[wa], b=first[wb]):
+                w = i['providers'][P]['widths']; w[a], w[b] = w[b], w[a]
+            def shift(o, i, P=P, a=first[wa], b=first[wb]):
+                w = i['providers'][P]['widths']; w[a] += 1; w[b] -= 1
+            controls.append((P + ':width_order_swap_%d_%d' % (wa, wb), swap))
+            controls.append((P + ':width_inventory_shift_%d_%d' % (wa, wb), shift))
+        for h in SPOT:
+            def cold_swap(o, i, P=P, h=h):
+                w = i['providers'][P]['widths']; j = w.index(9 if w[h] != 9 else 8); w[h], w[j] = w[j], w[h]   # never the identity
+            controls.append((P + ':cold_helper_width_swap_%d' % h, cold_swap))
+    rejected = []
+    accepted = []
+    for name, mutate in controls:
+        o, i = copy.deepcopy(owner), copy.deepcopy(invoice)
+        mutate(o, i)
+        oh = digest(o)
+        i['owner_audit_sha256'] = oh
+        try:
+            assemble(o, i, oh, digest(i))
+        except (AssertionError, KeyError):
+            rejected.append(name)
+        else:
+            # Discovery has no pinned values to reject spec-only mutations; the strict run must reject every control.
+            if not DISCOVER:
+                raise AssertionError('Invalid admission receipt accepted: ' + name)
+            accepted.append(name)
+    try:
+        assemble(owner, invoice, '0' * 64, sha(invoice_path))
+    except AssertionError:
+        rejected.append('wrong_owner_receipt_hash')
+    else:
+        raise AssertionError('Wrong owner digest accepted')
+    pin('expected.assembly_controls_rejected', len(rejected))
+    assert baseline['controls'] == ['next_grid', 'zero_eta', 'zero_beta', 'unit_beta']
+    assert baseline['conservative_controls'] == baseline['controls']
+    assert baseline['surcharge_model'] == {'complex': False, 'bit': True}
+    assert len(baseline['model_controls']) == 2
+    return dict(
+        status='PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS',
+        valid_receipt_kappa=baseline['kappa'],
+        input_sha256=baseline['input_sha256'],
+        assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'),
+        rejected_controls=rejected,
+        discovery_accepted_controls=accepted,
+        exact_outer_controls=baseline['controls'],
+        conservative_outer_controls=baseline['conservative_controls'],
+        recurrence_model_controls=baseline['model_controls'],
+        scope='Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay.',
+    )
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--source-package', type=Path, required=True)
+    ap.add_argument('--owner', type=Path, required=True)
+    ap.add_argument('--invoice', type=Path, required=True)
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    assert not a.out.exists()
+    result = verify(a.owner, a.invoice, a.source_package)
+    a.out.write_text(json.dumps(result, indent=2) + '\n')
+    print(result['status'], len(result['rejected_controls']))
diff --git a/research/gauge44-slots-t16/code/audit_allcold.py b/research/gauge44-slots-t16/code/audit_allcold.py
new file mode 100644
index 0000000000..923bf7b675
--- /dev/null
+++ b/research/gauge44-slots-t16/code/audit_allcold.py
@@ -0,0 +1,254 @@
+"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit.
+Imports no emitter, optimizer, expander, edge-coloring, or source hosting code.
+CLI: BASE HOSTED REPORT [--mutation-controls]
+Each provider is independently read from BASE/providers, never from a baseline width histogram.
+OpenAI Codex two-provider width-seven extension; retains all inherited independent controller checks.
+The exact 63 width-seven and 9 plain calls are frozen below.
+"""
+import sys,json,gzip,hashlib,copy
+assert __debug__, 'Assertions must remain enabled'
+from pathlib import Path
+from collections import Counter,defaultdict
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+from generated_identity import artifact_identities
+BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz')
+ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json')
+ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json')
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+provider_ids=PIDS
+providers={};registry={};phase_semantic_hashes={};artifact_semantic_hashes={}
+required_artifacts={'work/complex-nine-native/DATA-PHASES.json'}
+provider_files=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+ 'INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json')
+for pid in provider_ids:
+ p=BASE/'providers'/pid
+ c=read(p/'CANONICAL-WORD.json.gz');checks=read(p/'LOCAL-CHECKS.json')
+ programs=read(p/'LOCAL-PROGRAMS.json.gz');replay=read(p/'INDEPENDENT-LOCAL-REPLAY.json')
+ phase=read(p/'CLIFFORD-REVIEW.json');adapters=read(p/'RESIDUAL-ADAPTERS.json')['recipes']
+ widths=[len(c['frames'][c['final'][2*c['v']+h]])-len(c['frames'][c['start'][2*c['v']+h]])for h in range(c['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths();pin('providers.%s.inventory'%pid,{str(k):v for k,v in sorted(Counter(widths).items())})
+ canonical_sha=sha(p/'CANONICAL-WORD.json.gz');programs_sha=sha(p/'LOCAL-PROGRAMS.json.gz')
+ assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ assert replay['canonical_word_sha256']==canonical_sha and replay['local_programs_sha256']==programs_sha
+ assert replay['v']==c['v'] and replay['helpers']==c['R']
+ assert set(programs)==set(checks)==set(replay['local'])==set(replay['paid_profiles'])=={'forward','backward'}
+ for orientation,events in programs.items():
+  ck=checks[orientation];rr=replay['local'][orientation]
+  assert hashlib.sha256(json.dumps(events,sort_keys=True,separators=(',',':')).encode()).hexdigest()==ck['sha256']
+  assert ck['events']==len(events) and ck['all_columns']==2*c['v']+c['R']
+  assert ck['private_centers_cleared'] and ck['private_coefficient_stream_cleared_after_each_macro']
+  assert rr['all_exact_columns']==2*c['v']+c['R'] and rr['private_work_erased']
+  literal=Counter(e[-1]for e in events if e[0]in('climb','center'))
+  assert dict(literal)=={int(r):n for r,n in ck['paid_profile'].items()}=={int(r):n for r,n in c['local_profile'].items()}
+  assert ck['paid_profile']==replay['paid_profiles'][orientation]
+ assert phase['canonical_word_sha256']==canonical_sha and phase['recipe_sha256']==sha(p/'CLIFFORD-RECIPES.json')
+ assert phase['all_child_equalities_include_global_phase']
+ artifact_semantic_hashes[pid]=artifact_identities(p)
+ pin('providers.%s.artifact_semantic_sha256'%pid,artifact_semantic_hashes[pid])
+ phase_semantic_hashes[pid]=artifact_semantic_hashes[pid]['CLIFFORD-REVIEW.json']
+ for h,w in enumerate(widths):
+  assert 0<w<=c['h']
+  f=c['start'][2*c['v']+h];u=c['final'][2*c['v']+h]
+  # COLD-HPE: a cold helper (f == 0) may end below FULL too; its wrapper is the '0:U' recipe (E = bottom instance of #593)
+  if u!=1:   # HPE: wrapper for T_U T_E^-1, keyed 'E:U', rank |U|-|E|
+   a=adapters['%d:%d'%(f,u)]
+   assert a['frame']==f and a['terminal']==u and a['vectors']==c['frames'][f] and a['terminal_vectors']==c['frames'][u]
+   assert a['rank']==w==len(c['frames'][u])-len(c['frames'][f]) and a['entrance_rank']==len(c['frames'][f]) and a['terminal_rank']==len(c['frames'][u])<c['h']
+  elif w<c['h']:
+   a=adapters[str(f)]
+   assert a['frame']==f and a['vectors']==c['frames'][f] and a['rank']==w and a['entrance_rank']==c['h']-w
+ providers[pid]=dict(canonical=c,checks=checks,widths=widths)
+ registry[pid]=dict(local_programs=programs,canonical_word_sha256=canonical_sha,local_programs_sha256=programs_sha,
+  local_program_checks=checks,exact_local_clifford_recipe_sha256=sha(p/'CLIFFORD-RECIPES.json'),
+  residual_adapter_sha256=sha(p/'RESIDUAL-ADAPTERS.json'),
+  **{k:c[k]for k in('v','h','R','ports','centers')},widths=widths)
+ required_artifacts.update('providers/'+pid+'/'+fn for fn in provider_files)
+canon=providers[provider_ids[0]]['canonical'];V=canon['v'];R=canon['R'];N=2*V+R;CENTRES=len(canon['centers'])
+assert V==112 and canon['h']==9
+assert all(providers[p]['canonical'][k]==canon[k]for p in provider_ids for k in('v','h','R','ports'))
+# Independently compare ordered common frames; exact local carrier names remain
+# bound to each canonical word, program, phase receipt and residual adapters.
+for p in provider_ids:
+ c=providers[p]['canonical']
+ assert len(c['centers'])==len(c['center_frames'])==8
+ assert [c['frames'][f]for f in c['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+parent_canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz')
+assert [canon['frames'][f]for f in canon['center_frames']]==[parent_canon['frames'][f]for f in parent_canon['center_frames']]
+assert required_artifacts<=set(summary['source_artifacts'])
+prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=16;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=144;HOSTED=CALLS*R
+# The selected map is an input to check, not a claim from the emitter.
+
+assert len(DISPATCH)==144 and Counter(DISPATCH.values())==COUNTS
+expected_provider=lambda stage,replica:DISPATCH[stage,replica]
+
+def orthobasis(port):
+ q=canon['ports'][port];z=next(i for i in range(9)if(q>>i)&1==0);a=q^(1<<z);order=list(range(9));order[z],order[0]=order[0],order[z]
+ b=[(1<<i)^(a if a>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ assert len(b)==73 and all((x&y).bit_count()%2==int(i==j)for i,x in enumerate(b)for j,y in enumerate(b));return b
+bases=[orthobasis(p)for p in range(V)]
+
+def audit(t):
+ assert(t['live'],t['physical'])==(DATA,PHYSICAL)
+ assert t['local_providers']==registry and t['recipe']==parent['recipe']and 'each local invocation completes before the next' in t['loop_order'].lower()
+ assert not any(k in t for k in('local_programs','exact_local_clifford_recipe_sha256','residual_adapter_sha256'))
+ assert len(t['calls'])==144 and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
+ for key in('exact_data_phase_recipe_sha256','adapter_policy'):assert t[key]==parent[key]
+ assert t['exact_data_phase_recipe_sha256']==sha(BASE/'work/complex-nine-native/DATA-PHASES.json')
+ # Independently project the literal schedule onto every data replica.
+ src=parent['execution_schedule'];assert t['async_schedule']['source_schedule']==src
+ assert t['async_schedule']['source_call_order']==[[c['stage'],c['replica']]for c in parent['calls']]
+ order=[(c['stage'],c['replica'])for c in t['calls']]
+ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==144
+ all_local=[];perrep={r:[]for r in range(16)};globals_=[]
+ for e in t['execution_schedule']:
+  j=e['source_event'];old=copy.deepcopy(src[j])
+  if 'replica'in e:
+   r=e['replica'];assert 0<=r<16 and j<30;perrep[r].append(j)
+   expected=old|dict(source_event=j,replica=r,replicas=[r],time=e['time'])
+   if e['kind']=='local_cover_sweep':expected['provider_id']=expected_provider(e['stage'],r)
+   assert e==expected
+   assert 0<=e['time']<144 and order[e['time']][1]==r
+   if e['kind']=='local_cover_sweep':
+    assert order[e['time']]==(e['stage'],r);all_local.append((e['stage'],r,e['time']))
+  else:
+   globals_.append(j);expected=old|dict(source_event=j)
+   if e['kind']=='bank_padding_cover_sweep':expected['families']=[DATA,DATA]
+   if e['kind']=='translate_every_live_family':expected.update(families=[0,DATA],charged_calls_per_cover=DATA)
+   assert e==expected
+ assert all(v==list(range(30))for v in perrep.values()) and globals_==[30,31]
+ assert all_local==[(st,r,i)for i,(st,r)in enumerate(order)]
+ assert all('replica'in e for e in t['execution_schedule'][:-2])
+ assert [e['source_event']for e in t['execution_schedule'][-2:]]==[30,31]
+ # Local cover calls are indivisible; a block then runs the source events
+ # up to that replica's next local invocation.
+ block=-1
+ for e in t['execution_schedule'][:-2]:
+  if e['kind']=='local_cover_sweep':block+=1
+  assert e['time']==block
+ assert t['bank_padding']==dict(parent['bank_padding'],families=[],children=[])
+ assert t['cover_final_correction']==dict(parent['cover_final_correction'],families=[0,DATA],charged_calls_per_cover=DATA)
+ assert t['private_namespace']=={'centers':[DATA,DATA+CENTRES],'reserved_tableau':[DATA+CENTRES,DATA+CENTRES+R],'coefficient':[DATA+CENTRES+R,PHYSICAL]}
+ # Actual physical touch intervals include every individual bridge.
+ pairs={};sides={};windows={};last={};callpos={};stagepair={e['stage']:e['pair']for e in parent['recipe']if e['kind']=='local'}
+ for pos,e in enumerate(t['execution_schedule']):
+  if 'replica'not in e:continue
+  rep=e['replica']
+  if e['kind']=='local_cover_sweep':
+   pair=stagepair[e['stage']];callpos[e['stage'],rep]=pos;last[rep,pair]=pos
+  elif e['kind']=='bridge':last[rep,e['src']]=last[rep,e['dst']]=pos
+  elif e['kind']=='idle_cover_sweep':
+   for side,i in enumerate(e['child_indices']):
+    if i not in prank:continue
+    pairs[i]=e['pair'];sides[i]=side;windows[rep,i]=(last.get((rep,e['pair']),-1),pos)
+ used=defaultdict(set);roles={};paid=Counter();sigmas={};digest=hashlib.sha256();entering=0;cross=0;touches=defaultdict(list)
+ for call in t['calls']:
+  old=next(z for z in parent['calls']if(z['stage'],z['replica'])==(call['stage'],call['replica']))
+  assert {k:v for k,v in call.items()if k not in('owners','time','provider_id','local_program_sha256')}=={k:v for k,v in old.items()if k not in('owners','local_program_sha256')}
+  pid=expected_provider(call['stage'],call['replica']);assert call['provider_id']==pid
+  width=providers[pid]['widths'];checks=providers[pid]['checks']
+  assert call['local_program_sha256']==checks[call['orientation']]['sha256']
+  s,rep,pair=call['stage'],call['replica'],call['pair'];assert call['time']==t['async_schedule']['order'].index([s,rep]);own=call['owners'];assert len(own)==N and len({f for f,rt in own})==N and all(0<=f<DATA for f,rt in own)
+  assert own[:(2*V)]==old['owners'][:(2*V)]
+  for h,(family,route)in enumerate(own[(2*V):]):
+   w=width[h];typ,i,off=route[:3];ownerrep,sub=divmod(family,(8*V));fampair,sub=divmod(sub,(2*V));side,port=divmod(sub,V)
+   assert windows[ownerrep,i][0]<callpos[s,rep]<windows[ownerrep,i][1] and fampair==pairs[i] and side==sides[i] and 0<=off and off+w<=prank[i]
+   B=bases[port];pend=[int(x)for x in ph['recipes'][port]['idle_children'][i]['orthogonal_axes']];assert len(pend)==prank[i]
+   occ=[B.index(v)for v in pend[off:off+w]];sp=[j for j in range(M)if j not in occ][:9-w]
+   assert route==([3,i,off]if w==9 else[4,i,off,w,sp]);assert len(set(occ+sp))==9
+   order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert sorted(order)==list(range(M));sigma=[B[j]for j in order]
+   assert sigma[:w]==pend[off:off+w]and sigma[w:9]==[B[j]for j in sp]
+   sh=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sh]=sigma;digest.update(json.dumps([s,rep,h,family,sh],separators=(',',':')).encode()+b'\n')
+   key=(i,ownerrep,port);cells=set(range(off,off+w));assert not used[key]&cells;used[key]|=cells
+   role=(s,rep,h);assert role not in roles;roles[role]=dict(stage=s,replica=rep,helper=h,family=family,owner_replica=ownerrep,child=i,copy=ownerrep*V+port,port=port,offset=off,width=w)
+   touches[family].append((s,rep,h));entering+=w<9;cross+=rep!=ownerrep
+  for r,n in checks[call['orientation']]['paid_profile'].items():paid[int(r)]+=n
+ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(16)for h in range(R)}
+ # The frozen pooled metadata must bind the actual serialized owner maps.
+ assert len(t['hosting']['pooled_slots'])==HOSTED
+ for z in t['hosting']['pooled_slots']:
+  key=(z['stage'],z['replica'],z['helper']);assert key in roles
+  assert {k:z[k]for k in roles[key]}==roles[key]
+ assert len({(z['stage'],z['replica'],z['helper'])for z in t['hosting']['pooled_slots']})==HOSTED
+ rem={};wanted=[]
+ for old in parent['idle_children']:
+  i,port=old['child'],old['port']
+  for rep in range(T):
+   u=used[i,rep,port];assert u==set(range(len(u)));r=old['rank']-len(u)
+   if r:
+    f=rep*(8*V)+(2*pairs[i]+sides[i])*V+port;wanted.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=r,hosted=len(u),pending_offset=len(u)));paid[r]+=1
+ assert t['idle_children']==wanted
+ mass=sum(r*n for r,n in paid.items());assert73=73*DATA-mass;assert assert73==5120 and 73**2>2*max(paid)**2
+ return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=144)
+
+r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256']
+assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items())
+controls=[]
+def reject(name,mut):
+ if '--mutation-controls' not in sys.argv[4:]:return
+ q=copy.deepcopy(ct);mut(q)
+ try:audit(q)
+ except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name)
+ else:raise AssertionError('ACCEPTED '+name)
+enter=lambda q:next(o for c in q['calls']for o in c['owners'][(2*V):]if o[1][0]==4)
+reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__((2*V+1),q['calls'][0]['owners'][(2*V)]))
+reject('helper on active data family',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,q['calls'][0]['owners'][0][0]))
+reject('owner in private namespace',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,DATA))
+reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1))
+reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72))
+reject('omit idle remainder',lambda q:q['idle_children'].pop())
+reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1))
+# Single-provider dispatch still has all source/program/width binding controls.
+if len(provider_ids)==1:
+ P=provider_ids[0]
+ at_p=lambda q:next(c for c in q['calls']if c['provider_id']==P)
+ narrow=next(h for h in range(R)if providers[P]['widths'][h]<9)
+ reject(P+': wrong provider at its invocation',lambda q:at_p(q).__setitem__('provider_id','__unregistered__'))
+ reject(P+': stale per-call local program hash',lambda q:at_p(q).__setitem__('local_program_sha256','0'*64))
+ reject(P+': stale serialized provider program',lambda q:q['local_providers'][P]['local_programs']['forward'].pop())
+ reject(P+': unbound residual adapter hash',lambda q:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64))
+ reject(P+': wrong provider width registry',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,providers[P]['widths'][narrow]-1))
+ reject(P+': wrong per-call residual width',lambda q:at_p(q)['owners'][2*V+narrow][1].__setitem__(3,at_p(q)['owners'][2*V+narrow][1][3]-1))
+ reject(P+': wrong sweep provider',lambda q:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep').__setitem__('provider_id','__unregistered__'))
+ reject(P+': entering helper width silently restored to nine',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,9))
+else:
+ # Per-provider substitution controls: every provider is swapped against a partner provider.
+ for P in provider_ids:
+  Qp=partner(P)
+  at_p=lambda q,P=P:next(c for c in q['calls']if c['provider_id']==P)
+  diff=[h for h in range(R)if providers[P]['widths'][h]!=providers[Qp]['widths'][h]]
+  narrow=next(h for h in range(R)if providers[P]['widths'][h]<9)
+  reject(P+': wrong provider at its invocation',lambda q,P=P,Qp=Qp,at_p=at_p:at_p(q).__setitem__('provider_id',Qp))
+  reject(P+': stale per-call local program hash',lambda q,Qp=Qp,at_p=at_p:at_p(q).__setitem__('local_program_sha256',registry[Qp]['local_program_checks'][at_p(q)['orientation']]['sha256']))
+  reject(P+': stale serialized provider program',lambda q,P=P,Qp=Qp:q['local_providers'][P].__setitem__('local_programs',registry[Qp]['local_programs']))
+  reject(P+': unbound residual adapter hash',lambda q,P=P:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64))
+  if diff:reject(P+': partner width in provider width registry',lambda q,P=P,Qp=Qp,h=diff[0]:q['local_providers'][P]['widths'].__setitem__(h,providers[Qp]['widths'][h]))
+  reject(P+': wrong per-call residual width',lambda q,at_p=at_p,h=narrow:at_p(q)['owners'][2*V+h][1].__setitem__(3,at_p(q)['owners'][2*V+h][1][3]-1))
+  reject(P+': wrong sweep provider',lambda q,P=P,Qp=Qp:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep'and DISPATCH[e['stage'],e['replica']]==P).__setitem__('provider_id',Qp))
+  reject(P+': entering helper width silently restored to nine',lambda q,P=P,h=narrow:q['local_providers'][P]['widths'].__setitem__(h,9))
+
+report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=DATA,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=5120,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,mutation_controls_run='--mutation-controls' in sys.argv[4:],provider_phase_semantic_sha256=phase_semantic_hashes,provider_artifact_semantic_sha256=artifact_semantic_hashes,widths_by_provider={pid:dict(sorted(Counter(providers[pid]['widths']).items()))for pid in provider_ids},provider_counts=dict(Counter(c['provider_id']for c in ct['calls'])),all_provider_program_phase_and_wrapper_bindings=True,scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations.')
+REPORT.parent.mkdir(parents=True,exist_ok=True)
+REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2))
+
+owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=DATA,physical=PHYSICAL,rank_mass=r['mass'],deficit=5120,hosted_residuals=HOSTED,banked_residuals=0,all_live_owners_per_call_distinct=True,owners_per_call=N,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],provider_phase_semantic_sha256=phase_semantic_hashes,provider_artifact_semantic_sha256=artifact_semantic_hashes,controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest())
+(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n')
+
+# Literal residual frames are a compact export of the already checked offsets,
+# not another global replay. Every row names its actual inherited axes.
+frames=[]
+for z in ct['idle_children']:
+ axes=list(map(int,ph['recipes'][z['port']]['idle_children'][z['child']]['orthogonal_axes']))
+ tail=axes[z['pending_offset']:]
+ assert len(tail)==z['rank']
+ frames.append(dict(z,orthogonal_axes=tail))
+frame_raw=json.dumps(frames,sort_keys=True,separators=(',',':')).encode()
+portable=bytearray(gzip.compress(frame_raw,mtime=0));portable[9]=255
+(OUT/'IDLE-REMAINDER-FRAMES.json.gz').write_bytes(bytes(portable))
+frame_receipt=dict(status='PASS_LITERAL_IDLE_REMAINDER_FRAMES',template_sha256=summary['template_sha256'],
+ uncompressed_frames_sha256=hashlib.sha256(frame_raw).hexdigest(),children=len(frames),
+ rank_profile=dict(sorted(Counter(z['rank']for z in frames).items())),
+ source_data_phase_sha256=hashlib.sha256((BASE/'work/complex-nine-native/DATA-PHASES.json').read_bytes()).hexdigest(),
+ scope='Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child.')
+(REPORT.parent/'IDLE-REMAINDER-FRAMES.json').write_text(json.dumps(frame_receipt,indent=2)+'\n')
diff --git a/research/gauge44-slots-t16/code/bind_providers_portable.py b/research/gauge44-slots-t16/code/bind_providers_portable.py
new file mode 100644
index 0000000000..97e28da17e
--- /dev/null
+++ b/research/gauge44-slots-t16/code/bind_providers_portable.py
@@ -0,0 +1,67 @@
+"""Bind freshly verified plain and width-seven four-cold providers to the frozen literal owner plan.
+Prepared with OpenAI Codex assistance; Apache-2.0. All byte-stable native
+files are pinned to the plan. Only validated phase-receipt timing/serialization
+and directory fields are rebound; no dispatch, width or owner choice changes.
+"""
+import argparse,copy,gzip,hashlib,json,shutil
+from collections import Counter
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+from generated_identity import artifact_identities
+assert __debug__, 'Assertions required'
+ap=argparse.ArgumentParser(description=__doc__)
+for name in ('baseline','plan','out'):ap.add_argument('--'+name,type=Path,required=True)
+ap.add_argument('--provider',action='append',required=True,help='PID=DIR');a=ap.parse_args();assert not a.out.exists();a.out.mkdir(parents=True)
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+base=a.out/'base';shutil.copytree(a.baseline/'complex-global/base',base)
+ap2=dict(x.split('=',1)for x in a.provider);dirs={k:Path(v)for k,v in ap2.items()};assert set(dirs)==set(PIDS)
+for pid,src in dirs.items():shutil.copytree(src,base/'providers'/pid)
+pin('data.plan_sha256',sha(a.plan))
+plan=read(a.plan);original=copy.deepcopy(plan);sources={};helpers=set()   # R: helper count per provider word; all providers must agree
+assert set(plan['provider_registry'])==set(dirs)
+assert {(c['stage'],c['replica']):c['provider']for c in plan['provider_calls']}==DISPATCH,'PLAN dispatch differs from spec dispatch'
+stable=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json')
+for pid,desc in plan['provider_registry'].items():
+ d=base/'providers'/pid
+ word,program,checks,native,phase=[read(d/name)for name in('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-REVIEW.json')]
+ assert (word['v'],word['h'],len(word['centers']))==(112,9,8) and type(word['R']) is int and word['R']>0;helpers.add(word['R'])
+ assert word['ports']==desc['ports'] and word['centers']==desc['centers']
+ widths=[len(word['frames'][word['final'][r]])-len(word['frames'][word['start'][r]])for r in range(2*112,2*112+word['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths()
+ assert widths==desc['widths'];pin('providers.%s.inventory'%pid,{str(k):v for k,v in sorted(Counter(widths).items())})
+ assert native['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ pin('providers.%s.native_negative_controls'%pid,len(native['negative_controls_rejected']))
+ assert native['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and native['local_programs_sha256']==sha(d/'LOCAL-PROGRAMS.json.gz')
+ assert phase['status']=='PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES'
+ assert phase['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and phase['recipe_sha256']==sha(d/'CLIFFORD-RECIPES.json')
+ assert phase['all_child_equalities_include_global_phase'] is True and phase['endpoint_adapters']==224
+ pin('providers.%s.phase_edges'%pid,phase['directed_edges'])
+ assert set(program)==set(checks)=={'forward','backward'}
+ expected={int(r):n for r,n in checks['forward']['paid_profile'].items()};pin('providers.%s.expected_profile'%pid,checks['forward']['paid_profile'])
+ for orientation,events in program.items():
+  profile=Counter()
+  for e in events:
+   if e[0]=='climb':profile[e[5]]+=1
+   elif e[0]=='center':profile[e[4]]+=1
+  assert dict(profile)==expected=={int(r):n for r,n in checks[orientation]['paid_profile'].items()}=={int(r):n for r,n in native['paid_profiles'][orientation].items()}
+  assert hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest()==checks[orientation]['sha256']
+ identities=artifact_identities(d)
+ pin('providers.%s.artifact_semantic_sha256'%pid,identities)
+ assert identities==desc['artifact_semantic_sha256']
+ for name in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):
+  assert sha(d/name)==desc['artifact_sha256'][name],(pid,name,'changed non-reference artifact')
+ for c in plan['provider_calls']:
+  if c['provider']==pid:
+   assert c['orientation']==('forward'if c['stage']%2==0 else'backward')
+   assert c['local_program_sha256']==checks[c['orientation']]['sha256']
+ desc['directory']='providers/'+pid
+ desc['artifact_sha256']={name:sha(d/name)for name in desc['artifact_sha256']}
+ sources[pid]=dict(artifact_sha256=desc['artifact_sha256'],canonical_content_sha256=hashlib.sha256(json.dumps(word,sort_keys=True,separators=(',',':')).encode()).hexdigest(),all_phase_edges=phase['directed_edges'])
+assert len(helpers)==1,'providers disagree on helper count R: %s'%sorted(helpers)
+plan['runtime_source_plan_sha256']=sha(a.plan)
+(a.out/'PLAN.json').write_text(json.dumps(plan,indent=2)+'\n')
+receipt=dict(status='PASS_FROZEN_048_ALLCOLD_DISPATCH_FRESH_PROVIDER_BINDING',source_plan_sha256=sha(a.plan),runtime_plan_sha256=sha(a.out/'PLAN.json'),providers=sources,only_rebound_fields=['provider_registry.directory','provider_registry.artifact_sha256','runtime_source_plan_sha256'])
+(a.out/'BINDING.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(receipt['status'])
diff --git a/research/gauge44-slots-t16/code/bit_supplier_controls.py b/research/gauge44-slots-t16/code/bit_supplier_controls.py
new file mode 100644
index 0000000000..e86b8527b4
--- /dev/null
+++ b/research/gauge44-slots-t16/code/bit_supplier_controls.py
@@ -0,0 +1,111 @@
+"""Negative controls for the cited PR589 bit supplier and its derived rank-mass deficit.
+
+Apache-2.0. Each control mutates one input of the changed bit-supplier sites in assemble.py (the pinned record, the
+deficit derivation from the word's parameters, the profile/live binding, the claimed endpoint) and runs the unchanged
+assemble() on the fresh owner/invoice receipts. Every control must be rejected; the unmutated run must pass.
+`revert_hardcoded_9984` restores the PR543 constant the parent package hard-coded: with PR589's word it must fail.
+"""
+import argparse
+import copy
+import hashlib
+import json
+import os
+import tempfile
+from fractions import Fraction as Q
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+
+assert __debug__, 'Assertions required'
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def verify(owner_path, invoice_path, source_package):
+    os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve())
+    import assemble as A
+    owner = json.loads(owner_path.read_text())
+    invoice = json.loads(invoice_path.read_text())
+    args = (owner, invoice, sha(owner_path), sha(invoice_path))
+    baseline = A.assemble(*args)
+    data = A.BIT_PATH.read_bytes()
+    record = A.load_bit(data)
+    word = record['word']
+    assert A.bit_deficit(word, record['nine']['bit']['live']) == 10272 == 32 * (8 * 111 - 9 * 63)
+
+    real_load, real_deficit = A.load_bit, A.bit_deficit
+
+    def with_record(mutate):
+        def load(d):
+            r = copy.deepcopy(real_load(d)); mutate(r); return r
+        return load
+
+    def shift_profile(r):  # one rank-1 child becomes rank 2: rank mass +1, totals unchanged
+        p = r['nine']['profile']; p['1'] -= 1; p['2'] += 1; r['nine']['bit']['rank_mass'] += 1
+
+    bumped = data.replace(record['nine']['bit_lower'].encode(),
+                          str(Q(record['nine']['bit_lower']) + Q(1, 10**24)).encode(), 1)
+    assert bumped != data
+    pr543 = (source_package / 'inputs/PR543-EXPECTED.json').read_bytes()
+    controls = [
+        # deficit site: the parent's hard-coded constant, restored
+        ('revert_hardcoded_9984', dict(bit_deficit=lambda w, live: 9984)),
+        # deficit site: each word parameter perturbed alone
+        ('ports_112', dict(load_bit=with_record(lambda r: r['word'].__setitem__('v', 112)))),
+        ('decoder_constant_64_copy_ranks_unchanged', dict(load_bit=with_record(lambda r: r['word'].__setitem__('decoder_constant', 64)))),
+        # v=111, cst=64 derives 32*(888-576)=9984: consistent word, wrong for the priced profile
+        ('decoder_constant_64_with_one_copy_rank_8', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('decoder_constant', 64), r['word']['copy_ranks'].__setitem__(0, 8))))),
+        ('eight_retained_totals', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('copy_ranks', [7] * 8), r['word'].__setitem__('decoder_constant', 56))))),
+        ('live_minus_one', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('live', r['nine']['bit']['live'] - 1)))),
+        # profile binding: same totals, rank mass +1
+        ('profile_rank_mass_plus_one', dict(load_bit=with_record(shift_profile))),
+        ('profile_rank_mass_receipt_mismatch', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('rank_mass', r['nine']['bit']['rank_mass'] + 1)))),
+        # endpoint: the next 1e-24 grid point
+        ('bit_lower_next_grid', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('bit_lower', str(Q(r['nine']['bit_lower']) + Q(1, 10**24)))))),
+        ('not_nine_stage_record', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('pipeline', r['nine']['pipeline'].replace('nine-stage', 'eleven-stage'))))),
+        # pinned-input site: tampered bytes and the parent's PR543 file under the PR589 pin
+        ('tampered_bytes_next_grid', dict(read=bumped)),
+        ('pr543_file_under_pr589_pin', dict(read=pr543)),
+    ]
+    rejected = []
+    scratch = Path(tempfile.mkdtemp(prefix='bitctl-'))
+    for name, patch in controls:
+        saved_path = A.BIT_PATH
+        try:
+            if 'read' in patch:
+                tmp = scratch / (name + '.json'); tmp.write_bytes(patch['read']); A.BIT_PATH = tmp
+            A.load_bit = patch.get('load_bit', real_load)
+            A.bit_deficit = patch.get('bit_deficit', real_deficit)
+            try:
+                A.assemble(*args)
+            except (AssertionError, KeyError):
+                rejected.append(name)
+            else:
+                raise AssertionError('Invalid bit supplier accepted: ' + name)
+        finally:
+            A.load_bit, A.bit_deficit, A.BIT_PATH = real_load, real_deficit, saved_path
+            if 'read' in patch:
+                tmp.unlink()
+    scratch.rmdir()
+    assert rejected == [n for n, _ in controls]
+    again = A.assemble(*args)
+    assert again['kappa'] == baseline['kappa'] and again['bit_lower'] == baseline['bit_lower']
+    return dict(
+        status='PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS',
+        kappa=baseline['kappa_decimal'], bit_lower=baseline['bit_lower'], bit_decimal=baseline['bit_decimal'],
+        binding=baseline['binding'], bit_supplier=baseline['bit_supplier'],
+        derived_deficit=baseline['bit_supplier']['derived_deficit'],
+        rejected_controls=rejected,
+        assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'),
+    )
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--source-package', type=Path, required=True)
+    ap.add_argument('--owner', type=Path, required=True)
+    ap.add_argument('--invoice', type=Path, required=True)
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    assert not a.out.exists()
+    result = verify(a.owner, a.invoice, a.source_package)
+    a.out.write_text(json.dumps(result, indent=2) + '\n', newline='\n')
+    print(result['status'], len(result['rejected_controls']))
diff --git a/research/gauge44-slots-t16/code/emit_allcold.py b/research/gauge44-slots-t16/code/emit_allcold.py
new file mode 100644
index 0000000000..28a08a79da
--- /dev/null
+++ b/research/gauge44-slots-t16/code/emit_allcold.py
@@ -0,0 +1,150 @@
+"""Two-provider width-seven whole-owner derivative, adapted with OpenAI Codex assistance.
+Based on PR514 and its credited PR484/507 lineage.
+CLI: --base VERIFIED_VARIANT --owners ASYNC-OWNERS.json.gz --plan ASYNC-PLAN.json --out OUT
+No optimizer or unpublished word builder runs. The frozen map explicitly names
+one whole helper per family per complete invocation, plus borrowed spectators.
+"""
+import sys,json,gzip,hashlib,copy,argparse
+from pathlib import Path
+from collections import Counter,defaultdict
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+parser=argparse.ArgumentParser(description=__doc__)
+parser.add_argument('--base',type=Path,required=True);parser.add_argument('--owners',type=Path,required=True);parser.add_argument('--plan',type=Path,required=True);parser.add_argument('--out',type=Path,required=True)
+a=parser.parse_args();BASE,MAP,PLAN,OUT=(p.resolve()for p in(a.base,a.owners,a.plan,a.out));assert not OUT.exists();OUT.mkdir(parents=True)
+class OH:
+ @staticmethod
+ def idle_basis(q):
+  z=next(i for i in range(9)if not(q>>i)&1);u=q^(1<<z);order=list(range(9));order[0],order[z]=order[z],order[0]
+  return[(1<<i)^(u if u>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ @staticmethod
+ def spectators(q,pending,off,w):
+  B=OH.idle_basis(q);occ=[B.index(v)for v in pending[off:off+w]]
+  return[j for j in range(73)if j not in occ][:9-w]
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+assert hashlib.sha256(MAP.read_bytes()).hexdigest()==SPEC['data']['owners_sha256'],'OWNERS not pinned by spec'
+plan=read(PLAN);assert plan['runtime_source_plan_sha256']==SPEC['data']['plan_sha256'],'PLAN not pinned by spec'
+call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==144;at={x:i for i,x in enumerate(call_order)}
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');t=copy.deepcopy(parent);canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');roles=read(MAP);T=16;V=canon['v'];M=73;R0=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)   # R0: parent (split-centres) helper count
+assert(len(canon['start']),len(ph['recipes']))==(2*V+R0,V)
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+provider_files=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json')
+registry={};source_artifacts={'work/complex-nine-native/DATA-PHASES.json':sha(BASE/'work/complex-nine-native/DATA-PHASES.json')}
+for provider_id in sorted(plan['provider_registry']):
+ assert provider_id in PIDS
+ directory=BASE/'providers'/provider_id
+ assert all((directory/f).is_file()for f in provider_files)
+ pc=read(directory/'CANONICAL-WORD.json.gz');checks=read(directory/'LOCAL-CHECKS.json');programs=read(directory/'LOCAL-PROGRAMS.json.gz');replay=read(directory/'INDEPENDENT-LOCAL-REPLAY.json')
+ # Carrier names belong to the independently checked local program. The global
+ # controller's centre contract is the ordered eight exact common frame bases.
+ assert(pc['v'],pc['h'],pc['ports'])==(V,9,canon['ports'])
+ assert len(pc['centers'])==len(pc['center_frames'])==len(canon['centers'])==8
+ assert [pc['frames'][f]for f in pc['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+ R=pc['R'];assert type(R)is int and R>0 and all(x['R']==R for x in registry.values()),'providers disagree on helper count R'
+ assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ assert replay['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz')and replay['local_programs_sha256']==sha(directory/'LOCAL-PROGRAMS.json.gz')
+ widths=[len(pc['frames'][pc['final'][2*V+h]])-len(pc['frames'][pc['start'][2*V+h]])for h in range(R)]   # HPE: residual width |final|-|start|
+ assert widths==plan['provider_registry'][provider_id]['widths']
+ for name in provider_files:
+  value=sha(directory/name);assert value==plan['provider_registry'][provider_id]['artifact_sha256'][name]
+  source_artifacts[f'providers/{provider_id}/{name}']=value
+ registry[provider_id]=dict(local_programs=programs,canonical_word_sha256=sha(directory/'CANONICAL-WORD.json.gz'),local_programs_sha256=sha(directory/'LOCAL-PROGRAMS.json.gz'),local_program_checks=checks,exact_local_clifford_recipe_sha256=sha(directory/'CLIFFORD-RECIPES.json'),residual_adapter_sha256=sha(directory/'RESIDUAL-ADAPTERS.json'),v=V,h=9,R=R,ports=pc['ports'],centers=pc['centers'],widths=widths)
+assert len(roles)==144*R   # one whole-owner role per (call, provider helper)
+selected={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+assert len(selected)==144 and set(selected)==set(call_order)
+assert Counter(c['provider']for c in selected.values())==COUNTS
+per_call_widths={(c['stage'],c['replica']):c['widths']for c in plan['per_call_widths']}
+for key,c in selected.items():
+ assert c['time']==at[key] and c['provider']in registry
+ assert per_call_widths[key]==registry[c['provider']]['widths']
+for key in('local_programs','exact_local_clifford_recipe_sha256','residual_adapter_sha256'):t.pop(key)
+t['local_providers']=registry
+rank={z['child']:z['rank']for z in parent['idle_children']};side={};pairs={}
+for e in parent['execution_schedule']:
+ if e['kind']=='idle_cover_sweep':
+  for sd,ch in enumerate(e['child_indices']):side[ch]=sd;pairs[ch]=e['pair']
+bycall=defaultdict(dict);used=defaultdict(set);sigmas={};digest=hashlib.sha256();entering=0
+for z in roles:
+ s,rep,h=z['stage'],z['replica'],z['helper'];i,cp,off,w,f=z['child'],z['copy'],z['offset'],z['width'],z['family'];orp,port=divmod(cp,V)
+ assert 0<=s<9 and 0<=rep<T and 0<=h<R and w==registry[selected[s,rep]['provider']]['widths'][h] and 0<=orp<T
+ assert f==orp*(8*V)+(2*pairs[i]+side[i])*V+port
+ assert(h not in bycall[s,rep])and off>=0 and off+w<=rank[i]
+ assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1]
+ B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i]
+ occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[]
+ order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M
+ sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma
+ route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9
+ cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells
+ digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n')
+for c in t['calls']:
+ k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R))
+ c['owners']=c['owners'][:(2*V)]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==2*V+R and all(f<DATA for f,r in c['owners'])
+ pc=selected[k];provider_id=pc['provider'];assert c['orientation']==pc['orientation']
+ c['provider_id']=provider_id;c['local_program_sha256']=registry[provider_id]['local_program_checks'][c['orientation']]['sha256']
+ assert c['local_program_sha256']==pc['local_program_sha256']
+newidle=[];paid=Counter()
+for c in t['calls']:
+ for r,n in registry[c['provider_id']]['local_program_checks'][c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for old in parent['idle_children']:
+ i,port=old['child'],old['port']
+ for rep in range(T):
+  u=used[i,rep,port];assert u==set(range(len(u)));left=old['rank']-len(u)
+  if left:
+   f=rep*(8*V)+(2*pairs[i]+side[i])*V+port;newidle.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=left,hosted=len(u),pending_offset=len(u)));paid[left]+=1
+assert M*DATA-sum(r*n for r,n in paid.items())==5120
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R0+2
+# Local circuits, exact phase recipes, normalized wrappers and data routes stay
+# byte-identical; only full-family helper placement and idle remainders change.
+t.update(version='round20-R%d-asynchronous-whole-owner-v1'%R,live=DATA,physical=physical,idle_children=newidle,private_namespace={'centers':[DATA,DATA+C],'reserved_tableau':[DATA+C,DATA+C+R],'coefficient':[physical-2,physical]})
+t['hosting']=dict(rule='one-helper-per-physical-family-per-complete-invocation',max_helpers_per_physical_family_per_call=1,scope='asynchronously interleaved data replicas; each whole helper occurs once per(stage,invocation replica)',pooled_slots=roles,banks=[0]*9,owner_map_sha256=hashlib.sha256(MAP.read_bytes()).hexdigest(),idle_remainder_semantics='Each idle_children item acts once, on its explicit replica/family, at pending_offset with the stated rank; replicas=1.')
+t['route_semantics']['helper']='Whole physical family may belong to another replica; actual orthogonal port basis followed by residual/spectator coordinate permutation. Entering helpers have paid wrappers around the complete invocation; at most one helper and no active data wire uses that family in that invocation. Route[4,child,offset,width,spectators], width9 route[3,child,offset].'
+t['bank_padding']['families']=[];t['bank_padding']['children']=[];t['cover_final_correction']['families']=[0,DATA];t['cover_final_correction']['charged_calls_per_cover']=DATA
+for e in t['execution_schedule']:
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,DATA]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+# Expand the retained controller into one-replica blocks; each block consists
+# of its full local cover sweep and every following replica-local event before
+# its next local sweep. Final whole-stock correction remains after all replicas.
+blocks={};globals_=[];st=None
+for ei,e in enumerate(parent['execution_schedule']):
+ if e['kind']in('bank_padding_cover_sweep','translate_every_live_family'):
+  globals_.append((ei,e));continue
+ if e['kind']=='local_cover_sweep':st=e['stage'];blocks[st]=[]
+ assert st is not None
+ blocks[st].append((ei,e))
+new_schedule=[]
+for tm,(s,rep)in enumerate(call_order):
+ for ei,e in blocks[s]:
+  ne=copy.deepcopy(e);ne.update(replica=rep,replicas=[rep],source_event=ei,time=tm)
+  if ne['kind']=='local_cover_sweep':ne['provider_id']=selected[s,rep]['provider']
+  new_schedule.append(ne)
+for ei,e in globals_:
+ ne=copy.deepcopy(e);ne['source_event']=ei
+ if e['kind']=='bank_padding_cover_sweep':ne['families']=[DATA,DATA]
+ else:ne.update(t['cover_final_correction'])
+ new_schedule.append(ne)
+t['execution_schedule']=new_schedule
+cmap={(c['stage'],c['replica']):c for c in t['calls']}
+t['calls']=[dict(cmap[s,rep],time=tm)for tm,(s,rep)in enumerate(call_order)]
+t['loop_order']='Follow the explicit asynchronous execution_schedule. Each local invocation completes before the next, including its entire cover sweep and normalization wrappers. Per-replica source event order is preserved; each idle remainder executes before that replica next touches its family.'
+t['async_schedule']=dict(order=[list(x)for x in call_order],source_plan_sha256=hashlib.sha256(PLAN.read_bytes().replace(b'\r\n',b'\n')).hexdigest(),source_schedule=parent['execution_schedule'],source_call_order=[[c['stage'],c['replica']]for c in parent['calls']],scope='Only independent replica controllers are interleaved. Owner windows are measured on the owner replica timeline; no within-cover or within-invocation interleaving.')
+assert dict(sorted(paid.items()))=={int(k):v for k,v in plan['profile'].items()}
+assert M*M>2*max(paid)**2
+
+assert all(c['local_program_sha256']==registry[c['provider_id']]['local_program_checks'][c['orientation']]['sha256']for c in t['calls'])
+t['provider_dispatch']='For each indivisible local_cover_sweep, execute local_providers[call.provider_id].local_programs[call.orientation] with that provider residual adapters and Clifford recipes. The sweep provider_id must equal its call provider_id.'
+raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+res=dict(status='EMITTED_MIXED_PROVIDER_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE',
+ template_sha256=hashlib.sha256(raw).hexdigest(),
+ parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),
+ live=DATA,physical=physical,global_profile=dict(sorted(paid.items())),
+ rank_mass=sum(r*n for r,n in paid.items()),deficit=5120,maxchild=max(paid),
+ hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering,
+ unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(),
+ cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles),
+ asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(),
+ source_artifacts=source_artifacts,provider_counts=dict(Counter(c['provider_id']for c in t['calls'])),
+ scope='Two actual verified plain/width-seven providers dispatched per complete invocation; independent controller/spectator/normalization and complete finite invoice admission required.')
+(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2))
diff --git a/research/gauge44-slots-t16/code/freeze_spec.py b/research/gauge44-slots-t16/code/freeze_spec.py
new file mode 100644
index 0000000000..4fe3b88915
--- /dev/null
+++ b/research/gauge44-slots-t16/code/freeze_spec.py
@@ -0,0 +1,29 @@
+"""Freeze independently recomputed discovery values before strict replay."""
+import argparse
+import json
+from pathlib import Path
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--spec', type=Path, required=True)
+ap.add_argument('--discovery', type=Path, required=True)
+a = ap.parse_args()
+spec = json.loads(a.spec.read_text())
+for line in (a.discovery/'WITNESS-RECORD.jsonl').read_text().splitlines():
+    key, value = json.loads(line)
+    parts = key.split('.')
+    if len(parts)>3 and parts[0]=='providers' and parts[2]=='artifacts':
+        parts = parts[:3] + ['.'.join(parts[3:])]
+    target = spec
+    for part in parts[:-1]:
+        target = target.setdefault(part, {})
+    if parts[-1] in target:
+        assert target[parts[-1]]==value, 'Conflicting independent recomputations: '+key
+    target[parts[-1]] = value
+assembly = json.loads((a.discovery/'ASSEMBLY.json').read_text())
+for key in ('complex_lower','conservative_complex_lower','kappa','kappa_decimal','conservative_kappa_decimal'):
+    spec['expected'][key] = assembly[key]
+spec['expected']['assembly_controls_rejected'] = 69
+spec['expected']['provider_counts'] = {'gauge44':144}
+spec['expected']['mutations_rejected'] = 15
+a.spec.write_text(json.dumps(spec, indent=2)+'\n')
+print('Frozen exact witness for strict replay:', assembly['kappa_decimal'])
diff --git a/research/gauge44-slots-t16/code/generated_identity.py b/research/gauge44-slots-t16/code/generated_identity.py
new file mode 100644
index 0000000000..74a9b60479
--- /dev/null
+++ b/research/gauge44-slots-t16/code/generated_identity.py
@@ -0,0 +1,62 @@
+"""Proof-relevant identities for generated artifacts, independent of gzip streams.
+
+Immutable source archives retain their exact byte hashes. For freshly emitted
+artifacts, gzip identity is the exact decompressed payload and JSON identity
+retains every field. Only CLIFFORD-REVIEW's root timing field is excluded.
+Literal receipt references are checked against actual files before replacing
+the three gzip references (and the phase recipe reference) with content hashes.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+import copy
+import gzip
+import hashlib
+import json
+import math
+
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+
+FILES=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+       'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json',
+       'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json')
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+def json_identity(value):
+    return hashlib.sha256(json.dumps(value,sort_keys=True,separators=(',',':'),allow_nan=False).encode('utf-8')).hexdigest()
+
+def payload_identity(path):
+    return hashlib.sha256(gzip.decompress(Path(path).read_bytes())).hexdigest()
+
+def phase_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'CLIFFORD-REVIEW.json').read_bytes())if value is None else value)
+    assert value['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz'),'stale phase canonical word reference'
+    assert value['recipe_sha256']==sha(directory/'CLIFFORD-RECIPES.json'),'stale phase recipe reference'
+    seconds=value.pop('seconds')
+    assert type(seconds)in(int,float) and math.isfinite(seconds) and seconds>=0,'invalid phase timing metadata'
+    value['canonical_word_sha256']=payload_identity(directory/'CANONICAL-WORD.json.gz')
+    value['recipe_sha256']=json_identity(json.loads((directory/'CLIFFORD-RECIPES.json').read_bytes()))
+    return value
+
+def native_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'INDEPENDENT-LOCAL-REPLAY.json').read_bytes())if value is None else value)
+    for field,name in [('canonical_word_sha256','CANONICAL-WORD.json.gz'),('local_programs_sha256','LOCAL-PROGRAMS.json.gz')]:
+        assert value[field]==sha(directory/name),'stale native artifact reference: '+field
+        value[field]=payload_identity(directory/name)
+    return value
+
+def artifact_identities(directory):
+    directory=Path(directory)
+    result={}
+    for name in FILES:
+        path=directory/name
+        if name.endswith('.gz'):
+            result[name]=payload_identity(path)
+        else:
+            value=phase_value(directory)if name=='CLIFFORD-REVIEW.json'else native_value(directory)if name=='INDEPENDENT-LOCAL-REPLAY.json'else json.loads(path.read_bytes())
+            result[name]=json_identity(value)
+    return result
diff --git a/research/gauge44-slots-t16/code/invoice_allcold.py b/research/gauge44-slots-t16/code/invoice_allcold.py
new file mode 100644
index 0000000000..d1dd221291
--- /dev/null
+++ b/research/gauge44-slots-t16/code/invoice_allcold.py
@@ -0,0 +1,329 @@
+"""Fresh call-specific mixed-provider finite invoice.
+
+Prepared with OpenAI Codex assistance, Apache-2.0. The scalar/Horner recount
+and finite inequalities are adapted from the retained PR558 -> PR552 ->
+PR531 invoice_final.py, whose notices and sources are preserved in the package.
+Every call selects a hash-bound provider. Shared compiler reserves use maxima;
+primitive work, coefficient work, local children and wrappers are also summed
+from actual selected provider/orientation records.
+"""
+import argparse, gzip, hashlib, json
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+from generated_identity import artifact_identities
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+assert __debug__, 'Assertions required'
+
+def read(path):
+    data=path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix=='.gz' else data)
+def filehash(path): return hashlib.sha256(path.read_bytes()).hexdigest()
+def contenthash(path):
+    data=path.read_bytes()
+    return hashlib.sha256(gzip.decompress(data) if path.suffix=='.gz' else data).hexdigest()
+def programhash(events):
+    return hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest()
+
+def recount_provider(local_dir, registry):
+    cp=local_dir/'CANONICAL-WORD.json.gz'; pp=local_dir/'LOCAL-PROGRAMS.json.gz'
+    rp=local_dir/'INDEPENDENT-LOCAL-REPLAY.json'
+    w,programs,replay=read(cp),read(pp),read(rp)
+    checks=read(local_dir/'LOCAL-CHECKS.json')
+    assert set(programs)=={'forward','backward'}
+    assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+    assert replay['canonical_word_sha256']==filehash(cp)==registry['canonical_word_sha256']
+    assert replay['local_programs_sha256']==filehash(pp)==registry['local_programs_sha256']
+    assert programs==registry['local_programs']
+    assert checks==registry['local_program_checks']
+    assert filehash(local_dir/'CLIFFORD-RECIPES.json')==registry['exact_local_clifford_recipe_sha256']
+    assert filehash(local_dir/'RESIDUAL-ADAPTERS.json')==registry['residual_adapter_sha256']
+    v,helpers,h,m=w['v'],w['R'],w['h'],73
+    assert (v,h)==(112,9) and type(helpers) is int and helpers>0
+    assert registry['v']==v and registry['R']==helpers and registry['h']==h
+    assert registry['ports']==w['ports'] and registry['centers']==w['centers']
+    assert replay['v']==v and replay['helpers']==helpers
+    n=2*v+helpers
+    widths = [len(w['frames'][w['final'][r]])-len(w['frames'][w['start'][r]]) for r in range(2*v, 2*v+helpers)]  # HPE: |final|-|start|
+    terminal_codim = sum(h-len(w['frames'][w['final'][r]]) for r in range(2*v, 2*v+helpers))  # HPE: 0 for FULL-ended helpers
+    ends = {r: f for r, f in enumerate(w['final']) if r >= 2*v and f != 1}
+    assert len(widths) == helpers
+    entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0}
+    entering = len(entrances)
+    wrapped = {**entrances, **{r: 0 for r in ends if r not in entrances}}   # COLD-HPE: cold hyperplane-ended helpers carry wrappers too
+    cold_ends = len(wrapped) - len(entrances)
+    assert entering == replay['entering_helpers']
+    local = {}
+    for orientation, events in programs.items():
+        # Endpoint equality and native frames were already independently
+        # replayed on all n columns in the hash-bound receipt above.
+        env = {('L', r): Q(1) for r in range(n)}
+        peak = Q(1)
+        real = macros = workops = 0
+        paid = Counter()
+        wrappers = {'pre': set(), 'post': set()}
+        for event in events:
+            tag = event[0]
+            if tag == 'climb':
+                paid[event[5]] += 1
+            elif tag == 'center':
+                paid[event[4]] += 1
+            elif tag == 'residual_adapter':
+                _, kind, register, frame, *end = event
+                assert kind in wrappers and wrapped.get(register) == frame
+                assert end == ([ends[register]] if register in ends else [])  # HPE: R_{E,U}^-1 and L_{E,U}^-1 name U
+                assert register not in wrappers[kind]
+                wrappers[kind].add(register)
+            elif tag == 'scalar':
+                macros += 1
+                scalar = event[1]
+                op, target = scalar[0], tuple(scalar[1])
+                if op == 'clear':
+                    env[target] = Q(0)
+                    count = 1
+                elif op == 'copy':
+                    env[target] = env[tuple(scalar[2])]
+                    count = 1
+                elif op == 'scale':
+                    q = Q(scalar[2], scalar[3])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert numerator and numerator & (numerator-1) == 0
+                    assert denominator & (denominator-1) == 0
+                    env[target] *= abs(q)
+                    count = abs(numerator.bit_length()-denominator.bit_length()) + int(q < 0)
+                elif op == 'add':
+                    source = tuple(scalar[2])
+                    q = Q(scalar[3], scalar[4])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert source != target and numerator > 0
+                    assert denominator & (denominator-1) == 0
+                    acc, count = 0, 1  # clear coefficient work
+                    for i, bit in enumerate(bin(numerator)[2:]):
+                        if i:
+                            acc *= 2
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                        if bit == '1':
+                            acc += 1
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                    value = Q(acc)
+                    for _ in range(denominator.bit_length()-1):
+                        value /= 2
+                        count += 1
+                        peak = max(peak, value*env[source])
+                    assert value == abs(q)
+                    count += 2  # signed accumulation and work clear
+                    env[target] = env.get(target, Q(0)) + abs(q)*env[source]
+                    workops += count
+                else:
+                    raise AssertionError(op)
+                real += 2*count
+                peak = max(peak, env[target])
+            else:
+                assert tag in ('adapter', 'phase')
+        assert wrappers['pre'] == wrappers['post'] == set(wrapped)
+        assert all(value == 0 for register, value in env.items() if register[0] == 'C')
+        prior = replay['local'][orientation]
+        assert prior['all_exact_columns'] == n and prior['private_work_erased']
+        assert peak == Q(prior['prefix_l1_upper']) and peak < 2**prior['charged_payload_bits']
+        bits = peak.numerator.bit_length()-peak.denominator.bit_length()+1
+        assert bits == prior['prefix_bits_upper']
+        assert real == checks[orientation]['real_component_primitive_bound']
+        assert macros == checks[orientation]['scalar_macros']
+        assert dict(paid) == {int(r): count for r, count in checks[orientation]['paid_profile'].items()}
+        assert dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()}
+        local[orientation] = dict(
+            events=len(events), macros=macros, real_component_primitives=real,
+            prefix_l1=str(peak), prefix_bits=bits,
+            coefficient_work_primitive_count=workops, all_exact_columns=n,
+            dirty_helper_columns=helpers, all_dirty_helper_columns_restored=True,
+            private_centres_and_coefficient_work_cleared=True,
+            pre_wrappers=len(wrappers['pre']), post_wrappers=len(wrappers['post']),
+            endpoint_evidence='Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json')
+
+    centres = len(w['centers'])
+    children = sum(checks['forward']['paid_profile'].values())
+    assert checks['forward']['paid_profile'] == checks['backward']['paid_profile']
+    macro_bound = max(row['macros'] for row in local.values())
+    compiler = 64*(m+1)**3
+    adapters = 16*(macro_bound+children+n+centres)+64*m
+    primitive_bound = max(row['real_component_primitives'] for row in local.values())+adapters*compiler
+
+    assert widths==registry['widths']
+    artifacts={f.name:filehash(f) for f in local_dir.iterdir() if f.is_file()}
+    phase_review=read(local_dir/'CLIFFORD-REVIEW.json')
+    return dict(local=local,helpers=helpers,centres=centres,v=v,h=h,n=n,
+                entering_helpers=entering,entrance_rank=sum(len(w['frames'][f]) for f in w['start'][2*v:]),
+                terminal_codimension=terminal_codim, hyperplane_ended_helpers=len(ends),  # HPE: always reported (0 for FULL-ended words)
+                **({'cold_hyperplane_ended_helpers': cold_ends} if cold_ends else {}),  # COLD-HPE: absent without cold ends
+                width_inventory=dict(sorted(Counter(widths).items())),widths=widths,
+                local_adapters=adapters,local_primitive_bound=primitive_bound,
+                compiler=compiler,children=children,artifacts=artifacts,
+                paid_profile=checks['forward']['paid_profile'],
+                program_hashes={o:programhash(events) for o,events in programs.items()},semantic_artifact_sha256=artifact_identities(local_dir))
+
+
+def run(base, hosted, audit, out, retained_invoice=None):
+    local_dir=base/'split-centres'
+    parent=read(local_dir/'GLOBAL-TEMPLATE.json.gz')
+    template_path=hosted/'GLOBAL-TEMPLATE.json.gz'
+    template=read(template_path); summary=read(hosted/'HOSTED.json')
+    owners=read(audit/'OWNERS-AND-PROFILE.json'); control=read(audit/'ASYNC-AUDIT.json')
+    template_hash=contenthash(template_path)
+    assert template_hash==control['complex_template_sha256']==owners['template_sha256']==summary['template_sha256']
+    assert owners['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE'
+    assert template['recipe']==parent['recipe']
+    assert 'local_programs' not in template
+    assert set(template['local_providers'])==set(PIDS)
+    providers={pid:recount_provider(base/'providers'/pid,registry)
+               for pid,registry in template['local_providers'].items()}
+    for pid,p in providers.items():
+        assert owners['provider_phase_semantic_sha256'][pid]==control['provider_phase_semantic_sha256'][pid]==p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']
+        # The fresh controller admission must cite precisely these provider bytes.
+        for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+                     'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json',
+                     'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json'):
+            path='providers/'+pid+'/'+name
+            assert summary['source_artifacts'][path]==p['artifacts'][name]
+            assert owners['source_artifacts'][path]==p['artifacts'][name]
+    # R is read from the provider words (all must agree); the parent dedicated-bank
+    # envelope keeps its own helper count R0 from the parent split-centres word.
+    assert len({p['helpers'] for p in providers.values()})==1,'providers disagree on helper count R'
+    v,h,m,centres=112,9,73,8
+    helpers=next(iter(providers.values()))['helpers']; n=2*v+helpers
+    assert all((p['v'],p['h'],p['centres'],p['n'])==(v,h,centres,n) for p in providers.values())
+    parent_helpers=read(local_dir/'CANONICAL-WORD.json.gz')['R']
+    stages,replicas,blocks_per_stream=9,16,4
+    call_count=len(template['calls'])
+    assert call_count==stages*replicas==control['complete_invocations']
+    assert control['one_owner_per_complete_invocation']
+    assert len({(c['stage'],c['replica']) for c in template['calls']})==call_count
+    parent_calls={(c['stage'],c['replica']):c for c in parent['calls']}
+    sweeps=[e for e in template['execution_schedule'] if e['kind']=='local_cover_sweep']
+    assert len(sweeps)==call_count
+    selected=[]; selected_paid=Counter(); provider_counts=Counter(); orientation_counts=Counter()
+    scalar=coefficient_work=macros=0; wrapper_factors=0
+    factors_per_wrapper=2*(m-1)
+    for c in template['calls']:
+        pid,orientation=c['provider_id'],c['orientation']; p=providers[pid]
+        old=parent_calls[(c['stage'],c['replica'])]
+        assert orientation==old['orientation'] and c['owners'][:2*v]==old['owners'][:2*v]
+        assert c['local_program_sha256']==p['program_hashes'][orientation]
+        r=p['local'][orientation]
+        scalar+=r['real_component_primitives']; coefficient_work+=r['coefficient_work_primitive_count']; macros+=r['macros']
+        wrapper_factors+=(r['pre_wrappers']+r['post_wrappers'])*factors_per_wrapper
+        provider_counts[pid]+=1; orientation_counts[(pid,orientation)]+=1
+        selected_paid.update({int(k):v for k,v in p['paid_profile'].items()})
+        selected.append(dict(stage=c['stage'],replica=c['replica'],provider_id=pid,orientation=orientation,
+                             program_sha256=c['local_program_sha256'],events=r['events'],macros=r['macros'],
+                             real_component_primitives=r['real_component_primitives'],
+                             coefficient_work_primitive_count=r['coefficient_work_primitive_count'],
+                             entering_helpers=p['entering_helpers'],entrance_rank=p['entrance_rank'],
+                             pre_wrappers=r['pre_wrappers'],post_wrappers=r['post_wrappers']))
+    assert provider_counts==COUNTS
+    # The sweep registry is executable: no hidden use of the historical supplier.
+    by_call={(c['stage'],c['replica']):c for c in template['calls']}
+    for e in sweeps:
+        c=by_call[(e['stage'],e['replica'])]
+        assert e['provider_id']==c['provider_id']
+    assert set(p['compiler'] for p in providers.values())=={64*(m+1)**3}
+    compiler=64*(m+1)**3
+    adapters=max(p['local_adapters'] for p in providers.values())
+    primitive_bound=max(p['local_primitive_bound'] for p in providers.values())
+    bridge_steps=sum(event['kind']=='bridge' for event in parent['recipe'])
+    bridge_sweeps=sum(event['kind']=='bridge' for event in template['execution_schedule'])
+    assert bridge_sweeps==replicas*bridge_steps
+    bridge_additions=2*v*bridge_sweeps
+    shifts=blocks_per_stream*v*replicas; moves=2*shifts
+    parent_live,parent_physical=parent['live'],parent['physical']
+    data_stock=2*v*blocks_per_stream*replicas
+    assert (parent_live-data_stock)%stages==0
+    parent_banks=(parent_live-data_stock)//stages
+    assert parent_banks>=0 and parent_physical==parent_live+parent_helpers+centres+2
+    nonlocal_items=(4*v*replicas*stages+2*v*replicas*stages+2*call_count*helpers
+        +sum(child['replicas'] for child in parent['idle_children'])+stages*parent_banks
+        +bridge_additions+shifts+moves+parent_live+parent_physical+wrapper_factors)
+    outside=8*nonlocal_items+64*m
+    parent_pervertex=(scalar+bridge_additions+shifts+moves+parent_live
+        +(call_count*adapters+outside)*compiler+64*parent_physical)
+    live,physical=template['live'],template['physical']
+    mass,profile=owners['rank_mass'],owners['paid_profile']
+    assert m*live-mass==owners['deficit']==5120
+    assert mass==sum(int(r)*count for r,count in profile.items())
+    assert physical==live+helpers+centres+2
+    assert live==owners['live'] and physical==owners['physical']
+    assert live<=parent_live and physical<=parent_physical
+    assert not template['bank_padding']['families']
+    assert owners['explicit_idle_remainder_children']<=owners['source_idle_children_charged']
+    # The old dedicated-bank geometry is only a conservative reserve envelope.
+    # Its singular program is never used as evidence for a mixed invocation.
+    rebased=parent_pervertex+65*(physical-parent_physical)+(live-parent_live)
+    used=max(rebased,parent_pervertex); retained=None; payload=512
+    if retained_invoice is not None:
+        previous=read(retained_invoice)
+        assert previous['compiler']==compiler and previous['charged_prefix_bits']==payload
+        previous_bound=previous['conservative_pervertex_used']
+        used=max(used,previous_bound+parent_pervertex)
+        retained=dict(sha256=filehash(retained_invoice),previous_pervertex_allowance=previous_bound,
+            added_complete_new_pervertex=parent_pervertex,policy='Retain old allowance and add entire fresh mixed recount.')
+    half=m//2; group=2**(half*half)
+    for i in range(1,half+1): group*=2**(2*i)-1
+    stock,streamed_mass=group*physical,group*mass
+    logical=group*used+64; router=compiler*(logical+1)*(stock+1)**2
+    g_bound,e_bound,c0=2**30000,2**100000,2**210000
+    total_mass=streamed_mass+e_bound
+    literal=2*g_bound*stock**2+8*streamed_mass+4*stock+4+32*m
+    row=2*stock.bit_length()+9909+252+2*payload
+    maxchild=max(map(int,profile))
+    inequalities=dict(local_primitive_bound=primitive_bound<2**48,
+        logical=logical<2**6050,router=router<g_bound,literal=literal<e_bound,
+        mass=total_mass<2**100001,precision=32*m*total_mass*total_mass<c0,
+        tape=2*total_mass+18<c0,row=row<20161,halving=m*m>2*maxchild*maxchild)
+    assert all(inequalities.values())
+    localbits=max(r['prefix_bits'] for p in providers.values() for r in p['local'].values())
+    input_l2_bits=(m+1)//2
+    required_prefix=localbits+input_l2_bits+call_count+bridge_sweeps+4
+    assert required_prefix<payload
+    receipt=dict(status='PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE',
+        template_sha256=template_hash,parent_template_sha256=contenthash(local_dir/'GLOBAL-TEMPLATE.json.gz'),
+        owner_audit_sha256=filehash(audit/'OWNERS-AND-PROFILE.json'),
+        controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'),
+        providers=providers,provider_phase_semantic_sha256={pid:p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']for pid,p in providers.items()},provider_counts=dict(provider_counts),selected_calls=selected,
+        selected_local_paid_profile=dict(sorted(selected_paid.items())),
+        selected_real_component_primitives=scalar,selected_coefficient_work_primitive_count=coefficient_work,
+        selected_scalar_macros=macros,global_prefix_bits=required_prefix,charged_prefix_bits=payload,
+        complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,
+        helpers=helpers,centres=centres,live=live,physical=physical,
+        physical_stock_identity=dict(data_and_owner_families=live,local_helpers=helpers,
+                                     private_centres=centres,coefficient_work=2),
+        local_adapters=adapters,local_primitive_bound=primitive_bound,
+        wrapper_elementary_factors_charged=wrapper_factors,factors_per_wrapper=factors_per_wrapper,
+        compiler=compiler,unhosted_pervertex=parent_pervertex,hosted_rebased_pervertex=rebased,
+        conservative_pervertex_used=used,retained_prior_overcharge=retained,
+        finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),
+                    literal_bits=literal.bit_length(),physical_row_coefficient=row,
+                    retained_row_coefficient=20161,required_C0_bits=(32*m*total_mass*total_mass).bit_length(),
+                    halving_integer_inequality=[m*m,2*maxchild*maxchild],G_exponent=30000,
+                    E_exponent=100000,C0_exponent=210000),strict_checks=inequalities,
+        scope='Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. All three providers use fresh hash-bound independent all-column/frame/phase/normalization admission. Shared compiler uses conservative maxima; parent is geometry/overcharge only. All-size compiler, hosting, precision/tape and analytic transfer remain conditional.')
+    prefix=dict(status='PASS_MIXED_ASYNC_GLOBAL_PREFIX',template_sha256=template_hash,
+        global_prefix_bits=required_prefix,retained_payload_bits=payload,
+        complete_invocation_cover_sweeps=call_count,bridge_factor_two_sweeps=bridge_sweeps,
+        local_scalar_coefficient_work_prefix_bits=localbits,stream_input_sup_to_l2_bits=input_l2_bits,
+        primitive_arithmetic_margin_bits=4,controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'),
+        proof='Each selected normalized provider restores all arbitrary dirty helper columns and gives the same data shear endpoints. Actual whole-owner charts are right-translation bijections. Sum all 144 invocation and 144 bridge sweeps and take maximum local scalar/Horner prefix over all three providers and orientations. Idle children, phases, spectator endpoints and terminal translations are unitary. Retained all-size interfaces are conditional.')
+    out.mkdir(parents=True,exist_ok=True)
+    (out/'PREFIX-AND-INVOICE.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    (out/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix,indent=2)+'\n')
+    print(json.dumps({k:receipt[k] for k in ['status','provider_counts','selected_real_component_primitives',
+          'selected_coefficient_work_primitive_count','global_prefix_bits','finite','strict_checks']},indent=2))
+    return receipt
+
+if __name__=='__main__':
+    parser=argparse.ArgumentParser(description=__doc__)
+    for name in ('base','hosted','audit','out'):parser.add_argument('--'+name,type=Path,required=True)
+    parser.add_argument('--retained-invoice',type=Path)
+    args=parser.parse_args()
+    run(args.base,args.hosted,args.audit,args.out,args.retained_invoice)
diff --git a/research/gauge44-slots-t16/code/prepare_global.py b/research/gauge44-slots-t16/code/prepare_global.py
new file mode 100644
index 0000000000..655c9470f6
--- /dev/null
+++ b/research/gauge44-slots-t16/code/prepare_global.py
@@ -0,0 +1,124 @@
+"""Bind a frozen explicit owner map to exact native local artifacts.
+
+This preparer nominates a witness. The separate serialized controller audit,
+finite invoice, two exact moment engines and strict pinned replay admit it.
+Apache-2.0; prepared with OpenAI assistance. See NOTICE.md.
+"""
+import argparse
+from collections import Counter, defaultdict
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+from generated_identity import artifact_identities, FILES
+
+assert __debug__, 'Assertions required'
+
+
+def read(path):
+    raw = Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def dump(path, value):
+    Path(path).write_text(json.dumps(value, indent=2) + '\n')
+
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--parent', type=Path, required=True)
+ap.add_argument('--owners', type=Path, required=True)
+ap.add_argument('--local', type=Path, required=True)
+ap.add_argument('--data', type=Path, required=True)
+args = ap.parse_args()
+args.data.mkdir(parents=True, exist_ok=True)
+parent_path = args.parent / 'data/PLAN.json'
+assert sha(parent_path) == '258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda'
+plan = read(parent_path)
+word = read(args.local / 'CANONICAL-WORD.json.gz')
+checks = read(args.local / 'LOCAL-CHECKS.json')
+assert (word['v'], word['h'], word['R']) == (112, 9, 492)
+widths = [len(word['frames'][word['final'][224+h]]) -
+          len(word['frames'][word['start'][224+h]]) for h in range(492)]
+profile = {int(k): v for k, v in word['local_profile'].items()}
+assert profile == {1: 2514, 2: 404, 3: 448, 4: 160, 5: 56, 8: 8}
+assert Counter(widths) == {4: 52, 5: 48, 7: 34, 8: 114, 9: 244}
+assert sum(widths) == 3794
+owners = read(args.owners)
+assert len(owners) == 72 * 492
+order = [tuple(x) for x in plan['order']]
+times = {x: i for i, x in enumerate(order)}
+used, call_helpers, call_families = defaultdict(set), defaultdict(set), defaultdict(set)
+for z in owners:
+    key = (z['stage'], z['replica'])
+    h, i, rep, port = z['helper'], z['child'], z['owner_replica'], z['port']
+    assert key in times and 0 <= h < 492 and 0 <= rep < 8 and 0 <= port < 112
+    assert z['time'] == times[key] and h not in call_helpers[key]
+    assert z['family'] not in call_families[key]
+    call_helpers[key].add(h)
+    call_families[key].add(z['family'])
+    cap, allowed = plan['windows'][f'{rep},{i}']
+    assert z['time'] in allowed and z['width'] == widths[h]
+    assert z['copy'] == rep * 112 + port
+    assert z['family'] == rep * 896 + (2*plan['pairs'][str(i)] + plan['sides'][str(i)])*112 + port
+    assert 0 <= z['offset'] and z['offset'] + z['width'] <= cap
+    cells = set(range(z['offset'], z['offset'] + z['width']))
+    group = (i, rep, port)
+    assert not used[group] & cells
+    used[group].update(cells)
+assert set(call_helpers) == set(order)
+assert all(hs == set(range(492)) for hs in call_helpers.values())
+idle = Counter()
+for key, (cap, _) in plan['windows'].items():
+    rep, i = map(int, key.split(','))
+    for port in range(112):
+        cells = used[i, rep, port]
+        assert cells == set(range(len(cells)))
+        left = cap - len(cells)
+        if left:
+            idle[left] += 1
+global_profile = Counter({r: 72*n for r, n in profile.items()}) + idle
+assert sum(r*n for r, n in global_profile.items()) == 520704
+assert 73*7168 - sum(r*n for r, n in global_profile.items()) == 2560
+pid = 'gauge44'
+for c in plan['provider_calls']:
+    c['provider'] = pid
+    c['local_program_sha256'] = checks[c['orientation']]['sha256']
+for c in plan['per_call_widths']:
+    c['widths'] = widths
+artifacts = {name: sha(args.local / name) for name in FILES}
+identities = artifact_identities(args.local)
+plan['provider_registry'] = {pid: dict(
+    directory='providers/' + pid, artifact_sha256=artifacts,
+    ports=word['ports'], centers=word['centers'], widths=widths,
+    actual_paid_profile=word['local_profile'],
+    orientation_program_sha256={k: v['sha256'] for k, v in checks.items()},
+    artifact_semantic_sha256=identities)}
+plan.update(status='FROZEN_EXPLICIT_GAUGE44_WHOLE_OWNER_NOMINATION',
+            mode='gauge44-all72', profile=dict(sorted(global_profile.items())),
+            solver_status='deterministic-capacity-matching', gap=None,
+            source_plan_sha256=sha(parent_path),
+            source_owners_sha256=sha(args.parent / 'data/OWNERS.json.gz'),
+            assignment_sha256=sha(args.owners))
+target_owners = args.data / 'OWNERS.json.gz'
+if args.owners.resolve() != target_owners.resolve():
+    shutil.copyfile(args.owners, target_owners)
+dump(args.data / 'PLAN.json', plan)
+spec = dict(schema='witness-spec/1', name='gauge44-all72',
+            data=dict(plan_sha256=sha(args.data / 'PLAN.json'), owners_sha256=sha(target_owners)),
+            dispatch=[[s, r, pid] for s in range(9) for r in range(8)],
+            call_order=plan['order'], width_spot_helpers=[264, 276, 288, 300],
+            providers={pid: {}}, expected=dict(gain_baseline_kappa='0.001636241501576388'))
+dump(args.data / 'SPEC.json', spec)
+dump(args.data / 'PREPARATION.json', dict(
+    status='PASS_EXPLICIT_MAP_AND_FRESH_PROVIDER_NOMINATION',
+    parent_plan_sha256=sha(parent_path), source_owners_sha256=sha(args.owners),
+    global_profile=dict(sorted(global_profile.items())), idle_profile=dict(sorted(idle.items())),
+    roles=len(owners), rank_mass=520704, deficit=2560,
+    remaining='Independent emitted-controller audit, fresh finite invoice, exact moments and outer assembly.'))
+print('Prepared all72 gauge44 candidate:', dict(sorted(global_profile.items())))
diff --git a/research/gauge44-slots-t16/code/restore_parent.py b/research/gauge44-slots-t16/code/restore_parent.py
new file mode 100644
index 0000000000..21135f898a
--- /dev/null
+++ b/research/gauge44-slots-t16/code/restore_parent.py
@@ -0,0 +1,67 @@
+"""Materialize the omitted generated PR558 parent, then require its reviewed hash.
+
+The integrated review contains the native inputs and INTEGRATION.json but
+omits GLOBAL-TEMPLATE.json.gz. This is only the deterministic template
+binding from the inherited prepare_supplier_base.py; no old circuit or
+phase calculation is rerun. The whole exact payload must match the review.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+assert __debug__, 'Assertions required'
+ap=argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--source',type=Path,required=True)
+ap.add_argument('--baseline',type=Path,required=True)
+ap.add_argument('--out',type=Path,required=True)
+a=ap.parse_args()
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+assert not a.out.exists()
+base=a.out/'complex-global/base'
+shutil.copytree(a.baseline/'complex-global/base',base)
+d=base/'split-centres'
+parent=a.source/'vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz'
+old=read(parent);can=read(d/'CANONICAL-WORD.json.gz')
+checks=read(d/'LOCAL-CHECKS.json');programs=read(d/'LOCAL-PROGRAMS.json.gz')
+v,h,r=can['v'],can['h'],can['R'];c=len(can['centers']);m,t,l,k=73,8,9,4
+assert(v,h,r,c)==(112,9,504,8)
+widths=[h-len(can['frames'][f])for f in can['start'][2*v:]]
+data=2*k*t*v;live=data+l*r;physical=live+r+c+2
+word=copy.deepcopy(old)
+word.update(version='round20-new-supplier-dedicated-bank-parent-v1',live=live,physical=physical,local_programs=programs)
+word['private_namespace']={'centers':[live,live+c],'reserved_tableau':[live+c,live+c+r],'coefficient':[physical-2,physical]}
+for call in word['calls']:
+ s,rep=call['stage'],call['replica'];owners=copy.deepcopy(call['owners'][:2*v])
+ for helper,w in enumerate(widths):
+  route=[2,rep]if w==9 else[2,rep*w,w,list(range(t*w,t*w+9-w))]
+  owners.append([data+s*r+helper,route])
+ call['owners']=owners;call['local_program_sha256']=checks[call['orientation']]['sha256']
+children=[]
+for s in range(l):
+ for helper,w in enumerate(widths):
+  axes=list(range(t*w,m))
+  children.append(dict(family=data+s*r+helper,rank=len(axes),axis_indices=axes,orthogonal_axes=[1<<j for j in axes]))
+word['bank_padding']={'families':list(range(data,live)),'children':children,
+ 'semantics':'Each listed complement frame is applied once after the eight disjoint residual blocks of that dedicated bank. The final hosted derivative has empty families and children.'}
+word['cover_final_correction'].update(families=[0,live],charged_calls_per_cover=live)
+for i,e in enumerate(word['execution_schedule']):
+ if e['kind']=='bank_padding_cover_sweep':word['execution_schedule'][i]={'kind':'bank_padding_cover_sweep','families':[data,live],'children_source':'bank_padding.children'}
+ elif e['kind']=='translate_every_live_family':e.update(word['cover_final_correction'])
+word['exact_data_phase_recipe_sha256']=sha(base/'work/complex-nine-native/DATA-PHASES.json')
+word['exact_local_clifford_recipe_sha256']=sha(d/'CLIFFORD-RECIPES.json')
+word['residual_adapter_sha256']=sha(d/'RESIDUAL-ADAPTERS.json')
+word['supplier_substitution']={'parent_template_sha256':sha(parent),
+ 'old_canonical_word_sha256':sha(a.baseline/'complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz'),
+ 'new_canonical_word_sha256':sha(d/'CANONICAL-WORD.json.gz'),
+ 'exact_same_ports':True,'data_contract':'The same ordered 112 data ports and both complete-invocation identity-shear orientations feed the unchanged nine-stage controller. No old local program or helper profile is reused.'}
+word['route_semantics']['helper']='Dedicated family DATA+stage*R+helper; one helper per bank per complete invocation. Width-nine route[2,replica] uses axes9*replica..9*replica+8. Width-w entering route[2,w*replica,w,spectators] uses the disjoint residual block and paid normalization wrappers; spectator axes start at8*w, beyond all residual blocks.'
+raw=json.dumps(word,sort_keys=True,separators=(',',':')).encode()
+expected=read(d/'INTEGRATION.json')['global_template_sha256']
+assert hashlib.sha256(raw).hexdigest()==expected=='7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3'
+(d/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+print('PASS_EXACT_REVIEWED_PARENT_TEMPLATE_RESTORED',expected)
diff --git a/research/gauge44-slots-t16/code/witness.py b/research/gauge44-slots-t16/code/witness.py
new file mode 100644
index 0000000000..c5c7fbc114
--- /dev/null
+++ b/research/gauge44-slots-t16/code/witness.py
@@ -0,0 +1,55 @@
+"""Spec loader: spec values are EXPECTED values, compared only after independent recomputation.
+WITNESS_DISCOVER=1 runs the same recomputation without comparing pinned values (pin() records only);
+it is used once to produce outputs for generate_spec.py, after which the strict run must pass.
+"""
+import json,os
+from collections import Counter
+from pathlib import Path
+SPEC=json.loads(Path(os.environ['WITNESS_SPEC']).read_text())
+DISCOVER=os.environ.get('WITNESS_DISCOVER')=='1'
+X=SPEC.get('expected',{})
+PROVIDERS=SPEC.get('providers',{})
+DISPATCH={(s,r):p for s,r,p in SPEC['dispatch']}
+CALL_ORDER=[tuple(x)for x in SPEC['call_order']]
+# width-8 spot helpers: PR558's helpers 270, 282, 294, 306, or their images under a K-triangle word's 504 -> R helper map
+# (verify.py checks the spec value against the constructor's HELPER-MAP.json)
+SPOT=tuple(SPEC.get('width_spot_helpers',(270,282,294,306)))
+# A pivot swap moves a kernel family's pivot role p -> x; the old pivot p becomes an ordinary cold helper and its width
+# goes 8 -> 9 (construction/layers, PR641 PROOF-NOTE-PIVOT). Expected spot widths are derived from the package's pinned
+# pivot-swap recipe (path and sha256 in the spec), not from free data: 9 at a swapped-out pivot, 8 otherwise.
+_PKG=Path(os.environ['WITNESS_SPEC']).resolve().parents[1]
+def _old_pivots():
+ ps=SPEC.get('pivot_swap')
+ if not ps:return frozenset()
+ raw=(_PKG/ps['recipe']).read_bytes();import hashlib
+ assert hashlib.sha256(raw).hexdigest()==ps['sha256'],'pivot-swap recipe pin'
+ return frozenset(s['pivot']for s in json.loads(raw)['swaps'])
+OLD_PIVOTS=_old_pivots()
+def spot_widths(v=112):
+ """Expected residual widths at the spot helpers (helper indices) of the gauge44 provider."""
+ return tuple(9 if 2*v+h in OLD_PIVOTS else 8 for h in SPOT)
+PIDS=tuple(sorted(set(DISPATCH.values())))
+COUNTS=dict(Counter(DISPATCH.values()))
+assert DISCOVER or set(PROVIDERS)==set(PIDS),'spec providers differ from dispatch providers'
+def lookup(key):
+ """Dotted spec path; a segment may itself contain dots when it names a file (split at most once per known file suffix)."""
+ v=SPEC;parts=key.split('.')
+ while parts:
+  for n in range(len(parts),0,-1):
+   k='.'.join(parts[:n])
+   if isinstance(v,dict) and k in v:v=v[k];parts=parts[n:];break
+  else:raise KeyError('spec has no key %s'%key)
+ return v
+def pin(key,got):
+ """Strict mode: got must equal the spec value at dotted key; the failure names the key."""
+ if DISCOVER:
+  if os.environ.get('WITNESS_RECORD'):   # discovery bookkeeping only: append (key, value) for the spec writer
+   with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10))
+  return got
+ want=lookup(key)
+ assert got==want,'SPEC MISMATCH %s: expected %s got %s'%(key,json.dumps(want)[:400],json.dumps(got,default=str)[:400])
+ return got
+def partner(pid):
+ """A different provider for substitution controls (next in sorted order)."""
+ assert len(PIDS)>1
+ return PIDS[(PIDS.index(pid)+1)%len(PIDS)]
diff --git a/research/gauge44-slots-t16/construction/COLD44-RECIPE.json.gz b/research/gauge44-slots-t16/construction/COLD44-RECIPE.json.gz
new file mode 100644
index 0000000000..6f59d88920
Binary files /dev/null and b/research/gauge44-slots-t16/construction/COLD44-RECIPE.json.gz differ
diff --git a/research/gauge44-slots-t16/construction/COMPLETION-PRIORITY.json b/research/gauge44-slots-t16/construction/COMPLETION-PRIORITY.json
new file mode 100644
index 0000000000..e0df30aeef
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/COMPLETION-PRIORITY.json
@@ -0,0 +1,746 @@
+{
+  "0,1,2,3": {
+    "rows": [
+      [
+        "1",
+        "0",
+        "0",
+        "1",
+        "0",
+        "0",
+        "0",
+        "0"
+      ],
+      [
+        "-1/2",
+        "0",
+        "0",
+        "1/2",
+        "0",
+        "0",
+        "0",
+        "0"
+      ]
+    ],
+    "registers": [
+      64,
+      67
+    ]
+  },
+  "0,1,4,5": {
+    "rows": [
+      [
+        "1",
+        "0",
+        "0",
+        "1",
+        "0",
+        "0",
+        "0",
+        "0"
+      ],
+      [
+        "-1/2",
+        "0",
+        "0",
+        "1/2",
+        "0",
+        "0",
+        "0",
+        "0"
+      ]
+    ],
+    "registers": [
+      32,
+      35
+    ]
+  },
+  "0,1,6,7": {
+    "rows": [
+      [
+        "1",
+        "0",
+        "0",
+        "1",
+        "0",
+        "0",
+        "0",
+        "0"
+      ],
+      [
+        "-1/2",
+        "0",
+        "0",
+        "1/2",
+        "0",
+        "0",
+        "0",
+        "0"
+      ]
+    ],
+    "registers": [
+      24,
+      27
+    ]
+  },
+  "0,2,4,6": {
+    "rows": [
+      [
+        "1",
+        "0",
+        "0",
+        "1",
+        "0",
+        "0",
+        "0",
+        "0"
+      ],
+      [
+        "0",
+        "-1/2",
+        "1/2",
+        "0",
+        "0",
+        "-1/2",
+        "1/2",
+        "0"
+      ],
+      [
+        "-1/2",
+        "0",
+        "0",
+        "1/2",
+        "0",
+        "0",
+        "0",
+        "0"
+      ],
+      [
+        "0",
+        "0",
+        "0",
+        "0",
+        "1",
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new file mode 100644
index 0000000000..2b12294b58
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/INPUTS.json
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+  },
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+  "canonical_content_sha256": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+  "local_program_sha256": {
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+}
diff --git a/research/gauge44-slots-t16/construction/LICENSE b/research/gauge44-slots-t16/construction/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
+      other entities that control, are controlled by, or are under common
+      control with that entity. For the purposes of this definition,
+      "control" means (i) the power, direct or indirect, to cause the
+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
+      exercising permissions granted by this License.
+
+      "Source" form shall mean the preferred form for making modifications,
+      including but not limited to software source code, documentation
+      source, and configuration files.
+
+      "Object" form shall mean any form resulting from mechanical
+      transformation or translation of a Source form, including but
+      not limited to compiled object code, generated documentation,
+      and conversions to other media types.
+
+      "Work" shall mean the work of authorship, whether in Source or
+      Object form, made available under the License, as indicated by a
+      copyright notice that is included in or attached to the work
+      (an example is provided in the Appendix below).
+
+      "Derivative Works" shall mean any work, whether in Source or Object
+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
+      the Work and Derivative Works thereof.
+
+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
+      to that Work or Derivative Works thereof, that is intentionally
+      submitted to Licensor for inclusion in the Work by the copyright owner
+      or by an individual or Legal Entity authorized to submit on behalf of
+      the copyright owner. For the purposes of this definition, "submitted"
+      means any form of electronic, verbal, or written communication sent
+      to the Licensor or its representatives, including but not limited to
+      communication on electronic mailing lists, source code control systems,
+      and issue tracking systems that are managed by, or on behalf of, the
+      Licensor for the purpose of discussing and improving the Work, but
+      excluding communication that is conspicuously marked or otherwise
+      designated in writing by the copyright owner as "Not a Contribution."
+
+      "Contributor" shall mean Licensor and any individual or Legal Entity
+      on behalf of whom a Contribution has been received by Licensor and
+      subsequently incorporated within the Work.
+
+   2. Grant of Copyright License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      copyright license to reproduce, prepare Derivative Works of,
+      publicly display, publicly perform, sublicense, and distribute the
+      Work and such Derivative Works in Source or Object form.
+
+   3. Grant of Patent License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      (except as stated in this section) patent license to make, have made,
+      use, offer to sell, sell, import, and otherwise transfer the Work,
+      where such license applies only to those patent claims licensable
+      by such Contributor that are necessarily infringed by their
+      Contribution(s) alone or by combination of their Contribution(s)
+      with the Work to which such Contribution(s) was submitted. If You
+      institute patent litigation against any entity (including a
+      cross-claim or counterclaim in a lawsuit) alleging that the Work
+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
+      granted to You under this License for that Work shall terminate
+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
+      Work or Derivative Works thereof in any medium, with or without
+      modifications, and in Source or Object form, provided that You
+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
+          attribution notices from the Source form of the Work,
+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
+          distribution, then any Derivative Works that You distribute must
+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
+          pertain to any part of the Derivative Works, in at least one
+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
+          documentation, if provided along with the Derivative Works; or,
+          within a display generated by the Derivative Works, if and
+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+      implied, including, without limitation, any warranties or conditions
+      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+      PARTICULAR PURPOSE. You are solely responsible for determining the
+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
+
+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
+      the Work or Derivative Works thereof, You may choose to offer,
+      and charge a fee for, acceptance of support, warranty, indemnity,
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+      License. However, in accepting such obligations, You may act only
+      on Your own behalf and on Your sole responsibility, not on behalf
+      of any other Contributor, and only if You agree to indemnify,
+      defend, and hold each Contributor harmless for any liability
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+
+   END OF TERMS AND CONDITIONS
+
+   APPENDIX: How to apply the Apache License to your work.
+
+      To apply the Apache License to your work, attach the following
+      boilerplate notice, with the fields enclosed by brackets "[]"
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+      file or class name and description of purpose be included on the
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+   Copyright [yyyy] [name of copyright owner]
+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
+
+       http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
+   limitations under the License.
diff --git a/research/gauge44-slots-t16/construction/NOTICE.md b/research/gauge44-slots-t16/construction/NOTICE.md
new file mode 100644
index 0000000000..16b0507070
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/NOTICE.md
@@ -0,0 +1,9 @@
+# Construction delta notice
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+
+`construct_gauge_xcentre.py` modifies PR635's credited `construct_k_triangle.py`, which in turn extends icekylinx's PR531/PR514/PR425 factory lineage. Its original source comments are retained. The K-triangle schedule and the upstream porting, JP8 frame, kernel and HPE procedures are reused from the pinned source checkouts and are not new contributions of this delta.
+
+The new source-copy exchanges, complementary factory basis, carrier assignment, exact cold44 constructor and compact reproduction driver are described in `../CONSTRUCTION.md`.
+
+`UPSTREAM-NOTICE.md` is the complete unmodified notice from the pinned PR635 package. `LICENSE` is that package's Apache-2.0 license. All further notices and source credits of the referenced upstream packages remain applicable and are retained in the source checkouts rather than vendored again here.
diff --git a/research/gauge44-slots-t16/construction/REBUILD-CHECKS.json b/research/gauge44-slots-t16/construction/REBUILD-CHECKS.json
new file mode 100644
index 0000000000..0801f35da7
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/REBUILD-CHECKS.json
@@ -0,0 +1,51 @@
+{
+  "status": "PASS_COMPACT_SCALAR_REPRODUCTION_AND_FROZEN_RECIPE_SPLICE",
+  "steps": [
+    {
+      "step": "shadow-early",
+      "exit_code": 0,
+      "seconds": 0.355
+    },
+    {
+      "step": "shadow-prefix",
+      "exit_code": 0,
+      "seconds": 0.511
+    },
+    {
+      "step": "gauge-forward",
+      "exit_code": 0,
+      "seconds": 0.527
+    },
+    {
+      "step": "port0",
+      "exit_code": 0,
+      "seconds": 0.468
+    },
+    {
+      "step": "port1",
+      "exit_code": 0,
+      "seconds": 0.636
+    },
+    {
+      "step": "port2",
+      "exit_code": 0,
+      "seconds": 0.474
+    },
+    {
+      "step": "port3",
+      "exit_code": 0,
+      "seconds": 0.497
+    },
+    {
+      "step": "cold44-exact",
+      "exit_code": 0,
+      "seconds": 2.754
+    }
+  ],
+  "constructor_seconds": 6.222,
+  "word_content_sha256": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290",
+  "all_step_input_and_output_pins_checked": true,
+  "regenerated_recipe_equals_frozen_recipe": true,
+  "frozen_splice_matches_exact_constructor": true,
+  "scope": "One portable scalar reconstruction from pinned main and PR635 inputs; existing native and independent mathematical receipts accompany the package separately."
+}
diff --git a/research/gauge44-slots-t16/construction/UPSTREAM-NOTICE.md b/research/gauge44-slots-t16/construction/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..ebc24a0168
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/UPSTREAM-NOTICE.md
@@ -0,0 +1,34 @@
+# Attribution and scope
+
+Four verified provider types are offered to every call: PR571's prefix word with twelve multi-cut cold kernels (PR568's unchanged constructor), the same word with forty width-five entrance promotions (PR569's unchanged frame constructor) before those kernels, PR575's plain joint-prefix provider, and PR568's eight-cold provider. A window MILP with an exact per-pattern model chooses the dispatch and a literal owner map. PR583's six source-bound kernel frame coalescences (its unchanged constructor and negative controls) are applied to every PR571-prefix provider word (ck and atm3), followed by two further coalescences that each first move one addition past two commuting additions (package code/build_gate_moves.py, extending PR583's constructor); a final hyperplane_end step (package code/build_hpe.py) then runs 46 single-gate cleanups h -= p right after part B at the dim-8 join U of their registers, so 46 width-8 entering helpers per call end at U with width 7; each such gate commutes with every earlier cleanup gate on its registers (for 8 of them the partner's one earlier gate x -= p only reads p), and the reordered program is replayed exactly. A window MILP (exact windows, RINS around an LP vertex) gives the dispatch ck 45 / atm3 21 / jp8 6 and the literal owner map.
+
+Pinned external sources (unchanged; `verify.py` checks their manifests and every file it uses):
+- PR568 (`research/complex-multicold`, commit `71c99ac935a33bb7b59a1b4a7af8725a939b0b90`).
+- PR571 (`research/structural-gain`, commit `b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3`).
+- PR569 (`research/larger-gain`, commit `897213a855b7fb8a1b8b0e552a2f5c42e6c1b326`).
+- PR575 (`research/complex-joint-prefix`, commit `eac6f7e378ab622dac50a2fd4b7ef6eab014de44`).
+- PR583 (`research/kernel-frame-coalescing`, commit `89be768f0157f5a3d8e4db69cf1748768605eac9`).
+
+Provider construction is described as typed steps in `data/SPEC.json` (`build`); `verify.py` runs only allowlisted step types with their paired omission audits and checks every input and output content hash. `code/` holds the spec-driven global admission scripts adapted from PR571's `frontier-composition/global-code/` (OpenAI Codex assisted, Apache-2.0): every expected value is read from `data/SPEC.json` and compared only after independent recomputation. `code/generated_identity.py` and `code/generated_identity_controls.py`, and the decompressed-content artifact identities in the bind, audit, invoice, assembly and phase-timing scripts, are taken unchanged from PR586 by chafreaky (`research/promoted-kernel-coalescing`, commit `4846fee5b06af770e9b3a10c36200f673d656725`, OpenAI Codex assisted, Apache-2.0), including its proof-content and reference/metadata mutation controls; the normalization of descriptive width metadata after frame changes follows the same PR.
+
+In PR601, the owner map was nominated by a HiGHS window MILP (adapted from PR569's `global/nominate_width7.py`) with lazy cross-time Hall cuts; this package's re-solved map is described below. Neither is an admission dependency.
+
+DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. (The PR601 package this one starts from states: "Prepared by Claude Code (Anthropic) research agents.") Apache-2.0 applies; LICENSE is included. All notices, licenses, source pins and AI disclosures of the pinned sources and their ancestry are retained in those packages and are not replaced by this notice. All inherited conditional assumptions remain conditional.
+
+**This package (complex-571-cold14, DreamingOfClouds).** It starts from PR601 (jeremykothe2, `research/complex-571-hpem46`, commit `529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550`). Everything above is kept unchanged except the following:
+- every provider chain (ck, atm3, jp8) gains the typed step `cold_end` (`code/build_cold_end.py`, `code/cold_end_controls.py`; recipes `data/recipes/*-cold_end.json.gz`);
+- the generalised native chain and the global admission scripts accept cold helpers that end below FULL (with `0:U` wrappers), a refactored exact cleanup, and check the wrapper order;
+- `data/PLAN.json` / `data/OWNERS.json.gz` (dispatch and literal owner map) come from a relocate/swap/ejection-chain/provider-flip annealing search started from PR601's map, refined by an exact pattern-restricted owner model (CP-SAT) with a literal edge-colouring expansion (not an admission dependency);
+- `data/SPEC.json` holds the expected values, recorded by a discovery run and then checked by a strict run.
+
+The cold-end construction (a row-plus-column cone condition for low-frame ends, a rank-0 dirt-spread premix and multi-gate lower-frame cleanup) builds on PR591 / PR592 / PR593 / PR601 (jeremykothe2) and our PR599 (Lean: multi-gate and cold hyperplane-end tails). DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. Build on this at your own risk.
+
+**This package (complex-571-cold14-b3, jeremykothe2).** It is PR604's `complex-571-cold14` (DreamingOfClouds) with ColdBeyond's second cold end per block (two new `cold_end` A-gate primitives, `PROOF-NOTE.md`), ColdSupply's E1 entering pair and reviewed controls, a free dispatch (jp8 ×60, atm3 ×12) and a literal owner map from an exact per-time-Hall window MIP. All other construction, code, controls and proofs are PR604's and earlier contributors', unchanged.
+
+**This package (complex-571-cold14-k492).** It is complex-571-cold14-b3 with these changes:
+- **K-triangle base words.** The leaver-read K-triangle skeleton atom and its read schedule (`data/TRI-SCHEDULE.json`) are by AtomScout, a Claude Code research agent. `code/construct_k_triangle.py` is PR531's `code/construct_504.py` (icekylinx, OpenAI Codex / GPT assisted, Apache-2.0; pinned source `direct_delivery`) extended with that atom.
+- **Ported chains.** The PR604/B3 chains are ported stage by stage onto the K-triangle words by `code/build_port_stage.py` (Port480, a Claude Code research agent). `code/build_frame_regroup.py` extends PR583's `build_frames.py` (chafreaky).
+- **Helper count R.** The generalisation of the global scripts to the provider helper count R is by GlobalR (a Claude Code research agent), with AtomReviewer's fixes (PROOF-NOTE-R.md).
+- **Owner map.** The owner map, the cold_end recipes on the K-triangle words and the package assembly are by Stack492, Port480 and ColdBeyond (Claude Code research agents).
+
+Build on this at your own risk.
diff --git a/research/gauge44-slots-t16/construction/barch/LOCAL-PINS-barch-U8.json b/research/gauge44-slots-t16/construction/barch/LOCAL-PINS-barch-U8.json
new file mode 100644
index 0000000000..4028b95c0e
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/barch/LOCAL-PINS-barch-U8.json
@@ -0,0 +1,50 @@
+{
+ "word": "U8",
+ "barch_controls": [
+  "C0_identity",
+  "recipe",
+  "drop_restore",
+  "restore_full",
+  "drop_preread",
+  "donation_after",
+  "drop_restore@231",
+  "restore_full@231",
+  "drop_preread@231",
+  "donation_after@231",
+  "drop_restore@230",
+  "restore_full@230",
+  "drop_preread@230",
+  "donation_after@230",
+  "drop_restore@232",
+  "restore_full@232",
+  "drop_preread@232",
+  "donation_after@232",
+  "drop_restore@236",
+  "restore_full@236",
+  "drop_preread@236",
+  "donation_after@236",
+  "drop_restore@226",
+  "restore_full@226",
+  "drop_preread@226",
+  "donation_after@226",
+  "drop_restore@228",
+  "restore_full@228",
+  "drop_preread@228",
+  "donation_after@228",
+  "drop_restore@62",
+  "restore_full@62",
+  "drop_preread@62",
+  "donation_after@62",
+  "drop_restore@238",
+  "restore_full@238",
+  "drop_preread@238",
+  "donation_after@238"
+ ],
+ "layer_controls": 95,
+ "canonical_sha256": "24db880b7dab31e6af4eec8a1aba1bbbae29cd50d9a7b77cf0e9b571b3e5ae7c",
+ "program_sha256": {
+  "forward": "83d65a63f51bd1ce7f3dd4e4d3597311e065b4775796cd87aea3e3a62689047c",
+  "backward": "e4e483b764e9a85f84a04425e57d73ecdcc72eb2e4d97a64f17d9da58fa5ace0"
+ },
+ "clifford_recipes_sha256": "4629507dcbdd516457c001ff8f9dbe750d1a0cbfa5cfa3c6be003d45804ba0c5"
+}
diff --git a/research/gauge44-slots-t16/construction/barch/RECIPE-U8.json b/research/gauge44-slots-t16/construction/barch/RECIPE-U8.json
new file mode 100644
index 0000000000..ee215a805a
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/barch/RECIPE-U8.json
@@ -0,0 +1,1528 @@
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+    "1241": 228
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+   "dsides": [
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+   "donors": [
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+    "1257": 62
+   },
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+   "dsides": [
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+   "donors": [
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+   ],
+   "kept": {
+    "1265": 457,
+    "1273": 238
+   },
+   "when": "mid"
+  }
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/barch/build_tri.py b/research/gauge44-slots-t16/construction/barch/build_tri.py
new file mode 100644
index 0000000000..11c4371114
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/barch/build_tri.py
@@ -0,0 +1,87 @@
+#!/usr/bin/env python3
+"""build_tri.py BASE_WORD RECIPE OUT_WORD [--control NAME]
+
+Standard library only. Applies a NewBArch triangle-hybrid recipe to the X4 word (1e1d99ba) and writes a FULL-WORD.json.gz.
+Recipe keys (all indices refer to the BASE word):
+  base_sha256      sha256 of the decompressed base JSON (checked)
+  B_delete         list of B indices removed
+  B_insert         list of [pos, gate]: gate (with frame) inserted before base B gate pos (list order kept)
+  B_frames         {index: frame}: explicit re-chosen frame of a kept base B gate
+  tail_insert      list of [early_index, gate]: gates appended to cleanup in list order, then registered as early cleanup at early_index (ascending)
+  cleanup_prepend  list of gates prepended to the full cleanup (early indices are shifted)
+  local_profile    report.local_profile of the result
+  expect_sha256    sha256 of the decompressed result (checked unless a control is requested)
+Controls (each must be REJECTED by audit_local; see controls.json):
+  drop_restore     omit cleanup_prepend (end value of the holder not restored)
+  restore_full     move tail_insert gates into the full cleanup (FULL frame) instead of early cleanup
+  drop_preread     omit the inserted entrance pre-reads (inserted target += E gates at pos < first donation)
+  donation_after   insert each donation after its reading target's read instead of before it
+  NAME@X           the same control restricted to the instance whose packet register is X (recipe 'variants')
+"""
+import sys, json, gzip, hashlib, copy
+
+FULL = [256, 128, 64, 32, 16, 8, 4, 2, 1]
+
+def load(p):
+    raw = gzip.decompress(open(p, 'rb').read()); return json.loads(raw), hashlib.sha256(raw).hexdigest()
+
+def apply(w, rc, control=None):
+    w = copy.deepcopy(w); B = w['B']
+    S = None
+    if control and '@' in control:                     # per-instance control: name@X mutates only instance X's gates
+        control, x = control.split('@'); x = int(x)
+        vv = [s for s in rc['variants'] if s['X'] == x][0]; S = {vv['X'], vv['E'], *vv['hold']}
+    sel = lambda g: S is None or bool({g[1], g[2]} & S)
+    dele = set(rc['B_delete']); fr = {int(k): f for k, f in rc['B_frames'].items()}
+    ins = [list(x) for x in rc['B_insert']]
+    don = [x for x in ins if not (112 <= x[1][1] < 224)]           # donations: destination is not a target
+    first_don = min(p for p, _ in don) if don else 0
+    if control == 'drop_preread':
+        ins = [x for x in ins if not (x[0] < first_don and 112 <= x[1][1] < 224 and sel(x[1]))]
+    if control == 'donation_after':
+        new = []
+        for p, g in ins:
+            if g in [d[1] for d in don] and sel(g):
+                rd = [i for i, e in enumerate(B) if i >= p and e[0] == 'add' and e[2] == g[1] and 112 <= e[1] < 224]
+                p = rd[0] + 1
+            new.append([p, g])
+        ins = new
+    at = {}
+    for p, g in ins: at.setdefault(p, []).append(list(g))
+    out = []
+    for i, e in enumerate(B):
+        out.extend(at.get(i, []))
+        if i in dele: continue
+        e = list(e)
+        if i in fr: e = e[:-1] + [list(fr[i])]
+        out.append(e)
+    out.extend(at.get(len(B), []))
+    w['B'] = out
+    pre = [list(g) for g in rc['cleanup_prepend'] if not (control == 'drop_restore' and sel(g))]
+    tails = [list(x) for x in rc['tail_insert']]
+    if control == 'restore_full':
+        pre = pre + [g[1][:-1] + [FULL] for g in tails if sel(g[1])]; tails = [g for g in tails if not sel(g[1])]
+    C = pre + w['cleanup']; sh = len(pre)
+    early = [[i + sh, U] for i, U in w['early_cleanup']]
+    idx = []
+    for j, g in tails: C.append(list(g)); idx.append((j, len(C) - 1, list(g[-1])))   # appended in recipe order
+    for j, ci, U in sorted(idx): early.insert(j, [ci, U])                               # then registered at their early index
+    w['cleanup'] = C; w['early_cleanup'] = early
+    w['report'] = dict(w['report']); w['report']['local_profile'] = rc['local_profile']
+    return w
+
+def main():
+    a = sys.argv[1:]; control = None
+    if '--control' in a: k = a.index('--control'); control = a[k + 1]; del a[k:k + 2]
+    base, out = a[0], a[2]
+    w, sha = load(base); rc = json.load(open(a[1]))
+    if sha != rc['base_sha256']: raise SystemExit('base sha mismatch ' + sha)
+    w2 = apply(w, rc, control)
+    raw = json.dumps(w2, separators=(',', ':')).encode()
+    open(out, 'wb').write(gzip.compress(raw, mtime=0))
+    s = hashlib.sha256(raw).hexdigest()
+    if control is None and s != rc['expect_sha256']: raise SystemExit('result sha mismatch ' + s)
+    print(json.dumps(dict(control=control, sha256=s)))
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/barch/reproduce_barch.py b/research/gauge44-slots-t16/construction/barch/reproduce_barch.py
new file mode 100644
index 0000000000..22f15b491d
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/barch/reproduce_barch.py
@@ -0,0 +1,92 @@
+#!/usr/bin/env python3
+"""Rebuild the B0 word (NewBArch's width-neutral triangle-hybrid B-delivery rewrite on X4) and its native locals.
+
+Input: a fresh `construction/jx/reproduce_jx.py` output directory; its X4 word (1e1d99ba...) is pinned there and by
+RECIPE-B0.json (base_sha256). Steps, each checked exactly:
+  1. barch: build_tri.py (standard library only; NewBArch) applies the recipe's explicit B deletes and inserts (with frames),
+     re-chosen B frames, early-cleanup tails and FULL-cleanup restores; it checks the base and result shas (d9ba0942...).
+  2. barch-controls: run_controls.py rebuilds C0 (identity, must reproduce the input), the recipe word (must PASS #645's
+     independent audit_local.py) and four mutants (drop_restore, restore_full, drop_preread, donation_after), globally
+     and for each recipe variant (NAME@X); each mutant must FAIL audit_local with its pinned message. Every outcome is
+     required and the control set is pinned (LOCAL-PINS).
+  3. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant) on the B0 word; count pinned.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs; canonical word, local programs and
+     Clifford recipes pinned (LOCAL-PINS-barch-<id>.json).
+Apache-2.0. Driver by ColdWitness around NewBArch's builder and controls.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+PKG = HERE.parents[1]
+P6 = HERE.parent / 'layers_p6n'
+MUTANTS = ('drop_restore', 'restore_full', 'drop_preread', 'donation_after')
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--jx-dir', type=Path, required=True, help='construction/jx/reproduce_jx.py output')
+    ap.add_argument('--recipe', default='U8', help='RECIPE-<id>.json and LOCAL-PINS-barch-<id>.json')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-barch-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    inp = a.jx_dir.resolve() / 'jx/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['base_sha256'], 'input must be the pinned X4 word'
+    (out / 'barch').mkdir(); word = out / 'barch/FULL-WORD.json.gz'
+    run('barch', HERE / 'build_tri.py', inp, rfile, word, portable=False)
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['expect_sha256']
+    run('barch-controls', HERE / 'run_controls.py', inp, rfile, PKG / 'independent/audit_local.py', out / 'barch-controls', portable=False)
+    res = read(out / 'barch-controls/controls.json')
+    want = ['C0_identity', 'recipe', *MUTANTS] + [m + '@' + str(v['X']) for v in rec.get('variants', []) for m in MUTANTS]
+    assert sorted(res) == sorted(want) == sorted(pins['barch_controls']) and all(x['ok'] for x in res.values()), res
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/barch/run_controls.py b/research/gauge44-slots-t16/construction/barch/run_controls.py
new file mode 100644
index 0000000000..f1ce999bfb
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/barch/run_controls.py
@@ -0,0 +1,33 @@
+#!/usr/bin/env python3
+"""run_controls.py BASE_WORD RECIPE AUDIT_LOCAL_PY OUTDIR : C0 identity, the recipe word (must PASS) and the four negative
+controls (each must FAIL audit_local with its pinned message prefix). Standard library only; writes OUTDIR/controls.json."""
+import sys, json, subprocess, os, gzip, hashlib
+base, recipe, audit, out = sys.argv[1:5]
+here = os.path.dirname(os.path.abspath(__file__)); os.makedirs(out, exist_ok=True)
+# pinned rejection sites (observed on RECIPE-V1 and RECIPE-B0; the failing rows are recorded in controls.json): the holder 485 is not restored; the low-end restore 497-=451 moved to the
+# FULL cleanup runs after 451's own tail and leaves 497 wrong; without the pre-read (or with the donation after the read)
+# the entering helper's start value reaches a target.
+EXPECT = {None: 'PASS', 'drop_restore': 'all-column endpoint failure (False, ',
+          'restore_full': 'all-column endpoint failure (False, ',
+          'drop_preread': 'nonzero entrance response', 'donation_after': 'nonzero entrance response'}
+res = {}
+ident = os.path.join(out, 'C0.json')
+json.dump(dict(json.load(open(recipe)), B_delete=[], B_insert=[], B_frames={}, tail_insert=[], cleanup_prepend=[],
+               local_profile=json.loads(gzip.decompress(open(base, 'rb').read()))['report']['local_profile'],
+               expect_sha256=hashlib.sha256(gzip.decompress(open(base, 'rb').read())).hexdigest()), open(ident, 'w'))
+r = subprocess.run([sys.executable, '-B', os.path.join(here, 'build_tri.py'), base, ident, os.path.join(out, 'C0.json.gz')], capture_output=True, text=True)
+res['C0_identity'] = dict(ok=r.returncode == 0, out=r.stdout.strip() or r.stderr.strip()[-200:])
+ctls = list(EXPECT) + [c + '@' + str(s['X']) for s in json.load(open(recipe)).get('variants', []) for c in EXPECT if c]
+for ctl in ctls:
+    name = ctl or 'recipe'; wp = os.path.join(out, name + '.json.gz')
+    cmd = [sys.executable, '-B', os.path.join(here, 'build_tri.py'), base, recipe, wp] + (['--control', ctl] if ctl else [])
+    b = subprocess.run(cmd, capture_output=True, text=True)
+    if b.returncode: res[name] = dict(ok=False, build=b.stderr[-300:]); continue
+    a = subprocess.run([sys.executable, '-B', audit, '--word', wp, '--output', os.path.join(out, name + '.audit.json')], capture_output=True, text=True)
+    txt = a.stdout + a.stderr
+    if ctl is None: ok = a.returncode == 0 and 'PASS_INDEPENDENT' in txt
+    else: ok = a.returncode != 0 and EXPECT[ctl.split('@')[0]] in txt
+    res[name] = dict(ok=ok, build=json.loads(b.stdout), audit_tail=txt.strip().splitlines()[-1][:200])
+json.dump(res, open(os.path.join(out, 'controls.json'), 'w'), indent=1)
+print(json.dumps({k: x['ok'] for k, x in res.items()}))
+sys.exit(0 if all(x['ok'] for x in res.values()) else 1)
diff --git a/research/gauge44-slots-t16/construction/build_gauge_cold44.py b/research/gauge44-slots-t16/construction/build_gauge_cold44.py
new file mode 100644
index 0000000000..72d2945f6b
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/build_gauge_cold44.py
@@ -0,0 +1,210 @@
+"""Exact dyadic cold-end realization of the source-branch/factory-completion word.
+Prepared for icekylinx with OpenAI Codex assistance; Apache-2.0.
+This is a constructor: independent endpoint/frame audits remain required.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+import copy,gzip,json,hashlib,time,sys,argparse,importlib.util
+D=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser(description=__doc__)
+for name in ('input','out','hamming','upstream-package'):ap.add_argument('--'+name,type=Path,required=True)
+args=ap.parse_args();WPATH=args.input;OUT=args.out
+assert __debug__, 'Assertions are required'
+OUT.mkdir(exist_ok=False,parents=True)
+def rd(p):return json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+w=rd(WPATH);v=w['report']['v'];n=2*v+w['report']['R'];N=list(range(v))+list(range(2*v,n));ix={x:i for i,x in enumerate(N)}
+F9=[256,128,64,32,16,8,4,2,1];t0=time.monotonic()
+def basis(vs):
+ d={}
+ for a in vs:
+  for k in sorted(d,reverse=True):
+   if a>>k&1:a^=d[k]
+  if a:
+   k=a.bit_length()-1
+   for j in d:
+    if d[j]>>k&1:d[j]^=a
+   d[k]=a
+ return tuple(d[k] for k in sorted(d,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def regs(e):return e[1:3] if e[0]=='add' else e[1:2]
+def inverse(e):
+ e=copy.deepcopy(e)
+ if e[0]=='add':e[3]=-e[3]
+ else:e[2],e[3]=e[3],e[2]
+ return e
+def apply(e,M,mapping=None):
+ t=mapping[e[1]] if mapping is not None else e[1]
+ if e[0]=='add':
+  s=mapping[e[2]] if mapping is not None else e[2];q=Q(e[3],e[4])
+  for j,a in M[s].items():
+   x=M[t].get(j,Q(0))+q*a
+   if x:M[t][j]=x
+   else:M[t].pop(j,None)
+ else:
+  q=Q(e[2],e[3]);M[t]={j:q*a for j,a in M[t].items()}
+def rref(A):
+ a=[list(map(Q,row)) for row in A];nr=len(a);nc=len(a[0]) if nr else 0;row=0;piv=[]
+ for c in range(nc):
+  k=next((i for i in range(row,nr) if a[i][c]),None)
+  if k is None:continue
+  a[row],a[k]=a[k],a[row];q=a[row][c];a[row]=[x/q for x in a[row]]
+  for i in range(nr):
+   if i!=row and a[i][c]:q=a[i][c];a[i]=[x-q*y for x,y in zip(a[i],a[row])]
+  piv.append(c);row+=1
+  if row==nr:break
+ return a,piv
+def rank(A):return len(rref(A)[1])
+def null(A,nc=None):
+ if A:a,piv=rref(A);nc=len(a[0])
+ else:a=[];piv=[];assert nc is not None
+ free=[j for j in range(nc) if j not in piv];out=[[Q(0) for j in free] for i in range(nc)]
+ for k,c in enumerate(free):out[c][k]=Q(1)
+ for i,c in enumerate(piv):
+  for k,j in enumerate(free):out[c][k]=-a[i][j]
+ return out
+def mm(A,B):
+ if not A:return []
+ if not B:return [[] for row in A]
+ bt=list(zip(*B));return [[sum((a*b for a,b in zip(row,col)),Q(0)) for col in bt] for row in A]
+def tr(A):return list(map(list,zip(*A)))
+def inv(A):
+ n0=len(A);a,p=rref([row+[Q(i==j) for j in range(n0)] for i,row in enumerate(A)])
+ assert p[:n0]==list(range(n0))
+ return [row[n0:] for row in a]
+def unit(q):
+ if not q:return False
+ a=abs(q.numerator);b=q.denominator
+ return not a&(a-1) and not b&(b-1)
+def dyadic(q):return not q.denominator&(q.denominator-1)
+def opadd(t,s,q,F):return ['add',t,s,q.numerator,q.denominator,list(F)]
+def opscale(t,q,F):return ['scale',t,q.numerator,q.denominator,list(F)]
+def eliminate(M,ids,F,skip=()):
+ """Return legal dyadic row operations taking an invertible sparse matrix to I."""
+ skip=set(skip);ops=[];dim=len(M)
+ def add(i,j,q):
+  if q:
+   assert dyadic(q);e=opadd(ids[i],ids[j],q,F);ops.append(e)
+   for c,x in M[j].items():
+    z=M[i].get(c,Q(0))+q*x
+    if z:M[i][c]=z
+    else:M[i].pop(c,None)
+ def scale(i,q):
+  if q!=1:
+   assert unit(q);ops.append(opscale(ids[i],q,F));M[i]={c:q*x for c,x in M[i].items()}
+ def swap(i,j):
+  if i!=j:
+   add(i,j,Q(1));add(j,i,Q(-1));add(i,j,Q(1));scale(j,Q(-1))
+ for c in range(dim):
+  if c in skip:
+   assert M[c]=={c:Q(1)} and all(not M[i].get(c) for i in range(dim) if i!=c)
+   continue
+  cand=[i for i in range(c,dim) if i not in skip and M[i].get(c)]
+  k=next((i for i in cand if unit(M[i][c])),None)
+  if k is None:
+   # Elementary Euclidean row additions reduce the pivot-column numerator gcd.
+   assert cand,('singular',c)
+   while k is None:
+    cand.sort(key=lambda i:abs(M[i][c]));a=cand[0]
+    b=next((i for i in cand[1:] if M[i][c]),None)
+    if b is None:raise ValueError(('non-dyadic determinant pivot',c,M[a][c]))
+    rat=M[b][c]/M[a][c];q=rat.numerator//rat.denominator
+    if q==0:q=1 if rat>0 else -1
+    add(b,a,Q(-q));cand=[i for i in cand if M[i].get(c)]
+    k=next((i for i in cand if unit(M[i][c])),None)
+  swap(c,k);scale(c,1/M[c][c])
+  for i in range(dim):
+   if i!=c and M[i].get(c):
+    assert i not in skip
+    add(i,c,-M[i][c])
+ assert all(row=={i:Q(1)} for i,row in enumerate(M))
+ return ops
+def realize(A,ids,F):
+ M=[{j:Q(x) for j,x in enumerate(row) if x} for row in A]
+ return [inverse(e) for e in reversed(eliminate(M,ids,F))]
+# Reconstruct the actual non-target map after the inherited HPE tail.
+inherited_tail=[w['cleanup'][i][:-1]+[list(f)] for i,f in w.get('early_cleanup',[])]
+mainN=[e for e in w['A']+w['B'] if not v<=e[1]<2*v]
+M=[{i:Q(1)} for i in range(len(N))]
+for e in mainN+inherited_tail:apply(e,M,ix)
+MI=[{i:Q(1)} for i in range(len(N))]
+for e in reversed(mainN+inherited_tail):apply(inverse(e),MI,ix)
+cur={x:(w['ports'][x],) if x<v else basis(w.get('start_extra',{}).get(str(x),[])) for x in N}
+for e in w['A']+w['B']+inherited_tail:
+ for x in regs(e):
+  if x in cur:cur[x]=basis(e[-1])
+enter=set(map(int,w.get('start_extra',{})));protected=[ix[x] for x in N if x<v or x in enter]
+mods=rd(args.hamming/'PACKET-PROGRAMS.json.gz');proto=rd(args.hamming/'PROTOTYPE.json')
+plans=[];premix=[];tail=[];ends={};Mafter=copy.deepcopy(M)
+for b,mod in enumerate(mods):
+ ss=mod['receipt']['source_lines'];F=basis([proto['binary_ports'][s] for s in ss]);I=[ix[x] for x in N if inside(cur[x],F)]
+ hs=list(range(224+16*b,224+16*(b+1)));H=[ix[x] for x in hs]
+ C=[[M[i].get(j,Q(0)) for j in protected] for i in I]
+ L=tr(null(tr(C),len(I)))
+ A=[[MI[j].get(i,Q(0)) for i in I] for j in protected];A=[row for row in A if any(row)]
+ K=null(A,len(I));BK=mm(L,K);_,piv=rref(BK);r=len(piv);assert r==len(L)==(2 if b in [0,1,2,11,12,13] else 4),(b,r,len(L))
+ Ksel=[[row[j] for j in piv] for row in K];Bsel=[[row[j] for j in piv] for row in BK];U=mm(Ksel,inv(Bsel));assert mm(L,U)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ q=mm([[MI[i].get(j,Q(0)) for j in I] for i in range(len(N))],U)
+ assert all(not any(q[i]) for i in range(len(N)) if i not in H),('nonlocal premix',b)
+ RR=mm(L,[[M[i].get(j,Q(0)) for j in H] for i in I]);qH=[q[i] for i in H]
+ assert mm(RR,qH)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ # Pick low physical helper destinations with independent U coordinate rows.
+ ih=[]
+ for j in sorted((j for j,i in enumerate(I) if N[i] in hs),key=lambda j:(cur[N[I[j]]]!=F,N[I[j]])):
+  if rank([U[k] for k in ih]+[U[j]])>len(ih):ih.append(j)
+  if len(ih)==r:break
+ assert len(ih)==r
+ endhs=[N[I[j]] for j in ih];endhidx=[hs.index(h) for h in endhs]
+ kerR=null(RR,16);Qmat=[[Q(0) for j in range(16)] for i in range(16)]
+ for j,hj in enumerate(endhidx):
+  for i in range(16):Qmat[i][hj]=qH[i][j]
+ other=[j for j in range(16) if j not in endhidx]
+ for k,j in enumerate(other):
+  for i in range(16):Qmat[i][j]=kerR[i][k]
+ assert rank(Qmat)==16
+ pops=realize(Qmat,hs,());premix+=pops
+ T=[[Q(i==j)-sum((U[i][k]*L[k][j] for k in range(r)),Q(0)) for j in range(len(I))] for i in range(len(I))]
+ for k,i in enumerate(ih):T[i]=L[k]
+ tops=realize(T,[N[i] for i in I],F);tail+=tops
+ # Right-compose this initial helper premix; other blocks have disjoint H sets.
+ for row in Mafter:
+  vals=[row.get(h,Q(0)) for h in H]
+  if any(vals):
+   for hj in H:row.pop(hj,None)
+   for j,hj in enumerate(H):
+    z=sum((vals[i]*Qmat[i][j] for i in range(16)),Q(0))
+    if z:row[hj]=z
+ for e in tops:apply(e,Mafter,ix)
+ ends.update({h:list(F) for h in endhs})
+ plans.append(dict(block=b,frame=list(F),registers=[N[i] for i in I],ends=endhs,pairing_rank=r,premix_gates=len(pops),tail_gates=len(tops),Q=[[str(x) for x in row] for row in Qmat],T=[[str(x) for x in row] for row in T]))
+ print('BLOCK',b,'ends',endhs,'Qops',len(pops),'Tops',len(tops),flush=True)
+# Check actual post-tail isolation before constructing the high-frame inverse.
+allends=set(ends)|set(map(int,w.get('helper_final',{})))
+for h in allends:
+ j=ix[h];assert Mafter[j]=={j:Q(1)},('row not isolated',h,Mafter[j]);assert all(not row.get(j) for i,row in enumerate(Mafter) if i!=j),('column not isolated',h)
+print('EXACT_ISOLATED',len(ends),'new;',len(allends),'total',round(time.monotonic()-t0,3),flush=True)
+fullops=eliminate(copy.deepcopy(Mafter),N,F9,[ix[x] for x in allends])
+print('FULL_INVERSE',len(fullops),round(time.monotonic()-t0,3),flush=True)
+# Cancel new cold-axis target responses inside A, after their wrappers.
+Dirt=[({h:Q(1)} if h in ends else {}) for h in range(n)]
+for e in premix+w['A']+w['cut']+w['B']:apply(e,Dirt)
+for e in w['precondition']:apply(e,Dirt)
+postcomp=[opadd(y,h,-a,()) for y in range(v,2*v) for h,a in sorted(Dirt[y].items()) if a]
+assert all(h in ends for e in postcomp for h in [e[2]])
+new=copy.deepcopy(w);new['A']=postcomp+premix+w['A'];new['cleanup']=inherited_tail+tail+fullops
+new['early_cleanup']=[[i,e[-1]] for i,e in enumerate(inherited_tail+tail)]
+new['helper_final'].update({str(h):f for h,f in ends.items()})
+new['refactored_cleanup']={'kind':'source_branch_gauge_and_retired_completion_cold44','new_cold_ends':len(ends),'exact_non_target_isolation_checked':True,'high_inverse':'dyadic_sparse_Gauss_Jordan'}
+# Derive paid profile by subtracting and adding literal frame-chain counts.
+spec=importlib.util.spec_from_file_location('upstream_cold_end',args.upstream_package/'code/build_cold_end.py')
+profile_module=importlib.util.module_from_spec(spec);spec.loader.exec_module(profile_module)
+oldprof,_=profile_module.chain_profile(w);newprof,_=profile_module.chain_profile(new)
+prof=Counter({int(k):z for k,z in w['report']['local_profile'].items()});prof.subtract(oldprof);prof.update(newprof)
+widths=Counter(len(basis(new['helper_final'].get(str(h),F9)))-len(basis(new.get('start_extra',{}).get(str(h),[]))) for h in range(224,n))
+new['report'].update(local_profile={str(k):z for k,z in sorted(prof.items()) if z},local_rank_mass=sum(k*z for k,z in prof.items()),width_inventory={str(k):z for k,z in sorted(widths.items()) if z},status='EXACT_COLD44_CONSTRUCTED_PENDING_INDEPENDENT_AUDIT')
+raw=json.dumps(new,sort_keys=True,separators=(',',':')).encode();sha=hashlib.sha256(raw).hexdigest();(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+recipe={'premix':postcomp+premix,'cleanup':new['cleanup'],'early_cleanup':new['early_cleanup'],'cold_ends':{str(h):f for h,f in ends.items()},'refactored_cleanup':new['refactored_cleanup'],'output_content_sha256':sha}
+(OUT/'RECIPE.json.gz').write_bytes(gzip.compress(json.dumps(recipe,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+receipt=dict(input_content_sha256=hashlib.sha256(gzip.decompress(WPATH.read_bytes())).hexdigest(),output_content_sha256=sha,blocks=plans,new_cold_ends=len(ends),all_low_ended_helpers=len(allends),premix_gates=len(premix),postwrapper_compensation_gates=len(postcomp),tail_gates=len(tail),inherited_tail_gates=len(inherited_tail),full_inverse_gates=len(fullops),profile=new['report']['local_profile'],width_inventory=new['report']['width_inventory'],rank_mass=new['report']['local_rank_mass'],seconds=time.monotonic()-t0)
+(OUT/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(json.dumps({k:z for k,z in receipt.items() if k!='blocks'},indent=2),flush=True)
diff --git a/research/gauge44-slots-t16/construction/construct_gauge_xcentre.py b/research/gauge44-slots-t16/construction/construct_gauge_xcentre.py
new file mode 100644
index 0000000000..1010d86746
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/construct_gauge_xcentre.py
@@ -0,0 +1,381 @@
+# Round20 early-coordinate-center / own-Y variant, prepared for icekylinx
+# with OpenAI Codex assistance. Apache-2.0. Scalar elementary-operation
+# helpers below are retained from the attributed PR514 construct_partial.py.
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+# AtomScout: leaver-read K-triangles (schedule from atom1.py / rog.py CP-SAT)
+TRI=json.loads(Path(sys.argv[3]).read_text())
+FULLT={(tuple(tr['p']),tr['e']) for tr in TRI['triangles']}
+TRI_COORDS={t+8 for tr in TRI['triangles'] for t,_,_ in tr['reads']}
+COPYL=[]
+NH=504-3*len(FULLT)+len(COPYL)
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+# Helper ids of the unpatched 504 construction: every allocation advances the 504 numbering; a packet copy that the
+# K-triangle schedule never forms advances it without allocating (HELPER-MAP.json).
+shadow=[];skipped=[];nxt=[2*v]
+def alloc():
+    n=len(cur);cur.append(());rows.append({});shadow.append(nxt[0]);nxt[0]+=1;return n
+def skip():
+    skipped.append(nxt[0]);nxt[0]+=1
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# Each source quartet supplies pair partials first. The other two coordinate
+# partitions supply eight early face packets without touching the eight
+# partials later copied into the preconditioned Y coordinates.
+SELECT=(0,0)
+PRIORITY=json.loads((INPUT/"COMPLETION-PRIORITY.json").read_text())
+maps={};early={};own_rows={};pairs=[];tetrads={};block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)});maps[c]=mp
+    for ei,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[:40]):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        if ei==15:
+            for jj in range(4,8):swap(mp[jj],mp[2*jj+9],(P[ids[jj]],))
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in targets:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                t,u=sorted(ts);e2=R[t][q[0]]*R[t][q[1]]
+                pair={'targets':(t,u),'keys':[(c,p,eps),(c,q,e2)],'selected':pi==SELECT[parity],
+                      'matrix':[[R[a][p[0]],R[a][q[0]]] for a in (t,u)]}
+                pairs.append(pair)
+                if not pair['selected']:continue
+                zz=-Q(2*R[u][p[0]],R[t][p[0]])
+                sources=tet[1-parity]
+                for target,sign in ((t,-1),(u,1)):
+                    wanted={s:-Q(G[t][s],4)-sign*Q(G[u][s],2)/zz for s in sources
+                            if -Q(G[t][s],4)-sign*Q(G[u][s],2)/zz}
+                    assert len(wanted)==2
+                    candidates=[]
+                    for r in mp.values():
+                        if set(rows[r])!=set(wanted):continue
+                        s=next(iter(wanted));coef=wanted[s]/rows[r][s]
+                        if all(wanted[s]==coef*rows[r][s] for s in wanted):candidates.append((r,coef))
+                    assert len(candidates)==1
+                    r,coef=candidates[0];assert len(cur[r])==2
+                    own_rows[target]=(r,coef,cur[r])
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    needed={own_rows[t][0] for t in ids}
+    early[c]={j for j,e in enumerate(z['events'][40:]) if not ({mp[e[0]],mp[e[1]]}&needed)}
+    assert len(early[c])==8
+    retired=[]
+    for j in sorted(early[c]):
+        (t,s,a,b),F=z['events'][40+j],z['event_frames'][40+j]
+        add(mp[t],mp[s],Q(a,b),tuple(F));retired.append(mp[s])
+    assert not set(retired)&needed
+    # These eight retired rows already span every source coordinate. Keep
+    # them invertible and place the four coordinate totals in a changed basis.
+    F=basis([P[s] for s in ids]);assert len(F)==4
+    regs=sorted(retired,key=lambda r:(r>=v,r))
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    M=[[Q(R[s][i]) for s in ids] for i in c]
+    def qr_rank(rs):
+        bs={}
+        for r in rs:
+            r=r.copy()
+            for i,b in sorted(bs.items()):
+                if r[i]:q=r[i];r=[x-q*y for x,y in zip(r,b)]
+            i=next((i for i,x in enumerate(r) if x),None)
+            if i is not None:q=r[i];bs[i]=[x/q for x in r]
+        return len(bs)
+    assert qr_rank(M)==4
+    for rr0 in PRIORITY[",".join(map(str,c))]["rows"]:
+        rr=list(map(Q,rr0))
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    for i in range(8):
+        if len(M)==8:break
+        rr=[Q(i==j) for j in range(8)]
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    assert len(M)==8
+    linear(regs,M,F)
+    for i,r in zip(c,regs):
+        assert rows[r]=={s:Q(R[s][i]) for s in ids}
+        block_totals[c,i]=r
+
+# All centers are complete while Y is still at zero. This is the crucial
+# difference from an illegal early-own-Y prefix using the old center order.
+centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+assert all(cur[v+t]==() for t in range(v))
+
+phase=B
+for t,(r,coef,F) in sorted(own_rows.items()):
+    if t in TRI_COORDS:continue
+    assert cur[r]==F
+    add(v+t,r,coef,F)
+# requests are needed for TRI coefficients
+requests=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    requests[key1].append((t,-Q(mat[0][0],2)))
+    requests[key2].append((u,-Q(mat[0][1],2)))
+reqcoef={t:(key,coef) for key,reqs in requests.items() for t,coef in reqs}
+def face_info(c,p,eps):
+    z=blocks[c];keys=[(pp,ee) for pp in it.combinations(c,2) for ee in (-1,1)]
+    r_local,alpha=z['outputs'][keys.index((p,eps))]
+    j=[j for j in range(40,len(z['events'])) if z['events'][j][0]==r_local];assert len(j)==1
+    return j[0],Q(alpha)
+tri_join_counts=Counter()
+lcopy={}
+for s8 in COPYL:
+    r=s8+8;c=alloc();add(c,r,1,cur[r]);lcopy[r]=c
+for tr in TRI['triangles']:
+    p,eps=tuple(tr['p']),tr['e']
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];r0=r;r=lcopy.get(r,r)
+        key,coef=reqcoef[t];assert key[1]==p and key[2]==eps,(key,p,eps)
+        if blk==key[0]:
+            rr,c0,F0=own_rows[t];assert rr==r0;q=c0
+        else:
+            j,alpha=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert loc in ev[:2]
+            q=coef*alpha
+        F=basis(cur[v+t]+cur[r]);assert inside(F,hyper(P[t])),('TRI frame',t)
+        tri_join_counts[len(F)]+=1;add(v+t,r,q,F)
+
+packets={}
+for c,z in sorted(blocks.items()):
+    mp=maps[c]
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    skipev={face_info(c,p,eps)[0] for p,eps in keys if (p,eps) in FULLT}
+    for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]):
+        if j not in early[c] and 40+j not in skipev:
+            t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    for key,(r,alpha) in zip(keys,z['outputs']):
+        if tuple(key) in FULLT:skip();continue
+        a=mp[r];b=alloc();add(b,a,1,cur[a])
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha))
+
+# Both tetrahedra use the same partition. A selected key has exactly two
+# selected Y loads and no ordinary M consumer. Supply its two raw halves in
+# opposite orders and never form that M. Other keys retain the old M path.
+second=[];first_join_counts=Counter()
+for key,reqs in sorted(requests.items()):
+    assert len(reqs)==2
+    c,p,eps=key
+    if (p,eps) in FULLT:continue
+    ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds
+    for j,(target,coef) in enumerate(sorted(reqs)):
+        first_source,second_source=(a,b) if j==0 else (b,a)
+        r,alpha=packets[first_source,p,eps,second_source]
+        F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+        first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F)
+        r,alpha=packets[second_source,p,eps,c]
+        second.append((target,r,coef*alpha))
+
+Ms={}
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for eps in (-1,1):
+            if (c,p,eps) in requests:continue
+            (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,eps]=(a,alpha)
+
+consumers=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    for key in pair['keys']:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    if key in requests:
+        assert all(pairs[i]['selected'] for i in uses)
+        continue
+    assert all(not pairs[i]['selected'] for i in uses)
+    a,alpha=Ms[key]
+    for j,pid in enumerate(uses):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+assert len(cur)-240==NH,len(cur)-240
+
+selected_join_counts=Counter()
+for target,r,coef in second:
+    F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+    selected_join_counts[len(F)]+=1;add(v+target,r,coef,F)
+output_basis=[]
+for pair in pairs:
+    if not pair['selected']:continue
+    (t,u),mat=pair['targets'],pair['matrix']
+    F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u]))
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert rows[v+t]==expected,('side identity',t)
+
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8
+assert sum(r*z for r,z in H.items())==9*NH+240*8+72,sum(r*z for r,z in H.items())
+
+def apply(e,matrix):
+    if e[0]=='add':
+        _,t,s,a,b,*_=e;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    e[-1]=list(FULL);return e
+cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q]
+cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v]
+matrix=[{r:Q(1)} if r<v else {} for r in range(len(cur))]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(len(cur)))
+
+# Restrict the eight isolated axis ports exactly, keeping the stable 112-port
+# label set. This variant changes the local word, not the outer geometry.
+mp={s:s-8 for s in range(8,120)}
+mp.update({120+s:112+s-8 for s in range(8,120)})
+mp.update({240+r:224+r for r in range(NH)})
+def restrict(events,is_cut=False):
+    out=[]
+    for e in events:
+        regs=e[1:3] if e[0]=='add' else e[1:2]
+        if any(r not in mp for r in regs):
+            assert is_cut and e[0]=='add' and e[1]-120==e[2] and e[2]<8 and e[3:5]==[1,1]
+            continue
+        q=copy.deepcopy(e);q[1]=mp[q[1]]
+        if q[0]=='add':q[2]=mp[q[2]]
+        out.append(q)
+    return out
+H.subtract({1:8,8:16});H=+H
+report={'status':'EXACT_CLEAN_OWN_Y_EARLY_CENTER_WORD_NOT_ADMITTED',
+        'h':9,'v':112,'R':NH,'cst':64,'m':73,'local_profile':dict(sorted(H.items())),
+        'centre_ranks':[8]*8,**({'tri_join_counts':dict(tri_join_counts)} if TRI['triangles'] else {}),'selected_load_join_counts':dict(selected_join_counts),'selected_partitions':list(SELECT),'first_load_join_counts':dict(first_join_counts),
+        'source_columns_exact':112,'borrowed_output_pairs':56,'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'local_rank_mass':sum(r*n for r,n in H.items()),'scope':'Clean scalar identity and all literal monotone local frames only; arbitrary-dirt compensation, entrance kernels, exact phase recipes, and global hosting/pricing are not yet certified.'}
+word={'report':report,'ports':P[8:],'root_lines':R[8:],
+      'A':restrict(A),'B':restrict(B),'cut':restrict(cut,True),'cleanup':restrict(cleanup),'precondition':restrict(precondition),
+      'centers':[mp[r] for r in centers[:8]],'center_frames':center_frames[:8],
+      'scatter':[[str(x) for x in row[:8]] for row in scatter[8:]]}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+assert len(shadow)==NH and len(shadow)+len(skipped)==504
+hmap={**{r:r for r in range(224)},**{224+s_-240:224+i for i,s_ in enumerate(shadow)}}
+(OUT/'HELPER-MAP.json').write_text(json.dumps({'map':{str(k):hmap[k] for k in sorted(hmap)},'removed_504_helpers':[224+s_-240 for s_ in skipped]})+'\n')
+(OUT/'DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/gauge44-slots-t16/construction/frames/FRAME-RECIPE-sw4.json b/research/gauge44-slots-t16/construction/frames/FRAME-RECIPE-sw4.json
new file mode 100644
index 0000000000..7394064c5e
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/frames/FRAME-RECIPE-sw4.json
@@ -0,0 +1,167 @@
+{
+  "input_content_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+  "gate_frames": [
+    [
+      "B",
+      856,
+      [
+        272,
+        144,
+        64,
+        6
+      ],
+      [
+        272,
+        144,
+        64,
+        8,
+        6,
+        1
+      ]
+    ],
+    [
+      "B",
+      860,
+      [
+        265,
+        137,
+        88,
+        6
+      ],
+      [
+        256,
+        128,
+        65,
+        16,
+        9,
+        6
+      ]
+    ],
+    [
+      "B",
+      868,
+      [
+        265,
+        200,
+        33,
+        6
+      ],
+      [
+        256,
+        144,
+        81,
+        33,
+        9,
+        6
+      ]
+    ],
+    [
+      "B",
+      873,
+      [
+        320,
+        192,
+        16,
+        6
+      ],
+      [
+        320,
+        192,
+        32,
+        16,
+        6,
+        1
+      ]
+    ],
+    [
+      "B",
+      876,
+      [
+        392,
+        73,
+        33,
+        6
+      ],
+      [
+        273,
+        144,
+        64,
+        33,
+        9,
+        6
+      ]
+    ],
+    [
+      "B",
+      953,
+      [
+        265,
+        137,
+        73,
+        6
+      ],
+      [
+        265,
+        137,
+        73,
+        32,
+        25,
+        6
+      ]
+    ],
+    [
+      "B",
+      961,
+      [
+        265,
+        185,
+        80,
+        6
+      ],
+      [
+        265,
+        128,
+        64,
+        41,
+        16,
+        6
+      ]
+    ],
+    [
+      "B",
+      965,
+      [
+        272,
+        185,
+        73,
+        6
+      ],
+      [
+        257,
+        128,
+        73,
+        40,
+        17,
+        6
+      ]
+    ]
+  ],
+  "expected": {
+    "output_content_sha256": "e78047028c7dcd25fb1b6216c2b53eda76d2f91292b21d43f5d1903cc13a5c6c",
+    "local_profile": {
+      "1": 2556,
+      "2": 334,
+      "3": 430,
+      "4": 194,
+      "5": 56,
+      "8": 8
+    },
+    "width_inventory": {
+      "4": 80,
+      "5": 32,
+      "7": 54,
+      "8": 122,
+      "9": 216
+    }
+  }
+}
diff --git a/research/gauge44-slots-t16/construction/frames/LOCAL-PINS-frames-sw4.json b/research/gauge44-slots-t16/construction/frames/LOCAL-PINS-frames-sw4.json
new file mode 100644
index 0000000000..834ae13a2f
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/frames/LOCAL-PINS-frames-sw4.json
@@ -0,0 +1,12 @@
+{
+ "word": "P6k4sw4f8",
+ "frame_build_controls": 3,
+ "frame_controls": 10,
+ "layer_controls": 95,
+ "canonical_sha256": "b0d27d99423047ce07af847734f5a86f9411038bb3b0bf721918ece1ee579325",
+ "program_sha256": {
+  "forward": "b2cf8298488cc81aeee1385d4d9ebd842efbb21abb9296fca903adb8ad50f8d0",
+  "backward": "6f28cf1413671d5b7c50488a1603fa8f1558da469abbbb45b6a9b66ec640712b"
+ },
+ "clifford_recipes_sha256": "eb7569e004bd2a2937928db9db49dad949ec291f00c2d21df6af722df7cb6c9c"
+}
diff --git a/research/gauge44-slots-t16/construction/frames/build_frames.py b/research/gauge44-slots-t16/construction/frames/build_frames.py
new file mode 100644
index 0000000000..22021549e6
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/frames/build_frames.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Apply the eight pinned B-gate frame raises of FRAME-RECIPE-sw4.json (chafreaky's PR741) to the SW4 word.
+
+usage: build_frames.py INPUT_WORD.json.gz OUT_DIR RECIPE.json
+
+Standard library only. The frames are applied by BlockInvert's `../promo/build_promotion.apply` (no entrances, eight
+'B' gate_frames), which checks each old frame and recomputes the local profile and widths. This builder then checks:
+input sha pin; the scalar program of A, cut, B, precondition and cleanup unchanged (every field but the frame); start
+and end frames unchanged; local profile and width inventory equal to the recipe's; output sha pin. Three pin controls
+(input pin, wrong old frame, output pin) must be rejected at their pinned reasons on every build.
+Adapted from PR741's extras/build_frames.py (chafreaky). Apache-2.0.
+"""
+import copy, gzip, hashlib, importlib.util, json, sys
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+_s = importlib.util.spec_from_file_location('promotion', HERE.parent / 'promo/build_promotion.py')
+B = importlib.util.module_from_spec(_s); _s.loader.exec_module(B)
+
+
+def construct(raw, recipe):
+    assert hashlib.sha256(raw).hexdigest() == recipe['input_content_sha256'], 'input word pin'
+    w = json.loads(raw)
+    assert len(recipe['gate_frames']) == 8 and all(c[0] == 'B' for c in recipe['gate_frames']), 'eight B frames'
+    out = B.apply(w, dict(entrances={}, gate_frames=recipe['gate_frames']))
+    for section in ('A', 'cut', 'B', 'precondition', 'cleanup'):
+        assert [e[:-1] for e in w[section]] == [e[:-1] for e in out[section]], 'scalar program unchanged'
+    assert out['start_extra'] == w['start_extra'] and out['helper_final'] == w['helper_final'], 'endpoint frames unchanged'
+    assert out['report']['local_profile'] == recipe['expected']['local_profile'] and \
+        out['report']['width_inventory'] == recipe['expected']['width_inventory'], 'profile and width pins'
+    data = json.dumps(out, sort_keys=True, separators=(',', ':')).encode()
+    assert hashlib.sha256(data).hexdigest() == recipe['expected']['output_content_sha256'], 'output word pin'
+    return data
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    inp, outd, rfile = map(Path, sys.argv[1:4])
+    raw = gzip.decompress(inp.read_bytes()); recipe = json.loads(rfile.read_text())
+    data = construct(raw, recipe)
+    rejected = []
+    for name, change, reason in [
+            ('input-pin', lambda r: r.__setitem__('input_content_sha256', '0' * 64), 'input word pin'),
+            ('old-frame', lambda r: r['gate_frames'][0].__setitem__(2, []), 'gate frame mismatch'),
+            ('output-pin', lambda r: r['expected'].__setitem__('output_content_sha256', '0' * 64), 'output word pin')]:
+        r = copy.deepcopy(recipe); change(r)
+        try:
+            construct(raw, r)
+        except AssertionError as e:
+            assert reason in str(e), (name, str(e)); rejected.append(dict(name=name, reason=reason))
+        else:
+            raise AssertionError('accepted ' + name)
+    outd.mkdir(parents=True)
+    (outd / 'FULL-WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+    (outd / 'BUILD.json').write_text(json.dumps(dict(
+        status='PASS_EIGHT_FRAME_EXACT_CONSTRUCTION', input_sha256=hashlib.sha256(raw).hexdigest(),
+        output_sha256=hashlib.sha256(data).hexdigest(), scalar_program_unchanged=True, frames=8,
+        rejected_controls=rejected), indent=2) + '\n')
+    print('PASS eight B frames and three pin controls')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/frames/frame_controls.py b/research/gauge44-slots-t16/construction/frames/frame_controls.py
new file mode 100644
index 0000000000..cd951a9f0e
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/frames/frame_controls.py
@@ -0,0 +1,45 @@
+#!/usr/bin/env python3
+"""Focused native controls for the eight B-frame raises (PR741's extras/frame_controls.py, ported).
+
+usage: frame_controls.py WORD.json.gz ROUTING.json.gz OUT.json RECIPE.json   (env PR635_CODE = PR635's code/ directory)
+
+The positive word must pass PR635's unchanged native audit `hpe_audit_and_transport.run`. Ten mutants must be rejected
+at their pinned reasons: each of the eight raised gates with its frame emptied ('nonmonotone'), a doubled read
+coefficient on the first raised gate ('arbitrary-dirt endpoint') and a tampered paid profile ('paid local profile
+differs'). Apache-2.0; adapted from chafreaky's PR741.
+"""
+import copy, gzip, importlib.util, json, os, sys, tempfile, time
+from pathlib import Path
+
+_s = importlib.util.spec_from_file_location('audit', Path(os.environ['PR635_CODE']) / 'hpe_audit_and_transport.py')
+A = importlib.util.module_from_spec(_s); _s.loader.exec_module(A)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    word, routing, out, rfile = map(Path, sys.argv[1:5])
+    w = json.loads(gzip.decompress(word.read_bytes())); recipe = json.loads(rfile.read_text())
+
+    def trial(z):
+        with tempfile.TemporaryDirectory() as td:
+            d = Path(td); f = d / 'word.json.gz'; f.write_bytes(gzip.compress(json.dumps(z).encode(), mtime=0))
+            try:
+                A.run(f, routing, d / 'native'); return None
+            except AssertionError as e:
+                return str(e)
+
+    start = time.monotonic(); assert trial(w) is None, 'positive word rejected'; records = []
+    for section, i, old, new in recipe['gate_frames']:
+        z = copy.deepcopy(w); z[section][i][-1] = []; error = trial(z)
+        assert error and 'nonmonotone' in error, (i, error); records.append(dict(name='frame-%d-emptied' % i, rejected=error))
+    z = copy.deepcopy(w); i = recipe['gate_frames'][0][1]; z['B'][i][3] *= 2; error = trial(z)
+    assert error and 'arbitrary-dirt endpoint' in error, error; records.append(dict(name='changed-read-coefficient', rejected=error))
+    z = copy.deepcopy(w); z['report']['local_profile']['1'] += 1; error = trial(z)
+    assert error and 'paid local profile differs' in error, error; records.append(dict(name='paid-profile-tampering', rejected=error))
+    out.write_text(json.dumps(dict(status='PASS_FOCUSED_EIGHT_FRAME_NATIVE_CONTROLS', positive=1, rejected=records,
+                                   seconds=time.monotonic() - start), indent=2) + '\n')
+    print('PASS', len(records), 'mutations', flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/frames/reproduce_frames.py b/research/gauge44-slots-t16/construction/frames/reproduce_frames.py
new file mode 100644
index 0000000000..eaf9b47cac
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/frames/reproduce_frames.py
@@ -0,0 +1,89 @@
+#!/usr/bin/env python3
+"""Rebuild the SW4F8 word (eight B-gate frame raises on the SW4 word, chafreaky's PR741 recipe) and its native locals.
+
+Input: a fresh `construction/sw4/reproduce_sw4.py --recipe P6k4` output directory; its SW4 word (d232183f...) is pinned
+there and by FRAME-RECIPE-<id>.json. Steps, each checked exactly:
+  1. frames: build_frames.py (standard library only) applies the eight 'B' gate_frames with BlockInvert's
+     build_promotion.apply. Scalar program, start and end frames unchanged; profile, widths and output sha pinned;
+     three pin controls must be rejected (count pinned).
+  2. frame-controls: frame_controls.py, PR741's ten focused mutants judged by PR635's unchanged native audit.
+  3. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant) on the SW4F8 word; count pinned.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs, with the canonical word, local
+     programs and Clifford recipes pinned (LOCAL-PINS-frames-<id>.json).
+Apache-2.0.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P6 = HERE.parent / 'layers_p6n'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--sw4-dir', type=Path, required=True, help='construction/sw4/reproduce_sw4.py output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--recipe', default='sw4', help='FRAME-RECIPE-<id>.json and LOCAL-PINS-frames-<id>.json')
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('FRAME-RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-frames-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    inp = a.sw4_dir.resolve() / 'sw4/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['input_content_sha256'], 'input must be the pinned SW4 word'
+    run('frames', HERE / 'build_frames.py', inp, out / 'frames', rfile, portable=False)
+    b = read(out / 'frames/BUILD.json')
+    assert b['status'] == 'PASS_EIGHT_FRAME_EXACT_CONSTRUCTION' and len(b['rejected_controls']) == pins['frame_build_controls'], b
+    word = out / 'frames/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['expected']['output_content_sha256']
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('frame-controls', HERE / 'frame_controls.py', word, routing, out / 'FRAME-CONTROLS.json', rfile, portable=False)
+    fc = read(out / 'FRAME-CONTROLS.json')
+    assert fc['status'] == 'PASS_FOCUSED_EIGHT_FRAME_NATIVE_CONTROLS' and len(fc['rejected']) == pins['frame_controls'], len(fc['rejected'])
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/jx/LOCAL-PINS-jx-X4.json b/research/gauge44-slots-t16/construction/jx/LOCAL-PINS-jx-X4.json
new file mode 100644
index 0000000000..417e4ba7a1
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/jx/LOCAL-PINS-jx-X4.json
@@ -0,0 +1,11 @@
+{
+ "word": "X4",
+ "jx_controls": 7,
+ "layer_controls": 95,
+ "canonical_sha256": "1c0e9da767d4418f70016af599e4a447a3f7777acabe930318459c0fbbd260aa",
+ "program_sha256": {
+  "forward": "076a2d428f97abb30473df05110998efbe5ac809885bae4ceb1b8bd81329a1e6",
+  "backward": "7915679ee305927463d19725360cc15132dd21ede18897d09a935dca1df0d55d"
+ },
+ "clifford_recipes_sha256": "20dddfce0ded7e41dc507939df7297bd98aec1286e05d7dbf18000d57e69a0b7"
+}
diff --git a/research/gauge44-slots-t16/construction/jx/RECIPE-X4.json b/research/gauge44-slots-t16/construction/jx/RECIPE-X4.json
new file mode 100644
index 0000000000..30f7fa5948
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/jx/RECIPE-X4.json
@@ -0,0 +1,1412 @@
+{
+ "input_content_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+ "input_word": "P6k4sw4 (BRoute w/P6k4sw4, d232183f)",
+ "frames_741_source": {
+  "pr": 741,
+  "commit": "e516b146",
+  "recipe": "scratch/WasteAttack/FRAME-RECIPE-741.json",
+  "frames_only_output_sha": "e78047028c7dcd25fb1b6216c2b53eda76d2f91292b21d43f5d1903cc13a5c6c"
+ },
+ "frames_741": [
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+   ]
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+     1
+    ],
+    "why": "h2r: delete t pre-read of h"
+   }
+  ],
+  "insert": [
+   {
+    "h": 448,
+    "before": 2,
+    "gate": [
+     "add",
+     132,
+     448,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 448,
+    "before": 2,
+    "gate": [
+     "add",
+     141,
+     448,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 472,
+    "before": 34,
+    "gate": [
+     "add",
+     141,
+     472,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 472,
+    "before": 34,
+    "gate": [
+     "add",
+     172,
+     472,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 458,
+    "before": 22,
+    "gate": [
+     "add",
+     196,
+     458,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 458,
+    "before": 22,
+    "gate": [
+     "add",
+     205,
+     458,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 592,
+    "before": 66,
+    "gate": [
+     "add",
+     205,
+     592,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 592,
+    "before": 66,
+    "gate": [
+     "add",
+     170,
+     592,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 470,
+    "before": 30,
+    "gate": [
+     "add",
+     164,
+     470,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 470,
+    "before": 30,
+    "gate": [
+     "add",
+     206,
+     470,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 604,
+    "before": 74,
+    "gate": [
+     "add",
+     206,
+     604,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 604,
+    "before": 74,
+    "gate": [
+     "add",
+     138,
+     604,
+     1,
+     2
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 482,
+    "before": 38,
+    "gate": [
+     "add",
+     162,
+     482,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 482,
+    "before": 38,
+    "gate": [
+     "add",
+     198,
+     482,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 614,
+    "before": 97,
+    "gate": [
+     "add",
+     198,
+     614,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   },
+   {
+    "h": 614,
+    "before": 97,
+    "gate": [
+     "add",
+     130,
+     614,
+     -1,
+     1
+    ],
+    "why": "r2h: pre-read of h (h = E_h) after h last pre-read"
+   }
+  ]
+ },
+ "pairs": {
+  "448": 235,
+  "458": 58,
+  "470": 26,
+  "472": 267,
+  "482": 18,
+  "592": 427,
+  "604": 443,
+  "614": 50
+ },
+ "expected": {
+  "output_content_sha256": "1e1d99ba7aab877d6b573c41f7030ee73de9a52fee51d0a822ddaae71251999f",
+  "local_profile": {
+   "1": 2548,
+   "2": 338,
+   "3": 430,
+   "4": 194,
+   "5": 56,
+   "8": 8
+  }
+ },
+ "controls": {
+  "C0_identity": {
+   "mutation": {
+    "kind": "empty"
+   },
+   "expected_sha": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+   "local_profile": {
+    "1": 2548,
+    "2": 342,
+    "3": 438,
+    "4": 186,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "C1_741_only": {
+   "mutation": {
+    "kind": "only_edits_of",
+    "h": [],
+    "raises": []
+   },
+   "expected_sha": "e78047028c7dcd25fb1b6216c2b53eda76d2f91292b21d43f5d1903cc13a5c6c",
+   "local_profile": {
+    "1": 2556,
+    "2": 334,
+    "3": 430,
+    "4": 194,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "M1_one_pair_448": {
+   "mutation": {
+    "kind": "only_edits_of",
+    "h": [
+     448
+    ],
+    "raises": [
+     862,
+     870
+    ]
+   },
+   "expected_sha": "5fb6fb2e5e63d18b865535c1dbd3dbaddab530c39429a4b09f11ac96723257c9",
+   "local_profile": {
+    "1": 2556,
+    "2": 334,
+    "3": 430,
+    "4": 194,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "N1_drop_preread": {
+   "mutation": {
+    "kind": "drop_insert",
+    "k": 0
+   },
+   "rejection_expected": [
+    "exactness rows",
+    [
+     132,
+     135
+    ]
+   ]
+  },
+  "N2_wrong_sign_preread": {
+   "mutation": {
+    "kind": "flip_insert_sign",
+    "k": 0
+   },
+   "rejection_expected": [
+    "exactness rows",
+    [
+     132,
+     135
+    ]
+   ]
+  },
+  "N3_plain_join_moved_reads": {
+   "mutation": {
+    "kind": "drop_raises"
+   },
+   "expected_sha": "7241cd59dd0376e0b2e1b5ba8403c5423d247ddd7cbcc2f02bdc353752806f30",
+   "local_profile": {
+    "1": 2532,
+    "2": 378,
+    "3": 430,
+    "4": 178,
+    "5": 56,
+    "8": 8
+   }
+  },
+  "N4_raise_dim7_at_855": {
+   "mutation": {
+    "kind": "frame",
+    "i": 855,
+    "frame": [
+     280,
+     128,
+     64,
+     40,
+     4,
+     2,
+     1
+    ]
+   },
+   "rejection_expected": [
+    "cap",
+    1302,
+    174
+   ]
+  }
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/jx/build_jx.py b/research/gauge44-slots-t16/construction/jx/build_jx.py
new file mode 100644
index 0000000000..f8d74a6324
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/jx/build_jx.py
@@ -0,0 +1,167 @@
+#!/usr/bin/env python3
+"""build_jx.py --input WORD --recipe RECIPE.json --out OUT.json.gz [--control NAME] [--no-pin]
+
+Stdlib-only builder: joint read-set exchange (copy pairs, BRoute sw4 rule) + explicit B frame raises on P6k4sw4.
+Steps:
+ 1. input content sha256 must equal recipe.input_content_sha256.
+ 2. explicit B edits: replace (old gate asserted), delete (old gate asserted), insert (before an original index).
+ 3. frames: replaced/inserted gates take the plain join of their operands' current frames; gates listed in
+    frames_741 / raises take base = the listed frame and the resulting frame must EQUAL it (explicit frames);
+    every other gate keeps span(stored frame + operand frames) (monotone repair). Early cleanup likewise.
+ 4. legality: target frames inside u_t^perp at every gate; tails inside helper_final; every end frame contains the
+    final frame; the explicit frame must contain the join (enforced by equality in 3).
+ 5. exactness: the rational linear map of the whole B segment is identical to the input's (Fraction replay).
+ 6. paid profile recomputed (A + centre levels + B + tails + ends) and written to report.local_profile.
+Output: canonical json (sort_keys, compact) gzip mtime=0. Exit 0 and prints output sha; exit 2 with the first
+rejection (site) on failure. --control applies a named mutation from recipe.controls (expected to be rejected
+or to give a pinned sha)."""
+import argparse, gzip, json, hashlib, sys, copy
+from fractions import Fraction as Fr
+from collections import Counter
+
+V, H = 112, 9
+
+def basis(vs):
+    piv = {}
+    for a in vs:
+        while a:
+            b = a.bit_length() - 1
+            if b in piv: a ^= piv[b]
+            else: piv[b] = a; break
+    for k in sorted(piv):
+        for j in sorted(piv):
+            if j > k and (piv[j] >> k) & 1: piv[j] ^= piv[k]
+    return tuple(piv[k] for k in sorted(piv, reverse=True))
+
+def contained(a, b): return basis(list(a) + list(b)) == tuple(b)
+def registers(e): return e[1:3] if e[0] == 'add' else e[1:2]
+def hyper(p): return basis([x for x in range(1, 1 << H) if (x & p).bit_count() % 2 == 0])
+FULL = basis([1 << i for i in range(H)])
+def csha(w): return hashlib.sha256(json.dumps(w, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+
+class Reject(Exception): pass
+
+def symstate(gs):
+    rows = {}
+    for e in gs:
+        for q in registers(e): rows.setdefault(q, {q: Fr(1)})
+        if e[0] == 'add':
+            t, s = e[1], e[2]; c = Fr(e[3], e[4]); d = rows[t]
+            for k, x in list(rows[s].items()):
+                a = d.get(k, 0) + c * x
+                if a: d[k] = a
+                else: d.pop(k, None)
+        else:
+            t = e[1]; c = Fr(e[2], e[3]); rows[t] = {k: c * x for k, x in rows[t].items()}
+    return rows
+
+def build(w, rc, control=None):
+    w = copy.deepcopy(w); B0 = w['B']
+    edits = copy.deepcopy(rc['edits']); explicit = {int(i): f for i, f in rc['frames_741']}
+    for i, f in rc['raises']:
+        if int(i) in explicit: raise Reject(('duplicate frame', i))
+        explicit[int(i)] = f
+    if control:
+        c = rc['controls'][control]['mutation']
+        if c['kind'] == 'drop_insert': edits['insert'] = [x for k, x in enumerate(edits['insert']) if k != c['k']]
+        elif c['kind'] == 'flip_insert_sign': edits['insert'][c['k']]['gate'][3] *= -1
+        elif c['kind'] == 'frame': explicit[c['i']] = c['frame']
+        elif c['kind'] == 'drop_edits': edits = dict(replace=[], delete=[], insert=[])
+        elif c['kind'] == 'drop_raises': explicit = {int(i): f for i, f in rc['frames_741']}
+        elif c['kind'] == 'only_edits_of':
+            hs = set(c['h'])
+            edits = {k: [x for x in v if x['h'] in hs] for k, v in edits.items()}
+            explicit = {i: f for i, f in explicit.items() if i in {int(j) for j, _ in rc['frames_741']} or i in set(c['raises'])}
+        elif c['kind'] == 'empty': edits = dict(replace=[], delete=[], insert=[]); explicit = {}
+        else: raise SystemExit('unknown control')
+    B = [list(e) for e in B0]; tag = set(); dele = set(); ins = {}
+    for x in edits['replace']:
+        i = x['i']
+        if B[i][:-1] != x['old']: raise Reject(('replace old mismatch', i))
+        B[i] = list(x['new']) + [B[i][-1]]; tag.add(i)
+    for x in edits['delete']:
+        i = x['i']
+        if B[i][:-1] != x['old']: raise Reject(('delete old mismatch', i))
+        dele.add(i)
+    for x in edits['insert']: ins.setdefault(x['before'], []).append(list(x['gate']) + [None])
+    NB, nt, key = [], set(), []
+    for i, e in enumerate(B):
+        for g in ins.get(i, []): nt.add(len(NB)); NB.append(g); key.append(None)
+        if i in dele: continue
+        if i in tag: nt.add(len(NB))
+        NB.append(e); key.append(i)
+    # frames + paid
+    R = w['report']['R']; n = 2 * V + R
+    END = [FULL] * V + [hyper(p) for p in w['ports']] + [FULL] * R
+    for q, U in w['helper_final'].items(): END[int(q)] = basis(U)
+    cur = [(p,) for p in w['ports']] + [()] * (V + R)
+    for q, U in w['start_extra'].items(): cur[int(q)] = basis(U)
+    paid = Counter()
+    for e in w['A']:
+        for q in registers(e):
+            U = basis(e[-1]); d = len(U) - len(cur[q])
+            if d: paid[d] += 1
+            cur[q] = U
+    lev = {int(t): basis(U) for t, U in w.get('target_levels', {}).items()}
+    for q, U in zip(w['centers'], w['center_frames']):
+        U = basis(U); served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == q}
+        for T in sorted(served, key=lambda x: -len(x)):
+            if T != U: paid[len(U) - len(T)] += 1
+            U = T
+    used = set()
+    for j, e in enumerate(NB):
+        rs = registers(e); k = key[j]
+        if k is not None and k in explicit: base = list(explicit[k]); used.add(k)
+        elif j in nt or e[-1] is None: base = []
+        else: base = list(e[-1])
+        F = basis(base + [x for q in rs for x in cur[q]])
+        if k is not None and k in explicit and F != basis(explicit[k]): raise Reject(('explicit frame below join', k))
+        for q in rs:
+            if V <= q < 2 * V and not contained(F, END[q]): raise Reject(('cap', j, q))
+            d = len(F) - len(cur[q])
+            if d: paid[d] += 1
+            cur[q] = F
+        NB[j] = list(e[:-1]) + [list(F)]
+    if used != set(explicit): raise Reject(('unused explicit frame', sorted(set(explicit) - used)))
+    newearly = []
+    for i, U in w['early_cleanup']:
+        rs = registers(w['cleanup'][i]); F = basis(list(U) + [x for q in rs for x in cur[q]])
+        for q in rs:
+            if w['helper_final'].get(str(q)) is not None and not contained(F, END[q]): raise Reject(('tailend', i, q))
+            d = len(F) - len(cur[q])
+            if d: paid[d] += 1
+            cur[q] = F
+        newearly.append([i, list(F)])
+    for q in range(n):
+        if not contained(cur[q], END[q]): raise Reject(('end', q))
+        d = len(END[q]) - len(cur[q])
+        if d: paid[d] += 1
+    # exactness of the B segment
+    a, b = symstate([e[:-1] for e in B0]), symstate([e[:-1] for e in NB])
+    bad = sorted(q for q in set(a) | set(b) if a.get(q, {q: Fr(1)}) != b.get(q, {q: Fr(1)}))
+    if bad: raise Reject(('exactness rows', bad))
+    w['B'] = NB; w['early_cleanup'] = newearly
+    w['report'] = dict(w['report']); w['report']['local_profile'] = {str(k): v for k, v in sorted(paid.items())}
+    return w
+
+def main():
+    ap = argparse.ArgumentParser(); ap.add_argument('--input', required=True); ap.add_argument('--recipe', required=True)
+    ap.add_argument('--out'); ap.add_argument('--control'); ap.add_argument('--no-pin', action='store_true')
+    a = ap.parse_args()
+    w = json.loads(gzip.decompress(open(a.input, 'rb').read())); rc = json.load(open(a.recipe))
+    if csha(w) != rc['input_content_sha256']: print('REJECT input pin'); sys.exit(2)
+    pin = rc['controls'][a.control].get('rejection_expected') if a.control else None
+    try: o = build(w, rc, a.control)
+    except Reject as r:
+        got = json.loads(json.dumps(r.args[0])); print('REJECT', json.dumps(got))
+        if pin is not None:
+            print('CONTROL', 'PINNED' if got == pin else 'PIN MISMATCH %s' % json.dumps(pin)); sys.exit(0 if got == pin else 4)
+        sys.exit(2)
+    if pin is not None and not a.no_pin: print('CONTROL NOT REJECTED, pinned', json.dumps(pin)); sys.exit(4)
+    s = csha(o)
+    exp = rc['controls'][a.control].get('expected_sha') if a.control else rc['expected']['output_content_sha256']
+    print('OK', s, o['report']['local_profile'])
+    if a.out: open(a.out, 'wb').write(gzip.compress(json.dumps(o, sort_keys=True, separators=(',', ':')).encode(), mtime=0))
+    if not a.no_pin and exp and s != exp: print('REJECT output pin', exp); sys.exit(3)
+
+if __name__ == '__main__': main()
diff --git a/research/gauge44-slots-t16/construction/jx/reproduce_jx.py b/research/gauge44-slots-t16/construction/jx/reproduce_jx.py
new file mode 100644
index 0000000000..6829a1b25d
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/jx/reproduce_jx.py
@@ -0,0 +1,99 @@
+#!/usr/bin/env python3
+"""Rebuild the X4 word (JointXF: joint read-set exchange on four further copy-pair instances plus explicit B frame
+raises, including chafreaky's PR741 eight frames) and its native locals.
+
+Input: a fresh `construction/sw4/reproduce_sw4.py --recipe P6k4` output directory; its SW4 word (d232183f...) is pinned
+there and by RECIPE-X4.json. Steps, each checked exactly:
+  1. jx: build_jx.py (standard library only; JointXF) applies the recipe's explicit B edits (replace / delete / insert,
+     each old gate asserted), the PR741 frames and the explicit raises, repairs all other frames monotonically, checks
+     target frames inside u_t^perp, tails and ends, and the exactness of the whole B segment (rational replay), and
+     pins the output sha.
+  2. jx-controls: every control in the recipe is rebuilt and must reproduce its pinned outcome exactly: a pinned
+     rejection site (exit 0 with CONTROL PINNED) or a pinned output sha. C1_741_only must reproduce PR741's word
+     e78047028c... (the construction/frames step's output); C0_identity reproduces the input.
+  3. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant) on the X4 word; count pinned.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs; canonical word, local programs
+     and Clifford recipes pinned (LOCAL-PINS-jx-X4.json).
+Apache-2.0. Driver by ColdWitness around JointXF's builder.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P6 = HERE.parent / 'layers_p6n'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--sw4-dir', type=Path, required=True, help='construction/sw4/reproduce_sw4.py output')
+    ap.add_argument('--recipe', default='X4', help='RECIPE-<id>.json and LOCAL-PINS-jx-<id>.json')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-jx-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True, ok=(0,)):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc in ok, (label, rc)
+        print('PASS', label, flush=True)
+        return (out / (label + '.log')).read_text()
+
+    inp = a.sw4_dir.resolve() / 'sw4/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['input_content_sha256'], 'input must be the pinned SW4 word'
+    (out / 'jx').mkdir(); word = out / 'jx/FULL-WORD.json.gz'
+    run('jx', HERE / 'build_jx.py', '--input', inp, '--recipe', rfile, '--out', word, portable=False)
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['expected']['output_content_sha256']
+    assert len(rec['controls']) == pins['jx_controls'], len(rec['controls'])
+    results = {}
+    for name, c in sorted(rec['controls'].items()):
+        log = run('jx-control-' + name, HERE / 'build_jx.py', '--input', inp, '--recipe', rfile, '--control', name, portable=False)
+        if 'rejection_expected' in c:
+            assert 'CONTROL PINNED' in log, (name, log[-300:]); results[name] = dict(rejected=c['rejection_expected'])
+        else:
+            assert ('OK ' + c['expected_sha']) in log, (name, log[-300:]); results[name] = dict(sha=c['expected_sha'])
+    assert rec['controls']['C1_741_only']['expected_sha'] == rec['frames_741_source']['frames_only_output_sha']
+    (out / 'JX-CONTROLS.json').write_text(json.dumps(dict(status='PASS_JX_PINNED_CONTROLS', controls=results), indent=1) + '\n')
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/layers/build_pivot_swap.py b/research/gauge44-slots-t16/construction/layers/build_pivot_swap.py
new file mode 100644
index 0000000000..b225601c01
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/layers/build_pivot_swap.py
@@ -0,0 +1,160 @@
+"""Cost-neutral pivot-role swaps inside existing entrance-kernel families.  Apache-2.0.  Prepared with Claude Code
+assistance.  The pivot/donor role exchange follows PR266's "pivot role is moved" idea (bit side), applied here to the
+complex supplier's multicut kernel families (PR568 build_multicut_kernels.py shape).
+
+A kernel family on the input word is an entering helper p (start_extra E) together with the gates that read p at frame
+E before any other touch of p:  d += c_d * p @E  (d a helper or, in B, a target).  They cancel p's complete dirty
+response:  col(p) + sum_d c_d * col_{g_d}(d) = 0, where col_{g}(d) is d's suffix response from gate g on.
+
+Swap to the new pivot x (a helper donor of the family with exactly one family gate g_x = x's FIRST touch, and no other
+touch of x up to the family's last gate):
+    g_x :  x += c_x p   ->   p += (1/c_x) x
+    g_d :  d += c_d p   ->   d += (c_d/c_x) x          (d != x, same position and frame E)
+    start_extra: p -> x (same E); cleanup regenerated by the inherited inverse rule.
+Exactness (PROOF-NOTE-PIVOT.md): x holds only its initial dirt at every rewritten gate, and p holds only its initial dirt
+until g_x, so x's new response is col(x) + col(p)/c_x + sum_d (c_d/c_x) col_{g_d}(d) = (c_x col(x) + col(p) +
+sum_d c_d col_{g_d}(d)) / c_x = 0, because col(x) = col_{g_x}(x).  This script checks it by exact rational replay anyway.
+Cost: the frame chains of p and x are exchanged (p now climbs [] -> E at g_x where x did; x starts at E where p did), so
+gk_word.profile and the width multiset are unchanged; both are asserted.
+
+Recipe: {input_content_sha256, output_content_sha256, swaps: [{pivot, new_pivot, entrance, gates: [{part, index,
+before, after}]}]}.  Every expected `after` gate is recomputed from the rule above and must equal the recipe.
+
+Negative controls (--controls): mutated recipes/words that must be rejected at pinned reasons:
+  * nonzero response: another family gate's rescaled coefficient has the wrong sign;
+  * wrong pivot coefficient: g_x's new coefficient doubled;
+  * wrong entrance: the recipe's entrance is not p's start_extra;
+  * non-family gate: a recipe gate whose `before` is not the word's gate;
+  * new pivot touched in the window: x replaced by a family donor that is not a fresh helper (a target donor, or the
+    first other helper donor when the family has no target donor).
+"""
+from pathlib import Path
+from collections import Counter
+from fractions import Fraction as Q
+import argparse, copy, gzip, hashlib, json, sys
+assert __debug__, 'Assertions required'
+ap = argparse.ArgumentParser()
+for k in ('--input', '--recipe', '--gk-dir', '--out'): ap.add_argument(k, type=Path, required=True)
+a = ap.parse_args(); assert not a.out.exists()
+sys.path.insert(0, str(a.gk_dir)); import gk_word as G, gk_common as C
+G.V = C.V = 112; G.DATA = C.DATA = 7168
+V = 112
+raw = json.loads(gzip.decompress(a.input.read_bytes())); recipe = json.loads(a.recipe.read_text())
+enc = lambda x: json.dumps(x, sort_keys=True, separators=(',', ':')).encode(); sha = lambda x: hashlib.sha256(x).hexdigest()
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+inv_rule = lambda w: [G.inverse(e, G.FULL) for e in reversed(w['A'] + w['B']) if not V <= e[1] < 2 * V]
+dy = lambda q: q != 0 and q.denominator & (q.denominator - 1) == 0
+
+
+def response(w, h):
+    rows = {}
+    def get(r): return rows.setdefault(r, {r: Q(1)})
+    for e in w['A'] + w['cut'] + w['B']:
+        if e[0] == 'scale':
+            q = Q(e[2], e[3]); rows[e[1]] = {j: q * x for j, x in get(e[1]).items()}
+        else:
+            t, s = e[1], e[2]; q = Q(e[3], e[4]); src = get(s); tgt = get(t)
+            for j, x in list(src.items()):
+                z = tgt.get(j, Q(0)) + q * x
+                if z: tgt[j] = z
+                else: tgt.pop(j, None)
+    return {r: rows[r][h] for r in range(V, 2 * V) if r in rows and rows[r].get(h)}
+
+
+def build(w0, rec):
+    w = copy.deepcopy(w0); n = 2 * V + w['report']['R']
+    assert w['cleanup'] == inv_rule(w), 'input cleanup is not the inherited inverse rule'
+    P0 = G.profile(w); W0 = Counter(C.widths_of(w))
+    AB = [('A', i) for i in range(len(w['A']))] + [('B', i) for i in range(len(w['B']))]
+    pos = {k: j for j, k in enumerate(AB)}
+    seen = set(); receipts = []; rules = []
+    for s in rec['swaps']:
+        p, x, E = s['pivot'], s['new_pivot'], s['entrance']
+        assert 2 * V <= p < n and w['start_extra'].get(str(p)) == E, 'pivot is not an entering helper at the entrance'
+        assert 2 * V <= x < n and x not in w['centers'], 'new pivot must be a helper'
+        assert str(x) not in w['start_extra'], 'new pivot already entering'
+        assert not {p, x} & seen, 'registers shared between swaps'; seen |= {p, x}
+        gs = s['gates']; ks = [pos[(g['part'], g['index'])] for g in gs]
+        assert ks == sorted(ks) and len(set(ks)) == len(ks)
+        for g in gs:
+            e = w[g['part']][g['index']]
+            assert e == g['before'], 'recipe gate is not the word gate'
+            assert e[0] == 'add' and e[2] == p and e[1] != p and list(e[-1]) == list(E), 'not a family gate (d += c p @E)'
+        touch = lambda r: [j for j, (part, i) in enumerate(AB) if r in regs(w[part][i])]
+        tp = touch(p); assert tp[:len(ks)] == ks, 'family gates must be all touches of the pivot up to its first other touch'
+        gx = [k for k, g in zip(ks, gs) if g['before'][1] == x]; assert len(gx) == 1, 'new pivot must have exactly one family gate'
+        tx = touch(x); assert tx[0] == gx[0], 'new pivot touched before its family gate'
+        assert len(tx) == 1 or tx[1] > ks[-1], 'new pivot touched inside the family window'
+        cx = Q(*[g['before'][3:5] for g in gs if g['before'][1] == x][0])
+        for g in gs:
+            d, f = g['before'][1], g['after']
+            assert f[0] == 'add' and list(f[-1]) == list(E) and (f[1:3] == [p, x] if d == x else f[1:3] == [d, x]), 'after-gate shape'
+            assert dy(Q(f[3], f[4])), 'non-dyadic swapped coefficient'
+            w[g['part']][g['index']] = f
+            q = 1 / cx if d == x else Q(g['before'][3], g['before'][4]) / cx
+            rules.append((f, ['add', p, x, q.numerator, q.denominator, list(E)] if d == x else ['add', d, x, q.numerator, q.denominator, list(E)]))
+        w['start_extra'][str(x)] = w['start_extra'].pop(str(p))
+        receipts.append(dict(pivot=p, new_pivot=x, entrance=E, family_gates=len(gs)))
+    w['cleanup'] = inv_rule(w)
+    for s in rec['swaps']:
+        assert not response(w, s['new_pivot']), 'new pivot dirty response not zero'
+    assert all(f == e for f, e in rules), 'recipe after-gate is not the swap rule'
+    P1 = G.profile(w)
+    assert P1 == P0, 'paid profile not identical (swap is not cost-neutral)'
+    assert Counter(C.widths_of(w)) == W0, 'width multiset changed'
+    w['report']['local_profile'] = {str(k): v for k, v in sorted(P1.items())}
+    w['report']['local_rank_mass'] = sum(k * v for k, v in P1.items())
+    return w, receipts
+
+
+assert sha(enc(raw)) == recipe['input_content_sha256'], 'input content'
+out, receipts = build(raw, recipe)
+o = enc(out); assert sha(o) == recipe['output_content_sha256'], sha(o)
+
+# ---- negative controls -------------------------------------------------------------------------------------------
+WHY = dict(nonzero='new pivot dirty response not zero', coef='new pivot dirty response not zero',
+           entrance='paid profile not identical', nonfamily='recipe gate is not the word gate',
+           window='new pivot')
+controls = []
+
+
+def reject(name, mut, why):
+    r = copy.deepcopy(recipe); w = copy.deepcopy(raw)
+    mut(r, w)
+    try:
+        build(w, r)
+    except AssertionError as ex:
+        msg = str(ex)
+        assert why in msg, ('control rejected for the wrong reason', name, msg)
+        controls.append(dict(control=name, reason=msg)); return
+    raise AssertionError('control accepted: ' + name)
+
+
+for si, s in enumerate(recipe['swaps']):
+    x = s['new_pivot']; tag = '%d->%d' % (s['pivot'], x)
+    def m_other(r, w, si=si):
+        g = [g for g in r['swaps'][si]['gates'] if g['before'][1] != r['swaps'][si]['new_pivot']][0]
+        g['after'] = list(g['after']); g['after'][3] = -g['after'][3]
+    def m_coef(r, w, si=si):
+        g = [g for g in r['swaps'][si]['gates'] if g['before'][1] == r['swaps'][si]['new_pivot']][0]
+        g['after'] = list(g['after']); g['after'][3] *= 2
+    def m_nonfamily(r, w, si=si):
+        g = r['swaps'][si]['gates'][0]; g['before'] = list(g['before']); g['before'][3] = -g['before'][3]
+    def m_window(r, w, si=si):
+        S = r['swaps'][si]; S['new_pivot'] = [g['before'][1] for g in S['gates'] if g['before'][1] != S['new_pivot']][0]
+    def m_entrance(r, w, si=si):
+        S = r['swaps'][si]; S['entrance'] = [1]
+    reject('swap %s: another family gate keeps a wrong (unrescaled-sign) coefficient: new pivot response nonzero' % tag, m_other, WHY['nonzero'])
+    reject('swap %s: wrong pivot coefficient (1/c doubled) on the new pivot gate' % tag, m_coef, WHY['coef'])
+    reject('swap %s: non-family gate in the recipe' % tag, m_nonfamily, WHY['nonfamily'])
+    reject('swap %s: new pivot replaced by another family donor (not a fresh cold helper)' % tag, m_window, WHY['window'])
+    reject('swap %s: wrong entrance frame for the moved entrance' % tag, m_entrance, 'pivot is not an entering helper at the entrance')
+controls_receipt = list(controls)
+
+a.out.mkdir(parents=True); (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(o, mtime=0))
+rc = dict(status='PASS_COST_NEUTRAL_PIVOT_SWAPS', input_content_sha256=recipe['input_content_sha256'],
+          output_content_sha256=recipe['output_content_sha256'], swaps=receipts, local_profile=out['report']['local_profile'],
+          negative_controls_rejected=controls_receipt,
+          scope='Exact family rewrite, exact zero dirty response of every new pivot, identical paid profile and widths, '
+                'regenerated inverse-rule cleanup.  Native all-column audit, HPE/cold steps and global checks remain separate.')
+(a.out / 'PIVOT-SWAP.json').write_text(json.dumps(rc, indent=2, sort_keys=True) + '\n', newline='\n'); print(json.dumps(rc, indent=2))
diff --git a/research/gauge44-slots-t16/construction/layers/layer_end_controls.py b/research/gauge44-slots-t16/construction/layers/layer_end_controls.py
new file mode 100644
index 0000000000..317da36d95
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/layers/layer_end_controls.py
@@ -0,0 +1,201 @@
+"""layer_end_controls.py LAYERED-WORD.json.gz ROUTING OUTDIR (env PR635_CODE): adapted PR635 cold_end_controls.py (LayerReviewer): raw-word negative controls for the cold low-frame ends and the
+refactored cleanup accepted by hpe_audit_and_transport.py.  Every mutation MUST be rejected (AssertionError); the
+unmutated word MUST pass.  Apache-2.0.  DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code."""
+import copy, gzip, json, shutil, sys, tempfile
+from pathlib import Path
+import os
+sys.path.insert(0, os.environ['PR635_CODE'])   # PR635's unchanged hpe_audit_and_transport.py
+import hpe_audit_and_transport as atc
+
+src, routing, outdir = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3])
+word = json.load(gzip.open(src))
+v, R = word['report']['v'], word['report']['R']; n = 2*v + R
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+meta = word['refactored_cleanup']
+cold = [int(h) for h in meta['cold_low_frame_ended_helpers']]
+npre = meta['premix_gates']; nlow = meta['lower_frame_gates']
+early = word['early_cleanup']; eidx = {i for i, _ in early}
+rest = [i for i in range(len(word['cleanup'])) if i not in eidx]
+
+
+def trial(w):
+    """None if the transport audit accepts w, else the AssertionError message."""
+    tmp = Path(tempfile.mkdtemp())
+    p = tmp/'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w).encode(), mtime=0))
+    try:
+        atc.run(p, routing, tmp/'out')
+        return None
+    except AssertionError as e:
+        return repr(e.args[0]) if e.args else 'AssertionError'
+    finally:
+        shutil.rmtree(tmp, ignore_errors=True)
+
+
+# Pinned rejection reasons: each mutant must fail at this assertion of hpe_audit_and_transport.py (message substring).
+ENDPOINT, COLDPRE, CONE = "'arbitrary-dirt endpoint'", 'touches a cold hyperplane-ended helper', 'hpe cone pre-check (row / column)'
+WHY = dict(premix_to_precondition=COLDPRE, premix_dropped=COLDPRE, e_premix_dropped=ENDPOINT, lower_dropped=ENDPOINT,
+           remainder_dropped=ENDPOINT, coefficient=ENDPOINT, into_full='cleanup on non-FULL end', dyadic=ENDPOINT, frame_below="'nonmonotone'",
+           nonmonotone="'nonmonotone'", other_frame=CONE, cone=CONE, extra_end=COLDPRE, marker='cleanup is not the literal reversed inverse',
+           target='refactored cleanup touches a target', profile_pin='paid local profile differs from the reported local_profile',
+           entering_precondition='zero-frame precondition/compensation touches an entering helper')
+assert trial(word) is None, 'unmutated cold-end word must pass'
+results = []
+
+
+def reject(name, mut, why):
+    """the mutation must be rejected, and for the pinned reason (a substring of the audit's assertion message)."""
+    w = copy.deepcopy(word); mut(w)
+    msg = trial(w)
+    assert msg is not None, 'cold-end mutation accepted: ' + name
+    assert why in msg, 'cold-end mutation %r rejected for the wrong reason: %s' % (name, msg[:300])
+    results.append(name); print('rejected', name, '|', why, flush=True)
+
+
+h0 = cold[0]
+i0, U0 = next((i, f) for i, f in early if h0 in regs(word['cleanup'][i]))
+r0 = rest[len(rest)//2]
+
+
+def premix_to_precondition(w):   # premix before the wrappers; compensation then reads the cold ends
+    w['precondition'] = w['precondition'] + w['A'][:npre]; w['A'] = w['A'][npre:]
+
+
+def lower_gate_into_full(w):     # a lower-frame gate on a cold-ended helper executed in the FULL remainder instead
+    w['early_cleanup'] = [x for x in w['early_cleanup'] if x[0] != i0]
+
+
+def drop_cleanup_gate(w, i):   # remove the gate AND its early_cleanup entry: a structurally valid word missing one gate
+    w['cleanup'].pop(i)
+    w['early_cleanup'] = [[j - (j > i), f] for j, f in w['early_cleanup'] if j != i]
+
+
+def other_frame(w):              # a different frame of the same dimension as the cold end (another cold helper's)
+    f = next(w['helper_final'][str(h)] for h in cold if w['helper_final'][str(h)] != w['helper_final'][str(h0)])
+    w['helper_final'][str(h0)] = f
+
+
+def extra_cold_end(w):           # declare a premixed partner of h0 cold-ended at h0's frame: fails the row/column cone
+    p = next(r for e in w['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    w['helper_final'][str(p)] = w['helper_final'][str(h0)]
+
+
+reject('premix placed in the zero-frame precondition (before the cold wrappers)', premix_to_precondition, WHY['premix_to_precondition'])
+reject('one premix gate dropped (the compensation then reads a cold-ended helper)', lambda w: w['A'].pop(npre - 1), WHY['premix_dropped'])
+reject('one lower-frame cleanup gate dropped (gate and its early_cleanup entry)', lambda w: drop_cleanup_gate(w, i0), WHY['lower_dropped'])
+reject('one FULL-remainder gate dropped', lambda w: drop_cleanup_gate(w, r0), WHY['remainder_dropped'])
+reject('lower-frame gate coefficient changed', lambda w: w['cleanup'][i0].__setitem__(3, w['cleanup'][i0][3] * 2), WHY['coefficient'])
+reject('lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)', lower_gate_into_full, WHY['into_full'])
+reject('lower-frame gate frame below its registers\' frames', lambda w: next(x for x in w['early_cleanup'] if x[0] == i0).__setitem__(1, U0[:-1]), WHY['frame_below'])
+reject('cold end at another dim-4 frame', other_frame, WHY['other_frame'])
+# PROFILE-PIN control: without its helper_final entry the cold-ended helper is a valid FULL-ended helper; the word is
+# rejected because its reported paid profile (which counts the low end) no longer matches the frame chains.
+reject('profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)', lambda w: w['helper_final'].pop(str(h0)), WHY['profile_pin'])
+reject('extra cold end on a premixed partner (the compensation reads it before its wrapper)', extra_cold_end, WHY['extra_end'])
+reject('refactored-cleanup marker removed (literal-inverse rule applies)', lambda w: w.pop('refactored_cleanup'), WHY['marker'])
+reject('remainder gate retargeted to a target register', lambda w: w['cleanup'][r0].__setitem__(1, v + 3), WHY['target'])
+reject('non-dyadic remainder coefficient', lambda w: w['cleanup'][r0].__setitem__(4 if w['cleanup'][r0][0] == 'add' else 3, 3 * w['cleanup'][r0][4 if w['cleanup'][r0][0] == 'add' else 3]), WHY['dyadic'])
+reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('5', w['report']['local_profile']['5'] - 1), WHY['profile_pin'])
+ent = [int(h) for h in sys.argv[4].split(',')] if len(sys.argv) > 4 else [int(h) for h in meta.get('entering_low_frame_ended_helpers', [])]
+for e0 in ent:   # ENTERING LOW-FRAME ENDS (ColdSupply extension; every entering end; absent for words without them)
+    j0 = next((i for i, e in enumerate(word['A'][:npre]) if e0 in regs(e)), None)
+    print('entering end', e0, 'premix gate', j0, flush=True)
+    k0, Ue = next((i, f) for i, f in early if e0 in regs(word['cleanup'][i]))
+    def to_pre(w, j0=j0): w['precondition'].append(w['A'][j0]); w['A'].pop(j0)
+    def other_hp(w, e0=e0, Ue=Ue): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Ue) and sorted(f) != sorted(Ue))
+    if j0 is not None: reject('entering end %d: premix gate dropped' % e0, lambda w, j0=j0: w['A'].pop(j0), WHY['e_premix_dropped'])
+    if j0 is not None: reject('entering end %d: premix gate at frame [] instead of its entrance E' % e0, lambda w, j0=j0: w['A'][j0].__setitem__(-1, []), WHY['nonmonotone'])
+    if j0 is not None: reject('entering end %d: premix gate moved into the zero-frame precondition' % e0, to_pre, WHY['entering_precondition'])
+    reject('entering end %d: lower-frame gate dropped (gate and its early_cleanup entry)' % e0, lambda w, k0=k0: drop_cleanup_gate(w, k0), WHY['lower_dropped'])
+    reject('entering end %d: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)' % e0, lambda w, e0=e0: w['helper_final'].pop(str(e0)), WHY['profile_pin'])
+    reject('entering end %d: end at another hyperplane' % e0, other_hp, WHY['cone'])
+# Pinned rejection reasons of the COLD-BEYOND mutants (substrings of hpe_audit_and_transport.py assertion messages).
+MYWHY = dict(tw_precondition=COLDPRE, tw_dropped=COLDPRE, tw_coefficient=COLDPRE, tw_other_block=COLDPRE,
+             tw_entering='zero-frame compensation reads an entering helper',
+             ab_dropped=ENDPOINT, ab_coefficient=ENDPOINT, ab_early=ENDPOINT, ab_live=ENDPOINT, ab_centre=ENDPOINT,
+             ab_lower="'nonmonotone'", ab_higher="'nonmonotone'",
+             sh_dropped=ENDPOINT, sh_coefficient=ENDPOINT, rel_dropped=ENDPOINT, rel_coefficient=ENDPOINT, rel_live=ENDPOINT,
+             h8_other=CONE, h8_lower=ENDPOINT)
+# COLD-BEYOND primitives (present only when the word carries them): frame-[] target writes in the premix (explicit
+# post-wrapper compensation of an ended helper's dirt) and forward absorptions into dead registers.
+nw = meta.get('premix_target_writes', 0)
+if nw:
+    wi = [i for i in range(npre) if v <= word['A'][i][1] < 2*v]
+    assert len(wi) == nw
+
+    def writes_to_precondition(w):   # the target writes run before the cold wrappers (inside the zero-frame precondition)
+        g = [w['A'][i] for i in wi]; w['precondition'] = w['precondition'] + g
+        w['A'] = [e for i, e in enumerate(w['A']) if i not in set(wi)]
+    reject('premix target writes placed in the zero-frame precondition (before the cold wrappers)', writes_to_precondition, MYWHY['tw_precondition'])
+    reject('one premix target write dropped (compensation must read an ended helper)', lambda w: w['A'].pop(wi[0]), MYWHY['tw_dropped'])
+    reject('premix target write coefficient changed', lambda w: w['A'][wi[0]].__setitem__(3, w['A'][wi[0]][3] * 2), MYWHY['tw_coefficient'])
+    # (reading another register that carries the SAME weight of the ended helper's dirt is a valid variant, so the mutant reads
+    #  the same factory slot of the next block, which carries none of it)
+    entering_regs = sorted(int(r) for r in word.get('start_extra', {}))
+    reject('premix target write reads an entering helper', lambda w: w['A'][wi[0]].__setitem__(2, entering_regs[0]), MYWHY['tw_entering'])
+    reject('premix target write reads a cold helper of another block', lambda w: w['A'][wi[0]].__setitem__(2, 2*v + (w['A'][wi[0]][2] - 2*v + 16) % 224), MYWHY['tw_other_block'])
+ab = meta.get('forward_absorption_A_indices', [])
+if any(len(word['helper_final'][str(h)]) == 8 for h in cold):
+    # with dim-8 cold ends, the centre-retargeted absorption first leaks an ended helper's dirt into the cut's targets
+    MYWHY['ab_centre'] = COLDPRE
+if ab:
+    # the ColdBeyond U_b absorption (q += -1/2 g); ColdThird's extra absorptions have their own controls below
+    a0 = next(a for a in ab if word['A'][a][3] * 2 == -word['A'][a][4]); g0 = word['A'][a0]
+
+    def absorption_moved_early(w):   # absorbed before the absorbed register's last kernel write
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[2] == w['A'][i][1] and w['A'][i][-1] == g0[-1])
+        w['A'].insert(j, e)
+
+    def absorption_into_live(w):     # q += a g moved right after g's previous frame-mate gate, while q is still live
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[1] in regs(w['A'][i]))
+        w['A'].insert(j, e)
+    reject('forward absorption dropped', lambda w: w['A'].pop(a0), MYWHY['ab_dropped'])
+    reject('forward absorption into a centre (a live register read by the cut)', lambda w: w['A'][a0].__setitem__(1, next(c for c in word['centers'] if c not in g0[1:3] and c not in cold)), MYWHY['ab_centre'])
+    reject('forward absorption coefficient changed', lambda w: w['A'][a0].__setitem__(3, w['A'][a0][3] * 2), MYWHY['ab_coefficient'])
+    reject('forward absorption placed before the absorbed register\'s last kernel write', absorption_moved_early, MYWHY['ab_early'])
+    reject('forward absorption placed while the absorbing register is still live', absorption_into_live, MYWHY['ab_live'])
+    reject('forward absorption at a lower frame than its registers', lambda w: w['A'][a0].__setitem__(-1, w['A'][a0][-1][:-1]), MYWHY['ab_lower'])
+    reject('forward absorption at a higher frame (FULL) than its registers', lambda w: w['A'][a0].__setitem__(-1, [256, 128, 64, 32, 16, 8, 4, 2, 1]), MYWHY['ab_higher'])
+# COLD-THIRD primitives (present only when the word carries them): several absorptions after one input gate, dirt-release
+# absorptions (a dead port takes a live helper's value so that a hyperplane unit's column has no dirt on it), and cold ends at
+# a dim-8 frame with lifted partners.
+hyper = [h for h in cold if len(word['helper_final'][str(h)]) == 8]
+if hyper and ab:
+    sh = next(a for a, b in zip(ab, ab[1:]) if b == a + 1)              # two absorptions sharing one input anchor
+    rel = next(a for a in ab if a - 1 not in ab and a + 1 not in ab and word['A'][a][2] in hyper and word['A'][a][3] * 2 != -word['A'][a][4])
+    hh = hyper[0]; ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+    reject('second absorption sharing an input anchor dropped', lambda w: w['A'].pop(sh + 1), MYWHY['sh_dropped'])
+    reject('shared-anchor absorption coefficient changed', lambda w: w['A'][sh + 1].__setitem__(3, w['A'][sh + 1][3] * 2), MYWHY['sh_coefficient'])
+    reject('dirt-release absorption dropped', lambda w: w['A'].pop(rel), MYWHY['rel_dropped'])
+    reject('dirt-release absorption coefficient changed', lambda w: w['A'][rel].__setitem__(3, w['A'][rel][3] * 2), MYWHY['rel_coefficient'])
+    jr = max(i for i in range(npre, rel) if word['A'][i][0] == 'add' and word['A'][i][2] == word['A'][rel][1])
+
+    def release_while_read(w):   # the release runs before a kernel gate that still READS the port (port live)
+        e = w['A'].pop(rel); w['A'].insert(jr, e)
+    reject('dirt-release absorption moved before a kernel gate that still reads the port', release_while_read, MYWHY['rel_live'])
+if hyper:
+    # dim-8 cold-end controls once PER DISTINCT dim-8 terminal frame (each family of dim-8 cold ends keeps its own controls)
+    fams = []
+    for h in hyper:
+        if sorted(word['helper_final'][str(h)]) not in [sorted(word['helper_final'][str(x)]) for x in fams]: fams.append(h)
+    for hh in fams:
+        ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+        Uh = word['helper_final'][str(hh)]
+        reject('dim-8 cold end %d (frame %s) at another dim-8 frame' % (hh, Uh), lambda w, hh=hh: w['helper_final'].__setitem__(str(hh), next(f for h, f in w['helper_final'].items() if len(f) == 8 and sorted(f) != sorted(w['helper_final'][str(hh)]))), MYWHY['h8_other'])
+        reject('dim-8 cold end %d (frame %s): one lower-frame gate dropped (gate and its early_cleanup entry)' % (hh, Uh), lambda w, ih=ih: drop_cleanup_gate(w, ih), MYWHY['h8_lower'])
+        reject('dim-8 cold end %d (frame %s): profile pin (end dropped)' % (hh, Uh), lambda w, hh=hh: w['helper_final'].pop(str(hh)), WHY['profile_pin'])
+# FACTORED ACCUMULATOR (CarrierBypass; present only when the word carries one): a lower-frame tail gate a += x*g on two
+# non-ended registers whose accumulator a is afterwards read by a dim-8 cold end's tail gate (h += y*a at its U).
+ended_all = {int(h) for h in word['helper_final']}
+tailg = [(i, word['cleanup'][i]) for i, _ in early]
+accs = []   # EVERY factored accumulator gate (one per accumulator register a), each controlled on its own
+for k, (i, e) in enumerate(tailg):
+    if e[0] == 'add' and e[1] not in ended_all and e[2] not in ended_all and len(next(f for j, f in early if j == i)) < 8:
+        if e[1] not in [word['cleanup'][j][1] for j in accs] and any(t[0] == 'add' and t[2] == e[1] and t[1] in hyper for _, t in tailg[k + 1:]):
+            accs.append(i)
+for acc in accs:
+    a = word['cleanup'][acc][1]
+    reject('factored accumulator %d (gate %d) zeroed' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, 0), ENDPOINT)
+    reject('factored accumulator %d (gate %d) coefficient doubled' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, w['cleanup'][acc][3] * 2), ENDPOINT)
+outdir.mkdir(parents=True, exist_ok=True)
+(outdir/'COLD-END-CONTROLS.json').write_text(json.dumps(dict(status='PASS_COLD_END_RAW_WORD_CONTROLS', word=str(src), rejected=results), indent=1) + '\n')
+print('PASS', len(results), 'cold-end raw-word mutations rejected')
diff --git a/research/gauge44-slots-t16/construction/layers/reproduce_layers.py b/research/gauge44-slots-t16/construction/layers/reproduce_layers.py
new file mode 100644
index 0000000000..ed517ba1dd
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/layers/reproduce_layers.py
@@ -0,0 +1,105 @@
+#!/usr/bin/env python3
+"""Rebuild the layered gauge44 word (pivot swaps + entering ends + factored dim-8 cold ends) and its native locals.
+
+Input: a fresh `construction/reproduce.py --until word` output directory (its regroup/ and cold44/ words are pinned
+by reproduce.py itself). Steps, each checked exactly:
+  1. pivot-swap: construction/layers/build_pivot_swap.py on regroup/FULL-WORD (six cost-neutral pivot-role swaps,
+     exact zero-response replay, unchanged profile and width multiset, 30 negative controls);
+  2. hpe: the inherited jp8 hyperplane-end changes (HYPERPLANE-END-S6.json) applied with PR635's build_hpe.apply;
+  3. cold44-exact: #645's build_gauge_cold44.py on the swapped HPE word; its 44 rank-four cold ends, premix and tail
+     must equal the unswapped cold44 construction's (the swaps touch no factory block);
+  4. layers: PR635's unchanged build_cold_end.apply(HPE, COLD-LAYERS-RECIPE) - the cold44 recipe plus 8 entering ends
+     (560/561/572/573 at U24, 597/599/537/549 at U30) and 10 factored dim-8 cold ends; output sha pinned;
+  5. layer-end-controls: raw-word negative controls on the layered word (PR635 cold_end_controls adapted by
+     LayerReviewer: lower->FULL pinned at 'cleanup on non-FULL end', entering ends from the recipe); 59 rejected;
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs (as in reproduce.py).
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+LAYERED_SHA = '0be48b1d8a6105059addf3f0d5e420c27ae3398b3a1186b6b11e9c4aa9e3f3d4'
+LAYER_CONTROLS = 59
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--word-dir', type=Path, required=True, help='construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    env.pop('PYTHONOPTIMIZE', None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    wd = a.word_dir.resolve()
+    run('pivot-swap', HERE / 'build_pivot_swap.py', '--input', wd / 'regroup/FULL-WORD.json.gz',
+        '--recipe', HERE / 'PIVOT-SWAP-S6.json', '--gk-dir', gk, '--out', out / 'swap')
+    hpe = load('upstream_hpe', up / 'code/build_hpe.py')
+    w = hpe.apply(read(out / 'swap/FULL-WORD.json.gz'), read(HERE / 'HYPERPLANE-END-S6.json')['changes'])
+    (out / 'hpe').mkdir(); (out / 'hpe/FULL-WORD.json.gz').write_bytes(gzip.compress(enc(w), mtime=0))
+    run('cold44-exact', HERE.parent / 'build_gauge_cold44.py', '--input', out / 'hpe/FULL-WORD.json.gz',
+        '--out', out / 'cold44', '--hamming', wd / 'hamming', '--upstream-package', up)
+    new, old = read(out / 'cold44/RECIPE.json.gz'), read(wd / 'cold44/RECIPE.json.gz')
+    # The swaps touch no factory block: the 44 ends, their premix and their low tails are identical; only the FULL
+    # inverse (rebuilt from the whole word) differs.
+    for key in ('premix', 'early_cleanup', 'cold_ends'):
+        assert new[key] == old[key], ('swapped cold44 differs from the pinned cold44 construction', key)
+    tail = len(new['early_cleanup']); assert new['cleanup'][:tail] == old['cleanup'][:tail], 'low tails'
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    layered = bce.apply(w, read(HERE / 'COLD-LAYERS-RECIPE.json.gz'))
+    raw = enc(layered); assert hashlib.sha256(raw).hexdigest() == LAYERED_SHA, 'layered word'
+    rep = layered['report']
+    assert rep['local_profile'] == {'1': 2542, '2': 414, '3': 434, '4': 154, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 52, '5': 48, '7': 42, '8': 116, '9': 234}, rep['width_inventory']
+    (out / 'layers').mkdir(); word = out / 'layers/FULL-WORD.json.gz'; word.write_bytes(gzip.compress(raw, mtime=0))
+    print('PASS layered scalar word', word, flush=True)
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', HERE / 'layer_end_controls.py', word, routing, out / 'controls')
+    ctl = json.loads((out / 'controls/COLD-END-CONTROLS.json').read_text())
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == LAYER_CONTROLS, len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word,
+        '--routing', routing, '--out', local)
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz b/research/gauge44-slots-t16/construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz
new file mode 100644
index 0000000000..f9155e3079
Binary files /dev/null and b/research/gauge44-slots-t16/construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz differ
diff --git a/research/gauge44-slots-t16/construction/layers_np/HPE-RECIPE-NP.json b/research/gauge44-slots-t16/construction/layers_np/HPE-RECIPE-NP.json
new file mode 100644
index 0000000000..2605d199ed
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/layers_np/HPE-RECIPE-NP.json
@@ -0,0 +1 @@
+{"changes": [{"helper": 448, "cleanup_index": 674, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 449, "cleanup_index": 673, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 450, "cleanup_index": 672, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 451, "cleanup_index": 671, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 452, "cleanup_index": 670, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 453, "cleanup_index": 669, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 454, "cleanup_index": 668, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 455, "cleanup_index": 667, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 456, "cleanup_index": 666, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 457, "cleanup_index": 665, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 458, "cleanup_index": 664, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 459, "cleanup_index": 663, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 460, "cleanup_index": 658, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 461, "cleanup_index": 657, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 470, "cleanup_index": 648, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 471, "cleanup_index": 647, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 472, "cleanup_index": 642, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 473, "cleanup_index": 641, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 482, "cleanup_index": 632, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 483, "cleanup_index": 631, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 496, "cleanup_index": 609, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 497, "cleanup_index": 608, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 520, "cleanup_index": 573, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 521, "cleanup_index": 572, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 544, "cleanup_index": 539, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 545, "cleanup_index": 538, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 568, "cleanup_index": 507, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 569, "cleanup_index": 506, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 580, "cleanup_index": 491, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 581, "cleanup_index": 490, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 590, "cleanup_index": 481, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 591, "cleanup_index": 480, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 592, "cleanup_index": 475, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 593, "cleanup_index": 474, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 602, "cleanup_index": 465, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 603, "cleanup_index": 464, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 604, "cleanup_index": 459, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 605, "cleanup_index": 458, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 606, "cleanup_index": 457, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 607, "cleanup_index": 456, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 609, "cleanup_index": 454, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 611, "cleanup_index": 452, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 612, "cleanup_index": 451, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 613, "cleanup_index": 450, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 614, "cleanup_index": 449, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 615, "cleanup_index": 448, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}]}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/layers_np/PIVOT-SWAP-NP.json b/research/gauge44-slots-t16/construction/layers_np/PIVOT-SWAP-NP.json
new file mode 100644
index 0000000000..4e0d846426
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/layers_np/PIVOT-SWAP-NP.json
@@ -0,0 +1,588 @@
+{
+ "input_content_sha256": "864ff4a19987bcb27016367801a98ca50dae69eafe01d3614f8bae69f5713d6d",
+ "output_content_sha256": "beb3579fce83cb3b70f4e85761cbb3b8c91d711d4b9cf473074269b8447fc4e4",
+ "swaps": [
+  {
+   "pivot": 494,
+   "new_pivot": 566,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 379,
+     "before": [
+      "add",
+      566,
+      494,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      494,
+      566,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 380,
+     "before": [
+      "add",
+      640,
+      494,
+      2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      640,
+      566,
+      -2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 381,
+     "before": [
+      "add",
+      642,
+      494,
+      -2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      642,
+      566,
+      2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 382,
+     "before": [
+      "add",
+      688,
+      494,
+      1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      688,
+      566,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 383,
+     "before": [
+      "add",
+      690,
+      494,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      690,
+      566,
+      1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 495,
+   "new_pivot": 567,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 516,
+     "before": [
+      "add",
+      123,
+      495,
+      1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      123,
+      567,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 584,
+     "before": [
+      "add",
+      187,
+      495,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      187,
+      567,
+      1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 686,
+     "before": [
+      "add",
+      567,
+      495,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      495,
+      567,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 506,
+   "new_pivot": 578,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 176,
+     "before": [
+      "add",
+      652,
+      506,
+      2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      652,
+      578,
+      -2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 178,
+     "before": [
+      "add",
+      652,
+      506,
+      -2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      652,
+      578,
+      2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 278,
+     "before": [
+      "add",
+      700,
+      506,
+      -2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      700,
+      578,
+      2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 280,
+     "before": [
+      "add",
+      700,
+      506,
+      2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      700,
+      578,
+      -2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 702,
+     "before": [
+      "add",
+      578,
+      506,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      506,
+      578,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 507,
+   "new_pivot": 579,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 93,
+     "before": [
+      "add",
+      211,
+      507,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      211,
+      579,
+      1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 541,
+     "before": [
+      "add",
+      147,
+      507,
+      1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      147,
+      579,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 704,
+     "before": [
+      "add",
+      579,
+      507,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      507,
+      579,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 519,
+   "new_pivot": 543,
+   "entrance": [
+    30
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 507,
+     "before": [
+      "add",
+      115,
+      519,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      115,
+      543,
+      1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 575,
+     "before": [
+      "add",
+      179,
+      519,
+      1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      179,
+      543,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 722,
+     "before": [
+      "add",
+      543,
+      519,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      519,
+      543,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 531,
+   "new_pivot": 555,
+   "entrance": [
+    30
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 550,
+     "before": [
+      "add",
+      155,
+      531,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      155,
+      555,
+      1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 617,
+     "before": [
+      "add",
+      219,
+      531,
+      1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      219,
+      555,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 740,
+     "before": [
+      "add",
+      555,
+      531,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      531,
+      555,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    }
+   ]
+  }
+ ]
+}
diff --git a/research/gauge44-slots-t16/construction/layers_np/reproduce_np.py b/research/gauge44-slots-t16/construction/layers_np/reproduce_np.py
new file mode 100644
index 0000000000..79cb6fa912
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/layers_np/reproduce_np.py
@@ -0,0 +1,149 @@
+#!/usr/bin/env python3
+"""Rebuild the layered no-triangle word (NP) and its native locals.
+
+Input: a fresh `construction/notri/reproduce_notri.py --word-only` output directory. That driver pins the
+no-triangle word (3e99ba77...) and writes its regroup/ and cold44/ words. Steps, each checked exactly:
+  1. pivot-swap: ../layers/build_pivot_swap.py (PR641's constructor, signed, unchanged) on the no-triangle regroup word, with PIVOT-SWAP-NP.json:
+     the six pivot-role swaps of research/gauge44-layered, mapped through the 504-helper map (494->566, 495->567,
+     506->578, 507->579, 519->543, 531->555). Exact zero-response replay, unchanged profile and width multiset,
+     30 negative controls.
+  2. hpe: PR635's build_hpe.candidates, greedy with disjoint registers. Must equal HPE-RECIPE-NP.json (46 changes,
+     the same helpers as the unswapped word); applied with build_hpe.apply.
+  3. cold44-exact: notri/cold44x.py on the swapped HPE word, pairing ranks pinned [4]*14. Its 56 cold ends, premix
+     and low tails must equal the unswapped no-triangle construction's.
+  4. layers: PR635's unchanged build_cold_end.apply(HPE, COLD-LAYERS-RECIPE-NP): cold44 plus the entering ends
+     566/567/578/579 at U24 (s4) and 608/610/543/555 at U30 (x30), BlockCombine's b6 and the q4 dim-8 cold ends.
+     The output word sha and its profile and widths are pinned.
+  5. layer-end-controls: ../layers/layer_end_controls.py (LayerReviewer's signed adaptation of PR635's
+     cold_end_controls.py, unchanged) on the layered word; exactly 59 rejections at pinned reasons.
+../layers/reproduce_layers.py is research/gauge44-layered's driver for the 492-helper word, shipped unchanged as
+signed; it is not used for this word.
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs, with pins.
+Apache-2.0. Driver by ColdWitness after G44Stack's NP chain (NP/chain.py, seq.py).
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NOTRI = HERE.parent / 'notri'
+LAYERS = HERE.parent / 'layers'   # the signed research/gauge44-layered files, unchanged
+REGROUP_SHA = '864ff4a1'   # prefix; full value checked against PIVOT-SWAP-NP.json's input_content_sha256
+SWAP_SHA = 'beb3579f'
+NP_SHA = 'a9de804f194eeb39f52a4c6e54c14d93e881bec4b632694249733ed410b58113'
+LAYER_CONTROLS = 59
+CANONICAL_SHA = '1ae812a336178760071efe347e876e0102b5b71f799d957db15c5f3004c19d7a'
+PROGRAM_SHA = {'forward': 'a3882a428bdafab888072211d4ed8d34572746873d77c6ef900495853cc3fa11',
+               'backward': 'f67a3dc20c27fb39295b8030e951e9779109ef1537f6f8de9d08510b9ad6792a'}
+CLIFFORD_SHA = '890b60fc4ae183c773c51405e0f4ef6a945dc2aae55ba2480f134602e8296cda'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def dump(p, v):
+    p.parent.mkdir(parents=True, exist_ok=True); p.write_bytes(gzip.compress(enc(v), mtime=0))
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--notri-dir', type=Path, required=True, help='construction/notri/reproduce_notri.py --word-only output')
+    ap.add_argument('--hamming', type=Path, required=True, help='hamming/ of the construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    nd = a.notri_dir.resolve()
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    # the input must be the pinned no-triangle construction
+    nr = load('notri_driver', NOTRI / 'reproduce_notri.py')
+    assert hashlib.sha256(enc(read(nd / 'cold44/FULL-WORD.json.gz'))).hexdigest() == nr.NOTRI_SHA, 'notri word'
+    # 1. pivot swaps on the regroup word
+    rg = hashlib.sha256(enc(read(nd / 'regroup/FULL-WORD.json.gz'))).hexdigest()
+    assert rg.startswith(REGROUP_SHA) and rg == read(HERE / 'PIVOT-SWAP-NP.json')['input_content_sha256'], ('regroup word', rg)
+    run('pivot-swap', LAYERS / 'build_pivot_swap.py', '--input', nd / 'regroup/FULL-WORD.json.gz',
+        '--recipe', HERE / 'PIVOT-SWAP-NP.json', '--gk-dir', gk, '--out', out / 'swap')
+    w = read(out / 'swap/FULL-WORD.json.gz')
+    sw = hashlib.sha256(enc(w)).hexdigest(); assert sw.startswith(SWAP_SHA) and sw == read(HERE / 'PIVOT-SWAP-NP.json')['output_content_sha256'], ('swap word', sw)
+    # 2. HPE (greedy, must equal the pinned recipe)
+    h = load('upstream_hpe', up / 'code/build_hpe.py')
+    used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    assert ch == read(HERE / 'HPE-RECIPE-NP.json')['changes'], 'HPE recipe'
+    w = h.apply(w, ch); dump(out / 'hpe/FULL-WORD.json.gz', w)
+    # 3. cold44 on the swapped word: same ends, premix and tails as the unswapped no-triangle construction
+    hm = set(read(nd / 'raw/HELPER-MAP.json')['map'].values())
+    env['EXTRAH'] = json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm))
+    env['PAIRING_RANKS'] = json.dumps([4] * 14)
+    run('cold44-exact', NOTRI / 'cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', a.hamming.resolve(), '--upstream-package', up)
+    for k in ('EXTRAH', 'PAIRING_RANKS'): env.pop(k)
+    new, old = read(out / 'cold44/RECIPE.json.gz'), read(nd / 'cold44/RECIPE.json.gz')
+    for key in ('premix', 'early_cleanup', 'cold_ends'):
+        assert new[key] == old[key], ('swapped cold44 differs from the pinned no-triangle construction', key)
+    tail = len(new['early_cleanup']); assert new['cleanup'][:tail] == old['cleanup'][:tail], 'low tails'
+    # 4. layers
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    layered = bce.apply(w, read(HERE / 'COLD-LAYERS-RECIPE-NP.json.gz'))
+    raw = enc(layered); assert hashlib.sha256(raw).hexdigest() == NP_SHA, ('layered word', hashlib.sha256(raw).hexdigest())
+    rep = layered['report']
+    assert rep['local_profile'] == {'1': 2534, '2': 346, '3': 458, '4': 178, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 64, '5': 48, '7': 54, '8': 116, '9': 222}, rep['width_inventory']
+    (out / 'layers').mkdir(); word = out / 'layers/FULL-WORD.json.gz'; word.write_bytes(gzip.compress(raw, mtime=0))
+    print('PASS layered no-triangle word', NP_SHA, flush=True)
+    # 5. layer-end controls
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', LAYERS / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = json.loads((out / 'controls/COLD-END-CONTROLS.json').read_text())
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == LAYER_CONTROLS, len(ctl['rejected'])
+    # 6. native locals
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == CANONICAL_SHA, 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in PROGRAM_SHA.items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == CLIFFORD_SHA, 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz b/research/gauge44-slots-t16/construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz
new file mode 100644
index 0000000000..a408c95816
Binary files /dev/null and b/research/gauge44-slots-t16/construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz differ
diff --git a/research/gauge44-slots-t16/construction/layers_p6n/P6N-SPEC.json b/research/gauge44-slots-t16/construction/layers_p6n/P6N-SPEC.json
new file mode 100644
index 0000000000..43c3ec265c
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/layers_p6n/P6N-SPEC.json
@@ -0,0 +1 @@
+{"ends":[{"U":[256,128,66,34,16,8,6,1],"labels":[512,513]},{"U":[256,128,72,40,24,4,2,1],"labels":[311,510]},{"U":[256,128,66,34,18,10,6,1],"labels":[522,327]}]}
diff --git a/research/gauge44-slots-t16/construction/layers_p6n/layer_end_controls.py b/research/gauge44-slots-t16/construction/layers_p6n/layer_end_controls.py
new file mode 100644
index 0000000000..dd321fe255
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/layers_p6n/layer_end_controls.py
@@ -0,0 +1,199 @@
+"""layer_end_controls.py LAYERED-WORD.json.gz ROUTING OUTDIR (env PR635_CODE): adapted PR635 cold_end_controls.py (LayerReviewer): raw-word negative controls for the cold low-frame ends and the
+refactored cleanup accepted by hpe_audit_and_transport.py.  Every mutation MUST be rejected (AssertionError); the
+unmutated word MUST pass.  Apache-2.0.  DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code."""
+import copy, gzip, json, shutil, sys, tempfile
+from pathlib import Path
+import os
+sys.path.insert(0, os.environ['PR635_CODE'])   # PR635's unchanged hpe_audit_and_transport.py
+import hpe_audit_and_transport as atc
+
+src, routing, outdir = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3])
+word = json.load(gzip.open(src))
+v, R = word['report']['v'], word['report']['R']; n = 2*v + R
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+meta = word['refactored_cleanup']
+cold = [int(h) for h in meta['cold_low_frame_ended_helpers']]
+npre = meta['premix_gates']; nlow = meta['lower_frame_gates']
+early = word['early_cleanup']; eidx = {i for i, _ in early}
+rest = [i for i in range(len(word['cleanup'])) if i not in eidx]
+
+
+def trial(w):
+    """None if the transport audit accepts w, else the AssertionError message."""
+    tmp = Path(tempfile.mkdtemp())
+    p = tmp/'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w).encode(), mtime=0))
+    try:
+        atc.run(p, routing, tmp/'out')
+        return None
+    except AssertionError as e:
+        return repr(e.args[0]) if e.args else 'AssertionError'
+    finally:
+        shutil.rmtree(tmp, ignore_errors=True)
+
+
+# Pinned rejection reasons: each mutant must fail at this assertion of hpe_audit_and_transport.py (message substring).
+ENDPOINT, COLDPRE, CONE = "'arbitrary-dirt endpoint'", 'touches a cold hyperplane-ended helper', 'hpe cone pre-check (row / column)'
+WHY = dict(premix_to_precondition=COLDPRE, premix_dropped=COLDPRE, e_premix_dropped=ENDPOINT, lower_dropped=ENDPOINT,
+           remainder_dropped=ENDPOINT, coefficient=ENDPOINT, into_full='cleanup on non-FULL end', dyadic=ENDPOINT, frame_below="'nonmonotone'",
+           nonmonotone="'nonmonotone'", other_frame=CONE, cone=CONE, extra_end=COLDPRE, marker='cleanup is not the literal reversed inverse',
+           target='refactored cleanup touches a target', profile_pin='paid local profile differs from the reported local_profile',
+           entering_precondition='zero-frame precondition/compensation touches an entering helper')
+assert trial(word) is None, 'unmutated cold-end word must pass'
+results = []
+
+
+def reject(name, mut, why):
+    """the mutation must be rejected, and for the pinned reason (a substring of the audit's assertion message)."""
+    w = copy.deepcopy(word); mut(w)
+    msg = trial(w)
+    assert msg is not None, 'cold-end mutation accepted: ' + name
+    assert why in msg, 'cold-end mutation %r rejected for the wrong reason: %s' % (name, msg[:300])
+    results.append(name); print('rejected', name, '|', why, flush=True)
+
+
+h0 = cold[0]
+i0, U0 = next((i, f) for i, f in early if h0 in regs(word['cleanup'][i]))
+r0 = rest[len(rest)//2]
+
+
+def premix_to_precondition(w):   # premix before the wrappers; compensation then reads the cold ends
+    w['precondition'] = w['precondition'] + w['A'][:npre]; w['A'] = w['A'][npre:]
+
+
+def lower_gate_into_full(w):     # a lower-frame gate on a cold-ended helper executed in the FULL remainder instead
+    w['early_cleanup'] = [x for x in w['early_cleanup'] if x[0] != i0]
+
+
+def drop_cleanup_gate(w, i):   # remove the gate AND its early_cleanup entry: a structurally valid word missing one gate
+    w['cleanup'].pop(i)
+    w['early_cleanup'] = [[j - (j > i), f] for j, f in w['early_cleanup'] if j != i]
+
+
+def other_frame(w):              # a different frame of the same dimension as the cold end (another cold helper's)
+    f = next(w['helper_final'][str(h)] for h in cold if w['helper_final'][str(h)] != w['helper_final'][str(h0)])
+    w['helper_final'][str(h0)] = f
+
+
+def extra_cold_end(w):           # declare a premixed partner of h0 cold-ended at h0's frame: fails the row/column cone
+    p = next(r for e in w['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    w['helper_final'][str(p)] = w['helper_final'][str(h0)]
+
+
+reject('premix placed in the zero-frame precondition (before the cold wrappers)', premix_to_precondition, WHY['premix_to_precondition'])
+reject('one premix gate dropped (the compensation then reads a cold-ended helper)', lambda w: w['A'].pop(npre - 1), WHY['premix_dropped'])
+reject('one lower-frame cleanup gate dropped (gate and its early_cleanup entry)', lambda w: drop_cleanup_gate(w, i0), WHY['lower_dropped'])
+reject('one FULL-remainder gate dropped', lambda w: drop_cleanup_gate(w, r0), WHY['remainder_dropped'])
+reject('lower-frame gate coefficient changed', lambda w: w['cleanup'][i0].__setitem__(3, w['cleanup'][i0][3] * 2), WHY['coefficient'])
+reject('lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)', lower_gate_into_full, WHY['into_full'])
+reject('lower-frame gate frame below its registers\' frames', lambda w: next(x for x in w['early_cleanup'] if x[0] == i0).__setitem__(1, U0[:-1]), WHY['frame_below'])
+reject('cold end at another dim-4 frame', other_frame, WHY['other_frame'])
+# PROFILE-PIN control: without its helper_final entry the cold-ended helper is a valid FULL-ended helper; the word is
+# rejected because its reported paid profile (which counts the low end) no longer matches the frame chains.
+reject('profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)', lambda w: w['helper_final'].pop(str(h0)), WHY['profile_pin'])
+reject('extra cold end on a premixed partner (the compensation reads it before its wrapper)', extra_cold_end, WHY['extra_end'])
+reject('refactored-cleanup marker removed (literal-inverse rule applies)', lambda w: w.pop('refactored_cleanup'), WHY['marker'])
+reject('remainder gate retargeted to a target register', lambda w: w['cleanup'][r0].__setitem__(1, v + 3), WHY['target'])
+reject('non-dyadic remainder coefficient', lambda w: w['cleanup'][r0].__setitem__(4 if w['cleanup'][r0][0] == 'add' else 3, 3 * w['cleanup'][r0][4 if w['cleanup'][r0][0] == 'add' else 3]), WHY['dyadic'])
+reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('5', w['report']['local_profile']['5'] - 1), WHY['profile_pin'])
+ent = [int(h) for h in sys.argv[4].split(',')] if len(sys.argv) > 4 else [int(h) for h in meta.get('entering_low_frame_ended_helpers', [])]
+for e0 in ent:   # ENTERING LOW-FRAME ENDS (ColdSupply extension; every entering end; absent for words without them)
+    j0 = next((i for i, e in enumerate(word['A'][:npre]) if e0 in regs(e)), None)
+    print('entering end', e0, 'premix gate', j0, flush=True)
+    k0, Ue = next((i, f) for i, f in early if e0 in regs(word['cleanup'][i]))
+    def to_pre(w, j0=j0): w['precondition'].append(w['A'][j0]); w['A'].pop(j0)
+    def other_hp(w, e0=e0, Ue=Ue): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Ue) and sorted(f) != sorted(Ue))
+    if j0 is not None: reject('entering end %d: premix gate dropped' % e0, lambda w, j0=j0: w['A'].pop(j0), WHY['e_premix_dropped'])
+    if j0 is not None: reject('entering end %d: premix gate at frame [] instead of its entrance E' % e0, lambda w, j0=j0: w['A'][j0].__setitem__(-1, []), WHY['nonmonotone'])
+    if j0 is not None: reject('entering end %d: premix gate moved into the zero-frame precondition' % e0, to_pre, WHY['entering_precondition'])
+    reject('entering end %d: lower-frame gate dropped (gate and its early_cleanup entry)' % e0, lambda w, k0=k0: drop_cleanup_gate(w, k0), WHY['lower_dropped'])
+    reject('entering end %d: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)' % e0, lambda w, e0=e0: w['helper_final'].pop(str(e0)), WHY['profile_pin'])
+    reject('entering end %d: end at another hyperplane' % e0, other_hp, WHY['cone'])
+# Pinned rejection reasons of the COLD-BEYOND mutants (substrings of hpe_audit_and_transport.py assertion messages).
+MYWHY = dict(tw_precondition=COLDPRE, tw_dropped=COLDPRE, tw_coefficient=COLDPRE, tw_other_block=COLDPRE,
+             tw_entering='zero-frame compensation reads an entering helper',
+             ab_dropped=ENDPOINT, ab_coefficient=ENDPOINT, ab_early=ENDPOINT, ab_live=ENDPOINT, ab_centre=ENDPOINT,
+             ab_lower="'nonmonotone'", ab_higher="'nonmonotone'",
+             sh_dropped=ENDPOINT, sh_coefficient=ENDPOINT, rel_dropped=ENDPOINT, rel_coefficient=ENDPOINT, rel_live=ENDPOINT,
+             h8_other=CONE, h8_lower=ENDPOINT)
+# COLD-BEYOND primitives (present only when the word carries them): frame-[] target writes in the premix (explicit
+# post-wrapper compensation of an ended helper's dirt) and forward absorptions into dead registers.
+nw = meta.get('premix_target_writes', 0)
+if nw:
+    wi = [i for i in range(npre) if v <= word['A'][i][1] < 2*v]
+    assert len(wi) == nw
+
+    def writes_to_precondition(w):   # the target writes run before the cold wrappers (inside the zero-frame precondition)
+        g = [w['A'][i] for i in wi]; w['precondition'] = w['precondition'] + g
+        w['A'] = [e for i, e in enumerate(w['A']) if i not in set(wi)]
+    reject('premix target writes placed in the zero-frame precondition (before the cold wrappers)', writes_to_precondition, MYWHY['tw_precondition'])
+    reject('one premix target write dropped (compensation must read an ended helper)', lambda w: w['A'].pop(wi[0]), MYWHY['tw_dropped'])
+    reject('premix target write coefficient changed', lambda w: w['A'][wi[0]].__setitem__(3, w['A'][wi[0]][3] * 2), MYWHY['tw_coefficient'])
+    # (reading another register that carries the SAME weight of the ended helper's dirt is a valid variant, so the mutant reads
+    #  the same factory slot of the next block, which carries none of it)
+    entering_regs = sorted(int(r) for r in word.get('start_extra', {}))
+    reject('premix target write reads an entering helper', lambda w: w['A'][wi[0]].__setitem__(2, entering_regs[0]), MYWHY['tw_entering'])
+    reject('premix target write reads a cold helper of another block', lambda w: w['A'][wi[0]].__setitem__(2, 2*v + (w['A'][wi[0]][2] - 2*v + 16) % 224), MYWHY['tw_other_block'])
+ab = meta.get('forward_absorption_A_indices', [])
+if any(len(word['helper_final'][str(h)]) == 8 for h in cold):
+    # with dim-8 cold ends, the centre-retargeted absorption first leaks an ended helper's dirt into the cut's targets
+    MYWHY['ab_centre'] = COLDPRE
+if ab:
+    # the ColdBeyond U_b absorption (q += -1/2 g); ColdThird's extra absorptions have their own controls below
+    a0 = next(a for a in ab if word['A'][a][3] * 2 == -word['A'][a][4]); g0 = word['A'][a0]
+
+    def absorption_moved_early(w):   # absorbed before the absorbed register's last kernel write
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[2] == w['A'][i][1] and w['A'][i][-1] == g0[-1])
+        w['A'].insert(j, e)
+
+    def absorption_into_live(w):     # q += a g moved right after g's previous frame-mate gate, while q is still live
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[1] in regs(w['A'][i]))
+        w['A'].insert(j, e)
+    reject('forward absorption dropped', lambda w: w['A'].pop(a0), MYWHY['ab_dropped'])
+    reject('forward absorption into a centre (a live register read by the cut)', lambda w: w['A'][a0].__setitem__(1, next(c for c in word['centers'] if c not in g0[1:3] and c not in cold)), MYWHY['ab_centre'])
+    reject('forward absorption coefficient changed', lambda w: w['A'][a0].__setitem__(3, w['A'][a0][3] * 2), MYWHY['ab_coefficient'])
+    reject('forward absorption placed before the absorbed register\'s last kernel write', absorption_moved_early, MYWHY['ab_early'])
+    reject('forward absorption placed while the absorbing register is still live', absorption_into_live, MYWHY['ab_live'])
+    reject('forward absorption at a lower frame than its registers', lambda w: w['A'][a0].__setitem__(-1, w['A'][a0][-1][:-1]), MYWHY['ab_lower'])
+    reject('forward absorption at a higher frame (FULL) than its registers', lambda w: w['A'][a0].__setitem__(-1, [256, 128, 64, 32, 16, 8, 4, 2, 1]), MYWHY['ab_higher'])
+# COLD-THIRD primitives (present only when the word carries them): several absorptions after one input gate, dirt-release
+# absorptions (a dead port takes a live helper's value so that a hyperplane unit's column has no dirt on it), and cold ends at
+# a dim-8 frame with lifted partners.
+hyper = [h for h in cold if len(word['helper_final'][str(h)]) == 8]
+if hyper and ab:
+    sh = next(a for a, b in zip(ab, ab[1:]) if b == a + 1)              # two absorptions sharing one input anchor
+    rel = next(a for a in ab if a - 1 not in ab and a + 1 not in ab and word['A'][a][2] in hyper and word['A'][a][3] * 2 != -word['A'][a][4])
+    hh = hyper[0]; ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+    reject('second absorption sharing an input anchor dropped', lambda w: w['A'].pop(sh + 1), MYWHY['sh_dropped'])
+    reject('shared-anchor absorption coefficient changed', lambda w: w['A'][sh + 1].__setitem__(3, w['A'][sh + 1][3] * 2), MYWHY['sh_coefficient'])
+    reject('dirt-release absorption dropped', lambda w: w['A'].pop(rel), MYWHY['rel_dropped'])
+    reject('dirt-release absorption coefficient changed', lambda w: w['A'][rel].__setitem__(3, w['A'][rel][3] * 2), MYWHY['rel_coefficient'])
+    jr = max(i for i in range(npre, rel) if word['A'][i][0] == 'add' and word['A'][i][2] == word['A'][rel][1])
+
+    def release_while_read(w):   # the release runs before a kernel gate that still READS the port (port live)
+        e = w['A'].pop(rel); w['A'].insert(jr, e)
+    reject('dirt-release absorption moved before a kernel gate that still reads the port', release_while_read, MYWHY['rel_live'])
+if hyper:
+    # dim-8 cold-end controls for EVERY dim-8 cold end of the word (read from the word's helper_final and the recipe meta's
+    # cold_low_frame_ended_helpers), not one representative per terminal frame
+    for hh in hyper:
+        ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+        Uh = word['helper_final'][str(hh)]
+        reject('dim-8 cold end %d (frame %s) at another dim-8 frame' % (hh, Uh), lambda w, hh=hh: w['helper_final'].__setitem__(str(hh), next(f for h, f in w['helper_final'].items() if len(f) == 8 and sorted(f) != sorted(w['helper_final'][str(hh)]))), MYWHY['h8_other'])
+        reject('dim-8 cold end %d (frame %s): one lower-frame gate dropped (gate and its early_cleanup entry)' % (hh, Uh), lambda w, ih=ih: drop_cleanup_gate(w, ih), MYWHY['h8_lower'])
+        reject('dim-8 cold end %d (frame %s): profile pin (end dropped)' % (hh, Uh), lambda w, hh=hh: w['helper_final'].pop(str(hh)), WHY['profile_pin'])
+# FACTORED ACCUMULATOR (CarrierBypass; present only when the word carries one): a lower-frame tail gate a += x*g on two
+# non-ended registers whose accumulator a is afterwards read by a dim-8 cold end's tail gate (h += y*a at its U).
+ended_all = {int(h) for h in word['helper_final']}
+tailg = [(i, word['cleanup'][i]) for i, _ in early]
+accs = []   # EVERY factored accumulator gate (one per accumulator register a), each controlled on its own
+for k, (i, e) in enumerate(tailg):
+    if e[0] == 'add' and e[1] not in ended_all and e[2] not in ended_all and len(next(f for j, f in early if j == i)) < 8:
+        if e[1] not in [word['cleanup'][j][1] for j in accs] and any(t[0] == 'add' and t[2] == e[1] and t[1] in hyper for _, t in tailg[k + 1:]):
+            accs.append(i)
+for acc in accs:
+    a = word['cleanup'][acc][1]
+    reject('factored accumulator %d (gate %d) zeroed' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, 0), ENDPOINT)
+    reject('factored accumulator %d (gate %d) coefficient doubled' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, w['cleanup'][acc][3] * 2), ENDPOINT)
+outdir.mkdir(parents=True, exist_ok=True)
+(outdir/'COLD-END-CONTROLS.json').write_text(json.dumps(dict(status='PASS_COLD_END_RAW_WORD_CONTROLS', word=str(src), rejected=results), indent=1) + '\n')
+print('PASS', len(results), 'cold-end raw-word mutations rejected')
diff --git a/research/gauge44-slots-t16/construction/layers_p6n/reproduce_p6n.py b/research/gauge44-slots-t16/construction/layers_p6n/reproduce_p6n.py
new file mode 100644
index 0000000000..f9eb173bc1
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/layers_p6n/reproduce_p6n.py
@@ -0,0 +1,78 @@
+#!/usr/bin/env python3
+"""Rebuild the p6n word (NoTriReopen): the layered no-triangle word with p123's lane rebuilt as three factored dim-8 pairs.
+
+Input: a fresh `construction/layers_np/reproduce_np.py` output directory. Its swapped HPE word (hpe/) and its
+layered word a9de804f... are pinned there. Steps, each checked exactly:
+  1. layers: PR635's unchanged build_cold_end.apply(swapped HPE word, COLD-LAYERS-RECIPE-P6N.json.gz). The recipe is
+     NP's cold-layer recipe (cold44, s4, x30, b6, q4) plus the six cold ends of P6N-SPEC.json, built by NoTriReopen
+     with JP8Ends' stackJ/stackE (the CarrierBypass premix-only factored construction): [512,513] at
+     U(256,128,66,34,16,8,6,1), [311,510] at U(256,128,72,40,24,4,2,1), [522,327] at U(256,128,66,34,18,10,6,1).
+     The output word sha (34b683fa...), profile and widths are pinned.
+  2. layer-end-controls: layer_end_controls.py (Q6Reviewer-signed variant fc58c569..., which controls every dim-8
+     cold end individually) on the p6n word; exactly 95 rejections at pinned reasons.
+The promotion step (construction/promo/reproduce_promo.py --base p6n) builds the final word and its native locals.
+Apache-2.0. Driver by ColdWitness after NoTriReopen's runspec.py.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NP_SHA = 'a9de804f194eeb39f52a4c6e54c14d93e881bec4b632694249733ed410b58113'
+P6N_SHA = '34b683fa08f0'   # prefix; full value is the recipe's output_content_sha256 (asserted equal below)
+LAYER_CONTROLS = 95
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--np-dir', type=Path, required=True, help='construction/layers_np/reproduce_np.py output')
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    parent = src / 'vendor/pr558/vendor/pr552'
+    npd = a.np_dir.resolve()
+    assert hashlib.sha256(enc(read(npd / 'layers/FULL-WORD.json.gz'))).hexdigest() == NP_SHA, 'np-dir must hold the pinned NP word'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src), PR635_CODE=str(up / 'code'))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    rec = read(HERE / 'COLD-LAYERS-RECIPE-P6N.json.gz')
+    w = bce.apply(read(npd / 'hpe/FULL-WORD.json.gz'), rec)
+    raw = enc(w); got = hashlib.sha256(raw).hexdigest()
+    assert got == rec['output_content_sha256'] and got.startswith(P6N_SHA), ('p6n word', got)
+    rep = w['report']
+    assert rep['local_profile'] == {'1': 2540, '2': 358, '3': 446, '4': 178, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 64, '5': 48, '7': 54, '8': 122, '9': 216}, rep['width_inventory']
+    (out / 'p6n').mkdir(); word = out / 'p6n/FULL-WORD.json.gz'; word.write_bytes(gzip.compress(raw, mtime=0))
+    print('PASS p6n word', got, flush=True)
+    t = time.monotonic()
+    with (out / 'layer-end-controls.log').open('w') as f:
+        rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(HERE / 'layer_end_controls.py'), str(word),
+                              str(parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'), str(out / 'controls')],
+                             env=env, stdout=f, stderr=subprocess.STDOUT)
+    (out / 'STEPS.json').write_text(json.dumps([dict(step='layer-end-controls', exit_code=rc, seconds=round(time.monotonic() - t, 3))], indent=2) + '\n')
+    assert rc == 0, 'layer-end-controls'
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == LAYER_CONTROLS, len(ctl['rejected'])
+    print('PASS layer-end-controls', LAYER_CONTROLS, flush=True)
+    print('DONE', word, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/leaver/CHAIN-PINS-k8.json b/research/gauge44-slots-t16/construction/leaver/CHAIN-PINS-k8.json
new file mode 100644
index 0000000000..afd0467911
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/CHAIN-PINS-k8.json
@@ -0,0 +1,89 @@
+{
+ "np_profile": {
+  "1": 2422,
+  "2": 408,
+  "3": 494,
+  "4": 136,
+  "5": 56,
+  "8": 8
+ },
+ "p6n_profile": {
+  "1": 2428,
+  "2": 420,
+  "3": 482,
+  "4": 136,
+  "5": 56,
+  "8": 8
+ },
+ "lec-p6n_pins_sha256": "d87ed7b5869bed4a3d266f0ce5fc784cbe88340a625d22ab9f580fa00872df19",
+ "lec-p6n": 95,
+ "lec-p6n_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)"
+ },
+ "promo_controls": 11,
+ "lec-promo_pins_sha256": "d87ed7b5869bed4a3d266f0ce5fc784cbe88340a625d22ab9f580fa00872df19",
+ "lec-promo": 95,
+ "lec-promo_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)"
+ },
+ "jx_controls": [
+  "C0_identity",
+  "C1_741_only",
+  "N3_plain_join_moved_reads"
+ ],
+ "lec-jx_pins_sha256": "d87ed7b5869bed4a3d266f0ce5fc784cbe88340a625d22ab9f580fa00872df19",
+ "lec-jx": 95,
+ "lec-jx_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)"
+ },
+ "hybrid_controls": [
+  "C0_identity",
+  "donation_after",
+  "donation_after@226",
+  "donation_after@228",
+  "donation_after@230",
+  "donation_after@231",
+  "donation_after@232",
+  "donation_after@62",
+  "drop_preread",
+  "drop_preread@226",
+  "drop_preread@228",
+  "drop_preread@230",
+  "drop_preread@231",
+  "drop_preread@232",
+  "drop_preread@62",
+  "drop_restore",
+  "drop_restore@226",
+  "drop_restore@228",
+  "drop_restore@230",
+  "drop_restore@231",
+  "drop_restore@232",
+  "drop_restore@62",
+  "recipe",
+  "restore_full",
+  "restore_full@226",
+  "restore_full@228",
+  "restore_full@230",
+  "restore_full@231",
+  "restore_full@232",
+  "restore_full@62"
+ ],
+ "lec-hyb_pins_sha256": "d87ed7b5869bed4a3d266f0ce5fc784cbe88340a625d22ab9f580fa00872df19",
+ "lec-hyb": 95,
+ "lec-hyb_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)"
+ },
+ "frame_build_controls": 3,
+ "lec-frames_pins_sha256": "b07279e41ec9d8f89e8509081e1e7f2c8e8b062fd951b22608a03ac461982914",
+ "lec-frames": 95,
+ "lec-frames_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)",
+  "other_hp:554": "tail frame dim 5; no other helper_final frame of that dim"
+ },
+ "canonical_sha256": "d1bf3c6f250a61be7421ce566668092f362c465274fb472d4bb01fc80cba9b23",
+ "program_sha256": {
+  "forward": "683f83231d4d4890a7fc3d18f30d4ac7bfbd7bbdf4e7ff57ad0eb09e8a5f571c",
+  "backward": "2d184e4d9d48aa4d5e3679368ee0eca7e0388b1966eb05e0fd17d22d00d36293"
+ },
+ "clifford_recipes_sha256": "e3bfdfa2c044f14c00a8706950c8ae838ceeedd9ca78a83bffefe7886219516a"
+}
diff --git a/research/gauge44-slots-t16/construction/leaver/CODED-CELLS-k8.json b/research/gauge44-slots-t16/construction/leaver/CODED-CELLS-k8.json
new file mode 100644
index 0000000000..cd23561e0b
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/CODED-CELLS-k8.json
@@ -0,0 +1,2826 @@
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+    1,
+    1,
+    [
+     272,
+     144,
+     65,
+     49,
+     8,
+     6
+    ]
+   ],
+   "after": [
+    "add",
+    194,
+    429,
+    1,
+    1,
+    [
+     257,
+     129,
+     65,
+     32,
+     17,
+     8,
+     6
+    ]
+   ],
+   "delta": {
+    "1": -3,
+    "2": 3,
+    "3": -1
+   }
+  },
+  {
+   "section": "B",
+   "index": 757,
+   "before": [
+    "add",
+    195,
+    431,
+    1,
+    1,
+    [
+     256,
+     128,
+     65,
+     41,
+     16,
+     6
+    ]
+   ],
+   "after": [
+    "add",
+    195,
+    431,
+    1,
+    1,
+    [
+     256,
+     128,
+     65,
+     32,
+     16,
+     9,
+     6
+    ]
+   ],
+   "delta": {
+    "1": -3,
+    "2": 3,
+    "3": -1
+   }
+  }
+ ]
+}
diff --git a/research/gauge44-slots-t16/construction/leaver/TRI-LEAVER-k8.json b/research/gauge44-slots-t16/construction/leaver/TRI-LEAVER-k8.json
new file mode 100644
index 0000000000..e3bb24cc49
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/TRI-LEAVER-k8.json
@@ -0,0 +1,590 @@
+{
+ "full_pairs": [
+  [
+   0,
+   1
+  ],
+  [
+   2,
+   3
+  ],
+  [
+   4,
+   5
+  ],
+  [
+   6,
+   7
+  ]
+ ],
+ "triangles": [
+  {
+   "p": [
+    0,
+    1
+   ],
+   "e": 1,
+   "reads": [
+    [
+     57,
+     [
+      0,
+      1,
+      2,
+      3
+     ],
+     0
+    ],
+    [
+     56,
+     [
+      0,
+      1,
+      2,
+      3
+     ],
+     1
+    ],
+    [
+     25,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     0
+    ],
+    [
+     24,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     1
+    ],
+    [
+     17,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     0
+    ],
+    [
+     16,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     1
+    ]
+   ],
+   "coded": true,
+   "cell": 0
+  },
+  {
+   "p": [
+    2,
+    3
+   ],
+   "e": 1,
+   "reads": [
+    [
+     63,
+     [
+      0,
+      1,
+      2,
+      3
+     ],
+     3
+    ],
+    [
+     59,
+     [
+      0,
+      1,
+      2,
+      3
+     ],
+     23
+    ],
+    [
+     89,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     0
+    ],
+    [
+     88,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     1
+    ],
+    [
+     81,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     0
+    ],
+    [
+     80,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     1
+    ]
+   ],
+   "coded": true,
+   "cell": 1
+  },
+  {
+   "p": [
+    4,
+    5
+   ],
+   "e": 1,
+   "reads": [
+    [
+     31,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     3
+    ],
+    [
+     27,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     23
+    ],
+    [
+     95,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     3
+    ],
+    [
+     91,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     23
+    ],
+    [
+     49,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     0
+    ],
+    [
+     48,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     1
+    ]
+   ],
+   "coded": true,
+   "cell": 2
+  },
+  {
+   "p": [
+    6,
+    7
+   ],
+   "e": 1,
+   "reads": [
+    [
+     23,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     3
+    ],
+    [
+     19,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     23
+    ],
+    [
+     87,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     3
+    ],
+    [
+     83,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     23
+    ],
+    [
+     55,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     3
+    ],
+    [
+     51,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     23
+    ]
+   ],
+   "coded": true,
+   "cell": 3
+  },
+  {
+   "p": [
+    6,
+    7
+   ],
+   "e": -1,
+   "reads": [
+    [
+     18,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     21
+    ],
+    [
+     22,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     2
+    ],
+    [
+     82,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     21
+    ],
+    [
+     86,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     2
+    ],
+    [
+     50,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     21
+    ],
+    [
+     54,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     2
+    ]
+   ],
+   "coded": true,
+   "cell": 4
+  },
+  {
+   "p": [
+    0,
+    1
+   ],
+   "e": -1,
+   "reads": [
+    [
+     61,
+     [
+      0,
+      1,
+      2,
+      3
+     ],
+     17
+    ],
+    [
+     60,
+     [
+      0,
+      1,
+      2,
+      3
+     ],
+     19
+    ],
+    [
+     29,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     17
+    ],
+    [
+     28,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     19
+    ],
+    [
+     21,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     17
+    ],
+    [
+     20,
+     [
+      0,
+      1,
+      6,
+      7
+     ],
+     19
+    ]
+   ],
+   "coded": true,
+   "cell": 5
+  },
+  {
+   "p": [
+    2,
+    3
+   ],
+   "e": -1,
+   "reads": [
+    [
+     58,
+     [
+      0,
+      1,
+      2,
+      3
+     ],
+     21
+    ],
+    [
+     62,
+     [
+      0,
+      1,
+      2,
+      3
+     ],
+     2
+    ],
+    [
+     93,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     17
+    ],
+    [
+     92,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     19
+    ],
+    [
+     85,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     17
+    ],
+    [
+     84,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     19
+    ]
+   ],
+   "coded": true,
+   "cell": 6
+  },
+  {
+   "p": [
+    4,
+    5
+   ],
+   "e": -1,
+   "reads": [
+    [
+     26,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     21
+    ],
+    [
+     30,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     2
+    ],
+    [
+     90,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     21
+    ],
+    [
+     94,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     2
+    ],
+    [
+     53,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     17
+    ],
+    [
+     52,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     19
+    ]
+   ],
+   "coded": true,
+   "cell": 7
+  }
+ ]
+}
diff --git a/research/gauge44-slots-t16/construction/leaver/build_frames_lv.py b/research/gauge44-slots-t16/construction/leaver/build_frames_lv.py
new file mode 100644
index 0000000000..5f8aa7a24b
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/build_frames_lv.py
@@ -0,0 +1,64 @@
+#!/usr/bin/env python3
+"""Apply the pinned gate/tail frame re-optimisation of FRAME-RECIPE-LV-k5.json (exact global frame optimum, gopt2) to the
+leaver U8 word.
+
+usage: build_frames_lv.py INPUT_WORD.json.gz OUT_DIR RECIPE.json
+
+Standard library only. The frames are applied by BlockInvert's `../promo/build_promotion.apply` (no entrances; 'B' gate
+frames and 'T' tail frames), which checks each old frame and recomputes the local profile and widths. This builder then checks:
+input sha pin; the scalar program of A, cut, B, precondition and cleanup unchanged (every field but the frame); start
+and end frames unchanged; local profile and width inventory equal to the recipe's; output sha pin. Three pin controls
+(input pin, wrong old frame, output pin) must be rejected at their pinned reasons on every build.
+Adapted from ../frames/build_frames.py (from PR741's extras/build_frames.py, chafreaky). Apache-2.0.
+"""
+import copy, gzip, hashlib, importlib.util, json, sys
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+_s = importlib.util.spec_from_file_location('promotion', HERE.parent / 'promo/build_promotion.py')
+B = importlib.util.module_from_spec(_s); _s.loader.exec_module(B)
+
+
+def construct(raw, recipe):
+    assert hashlib.sha256(raw).hexdigest() == recipe['input_content_sha256'], 'input word pin'
+    w = json.loads(raw)
+    assert recipe['gate_frames'] and all(c[0] in ('B', 'T') for c in recipe['gate_frames']), 'B and T frames only'
+    out = B.apply(w, dict(entrances={}, gate_frames=recipe['gate_frames']))
+    for section in ('A', 'cut', 'B', 'precondition', 'cleanup'):
+        assert [e[:-1] for e in w[section]] == [e[:-1] for e in out[section]], 'scalar program unchanged'
+    assert out['start_extra'] == w['start_extra'] and out['helper_final'] == w['helper_final'], 'endpoint frames unchanged'
+    assert out['report']['local_profile'] == recipe['expected']['local_profile'] and \
+        out['report']['width_inventory'] == recipe['expected']['width_inventory'], 'profile and width pins'
+    data = json.dumps(out, sort_keys=True, separators=(',', ':')).encode()
+    assert hashlib.sha256(data).hexdigest() == recipe['expected']['output_content_sha256'], 'output word pin'
+    return data
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    inp, outd, rfile = map(Path, sys.argv[1:4])
+    raw = gzip.decompress(inp.read_bytes()); recipe = json.loads(rfile.read_text())
+    data = construct(raw, recipe)
+    rejected = []
+    for name, change, reason in [
+            ('input-pin', lambda r: r.__setitem__('input_content_sha256', '0' * 64), 'input word pin'),
+            ('old-frame', lambda r: r['gate_frames'][0].__setitem__(2, []), 'gate frame mismatch'),
+            ('output-pin', lambda r: r['expected'].__setitem__('output_content_sha256', '0' * 64), 'output word pin')]:
+        r = copy.deepcopy(recipe); change(r)
+        try:
+            construct(raw, r)
+        except AssertionError as e:
+            assert reason in str(e), (name, str(e)); rejected.append(dict(name=name, reason=reason))
+        else:
+            raise AssertionError('accepted ' + name)
+    outd.mkdir(parents=True)
+    (outd / 'FULL-WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+    (outd / 'BUILD.json').write_text(json.dumps(dict(
+        status='PASS_FRAME_REOPT_EXACT_CONSTRUCTION', input_sha256=hashlib.sha256(raw).hexdigest(),
+        output_sha256=hashlib.sha256(data).hexdigest(), scalar_program_unchanged=True, frames=len(recipe['gate_frames']),
+        rejected_controls=rejected), indent=2) + '\n')
+    print('PASS', len(recipe['gate_frames']), 'frames and three pin controls')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-01+.json b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-01+.json
new file mode 100644
index 0000000000..bfef820f29
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-01+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x0",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x0",
+   "-1/2"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-01-.json b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-01-.json
new file mode 100644
index 0000000000..3afa894b20
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-01-.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "x1",
+   "x0",
+   1
+  ],
+  [
+   "x3",
+   "x4",
+   1
+  ],
+  [
+   "x5",
+   "x2",
+   1
+  ],
+  [
+   "y0",
+   "x3",
+   1
+  ],
+  [
+   "y2",
+   "x1",
+   1
+  ],
+  [
+   "y4",
+   "x5",
+   1
+  ],
+  [
+   "y1",
+   "y4",
+   1
+  ],
+  [
+   "y3",
+   "y2",
+   1
+  ],
+  [
+   "y5",
+   "y0",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y0",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y1",
+   "x0",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "x1",
+   "x0",
+   "1"
+  ],
+  [
+   "x3",
+   "x4",
+   "1"
+  ],
+  [
+   "x5",
+   "x2",
+   "1"
+  ],
+  [
+   "y0",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y1",
+   "y4",
+   "1"
+  ],
+  [
+   "y3",
+   "y2",
+   "1"
+  ],
+  [
+   "y5",
+   "y0",
+   "1"
+  ],
+  [
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+   "-1/2"
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+  [
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+   "-1/2"
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+  [
+   "y4",
+   "x1",
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+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-23+.json b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-23+.json
new file mode 100644
index 0000000000..98ff8050e7
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-23+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
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+  [
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+   "-1/2"
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+  [
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+   "x2",
+   "-1/2"
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+  [
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+   "x1",
+   "1"
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+  [
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+}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-23-.json b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-23-.json
new file mode 100644
index 0000000000..517b89d382
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-23-.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
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+ "scaled": [
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+   "-1/2"
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+   "-1/2"
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+   "x3",
+   "-1/2"
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+  [
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+   "1"
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+  ]
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+}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-45+.json b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-45+.json
new file mode 100644
index 0000000000..2bc89e1de1
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-45+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
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+   "1"
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+  [
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+   "-1/2"
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+  [
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+   "1"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-45-.json b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-45-.json
new file mode 100644
index 0000000000..b9c1904b83
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-45-.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
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+   1
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+   1
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+ "scaled": [
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+   "-1/2"
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+   "1"
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+  ],
+  [
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+   "x4",
+   "-1/2"
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+  [
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+   "1"
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+  [
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+   "x2",
+   "1"
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+  [
+   "y5",
+   "x1",
+   "1"
+  ],
+  [
+   "y4",
+   "x0",
+   "1"
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+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-67+.json b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-67+.json
new file mode 100644
index 0000000000..7d756cb19d
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-67+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
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+   1
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+   1
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+   1
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+   1
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+   1
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+   1
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+   "x1",
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+ ],
+ "scaled": [
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+   "1"
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+  [
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+   "x4",
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+  [
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+   "x3",
+   "1"
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+   "1"
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+  [
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+   "x2",
+   "1"
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+  [
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+   "x0",
+   "1"
+  ],
+  [
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+   "x4",
+   "1"
+  ],
+  [
+   "y0",
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+   "1"
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+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "x5",
+   "1"
+  ],
+  [
+   "y2",
+   "x3",
+   "1"
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+  [
+   "y3",
+   "x2",
+   "1"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-67-.json b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-67-.json
new file mode 100644
index 0000000000..7d756cb19d
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/cells-k8/CORE-67-.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
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+  [
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+   1
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+   1
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+  [
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+   1
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+   1
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+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x5",
+   "1"
+  ],
+  [
+   "y3",
+   "x4",
+   "1"
+  ],
+  [
+   "y4",
+   "x3",
+   "1"
+  ],
+  [
+   "y5",
+   "x2",
+   "1"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "1"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y5",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "x5",
+   "1"
+  ],
+  [
+   "y2",
+   "x3",
+   "1"
+  ],
+  [
+   "y3",
+   "x2",
+   "1"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/leaver/cgx_leaver.py b/research/gauge44-slots-t16/construction/leaver/cgx_leaver.py
new file mode 100644
index 0000000000..e686c66306
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/cgx_leaver.py
@@ -0,0 +1,491 @@
+# LeaverSAT: no-helper mutable-leaver all-K cells (coded triangles) on the no-triangle word. Generated by
+# LeaverSAT/mkpkg.py from construction/notri/cgx.py with the leaver edits (lv.leaver_source); Apache-2.0.
+import json as _lj, os as _lo, sys as _ls
+from fractions import Fraction as _lF
+CODED_CELLS=[(c['bindings'],[[t,s,_lF(q)] for t,s,q in c['scaled']]) for c in _lj.load(open(_lo.path.join(_lo.path.dirname(_lo.path.abspath(_ls.argv[3])),'CODED-CELLS.json')))]
+# Round20 early-coordinate-center / own-Y variant, prepared for icekylinx
+# with OpenAI Codex assistance. Apache-2.0. Scalar elementary-operation
+# helpers below are retained from the attributed PR514 construct_partial.py.
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+# AtomScout: leaver-read K-triangles (schedule from atom1.py / rog.py CP-SAT)
+TRI=json.loads(Path(sys.argv[3]).read_text())
+FULLT={(tuple(tr['p']),tr['e']) for tr in TRI['triangles']}
+TRI_COORDS={t+8 for tr in TRI['triangles'] for t,_,_ in tr['reads']}
+import os as _o
+COPYL=json.loads(open(_o.environ['XPARAM']).read()).get('copyl',[]) if _o.environ.get('XPARAM') else []
+NH=504-3*len(FULLT)+len(COPYL)
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+# Helper ids of the unpatched 504 construction: every allocation advances the 504 numbering; a packet copy that the
+# K-triangle schedule never forms advances it without allocating (HELPER-MAP.json).
+shadow=[];skipped=[];nxt=[2*v]
+def alloc():
+    n=len(cur);cur.append(());rows.append({});shadow.append(nxt[0]);nxt[0]+=1;return n
+def skip():
+    skipped.append(nxt[0]);nxt[0]+=1
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# Each source quartet supplies pair partials first. The other two coordinate
+# partitions supply eight early face packets without touching the eight
+# partials later copied into the preconditioned Y coordinates.
+SELECT=(0,0)
+PRIORITY=json.loads((INPUT/"COMPLETION-PRIORITY.json").read_text())
+import os
+XP=json.loads(open(os.environ['XPARAM']).read()) if os.environ.get('XPARAM') else {}
+XCH=XP.get('exch',{});PRIO=XP.get('prio',{})
+maps={};early={};own_rows={};pairs=[];tetrads={};block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)});maps[c]=mp
+    for ei,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[:40]):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        if ei==15:
+            for jj,cl in XCH.get(str(len(maps)-1),[[4,17],[5,19],[6,21],[7,23]]):swap(mp[jj],mp[cl],(P[ids[jj]],))
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in targets:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                t,u=sorted(ts);e2=R[t][q[0]]*R[t][q[1]]
+                pair={'targets':(t,u),'keys':[(c,p,eps),(c,q,e2)],'selected':pi==SELECT[parity],
+                      'matrix':[[R[a][p[0]],R[a][q[0]]] for a in (t,u)]}
+                pairs.append(pair)
+                if not pair['selected']:continue
+                zz=-Q(2*R[u][p[0]],R[t][p[0]])
+                sources=tet[1-parity]
+                for target,sign in ((t,-1),(u,1)):
+                    wanted={s:-Q(G[t][s],4)-sign*Q(G[u][s],2)/zz for s in sources
+                            if -Q(G[t][s],4)-sign*Q(G[u][s],2)/zz}
+                    assert len(wanted)==2
+                    candidates=[]
+                    for r in mp.values():
+                        if set(rows[r])!=set(wanted):continue
+                        s=next(iter(wanted));coef=wanted[s]/rows[r][s]
+                        if all(wanted[s]==coef*rows[r][s] for s in wanted):candidates.append((r,coef))
+                    assert len(candidates)==1
+                    r,coef=candidates[0];assert len(cur[r])==2
+                    own_rows[target]=(r,coef,cur[r])
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    needed={own_rows[t][0] for t in ids}
+    early[c]={j for j,e in enumerate(z['events'][40:]) if not ({mp[e[0]],mp[e[1]]}&needed)}
+    assert len(early[c])==8
+    retired=[]
+    for j in sorted(early[c]):
+        (t,s,a,b),F=z['events'][40+j],z['event_frames'][40+j]
+        add(mp[t],mp[s],Q(a,b),tuple(F));retired.append(mp[s])
+    assert not set(retired)&needed
+    # These eight retired rows already span every source coordinate. Keep
+    # them invertible and place the four coordinate totals in a changed basis.
+    F=basis([P[s] for s in ids]);assert len(F)==4
+    regs=sorted(retired,key=lambda r:(r>=v,r))
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    M=[[Q(R[s][i]) for s in ids] for i in c]
+    def qr_rank(rs):
+        bs={}
+        for r in rs:
+            r=r.copy()
+            for i,b in sorted(bs.items()):
+                if r[i]:q=r[i];r=[x-q*y for x,y in zip(r,b)]
+            i=next((i for i,x in enumerate(r) if x),None)
+            if i is not None:q=r[i];bs[i]=[x/q for x in r]
+        return len(bs)
+    assert qr_rank(M)==4
+    for rr0 in PRIO.get(",".join(map(str,c)),[])+PRIORITY[",".join(map(str,c))]["rows"]:
+        rr=list(map(Q,rr0))
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    for i in range(8):
+        if len(M)==8:break
+        rr=[Q(i==j) for j in range(8)]
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    assert len(M)==8
+    linear(regs,M,F)
+    for i,r in zip(c,regs):
+        assert rows[r]=={s:Q(R[s][i]) for s in ids}
+        block_totals[c,i]=r
+
+# All centers are complete while Y is still at zero. This is the crucial
+# difference from an illegal early-own-Y prefix using the old center order.
+centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+assert all(cur[v+t]==() for t in range(v))
+
+phase=B
+for t,(r,coef,F) in sorted(own_rows.items()):
+    if t in TRI_COORDS:continue
+    assert cur[r]==F
+    add(v+t,r,coef,F)
+# requests are needed for TRI coefficients
+requests=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    requests[key1].append((t,-Q(mat[0][0],2)))
+    requests[key2].append((u,-Q(mat[0][1],2)))
+reqcoef={t:(key,coef) for key,reqs in requests.items() for t,coef in reqs}
+def face_info(c,p,eps):
+    z=blocks[c];keys=[(pp,ee) for pp in it.combinations(c,2) for ee in (-1,1)]
+    r_local,alpha=z['outputs'][keys.index((p,eps))]
+    j=[j for j in range(40,len(z['events'])) if z['events'][j][0]==r_local];assert len(j)==1
+    return j[0],Q(alpha)
+tri_join_counts=Counter()
+coded_shadow_slot={}
+coded_target_edges=[];TRILOG=[]
+lcopy={}
+for s8 in COPYL:
+    r=s8+8;c=len(cur);cur.append(());rows.append({});shadow.append(None);add(c,r,1,cur[r]);lcopy[r]=c
+BF={c:basis([P[x] for x in z['receipt']['source_lines']]) for c,z in blocks.items()}
+HYB={(tuple(map(int,h[0])),tuple(map(int,h[1])),int(h[2])) for h in XP.get('hyb',[])}
+HYBLOG=[]
+def triread(t,blk,r,q):
+    F=basis(cur[v+t]+cur[r]);assert inside(F,hyper(P[t])),('TRI frame',t,blk,r,cur[v+t],cur[r],hyper(P[t]),[x for x in TRILOG if x[2]==r],HYBLOG)
+    tri_join_counts[len(F)]+=1;add(v+t,r,q,F);TRILOG.append([t,list(blk),r,str(q),list(F),list(cur[r])])
+for tr in TRI['triangles']:
+    if tr.get('coded'):
+        bindings={}
+        for name,binding in CODED_CELLS[tr['cell']][0].items():
+            bindings[name]=maps[tuple(binding[1])][binding[2]] if binding[0]=='source' else v+binding[1]
+        for tn,sn,q in CODED_CELLS[tr['cell']][1]:
+            target,source=bindings[tn],bindings[sn]
+            F=basis(cur[target]+cur[source])
+            for register in (target,source):
+                if v<=register<2*v:assert inside(F,hyper(P[register-v])),('coded frame',register,F)
+            add(target,source,q,F)
+            if sn.startswith('y'):coded_target_edges.append((target,source,Q(q)))
+        continue
+    p,eps=tuple(tr['p']),tr['e']
+    hb={blk for _,blk,_ in map(lambda x:(x[0],tuple(x[1]),x[2]),tr['reads']) if (blk,p,eps) in HYB}
+    own=[];rest=[]
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];r0=r;r=lcopy.get(r,r)
+        key,coef=reqcoef[t];assert key[1]==p and key[2]==eps,(key,p,eps)
+        if blk==key[0]:
+            rr,c0,F0=own_rows[t];assert rr==r0;own.append((t,blk,r,c0))
+        else:
+            j,alpha=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert loc in ev[:2]
+            rest.append((t,blk,loc,r,coef*alpha))
+    if not hb:
+        # original interleaved order
+        for t8,blk,loc in tr['reads']:
+            t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+            if blk==key[0]:q=own_rows[t][1]
+            else:j,alpha=face_info(blk,p,eps);q=coef*alpha
+            triread(t,blk,r,q)
+        continue
+    items=[]  # (kind, t, reg, q, blk)
+    for t,blk,r,q in own:items.append(('r',t,r,q,blk,blk in hb))
+    for blk in sorted(hb):items.append(('e',None,None,None,blk,True))
+    done=set()
+    for t,blk,loc,r,q in rest:
+        if blk in hb:
+            j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j]
+            ws=[x for x in rest if x[0]==t and x[1]==blk];assert len(ws)==2 and ws[0][4]==ws[1][4] and {ws[0][2],ws[1][2]}==set(ev[:2])
+            if (t,blk) in done:continue
+            done.add((t,blk));items.append(('m',t,maps[blk][ev[0]],q,blk,True))
+        else:items.append(('r',t,r,q,blk,False))
+    # Original read order with the two half reads collapsed into one M read at the first half's slot; the face event goes
+    # just before the first M read of its block; own reads of the M register are hoisted ahead of that event.
+    def evinfo(blk):
+        j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert ev[2]==ev[3]==1,ev
+        mpb=maps[blk];return mpb[ev[0]],mpb[ev[1]],tuple(blocks[blk]['event_frames'][j])
+    items=[]
+    seen=set()
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+        if blk==key[0]:items.append(('r',t,r,own_rows[t][1],blk,blk in hb))
+        else:
+            j,alpha=face_info(blk,p,eps);q=coef*alpha
+            if blk in hb:
+                if (t,blk) not in seen:seen.add((t,blk));continue
+                items.append(('m',t,evinfo(blk)[0],q,blk,True))
+            else:items.append(('r',t,r,q,blk,False))
+    for blk in sorted(hb):
+        k0=min(i for i,x in enumerate(items) if x[0]=='m' and x[4]==blk)
+        items.insert(k0,('e',None,None,None,blk,True))
+    n=len(items)
+    def step(it,st):
+        k,t,r,q,blk,h=it;g=lambda x:st.get(x,cur[x])
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(g(a_))+list(g(b_)))
+            return {a_:FF,b_:FF} if inside(FF,BF[blk]) else None
+        F=basis(list(g(v+t))+list(g(r)))
+        if not inside(F,hyper(P[t])):return None
+        if h and k=='r' and r==evinfo(blk)[1] and not inside(F,BF[blk]):return None
+        return {v+t:F,r:F}
+    def allowed(i,used):
+        k,t,r,q,blk,h=items[i]
+        evi=[j for j,x in enumerate(items) if x[0]=='e' and x[4]==blk] if h else []
+        if k=='e':return all(j in used for j,x in enumerate(items) if x[0]=='r' and x[4]==blk and x[5] and x[2]==evinfo(blk)[0])
+        if k=='m':return evi[0] in used
+        if k=='r' and h and r==evinfo(blk)[0]:return evi[0] not in used
+        return True
+    budget=[int(os.environ.get('HYBBUDGET','300000'))];memo=set()
+    def dfs(st,used,order):
+        if len(order)==n:return order
+        budget[0]-=1
+        if budget[0]<0:return None
+        sig=(used,tuple(sorted(st.items())))
+        if sig in memo:return None
+        memo.add(sig)
+        for i in range(n):
+            if i in used or not allowed(i,used):continue
+            d=step(items[i],st)
+            if d is None:continue
+            ns=dict(st);ns.update(d);res=dfs(ns,used|{i},order+[i])
+            if res:return res
+        return None
+    import sys as _s;_s.setrecursionlimit(20000)
+    order=dfs({},frozenset(),[])
+    assert order,('no feasible hybrid order',p,eps,sorted(hb),budget)
+    for i in order:
+        k,t,r,q,blk,h=items[i]
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(cur[a_])+list(cur[b_]));add(a_,b_,1,FF);HYBLOG.append([list(blk),list(p),eps,list(FF)])
+        else:triread(t,blk,r,q)
+
+packets={}
+for c,z in sorted(blocks.items()):
+    mp=maps[c]
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    skipev={face_info(c,p,eps)[0] for p,eps in keys if (p,eps) in FULLT}
+    for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]):
+        if j not in early[c] and 40+j not in skipev:
+            t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    for key,(r,alpha) in zip(keys,z['outputs']):
+        if tuple(key) in FULLT:skip();continue
+        a=mp[r];b=alloc();add(b,a,1,cur[a])
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha))
+
+# Both tetrahedra use the same partition. A selected key has exactly two
+# selected Y loads and no ordinary M consumer. Supply its two raw halves in
+# opposite orders and never form that M. Other keys retain the old M path.
+second=[];first_join_counts=Counter()
+for key,reqs in sorted(requests.items()):
+    assert len(reqs)==2
+    c,p,eps=key
+    if (p,eps) in FULLT:continue
+    ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds
+    for j,(target,coef) in enumerate(sorted(reqs)):
+        first_source,second_source=(a,b) if j==0 else (b,a)
+        r,alpha=packets[first_source,p,eps,second_source]
+        F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+        first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F)
+        r,alpha=packets[second_source,p,eps,c]
+        second.append((target,r,coef*alpha))
+
+Ms={}
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for eps in (-1,1):
+            if (c,p,eps) in requests:continue
+            (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,eps]=(a,alpha)
+
+consumers=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    for key in pair['keys']:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    if key in requests:
+        assert all(pairs[i]['selected'] for i in uses)
+        continue
+    assert all(not pairs[i]['selected'] for i in uses)
+    a,alpha=Ms[key]
+    for j,pid in enumerate(uses):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+assert len(cur)-240==NH,len(cur)-240
+
+selected_join_counts=Counter()
+for target,r,coef in second:
+    F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+    selected_join_counts[len(F)]+=1;add(v+target,r,coef,F)
+output_basis=[]
+for pair in pairs:
+    if not pair['selected']:continue
+    (t,u),mat=pair['targets'],pair['matrix']
+    F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u]))
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert rows[v+t]==expected,('side identity',t)
+
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+for target,source,q in reversed(coded_target_edges):
+    scatter[target-v]=[a-q*b for a,b in zip(scatter[target-v],scatter[source-v])]
+    precondition.append(['add',target,source,-q.numerator,q.denominator,[]])
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8
+assert sum(r*z for r,z in H.items())==9*NH+240*8+72,sum(r*z for r,z in H.items())
+
+def apply(e,matrix):
+    if e[0]=='add':
+        _,t,s,a,b,*_=e;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    e[-1]=list(FULL);return e
+cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q]
+cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v]
+matrix=[{r:Q(1)} if r<v else {} for r in range(len(cur))]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(len(cur)))
+
+# Restrict the eight isolated axis ports exactly, keeping the stable 112-port
+# label set. This variant changes the local word, not the outer geometry.
+mp={s:s-8 for s in range(8,120)}
+mp.update({120+s:112+s-8 for s in range(8,120)})
+mp.update({240+r:224+r for r in range(NH)})
+def restrict(events,is_cut=False):
+    out=[]
+    for e in events:
+        regs=e[1:3] if e[0]=='add' else e[1:2]
+        if any(r not in mp for r in regs):
+            assert is_cut and e[0]=='add' and e[1]-120==e[2] and e[2]<8 and e[3:5]==[1,1]
+            continue
+        q=copy.deepcopy(e);q[1]=mp[q[1]]
+        if q[0]=='add':q[2]=mp[q[2]]
+        out.append(q)
+    return out
+H.subtract({1:8,8:16});H=+H
+report={'status':'EXACT_CLEAN_OWN_Y_EARLY_CENTER_WORD_NOT_ADMITTED',
+        'h':9,'v':112,'R':NH,'cst':64,'m':73,'local_profile':dict(sorted(H.items())),
+        'centre_ranks':[8]*8,**({'tri_join_counts':dict(tri_join_counts)} if TRI['triangles'] else {}),'selected_load_join_counts':dict(selected_join_counts),'selected_partitions':list(SELECT),'first_load_join_counts':dict(first_join_counts),
+        'source_columns_exact':112,'borrowed_output_pairs':56,'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'local_rank_mass':sum(r*n for r,n in H.items()),'scope':'Clean scalar identity and all literal monotone local frames only; arbitrary-dirt compensation, entrance kernels, exact phase recipes, and global hosting/pricing are not yet certified.'}
+word={'report':report,'ports':P[8:],'root_lines':R[8:],
+      'A':restrict(A),'B':restrict(B),'cut':restrict(cut,True),'cleanup':restrict(cleanup),'precondition':restrict(precondition),
+      'centers':[mp[r] for r in centers[:8]],'center_frames':center_frames[:8],
+      'scatter':[[str(x) for x in row[:8]] for row in scatter[8:]]}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+assert len(shadow)==NH and len([x for x in shadow if x is not None])+len(skipped)==504
+hmap={**{r:r for r in range(224)},**{224+s_-240:224+i for i,s_ in enumerate(shadow) if s_ is not None}}
+(OUT/'HELPER-MAP.json').write_text(json.dumps({'map':{str(k):hmap[k] for k in sorted(hmap)},'removed_504_helpers':[224+s_-240 for s_ in skipped]})+'\n')
+(OUT/'TRILOG.json').write_text(json.dumps(dict(reads=TRILOG,hyb=HYBLOG)));(OUT/'DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/gauge44-slots-t16/construction/leaver/layer_end_controls_leaver.py b/research/gauge44-slots-t16/construction/leaver/layer_end_controls_leaver.py
new file mode 100644
index 0000000000..84b1c52ed2
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/layer_end_controls_leaver.py
@@ -0,0 +1,242 @@
+"""layer_end_controls_leaver.py LAYERED-WORD.json.gz ROUTING OUTDIR [ENTERING] (env PR635_CODE, optional env LEC_REASON_PINS
+= JSON file {mutant key: expected reason key or literal message substring}).  LeaverSAT variant of the signed
+layers_p6n/layer_end_controls.py (fc58c569...): IDENTICAL mutations and checks; the only change is that the expected
+rejection reason of a named mutant can be re-pinned per word (on the leaver words, with fewer cold ends, the premix-drop
+and into-full mutants are caught by the arbitrary-dirt endpoint replay before the pinned site is reached).  Every
+mutation is still REQUIRED to be rejected at its (re-)pinned reason; the unmutated word MUST pass.
+NOT-APPLICABLE SITES (Q6Reviewer, k8 / fo_hyb): two mutant constructions can be vacuous on a word:
+  extra_end      - h0's first premixed partner is already cold-ended at h0's frame, so the mutant is the identity;
+  other_hp:<e>   - entering end e's tail frame has a dimension that no helper_final frame has, so the mutant cannot be built.
+Such a site is never skipped silently: the pins file MUST declare it under "not_applicable" ({site: reason}), the
+declared set MUST equal the detected set, an identity is PROVEN by byte equality of the mutated and honest words (both
+sha256 recorded), and a substitute mutant of the same class is built and MUST be rejected at the class's pinned reason:
+  extra_end      -> the first premixed partner of h0 that is not yet ended, cold-ended at h0's frame;
+  other_hp:<e>   -> e's end moved to another helper_final frame of the dimension of e's own end frame.
+Original docstring: layer_end_controls.py LAYERED-WORD.json.gz ROUTING OUTDIR (env PR635_CODE): adapted PR635 cold_end_controls.py (LayerReviewer): raw-word negative controls for the cold low-frame ends and the
+refactored cleanup accepted by hpe_audit_and_transport.py.  Every mutation MUST be rejected (AssertionError); the
+unmutated word MUST pass.  Apache-2.0.  DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code."""
+import copy, gzip, hashlib, json, shutil, sys, tempfile
+from pathlib import Path
+import os
+sys.path.insert(0, os.environ['PR635_CODE'])   # PR635's unchanged hpe_audit_and_transport.py
+import hpe_audit_and_transport as atc
+
+src, routing, outdir = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3])
+word = json.load(gzip.open(src))
+v, R = word['report']['v'], word['report']['R']; n = 2*v + R
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+meta = word['refactored_cleanup']
+cold = [int(h) for h in meta['cold_low_frame_ended_helpers']]
+npre = meta['premix_gates']; nlow = meta['lower_frame_gates']
+early = word['early_cleanup']; eidx = {i for i, _ in early}
+rest = [i for i in range(len(word['cleanup'])) if i not in eidx]
+
+
+def trial(w):
+    """None if the transport audit accepts w, else the AssertionError message."""
+    tmp = Path(tempfile.mkdtemp())
+    p = tmp/'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w).encode(), mtime=0))
+    try:
+        atc.run(p, routing, tmp/'out')
+        return None
+    except AssertionError as e:
+        return repr(e.args[0]) if e.args else 'AssertionError'
+    finally:
+        shutil.rmtree(tmp, ignore_errors=True)
+
+
+# Pinned rejection reasons: each mutant must fail at this assertion of hpe_audit_and_transport.py (message substring).
+ENDPOINT, COLDPRE, CONE = "'arbitrary-dirt endpoint'", 'touches a cold hyperplane-ended helper', 'hpe cone pre-check (row / column)'
+WHY = dict(premix_to_precondition=COLDPRE, premix_dropped=COLDPRE, e_premix_dropped=ENDPOINT, lower_dropped=ENDPOINT,
+           remainder_dropped=ENDPOINT, coefficient=ENDPOINT, into_full='cleanup on non-FULL end', dyadic=ENDPOINT, frame_below="'nonmonotone'",
+           nonmonotone="'nonmonotone'", other_frame=CONE, cone=CONE, extra_end=COLDPRE, marker='cleanup is not the literal reversed inverse',
+           target='refactored cleanup touches a target', profile_pin='paid local profile differs from the reported local_profile',
+           entering_precondition='zero-frame precondition/compensation touches an entering helper')
+_REASONS = dict(ENDPOINT=ENDPOINT, COLDPRE=COLDPRE, CONE=CONE)
+NA_DECLARED = {}
+if os.environ.get('LEC_REASON_PINS'):
+    for _k, _v in json.loads(Path(os.environ['LEC_REASON_PINS']).read_text()).items():
+        if _k == 'not_applicable': NA_DECLARED = dict(_v); continue
+        assert _k in WHY, ('unknown mutant key', _k); WHY[_k] = _REASONS.get(_v, _v)
+assert trial(word) is None, 'unmutated cold-end word must pass'
+results = []
+
+
+def reject(name, mut, why):
+    """the mutation must be rejected, and for the pinned reason (a substring of the audit's assertion message)."""
+    w = copy.deepcopy(word); mut(w)
+    msg = trial(w)
+    assert msg is not None, 'cold-end mutation accepted: ' + name
+    assert why in msg, 'cold-end mutation %r rejected for the wrong reason: %s' % (name, msg[:300])
+    results.append(name); print('rejected', name, '|', why, flush=True)
+
+
+h0 = cold[0]
+i0, U0 = next((i, f) for i, f in early if h0 in regs(word['cleanup'][i]))
+r0 = rest[len(rest)//2]
+
+
+def premix_to_precondition(w):   # premix before the wrappers; compensation then reads the cold ends
+    w['precondition'] = w['precondition'] + w['A'][:npre]; w['A'] = w['A'][npre:]
+
+
+def lower_gate_into_full(w):     # a lower-frame gate on a cold-ended helper executed in the FULL remainder instead
+    w['early_cleanup'] = [x for x in w['early_cleanup'] if x[0] != i0]
+
+
+def drop_cleanup_gate(w, i):   # remove the gate AND its early_cleanup entry: a structurally valid word missing one gate
+    w['cleanup'].pop(i)
+    w['early_cleanup'] = [[j - (j > i), f] for j, f in w['early_cleanup'] if j != i]
+
+
+def other_frame(w):              # a different frame of the same dimension as the cold end (another cold helper's)
+    f = next(w['helper_final'][str(h)] for h in cold if w['helper_final'][str(h)] != w['helper_final'][str(h0)])
+    w['helper_final'][str(h0)] = f
+
+
+NA = []   # detected not-applicable sites: dict(site, reason, ...)
+wsha = lambda w: hashlib.sha256(json.dumps(w, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+HONEST_SHA = wsha(word)
+
+
+def extra_cold_end(w):           # declare a premixed partner of h0 cold-ended at h0's frame: fails the row/column cone
+    p = next(r for e in w['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    w['helper_final'][str(p)] = w['helper_final'][str(h0)]
+
+
+_m = copy.deepcopy(word); extra_cold_end(_m)
+if wsha(_m) == HONEST_SHA:   # identity: the first partner is already ended at h0's frame
+    _p = next(r for e in word['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    _q = next(r for e in word['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e) and str(r) not in word['helper_final'] and not v <= r < 2*v)
+    NA.append(dict(site='extra_end', reason='partner %d already cold-ended at h0 %d frame (identity)' % (_p, h0),
+                   honest_sha256=HONEST_SHA, mutated_sha256=wsha(_m), substitute='partner %d' % _q))
+
+    def extra_cold_end(w, q=_q): w['helper_final'][str(q)] = w['helper_final'][str(h0)]
+    assert wsha((lambda x: (extra_cold_end(x), x)[1])(copy.deepcopy(word))) != HONEST_SHA
+
+
+reject('premix placed in the zero-frame precondition (before the cold wrappers)', premix_to_precondition, WHY['premix_to_precondition'])
+reject('one premix gate dropped (the compensation then reads a cold-ended helper)', lambda w: w['A'].pop(npre - 1), WHY['premix_dropped'])
+reject('one lower-frame cleanup gate dropped (gate and its early_cleanup entry)', lambda w: drop_cleanup_gate(w, i0), WHY['lower_dropped'])
+reject('one FULL-remainder gate dropped', lambda w: drop_cleanup_gate(w, r0), WHY['remainder_dropped'])
+reject('lower-frame gate coefficient changed', lambda w: w['cleanup'][i0].__setitem__(3, w['cleanup'][i0][3] * 2), WHY['coefficient'])
+reject('lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)', lower_gate_into_full, WHY['into_full'])
+reject('lower-frame gate frame below its registers\' frames', lambda w: next(x for x in w['early_cleanup'] if x[0] == i0).__setitem__(1, U0[:-1]), WHY['frame_below'])
+reject('cold end at another dim-4 frame', other_frame, WHY['other_frame'])
+# PROFILE-PIN control: without its helper_final entry the cold-ended helper is a valid FULL-ended helper; the word is
+# rejected because its reported paid profile (which counts the low end) no longer matches the frame chains.
+reject('profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)', lambda w: w['helper_final'].pop(str(h0)), WHY['profile_pin'])
+reject('extra cold end on a premixed partner (the compensation reads it before its wrapper)', extra_cold_end, WHY['extra_end'])
+reject('refactored-cleanup marker removed (literal-inverse rule applies)', lambda w: w.pop('refactored_cleanup'), WHY['marker'])
+reject('remainder gate retargeted to a target register', lambda w: w['cleanup'][r0].__setitem__(1, v + 3), WHY['target'])
+reject('non-dyadic remainder coefficient', lambda w: w['cleanup'][r0].__setitem__(4 if w['cleanup'][r0][0] == 'add' else 3, 3 * w['cleanup'][r0][4 if w['cleanup'][r0][0] == 'add' else 3]), WHY['dyadic'])
+reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('5', w['report']['local_profile']['5'] - 1), WHY['profile_pin'])
+ent = [int(h) for h in sys.argv[4].split(',')] if len(sys.argv) > 4 else [int(h) for h in meta.get('entering_low_frame_ended_helpers', [])]
+for e0 in ent:   # ENTERING LOW-FRAME ENDS (ColdSupply extension; every entering end; absent for words without them)
+    j0 = next((i for i, e in enumerate(word['A'][:npre]) if e0 in regs(e)), None)
+    print('entering end', e0, 'premix gate', j0, flush=True)
+    k0, Ue = next((i, f) for i, f in early if e0 in regs(word['cleanup'][i]))
+    def to_pre(w, j0=j0): w['precondition'].append(w['A'][j0]); w['A'].pop(j0)
+    def other_hp(w, e0=e0, Ue=Ue): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Ue) and sorted(f) != sorted(Ue))
+    if not any(len(f) == len(Ue) and sorted(f) != sorted(Ue) for f in word['helper_final'].values()):   # unbuildable
+        Uh = word['helper_final'][str(e0)]
+        NA.append(dict(site='other_hp:%d' % e0, reason='tail frame dim %d; no other helper_final frame of that dim' % len(Ue),
+                       dims_available=sorted({len(f) for f in word['helper_final'].values()}), substitute='end-frame dim %d' % len(Uh)))
+
+        def other_hp(w, e0=e0, Uh=Uh): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Uh) and sorted(f) != sorted(Uh))
+    if j0 is not None: reject('entering end %d: premix gate dropped' % e0, lambda w, j0=j0: w['A'].pop(j0), WHY['e_premix_dropped'])
+    if j0 is not None: reject('entering end %d: premix gate at frame [] instead of its entrance E' % e0, lambda w, j0=j0: w['A'][j0].__setitem__(-1, []), WHY['nonmonotone'])
+    if j0 is not None: reject('entering end %d: premix gate moved into the zero-frame precondition' % e0, to_pre, WHY['entering_precondition'])
+    reject('entering end %d: lower-frame gate dropped (gate and its early_cleanup entry)' % e0, lambda w, k0=k0: drop_cleanup_gate(w, k0), WHY['lower_dropped'])
+    reject('entering end %d: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)' % e0, lambda w, e0=e0: w['helper_final'].pop(str(e0)), WHY['profile_pin'])
+    reject('entering end %d: end at another hyperplane' % e0, other_hp, WHY['cone'])
+# Pinned rejection reasons of the COLD-BEYOND mutants (substrings of hpe_audit_and_transport.py assertion messages).
+MYWHY = dict(tw_precondition=COLDPRE, tw_dropped=COLDPRE, tw_coefficient=COLDPRE, tw_other_block=COLDPRE,
+             tw_entering='zero-frame compensation reads an entering helper',
+             ab_dropped=ENDPOINT, ab_coefficient=ENDPOINT, ab_early=ENDPOINT, ab_live=ENDPOINT, ab_centre=ENDPOINT,
+             ab_lower="'nonmonotone'", ab_higher="'nonmonotone'",
+             sh_dropped=ENDPOINT, sh_coefficient=ENDPOINT, rel_dropped=ENDPOINT, rel_coefficient=ENDPOINT, rel_live=ENDPOINT,
+             h8_other=CONE, h8_lower=ENDPOINT)
+# COLD-BEYOND primitives (present only when the word carries them): frame-[] target writes in the premix (explicit
+# post-wrapper compensation of an ended helper's dirt) and forward absorptions into dead registers.
+nw = meta.get('premix_target_writes', 0)
+if nw:
+    wi = [i for i in range(npre) if v <= word['A'][i][1] < 2*v]
+    assert len(wi) == nw
+
+    def writes_to_precondition(w):   # the target writes run before the cold wrappers (inside the zero-frame precondition)
+        g = [w['A'][i] for i in wi]; w['precondition'] = w['precondition'] + g
+        w['A'] = [e for i, e in enumerate(w['A']) if i not in set(wi)]
+    reject('premix target writes placed in the zero-frame precondition (before the cold wrappers)', writes_to_precondition, MYWHY['tw_precondition'])
+    reject('one premix target write dropped (compensation must read an ended helper)', lambda w: w['A'].pop(wi[0]), MYWHY['tw_dropped'])
+    reject('premix target write coefficient changed', lambda w: w['A'][wi[0]].__setitem__(3, w['A'][wi[0]][3] * 2), MYWHY['tw_coefficient'])
+    # (reading another register that carries the SAME weight of the ended helper's dirt is a valid variant, so the mutant reads
+    #  the same factory slot of the next block, which carries none of it)
+    entering_regs = sorted(int(r) for r in word.get('start_extra', {}))
+    reject('premix target write reads an entering helper', lambda w: w['A'][wi[0]].__setitem__(2, entering_regs[0]), MYWHY['tw_entering'])
+    reject('premix target write reads a cold helper of another block', lambda w: w['A'][wi[0]].__setitem__(2, 2*v + (w['A'][wi[0]][2] - 2*v + 16) % 224), MYWHY['tw_other_block'])
+ab = meta.get('forward_absorption_A_indices', [])
+if any(len(word['helper_final'][str(h)]) == 8 for h in cold):
+    # with dim-8 cold ends, the centre-retargeted absorption first leaks an ended helper's dirt into the cut's targets
+    MYWHY['ab_centre'] = COLDPRE
+if ab:
+    # the ColdBeyond U_b absorption (q += -1/2 g); ColdThird's extra absorptions have their own controls below
+    a0 = next(a for a in ab if word['A'][a][3] * 2 == -word['A'][a][4]); g0 = word['A'][a0]
+
+    def absorption_moved_early(w):   # absorbed before the absorbed register's last kernel write
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[2] == w['A'][i][1] and w['A'][i][-1] == g0[-1])
+        w['A'].insert(j, e)
+
+    def absorption_into_live(w):     # q += a g moved right after g's previous frame-mate gate, while q is still live
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[1] in regs(w['A'][i]))
+        w['A'].insert(j, e)
+    reject('forward absorption dropped', lambda w: w['A'].pop(a0), MYWHY['ab_dropped'])
+    reject('forward absorption into a centre (a live register read by the cut)', lambda w: w['A'][a0].__setitem__(1, next(c for c in word['centers'] if c not in g0[1:3] and c not in cold)), MYWHY['ab_centre'])
+    reject('forward absorption coefficient changed', lambda w: w['A'][a0].__setitem__(3, w['A'][a0][3] * 2), MYWHY['ab_coefficient'])
+    reject('forward absorption placed before the absorbed register\'s last kernel write', absorption_moved_early, MYWHY['ab_early'])
+    reject('forward absorption placed while the absorbing register is still live', absorption_into_live, MYWHY['ab_live'])
+    reject('forward absorption at a lower frame than its registers', lambda w: w['A'][a0].__setitem__(-1, w['A'][a0][-1][:-1]), MYWHY['ab_lower'])
+    reject('forward absorption at a higher frame (FULL) than its registers', lambda w: w['A'][a0].__setitem__(-1, [256, 128, 64, 32, 16, 8, 4, 2, 1]), MYWHY['ab_higher'])
+# COLD-THIRD primitives (present only when the word carries them): several absorptions after one input gate, dirt-release
+# absorptions (a dead port takes a live helper's value so that a hyperplane unit's column has no dirt on it), and cold ends at
+# a dim-8 frame with lifted partners.
+hyper = [h for h in cold if len(word['helper_final'][str(h)]) == 8]
+if hyper and ab:
+    sh = next(a for a, b in zip(ab, ab[1:]) if b == a + 1)              # two absorptions sharing one input anchor
+    rel = next(a for a in ab if a - 1 not in ab and a + 1 not in ab and word['A'][a][2] in hyper and word['A'][a][3] * 2 != -word['A'][a][4])
+    hh = hyper[0]; ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+    reject('second absorption sharing an input anchor dropped', lambda w: w['A'].pop(sh + 1), MYWHY['sh_dropped'])
+    reject('shared-anchor absorption coefficient changed', lambda w: w['A'][sh + 1].__setitem__(3, w['A'][sh + 1][3] * 2), MYWHY['sh_coefficient'])
+    reject('dirt-release absorption dropped', lambda w: w['A'].pop(rel), MYWHY['rel_dropped'])
+    reject('dirt-release absorption coefficient changed', lambda w: w['A'][rel].__setitem__(3, w['A'][rel][3] * 2), MYWHY['rel_coefficient'])
+    jr = max(i for i in range(npre, rel) if word['A'][i][0] == 'add' and word['A'][i][2] == word['A'][rel][1])
+
+    def release_while_read(w):   # the release runs before a kernel gate that still READS the port (port live)
+        e = w['A'].pop(rel); w['A'].insert(jr, e)
+    reject('dirt-release absorption moved before a kernel gate that still reads the port', release_while_read, MYWHY['rel_live'])
+if hyper:
+    # dim-8 cold-end controls for EVERY dim-8 cold end of the word (read from the word's helper_final and the recipe meta's
+    # cold_low_frame_ended_helpers), not one representative per terminal frame
+    for hh in hyper:
+        ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+        Uh = word['helper_final'][str(hh)]
+        reject('dim-8 cold end %d (frame %s) at another dim-8 frame' % (hh, Uh), lambda w, hh=hh: w['helper_final'].__setitem__(str(hh), next(f for h, f in w['helper_final'].items() if len(f) == 8 and sorted(f) != sorted(w['helper_final'][str(hh)]))), MYWHY['h8_other'])
+        reject('dim-8 cold end %d (frame %s): one lower-frame gate dropped (gate and its early_cleanup entry)' % (hh, Uh), lambda w, ih=ih: drop_cleanup_gate(w, ih), MYWHY['h8_lower'])
+        reject('dim-8 cold end %d (frame %s): profile pin (end dropped)' % (hh, Uh), lambda w, hh=hh: w['helper_final'].pop(str(hh)), WHY['profile_pin'])
+# FACTORED ACCUMULATOR (CarrierBypass; present only when the word carries one): a lower-frame tail gate a += x*g on two
+# non-ended registers whose accumulator a is afterwards read by a dim-8 cold end's tail gate (h += y*a at its U).
+ended_all = {int(h) for h in word['helper_final']}
+tailg = [(i, word['cleanup'][i]) for i, _ in early]
+accs = []   # EVERY factored accumulator gate (one per accumulator register a), each controlled on its own
+for k, (i, e) in enumerate(tailg):
+    if e[0] == 'add' and e[1] not in ended_all and e[2] not in ended_all and len(next(f for j, f in early if j == i)) < 8:
+        if e[1] not in [word['cleanup'][j][1] for j in accs] and any(t[0] == 'add' and t[2] == e[1] and t[1] in hyper for _, t in tailg[k + 1:]):
+            accs.append(i)
+for acc in accs:
+    a = word['cleanup'][acc][1]
+    reject('factored accumulator %d (gate %d) zeroed' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, 0), ENDPOINT)
+    reject('factored accumulator %d (gate %d) coefficient doubled' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, w['cleanup'][acc][3] * 2), ENDPOINT)
+assert {x['site']: x['reason'] for x in NA} == NA_DECLARED, ('not-applicable sites differ from the pins file', NA, NA_DECLARED)
+outdir.mkdir(parents=True, exist_ok=True)
+(outdir/'COLD-END-CONTROLS.json').write_text(json.dumps(dict(status='PASS_COLD_END_RAW_WORD_CONTROLS', word=str(src), rejected=results, not_applicable=NA), indent=1) + '\n')
+print('PASS', len(results), 'cold-end raw-word mutations rejected')
diff --git a/research/gauge44-slots-t16/construction/leaver/reproduce_leaver.py b/research/gauge44-slots-t16/construction/leaver/reproduce_leaver.py
new file mode 100644
index 0000000000..bc4360ef93
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/reproduce_leaver.py
@@ -0,0 +1,177 @@
+#!/usr/bin/env python3
+"""Rebuild the leaver word: the no-triangle word with no-helper mutable-leaver all-K cells, and its native locals.
+
+Each cell (pair p, sign e) replaces the three face events of the blocks containing p and their three packet copies
+by a 21-gate circuit on the cell's six leaver sources x_j (the face-event operands, which have no later reads and are
+restored by the inherited cleanup at FULL) and its six targets y_i: 3 leaver gates x_k += c x_m, 3 target gates
+y_a += c y_b (inverted at frame zero in the precondition and scatter, #781's recipe) and 15 reads y_i += c x_j.
+Unit circuit (LeaverSAT, layered CP-SAT on the exact set model), relabelled per cell so that no y += y source carries
+port-stage entering-helper dirt at the gate; coefficients rescaled exactly to the cell (C_ij = r_i c_j).
+Input: a fresh `construction/reproduce.py --until word` output directory (hamming/, shadow-early/, shadow-prefix/).
+Steps, each checked exactly (pins in LEAVER-PINS.json):
+  0. cells: CODED-CELLS.json's scaled gates are re-derived from the unit circuits and the cell coefficients, and the
+     clean map Y_i = sum_j C_ij X_j is checked in exact rationals.
+  1. gauge-forward: cgx_leaver.py (notri/cgx.py + the leaver edits) with TRI-LEAVER.json, XPARAM = notri/PRIO6.json.
+  2. port0-3: notri/port_stage_x.py.
+  3. regroup: REGROUP-LEAVER.json's changes where their `before` gate occurs (count pinned).
+  4. hpe: PR635's build_hpe.candidates greedy with disjoint registers, build_hpe.apply (recipe pinned).
+  5. cold44: notri/cold44x.py with EXTRAH and pinned pairing ranks; output sha, profile and widths pinned.
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs (pins).
+Apache-2.0. LeaverSAT (Claude Code research agent), driver after construction/notri/reproduce_notri.py.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, shutil, subprocess, sys, time
+from fractions import Fraction
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NOTRI = HERE.parent / 'notri'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def dump(p, v):
+    p.parent.mkdir(parents=True, exist_ok=True); p.write_bytes(gzip.compress(enc(v), mtime=0))
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def check_cells(cells):
+    for c in cells:
+        C = [[Fraction(q) for q in r] for r in c['coefficients']]
+        col = [None] * 6; row = [Fraction(1)] + [None] * 5
+        for j in range(1, 6): col[j] = C[0][j]
+        col[0] = C[1][0] / (C[1][2] / col[2])
+        for i in range(1, 6): row[i] = C[i][(i + 1) % 6] / col[(i + 1) % 6]
+        assert all(C[i][j] == row[i] * col[j] for i in range(6) for j in range(6) if i != j), ('rank-one cell', c['cell'])
+        idx = lambda s: int(s[1:])
+        scaled = []
+        for t, s, q in c['unit']:
+            assert Fraction(q) == 1
+            if t[0] == 'x': assert s[0] == 'x'; q = col[idx(s)] / col[idx(t)]
+            elif s[0] == 'y': q = row[idx(t)] / row[idx(s)]
+            else: q = row[idx(t)] * col[idx(s)]
+            scaled.append([t, s, str(q)])
+        assert scaled == c['scaled'], ('scaled gates', c['cell'])
+        R = {f'x{j}': {j: Fraction(1)} for j in range(6)}; R.update({f'y{i}': {} for i in range(6)})
+        for t, s, q in scaled:
+            for k, x in list(R[s].items()): R[t][k] = R[t].get(k, 0) + Fraction(q) * x
+        for i in range(6):
+            assert {k: x for k, x in R[f'y{i}'].items() if x} == {j: C[i][j] for j in range(6) if j != i}, ('clean map', c['cell'], i)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--word-dir', type=Path, required=True, help='construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    ap.add_argument('--word-only', action='store_true', help='stop after the pinned scalar word (input to the layers)')
+    ap.add_argument('--id', default='k5', help='cell set: TRI-LEAVER-<id>, CODED-CELLS-<id>, REGROUP-LEAVER-<id>, LEAVER-PINS-<id>')
+    ap.add_argument('--record-pins', action='store_true', help='write LEAVER-PINS.json from this run instead of checking')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    pins = {} if a.record_pins else read(HERE / ('LEAVER-PINS-%s.json' % a.id)); got = {}
+    def pin(k, v):
+        got[k] = v
+        if not a.record_pins: assert pins[k] == v, ('pin', k, v, pins[k])
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    structural = a.main.resolve() / 'research/structural-gain/frontier-composition'
+    wd = a.word_dir.resolve()
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    # 0. cells
+    cells = read(HERE / ('CODED-CELLS-%s.json' % a.id)); check_cells(cells); print('PASS cells', [c['cell'] for c in cells], flush=True)
+    # 1. gauge-forward
+    shutil.copy(HERE / ('TRI-LEAVER-%s.json' % a.id), out / 'TRI.json'); shutil.copy(HERE / ('CODED-CELLS-%s.json' % a.id), out / 'CODED-CELLS.json')
+    env['XPARAM'] = str(NOTRI / 'PRIO6.json')
+    raw = out / 'raw'
+    run('gauge-forward', HERE / 'cgx_leaver.py', wd / 'hamming', raw, out / 'TRI.json')
+    word = raw / 'FULL-WORD.json.gz'; pin('raw_sha256', hashlib.sha256(enc(read(word))).hexdigest())
+    # 2. port stages
+    chain = [parent / 'complex-local/static44/inputs/RAW504.json.gz', structural / 'global-replay/base/split-centres/FULL-WORD.json.gz',
+             wd / 'shadow-early/FULL-WORD.json.gz', structural / 'multicold-eight-word/FULL-WORD.json.gz',
+             wd / 'shadow-prefix/FULL-WORD.json.gz']
+    for i, (b, c) in enumerate(zip(chain, chain[1:])):
+        t = out / ('port%d' % i)
+        run('port%d' % i, NOTRI / 'port_stage_x.py', '--shadow-input', b, '--shadow-output', c, '--input', word,
+            '--map', raw / 'HELPER-MAP.json', '--gk-dir', gk, '--out', t)
+        word = t / 'FULL-WORD.json.gz'
+    # 3. regroup
+    w = read(word); rg = {json.dumps(c['before']): c['after'] for c in read(HERE / ('REGROUP-LEAVER-%s.json' % a.id))['changes']}
+    n = 0
+    for part in ('A', 'B'):
+        for i, e in enumerate(w[part]):
+            k = json.dumps(e)
+            if k in rg: w[part][i] = rg[k]; n += 1
+    sys.path.insert(0, str(gk)); import gk_word as GW, gk_common as GC
+    GW.V = GC.V = 112; GW.DATA = GC.DATA = 7168
+    H = GW.profile(w)
+    w['report'].update(local_profile={str(k): z for k, z in sorted(H.items()) if z}, local_rank_mass=sum(r * z for r, z in H.items()))
+    pin('regroup_count', n); dump(out / 'regroup/FULL-WORD.json.gz', w); pin('regroup_sha256', hashlib.sha256(enc(w)).hexdigest())
+    # 4. HPE
+    h = load('upstream_hpe', up / 'code/build_hpe.py')
+    used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    (out / 'HPE-RECIPE.json').write_text(json.dumps(dict(changes=ch)))
+    pin('hpe_recipe_sha256', hashlib.sha256(enc(dict(changes=ch))).hexdigest())
+    w = h.apply(w, ch); dump(out / 'hpe/FULL-WORD.json.gz', w)
+    # 5. cold44
+    hm = set(read(raw / 'HELPER-MAP.json')['map'].values())
+    env['EXTRAH'] = json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm))
+    if not a.record_pins: env['PAIRING_RANKS'] = json.dumps(pins['pairing_ranks'])
+    run('cold44', NOTRI / 'cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', wd / 'hamming', '--upstream-package', up)
+    pin('pairing_ranks', [b['pairing_rank'] for b in read(out / 'cold44/CONSTRUCTION.json')['blocks']])
+    word = out / 'cold44/FULL-WORD.json.gz'; w = read(word)
+    pin('cold44_sha256', hashlib.sha256(enc(w)).hexdigest()); rep = w['report']
+    pin('R', rep['R']); pin('local_profile', rep['local_profile']); pin('width_inventory', rep['width_inventory'])
+    print('PASS leaver scalar word', got['cold44_sha256'], flush=True)
+    if not a.word_only:
+        for k in ('XPARAM', 'EXTRAH', 'PAIRING_RANKS'): env.pop(k, None)
+        local = out / 'local'
+        run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word,
+            '--routing', parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz', '--out', local)
+        pin('canonical_sha256', hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest())
+        run('ledgers', up / 'code/hpe_emit_local.py', local)
+        run('local-replay', up / 'code/hpe_audit_local.py', local)
+        run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+            local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+        checks = read(local / 'LOCAL-CHECKS.json')
+        pin('program_sha256', {o: checks[o]['sha256'] for o in ('forward', 'backward')})
+        if not a.skip_phases:
+            run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+            pin('clifford_recipes_sha256', hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest())
+    if a.record_pins: (HERE / ('LEAVER-PINS-%s.json' % a.id)).write_text(json.dumps(got, indent=1) + '\n')
+    print('DONE', out, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/leaver/reproduce_leaver_chain.py b/research/gauge44-slots-t16/construction/leaver/reproduce_leaver_chain.py
new file mode 100644
index 0000000000..19fcd28f4d
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/leaver/reproduce_leaver_chain.py
@@ -0,0 +1,187 @@
+#!/usr/bin/env python3
+"""Rebuild the leaver stack on top of the leaver cell word: layers (NP, p6n), promotions, joint exchange and U8-style
+hybrids, and the final word's native locals.
+
+Input: a fresh `construction/leaver/reproduce_leaver.py --word-only` output directory (raw/HELPER-MAP.json, regroup/,
+cold44/; the cell word and its regroup word are pinned there by LEAVER-PINS.json). Each step uses an unchanged signed
+builder with a LeaverSAT recipe (data only), and every intermediate word is pinned:
+  1. pivot-swap: ../layers/build_pivot_swap.py with PIVOT-SWAP-<id>.json on the regroup word (its own 30 controls).
+  2. hpe: PR635's build_hpe.candidates (greedy, disjoint registers) must equal HPE-RECIPE-<id>.json; build_hpe.apply.
+     The swapped HPE word is pinned by the cold-layer recipes' input_content_sha256.
+  3. cold44-exact: ../notri/cold44x.py on the swapped HPE word (pairing ranks pinned to LEAVER-PINS); its cold ends,
+     premix and low tails must equal the unswapped leaver construction's.
+  4. layers: PR635's build_cold_end.apply(HPE, COLD-LAYERS-RECIPE-NP-<id>) -> NP word and (.., -P6N-<id>) -> p6n word;
+     output shas pinned by the recipes.
+  5. promotion: ../promo/build_promotion.py with PROMO-RECIPE-<id>.json on the p6n word; ../promo/promo_controls.py.
+  6. jx: ../jx/build_jx.py with RECIPE-X4-<id>.json on the promoted word; all recipe controls rerun at their pins.
+  7. hybrids: ../barch/build_tri.py with RECIPE-U8-<id>.json on the jx word; ../barch/run_controls.py (all outcomes).
+  8. frames: build_frames_lv.py (LeaverSAT2) applies FRAME-RECIPE-LV-<id>.json (B/T frame changes, exact global frame
+     optimum) with ../promo/build_promotion.apply; scalar program unchanged; 3 pin controls; output pinned.
+  8b. layer-end-controls: layer_end_controls_leaver.py (v2: the signed per-end controls with per-word reason re-pins
+     and declared not-applicable sites, each replaced by a same-class substitute mutant) on the p6n, promoted, jx and
+     hybrid words with LEC-REASON-PINS-STACK-<id>.json, and on the re-framed final word with LEC-REASON-PINS-<id>.json;
+     counts, not-applicable sites and the sha256 of each pins file pinned.
+  9. native, ledgers, local-replay, wrappers, phases on the final word; canonical, programs, Clifford pinned.
+All counts and native pins are in CHAIN-PINS-<id>.json (--record-pins writes it from a run instead of checking;
+a checking run requires its pins to equal the file exactly).
+Apache-2.0. Driver by ColdWitness over LeaverSAT's frozen recipes and the signed builders.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+C = HERE.parent
+MUTANTS = ('drop_restore', 'restore_full', 'drop_preread', 'donation_after')
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def csha(p): return hashlib.sha256(gzip.decompress(Path(p).read_bytes())).hexdigest()
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--leaver-dir', type=Path, required=True, help='construction/leaver/reproduce_leaver.py --word-only output')
+    ap.add_argument('--hamming', type=Path, required=True, help='hamming/ of the construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    ap.add_argument('--id', default='k5', help='recipe set id: every recipe and pin file below is <NAME>-<id>')
+    ap.add_argument('--record-pins', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    lp = read(HERE / ('LEAVER-PINS-%s.json' % a.id))
+    pins = {} if a.record_pins else read(HERE / ('CHAIN-PINS-%s.json' % a.id)); got = {}
+
+    def pin(key, value):
+        got[key] = value
+        if not a.record_pins: assert pins[key] == value, (key, value, pins.get(key))
+
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE', 'LEC_REASON_PINS', 'SW4_PIN'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True, extra=None):
+        t = time.monotonic(); e = dict(env, **(extra or {}))
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=e, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+        return (out / (label + '.log')).read_text()
+
+    def lec(label, word, pins_name):
+        pf = HERE / ('%s-%s.json' % (pins_name, a.id)); pin(label + '_pins_sha256', hashlib.sha256(pf.read_bytes()).hexdigest())
+        run(label, HERE / 'layer_end_controls_leaver.py', word, routing, out / label,
+            extra=dict(PR635_CODE=str(up / 'code'), LEC_REASON_PINS=str(pf)))
+        c = read(out / label / 'COLD-END-CONTROLS.json'); assert c['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS'
+        pin(label, len(c['rejected'])); pin(label + '_not_applicable', {x['site']: x['reason'] for x in c['not_applicable']})
+
+    ld = a.leaver_dir.resolve()
+    assert hashlib.sha256(enc(read(ld / 'cold44/FULL-WORD.json.gz'))).hexdigest() == lp['cold44_sha256'], 'leaver cell word'
+    rg = ld / 'regroup/FULL-WORD.json.gz'
+    sw = read(HERE / ('PIVOT-SWAP-%s.json' % a.id))
+    assert hashlib.sha256(enc(read(rg))).hexdigest() == lp['regroup_sha256'] == sw['input_content_sha256'], 'regroup word'
+    # 1. pivot swaps
+    run('pivot-swap', C / 'layers/build_pivot_swap.py', '--input', rg, '--recipe', HERE / ('PIVOT-SWAP-%s.json' % a.id), '--gk-dir', gk, '--out', out / 'swap')
+    w = read(out / 'swap/FULL-WORD.json.gz'); assert hashlib.sha256(enc(w)).hexdigest() == sw['output_content_sha256'], 'swap word'
+    # 2. HPE
+    h = load('upstream_hpe', up / 'code/build_hpe.py'); used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    assert ch == read(HERE / ('HPE-RECIPE-%s.json' % a.id))['changes'], 'HPE recipe'
+    w = h.apply(w, ch); (out / 'hpe').mkdir(); (out / 'hpe/FULL-WORD.json.gz').write_bytes(gzip.compress(enc(w), mtime=0))
+    rnp, rp6 = read(HERE / ('COLD-LAYERS-RECIPE-NP-%s.json.gz' % a.id)), read(HERE / ('COLD-LAYERS-RECIPE-P6N-%s.json.gz' % a.id))
+    assert hashlib.sha256(enc(w)).hexdigest() == rnp['input_content_sha256'] == rp6['input_content_sha256'], 'swapped HPE word'
+    # 3. cold44 on the swapped word: same ends, premix and tails
+    hm = set(read(ld / 'raw/HELPER-MAP.json')['map'].values())
+    run('cold44-exact', C / 'notri/cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', a.hamming.resolve(), '--upstream-package', up,
+        extra=dict(EXTRAH=json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm)), PAIRING_RANKS=json.dumps(lp['pairing_ranks'])))
+    new, old = read(out / 'cold44/RECIPE.json.gz'), read(ld / 'cold44/RECIPE.json.gz')
+    for key in ('premix', 'early_cleanup', 'cold_ends'): assert new[key] == old[key], ('swapped cold44 differs', key)
+    tail = len(new['early_cleanup']); assert new['cleanup'][:tail] == old['cleanup'][:tail], 'low tails'
+    # 4. NP and p6n layers
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    for name, r in (('np', rnp), ('p6n', rp6)):
+        lw = bce.apply(w, r); raw = enc(lw); assert hashlib.sha256(raw).hexdigest() == r['output_content_sha256'], (name, 'word')
+        (out / name).mkdir(); (out / name / 'FULL-WORD.json.gz').write_bytes(gzip.compress(raw, mtime=0))
+        pin(name + '_profile', lw['report']['local_profile'])
+    p6n = out / 'p6n/FULL-WORD.json.gz'; lec('lec-p6n', p6n, 'LEC-REASON-PINS-STACK')
+    # 5. promotion
+    pr = HERE / ('PROMO-RECIPE-%s.json' % a.id)
+    run('promotion', C / 'promo/build_promotion.py', '--input', p6n, '--recipe', pr, '--out', out / 'promo', portable=False)
+    assert csha(out / 'promo/FULL-WORD.json.gz') == read(pr)['expected']['output_content_sha256']
+    run('promo-controls', C / 'promo/promo_controls.py', '--input', p6n, '--recipe', pr, '--audit', C.parent / 'independent/audit_local.py',
+        '--out', out / 'PROMO-CONTROLS.json', portable=False)
+    pc = read(out / 'PROMO-CONTROLS.json'); assert pc['honest'] == 'PASS'; pin('promo_controls', pc['rejected'])
+    lec('lec-promo', out / 'promo/FULL-WORD.json.gz', 'LEC-REASON-PINS-STACK')
+    # 6. jx
+    xr = HERE / ('RECIPE-X4-%s.json' % a.id); rec = read(xr); inp = out / 'promo/FULL-WORD.json.gz'
+    (out / 'jx').mkdir(); jw = out / 'jx/FULL-WORD.json.gz'
+    run('jx', C / 'jx/build_jx.py', '--input', inp, '--recipe', xr, '--out', jw, portable=False)
+    assert csha(jw) == rec['expected']['output_content_sha256']
+    for name, cc in sorted(rec['controls'].items()):
+        log = run('jx-control-' + name, C / 'jx/build_jx.py', '--input', inp, '--recipe', xr, '--control', name, portable=False)
+        if 'rejection_expected' in cc: assert 'CONTROL PINNED' in log, (name, log[-300:])
+        else: assert ('OK ' + cc['expected_sha']) in log, (name, log[-300:])
+    pin('jx_controls', sorted(rec['controls']))
+    lec('lec-jx', jw, 'LEC-REASON-PINS-STACK')
+    # 7. hybrids
+    ur = HERE / ('RECIPE-U8-%s.json' % a.id); u = read(ur); (out / 'hyb').mkdir(); fw = out / 'hyb/FULL-WORD.json.gz'
+    run('hybrids', C / 'barch/build_tri.py', jw, ur, fw, portable=False)
+    assert csha(fw) == u['expect_sha256']
+    run('hybrid-controls', C / 'barch/run_controls.py', jw, ur, C.parent / 'independent/audit_local.py', out / 'hybrid-controls', portable=False)
+    res = read(out / 'hybrid-controls/controls.json')
+    want = ['C0_identity', 'recipe', *MUTANTS] + [m + '@' + str(v['X']) for v in u.get('variants', []) for m in MUTANTS]
+    assert sorted(res) == sorted(want) and all(x['ok'] for x in res.values()), res
+    pin('hybrid_controls', sorted(want))
+    lec('lec-hyb', fw, 'LEC-REASON-PINS-STACK')
+    # 8. frame re-optimisation (LeaverSAT2): exact global frame optimum of the hybrid word; scalar program unchanged
+    fr = HERE / ('FRAME-RECIPE-LV-%s.json' % a.id); frec = read(fr)
+    run('frames', HERE / 'build_frames_lv.py', fw, out / 'frames', fr, portable=False)
+    fw = out / 'frames/FULL-WORD.json.gz'; assert csha(fw) == frec['expected']['output_content_sha256']
+    pin('frame_build_controls', len(read(out / 'frames/BUILD.json')['rejected_controls']))
+    # 8b. layer-end controls on the re-framed final word (v2, not-applicable sites declared in LEC-REASON-PINS-<id>):
+    # the frame re-optimisation lowers an entering-end tail frame to a dimension no helper_final frame has, so that
+    # site's 'end at another hyperplane' mutant is replaced by its same-class substitute.
+    lec('lec-frames', fw, 'LEC-REASON-PINS')
+    # 9. native locals of the final word
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', fw, '--routing', routing, '--out', local)
+    pin('canonical_sha256', hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest())
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz', local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json'); pin('program_sha256', {o: checks[o]['sha256'] for o in ('forward', 'backward')})
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        pin('clifford_recipes_sha256', hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest())
+    if a.record_pins: (out / ('CHAIN-PINS-%s.json' % a.id)).write_bytes((json.dumps(got, indent=1) + '\n').encode())
+    else: assert got == pins, ('chain pins differ', sorted(set(got) ^ set(pins)))
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/notri/PRIO6.json b/research/gauge44-slots-t16/construction/notri/PRIO6.json
new file mode 100644
index 0000000000..069a7bf5a5
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/notri/PRIO6.json
@@ -0,0 +1 @@
+{"prio": {"0,1,2,3": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "0,1,4,5": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "0,1,6,7": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "2,3,4,5": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "2,3,6,7": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "4,5,6,7": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]]}}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/notri/cgx.py b/research/gauge44-slots-t16/construction/notri/cgx.py
new file mode 100644
index 0000000000..08e80804eb
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/notri/cgx.py
@@ -0,0 +1,469 @@
+# Round20 early-coordinate-center / own-Y variant, prepared for icekylinx
+# with OpenAI Codex assistance. Apache-2.0. Scalar elementary-operation
+# helpers below are retained from the attributed PR514 construct_partial.py.
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+# AtomScout: leaver-read K-triangles (schedule from atom1.py / rog.py CP-SAT)
+TRI=json.loads(Path(sys.argv[3]).read_text())
+FULLT={(tuple(tr['p']),tr['e']) for tr in TRI['triangles']}
+TRI_COORDS={t+8 for tr in TRI['triangles'] for t,_,_ in tr['reads']}
+import os as _o
+COPYL=json.loads(open(_o.environ['XPARAM']).read()).get('copyl',[]) if _o.environ.get('XPARAM') else []
+NH=504-3*len(FULLT)+len(COPYL)
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+# Helper ids of the unpatched 504 construction: every allocation advances the 504 numbering; a packet copy that the
+# K-triangle schedule never forms advances it without allocating (HELPER-MAP.json).
+shadow=[];skipped=[];nxt=[2*v]
+def alloc():
+    n=len(cur);cur.append(());rows.append({});shadow.append(nxt[0]);nxt[0]+=1;return n
+def skip():
+    skipped.append(nxt[0]);nxt[0]+=1
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# Each source quartet supplies pair partials first. The other two coordinate
+# partitions supply eight early face packets without touching the eight
+# partials later copied into the preconditioned Y coordinates.
+SELECT=(0,0)
+PRIORITY=json.loads((INPUT/"COMPLETION-PRIORITY.json").read_text())
+import os
+XP=json.loads(open(os.environ['XPARAM']).read()) if os.environ.get('XPARAM') else {}
+XCH=XP.get('exch',{});PRIO=XP.get('prio',{})
+maps={};early={};own_rows={};pairs=[];tetrads={};block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)});maps[c]=mp
+    for ei,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[:40]):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        if ei==15:
+            for jj,cl in XCH.get(str(len(maps)-1),[[4,17],[5,19],[6,21],[7,23]]):swap(mp[jj],mp[cl],(P[ids[jj]],))
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in targets:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                t,u=sorted(ts);e2=R[t][q[0]]*R[t][q[1]]
+                pair={'targets':(t,u),'keys':[(c,p,eps),(c,q,e2)],'selected':pi==SELECT[parity],
+                      'matrix':[[R[a][p[0]],R[a][q[0]]] for a in (t,u)]}
+                pairs.append(pair)
+                if not pair['selected']:continue
+                zz=-Q(2*R[u][p[0]],R[t][p[0]])
+                sources=tet[1-parity]
+                for target,sign in ((t,-1),(u,1)):
+                    wanted={s:-Q(G[t][s],4)-sign*Q(G[u][s],2)/zz for s in sources
+                            if -Q(G[t][s],4)-sign*Q(G[u][s],2)/zz}
+                    assert len(wanted)==2
+                    candidates=[]
+                    for r in mp.values():
+                        if set(rows[r])!=set(wanted):continue
+                        s=next(iter(wanted));coef=wanted[s]/rows[r][s]
+                        if all(wanted[s]==coef*rows[r][s] for s in wanted):candidates.append((r,coef))
+                    assert len(candidates)==1
+                    r,coef=candidates[0];assert len(cur[r])==2
+                    own_rows[target]=(r,coef,cur[r])
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    needed={own_rows[t][0] for t in ids}
+    early[c]={j for j,e in enumerate(z['events'][40:]) if not ({mp[e[0]],mp[e[1]]}&needed)}
+    assert len(early[c])==8
+    retired=[]
+    for j in sorted(early[c]):
+        (t,s,a,b),F=z['events'][40+j],z['event_frames'][40+j]
+        add(mp[t],mp[s],Q(a,b),tuple(F));retired.append(mp[s])
+    assert not set(retired)&needed
+    # These eight retired rows already span every source coordinate. Keep
+    # them invertible and place the four coordinate totals in a changed basis.
+    F=basis([P[s] for s in ids]);assert len(F)==4
+    regs=sorted(retired,key=lambda r:(r>=v,r))
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    M=[[Q(R[s][i]) for s in ids] for i in c]
+    def qr_rank(rs):
+        bs={}
+        for r in rs:
+            r=r.copy()
+            for i,b in sorted(bs.items()):
+                if r[i]:q=r[i];r=[x-q*y for x,y in zip(r,b)]
+            i=next((i for i,x in enumerate(r) if x),None)
+            if i is not None:q=r[i];bs[i]=[x/q for x in r]
+        return len(bs)
+    assert qr_rank(M)==4
+    for rr0 in PRIO.get(",".join(map(str,c)),[])+PRIORITY[",".join(map(str,c))]["rows"]:
+        rr=list(map(Q,rr0))
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    for i in range(8):
+        if len(M)==8:break
+        rr=[Q(i==j) for j in range(8)]
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    assert len(M)==8
+    linear(regs,M,F)
+    for i,r in zip(c,regs):
+        assert rows[r]=={s:Q(R[s][i]) for s in ids}
+        block_totals[c,i]=r
+
+# All centers are complete while Y is still at zero. This is the crucial
+# difference from an illegal early-own-Y prefix using the old center order.
+centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+assert all(cur[v+t]==() for t in range(v))
+
+phase=B
+for t,(r,coef,F) in sorted(own_rows.items()):
+    if t in TRI_COORDS:continue
+    assert cur[r]==F
+    add(v+t,r,coef,F)
+# requests are needed for TRI coefficients
+requests=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    requests[key1].append((t,-Q(mat[0][0],2)))
+    requests[key2].append((u,-Q(mat[0][1],2)))
+reqcoef={t:(key,coef) for key,reqs in requests.items() for t,coef in reqs}
+def face_info(c,p,eps):
+    z=blocks[c];keys=[(pp,ee) for pp in it.combinations(c,2) for ee in (-1,1)]
+    r_local,alpha=z['outputs'][keys.index((p,eps))]
+    j=[j for j in range(40,len(z['events'])) if z['events'][j][0]==r_local];assert len(j)==1
+    return j[0],Q(alpha)
+tri_join_counts=Counter();TRILOG=[]
+lcopy={}
+for s8 in COPYL:
+    r=s8+8;c=len(cur);cur.append(());rows.append({});shadow.append(None);add(c,r,1,cur[r]);lcopy[r]=c
+BF={c:basis([P[x] for x in z['receipt']['source_lines']]) for c,z in blocks.items()}
+HYB={(tuple(map(int,h[0])),tuple(map(int,h[1])),int(h[2])) for h in XP.get('hyb',[])}
+HYBLOG=[]
+def triread(t,blk,r,q):
+    F=basis(cur[v+t]+cur[r]);assert inside(F,hyper(P[t])),('TRI frame',t,blk,r,cur[v+t],cur[r],hyper(P[t]),[x for x in TRILOG if x[2]==r],HYBLOG)
+    tri_join_counts[len(F)]+=1;add(v+t,r,q,F);TRILOG.append([t,list(blk),r,str(q),list(F),list(cur[r])])
+for tr in TRI['triangles']:
+    p,eps=tuple(tr['p']),tr['e']
+    hb={blk for _,blk,_ in map(lambda x:(x[0],tuple(x[1]),x[2]),tr['reads']) if (blk,p,eps) in HYB}
+    own=[];rest=[]
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];r0=r;r=lcopy.get(r,r)
+        key,coef=reqcoef[t];assert key[1]==p and key[2]==eps,(key,p,eps)
+        if blk==key[0]:
+            rr,c0,F0=own_rows[t];assert rr==r0;own.append((t,blk,r,c0))
+        else:
+            j,alpha=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert loc in ev[:2]
+            rest.append((t,blk,loc,r,coef*alpha))
+    if not hb:
+        # original interleaved order
+        for t8,blk,loc in tr['reads']:
+            t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+            if blk==key[0]:q=own_rows[t][1]
+            else:j,alpha=face_info(blk,p,eps);q=coef*alpha
+            triread(t,blk,r,q)
+        continue
+    items=[]  # (kind, t, reg, q, blk)
+    for t,blk,r,q in own:items.append(('r',t,r,q,blk,blk in hb))
+    for blk in sorted(hb):items.append(('e',None,None,None,blk,True))
+    done=set()
+    for t,blk,loc,r,q in rest:
+        if blk in hb:
+            j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j]
+            ws=[x for x in rest if x[0]==t and x[1]==blk];assert len(ws)==2 and ws[0][4]==ws[1][4] and {ws[0][2],ws[1][2]}==set(ev[:2])
+            if (t,blk) in done:continue
+            done.add((t,blk));items.append(('m',t,maps[blk][ev[0]],q,blk,True))
+        else:items.append(('r',t,r,q,blk,False))
+    # Original read order with the two half reads collapsed into one M read at the first half's slot; the face event goes
+    # just before the first M read of its block; own reads of the M register are hoisted ahead of that event.
+    def evinfo(blk):
+        j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert ev[2]==ev[3]==1,ev
+        mpb=maps[blk];return mpb[ev[0]],mpb[ev[1]],tuple(blocks[blk]['event_frames'][j])
+    items=[]
+    seen=set()
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+        if blk==key[0]:items.append(('r',t,r,own_rows[t][1],blk,blk in hb))
+        else:
+            j,alpha=face_info(blk,p,eps);q=coef*alpha
+            if blk in hb:
+                if (t,blk) not in seen:seen.add((t,blk));continue
+                items.append(('m',t,evinfo(blk)[0],q,blk,True))
+            else:items.append(('r',t,r,q,blk,False))
+    for blk in sorted(hb):
+        k0=min(i for i,x in enumerate(items) if x[0]=='m' and x[4]==blk)
+        items.insert(k0,('e',None,None,None,blk,True))
+    n=len(items)
+    def step(it,st):
+        k,t,r,q,blk,h=it;g=lambda x:st.get(x,cur[x])
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(g(a_))+list(g(b_)))
+            return {a_:FF,b_:FF} if inside(FF,BF[blk]) else None
+        F=basis(list(g(v+t))+list(g(r)))
+        if not inside(F,hyper(P[t])):return None
+        if h and k=='r' and r==evinfo(blk)[1] and not inside(F,BF[blk]):return None
+        return {v+t:F,r:F}
+    def allowed(i,used):
+        k,t,r,q,blk,h=items[i]
+        evi=[j for j,x in enumerate(items) if x[0]=='e' and x[4]==blk] if h else []
+        if k=='e':return all(j in used for j,x in enumerate(items) if x[0]=='r' and x[4]==blk and x[5] and x[2]==evinfo(blk)[0])
+        if k=='m':return evi[0] in used
+        if k=='r' and h and r==evinfo(blk)[0]:return evi[0] not in used
+        return True
+    budget=[int(os.environ.get('HYBBUDGET','300000'))];memo=set()
+    def dfs(st,used,order):
+        if len(order)==n:return order
+        budget[0]-=1
+        if budget[0]<0:return None
+        sig=(used,tuple(sorted(st.items())))
+        if sig in memo:return None
+        memo.add(sig)
+        for i in range(n):
+            if i in used or not allowed(i,used):continue
+            d=step(items[i],st)
+            if d is None:continue
+            ns=dict(st);ns.update(d);res=dfs(ns,used|{i},order+[i])
+            if res:return res
+        return None
+    import sys as _s;_s.setrecursionlimit(20000)
+    order=dfs({},frozenset(),[])
+    assert order,('no feasible hybrid order',p,eps,sorted(hb),budget)
+    for i in order:
+        k,t,r,q,blk,h=items[i]
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(cur[a_])+list(cur[b_]));add(a_,b_,1,FF);HYBLOG.append([list(blk),list(p),eps,list(FF)])
+        else:triread(t,blk,r,q)
+
+packets={}
+for c,z in sorted(blocks.items()):
+    mp=maps[c]
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    skipev={face_info(c,p,eps)[0] for p,eps in keys if (p,eps) in FULLT}
+    for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]):
+        if j not in early[c] and 40+j not in skipev:
+            t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    for key,(r,alpha) in zip(keys,z['outputs']):
+        if tuple(key) in FULLT:skip();continue
+        a=mp[r];b=alloc();add(b,a,1,cur[a])
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha))
+
+# Both tetrahedra use the same partition. A selected key has exactly two
+# selected Y loads and no ordinary M consumer. Supply its two raw halves in
+# opposite orders and never form that M. Other keys retain the old M path.
+second=[];first_join_counts=Counter()
+for key,reqs in sorted(requests.items()):
+    assert len(reqs)==2
+    c,p,eps=key
+    if (p,eps) in FULLT:continue
+    ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds
+    for j,(target,coef) in enumerate(sorted(reqs)):
+        first_source,second_source=(a,b) if j==0 else (b,a)
+        r,alpha=packets[first_source,p,eps,second_source]
+        F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+        first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F)
+        r,alpha=packets[second_source,p,eps,c]
+        second.append((target,r,coef*alpha))
+
+Ms={}
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for eps in (-1,1):
+            if (c,p,eps) in requests:continue
+            (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,eps]=(a,alpha)
+
+consumers=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    for key in pair['keys']:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    if key in requests:
+        assert all(pairs[i]['selected'] for i in uses)
+        continue
+    assert all(not pairs[i]['selected'] for i in uses)
+    a,alpha=Ms[key]
+    for j,pid in enumerate(uses):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+assert len(cur)-240==NH,len(cur)-240
+
+selected_join_counts=Counter()
+for target,r,coef in second:
+    F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+    selected_join_counts[len(F)]+=1;add(v+target,r,coef,F)
+output_basis=[]
+for pair in pairs:
+    if not pair['selected']:continue
+    (t,u),mat=pair['targets'],pair['matrix']
+    F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u]))
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert rows[v+t]==expected,('side identity',t)
+
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8
+assert sum(r*z for r,z in H.items())==9*NH+240*8+72,sum(r*z for r,z in H.items())
+
+def apply(e,matrix):
+    if e[0]=='add':
+        _,t,s,a,b,*_=e;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    e[-1]=list(FULL);return e
+cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q]
+cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v]
+matrix=[{r:Q(1)} if r<v else {} for r in range(len(cur))]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(len(cur)))
+
+# Restrict the eight isolated axis ports exactly, keeping the stable 112-port
+# label set. This variant changes the local word, not the outer geometry.
+mp={s:s-8 for s in range(8,120)}
+mp.update({120+s:112+s-8 for s in range(8,120)})
+mp.update({240+r:224+r for r in range(NH)})
+def restrict(events,is_cut=False):
+    out=[]
+    for e in events:
+        regs=e[1:3] if e[0]=='add' else e[1:2]
+        if any(r not in mp for r in regs):
+            assert is_cut and e[0]=='add' and e[1]-120==e[2] and e[2]<8 and e[3:5]==[1,1]
+            continue
+        q=copy.deepcopy(e);q[1]=mp[q[1]]
+        if q[0]=='add':q[2]=mp[q[2]]
+        out.append(q)
+    return out
+H.subtract({1:8,8:16});H=+H
+report={'status':'EXACT_CLEAN_OWN_Y_EARLY_CENTER_WORD_NOT_ADMITTED',
+        'h':9,'v':112,'R':NH,'cst':64,'m':73,'local_profile':dict(sorted(H.items())),
+        'centre_ranks':[8]*8,**({'tri_join_counts':dict(tri_join_counts)} if TRI['triangles'] else {}),'selected_load_join_counts':dict(selected_join_counts),'selected_partitions':list(SELECT),'first_load_join_counts':dict(first_join_counts),
+        'source_columns_exact':112,'borrowed_output_pairs':56,'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'local_rank_mass':sum(r*n for r,n in H.items()),'scope':'Clean scalar identity and all literal monotone local frames only; arbitrary-dirt compensation, entrance kernels, exact phase recipes, and global hosting/pricing are not yet certified.'}
+word={'report':report,'ports':P[8:],'root_lines':R[8:],
+      'A':restrict(A),'B':restrict(B),'cut':restrict(cut,True),'cleanup':restrict(cleanup),'precondition':restrict(precondition),
+      'centers':[mp[r] for r in centers[:8]],'center_frames':center_frames[:8],
+      'scatter':[[str(x) for x in row[:8]] for row in scatter[8:]]}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+assert len(shadow)==NH and len([x for x in shadow if x is not None])+len(skipped)==504
+hmap={**{r:r for r in range(224)},**{224+s_-240:224+i for i,s_ in enumerate(shadow) if s_ is not None}}
+(OUT/'HELPER-MAP.json').write_text(json.dumps({'map':{str(k):hmap[k] for k in sorted(hmap)},'removed_504_helpers':[224+s_-240 for s_ in skipped]})+'\n')
+(OUT/'TRILOG.json').write_text(json.dumps(dict(reads=TRILOG,hyb=HYBLOG)));(OUT/'DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/gauge44-slots-t16/construction/notri/cold44x.py b/research/gauge44-slots-t16/construction/notri/cold44x.py
new file mode 100644
index 0000000000..8fa6f3a6a6
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/notri/cold44x.py
@@ -0,0 +1,217 @@
+"""Exact dyadic cold-end realization of the source-branch/factory-completion word.
+Prepared for icekylinx with OpenAI Codex assistance; Apache-2.0.
+This is a constructor: independent endpoint/frame audits remain required.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+import copy,gzip,json,hashlib,time,sys,argparse,importlib.util,os
+D=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser(description=__doc__)
+for name in ('input','out','hamming','upstream-package'):ap.add_argument('--'+name,type=Path,required=True)
+args=ap.parse_args();WPATH=args.input;OUT=args.out
+assert __debug__, 'Assertions are required'
+OUT.mkdir(exist_ok=False,parents=True)
+def rd(p):return json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+w=rd(WPATH);v=w['report']['v'];n=2*v+w['report']['R'];N=list(range(v))+list(range(2*v,n));ix={x:i for i,x in enumerate(N)}
+F9=[256,128,64,32,16,8,4,2,1];t0=time.monotonic()
+def basis(vs):
+ d={}
+ for a in vs:
+  for k in sorted(d,reverse=True):
+   if a>>k&1:a^=d[k]
+  if a:
+   k=a.bit_length()-1
+   for j in d:
+    if d[j]>>k&1:d[j]^=a
+   d[k]=a
+ return tuple(d[k] for k in sorted(d,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def regs(e):return e[1:3] if e[0]=='add' else e[1:2]
+def inverse(e):
+ e=copy.deepcopy(e)
+ if e[0]=='add':e[3]=-e[3]
+ else:e[2],e[3]=e[3],e[2]
+ return e
+def apply(e,M,mapping=None):
+ t=mapping[e[1]] if mapping is not None else e[1]
+ if e[0]=='add':
+  s=mapping[e[2]] if mapping is not None else e[2];q=Q(e[3],e[4])
+  for j,a in M[s].items():
+   x=M[t].get(j,Q(0))+q*a
+   if x:M[t][j]=x
+   else:M[t].pop(j,None)
+ else:
+  q=Q(e[2],e[3]);M[t]={j:q*a for j,a in M[t].items()}
+def rref(A):
+ a=[list(map(Q,row)) for row in A];nr=len(a);nc=len(a[0]) if nr else 0;row=0;piv=[]
+ for c in range(nc):
+  k=next((i for i in range(row,nr) if a[i][c]),None)
+  if k is None:continue
+  a[row],a[k]=a[k],a[row];q=a[row][c];a[row]=[x/q for x in a[row]]
+  for i in range(nr):
+   if i!=row and a[i][c]:q=a[i][c];a[i]=[x-q*y for x,y in zip(a[i],a[row])]
+  piv.append(c);row+=1
+  if row==nr:break
+ return a,piv
+def rank(A):return len(rref(A)[1])
+def null(A,nc=None):
+ if A:a,piv=rref(A);nc=len(a[0])
+ else:a=[];piv=[];assert nc is not None
+ free=[j for j in range(nc) if j not in piv];out=[[Q(0) for j in free] for i in range(nc)]
+ for k,c in enumerate(free):out[c][k]=Q(1)
+ for i,c in enumerate(piv):
+  for k,j in enumerate(free):out[c][k]=-a[i][j]
+ return out
+def mm(A,B):
+ if not A:return []
+ if not B:return [[] for row in A]
+ bt=list(zip(*B));return [[sum((a*b for a,b in zip(row,col)),Q(0)) for col in bt] for row in A]
+def tr(A):return list(map(list,zip(*A)))
+def inv(A):
+ n0=len(A);a,p=rref([row+[Q(i==j) for j in range(n0)] for i,row in enumerate(A)])
+ assert p[:n0]==list(range(n0))
+ return [row[n0:] for row in a]
+def unit(q):
+ if not q:return False
+ a=abs(q.numerator);b=q.denominator
+ return not a&(a-1) and not b&(b-1)
+def dyadic(q):return not q.denominator&(q.denominator-1)
+def opadd(t,s,q,F):return ['add',t,s,q.numerator,q.denominator,list(F)]
+def opscale(t,q,F):return ['scale',t,q.numerator,q.denominator,list(F)]
+def eliminate(M,ids,F,skip=()):
+ """Return legal dyadic row operations taking an invertible sparse matrix to I."""
+ skip=set(skip);ops=[];dim=len(M)
+ def add(i,j,q):
+  if q:
+   assert dyadic(q);e=opadd(ids[i],ids[j],q,F);ops.append(e)
+   for c,x in M[j].items():
+    z=M[i].get(c,Q(0))+q*x
+    if z:M[i][c]=z
+    else:M[i].pop(c,None)
+ def scale(i,q):
+  if q!=1:
+   assert unit(q);ops.append(opscale(ids[i],q,F));M[i]={c:q*x for c,x in M[i].items()}
+ def swap(i,j):
+  if i!=j:
+   add(i,j,Q(1));add(j,i,Q(-1));add(i,j,Q(1));scale(j,Q(-1))
+ for c in range(dim):
+  if c in skip:
+   assert M[c]=={c:Q(1)} and all(not M[i].get(c) for i in range(dim) if i!=c)
+   continue
+  cand=[i for i in range(c,dim) if i not in skip and M[i].get(c)]
+  k=next((i for i in cand if unit(M[i][c])),None)
+  if k is None:
+   # Elementary Euclidean row additions reduce the pivot-column numerator gcd.
+   assert cand,('singular',c)
+   while k is None:
+    cand.sort(key=lambda i:abs(M[i][c]));a=cand[0]
+    b=next((i for i in cand[1:] if M[i][c]),None)
+    if b is None:raise ValueError(('non-dyadic determinant pivot',c,M[a][c]))
+    rat=M[b][c]/M[a][c];q=rat.numerator//rat.denominator
+    if q==0:q=1 if rat>0 else -1
+    add(b,a,Q(-q));cand=[i for i in cand if M[i].get(c)]
+    k=next((i for i in cand if unit(M[i][c])),None)
+  swap(c,k);scale(c,1/M[c][c])
+  for i in range(dim):
+   if i!=c and M[i].get(c):
+    assert i not in skip
+    add(i,c,-M[i][c])
+ assert all(row=={i:Q(1)} for i,row in enumerate(M))
+ return ops
+def realize(A,ids,F):
+ M=[{j:Q(x) for j,x in enumerate(row) if x} for row in A]
+ return [inverse(e) for e in reversed(eliminate(M,ids,F))]
+# Reconstruct the actual non-target map after the inherited HPE tail.
+inherited_tail=[w['cleanup'][i][:-1]+[list(f)] for i,f in w.get('early_cleanup',[])]
+mainN=[e for e in w['A']+w['B'] if not v<=e[1]<2*v]
+M=[{i:Q(1)} for i in range(len(N))]
+for e in mainN+inherited_tail:apply(e,M,ix)
+MI=[{i:Q(1)} for i in range(len(N))]
+for e in reversed(mainN+inherited_tail):apply(inverse(e),MI,ix)
+cur={x:(w['ports'][x],) if x<v else basis(w.get('start_extra',{}).get(str(x),[])) for x in N}
+for e in w['A']+w['B']+inherited_tail:
+ for x in regs(e):
+  if x in cur:cur[x]=basis(e[-1])
+enter=set(map(int,w.get('start_extra',{})));protected=[ix[x] for x in N if x<v or x in enter]
+EXTRAH=json.loads(os.environ.get('EXTRAH','[]'))
+PAIRING_RANKS=json.loads(os.environ['PAIRING_RANKS']) if os.environ.get('PAIRING_RANKS') else None   # per-block pin, set by the driver
+mods=rd(args.hamming/'PACKET-PROGRAMS.json.gz');proto=rd(args.hamming/'PROTOTYPE.json')
+plans=[];premix=[];tail=[];ends={};Mafter=copy.deepcopy(M)
+for b,mod in enumerate(mods):
+ ss=mod['receipt']['source_lines'];F=basis([proto['binary_ports'][s] for s in ss]);I=[ix[x] for x in N if inside(cur[x],F)]
+ hs=list(range(224+16*b,224+16*(b+1)))+[x for x in EXTRAH if ix[x] in I];H=[ix[x] for x in hs];NB=len(hs)
+ C=[[M[i].get(j,Q(0)) for j in protected] for i in I]
+ L=tr(null(tr(C),len(I)))
+ A=[[MI[j].get(i,Q(0)) for i in I] for j in protected];A=[row for row in A if any(row)]
+ K=null(A,len(I));BK=mm(L,K);_,piv=rref(BK);r=len(piv);print('PAIR',b,'I',len(I),'L',len(L),'K',len(K),'r',r,flush=True);assert r==len(L),(b,r,len(L))
+ if PAIRING_RANKS is not None: assert r==PAIRING_RANKS[b],('pinned pairing rank',b,r,PAIRING_RANKS[b])
+ if os.environ.get('DIAG'):
+  print(' regs',[(N[i],cur[N[i]],rank([C[k]]) ) for k,i in enumerate(I)],'rankC',rank(C) if C else 0,flush=True)
+  for row in L: print('  Lrow',{N[I[k]]:str(x) for k,x in enumerate(row) if x})
+ if r==0:plans.append(dict(block=b,frame=list(F),registers=[N[i] for i in I],ends=[],pairing_rank=0));continue
+ Ksel=[[row[j] for j in piv] for row in K];Bsel=[[row[j] for j in piv] for row in BK];U=mm(Ksel,inv(Bsel));assert mm(L,U)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ q=mm([[MI[i].get(j,Q(0)) for j in I] for i in range(len(N))],U)
+ assert all(not any(q[i]) for i in range(len(N)) if i not in H),('nonlocal premix',b)
+ RR=mm(L,[[M[i].get(j,Q(0)) for j in H] for i in I]);qH=[q[i] for i in H]
+ assert mm(RR,qH)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ # Pick low physical helper destinations with independent U coordinate rows.
+ ih=[]
+ for j in sorted((j for j,i in enumerate(I) if N[i] in hs),key=lambda j:(cur[N[I[j]]]!=F,N[I[j]])):
+  if rank([U[k] for k in ih]+[U[j]])>len(ih):ih.append(j)
+  if len(ih)==r:break
+ assert len(ih)==r
+ endhs=[N[I[j]] for j in ih];endhidx=[hs.index(h) for h in endhs]
+ kerR=null(RR,NB);Qmat=[[Q(0) for j in range(NB)] for i in range(NB)]
+ for j,hj in enumerate(endhidx):
+  for i in range(NB):Qmat[i][hj]=qH[i][j]
+ other=[j for j in range(NB) if j not in endhidx]
+ for k,j in enumerate(other):
+  for i in range(NB):Qmat[i][j]=kerR[i][k]
+ assert rank(Qmat)==NB
+ pops=realize(Qmat,hs,());premix+=pops
+ T=[[Q(i==j)-sum((U[i][k]*L[k][j] for k in range(r)),Q(0)) for j in range(len(I))] for i in range(len(I))]
+ for k,i in enumerate(ih):T[i]=L[k]
+ tops=realize(T,[N[i] for i in I],F);tail+=tops
+ # Right-compose this initial helper premix; other blocks have disjoint H sets.
+ for row in Mafter:
+  vals=[row.get(h,Q(0)) for h in H]
+  if any(vals):
+   for hj in H:row.pop(hj,None)
+   for j,hj in enumerate(H):
+    z=sum((vals[i]*Qmat[i][j] for i in range(NB)),Q(0))
+    if z:row[hj]=z
+ for e in tops:apply(e,Mafter,ix)
+ ends.update({h:list(F) for h in endhs})
+ plans.append(dict(block=b,frame=list(F),registers=[N[i] for i in I],ends=endhs,pairing_rank=r,premix_gates=len(pops),tail_gates=len(tops),Q=[[str(x) for x in row] for row in Qmat],T=[[str(x) for x in row] for row in T]))
+ print('BLOCK',b,'ends',endhs,'Qops',len(pops),'Tops',len(tops),flush=True)
+# Check actual post-tail isolation before constructing the high-frame inverse.
+allends=set(ends)|set(map(int,w.get('helper_final',{})))
+for h in allends:
+ j=ix[h];assert Mafter[j]=={j:Q(1)},('row not isolated',h,Mafter[j]);assert all(not row.get(j) for i,row in enumerate(Mafter) if i!=j),('column not isolated',h)
+print('EXACT_ISOLATED',len(ends),'new;',len(allends),'total',round(time.monotonic()-t0,3),flush=True)
+fullops=eliminate(copy.deepcopy(Mafter),N,F9,[ix[x] for x in allends])
+print('FULL_INVERSE',len(fullops),round(time.monotonic()-t0,3),flush=True)
+# Cancel new cold-axis target responses inside A, after their wrappers.
+Dirt=[({h:Q(1)} if h in ends else {}) for h in range(n)]
+for e in premix+w['A']+w['cut']+w['B']:apply(e,Dirt)
+for e in w['precondition']:apply(e,Dirt)
+postcomp=[opadd(y,h,-a,()) for y in range(v,2*v) for h,a in sorted(Dirt[y].items()) if a]
+assert all(h in ends for e in postcomp for h in [e[2]])
+new=copy.deepcopy(w);new['A']=postcomp+premix+w['A'];new['cleanup']=inherited_tail+tail+fullops
+new['early_cleanup']=[[i,e[-1]] for i,e in enumerate(inherited_tail+tail)]
+new['helper_final'].update({str(h):f for h,f in ends.items()})
+new['refactored_cleanup']={'kind':'source_branch_gauge_and_retired_completion_cold44','new_cold_ends':len(ends),'exact_non_target_isolation_checked':True,'high_inverse':'dyadic_sparse_Gauss_Jordan'}
+# Derive paid profile by subtracting and adding literal frame-chain counts.
+spec=importlib.util.spec_from_file_location('upstream_cold_end',args.upstream_package/'code/build_cold_end.py')
+profile_module=importlib.util.module_from_spec(spec);spec.loader.exec_module(profile_module)
+oldprof,_=profile_module.chain_profile(w);newprof,_=profile_module.chain_profile(new)
+prof=Counter({int(k):z for k,z in w['report']['local_profile'].items()});prof.subtract(oldprof);prof.update(newprof)
+widths=Counter(len(basis(new['helper_final'].get(str(h),F9)))-len(basis(new.get('start_extra',{}).get(str(h),[]))) for h in range(224,n))
+new['report'].update(local_profile={str(k):z for k,z in sorted(prof.items()) if z},local_rank_mass=sum(k*z for k,z in prof.items()),width_inventory={str(k):z for k,z in sorted(widths.items()) if z},status='EXACT_COLD44_CONSTRUCTED_PENDING_INDEPENDENT_AUDIT')
+raw=json.dumps(new,sort_keys=True,separators=(',',':')).encode();sha=hashlib.sha256(raw).hexdigest();(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+recipe={'premix':postcomp+premix,'cleanup':new['cleanup'],'early_cleanup':new['early_cleanup'],'cold_ends':{str(h):f for h,f in ends.items()},'refactored_cleanup':new['refactored_cleanup'],'output_content_sha256':sha}
+(OUT/'RECIPE.json.gz').write_bytes(gzip.compress(json.dumps(recipe,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+receipt=dict(input_content_sha256=hashlib.sha256(gzip.decompress(WPATH.read_bytes())).hexdigest(),output_content_sha256=sha,blocks=plans,new_cold_ends=len(ends),all_low_ended_helpers=len(allends),premix_gates=len(premix),postwrapper_compensation_gates=len(postcomp),tail_gates=len(tail),inherited_tail_gates=len(inherited_tail),full_inverse_gates=len(fullops),profile=new['report']['local_profile'],width_inventory=new['report']['width_inventory'],rank_mass=new['report']['local_rank_mass'],seconds=time.monotonic()-t0)
+(OUT/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(json.dumps({k:z for k,z in receipt.items() if k!='blocks'},indent=2),flush=True)
diff --git a/research/gauge44-slots-t16/construction/notri/port_stage_x.py b/research/gauge44-slots-t16/construction/notri/port_stage_x.py
new file mode 100644
index 0000000000..81ac65ceff
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/notri/port_stage_x.py
@@ -0,0 +1,125 @@
+"""Port one 504-helper construction stage onto the K-triangle word.  Apache-2.0.  Prepared with Claude Code assistance.
+
+usage: build_port_stage.py --shadow-input I4 --shadow-output O4 --input I8 --map HELPER-MAP.json --gk-dir GK --out DIR
+
+The shadow pair (I4 -> O4) is one stage of a 504-helper chain, rebuilt in the same run from pinned sources.  I8 is the
+K-triangle word at the matching point of its own chain, and HELPER-MAP.json is the 504 -> R register map written by
+construct_k_triangle.py.  Registers below 448 keep their ids; the removed packet copies have no image.
+
+The port does the following:
+* It renumbers I4 and O4 through the map and drops their gates that touch a removed register.
+* It matches gates by scalar operation (the gate without its frame), aligning I4 with O4 and I4 with I8 separately.
+* It builds O8 in O4 gate order:
+  * each matched gate is taken from I8, with O4's frame wherever the stage changed that frame;
+  * each gate the stage introduced is taken from O4;
+  * each I8-only gate (the K-triangle reads) stays after the O4 image of its I8 predecessor.
+* It replays the stage's entrance (start_extra) and target_levels changes.
+* It rebuilds the cleanup with the inherited inverse rule.
+
+The constructor is a search transfer only.  The verifier certifies the output independently: the generalised native
+audit (exact forward and inverse replay of every column, native frame chains) runs on every ported word, and every
+input and output is pinned by content hash."""
+import argparse, copy, difflib, gzip, hashlib, json, sys
+from collections import Counter
+from pathlib import Path
+
+assert __debug__, 'Assertions required'
+FULL = [256, 128, 64, 32, 16, 8, 4, 2, 1]
+
+
+def regs(g): return (g[1], g[2]) if g[0] == 'add' else (g[1],)
+
+
+def key(g): return json.dumps(g[:-1])
+
+
+def inverse(e):
+    e = copy.deepcopy(e)
+    if e[0] == 'add': e[3] *= -1
+    else: e[2], e[3] = e[3], e[2]
+    e[-1] = list(FULL); return e
+
+
+def align(xs, ys):
+    """index map xs -> ys over runs of equal scalar operations"""
+    sm = difflib.SequenceMatcher(None, [key(g) for g in xs], [key(g) for g in ys], autojunk=False)
+    return {i1 + k: j1 + k for tag, i1, i2, j1, j2 in sm.get_opcodes() if tag == 'equal' for k in range(i2 - i1)}
+
+
+def transfer_section(I4, O4, I8, stats):
+    a, b = align(I4, O4), align(I4, I8)
+    o2i = {j: i for i, j in a.items()}; i8from4 = {j: i for i, j in b.items()}
+    anchor = {j8: a[i4] for j8, i4 in i8from4.items() if i4 in a}
+    pending, last = {}, -1
+    for j8, g in enumerate(I8):
+        if j8 in anchor: last = anchor[j8]
+        elif j8 not in i8from4: pending.setdefault(last, []).append(copy.deepcopy(g)); stats['kept_own'] += 1
+        else: stats['dropped_by_stage'] += 1
+    out = list(pending.get(-1, []))
+    for k, g in enumerate(O4):
+        if k in o2i:
+            i4 = o2i[k]
+            if i4 in b:
+                g8 = copy.deepcopy(I8[b[i4]])
+                if I4[i4][-1] != g[-1]: g8[-1] = copy.deepcopy(g[-1]); stats['frames_changed'] += 1
+                out.append(g8)
+        else:
+            out.append(copy.deepcopy(g)); stats['introduced'] += 1
+        out.extend(pending.get(k, []))
+    return out
+
+
+def main():
+    ap = argparse.ArgumentParser()
+    for k in ('--shadow-input', '--shadow-output', '--input', '--map', '--gk-dir', '--out'): ap.add_argument(k, type=Path, required=True)
+    a = ap.parse_args(); assert not a.out.exists()
+    sys.path.insert(0, str(a.gk_dir)); import gk_word as G, gk_common as C
+    G.V = C.V = 112
+    rd = lambda p: json.loads(gzip.decompress(p.read_bytes()))
+    enc = lambda x: json.dumps(x, sort_keys=True, separators=(',', ':')).encode(); sha = lambda x: hashlib.sha256(x).hexdigest()
+    I4, O4, I8 = rd(a.shadow_input), rd(a.shadow_output), rd(a.input)
+    fm = {int(k): int(v) for k, v in json.loads(a.map.read_text())['map'].items()}
+    assert all(fm[k] == k for k in fm if k < 448), 'only ids >= 448 may move'
+    R = I8['report']['R']; EXTRA = set(range(224 + R)) - set(fm.values()); assert len(set(fm.values())) == len(fm) and set(fm.values()) <= set(range(224 + R)), 'map is not injective into the K-triangle registers'
+    assert I4['report'].get('R', 504) == 504 and len(fm) + len(set(range(728)) - set(fm)) == 728
+    rem = set(range(728)) - set(fm)
+    rn = lambda r: fm[r]
+    touches = lambda g: any(r in rem for r in regs(g))
+    def rg(g):
+        g = copy.deepcopy(g); g[1] = rn(g[1])
+        if g[0] == 'add': g[2] = rn(g[2])
+        return g
+    def rn_word(w):
+        w = copy.deepcopy(w)
+        for s in ('A', 'B', 'cut', 'precondition', 'cleanup'):
+            if s in w: w[s] = [rg(g) for g in w[s] if not touches(g)]
+        for k in ('start_extra', 'helper_final'):
+            if k in w: w[k] = {str(rn(int(r))): f for r, f in w[k].items() if int(r) not in rem}
+        return w
+    I4r, O4r = rn_word(I4), rn_word(O4)
+    O8 = copy.deepcopy(I8); stats = {s: Counter() for s in ('A', 'B')}
+    for s in ('A', 'B'): O8[s] = transfer_section(I4r[s], O4r[s], I8[s], stats[s])
+    for k in ('start_extra', 'target_levels'):
+        x, y = I4r.get(k, {}), O4r.get(k, {}); d = dict(I8.get(k, {}))
+        for r in set(x) | set(y):
+            if x.get(r) != y.get(r):
+                if r in y: d[r] = y[r]
+                else: d.pop(r, None)
+        if k in O4 or k in I8: O8[k] = dict(sorted(d.items(), key=lambda kv: int(kv[0])))
+    for k in O4:
+        if k not in ('A', 'B', 'cleanup', 'report', 'start_extra', 'target_levels', 'cut', 'precondition'):
+            assert O4r[k] == I4r[k], 'stage changed an unported field: ' + k
+    O8['cleanup'] = [inverse(e) for e in reversed(O8['A'] + O8['B']) if not 112 <= e[1] < 224]
+    H = G.profile(O8)
+    ws = [9 - len(G.basis(O8['start_extra'].get(str(224 + h), []))) for h in range(R)]
+    O8['report'] = dict(I8['report'], local_profile={str(k): v for k, v in sorted(H.items())}, local_rank_mass=sum(k * v for k, v in H.items()),
+                        width_inventory={str(k): v for k, v in sorted(Counter(ws).items())})
+    a.out.mkdir(parents=True); (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(enc(O8), mtime=0))
+    receipt = dict(status='PORTED_STAGE_PENDING_NATIVE_AUDIT', R=R, removed_504_helpers=sorted(rem),
+                   shadow_input_content_sha256=sha(enc(I4)), shadow_output_content_sha256=sha(enc(O4)), input_content_sha256=sha(enc(I8)),
+                   output_content_sha256=sha(enc(O8)), sections={s: dict(v) for s, v in stats.items()}, local_profile=O8['report']['local_profile'],
+                   scope='Transfer construction only; exactness, frame chains and profile are certified by the native audit run on the output.')
+    (a.out / 'PORT-STAGE.json').write_text(json.dumps(receipt, indent=2, sort_keys=True) + '\n', newline='\n'); print(json.dumps(receipt, indent=2))
+
+
+main()
diff --git a/research/gauge44-slots-t16/construction/notri/reproduce_notri.py b/research/gauge44-slots-t16/construction/notri/reproduce_notri.py
new file mode 100644
index 0000000000..a85f2acf15
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/notri/reproduce_notri.py
@@ -0,0 +1,166 @@
+#!/usr/bin/env python3
+"""Rebuild the no-triangle gauge44 word (R = 504) and its native locals.
+
+The no-triangle word is #645's gauge44 chain with none of the four (p,-1) K-triangles. In the six K-blocks
+{0,1,2,11,12,13}, the completion priority is extended by the 6-row list PRIO6.json, the list blocks 3-10 already use.
+Each block then pairs at rank 4, giving 56 rank-four cold ends instead of 44 (PartialK).
+
+Input: a fresh `construction/reproduce.py --until word` output directory. Its shadow-early and shadow-prefix words and
+its hamming inputs are pinned by reproduce.py itself. Steps, each checked exactly:
+  1. gauge-forward: cgx.py, #645's construct_gauge_xcentre.py generalised by PartialK. The extra rows come from XPARAM,
+     and the K-triangle schedule comes from the TRI file. Run on the triangle set {} with XPARAM = PRIO6.json.
+  2. port0-3: port_stage_x.py, PR635's build_port_stage.py with the helper map allowed to be injective rather than onto.
+     With R = 504 and no triangles, the map is onto again.
+  3. regroup: PR635's k492 frame-regroup changes, applied where their `before` gate occurs. For this word none occurs,
+     and that count (0) is pinned.
+  4. hpe: PR635's build_hpe.candidates, taken greedily with disjoint registers, and build_hpe.apply. 46 changes, pinned.
+  5. cold44: cold44x.py, #645's build_gauge_cold44.py generalised by PartialK to blocks whose helper list includes the
+     helpers outside the 224+16b ranges (EXTRAH). 56 cold ends; the 14 pairing ranks are pinned to [4]*14 inside cold44x (PAIRING_RANKS) and rechecked here. The output word content sha256 is pinned (3e99ba77...).
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs, as in reproduce.py.
+--control-g44 instead runs steps 1-5 with #645's four triangles and no XPARAM. It must reproduce #645's pinned gauge44
+cold44 word (78c7aada...), the same word #645's own reproduce.py builds. This shows the generalised scripts reduce to
+#645's constructors.
+Apache-2.0. Driver by ColdWitness from PartialK's variant.py; constructors credited above.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NOTRI_SHA = '3e99ba778ab8a97853f50912776247802b529439937176363f6c42786163b1f9'
+G44_SHA = '78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290'
+# native-local pins (the strict locals the SPEC was frozen against: PartialK runs/none_p6/local)
+CANONICAL_SHA = '4265a3bb7f9b46967dfadfca5f2cc1f5b3e6e8681f16c02590f1b9430c013637'
+PROGRAM_SHA = {'forward': '0afda28699e15cf5a5a17aee5475ac608c9fb68b15766d463b93ec8e2df4ae85',
+               'backward': '5be6cb4ea7a1da36d7bbe7eb2392873c058dd3cbb3cc2eeadd55ecca9310ca8a'}
+CLIFFORD_SHA = '4b5789e43e04d71f02c2d480450ec0b354007d9cf523bda76c7345730806344b'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def dump(p, v):
+    p.parent.mkdir(parents=True, exist_ok=True); p.write_bytes(gzip.compress(enc(v), mtime=0))
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--word-dir', type=Path, required=True, help='construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--control-g44', action='store_true', help='rebuild #645 gauge44 (4 triangles) instead; word only')
+    ap.add_argument('--skip-phases', action='store_true')
+    ap.add_argument('--word-only', action='store_true', help='stop after the pinned scalar word (input to construction/layers_np)')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    structural = a.main.resolve() / 'research/structural-gain/frontier-composition'
+    wd = a.word_dir.resolve()
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    # 1. gauge-forward on the chosen K-triangle set
+    tri = read(up / 'data/TRI-SCHEDULE.json')
+    if not a.control_g44:
+        tri = dict(full_pairs=tri['full_pairs'], triangles=[])
+        env['XPARAM'] = str(HERE / 'PRIO6.json')
+    (out / 'TRI.json').write_text(json.dumps(tri))
+    raw = out / 'raw'
+    run('gauge-forward', HERE / 'cgx.py', wd / 'hamming', raw, out / 'TRI.json')
+    word = raw / 'FULL-WORD.json.gz'
+    # 2. port stages (same chain as reproduce.py)
+    chain = [parent / 'complex-local/static44/inputs/RAW504.json.gz', structural / 'global-replay/base/split-centres/FULL-WORD.json.gz',
+             wd / 'shadow-early/FULL-WORD.json.gz', structural / 'multicold-eight-word/FULL-WORD.json.gz',
+             wd / 'shadow-prefix/FULL-WORD.json.gz']
+    for i, (b, c) in enumerate(zip(chain, chain[1:])):
+        t = out / ('port%d' % i)
+        run('port%d' % i, HERE / 'port_stage_x.py', '--shadow-input', b, '--shadow-output', c, '--input', word,
+            '--map', raw / 'HELPER-MAP.json', '--gk-dir', gk, '--out', t)
+        word = t / 'FULL-WORD.json.gz'
+    # 3. PR635 frame regroup where its `before` gate occurs
+    w = read(word); rg = {json.dumps(c['before']): c['after'] for c in read(up / 'data/recipes/k492-jp8-frame_regroup.json')['changes']}
+    n = 0
+    for part in ('A', 'B'):
+        for i, e in enumerate(w[part]):
+            k = json.dumps(e)
+            if k in rg: w[part][i] = rg[k]; n += 1
+    sys.path.insert(0, str(gk)); import gk_word as GW, gk_common as GC
+    GW.V = GC.V = 112; GW.DATA = GC.DATA = 7168
+    H = GW.profile(w)
+    w['report'].update(local_profile={str(k): z for k, z in sorted(H.items()) if z}, local_rank_mass=sum(r * z for r, z in H.items()))
+    assert n == (24 if a.control_g44 else 0), ('regroup count', n)
+    dump(out / 'regroup/FULL-WORD.json.gz', w)
+    # 4. HPE: PR635's candidates, greedy with disjoint registers
+    h = load('upstream_hpe', up / 'code/build_hpe.py')
+    used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    assert len(ch) == (34 if a.control_g44 else 46), ('hpe count', len(ch))
+    (out / 'HPE-RECIPE.json').write_text(json.dumps(dict(changes=ch)))
+    w = h.apply(w, ch); dump(out / 'hpe/FULL-WORD.json.gz', w)
+    # 5. cold44 (generalised): helpers outside the 224+16b ranges join their blocks
+    hm = set(read(raw / 'HELPER-MAP.json')['map'].values())
+    env['EXTRAH'] = json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm))
+    ranks = [2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2] if a.control_g44 else [4] * 14
+    env['PAIRING_RANKS'] = json.dumps(ranks)   # cold44x asserts every block's pairing rank
+    run('cold44', HERE / 'cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', wd / 'hamming', '--upstream-package', up)
+    assert [b['pairing_rank'] for b in read(out / 'cold44/CONSTRUCTION.json')['blocks']] == ranks, 'pairing ranks'
+    word = out / 'cold44/FULL-WORD.json.gz'; w = read(word)
+    got = hashlib.sha256(enc(w)).hexdigest()
+    assert got == (G44_SHA if a.control_g44 else NOTRI_SHA), ('word', got)
+    rep = w['report']
+    if a.control_g44:
+        print('PASS control: #645 gauge44 word reproduced', got, flush=True); return
+    assert rep['R'] == 504 and rep['local_rank_mass'] == 5674
+    assert rep['local_profile'] == {'1': 2506, '2': 336, '3': 472, '4': 184, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 64, '5': 48, '7': 46, '8': 114, '9': 232}, rep['width_inventory']
+    print('PASS no-triangle scalar word', got, flush=True)
+    if a.word_only:
+        return
+    # 6. native locals (PR635, as in reproduce.py)
+    for k in ('XPARAM', 'EXTRAH', 'PAIRING_RANKS'): env.pop(k, None)
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word,
+        '--routing', parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz', '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == CANONICAL_SHA, 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in PROGRAM_SHA.items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == CLIFFORD_SHA, 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/promo/LOCAL-PINS-p6n-k4.json b/research/gauge44-slots-t16/construction/promo/LOCAL-PINS-p6n-k4.json
new file mode 100644
index 0000000000..c43b391a43
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/promo/LOCAL-PINS-p6n-k4.json
@@ -0,0 +1,11 @@
+{
+ "word": "P6k4",
+ "layer_controls": 95,
+ "promo_controls": 11,
+ "canonical_sha256": "c0c5734a2eb6984ccd1e314dbcea2a6971b9708e5f611aa8912fcf47f02de61d",
+ "program_sha256": {
+  "forward": "6cfedac02e899df7fa50a3e38845982a4e9dbc866e9decc4052e011532bdb30f",
+  "backward": "207d9352aeea7d56a6da865745a1ad756e28531fbf9bcb0cd54950aac7270381"
+ },
+ "clifford_recipes_sha256": "1c1d037d602b503b35f01a65d0ccc07ac63fde9df501b0a61e3e189a44a779de"
+}
diff --git a/research/gauge44-slots-t16/construction/promo/PROMO-RECIPE-p6n-k4.json b/research/gauge44-slots-t16/construction/promo/PROMO-RECIPE-p6n-k4.json
new file mode 100644
index 0000000000..3f336c07ea
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/promo/PROMO-RECIPE-p6n-k4.json
@@ -0,0 +1,971 @@
+{
+ "input_content_sha256": "34b683fa08f054fe725704ec15b1c8da42f846430999d14d0cae0fcd42296fe2",
+ "groups": [
+  627,
+  629,
+  630,
+  631,
+  635,
+  637,
+  638,
+  639,
+  651,
+  653,
+  654,
+  655,
+  659,
+  661,
+  662,
+  663
+ ],
+ "entrances": {
+  "627": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "629": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "630": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "631": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "635": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "637": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "638": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "639": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "651": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "653": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "654": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "655": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "659": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ],
+  "661": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ],
+  "662": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ],
+  "663": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ]
+ },
+ "gate_frames": [
+  [
+   "B",
+   420,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   421,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   422,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   423,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   424,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   425,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   426,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   427,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   428,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   429,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   430,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   431,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   432,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   433,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   434,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   435,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   436,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   437,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   438,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   439,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   440,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   441,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   442,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   443,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   444,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   445,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   446,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   447,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   448,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   449,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   450,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   451,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   452,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   453,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   454,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   455,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   456,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   457,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   458,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   459,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   460,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   461,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   462,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   463,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   464,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   465,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   466,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   467,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ]
+ ],
+ "expected": {
+  "output_content_sha256": "0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073",
+  "local_profile": {
+   "1": 2572,
+   "2": 326,
+   "3": 430,
+   "4": 194,
+   "5": 56,
+   "8": 8
+  },
+  "width_inventory": {
+   "4": 80,
+   "5": 32,
+   "7": 54,
+   "8": 122,
+   "9": 216
+  }
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/promo/build_promotion.py b/research/gauge44-slots-t16/construction/promo/build_promotion.py
new file mode 100644
index 0000000000..f1daad34c2
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/promo/build_promotion.py
@@ -0,0 +1,109 @@
+"""Entrance promotions E4 -> E5 of whole kernel groups: deterministic constructor.  Apache-2.0.
+BlockInvert (Claude Code research agent) for the gauge44 lineage.
+
+usage: build_promotion.py --input FULL-WORD.json.gz --recipe PROMO-RECIPE.json --out DIR
+
+The recipe is data only:
+  input_content_sha256   sha256 of the decompressed input word (pinned);
+  entrances              {helper: frame vectors}: new start frames (each strictly contains the old one);
+  gate_frames            [[section, index, old frame, new frame], ...]: section 'A' / 'B' (main gates) or 'T'
+                         (early_cleanup entry index); the old frame must match the input exactly (as a span);
+  expected               output_content_sha256, local_profile, width_inventory.
+The scalar program is unchanged (only frame annotations and start frames move), so the endpoint, the
+zero-target-response entrance condition and every cone are those of the input; the independent audit
+(audit_local.py) re-checks all of them, plus monotone chains and the recomputed profile/widths."""
+import argparse, gzip, hashlib, json
+from collections import Counter
+from pathlib import Path
+
+
+def span(vs):
+    p = {}
+    for x in vs:
+        for k in sorted(p, reverse=True):
+            if x >> k & 1: x ^= p[k]
+        if x:
+            k = x.bit_length() - 1
+            for j in list(p):
+                if p[j] >> k & 1: p[j] ^= x
+            p[k] = x
+    return tuple(p[k] for k in sorted(p, reverse=True))
+
+
+def regs(e): return [e[1]] + ([e[2]] if e[0] == 'add' else [])
+
+
+def chain_profile(w):
+    """paid climbs of the A, B, early-tail and final chains, target ends included (centre descents unchanged, not counted)."""
+    v, R = w['report']['v'], w['report']['R']; n = 2*v + R
+    cur = [() for _ in range(n)]
+    for i, p in enumerate(w['ports']): cur[i] = span([p])
+    for r, f in w.get('start_extra', {}).items(): cur[int(r)] = span(f)
+    prof = Counter()
+
+    def climb(r, F):
+        assert span(list(cur[r]) + list(F)) == F, ('nonmonotone', r)
+        if len(F) > len(cur[r]): prof[len(F) - len(cur[r])] += 1
+        cur[r] = F
+    for part in ('A', 'B'):
+        for e in w[part]:
+            for r in regs(e): climb(r, span(e[-1]))
+    for i, f in w.get('early_cleanup', []):
+        for r in regs(w['cleanup'][i]): climb(r, span(f))
+    full = span([1 << i for i in range(9)])
+    final = {int(r): span(f) for r, f in w.get('helper_final', {}).items()}
+    for r in range(n):
+        if v <= r < 2*v:     # targets end at their port hyperplane (as in the independent audit); counted on both sides
+            climb(r, span([x for x in range(1, 512) if (x & w['ports'][r - v]).bit_count() % 2 == 0])); continue
+        climb(r, final.get(r, full))
+    return prof
+
+
+def widths(w):
+    v, R = w['report']['v'], w['report']['R']; full = [1 << i for i in range(9)]
+    return Counter(len(span(w['helper_final'].get(str(r), full))) - len(span(w['start_extra'].get(str(r), [])))
+                   for r in range(2*v, 2*v + R))
+
+
+def apply(w, r):
+    nw = json.loads(json.dumps(w))
+    for h, F in r['entrances'].items():
+        assert h in nw['start_extra'], ('not an entering helper', h)
+        old, new = span(nw['start_extra'][h]), span(F)
+        assert len(new) > len(old) and span(list(old) + list(new)) == new, ('not a promotion', h)
+        nw['start_extra'][h] = list(new)
+    for sec, i, old, new in r['gate_frames']:
+        if sec in ('A', 'B'):
+            assert span(nw[sec][i][-1]) == span(old), ('gate frame mismatch', sec, i)
+            nw[sec][i][-1] = list(span(new))
+        else:
+            assert sec == 'T' and span(nw['early_cleanup'][i][1]) == span(old), ('tail frame mismatch', i)
+            nw['early_cleanup'][i][1] = list(span(new))
+    old_prof, new_prof = chain_profile(w), chain_profile(nw)
+    lp = Counter({int(k): c for k, c in w['report']['local_profile'].items()}); lp.subtract(old_prof); lp.update(new_prof)
+    assert min(lp.values()) >= 0
+    inv = widths(nw)
+    rep = dict(w['report'])
+    rep['local_profile'] = {str(k): c for k, c in sorted(lp.items()) if c}
+    rep['local_rank_mass'] = sum(k*c for k, c in lp.items())
+    rep['width_inventory'] = {str(k): c for k, c in sorted(inv.items()) if c}
+    nw['report'] = rep
+    return nw
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(); ap.add_argument('--input', type=Path, required=True)
+    ap.add_argument('--recipe', type=Path, required=True); ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    raw = gzip.decompress(a.input.read_bytes()); r = json.loads(a.recipe.read_text())
+    assert hashlib.sha256(raw).hexdigest() == r['input_content_sha256'], 'input word pin'
+    nw = apply(json.loads(raw), r)
+    data = json.dumps(nw, separators=(',', ':')).encode()
+    x = r['expected']
+    assert nw['report']['local_profile'] == x['local_profile'], 'profile pin'
+    assert nw['report']['width_inventory'] == x['width_inventory'], 'width pin'
+    assert hashlib.sha256(data).hexdigest() == x['output_content_sha256'], 'output word pin'
+    a.out.mkdir(parents=True, exist_ok=True)
+    (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+    print('PASS', len(r['entrances']), 'promoted entrances;', len(r['gate_frames']), 'gate frames;',
+          'profile', x['local_profile'], 'sha', x['output_content_sha256'])
diff --git a/research/gauge44-slots-t16/construction/promo/make_recipe.py b/research/gauge44-slots-t16/construction/promo/make_recipe.py
new file mode 100644
index 0000000000..618d609453
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/promo/make_recipe.py
@@ -0,0 +1,12 @@
+"""make_recipe.py BASEWORD SOLUTION.json BUILTWORD OUT: discovery-side recipe writer (CP-SAT solution -> data recipe)."""
+import sys, json, gzip, hashlib
+base = gzip.decompress(open(sys.argv[1], 'rb').read()); s = json.load(open(sys.argv[2]))
+built = gzip.decompress(open(sys.argv[3], 'rb').read()); bw = json.loads(built)
+key = {'A': 0, 'B': 1, 'T': 2}
+r = dict(input_content_sha256=hashlib.sha256(base).hexdigest(),
+         groups=sorted(int(h) for h in s['newstarts']),
+         entrances={h: s['newstarts'][h] for h in sorted(s['newstarts'], key=int)},
+         gate_frames=sorted(s['changed'], key=lambda c: (key[c[0]], c[1])),
+         expected=dict(output_content_sha256=hashlib.sha256(built).hexdigest(),
+                       local_profile=bw['report']['local_profile'], width_inventory=bw['report']['width_inventory']))
+json.dump(r, open(sys.argv[4], 'w'), indent=1)
diff --git a/research/gauge44-slots-t16/construction/promo/promo_controls.py b/research/gauge44-slots-t16/construction/promo/promo_controls.py
new file mode 100644
index 0000000000..20ee51f7db
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/promo/promo_controls.py
@@ -0,0 +1,115 @@
+"""Promotion controls: mutate the promoted word / recipe and require rejection at a pinned site.  Apache-2.0.
+BlockInvert (Claude Code research agent).
+
+usage: promo_controls.py --input BASE-FULL-WORD.json.gz --recipe PROMO-RECIPE.json --audit audit_local.py --out CONTROLS.json
+
+Word-level mutants are checked by the independent audit (audit_local.py, imported from the given path; it shares no
+code with the constructor); recipe-level mutants by build_promotion.apply / its pins.  Each mutant must raise with the
+pinned message prefix; the honest word must pass both."""
+import argparse, gzip, hashlib, importlib.util, json, sys, tempfile
+from pathlib import Path
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+import build_promotion as B
+
+ap = argparse.ArgumentParser()
+for k in ('input', 'recipe', 'audit', 'out'): ap.add_argument('--' + k, type=Path, required=True)
+a = ap.parse_args()
+s = importlib.util.spec_from_file_location('audit_local', a.audit); AL = importlib.util.module_from_spec(s); s.loader.exec_module(AL)
+raw = gzip.decompress(a.input.read_bytes()); base = json.loads(raw); r = json.loads(a.recipe.read_text())
+assert hashlib.sha256(raw).hexdigest() == r['input_content_sha256']
+honest = B.apply(base, r)
+v = base['report']['v']
+tmp = Path(tempfile.mkdtemp())
+
+
+def audit(w):
+    p = tmp / 'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w, separators=(',', ':')).encode(), mtime=0))
+    import io, contextlib
+    with contextlib.redirect_stdout(io.StringIO()):
+        AL.run(p, tmp / 'r.json')
+
+
+def first_gate(w, h):
+    for sec in ('A', 'B'):
+        for i, e in enumerate(w[sec]):
+            if h in B.regs(e): return sec, i
+    raise AssertionError(h)
+
+
+results = []
+
+
+def expect(name, fn, prefix):
+    try:
+        fn(); got = 'ACCEPTED'
+    except (RuntimeError, AssertionError) as e:
+        got = str(e.args[0]) if e.args else type(e).__name__
+    ok = got.startswith(prefix)
+    results.append(dict(control=name, expected=prefix, got=got[:160], rejected_at_pinned_site=ok))
+    print(('OK  ' if ok else 'BAD ') + name + ': ' + got[:120], flush=True)
+
+
+# honest
+audit(honest); print('honest word: audit PASS', flush=True)
+H = sorted(int(h) for h in r['entrances'])
+h0 = str(H[0]); E5 = B.span(r['entrances'][h0]); sec, i = first_gate(honest, int(h0)); F1 = B.span(honest[sec][i][-1])
+full = B.span([1 << k for k in range(9)])
+
+
+def mut(f):
+    w = json.loads(json.dumps(honest)); f(w); return w
+
+
+# 1. promoted entrance moved to a dim-5 frame NOT inside its first gate frame
+def bad_entrance(w):
+    for x in range(1, 512):
+        G = B.span(list(B.span(base['start_extra'][h0])) + [x])
+        if len(G) == 5 and B.span(list(G) + list(F1)) != F1:
+            w['start_extra'][h0] = list(G); return
+    raise AssertionError('no frame')
+expect('entrance_outside_first_gate_frame', lambda: audit(mut(bad_entrance)), 'frame not monotone')
+# 2. a raised gauge gate of a promoted helper left at its old (E4) frame
+old_of = {(c[0], c[1]): c[2] for c in r['gate_frames']}
+assert (sec, i) in old_of, 'first gate of a promoted helper is a raised gate'
+expect('raised_gate_missing', lambda: audit(mut(lambda w: w[sec][i].__setitem__(-1, list(B.span(old_of[(sec, i)]))))), 'frame not monotone')
+# 2b. per promoted group: its first helper's raised entry gate left at the old frame
+for hg in H[4::4]:
+    sg, ig = first_gate(honest, hg)
+    if (sg, ig) in old_of:
+        expect('raised_gate_missing_group_%d' % hg, lambda sg=sg, ig=ig: audit(mut(lambda w: w[sg][ig].__setitem__(-1, list(B.span(old_of[(sg, ig)]))))), 'frame not monotone')
+# 3. every raised gate kept but one entrance reverted to E4 (report kept): the paid profile no longer matches
+expect('entrance_reverted_profile', lambda: audit(mut(lambda w: w['start_extra'].__setitem__(h0, list(B.span(base['start_extra'][h0]))))), 'paid profile mismatch')
+# 4. an E4 helper outside the promoted groups promoted alone (no raised gates)
+others = sorted(int(h) for h, f in base['start_extra'].items() if len(B.span(f)) == 4 and h not in r['entrances'])
+if others:
+    h1 = str(others[0])
+    expect('ungrouped_promotion', lambda: audit(mut(lambda w: w['start_extra'].__setitem__(h1, list(E5)))), 'frame not monotone')
+# 5. recipe-level: wrong old frame for a raised gate; non-promotion entrance; input pin
+def r_bad_old():
+    q = json.loads(json.dumps(r)); q['gate_frames'][0][2] = list(full); B.apply(base, q)
+expect('recipe_gate_old_frame', r_bad_old, "('gate frame mismatch'" if r['gate_frames'][0][0] != 'T' else "('tail frame mismatch'")
+def r_demote():
+    q = json.loads(json.dumps(r)); q['entrances'][h0] = base['start_extra'][h0]; B.apply(base, q)
+expect('recipe_not_a_promotion', r_demote, "('not a promotion'")
+def r_pin():   # the driver's own __main__ path on a tampered input word (one gate scalar changed)
+    import subprocess
+    t = json.loads(raw); e = t['B'][0]
+    if e[0] == 'add': e[3] += e[4]
+    else: e[2] = -e[2]
+    p = tmp / 'tampered.json.gz'; p.write_bytes(gzip.compress(json.dumps(t, separators=(',', ':')).encode(), mtime=0))
+    q = subprocess.run([sys.executable, '-B', str(Path(B.__file__)), '--input', str(p), '--recipe', str(a.recipe), '--out', str(tmp / 'o')],
+                       capture_output=True, text=True)
+    assert q.returncode == 0, q.stderr.strip().splitlines()[-1].split('AssertionError: ', 1)[-1]
+expect('recipe_input_pin', r_pin, 'input word pin')
+# 6. scalar tamper inside a promoted group's raised gate (frames intact): exactness must fail
+def scal(w):
+    e = w[sec][i]
+    if e[0] == 'add': e[3] = e[3] + e[4]
+    else: e[2] = -e[2]
+expect('raised_gate_scalar_tamper', lambda: audit(mut(scal)), '')
+results[-1]['rejected_at_pinned_site'] = results[-1]['got'] != 'ACCEPTED'
+bad = [x for x in results if not x['rejected_at_pinned_site']]
+a.out.write_text(json.dumps(dict(recipe=r['expected']['output_content_sha256'], honest='PASS', controls=results,
+                                 rejected=len(results) - len(bad)), indent=1))
+assert not bad, bad
+print('PASS', len(results), 'controls rejected at pinned sites')
diff --git a/research/gauge44-slots-t16/construction/promo/reproduce_promo.py b/research/gauge44-slots-t16/construction/promo/reproduce_promo.py
new file mode 100644
index 0000000000..6e04aa71b1
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/promo/reproduce_promo.py
@@ -0,0 +1,99 @@
+#!/usr/bin/env python3
+"""Rebuild a promoted no-triangle layered word (entrance promotions E4 -> E5) and its native locals.
+
+Input (--base): `np` = a fresh `construction/layers_np/reproduce_np.py` output (word a9de804f...), or `p6n` = a fresh
+`construction/layers_p6n/reproduce_p6n.py` output (word 34b683fa...). Recipe k: PROMO-RECIPE-<k>.json (BlockInvert;
+data only; it pins its input word) and LOCAL-PINS-<k>.json. Steps, each
+checked exactly:
+  1. promotion: BlockInvert's build_promotion.py. It pins the input word and the recipe's output sha, profile and
+     widths; every old frame must match the input; only frame annotations and start frames move (no scalar change).
+  2. promo-controls: BlockInvert's promo_controls.py. The honest word must pass #645's independent audit_local.py,
+     and its recipe- and word-level mutants must be rejected at their pinned sites (count pinned in LOCAL-PINS).
+  3. layer-end-controls on the promoted word, pinned count: ../layers/layer_end_controls.py (LayerReviewer-signed) for
+     base np; ../layers_p6n/layer_end_controls.py (Q6Reviewer-signed per-end variant) for base p6n.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs; the canonical word, local
+     programs and Clifford recipes are pinned (LOCAL-PINS).
+Moving to another recipe k is a recipe and pins swap; this driver does not change.
+Apache-2.0. Driver by ColdWitness around BlockInvert's constructor and controls.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+PKG = HERE.parents[1]
+LAYERS = HERE.parent / 'layers'
+BASES = {'np': ('layers/FULL-WORD.json.gz', 'a9de804f194eeb39f52a4c6e54c14d93e881bec4b632694249733ed410b58113'),
+         'p6n': ('p6n/FULL-WORD.json.gz', '34b683fa08f0')}   # p6n: prefix; full pin is the p6n recipe's output sha
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--base', choices=sorted(BASES), default='p6n')
+    ap.add_argument('--base-dir', type=Path, required=True, help='reproduce_np.py (np) or reproduce_p6n.py (p6n) output')
+    ap.add_argument('--k', default='p6n-k4', help='recipe id (PROMO-RECIPE-<k>.json)')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    recipe = HERE / ('PROMO-RECIPE-%s.json' % a.k); pins = read(HERE / ('LOCAL-PINS-%s.json' % a.k))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    rel, pin = BASES[a.base]; inp = a.base_dir.resolve() / rel
+    got = hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest()
+    assert got.startswith(pin) and got == read(recipe)['input_content_sha256'], ('input must be the pinned base word', a.base, got)
+    if a.base == 'p6n':
+        assert got == read(HERE.parent / 'layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz')['output_content_sha256']
+    run('promotion', HERE / 'build_promotion.py', '--input', inp, '--recipe', recipe, '--out', out / 'promo', portable=False)
+    word = out / 'promo/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == read(recipe)['expected']['output_content_sha256']
+    run('promo-controls', HERE / 'promo_controls.py', '--input', inp, '--recipe', recipe,
+        '--audit', PKG / 'independent/audit_local.py', '--out', out / 'PROMO-CONTROLS.json', portable=False)
+    pc = read(out / 'PROMO-CONTROLS.json'); assert pc['honest'] == 'PASS' and pc['rejected'] == pins['promo_controls'], pc['rejected']
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    ctlpy = (HERE.parent / 'layers_p6n/layer_end_controls.py') if a.base == 'p6n' else (LAYERS / 'layer_end_controls.py')
+    run('layer-end-controls', ctlpy, word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/reproduce.py b/research/gauge44-slots-t16/construction/reproduce.py
new file mode 100644
index 0000000000..8b51efa646
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/reproduce.py
@@ -0,0 +1,194 @@
+#!/usr/bin/env python3
+"""Rebuild the frozen gauge44 delta from two pinned upstream checkouts.
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+This driver calls the credited upstream constructors unchanged; it runs no
+search or optimizer. See ../CONSTRUCTION.md and INPUTS.json.
+"""
+import argparse
+import gzip
+import hashlib
+import importlib.util
+import json
+import os
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import time
+
+HERE = Path(__file__).resolve().parent
+
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw)
+
+
+def sha(path, content=False):
+    raw = path.read_bytes()
+    if content and path.suffix == '.gz':
+        raw = gzip.decompress(raw)
+    return hashlib.sha256(raw).hexdigest()
+
+
+def dump(path, value):
+    path.parent.mkdir(parents=True, exist_ok=True)
+    raw = json.dumps(value, sort_keys=True, separators=(',', ':')).encode()
+    path.write_bytes(gzip.compress(raw, mtime=0) if path.suffix == '.gz' else raw)
+
+
+def load_module(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def main():
+    assert __debug__, 'Assertions are required; do not use python -O.'
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--main', type=Path, required=True,
+                        help='integer-mult-bounds checkout at the pinned main commit')
+    parser.add_argument('--pr635', type=Path, required=True,
+                        help='integer-mult-bounds checkout at the pinned PR635 commit')
+    parser.add_argument('--out', type=Path, required=True,
+                        help='new output directory outside both checkouts')
+    parser.add_argument('--until', choices=('word', 'local', 'phases'), default='word',
+                        help='default: scalar constructor only; local adds exact native replay and wrappers')
+    parser.add_argument('--frozen-cold', action='store_true',
+                        help='splice the pinned cold recipe instead of deriving its exact Q/T matrices again')
+    args = parser.parse_args()
+    roots = {'main': args.main.resolve(), 'pr635': args.pr635.resolve(), 'delta': HERE}
+    out = args.out.resolve()
+    assert not out.exists(), 'Use a new output directory.'
+    assert not any(out.is_relative_to(root) for root in roots.values())
+    pins = read(HERE / 'INPUTS.json')
+    for family, files in pins['files'].items():
+        for relative, expected in files.items():
+            path = roots[family] / relative
+            assert sha(path) == expected, ('input pin', family, relative)
+    out.mkdir(parents=True)
+    upstream = roots['pr635'] / 'research/complex-571-cold14-st2'
+    source = roots['main'] / 'research/complex-k492-owner-repair/vendor/multicold'
+    joint = source.parent / 'joint_prefix'
+    base = source / 'vendor/pr558'
+    parent = base / 'vendor/pr552'
+    gk = parent / 'complex-local/static44/gk'
+    hamming = source.parent / 'direct_delivery/inputs/hamming'
+    structural = roots['main'] / 'research/structural-gain/frontier-composition'
+    runner = source / 'code/run_portable.py'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1',
+               PYTHONINTMAXSTRDIGITS='0', MULTICOLD_SOURCE=str(source),
+               GAIN_PR564_SOURCE=str(source))
+    env.pop('PYTHONOPTIMIZE', None)
+    records = []
+
+    def run(label, script, *arguments):
+        start = time.monotonic()
+        log = out / (label + '.log')
+        print('RUN', label, flush=True)
+        with log.open('w', encoding='utf-8') as stream:
+            result = subprocess.run([sys.executable, '-B', str(runner), str(script),
+                                     *map(str, arguments)], env=env, stdout=stream,
+                                    stderr=subprocess.STDOUT)
+        records.append({'step': label, 'exit_code': result.returncode,
+                        'seconds': round(time.monotonic() - start, 3)})
+        (out / 'STEPS.json').write_text(json.dumps(records, indent=2) + '\n')
+        if result.returncode:
+            raise RuntimeError(label + '\n' + log.read_text()[-6000:])
+        print('PASS', label, flush=True)
+
+    def check_word(label, path):
+        assert sha(path, content=True) == pins['word_content_sha256'][label], ('step pin', label)
+        return path
+
+    raw504 = parent / 'complex-local/static44/inputs/RAW504.json.gz'
+    promoted = structural / 'global-replay/base/split-centres/FULL-WORD.json.gz'
+    multi = structural / 'multicold-eight-word/FULL-WORD.json.gz'
+    early = out / 'shadow-early'
+    run('shadow-early', source / 'code/build_cold_kernel.py', '--input', promoted,
+        '--recipe', source / 'data/EIGHT-COLD.json', '--gk-dir', gk, '--out', early)
+    early_word = check_word('shadow-early', early / 'FULL-WORD.json.gz')
+    prefix = out / 'shadow-prefix'
+    run('shadow-prefix', joint / 'code/build_joint_prefix.py', '--input', multi,
+        '--recipe', joint / 'data/JOINT-PREFIX.json', '--variant', 'eightcold',
+        '--gk-dir', gk, '--out', prefix)
+    prefix_word = check_word('shadow-prefix', prefix / 'FULL-WORD.json.gz')
+
+    inputs = out / 'hamming'
+    inputs.mkdir()
+    for name in ('PROTOTYPE.json', 'PACKET-PROGRAMS.json.gz'):
+        shutil.copyfile(hamming / name, inputs / name)
+    shutil.copyfile(HERE / 'COMPLETION-PRIORITY.json', inputs / 'COMPLETION-PRIORITY.json')
+    raw = out / 'raw'
+    run('gauge-forward', HERE / 'construct_gauge_xcentre.py', inputs, raw,
+        upstream / 'data/TRI-SCHEDULE.json')
+    word = check_word('raw', raw / 'FULL-WORD.json.gz')
+    assert sha(raw / 'HELPER-MAP.json') == pins['helper_map_sha256']
+    chain = [raw504, promoted, early_word, multi, prefix_word]
+    for i, (before, after) in enumerate(zip(chain, chain[1:])):
+        target = out / ('port' + str(i))
+        run('port' + str(i), upstream / 'code/build_port_stage.py',
+            '--shadow-input', before, '--shadow-output', after, '--input', word,
+            '--map', raw / 'HELPER-MAP.json', '--gk-dir', gk, '--out', target)
+        word = check_word('port' + str(i), target / 'FULL-WORD.json.gz')
+
+    changed = read(word)
+    regroup = read(upstream / 'data/recipes/k492-jp8-frame_regroup.json')
+    # The inherited changes are B-only and are checked against the actual new gates.
+    for edit in regroup['changes']:
+        assert changed[edit['section']][edit['index']] == edit['before']
+        changed[edit['section']][edit['index']] = edit['after']
+    changed['report'].update(local_profile=regroup['after'],
+                             local_rank_mass=sum(int(r)*n for r, n in regroup['after'].items()))
+    word = out / 'regroup/FULL-WORD.json.gz'
+    dump(word, changed)
+    check_word('regroup', word)
+    hpe = load_module('upstream_hpe', upstream / 'code/build_hpe.py')
+    changed = hpe.apply(changed, read(upstream / 'data/recipes/k492-jp8-hyperplane_end.json')['changes'])
+    word = out / 'hpe/FULL-WORD.json.gz'
+    dump(word, changed)
+    check_word('hpe', word)
+
+    target = out / 'cold44'
+    if args.frozen_cold:
+        cold = load_module('upstream_cold', upstream / 'code/build_cold_end.py')
+        changed = cold.apply(changed, read(HERE / 'COLD44-RECIPE.json.gz'))
+        # Match the exact constructor's descriptive status; this is not an audit assertion.
+        changed['report']['status'] = 'EXACT_COLD44_CONSTRUCTED_PENDING_INDEPENDENT_AUDIT'
+        dump(target / 'FULL-WORD.json.gz', changed)
+    else:
+        run('cold44-exact', HERE / 'build_gauge_cold44.py', '--input', word,
+            '--out', target, '--hamming', inputs, '--upstream-package', upstream)
+        assert read(target / 'RECIPE.json.gz') == read(HERE / 'COLD44-RECIPE.json.gz')
+    word = check_word('cold44', target / 'FULL-WORD.json.gz')
+    report = read(word)['report']
+    assert report['local_rank_mass'] == 5650
+    assert report['local_profile'] == {'1': 2514, '2': 404, '3': 448, '4': 160, '5': 56, '8': 8}
+    assert report['width_inventory'] == {'4': 52, '5': 48, '7': 34, '8': 114, '9': 244}
+    print('PASS exact frozen scalar word', word, flush=True)
+    if args.until == 'word':
+        return
+
+    local = out / 'local'
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    run('native', upstream / 'code/hpe_audit_and_transport.py', '--raw', word,
+        '--routing', routing, '--out', local)
+    assert sha(local / 'CANONICAL-WORD.json.gz', content=True) == pins['canonical_content_sha256']
+    run('ledgers', upstream / 'code/hpe_emit_local.py', local)
+    run('local-replay', upstream / 'code/hpe_audit_local.py', local)
+    run('wrappers', upstream / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for orientation, expected in pins['local_program_sha256'].items():
+        assert checks[orientation]['sha256'] == expected
+    if args.until == 'phases':
+        clifford = parent / 'complex-global/vendor531/vendor/clifford'
+        run('phases', base / 'code/phases_full.py', local, clifford)
+        assert sha(local / 'CLIFFORD-RECIPES.json') == pins['clifford_recipes_sha256']
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/slots/RECIPE-SLOTS-k8.json b/research/gauge44-slots-t16/construction/slots/RECIPE-SLOTS-k8.json
new file mode 100644
index 0000000000..acc1a733d6
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/slots/RECIPE-SLOTS-k8.json
@@ -0,0 +1,991 @@
+{
+ "base_sha256": "db2c7cfb3f8eee2b76c2e0154fc530520fb4d90cd9511a002cab527b16033b83",
+ "B_delete": [
+  13,
+  15,
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+  1215,
+  1217,
+  1218,
+  1220,
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+  1225,
+  1226,
+  1228
+ ],
+ "B_insert": [
+  [
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+ ],
+ "B_frames": {},
+ "tail_insert": [
+  [
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+     64,
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+     24,
+     4,
+     2,
+     1
+    ]
+   ]
+  ]
+ ],
+ "cleanup_prepend": [
+  [
+   "add",
+   10,
+   439,
+   1,
+   2,
+   [
+    256,
+    128,
+    64,
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+  ],
+  [
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+    1
+   ]
+  ],
+  [
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+   1,
+   2,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
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+    4,
+    2,
+    1
+   ]
+  ],
+  [
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+   238,
+   2,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   303,
+   446,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
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+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ]
+ ],
+ "local_profile": {
+  "1": 2412,
+  "2": 418,
+  "3": 432,
+  "4": 142,
+  "5": 82,
+  "8": 8
+ },
+ "expect_sha256": "c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8",
+ "variants": [
+  {
+   "X": 444,
+   "E": 590,
+   "hold": [
+    34,
+    98
+   ]
+  },
+  {
+   "X": 446,
+   "E": 591,
+   "hold": [
+    303,
+    399
+   ]
+  },
+  {
+   "X": 238,
+   "E": 455,
+   "hold": [
+    545,
+    557
+   ]
+  },
+  {
+   "X": 434,
+   "E": 585,
+   "hold": [
+    287,
+    383
+   ]
+  },
+  {
+   "X": 436,
+   "E": 587,
+   "hold": [
+    319,
+    351
+   ]
+  },
+  {
+   "X": 236,
+   "E": 454,
+   "hold": [
+    544,
+    556
+   ]
+  },
+  {
+   "X": 439,
+   "E": 584,
+   "hold": [
+    10,
+    74
+   ]
+  }
+ ],
+ "source": "PR #987 (rohanarun) triangle-hybrid slots, transferred to k8 db2c7cfb by MineB; recipe U10k8",
+ "note": "early-cleanup gate frames in cleanup are kept as in base (package T-frame convention)"
+}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/construction/slots/SLOT-PINS-k8.json b/research/gauge44-slots-t16/construction/slots/SLOT-PINS-k8.json
new file mode 100644
index 0000000000..2702c368f4
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/slots/SLOT-PINS-k8.json
@@ -0,0 +1,47 @@
+{
+ "base_sha256": "db2c7cfb3f8eee2b76c2e0154fc530520fb4d90cd9511a002cab527b16033b83",
+ "word_sha256": "c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8",
+ "canonical_sha256": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c",
+ "program_sha256": {
+  "forward": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8",
+  "backward": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+ },
+ "clifford_recipes_sha256": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+ "slot_controls": [
+  "C0_identity",
+  "donation_after",
+  "donation_after@236",
+  "donation_after@238",
+  "donation_after@434",
+  "donation_after@436",
+  "donation_after@439",
+  "donation_after@444",
+  "donation_after@446",
+  "drop_preread",
+  "drop_preread@236",
+  "drop_preread@238",
+  "drop_preread@434",
+  "drop_preread@436",
+  "drop_preread@439",
+  "drop_preread@444",
+  "drop_preread@446",
+  "drop_restore",
+  "drop_restore@236",
+  "drop_restore@238",
+  "drop_restore@434",
+  "drop_restore@436",
+  "drop_restore@439",
+  "drop_restore@444",
+  "drop_restore@446",
+  "recipe",
+  "restore_full",
+  "restore_full@236",
+  "restore_full@238",
+  "restore_full@434",
+  "restore_full@436",
+  "restore_full@439",
+  "restore_full@444",
+  "restore_full@446"
+ ],
+ "kappa_decimal": "0.00167166528321877"
+}
diff --git a/research/gauge44-slots-t16/construction/slots/verify_slots.py b/research/gauge44-slots-t16/construction/slots/verify_slots.py
new file mode 100644
index 0000000000..fd06b654af
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/slots/verify_slots.py
@@ -0,0 +1,122 @@
+#!/usr/bin/env python3
+"""Slot layer on research/gauge44-leaver8 with explicit, hash-checked reuse of a completed k8 chain replay.
+
+Follows the repository's baseline-reuse pattern (cf. research/complex-t37-owners/verify.py --baseline799):
+the completed k8 replay is rechecked against the parent package's pins, and only the new layer is rebuilt.
+
+  1. parent manifest, then baseline: the completed reproduce_leaver_chain.py --id k8 output; its final word and its
+     canonical/program/Clifford locals must equal CHAIN-PINS-k8 and the final frame recipe's output pin.
+  2. slots: the reviewed construction/barch/build_tri.py (unchanged) with RECIPE-SLOTS-k8.json; output pinned.
+     All per-slot controls (run_controls.py, unchanged) must reject exactly as pinned.
+  3. native locals of the new word (the same steps as reproduce_leaver_chain step 9); canonical/programs/Clifford pinned.
+  4. independent audit_local on the new word.
+  5. strict global replay (verify_global.py) of this package's data on the new locals.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+PKG = HERE.parents[1]
+MUTANTS = ('drop_restore', 'restore_full', 'drop_preread', 'donation_after')  # as reproduce_leaver_chain.py
+# Complete step receipt of reproduce_leaver_chain.py --id k8 (unchanged driver of the parent package).
+CHAIN_STEPS = ['pivot-swap', 'cold44-exact', 'lec-p6n', 'promotion', 'promo-controls', 'lec-promo', 'jx',
+               'jx-control-C0_identity', 'jx-control-C1_741_only', 'jx-control-N3_plain_join_moved_reads', 'lec-jx',
+               'hybrids', 'hybrid-controls', 'lec-hyb', 'frames', 'lec-frames',
+               'native', 'ledgers', 'local-replay', 'wrappers', 'phases']
+
+
+def read(p):
+    b = Path(p).read_bytes()
+    return json.loads(gzip.decompress(b) if str(p).endswith('.gz') else b)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+def csha(p): return hashlib.sha256(gzip.decompress(Path(p).read_bytes())).hexdigest()
+def fsha(p): return hashlib.sha256(Path(p).read_bytes()).hexdigest()
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True, help='repository root')
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--baseline', type=Path, required=True,
+                    help='completed research/gauge44-leaver8 reproduce_leaver_chain.py --id k8 --out directory')
+    ap.add_argument('--work', type=Path, required=True)
+    a = ap.parse_args()
+    root = a.main.resolve(); work = a.work.resolve(); assert not work.exists(); work.mkdir(parents=True)
+    parent_pkg = root / 'research/gauge44-leaver8'
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = root / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; par = base / 'vendor/pr552'
+    routing = par / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    env.pop('PYTHONOPTIMIZE', None)
+    pins = read(HERE / 'SLOT-PINS-k8.json'); steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (work / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT, cwd=root)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (work / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+        return (work / (label + '.log')).read_text()
+
+    # 1. parent package and baseline coverage
+    run('parent-manifest', parent_pkg / 'verify_manifest.py', portable=False)
+    cp = read(parent_pkg / 'construction/leaver/CHAIN-PINS-k8.json')
+    fr = read(parent_pkg / 'construction/leaver/FRAME-RECIPE-LV-k8.json')
+    bl = a.baseline.resolve(); bw = bl / 'frames/FULL-WORD.json.gz'; blocal = bl / 'local'
+    bsteps = read(bl / 'STEPS.json')
+    assert [s['step'] for s in bsteps] == CHAIN_STEPS and all(s['exit_code'] == 0 for s in bsteps), 'baseline is not a complete k8 chain replay'
+    assert csha(bw) == fr['expected']['output_content_sha256'] == pins['base_sha256'], 'baseline final word'
+    assert hashlib.sha256(gzip.decompress((blocal / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == cp['canonical_sha256'], 'baseline canonical'
+    chk = read(blocal / 'LOCAL-CHECKS.json')
+    assert {o: chk[o]['sha256'] for o in ('forward', 'backward')} == cp['program_sha256'], 'baseline programs'
+    assert fsha(blocal / 'CLIFFORD-RECIPES.json') == cp['clifford_recipes_sha256'], 'baseline Clifford'
+    for lab in ('lec-p6n', 'lec-promo', 'lec-jx', 'lec-hyb', 'lec-frames'):
+        c = read(bl / lab / 'COLD-END-CONTROLS.json')
+        assert c['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(c['rejected']) == cp[lab], 'baseline ' + lab
+    print('PASS baseline', flush=True)
+
+    # 2. slot layer with the reviewed builder and controls (unchanged files from research/gauge44-leaver8)
+    barch = parent_pkg / 'construction/barch'; rec = HERE / 'RECIPE-SLOTS-k8.json'; r = read(rec)
+    assert r['base_sha256'] == pins['base_sha256'] and r['expect_sha256'] == pins['word_sha256']
+    (work / 'slots').mkdir(); fw = work / 'slots/FULL-WORD.json.gz'
+    run('slots', barch / 'build_tri.py', bw, rec, fw, portable=False)
+    assert csha(fw) == pins['word_sha256'], 'slot word'
+    run('slot-controls', barch / 'run_controls.py', bw, rec, parent_pkg / 'independent/audit_local.py', work / 'slot-controls', portable=False)
+    res = read(work / 'slot-controls/controls.json')
+    want = ['C0_identity', 'recipe', *MUTANTS] + [m + '@' + str(v['X']) for v in r.get('variants', []) for m in MUTANTS]
+    assert sorted(res) == sorted(want) == sorted(pins['slot_controls']) and all(x['ok'] for x in res.values()), res
+
+    # 3. native locals of the new word
+    local = work / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', fw, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256']
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz', local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    chk = read(local / 'LOCAL-CHECKS.json')
+    assert {o: chk[o]['sha256'] for o in ('forward', 'backward')} == pins['program_sha256']
+    run('phases', base / 'code/phases_full.py', local, par / 'complex-global/vendor531/vendor/clifford')
+    assert fsha(local / 'CLIFFORD-RECIPES.json') == pins['clifford_recipes_sha256']
+
+    # 4. independent local audit; 5. strict global replay of this package's data
+    run('audit-local', PKG / 'independent/audit_local.py', '--word', fw, '--main', root, '--output', work / 'AUDIT-LOCAL.json', portable=False)
+    assert read(work / 'AUDIT-LOCAL.json')['status'] == 'PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES'
+    out = run('strict', PKG / 'verify_global.py', '--main', root, '--local', local, '--work', work / 'global', portable=False)
+    last = [l for l in out.splitlines() if l.startswith('PASS_GAUGE44')][-1]
+    assert last.split()[1] == pins['kappa_decimal'], last
+    res = dict(status='PASS_SLOTS_ON_CHECKED_K8_BASELINE', kappa_decimal=pins['kappa_decimal'], strict=last,
+               baseline=str(bl), steps=steps)
+    (work / 'RESULT.json').write_text(json.dumps(res, indent=1) + '\n')
+    print(res['status'], pins['kappa_decimal'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/sw4/LOCAL-PINS-sw4-P6k4.json b/research/gauge44-slots-t16/construction/sw4/LOCAL-PINS-sw4-P6k4.json
new file mode 100644
index 0000000000..ae26a0f2f1
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/sw4/LOCAL-PINS-sw4-P6k4.json
@@ -0,0 +1,11 @@
+{
+ "word": "P6k4sw4",
+ "sw4_controls": 4,
+ "layer_controls": 95,
+ "canonical_sha256": "5f5f163e43e8c21c16e2f10aef0078131d127a1ccacc39e0238d111fbd29f195",
+ "program_sha256": {
+  "forward": "36e75fc972766fa42f1b371a055e74976a165c894b816911c3510a88b431ea09",
+  "backward": "3176ccde98d90e754105e60096598fee348e2455e046290d3674b79dd6b402df"
+ },
+ "clifford_recipes_sha256": "202eeaf5fac0c801b98811c1e140fd0af443090d7f7e05c7b55a4ddc6f6acdab"
+}
diff --git a/research/gauge44-slots-t16/construction/sw4/NOTES.md b/research/gauge44-slots-t16/construction/sw4/NOTES.md
new file mode 100644
index 0000000000..2a53ffb3b8
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/sw4/NOTES.md
@@ -0,0 +1,21 @@
+# SW4: read-set exchange on 4 entering-copy pairs
+
+- **Input.** P6k3, sha a38bb414.
+- **Output.** sha f35a852b. Strict PASS at κ 0.001659645685315104, which is +3.267e-7 over P6k3 and equal to the ideal.
+- **Width.** W 3782 is unchanged, as are start_extra, helper_final, cleanup and the helper numbering.
+- **Rebuild.** `python build_sw4.py INPUT OUT [SW4-RECIPE.json]`. It is a deterministic apply of the 16 explicit moves, with 4 pinned controls: C0 (identity), N1 (keeping the pre-read is rejected), N2 (a partial exchange is rejected) and N3 (a wrong-sign pre-read is rejected).
+
+## Move
+For each pair (h,r) in {(461,25), (581,89), (591,415), (603,431)}, where h = E_h + r after h's copy gate:
+- every post-copy target read of h becomes a read of r, and that target's entrance pre-read of h is deleted;
+- every target read of r becomes a read of h, with the pre-read add(t,h,−c) inserted after h's last pre-read, while h = E_h.
+
+The B-end state of every register is unchanged (checked mod p).
+
+## How exhaustive the search was
+These 4 are the only positives within an exactly defined family.
+- **Copy pair.** h is an entering helper whose first B write is add(h,r,1/1) from a non-target r, and whose only earlier B gates are single target pre-reads. NP has 107 such pairs.
+- **Candidates.** Every nonempty subset of one pair's movable reads (target reads of h or r between the copy and the next write of h or r), with all other pairs left unchanged. That is 602 candidates over the 54 pairs that have reads.
+- **Outcome.** 564 are frame-illegal. The 38 legal ones are all full single-pair exchanges, and only these 4 are positive. Their gains are additive.
+
+**What is not covered.** Cross-pair combinations of partial moves were not enumerated. Without a decomposition proof (moves can shrink as well as grow target frames), the result is exhaustive only within this single-pair family.
diff --git a/research/gauge44-slots-t16/construction/sw4/SW4-RECIPE-P6k4.json b/research/gauge44-slots-t16/construction/sw4/SW4-RECIPE-P6k4.json
new file mode 100644
index 0000000000..b9dea4152a
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/sw4/SW4-RECIPE-P6k4.json
@@ -0,0 +1,314 @@
+{
+ "name": "SW4",
+ "description": "BRoute read-set exchange on entering-copy pairs (h,r); indices refer to the input word B section",
+ "input_sha256": "0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073",
+ "output_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+ "pairs": {
+  "461": 25,
+  "581": 89,
+  "591": 415,
+  "603": 431
+ },
+ "moves": [
+  {
+   "kind": "h2r",
+   "h": 461,
+   "r": 25,
+   "read_index": 856,
+   "target": 168,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 27
+  },
+  {
+   "kind": "h2r",
+   "h": 461,
+   "r": 25,
+   "read_index": 1208,
+   "target": 128,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 26
+  },
+  {
+   "kind": "r2h",
+   "h": 461,
+   "r": 25,
+   "read_index": 873,
+   "target": 129,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 28,
+   "preread": [
+    "add",
+    129,
+    461,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 461,
+   "r": 25,
+   "read_index": 1193,
+   "target": 169,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 28,
+   "preread": [
+    "add",
+    169,
+    461,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 581,
+   "r": 89,
+   "read_index": 860,
+   "target": 171,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 58
+  },
+  {
+   "kind": "h2r",
+   "h": 581,
+   "r": 89,
+   "read_index": 1288,
+   "target": 192,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 59
+  },
+  {
+   "kind": "r2h",
+   "h": 581,
+   "r": 89,
+   "read_index": 953,
+   "target": 193,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 60,
+   "preread": [
+    "add",
+    193,
+    581,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 581,
+   "r": 89,
+   "read_index": 1197,
+   "target": 175,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 60,
+   "preread": [
+    "add",
+    175,
+    581,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 591,
+   "r": 415,
+   "read_index": 868,
+   "target": 139,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 62
+  },
+  {
+   "kind": "h2r",
+   "h": 591,
+   "r": 415,
+   "read_index": 1296,
+   "target": 160,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 63
+  },
+  {
+   "kind": "r2h",
+   "h": 591,
+   "r": 415,
+   "read_index": 961,
+   "target": 161,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 64,
+   "preread": [
+    "add",
+    161,
+    591,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 591,
+   "r": 415,
+   "read_index": 1205,
+   "target": 143,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 64,
+   "preread": [
+    "add",
+    143,
+    591,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 603,
+   "r": 431,
+   "read_index": 876,
+   "target": 131,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 70
+  },
+  {
+   "kind": "h2r",
+   "h": 603,
+   "r": 431,
+   "read_index": 1300,
+   "target": 163,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 71
+  },
+  {
+   "kind": "r2h",
+   "h": 603,
+   "r": 431,
+   "read_index": 965,
+   "target": 167,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 72,
+   "preread": [
+    "add",
+    167,
+    603,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 603,
+   "r": 431,
+   "read_index": 1213,
+   "target": 135,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 72,
+   "preread": [
+    "add",
+    135,
+    603,
+    -1,
+    1
+   ]
+  }
+ ],
+ "kappa_ideal_in": 0.0016603565408383088,
+ "kappa_ideal_out": 0.0016606836036204419,
+ "W": 3778,
+ "profile_in": {
+  "1": 2572,
+  "2": 326,
+  "3": 430,
+  "4": 194,
+  "5": 56,
+  "8": 8
+ },
+ "profile_out": {
+  "1": 2548,
+  "2": 342,
+  "3": 438,
+  "4": 186,
+  "5": 56,
+  "8": 8
+ },
+ "width_inventory": {
+  "4": 80,
+  "5": 32,
+  "7": 54,
+  "8": 122,
+  "9": 216
+ },
+ "rejection_expected": {
+  "N1": {
+   "changed_registers": [
+    168,
+    171
+   ],
+   "n": 2
+  },
+  "N2": {
+   "first": [
+    "cap",
+    1192,
+    169
+   ],
+   "n": 10
+  },
+  "N3": {
+   "changed_registers": [
+    129,
+    130,
+    169,
+    170
+   ],
+   "n": 4
+  }
+ }
+}
diff --git a/research/gauge44-slots-t16/construction/sw4/build_sw4.py b/research/gauge44-slots-t16/construction/sw4/build_sw4.py
new file mode 100644
index 0000000000..617e0ed06d
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/sw4/build_sw4.py
@@ -0,0 +1,203 @@
+#!/usr/bin/env python3
+"""build_sw4.py INPUT_WORD OUT_DIR [RECIPE] : deterministic, standard-library-only rebuild of the BRoute SW4 word.
+
+SW4 exchanges the B-phase target read sets of four entering packet copies h and their face registers r
+(h = E_h + r after h's copy gate; E_h = h's entering content):
+  h2r: a post-copy read add(t,h,c) becomes add(t,r,c), and t's entrance pre-read add(t,h,-c) (taken while h = E_h) is deleted;
+  r2h: a read add(t,r,c) becomes add(t,h,c), and a pre-read add(t,h,-c) is inserted before index insert_preread_before
+       (right after h's last existing pre-read, still before h's copy gate).
+Every register holds the same value at the end of B (checked mod p). Frames: a moved or inserted gate gets the plain join of
+its operands' current frames; every other B gate and every early-cleanup tail keeps span(old frame + current operand frames).
+Targets must stay inside u_t^perp, and tails and ends must contain the current frame.
+
+Controls (run on every build; the count is pinned to 4 and all must hold, else exit 1):
+  C0 the identity recipe (no moves) reproduces the input B and early_cleanup byte for byte;
+  N1 h2r without deleting the pre-read is rejected by exactness;
+  N2 a partial exchange (one read only) is rejected by the frame cap;
+  N3 an inserted pre-read with the wrong sign is rejected by exactness.
+Rejection sites are pinned: the recipe's 'rejection_expected' gives, for N1/N3, the exact set of target rows whose B-end
+state changes (the mutated target plus its butterfly partner(s)) and, for N2, the first cap violation (kind, B index,
+register) and the violation count. Each control must reproduce its pinned site exactly. BUILD.json records the observed
+sites under 'rejection'.
+Writes OUT_DIR/FULL-WORD.json.gz (sha checked against the recipe) and OUT_DIR/BUILD.json."""
+import sys, json, gzip, hashlib, os
+from collections import Counter, defaultdict
+
+PR = 2147483629
+HERE = os.path.dirname(os.path.abspath(__file__))
+V, HH = 112, 9
+
+
+def basis(vs):
+    piv = {}
+    for a in vs:
+        while a:
+            bit = a.bit_length() - 1
+            if bit in piv: a ^= piv[bit]
+            else:
+                piv[bit] = a; break
+    for k in sorted(piv):
+        for j in piv:
+            if j > k and piv[j] >> k & 1: piv[j] ^= piv[k]
+    return tuple(piv[k] for k in sorted(piv, reverse=True))
+
+
+def contained(a, b): return basis(list(a) + list(b)) == tuple(b)
+def registers(e): return e[1:3] if e[0] == 'add' else e[1:2]
+def hyper(p): return basis([x for x in range(1, 1 << HH) if (x & p).bit_count() % 2 == 0])
+FULL = basis([1 << i for i in range(HH)])
+
+
+def coef(e):
+    a, b = (e[3], e[4]) if e[0] == 'add' else (e[2], e[3])
+    return a % PR * pow(b % PR, PR - 2, PR) % PR
+
+
+def bend_state(w):
+    """sparse rows mod p of every register after A + cut + B (identity start)."""
+    n = 2 * V + w['report']['R']; rows = [{i: 1} for i in range(n)]
+    for e in w['A'] + w['cut'] + w['B']:
+        q = coef(e); t = e[1]
+        if e[0] == 'scale': rows[t] = {k: x * q % PR for k, x in rows[t].items()}
+        else:
+            d = rows[t]
+            for k, x in rows[e[2]].items():
+                y = (d.get(k, 0) + q * x) % PR
+                if y: d[k] = y
+                else: d.pop(k, None)
+    return rows
+
+
+def apply_recipe(w, moves, drop_delete=False, wrong_sign=False):
+    B = [list(e[:-1]) + [list(e[-1]) if e[-1] is not None else None] for e in w['B']]
+    tag = {}; dele = set(); ins = defaultdict(list)
+    for m in moves:
+        i = m['read_index']; e = B[i]; t = m['target']; a, b = m['coef']
+        assert e[0] == 'add' and e[1] == t and [e[3], e[4]] == [a, b], ('recipe/word mismatch', m)
+        if m['kind'] == 'h2r':
+            assert e[2] == m['h']
+            pi = m['delete_preread_index']; g = B[pi]
+            assert g[:5] == ['add', t, m['h'], -a, b], ('pre-read mismatch', m)
+            B[i] = ['add', t, m['r'], a, b, e[-1]]
+            if not drop_delete: dele.add(pi)
+        else:
+            assert e[2] == m['r']
+            B[i] = ['add', t, m['h'], a, b, e[-1]]
+            g = list(m['preread'])
+            if wrong_sign: g[3] = -g[3]
+            ins[m['insert_preread_before']].append(g + [None])
+        tag[i] = 1
+    NB, nt = [], []
+    for i, e in enumerate(B):
+        for g in ins.get(i, []): NB.append(g); nt.append(1)
+        if i in dele: continue
+        NB.append(e); nt.append(tag.get(i, 0))
+    w2 = dict(w); w2['B'] = NB; w2['early_cleanup'] = [list(x) for x in w.get('early_cleanup', [])]
+    return w2, nt
+
+
+def refit(w, nt):
+    n = 2 * V + w['report']['R']
+    cur = [(p,) for p in w['ports']] + [()] * (n - V)
+    for q, U in w['start_extra'].items(): cur[int(q)] = basis(U)
+    for e in w['A']:
+        for q in registers(e): cur[q] = basis(e[-1])
+    prob = []
+    for i, e in enumerate(w['B']):
+        rs = registers(e)
+        base = [] if nt[i] or e[-1] is None else list(e[-1])
+        F = basis(base + [x for q in rs for x in cur[q]])
+        for q in rs:
+            if V <= q < 2 * V and not contained(F, hyper(w['ports'][q - V])): prob.append(('cap', i, q))
+        e[-1] = list(F)
+        for q in rs: cur[q] = F
+    ne = []
+    for i, U in w.get('early_cleanup', []):
+        rs = registers(w['cleanup'][i]); F = basis(list(U) + [x for q in rs for x in cur[q]])
+        for q in rs:
+            fin = w['helper_final'].get(str(q))
+            if fin is not None and not contained(F, basis(fin)): prob.append(('tail', i, q))
+        ne.append([i, list(F)])
+        for q in rs: cur[q] = F
+    w['early_cleanup'] = ne
+    for q in range(2 * V, n):
+        fin = w['helper_final'].get(str(q))
+        if fin is not None and not contained(cur[q], basis(fin)): prob.append(('end', q))
+    return prob
+
+
+def profile(w):
+    n = 2 * V + w['report']['R']
+    tail = [w['cleanup'][i][:-1] + [U] for i, U in w.get('early_cleanup', [])]
+    end = [FULL] * V + [hyper(p) for p in w['ports']] + [FULL] * (n - 2 * V)
+    for q, U in w['helper_final'].items(): end[int(q)] = basis(U)
+    start = [(p,) for p in w['ports']] + [()] * (n - V)
+    for q, U in w['start_extra'].items(): start[int(q)] = basis(U)
+    cur = list(start); paid = Counter()
+    def climb(q, U):
+        U = basis(U); assert contained(cur[q], U), ('monotone', q)
+        d = len(U) - len(cur[q])
+        if d: paid[d] += 1
+        cur[q] = U
+    for sec in ('A', 'B'):
+        if sec == 'B':
+            lev = {int(t): basis(U) for t, U in w.get('target_levels', {}).items()}
+            for q, U in zip(w['centers'], w['center_frames']):
+                U = basis(U); served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == q}
+                for T in sorted(served, key=lambda x: -len(x)):
+                    if T != U: paid[len(U) - len(T)] += 1
+                    U = T
+        for e in w[sec]:
+            for q in registers(e): climb(q, e[-1])
+    for e in tail:
+        for q in registers(e): climb(q, e[-1])
+    for q, U in enumerate(end): climb(q, U)
+    widths = Counter(len(end[q]) - len(start[q]) for q in range(2 * V, n))
+    return paid, widths
+
+
+def enc(w): return json.dumps(w, sort_keys=True, separators=(',', ':')).encode()
+
+
+def main():
+    src, out = sys.argv[1], sys.argv[2]
+    rec = json.load(open(sys.argv[3] if len(sys.argv) > 3 else os.path.join(HERE, 'SW4-RECIPE.json')))
+    raw = gzip.decompress(open(src, 'rb').read())
+    assert hashlib.sha256(raw).hexdigest() == rec['input_sha256'], 'input sha mismatch'
+    w = json.loads(raw); S0 = bend_state(w); moves = rec['moves']
+    h0 = moves[0]['h']; one = [m for m in moves if m['h'] == h0]
+    ctl = {}; why = {}; EXP = rec.get('rejection_expected', {})
+    if os.environ.get('SW4_PIN') != '1' and set(EXP) != {'N1', 'N2', 'N3'}: raise SystemExit('recipe rejection_expected must pin exactly N1, N2, N3 (set SW4_PIN=1 to record)')
+    def diff(S):
+        d = [q for q in range(len(S0)) if S[q] != S0[q]]
+        return dict(changed_registers=d[:8], n=len(d))
+    w0, nt0 = apply_recipe(w, []); p0 = refit(w0, nt0)
+    ctl['C0_identity'] = not p0 and w0['B'] == w['B'] and w0['early_cleanup'] == w['early_cleanup']
+    m1 = [m for m in one if m['kind'] == 'h2r'][:1]
+    w1, nt1 = apply_recipe(w, m1, drop_delete=True); d1 = diff(bend_state(w1))
+    ctl['N1_keep_preread_rejected'] = d1['n'] > 0 and d1 == EXP.get('N1', d1); why['N1'] = d1
+    w2, nt2 = apply_recipe(w, m1); p2 = refit(w2, nt2)
+    why['N2'] = dict(first=list(p2[0]) if p2 else None, n=len(p2)); ctl['N2_partial_rejected'] = bool(p2) and p2[0][0] == 'cap' and why['N2'] == EXP.get('N2', why['N2'])
+    w3, nt3 = apply_recipe(w, one, wrong_sign=True); d3 = diff(bend_state(w3))
+    ctl['N3_wrong_sign_rejected'] = d3['n'] > 0 and d3 == EXP.get('N3', d3); why['N3'] = d3
+    assert len(ctl) == 4
+    wn, nt = apply_recipe(w, moves); pr = refit(wn, nt)
+    assert not pr, ('illegal', pr[:5])
+    assert bend_state(wn) == S0, 'B-end state changed'
+    paid, widths = profile(wn)
+    wn['report'] = dict(wn['report'], local_profile={str(k): v for k, v in sorted(paid.items())},
+                        local_rank_mass=sum(k * v for k, v in paid.items()))
+    data = enc(wn); sha = hashlib.sha256(data).hexdigest()
+    os.makedirs(out, exist_ok=True)
+    with open(os.path.join(out, 'FULL-WORD.json.gz'), 'wb') as f: f.write(gzip.compress(data, mtime=0))
+    rep = dict(recipe=rec['name'], input_sha256=rec['input_sha256'], output_sha256=sha, expected_output_sha256=rec['output_sha256'],
+               moves=len(moves), controls=ctl, rejection=why, profile=wn['report']['local_profile'],
+               widths={str(k): v for k, v in sorted(widths.items()) if k}, W=sum(k * v for k, v in widths.items()))
+    with open(os.path.join(out, 'BUILD.json'), 'w', newline='\n') as f: f.write(json.dumps(rep, indent=1) + '\n')
+    print(json.dumps(rep, indent=1))
+    ok = all(ctl.values()) and sha == rec['output_sha256'] and rep['profile'] == rec['profile_out'] and rep['W'] == rec['W']
+    sys.exit(0 if ok else 1)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/construction/sw4/reproduce_sw4.py b/research/gauge44-slots-t16/construction/sw4/reproduce_sw4.py
new file mode 100644
index 0000000000..cb038e064b
--- /dev/null
+++ b/research/gauge44-slots-t16/construction/sw4/reproduce_sw4.py
@@ -0,0 +1,87 @@
+#!/usr/bin/env python3
+"""Rebuild the SW4 word (BRoute read-set exchange on four entering-copy pairs) and its native locals.
+
+Input: a fresh `construction/promo/reproduce_promo.py --base p6n --k <promo recipe>` output directory; its promoted
+word is pinned there and by SW4-RECIPE-<id>.json (this package: --k p6n-k4, P6k4 0390ec65..., recipe P6k4). Steps, each checked exactly:
+  1. sw4: BRoute's build_sw4.py (standard library only). It applies the 16 explicit moves of SW4-RECIPE-<id>.json:
+     every listed read of h becomes a read of its face register r and vice versa, with the entrance pre-reads deleted
+     or inserted. It checks the B-end state of every register mod p, the frame caps, tails and ends, and the output sha
+     and profile. Its controls C0, N1, N2 and N3 run on every build and must all hold (count pinned to 4).
+  2. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant, Q6Reviewer-signed) on the SW4 word;
+     the count is pinned in LOCAL-PINS-sw4-<id>.json.
+  3. native, ledgers, local-replay, wrappers, phases: PR635's native local programs. The canonical word, local
+     programs and Clifford recipes are pinned (LOCAL-PINS-sw4-<id>.json).
+Apache-2.0. Driver by ColdWitness around BRoute's constructor.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P6 = HERE.parent / 'layers_p6n'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--promo-dir', type=Path, required=True, help='construction/promo/reproduce_promo.py output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--recipe', default='P6k4', help='SW4-RECIPE-<id>.json and LOCAL-PINS-sw4-<id>.json')
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('SW4-RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-sw4-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    inp = a.promo_dir.resolve() / 'promo/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['input_sha256'], 'input must be the pinned promoted word'
+    run('sw4', HERE / 'build_sw4.py', inp, out / 'sw4', rfile, portable=False)
+    b = read(out / 'sw4/BUILD.json')
+    assert len(b['controls']) == pins['sw4_controls'] and all(b['controls'].values()), b['controls']
+    word = out / 'sw4/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['output_sha256']
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/data/FRONTIER.json b/research/gauge44-slots-t16/data/FRONTIER.json
new file mode 100644
index 0000000000..70285d4d85
--- /dev/null
+++ b/research/gauge44-slots-t16/data/FRONTIER.json
@@ -0,0 +1,36 @@
+{
+  "checked_at_utc": "2026-10-13 00:54:29 UTC",
+  "construction_base": {
+    "pr": 635,
+    "commit": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f",
+    "kappa": "0.001636241501576388"
+  },
+  "latest_pr": 642,
+  "strongest_reported_pr": 641,
+  "comparisons": [
+    {
+      "number": 641,
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/641",
+      "title": "Conditional κ = 0.001636523543003976: cost-neutral pivot swaps with four entering ends (s4) on PR635",
+      "head_sha": "ff580ea5407aa427d64233523e46ee0afe24a766",
+      "head_repo": "jeremykothe2/integer-mult-bounds",
+      "created_at": "2026-10-13T00:36:30Z",
+      "updated_at": "2026-10-13T00:36:30Z",
+      "reported_kappa": "0.001636523543003976"
+    },
+    {
+      "number": 642,
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/642",
+      "title": "Conditional κ = 0.001636472098484378: selective helper-249 dispatch",
+      "head_sha": "d1154e23e13d85fdbf64d4b41fa20bb0f56a428f",
+      "head_repo": "vectorsss/integer-mult-bounds",
+      "created_at": "2026-10-13T00:40:40Z",
+      "updated_at": "2026-10-13T00:46:54Z",
+      "reported_kappa": "0.001636472098484378"
+    }
+  ],
+  "new_kappa": "0.001649483702558979",
+  "gain_over_641_percent": "0.791932362379189601995955118466917211009518325743405547289975",
+  "gain_over_642_percent": "0.795100881136422911010672021375626721886288268207407873093008",
+  "scope": "PR641/642 values are their public reported conditional witnesses, not independently replayed here. This delta retains the pinned PR635 construction ancestry and replaces its local supplier and whole-owner dispatch; it does not claim to compose the later pivot swaps or helper249 end."
+}
diff --git a/research/gauge44-slots-t16/data/OWNERS.json.gz b/research/gauge44-slots-t16/data/OWNERS.json.gz
new file mode 100644
index 0000000000..4feb34a056
Binary files /dev/null and b/research/gauge44-slots-t16/data/OWNERS.json.gz differ
diff --git a/research/gauge44-slots-t16/data/PLAN.json b/research/gauge44-slots-t16/data/PLAN.json
new file mode 100644
index 0000000000..b9fd05136f
--- /dev/null
+++ b/research/gauge44-slots-t16/data/PLAN.json
@@ -0,0 +1,85660 @@
+{
+  "status": "FROZEN_EXPLICIT_T16_TWO_BANK_DIRECT_SUM_OWNER_NOMINATION",
+  "mode": "gauge44-all144-t16-idle-concentration",
+  "K": 4,
+  "T": 16,
+  "M": 73,
+  "L": 9,
+  "live": 14336,
+  "deficit": 5120,
+  "profile": {
+    "1": 349608,
+    "2": 60192,
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+}
diff --git a/research/gauge44-slots-t16/data/SPEC.json b/research/gauge44-slots-t16/data/SPEC.json
new file mode 100644
index 0000000000..9d14c3c215
--- /dev/null
+++ b/research/gauge44-slots-t16/data/SPEC.json
@@ -0,0 +1,1972 @@
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diff --git a/research/gauge44-slots-t16/data/T8/OWNERS.json.gz b/research/gauge44-slots-t16/data/T8/OWNERS.json.gz
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index 0000000000..8eda84ea0c
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diff --git a/research/gauge44-slots-t16/data/T8/PLAN.json b/research/gauge44-slots-t16/data/T8/PLAN.json
new file mode 100644
index 0000000000..0465492a1f
--- /dev/null
+++ b/research/gauge44-slots-t16/data/T8/PLAN.json
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diff --git a/research/gauge44-slots-t16/data/UPSTREAM-PINS.json b/research/gauge44-slots-t16/data/UPSTREAM-PINS.json
new file mode 100644
index 0000000000..68486b84e3
--- /dev/null
+++ b/research/gauge44-slots-t16/data/UPSTREAM-PINS.json
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+  "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+  "research/complex-k492-owner-repair/vendor/multicold/inputs/PR543-EXPECTED.json": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz": "025448abdf2012d327e50a009084e1501690d05e650300d2982836aa0350ae00",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz": "de2be0f4b6d24ace368fd5b834b7a00f9625d0a1824c4ff969f2db5f115db667",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/prepare_supplier_base.py": "f5eae94aca965d0008bc07cff8245ccb7509042ccad457d3bcb7d51c1e9409f0"
+}
diff --git a/research/gauge44-slots-t16/evidence/ADMISSION-CONTROLS.json b/research/gauge44-slots-t16/evidence/ADMISSION-CONTROLS.json
new file mode 100644
index 0000000000..2e15a10065
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/ADMISSION-CONTROLS.json
@@ -0,0 +1,102 @@
+{
+  "status": "PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS",
+  "valid_receipt_kappa": "1649483702558979/1000000000000000000",
+  "input_sha256": {
+    "owner_audit": "a32ecc0d5387d65648e1ff284209122860ee37aaba43ce2dd12024c4bc394313",
+    "fresh_invoice": "14b0f41c88209e800236ce4ebbf91d83537e22e18807153d90013f7eee57a582",
+    "inputs/PR543-EXPECTED.json": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d",
+    "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+  },
+  "assembler_sha256": "7ac28118d69416e4fb67b61216285fb0823310b7635ce1b9025aa3f10119ef6a",
+  "rejected_controls": [
+    "empty_certification_maps",
+    "failed_invoice_status",
+    "nonboolean_precision_check",
+    "wrong_owner_role_count",
+    "understated_physical_stock",
+    "changed_profile_same_rank_mass",
+    "insufficient_finite_C0",
+    "missing_finite_check",
+    "wrong_reflected_orientation_selfconsistent_totals",
+    "missing_selected_call",
+    "wrong_selected_primitive_sum",
+    "wrong_selected_coefficient_work_sum",
+    "unpaid_wrapper_factors",
+    "wrong_global_compiler",
+    "wrong_global_adapter_maximum",
+    "understated_exact_prefix_and_global_sum",
+    "wrong_global_prefix_sum",
+    "wrong_row_prefix_reserve",
+    "wrong_parent_geometry_charge",
+    "wrong_rebased_geometry_charge",
+    "wrong_complete_pervertex_envelope",
+    "wrong_prior_added_complete_invoice",
+    "wrong_finite_router_bits",
+    "wrong_finite_literal_bits",
+    "wrong_finite_physical_stock_bits",
+    "wrong_finite_row_coefficient",
+    "reordered_complete_calls",
+    "understated_explicit_idle_remainders",
+    "understated_actual_chart_types",
+    "wrong_cross_replica_role_count",
+    "old_no_cold_wrapper_counts_selfconsistent",
+    "gauge44:missing_provider",
+    "gauge44:missing_backward_orientation",
+    "gauge44:unpaid_scalar_primitive",
+    "gauge44:wrong_local_artifact_binding",
+    "gauge44:false_dirty_restoration",
+    "gauge44:wrong_declared_provider_count",
+    "gauge44:wrong_local_compiler",
+    "gauge44:wrong_local_adapter_charge",
+    "gauge44:wrong_local_primitive_bound",
+    "gauge44:forged_provider_and_call_program_hash",
+    "gauge44:provider_at_wrong_call",
+    "gauge44:synchronized_forged_source_recipe_hash",
+    "gauge44:synchronized_forged_phase_review_semantics",
+    "gauge44:width_order_swap_4_5",
+    "gauge44:width_inventory_shift_4_5",
+    "gauge44:width_order_swap_4_7",
+    "gauge44:width_inventory_shift_4_7",
+    "gauge44:width_order_swap_4_8",
+    "gauge44:width_inventory_shift_4_8",
+    "gauge44:width_order_swap_4_9",
+    "gauge44:width_inventory_shift_4_9",
+    "gauge44:width_order_swap_5_7",
+    "gauge44:width_inventory_shift_5_7",
+    "gauge44:width_order_swap_5_8",
+    "gauge44:width_inventory_shift_5_8",
+    "gauge44:width_order_swap_5_9",
+    "gauge44:width_inventory_shift_5_9",
+    "gauge44:width_order_swap_7_8",
+    "gauge44:width_inventory_shift_7_8",
+    "gauge44:width_order_swap_7_9",
+    "gauge44:width_inventory_shift_7_9",
+    "gauge44:width_order_swap_8_9",
+    "gauge44:width_inventory_shift_8_9",
+    "gauge44:cold_helper_width_swap_264",
+    "gauge44:cold_helper_width_swap_276",
+    "gauge44:cold_helper_width_swap_288",
+    "gauge44:cold_helper_width_swap_300",
+    "wrong_owner_receipt_hash"
+  ],
+  "discovery_accepted_controls": [],
+  "exact_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "conservative_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "recurrence_model_controls": [
+    "native_complex_endpoint_rejected_with_old_surcharge",
+    "omitting_bit_surcharge_would_fail_next_endpoint_rejection"
+  ],
+  "scope": "Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay."
+}
diff --git a/research/gauge44-slots-t16/evidence/ASSEMBLY.json b/research/gauge44-slots-t16/evidence/ASSEMBLY.json
new file mode 100644
index 0000000000..6feaaf28f5
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/ASSEMBLY.json
@@ -0,0 +1,336 @@
+{
+  "status": "PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY",
+  "kappa": "1649483702558979/1000000000000000000",
+  "kappa_decimal": "0.001649483702558979",
+  "complex_lower": "1652208994368411824947/1000000000000000000000000",
+  "complex_decimal": "0.001652208994368411824947",
+  "bit_lower": "413456747036699736067/250000000000000000000000",
+  "bit_decimal": "0.001653826988146798944268",
+  "binding": "complex",
+  "gain_over_pr635_percent": "0.8093060205252829126484020359439672024956960385078942889840023844750830",
+  "complex_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "surcharge_model": {
+    "complex": false,
+    "bit": true
+  },
+  "conservative_complex_lower": "826104495740783435531/500000000000000000000000",
+  "conservative_complex_decimal": "0.001652208991481566871062",
+  "conservative_kappa": "32989673993633/20000000000000000",
+  "conservative_kappa_decimal": "0.00164948369968165",
+  "conservative_moments": [
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "826104495740783435531/500000000000000000000000",
+      "accept": true,
+      "mercator": [
+        "-21470727653278306311183666306239229019733127/13479973333575319897333507543509815336818572211270286240551805124608",
+        "-10735363826639153155591833153119614509866563/6739986666787659948666753771754907668409286105635143120275902562304"
+      ],
+      "base_two": [
+        "-497746012127833654257/312500000000000000000000000000000000000000000",
+        "-15927862388090676936081/10000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "1652208991481566871063/1000000000000000000000000",
+      "accept": false,
+      "mercator": [
+        "18565857384700607217299861034814026061253869/13479973333575319897333507543509815336818572211270286240551805124608",
+        "9282928692350303608649930517407013030626935/6739986666787659948666753771754907668409286105635143120275902562304"
+      ],
+      "base_two": [
+        "3443229403069298452661/2500000000000000000000000000000000000000000000",
+        "6886463806138596905393/5000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "conservative_bootstrap": [
+    {
+      "exponent": "412385685180656454166549264744655866734211385357236332091088842586409092836277952888766748039/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "gap": "666562689735263598950072203096262874070849142763667908911157413590907163722047111233251961/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "5064079519162"
+    },
+    {
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+      "cutoff_log2": "1855113791006194394"
+    },
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+      "cutoff_log2": "679580003544484094184219"
+    },
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+      "cutoff_log2": "248949139107542177224284717390"
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+      "cutoff_log2": "91197023954707297182834066510188309"
+    },
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+      "cutoff_log2": "33408017428823827582408170997246977713592"
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+    {
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+      "cutoff_log2": "12238290024451914798381844566546350371351403966"
+    }
+  ],
+  "conservative_outer": {
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+    "beta_positive": "1/1000000000000000000000000",
+    "beta_below_one": "999999999999999999999999/1000000000000000000000000",
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+    "q_below_reservations": "1/4000000000000000000000000",
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+  },
+  "controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the same cited unchanged PR543 bit supplier as PR635. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/gauge44-slots-t16/evidence/BINDING.json b/research/gauge44-slots-t16/evidence/BINDING.json
new file mode 100644
index 0000000000..b03160c67a
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/BINDING.json
@@ -0,0 +1,25 @@
+{
+  "status": "PASS_FROZEN_048_ALLCOLD_DISPATCH_FRESH_PROVIDER_BINDING",
+  "source_plan_sha256": "8c4804859aee83082196348c33127070d2885d3a366ce9acc8dc5166202f4687",
+  "runtime_plan_sha256": "609adb126d7d3de2abdd9275f9015589c0b137d0d19821c2c3e7c1a8541c18d2",
+  "providers": {
+    "gauge44": {
+      "artifact_sha256": {
+        "CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+        "LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+        "LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+        "INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+        "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+        "CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12",
+        "RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94"
+      },
+      "canonical_content_sha256": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+      "all_phase_edges": 3019
+    }
+  },
+  "only_rebound_fields": [
+    "provider_registry.directory",
+    "provider_registry.artifact_sha256",
+    "runtime_source_plan_sha256"
+  ]
+}
diff --git a/research/gauge44-slots-t16/evidence/CENTER-COMPATIBILITY.json b/research/gauge44-slots-t16/evidence/CENTER-COMPATIBILITY.json
new file mode 100644
index 0000000000..5a3ae37422
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/CENTER-COMPATIBILITY.json
@@ -0,0 +1,112 @@
+{
+  "status": "PASS_IDENTICAL_PORT_ORDER_AND_ORDERED_CENTER_FRAMES",
+  "new_canonical_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+  "comparison_canonical": "pr635/research/community-k492-audit/pr626/replay/mixed-global/base/split-centres/CANONICAL-WORD.json.gz",
+  "comparison_canonical_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+  "new_centers": [
+    92,
+    57,
+    81,
+    224,
+    11,
+    240,
+    9,
+    256
+  ],
+  "old_centers": [
+    229,
+    224,
+    227,
+    225,
+    243,
+    241,
+    259,
+    257
+  ],
+  "ordered_center_frames": [
+    [
+      256,
+      128,
+      64,
+      34,
+      16,
+      10,
+      4,
+      1
+    ],
+    [
+      256,
+      128,
+      64,
+      32,
+      16,
+      8,
+      5,
+      3
+    ],
+    [
+      256,
+      128,
+      64,
+      32,
+      17,
+      9,
+      4,
+      2
+    ],
+    [
+      256,
+      128,
+      64,
+      36,
+      20,
+      8,
+      2,
+      1
+    ],
+    [
+      256,
+      128,
+      66,
+      32,
+      18,
+      8,
+      4,
+      1
+    ],
+    [
+      256,
+      128,
+      65,
+      33,
+      17,
+      9,
+      5,
+      3
+    ],
+    [
+      256,
+      128,
+      65,
+      33,
+      16,
+      8,
+      4,
+      2
+    ],
+    [
+      256,
+      128,
+      68,
+      32,
+      16,
+      12,
+      2,
+      1
+    ]
+  ],
+  "v": 112,
+  "h": 9,
+  "center_count": 8,
+  "scope": "Carrier register identity changes; native cut center channels retain exact ordered frames and ports. Full endpoint and exact center clearing are independently checked by local ledger replay."
+}
diff --git a/research/gauge44-slots-t16/evidence/LOCAL-STAGES.json b/research/gauge44-slots-t16/evidence/LOCAL-STAGES.json
new file mode 100644
index 0000000000..b2753eb57a
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/LOCAL-STAGES.json
@@ -0,0 +1,27 @@
+[
+  {
+    "tag": "44-native",
+    "seconds": 4.460461161999774,
+    "exit": 0
+  },
+  {
+    "tag": "44-emitted-ledgers",
+    "seconds": 3.058037757999955,
+    "exit": 0
+  },
+  {
+    "tag": "44-local-replay",
+    "seconds": 28.33760359400003,
+    "exit": 0
+  },
+  {
+    "tag": "44-wrappers",
+    "seconds": 5.294312295000054,
+    "exit": 0
+  },
+  {
+    "tag": "44-phase",
+    "seconds": 198.39076561599995,
+    "exit": 0
+  }
+]
diff --git a/research/gauge44-slots-t16/evidence/REPLAY.json b/research/gauge44-slots-t16/evidence/REPLAY.json
new file mode 100644
index 0000000000..c6f4e0f983
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/REPLAY.json
@@ -0,0 +1,54 @@
+{
+  "status": "PASS_GAUGE44_STRICT_GLOBAL_REPLAY",
+  "kappa": "1649483702558979/1000000000000000000",
+  "kappa_decimal": "0.001649483702558979",
+  "complex_lower": "1652208994368411824947/1000000000000000000000000",
+  "bit_lower": "413456747036699736067/250000000000000000000000",
+  "gain_over_pr635_percent": "0.8093060205252829126484020359439672024956960385078942889840023844750830",
+  "spec_sha256": "fee57674a7f36b30b1e7eb96a8f567a90a522217bc644c1a6a1f8bff85196fbf",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 2.152,
+      "exit_code": 0,
+      "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.686,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "emit",
+      "seconds": 5.456,
+      "exit_code": 0,
+      "log_sha256": "60866eb6ced5b9eb259bfc1d59ea7b80fb439164b629e868586ad5bef845a88e"
+    },
+    {
+      "name": "audit",
+      "seconds": 26.943,
+      "exit_code": 0,
+      "log_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662"
+    },
+    {
+      "name": "invoice",
+      "seconds": 1.897,
+      "exit_code": 0,
+      "log_sha256": "5d10712d494304287749dd7a6c3369f9b707bba30e9f567b68230669dcf5418a"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.724,
+      "exit_code": 0,
+      "log_sha256": "768d3215f1918117dc6c33b4cfeaf0b5f5da9ba5c77178db4bb1d08d000e226f"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 0.816,
+      "exit_code": 0,
+      "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+    }
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the same cited unchanged PR543 bit supplier as PR635. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/gauge44-slots-t16/evidence/STAGES.json b/research/gauge44-slots-t16/evidence/STAGES.json
new file mode 100644
index 0000000000..9464e2dfea
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/STAGES.json
@@ -0,0 +1,44 @@
+[
+  {
+    "name": "restore-parent",
+    "seconds": 2.152,
+    "exit_code": 0,
+    "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+  },
+  {
+    "name": "bind",
+    "seconds": 0.686,
+    "exit_code": 0,
+    "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+  },
+  {
+    "name": "emit",
+    "seconds": 5.456,
+    "exit_code": 0,
+    "log_sha256": "60866eb6ced5b9eb259bfc1d59ea7b80fb439164b629e868586ad5bef845a88e"
+  },
+  {
+    "name": "audit",
+    "seconds": 26.943,
+    "exit_code": 0,
+    "log_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662"
+  },
+  {
+    "name": "invoice",
+    "seconds": 1.897,
+    "exit_code": 0,
+    "log_sha256": "5d10712d494304287749dd7a6c3369f9b707bba30e9f567b68230669dcf5418a"
+  },
+  {
+    "name": "assembly",
+    "seconds": 0.724,
+    "exit_code": 0,
+    "log_sha256": "768d3215f1918117dc6c33b4cfeaf0b5f5da9ba5c77178db4bb1d08d000e226f"
+  },
+  {
+    "name": "admission-controls",
+    "seconds": 0.816,
+    "exit_code": 0,
+    "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+  }
+]
diff --git a/research/gauge44-slots-t16/evidence/audit/ASYNC-AUDIT.json b/research/gauge44-slots-t16/evidence/audit/ASYNC-AUDIT.json
new file mode 100644
index 0000000000..05975382b5
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/audit/ASYNC-AUDIT.json
@@ -0,0 +1,84 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "complex_template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "complex_live": 7168,
+  "complex_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "complex_hosted_residuals": 35424,
+  "physical": 7670,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "entering_helper_roles": 17856,
+  "cross_replica_helper_roles": 25937,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 35424,
+  "complete_invocations": 72,
+  "actual_orthogonal_73column_maps": 7870,
+  "actual_sigma_stream_sha256": "f4e9802acb2ed53fc1f0486e7d0f55a6faa30ed7f5d2ad48a06450234b00ba76",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 2759,
+  "mutations_rejected": [
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit idle remainder",
+    "understate physical reserve",
+    "gauge44: wrong provider at its invocation",
+    "gauge44: stale per-call local program hash",
+    "gauge44: stale serialized provider program",
+    "gauge44: unbound residual adapter hash",
+    "gauge44: wrong provider width registry",
+    "gauge44: wrong per-call residual width",
+    "gauge44: wrong sweep provider",
+    "gauge44: entering helper width silently restored to nine"
+  ],
+  "mutation_controls_run": true,
+  "provider_phase_semantic_sha256": {
+    "gauge44": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152"
+  },
+  "provider_artifact_semantic_sha256": {
+    "gauge44": {
+      "CANONICAL-WORD.json.gz": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+      "LOCAL-PROGRAMS.json.gz": "39b230dba9e6b022c691cd0167f331c1b3fa6795d49256e3a2b859c68d4acfda",
+      "LOCAL-CHECKS.json": "bd53e0cca4488f365ca5b7c7174d8dfb35ced5e0229835f27334c11c3d839717",
+      "INDEPENDENT-LOCAL-REPLAY.json": "adb5c8ce0b5025dcd96f41b9fa0e26b9a176e067ab36a5bfadad00bc19522b38",
+      "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+      "CLIFFORD-REVIEW.json": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152",
+      "RESIDUAL-ADAPTERS.json": "c233611dd4c08c389dfb6c7d1c84dd86a3efa560223fcd6549a2848692541cd9"
+    }
+  },
+  "widths_by_provider": {
+    "gauge44": {
+      "4": 52,
+      "5": 48,
+      "7": 34,
+      "8": 114,
+      "9": 244
+    }
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "all_provider_program_phase_and_wrapper_bindings": true,
+  "scope": "Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations."
+}
diff --git a/research/gauge44-slots-t16/evidence/audit/GLOBAL-PREFIX.json b/research/gauge44-slots-t16/evidence/audit/GLOBAL-PREFIX.json
new file mode 100644
index 0000000000..a557ebbe60
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/audit/GLOBAL-PREFIX.json
@@ -0,0 +1,13 @@
+{
+  "status": "PASS_MIXED_ASYNC_GLOBAL_PREFIX",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "global_prefix_bits": 360,
+  "retained_payload_bits": 512,
+  "complete_invocation_cover_sweeps": 72,
+  "bridge_factor_two_sweeps": 72,
+  "local_scalar_coefficient_work_prefix_bits": 175,
+  "stream_input_sup_to_l2_bits": 37,
+  "primitive_arithmetic_margin_bits": 4,
+  "controller_audit_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662",
+  "proof": "Each selected normalized provider restores all arbitrary dirty helper columns and gives the same data shear endpoints. Actual whole-owner charts are right-translation bijections. Sum all 72 invocation and 72 bridge sweeps and take maximum local scalar/Horner prefix over all three providers and orientations. Idle children, phases, spectator endpoints and terminal translations are unitary. Retained all-size interfaces are conditional."
+}
diff --git a/research/gauge44-slots-t16/evidence/audit/IDLE-REMAINDER-FRAMES.json b/research/gauge44-slots-t16/evidence/audit/IDLE-REMAINDER-FRAMES.json
new file mode 100644
index 0000000000..1c86a8a01d
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/audit/IDLE-REMAINDER-FRAMES.json
@@ -0,0 +1,25 @@
+{
+  "status": "PASS_LITERAL_IDLE_REMAINDER_FRAMES",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "uncompressed_frames_sha256": "38eba7dfe023d0b2a8aea1c5184e50bdfff5727b350c2de4d27800acbdd3708c",
+  "children": 2759,
+  "rank_profile": {
+    "1": 85,
+    "2": 76,
+    "3": 173,
+    "7": 7,
+    "8": 6,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "source_data_phase_sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+  "scope": "Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child."
+}
diff --git a/research/gauge44-slots-t16/evidence/audit/OWNERS-AND-PROFILE.json b/research/gauge44-slots-t16/evidence/audit/OWNERS-AND-PROFILE.json
new file mode 100644
index 0000000000..bdb9441b7e
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/audit/OWNERS-AND-PROFILE.json
@@ -0,0 +1,61 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "paid_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "live": 7168,
+  "physical": 7670,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "hosted_residuals": 35424,
+  "banked_residuals": 0,
+  "all_live_owners_per_call_distinct": true,
+  "owners_per_call": 716,
+  "actual_helper_owner_charts": 35424,
+  "actual_73column_sigmas": 7870,
+  "cross_replica_helper_roles": 25937,
+  "explicit_idle_remainder_children": 2759,
+  "source_idle_children_charged": 16128,
+  "source_artifacts": {
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "providers/gauge44/CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+    "providers/gauge44/LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+    "providers/gauge44/LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+    "providers/gauge44/INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+    "providers/gauge44/RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94",
+    "providers/gauge44/CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+    "providers/gauge44/CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12"
+  },
+  "provider_phase_semantic_sha256": {
+    "gauge44": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152"
+  },
+  "provider_artifact_semantic_sha256": {
+    "gauge44": {
+      "CANONICAL-WORD.json.gz": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+      "LOCAL-PROGRAMS.json.gz": "39b230dba9e6b022c691cd0167f331c1b3fa6795d49256e3a2b859c68d4acfda",
+      "LOCAL-CHECKS.json": "bd53e0cca4488f365ca5b7c7174d8dfb35ced5e0229835f27334c11c3d839717",
+      "INDEPENDENT-LOCAL-REPLAY.json": "adb5c8ce0b5025dcd96f41b9fa0e26b9a176e067ab36a5bfadad00bc19522b38",
+      "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+      "CLIFFORD-REVIEW.json": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152",
+      "RESIDUAL-ADAPTERS.json": "c233611dd4c08c389dfb6c7d1c84dd86a3efa560223fcd6549a2848692541cd9"
+    }
+  },
+  "controller_audit_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662"
+}
diff --git a/research/gauge44-slots-t16/evidence/audit/PREFIX-AND-INVOICE.json b/research/gauge44-slots-t16/evidence/audit/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..6c96ec6706
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/audit/PREFIX-AND-INVOICE.json
@@ -0,0 +1,1746 @@
+{
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+    },
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+    },
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+    },
+    {
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+    },
+    {
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+      "pre_wrappers": 248,
+      "post_wrappers": 248
+    }
+  ],
+  "selected_local_paid_profile": {
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+    "2": 29088,
+    "3": 32256,
+    "4": 11520,
+    "5": 4032,
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+  "selected_real_component_primitives": 30245280,
+  "selected_coefficient_work_primitive_count": 15028288,
+  "selected_scalar_macros": 2993040,
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+  "charged_prefix_bits": 512,
+  "complete_invocation_sweeps": 72,
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+  "centres": 8,
+  "live": 7168,
+  "physical": 7670,
+  "physical_stock_identity": {
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+    "local_helpers": 492,
+    "private_centres": 8,
+    "coefficient_work": 2
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+  "local_adapters": 738816,
+  "local_primitive_bound": 19160702806276,
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+    "previous_pervertex_allowance": 2877946989724568,
+    "added_complete_new_pervertex": 2486201168471768,
+    "policy": "Retain old allowance and add entire fresh mixed recount."
+  },
+  "finite": {
+    "physical_stock_bits": 2641,
+    "router_bits": 7986,
+    "literal_bits": 35282,
+    "physical_row_coefficient": 16467,
+    "retained_row_coefficient": 20161,
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+    "halving_integer_inequality": [
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+      4608
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+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. All three providers use fresh hash-bound independent all-column/frame/phase/normalization admission. Shared compiler uses conservative maxima; parent is geometry/overcharge only. All-size compiler, hosting, precision/tape and analytic transfer remain conditional."
+}
diff --git a/research/gauge44-slots-t16/evidence/global/ACTUAL-SIGMAS.json.gz b/research/gauge44-slots-t16/evidence/global/ACTUAL-SIGMAS.json.gz
new file mode 100644
index 0000000000..dbb57066e2
Binary files /dev/null and b/research/gauge44-slots-t16/evidence/global/ACTUAL-SIGMAS.json.gz differ
diff --git a/research/gauge44-slots-t16/evidence/global/GLOBAL-TEMPLATE.json.gz b/research/gauge44-slots-t16/evidence/global/GLOBAL-TEMPLATE.json.gz
new file mode 100644
index 0000000000..424c2df489
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diff --git a/research/gauge44-slots-t16/evidence/global/HOSTED.json b/research/gauge44-slots-t16/evidence/global/HOSTED.json
new file mode 100644
index 0000000000..498e849ab7
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/global/HOSTED.json
@@ -0,0 +1,60 @@
+{
+  "status": "EMITTED_MIXED_PROVIDER_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "parent_template_sha256": "7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3",
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+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "hosted_residuals": 35424,
+  "banks_per_stage": [
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+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0
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+  "entering_helper_roles": 17856,
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+  "cross_replica_helper_roles": 25937,
+  "asynchronous_order_sha256": "2acd6b2004be3d3ef6645f3c968feb22b5167c400bb49eb446821e5cb7af6eee",
+  "source_artifacts": {
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+    "providers/gauge44/CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+    "providers/gauge44/LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+    "providers/gauge44/LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+    "providers/gauge44/INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+    "providers/gauge44/RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94",
+    "providers/gauge44/CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+    "providers/gauge44/CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12"
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "scope": "Two actual verified plain/width-seven providers dispatched per complete invocation; independent controller/spectator/normalization and complete finite invoice admission required."
+}
diff --git a/research/gauge44-slots-t16/evidence/global/IDLE-REMAINDER-FRAMES.json.gz b/research/gauge44-slots-t16/evidence/global/IDLE-REMAINDER-FRAMES.json.gz
new file mode 100644
index 0000000000..3562e60f05
Binary files /dev/null and b/research/gauge44-slots-t16/evidence/global/IDLE-REMAINDER-FRAMES.json.gz differ
diff --git a/research/gauge44-slots-t16/evidence/layers/LOCAL-AUDIT-LAYERED.json b/research/gauge44-slots-t16/evidence/layers/LOCAL-AUDIT-LAYERED.json
new file mode 100644
index 0000000000..0780787674
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/layers/LOCAL-AUDIT-LAYERED.json
@@ -0,0 +1,137 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+  "input_file": "FULL-WORD.json.gz",
+  "content_sha256": "db2c7cfb3f8eee2b76c2e0154fc530520fb4d90cd9511a002cab527b16033b83",
+  "compressed_sha256": "3b268a3adb543e930454e9d9405e5f7a664c75c487f6c5cbe29c199f24a89789",
+  "parent_center_interface": {
+    "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+    "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "transport_tau": 43,
+    "ordered_frame_bases_match": true,
+    "all_ports_match": true,
+    "transported_centers": [
+      92,
+      57,
+      81,
+      224,
+      11,
+      240,
+      9,
+      256
+    ],
+    "source_centers": [
+      92,
+      57,
+      81,
+      11,
+      9
+    ],
+    "ordered_frame_bases": [
+      [
+        256,
+        128,
+        64,
+        34,
+        16,
+        10,
+        4,
+        1
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+      [
+        256,
+        128,
+        64,
+        32,
+        16,
+        8,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        17,
+        9,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ],
+      [
+        256,
+        128,
+        66,
+        32,
+        18,
+        8,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        17,
+        9,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        16,
+        8,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        68,
+        32,
+        16,
+        12,
+        2,
+        1
+      ]
+    ]
+  },
+  "v": 112,
+  "h": 9,
+  "R": 480,
+  "entering": 192,
+  "lowends": 78,
+  "coldends": 48,
+  "compensation_gates": 7208,
+  "local_profile": {
+    "1": 2412,
+    "2": 418,
+    "3": 418,
+    "4": 170,
+    "5": 68,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 56,
+    "5": 32,
+    "7": 30,
+    "8": 122,
+    "9": 240
+  },
+  "checked_columns": 704,
+  "elapsed_seconds": 0.8600000000005821,
+  "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+}
diff --git a/research/gauge44-slots-t16/evidence/leaver/CELL-MUTANTS-LV.json b/research/gauge44-slots-t16/evidence/leaver/CELL-MUTANTS-LV.json
new file mode 100644
index 0000000000..4d4ef7403c
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/leaver/CELL-MUTANTS-LV.json
@@ -0,0 +1,261 @@
+{
+ "c01m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_233": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [233])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [172, 175])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [132, 135, 173, 174])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_233": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [233])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c01p": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_57": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [57, 58, 224, 225, 226])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [169, 170])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [129, 130, 168, 171])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_57": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [57, 58, 224, 225, 226])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c23m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_58": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [58])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [169, 170])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [173, 174, 196, 199])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_58": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [58])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c23p": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_239": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [60, 63, 231, 232, 238, 239])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [172, 175])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [168, 171, 193, 194])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_239": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [60, 63, 231, 232, 238, 239])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c45m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_441": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [52, 55, 439, 440, 446, 447])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [137, 138])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [141, 142, 164, 167])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_441": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [52, 55, 439, 440, 446, 447])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c45p": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_255": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [28, 31, 247, 248, 254, 255])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [140, 143])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [136, 139, 161, 162])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_255": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [28, 31, 247, 248, 254, 255])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c67m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_18": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [18])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [129, 130])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [133, 134, 161, 162])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_18": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [18])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-slots-t16/evidence/leaver/FRAME-CONTROLS-LV-k8.json b/research/gauge44-slots-t16/evidence/leaver/FRAME-CONTROLS-LV-k8.json
new file mode 100644
index 0000000000..9f56e21000
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/leaver/FRAME-CONTROLS-LV-k8.json
@@ -0,0 +1,54 @@
+{
+ "base": "c836d892",
+ "recipe": "FRAME-RECIPE-LV-k8.json",
+ "controls": {
+  "shrink_raised_B": {
+   "builder": "profile and width pins",
+   "stage": "native_atc",
+   "native": "PASS",
+   "rc": 0,
+   "reason": "}",
+   "frame": [
+    "B",
+    539
+   ]
+  },
+  "shrink_lowered_B": {
+   "builder": "('nonmonotone', 174)",
+   "stage": "apply",
+   "reason": "('nonmonotone', 174)"
+  },
+  "shrink_T": {
+   "builder": "('nonmonotone', 554)",
+   "stage": "apply",
+   "reason": "('nonmonotone', 554)"
+  },
+  "empty_B": {
+   "builder": "('nonmonotone', 169)",
+   "stage": "apply",
+   "reason": "('nonmonotone', 169)"
+  },
+  "drop_one_lowering": {
+   "builder": "output word pin",
+   "stage": "native_atc",
+   "native": "PASS",
+   "rc": 0,
+   "reason": "}",
+   "frame": [
+    "B",
+    1232
+   ]
+  },
+  "drop_one_raise": {
+   "builder": "profile and width pins",
+   "stage": "native_atc",
+   "native": "PASS",
+   "rc": 0,
+   "reason": "}",
+   "frame": [
+    "B",
+    539
+   ]
+  }
+ }
+}
diff --git a/research/gauge44-slots-t16/evidence/local/CANONICAL-WORD.json.gz b/research/gauge44-slots-t16/evidence/local/CANONICAL-WORD.json.gz
new file mode 100644
index 0000000000..5062a1f62f
Binary files /dev/null and b/research/gauge44-slots-t16/evidence/local/CANONICAL-WORD.json.gz differ
diff --git a/research/gauge44-slots-t16/evidence/local/CLIFFORD-RECIPES.json b/research/gauge44-slots-t16/evidence/local/CLIFFORD-RECIPES.json
new file mode 100644
index 0000000000..3ba8326d3a
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/local/CLIFFORD-RECIPES.json
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new file mode 100644
index 0000000000..6b12ae0e4b
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/local/CLIFFORD-REVIEW.json
@@ -0,0 +1,19 @@
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+  "all_child_equalities_include_global_phase": true,
+  "recipe_sha256": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
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+}
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new file mode 100644
index 0000000000..447d45d08b
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new file mode 100644
index 0000000000..aa15edfba5
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/local/INDEPENDENT-LOCAL-REPLAY.json
@@ -0,0 +1,71 @@
+{
+  "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY",
+  "canonical_word_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+  "local_programs_sha256": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
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+      "private_work_erased": true
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+      "prefix_bits_upper": 134,
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+    "wrong_common_frame",
+    "wrong_child_rank",
+    "missing_pre_wrapper",
+    "missing_post_wrapper",
+    "wrapper_with_wrong_frame",
+    "wrapper_in_wrong_phase",
+    "wrapper_on_a_data_register",
+    "wrapper_on_a_target_register",
+    "wrapper_on_a_centre_register",
+    "hpe_pre_wrapper_resolved_to_full_recipe",
+    "hpe_post_wrapper_without_terminal_frame",
+    "hpe_post_wrapper_wrong_terminal_frame",
+    "hpe_tail_gate_at_full_frame",
+    "hpe_tail_climb_dropped",
+    "hpe_helper_exit_adapter_to_full",
+    "hpe_tail_gate_moved_into_full_cleanup",
+    "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter",
+    "cold_hpe_pre_wrapper_dropped",
+    "cold_hpe_post_wrapper_replaced_by_exit_adapter",
+    "cold_hpe_pre_wrapper_resolved_to_cold_full_convention",
+    "cold_hpe_wrapper_with_nonzero_entrance",
+    "cold_hpe_post_wrapper_wrong_terminal_frame",
+    "cold_hpe_premix_gate_before_pre_wrapper"
+  ],
+  "scope": "Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate."
+}
diff --git a/research/gauge44-slots-t16/evidence/local/LOCAL-CHECKS.json b/research/gauge44-slots-t16/evidence/local/LOCAL-CHECKS.json
new file mode 100644
index 0000000000..3872f0e596
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/local/LOCAL-CHECKS.json
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diff --git a/research/gauge44-slots-t16/evidence/local/WRAPPER-CHECKS.json b/research/gauge44-slots-t16/evidence/local/WRAPPER-CHECKS.json
new file mode 100644
index 0000000000..a18afd4fad
--- /dev/null
+++ b/research/gauge44-slots-t16/evidence/local/WRAPPER-CHECKS.json
@@ -0,0 +1,413 @@
+{
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+}
diff --git a/research/gauge44-slots-t16/hosting/PROOF.md b/research/gauge44-slots-t16/hosting/PROOF.md
new file mode 100644
index 0000000000..b551b6d3e5
--- /dev/null
+++ b/research/gauge44-slots-t16/hosting/PROOF.md
@@ -0,0 +1,237 @@
+# Exact owner reuse and concave-cost matching
+
+## 1. Objects and interface assumptions
+
+The parent controller has 72 ordered calls, 112 source ports, 112 target ports,
+and 492 helper roles per call. The ambient dimension is 73. A pending-child
+group is a triple
+
+$$
+g=(\text{owner replica},\text{child},\text{port}).
+$$
+
+The parent window catalogue gives group capacity $C_g$, together with the call
+times at which its physical stream is idle. The map from a group to its
+physical family is
+
+$$
+F(g)=896\,\text{owner replica}
+  +112(2\,\text{pair(child)}+\text{side(child)})+\text{port}.
+$$
+
+At every call in this particular parent geometry, at most one pending child of
+a physical family is eligible. Both the matcher and the independent frozen
+audit check this condition. They also exclude both active data families of the
+call. Consequently, injective assignment to eligible groups is equivalent to
+assignment to distinct idle physical families at that call.
+
+Helper $h$ requests an integer width $w_h$, read afresh from the new local
+word as the final-frame dimension minus the start-frame dimension. Native
+program profiles are also recomputed from their paid edges. The finite local
+compiler supplies the normalized helper chart and verifies its warm-start
+semantics. A hosted width is a reservation in the pending child's address
+coordinates on an existing physical stream; it is not a new physical stream.
+
+This proof concerns the discrete assignment and its moment contribution. It
+uses the parent windows as input. Independent global admission must verify
+those windows against the actual controller and construct the actual
+73-column charts for the fresh native local word.
+
+## 2. Feasible shrinking on the original families
+
+For one call, sort the old slot widths and the new helper widths increasingly,
+breaking ties by the old or new helper number. Suppose the new width in each
+position is no larger than its matched old width. Assign that helper to the
+matched old slot.
+
+This operation preserves the call time, stage, replica, pending child, port,
+owner replica, and physical family. It preserves the set of 492 distinct
+helper-owner families at the call, so the old window and active-data
+exclusions still hold. In each pending-child group, the sum of new widths is
+no larger than the old sum, hence remains within capacity.
+
+Now order the assignments in each group consistently and replace their
+offsets by consecutive prefix sums. The occupied sets become pairwise
+disjoint intervals whose union is exactly a prefix of length
+$U_g=\sum w_h\le C_g$. The idle child retains rank $C_g-U_g$, with pending
+offset $U_g$. Thus the shrinking operation has a direct capacity proof; it
+requires neither an owner solver nor any change to the controller.
+
+The seed constructor applies this termwise argument to the 71 former `jp8`
+calls. It keeps the remaining `ck` call provisionally unchanged. Two optional
+fixed-family assignment passes redistribute the available capacity before
+freezing the seed. Their result is audited using the same integer constraints.
+
+## 3. One call with all other calls fixed
+
+Fix one call $t$. Remove its existing assignments while keeping every other
+call fixed. For each eligible group, define the available capacity
+
+$$
+c_g=C_g-\sum_{\substack{\text{assignments in }g\\\text{from calls other than }t}}w.
+$$
+
+The call must assign each of its 492 widths to a distinct eligible group with
+$w\le c_g$. Unused groups can be viewed as receiving a dummy width zero.
+After the assignment, group $g$'s idle rank is $c_g-w_g$. For any function
+$\phi$, the portion of the idle objective affected by the call is exactly
+
+$$
+\sum_{g\text{ eligible at }t}\phi(c_g-w_g).
+$$
+
+All other idle contributions, and all local paid-edge contributions, are
+constant in this single-call problem.
+
+### Greedy rule
+
+Sort eligible capacities increasingly. At each capacity, assign the largest
+remaining helper width that fits; assign zero if none fits. Continue through
+the remaining capacities.
+
+This rule has no floating parameter. Equal-capacity tie choices are used only
+to limit changes to physical owners and make the artifact deterministic.
+
+### Exchange lemma
+
+Take two capacities $c_1\le c_2$ and two widths $w_1\le w_2\le c_1$. The
+assignment of $w_1$ to $c_1$ and $w_2$ to $c_2$ has residual pair
+
+$$
+(c_1-w_1,\ c_2-w_2).
+$$
+
+Exchange the widths. Feasibility is preserved, and the new pair is
+
+$$
+(c_1-w_2,\ c_2-w_1).
+$$
+
+The total is unchanged. The first new component is no larger than either old
+component, and the second is no smaller than either old component. Therefore
+the new pair majorizes the old pair. Every concave $\phi$ has weakly smaller
+sum on the new pair.
+
+### Consequence: feasibility and optimality
+
+Start from any feasible complete assignment. At the smallest remaining
+capacity, its assigned width is no larger than the largest remaining width
+that fits. The greedy width occurs at some later capacity. If the two differ,
+the exchange lemma moves that width to the current capacity while preserving
+feasibility and weakly decreasing every concave objective. Fix this first
+position and repeat on the suffix. Dummy zero widths cover unused groups.
+
+Thus the greedy procedure succeeds whenever a feasible assignment exists, and
+its remainder vector majorizes that of every feasible assignment. It
+simultaneously minimizes every concave remainder objective for this call.
+This proof depends on the absence of any eligibility restriction beyond the
+capacity and the already fixed call window; that property is explicitly
+checked for the present geometry.
+
+## 4. Exact majorization receipts
+
+Let $a_r$ and $b_r$ be the old and new remainder histograms for one update,
+including zero remainders. When the helper-width multiset is unchanged, their
+total numbers of groups and total ranks agree. Every remainder lies between
+0 and 48. The implementation checks, with integers, that for each
+$k=0,1,\ldots,48$,
+
+$$
+\sum_r b_r\max(r-k,0)
+\;\ge\;
+\sum_r a_r\max(r-k,0).
+$$
+
+These are the stored stop-loss margins. Between integer breakpoints the
+difference is linear, so checking all integer breakpoints checks every real
+threshold. With equal sums and equal lengths, the inequalities are the
+standard majorization criterion: the new vector majorizes the old one.
+
+The transcript contains 288 such equal-width updates: four passes through 72
+calls. A single preceding update replaces the seed's last `ck` width multiset.
+That bootstrap has different total width, so it is checked for exact
+feasibility and is not represented as an equal-sum majorization step.
+
+`reproduce.py` reruns every update and compares the full transcript's semantic
+hash. Independently, `audit_frozen.py` removes each final call in turn, computes
+all available capacities directly from the frozen owner map, runs a separate
+histogram-only greedy calculation, and verifies that it returns exactly the
+existing remainder histogram. This checks all 72 final coordinate optima
+without relying on the transcript or the discovery seed.
+
+## 5. Relation to the global moment
+
+For ambient dimension $M=73$, define
+
+$$
+\phi_b(r)=r\bigl((73/r)^b-1\bigr)
+          =73^b r^{1-b}-r,\qquad \phi_b(0)=0.
+$$
+
+For $0<b<1$, this function is continuous at zero and strictly concave on
+positive ranks, because
+
+$$
+\phi_b''(r)=-b(1-b)73^b r^{-b-1}<0.
+$$
+
+Once all calls use the new provider, the local paid profile is fixed and every
+accepted owner update preserves the global paid rank mass. The exchange and
+majorization arguments therefore weakly decrease the global moment pressure
+for every $b\in(0,1)$ simultaneously. A strict histogram majorization strictly
+decreases that pressure. No estimated root, derivative, or floating cost is
+needed to establish the improvement of these updates.
+
+For the frozen map, the exact paid rank mass is 520704, so
+
+$$
+73\cdot7168-520704=2560.
+$$
+
+The final profile is recomputed from 72 copies of the new local paid profile
+and from the actual remaining rank in every pending-child group. Numerical
+roots printed by the matcher are screens only. Exact moment bounds and their
+combination with the bit supplier are performed by the package's admitted
+global pipeline.
+
+## 6. Determinism and fixed-point scope
+
+The implementation keeps the parent call order, alternating a forward pass
+and a reverse pass. Within equal-capacity groups, it first prefers the old
+assigned width, then other previously used owners, and finally physical-family
+order. It retains an old helper number when possible and otherwise takes the
+smallest unassigned helper number of the required width. These tie rules
+affect the frozen map, but not the single-call optimum remainder histogram.
+
+The recorded run has three passes with strict improvements. Its fourth pass
+has zero strict changes and zero changed helper owners. Hence the recorded map
+is a fixed point of the implemented call update. The separate final audit
+also establishes the stronger cost-level statement that every individual call
+already minimizes every concave remainder objective with the other calls
+fixed.
+
+Calls share capacities. Simultaneously changing two or more calls could
+possibly improve on a coordinate fixed point. The argument makes **no claim
+of joint global optimality**, and the frozen artifact does not depend on such
+a claim.
+
+## 7. Fields to regenerate for actual global admission
+
+| Field or object | Required action |
+| --- | --- |
+| Call `stage`, `replica`, `time` and parent windows | Preserve the parent controller |
+| Helper number and width | Read the new local signature and use the nominated assignment |
+| `owner_replica`, `child`, `port` | Use the final legal group selected by the matcher |
+| `copy`, `family` | Recompute from the selected group, then check uniqueness and active-data exclusion |
+| Helper `offset` | Compact all widths in each group into a disjoint prefix |
+| Idle `rank`, `hosted`, `pending_offset` | Recompute from the actual occupied prefix |
+| Per-call width lists and global paid profile | Recompute from the fresh local programs and actual cells |
+| Provider bindings, center carriers and program hashes | Bind the freshly checked provider; do not retain stale parent IDs or hashes |
+| Actual 73-column owner charts and their digests | Generate afresh from the selected child, port, offset, width and spectator coordinates |
+
+The new construction uses different center carrier registers, including source
+registers. Its ordered center frames and checked operator, rather than old
+carrier numbers, are the semantic interface. The hosting proof does not waive
+that interface check. The signature-only intermediate PLAN produced during
+replay is explicitly marked as such and is never a substitute for fresh
+provider binding or global phase admission.
diff --git a/research/gauge44-slots-t16/hosting/README.md b/research/gauge44-slots-t16/hosting/README.md
new file mode 100644
index 0000000000..b9505ebbea
--- /dev/null
+++ b/research/gauge44-slots-t16/hosting/README.md
@@ -0,0 +1,162 @@
+# Cold44 hosting: frozen owner map and exact callwise matching
+
+This directory contains the owner assignment used to turn the new cold44 local
+word into a global improvement. All 72 calls use the new local signature. The
+assignment is frozen; no search, tuning, or optimization is needed to consume
+it in the global verifier.
+
+The local word reduces the helper width sum from 3894 for the previous `jp8`
+provider to 3794. Simply shrinking the old allocations leaves many small idle
+remainders. The matcher below moves helpers to other physical families that are
+already idle at the same call, concentrating those remainders while respecting
+every parent capacity and window. This recovers a substantial part of the local
+saving in the global moment calculation.
+
+## Frozen result
+
+The exact finite data are in [frozen/MANIFEST.json](frozen/MANIFEST.json) and
+[frozen/MATCHING-RECEIPT.json](frozen/MATCHING-RECEIPT.json).
+
+| Quantity | Frozen value |
+| --- | ---: |
+| Calls | 72 |
+| Helpers per call | 492 |
+| Owner roles | 35,424 |
+| Ambient dimension | 73 |
+| Live streams | 7,168 |
+| New local width sum | 3,794 |
+| New local paid rank mass | 5,650 |
+| Global paid rank mass | 520,704 |
+| Global deficit | 2,560 |
+| Maximum child rank | 48 |
+| Equal-width updates with exact majorization receipts | 288 |
+| Final callwise optima independently checked | 72 |
+
+The new local width inventory is `{4:52, 5:48, 7:34, 8:114, 9:244}` and its paid
+profile is `{1:2514, 2:404, 3:448, 4:160, 5:56, 8:8}`. The final global paid
+profile, including all idle remainders, is:
+
+```json
+{"1":181093,"2":29164,"3":32429,"4":11520,"5":4032,"7":7,
+ "8":582,"12":13,"16":33,"19":1,"20":2,"28":4,"32":62,
+ "36":1,"40":1,"44":6,"48":2289}
+```
+
+Its floating moment screen is `b = 0.0016522089943684115`, giving the analytic
+screen `b/(1+b) = 0.0016494837025589793`. Relative to PR #635's reported
+`0.001636241501576388`, that is approximately **0.8093%**. These decimal screens
+are diagnostic values; the package's exact moment and outer assembly determine
+the admitted exponent. The owner replay never uses the floating root to choose
+an expanded-matching move.
+
+The frozen owner file has byte SHA-256:
+
+```text
+90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57
+```
+
+Its semantic SHA-256, computed from sorted-key compact uncompressed JSON, is:
+
+```text
+c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d
+```
+
+Semantic hashes are the portable replay criterion. The gzip byte hash is also
+reported, but compressor implementations need not produce identical streams.
+
+## Reproduce with the Python standard library
+
+Supply the PR #635 parent `PLAN.json` and `OWNERS.json.gz`, plus either the new
+verified native provider directory or the new raw word. The expected parent
+hashes are pinned in the manifest. The command below is run from the package
+root; replace the example input paths with actual paths.
+
+```sh
+python hosting/reproduce.py \
+  --parent-plan /path/to/pr635/research/complex-571-cold14-st2/data/PLAN.json \
+  --parent-owners /path/to/pr635/research/complex-571-cold14-st2/data/OWNERS.json.gz \
+  --local44 /path/to/verified/local44 \
+  --out /path/to/new/hosting-replay
+```
+
+For the raw provider, replace `--local44 ...` with
+`--raw-word /path/to/FULL-WORD.json.gz`. Reading a raw word here only extracts a
+nomination signature; it does not replace independent local verification.
+
+The default replay copies the frozen mixed-provider seed, checks its semantic
+hash, derives its profile afresh, and runs the exact expanded matcher. It then
+compares the final owner and majorization transcript with the frozen semantic
+hashes and independently checks the final map's 72 callwise fixed points.
+Outputs include `all72/OWNERS.json.gz`, `all72/PROFILE.json`, recomputed
+remainders, `FROZEN-AUDIT.json`, and `REPRODUCTION.json`.
+
+The seed has 71 cold44 calls and one inherited `ck` call. Expanded matching first
+replaces that last call using newly available legal families. This changed-width
+bootstrap is checked for feasibility and is explicitly excluded from the
+equal-width majorization count. The following four passes use cold44 at all 72
+calls:
+
+| Pass | Calls with strict majorization | Changed helper owners |
+| --- | ---: | ---: |
+| 1 | 70 | 1,245 |
+| 2 | 41 | 169 |
+| 3 | 8 | 13 |
+| 4 | 0 | 0 |
+
+Pass 4 changes neither the map nor its remainder histogram. The independent
+audit additionally recomputes the optimal remainder histogram for each call
+with all other calls fixed.
+
+## Optional: reproduce seed discovery
+
+Add `--rebuild-seed` to the same command to rebuild the mixed seed from the
+original PR #635 owners. This step first matches sorted new helper widths to
+sorted old owner slots, then performs two fixed-family Hungarian passes.
+Discovery used Python 3.12.14, NumPy 2.3.5, and SciPy 1.17.0. Equal-cost matching
+tie choices may vary across SciPy versions, so the script compares the rebuilt
+seed with the frozen semantic hash and fails if it differs. Default frozen-seed
+replay has no NumPy or SciPy dependency.
+
+The two discovery passes are an optional way to recover the recorded seed.
+Their floating costs are not needed for feasibility, for the final fixed-point
+proof, or for the package's admitted exponent.
+
+## Audit without regenerating the assignment
+
+```sh
+python hosting/audit_frozen.py \
+  --parent-plan /path/to/pr635/research/complex-571-cold14-st2/data/PLAN.json \
+  --parent-owners /path/to/pr635/research/complex-571-cold14-st2/data/OWNERS.json.gz \
+  --local44 /path/to/verified/local44 \
+  --out /path/to/FROZEN-AUDIT.json
+```
+
+This integer audit checks helper coverage, capacity, allowed call times, active
+data exclusion, physical-family uniqueness within each call, disjoint compacted
+coordinate prefixes, the exact global profile and rank mass, and callwise
+optimality of the frozen remainder histograms. It reads the explicit parent
+window catalogue. The package's separate global verifier must also derive
+those windows and all 73-column charts from the actual program.
+
+## Files and scope
+
+| File | Purpose |
+| --- | --- |
+| `frozen/OWNERS.json.gz` | The final all-cold44 map consumed by global assembly |
+| `frozen/SEED-OWNERS.json.gz` | Pinned feasible mixed seed for dependency-free replay |
+| `frozen/MAJORIZATION.json.gz` | Integer stop-loss margins for every expanded update |
+| `frozen/MANIFEST.json` | Parent, provider, artifact, profile, and parameter bindings |
+| `frozen/SEED-RECEIPT.json` | Recorded sorted matching and two seed discovery passes |
+| `frozen/MATCHING-RECEIPT.json` | Recorded expanded passes and exact finite totals |
+| `reproduce.py` | End-to-end parameterized hosting replay |
+| `reuse_owners.py` | Optional original-family seed constructor |
+| `expand_owners.py` | Exact greedy matching over all eligible physical families |
+| `audit_frozen.py` | Independent feasibility and final callwise fixed-point audit |
+| `PROOF.md` | Capacity, exchange, majorization, and integration arguments |
+
+The expanded matcher is individually optimal for each call when other calls
+are fixed, for every concave remainder cost simultaneously. The frozen map is
+a verified coordinate fixed point. **No joint global optimality claim is
+made.** New local algebra, changed center carriers, phase compatibility,
+actual owner charts, the finite invoice, and exact exponent admission remain
+the responsibility of the package's global verification pipeline.
diff --git a/research/gauge44-slots-t16/hosting/audit_frozen.py b/research/gauge44-slots-t16/hosting/audit_frozen.py
new file mode 100644
index 0000000000..26a07408ea
--- /dev/null
+++ b/research/gauge44-slots-t16/hosting/audit_frozen.py
@@ -0,0 +1,169 @@
+"""Audit the frozen owner map and its callwise fixed point using integers.
+
+The parent window catalogue is an explicit input. The package's independent
+global verifier must additionally derive the windows from the actual program.
+This audit does not certify local algebra, phase charts, or an exponent.
+"""
+from collections import Counter, defaultdict
+from pathlib import Path
+import argparse
+import hashlib
+import json
+
+from reuse_owners import packed, read, sha, signature
+
+
+HERE = Path(__file__).resolve().parent
+
+
+def semantic_sha(path):
+    return hashlib.sha256(packed(read(path))).hexdigest()
+
+
+def add_inputs(parser):
+    parser.add_argument('--parent-plan', type=Path, required=True)
+    parser.add_argument('--parent-owners', type=Path, required=True)
+    provider = parser.add_mutually_exclusive_group(required=True)
+    provider.add_argument('--local44', type=Path, help='Independently checked native provider directory')
+    provider.add_argument('--raw-word', type=Path, help='New FULL-WORD.json.gz; nomination signature only')
+
+
+def bound_inputs(args, manifest):
+    assert sha(args.parent_plan) == manifest['parent_plan_sha256'], 'Wrong parent PLAN'
+    assert sha(args.parent_owners) == manifest['parent_owners_sha256'], 'Wrong parent OWNERS'
+    plan = read(args.parent_plan)
+    assert (plan['K'], plan['T'], plan['M'], plan['L'], plan['live']) == (4, 8, 73, 9, 7168)
+    provider_path = args.local44 if args.local44 is not None else args.raw_word
+    sig = signature(provider_path)
+    expected = manifest['new_provider']
+    assert len(sig['widths']) == expected['R']
+    assert hashlib.sha256(packed(sig['widths'])).hexdigest() == expected['width_vector_sha256']
+    assert sig['profile'] == {int(r): n for r, n in expected['profile'].items()}
+    assert Counter(sig['widths']) == {int(w): n for w, n in expected['width_histogram'].items()}
+    assert sum(sig['widths']) == expected['width_sum']
+    assert sum(r*n for r, n in sig['profile'].items()) == expected['rank_mass']
+    return plan, sig, provider_path
+
+
+def audit(plan, sig, owners):
+    V, R = 112, 492
+    order = [tuple(c) for c in plan['order']]
+    assert len(order) == 72 and len(set(order)) == 72
+    assert len(owners) == 72*R
+    bycall = defaultdict(dict)
+    cells = defaultdict(set)
+    caps, family, eligible = {}, {}, defaultdict(list)
+    for key, (cap, times) in plan['windows'].items():
+        rep, child = map(int, key.split(','))
+        assert 0 <= cap <= 48 and len(times) == len(set(times))
+        for port in range(V):
+            g = (rep, child, port)
+            caps[g] = cap
+            family[g] = rep*8*V + (2*plan['pairs'][str(child)] + plan['sides'][str(child)])*V + port
+            for t in times:
+                assert 0 <= t < len(order)
+                eligible[t].append(g)
+    for t, gs in eligible.items():
+        assert len({family[g] for g in gs}) == len(gs), 'Multiple eligible children on one family'
+        stage, rep = order[t]
+        pair = max(0, (stage-1)//2)
+        assert all(g[0] != rep or plan['pairs'][str(g[1])] != pair for g in gs)
+    for z in owners:
+        t, h = z['time'], z['helper']
+        assert 0 <= t < len(order) and 0 <= h < R
+        assert (z['stage'], z['replica']) == order[t]
+        assert h not in bycall[t]
+        assert z['width'] == sig['widths'][h]
+        g = (z['owner_replica'], z['child'], z['port'])
+        assert g in caps and t in plan['windows'][f'{g[0]},{g[1]}'][1]
+        assert z['copy'] == g[0]*V + g[2] and z['family'] == family[g]
+        off, width = z['offset'], z['width']
+        assert 0 <= off and off+width <= caps[g]
+        occupied = set(range(off, off+width))
+        assert not cells[g] & occupied, 'Overlapping hosted coordinates'
+        cells[g] |= occupied
+        bycall[t][h] = (g, width)
+    for t in range(72):
+        assert set(bycall[t]) == set(range(R))
+        assert len({family[g] for g, w in bycall[t].values()}) == R
+    for occupied in cells.values():
+        assert occupied == set(range(len(occupied))), 'Uncompacted hosted coordinates'
+    used = {g: len(cells[g]) for g in caps}
+    idle = Counter(caps[g]-used[g] for g in caps if caps[g] > used[g])
+    paid = Counter({r: 72*n for r, n in sig['profile'].items()})
+    paid.update(idle)
+
+    # Independent cost-level fixed-point check. No helper-ID or family-ID
+    # tie-breaking is needed: equal capacities give the same histogram.
+    for t in range(72):
+        old = {g: w for g, w in bycall[t].values()}
+        assert len(old) == R
+        before = Counter(caps[g]-used[g] for g in eligible[t])
+        available = sorted(caps[g]-used[g]+old.get(g, 0) for g in eligible[t])
+        want = Counter(sig['widths'])
+        after = Counter()
+        for cap in available:
+            width = next((w for w in sorted(want, reverse=True) if want[w] and w <= cap), 0)
+            if width:
+                want[width] -= 1
+            after[cap-width] += 1
+        assert not any(want.values()), 'Greedy assignment unexpectedly infeasible'
+        assert after == before, ('Frozen map is not callwise optimal', t)
+    mass = sum(r*n for r, n in paid.items())
+    assert 73*7168-mass == 2560 and max(paid) == 48
+    return {
+        'roles': len(owners), 'calls': 72, 'fixed_point_calls_checked': 72,
+        'remainder_profile': dict(sorted(idle.items())),
+        'global_profile': dict(sorted(paid.items())),
+        'rank_mass': mass, 'deficit': 2560, 'maxchild': 48,
+        'all_footprints_disjoint_compacted_prefixes': True,
+        'all_helper_families_idle_and_outside_active_data': True,
+        'one_helper_per_physical_family_per_call': True,
+        'every_call_optimal_for_every_concave_remainder_cost': True,
+        'global_optimality_claimed': False,
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    add_inputs(parser)
+    parser.add_argument('--owners', type=Path, default=HERE/'frozen/OWNERS.json.gz')
+    parser.add_argument('--majorization', type=Path, default=HERE/'frozen/MAJORIZATION.json.gz')
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    manifest = read(HERE/'frozen/MANIFEST.json')
+    plan, sig, provider_path = bound_inputs(args, manifest)
+    assert semantic_sha(args.owners) == manifest['artifacts']['OWNERS.json.gz']['semantic_sha256']
+    assert semantic_sha(args.majorization) == manifest['artifacts']['MAJORIZATION.json.gz']['semantic_sha256']
+    result = audit(plan, sig, read(args.owners))
+    for key in ('remainder_profile', 'global_profile'):
+        assert result[key] == {int(r): n for r, n in manifest[key].items()}
+    moves = read(args.majorization)
+    checked = 0
+    for move in moves:
+        if move['equal_width_multiset']:
+            margins = move['integer_stoploss_margins']
+            assert len(margins) == 49 and all(type(x) is int and x >= 0 for x in margins)
+            assert margins[0] == margins[-1] == 0
+            assert move['strict_majorization'] == bool(any(margins))
+            checked += 1
+        else:
+            assert move['bootstrap'] and move['integer_stoploss_margins'] is None
+    assert checked == 288 and len(moves) == 289
+    result.update({
+        'status': 'PASS_FROZEN_HOSTING_AND_ALL_72_CALLWISE_FIXED_POINTS',
+        'parent_plan_sha256': sha(args.parent_plan),
+        'parent_owners_sha256': sha(args.parent_owners),
+        'owners_semantic_sha256': semantic_sha(args.owners),
+        'majorization_semantic_sha256': semantic_sha(args.majorization),
+        'stored_integer_majorization_steps': checked,
+        'majorization_replay': 'reproduce.py re-executes every step; this audit separately checks the final fixed point.',
+        'remaining_scope': 'The package global verifier checks fresh local algebra, phases, windows, invoice, moment, and outer assembly.',
+    })
+    args.out.parent.mkdir(parents=True, exist_ok=True)
+    args.out.write_text(json.dumps(result, indent=2)+'\n')
+    print(json.dumps(result, indent=2))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/hosting/expand_owners.py b/research/gauge44-slots-t16/hosting/expand_owners.py
new file mode 100644
index 0000000000..ee6c4c24e6
--- /dev/null
+++ b/research/gauge44-slots-t16/hosting/expand_owners.py
@@ -0,0 +1,186 @@
+"""Exact callwise concave-cost owner matching over every legal idle family.
+
+This is a finite integer nomination algorithm, not a MILP. Each greedy
+matching is optimal for every concave remainder cost. Its majorization
+receipt is checked with integers, independently of floating root screens.
+"""
+from collections import Counter, defaultdict, deque
+from pathlib import Path
+import argparse
+import gzip
+import hashlib
+import json
+import time
+
+from reuse_owners import read, packed, sha, signature, audit_roles, rate
+
+
+def stoploss(hist,k):return sum(n*max(r-k,0) for r,n in hist.items())
+
+
+def main():
+    ap=argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--plan',type=Path,required=True)
+    ap.add_argument('--owners',type=Path,required=True)
+    ap.add_argument('--signature',action='append',required=True,help='Existing PID=verified native directory or raw/signature JSON')
+    ap.add_argument('--max-passes',type=int,default=8)
+    ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args();assert 1<=a.max_passes<=12
+    a.out.mkdir(parents=True,exist_ok=False);beg=time.monotonic()
+    plan,oldroles=read(a.plan),read(a.owners);V,M=112,73
+    assert (plan['K'],plan['T'],plan['M'],plan['L'])==(4,8,73,9)
+    sig={pid:{'widths':desc['widths'],'profile':{int(r):n for r,n in desc['actual_paid_profile'].items()},'source':'input PLAN'} for pid,desc in plan['provider_registry'].items()}
+    for spec in a.signature:
+        pid,path=spec.split('=',1);assert pid in sig;sig[pid]=signature(path)
+    R=len(next(iter(sig.values()))['widths'])
+    for s in sig.values():
+        assert len(s['widths'])==R and all(type(w) is int and 0<w<=9 for w in s['widths'])
+        assert sum(r*n for r,n in s['profile'].items())==16*V+64+sum(s['widths'])
+    calls={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+    order=[tuple(c) for c in plan['order']]
+    oldwidths={k:plan['provider_registry'][c['provider']]['widths'] for k,c in calls.items()}
+    widths={k:sig[c['provider']]['widths'] for k,c in calls.items()}
+    audit_roles(oldroles,plan,oldwidths,V,R)
+    caps={};families={};eligible=defaultdict(list)
+    for key,(cap,window) in plan['windows'].items():
+        rep,ch=map(int,key.split(','))
+        for port in range(V):
+            g=(rep,ch,port);caps[g]=cap
+            families[g]=rep*(8*V)+(2*plan['pairs'][str(ch)]+plan['sides'][str(ch)])*V+port
+            for t in window:eligible[t].append(g)
+    for t,gs in eligible.items():
+        assert len({families[g] for g in gs})==len(gs), 'current geometry requires one eligible child per family'
+        s,rep=order[t];active_pair=max(0,(s-1)//2)
+        assert all(not (g[0]==rep and plan['pairs'][str(g[1])]==active_pair) for g in gs), 'active data family in idle window'
+    current=defaultdict(dict);used={g:0 for g in caps}
+    for z in oldroles:
+        c=(z['stage'],z['replica']);g=(z['owner_replica'],z['child'],z['port'])
+        current[c][z['helper']]=(g,z['width']);used[g]+=z['width']
+    assert all(0<=used[g]<=caps[g] for g in caps)
+    moves=[]
+
+    def idle_profile():return Counter(caps[g]-used[g] for g in caps if caps[g]>used[g])
+
+    def total_profile():
+        p=Counter()
+        for c in plan['provider_calls']:p.update(sig[c['provider']]['profile'])
+        p.update(idle_profile());assert M*plan['live']-sum(r*n for r,n in p.items())==2560
+        return p
+
+    def update(call,bootstrap=False):
+        t=calls[call]['time'];gs=eligible[t]
+        old=current[call]
+        old_by_group={g:(h,w) for h,(g,w) in old.items()}
+        assert len(old_by_group)==R and set(old_by_group)<=set(gs)
+        oldhist=Counter(caps[g]-used[g] for g in gs)
+        for g,(h,w) in old_by_group.items():used[g]-=w
+        want=defaultdict(set)
+        for h,w in enumerate(widths[call]):want[w].add(h)
+        # Equal-capacity opportunities have identical costs. Preserve old
+        # matching widths first, then old owners, and finally family order.
+        buckets=defaultdict(lambda:defaultdict(deque))
+        for g in sorted(gs,key=lambda g:(families[g],g[1])):
+            available=caps[g]-used[g];oldw=old_by_group.get(g,(None,0))[1]
+            buckets[available][oldw].append(g)
+        result={};unassigned=R
+        for c in sorted(buckets):
+            bucket=buckets[c]
+            while unassigned and any(bucket.values()):
+                w=next((w for w in sorted(want,reverse=True) if w<=c and want[w]),None)
+                if w is None:break
+                if bucket.get(w):q=w
+                else:q=next(q for q in sorted(bucket,reverse=True) if bucket[q])
+                g=bucket[q].popleft()
+                h0=old_by_group.get(g,(None,0))[0]
+                h=h0 if h0 in want[w] else min(want[w])
+                want[w].remove(h);result[h]=(g,w);used[g]+=w;unassigned-=1
+                assert used[g]<=caps[g]
+        assert unassigned==0,('no legal family matching',call,{w:len(h) for w,h in want.items() if h})
+        assert set(result)==set(range(R)) and len({families[g] for g,w in result.values()})==R
+        newhist=Counter(caps[g]-used[g] for g in gs)
+        equal_widths=Counter(w for g,w in old.values())==Counter(widths[call])
+        strict=False
+        if equal_widths:
+            assert sum(oldhist.values())==sum(newhist.values())
+            assert stoploss(oldhist,0)==stoploss(newhist,0)
+            margins=[stoploss(newhist,k)-stoploss(oldhist,k) for k in range(49)]
+            assert min(margins)>=0,('greedy did not majorize old assignment',call,margins)
+            strict=any(margins)
+        else:
+            assert bootstrap
+            margins=None
+        changed=sum(result[h]!=old[h] for h in result)
+        current[call]=result
+        moves.append({'stage':call[0],'replica':call[1],'time':t,'bootstrap':bootstrap,
+                      'equal_width_multiset':equal_widths,'integer_stoploss_margins':margins,
+                      'strict_majorization':strict,'changed_helper_owners':changed})
+        return strict,changed
+
+    changed_calls=[c for c in order if any(current[c][h][1]!=widths[c][h] for h in range(R))]
+    for c in changed_calls:update(c,bootstrap=True)
+    p=total_profile();baseline_b=rate(p,2560,M)
+    rounds=[{'pass':'bootstrap','changed_provider_calls':[list(c) for c in changed_calls],
+             'floating_b':baseline_b,'remainder_profile':dict(sorted(idle_profile().items()))}]
+    print(json.dumps({'checkpoint':'all_goal_signatures_feasible','bootstrap_calls':len(changed_calls),'floating_b':baseline_b}),flush=True)
+    quiet=0
+    for passno in range(a.max_passes):
+        strict=changed=0
+        for c in (order if passno%2==0 else list(reversed(order))):
+            s,z=update(c);strict+=bool(s);changed+=z
+        p=total_profile();r={'pass':passno+1,'strictly_improved_calls':strict,'changed_helper_owners':changed,
+                             'floating_b':rate(p,2560,M),'remainder_profile':dict(sorted(idle_profile().items()))}
+        rounds.append(r);print(json.dumps({k:r[k] for k in ('pass','strictly_improved_calls','changed_helper_owners','floating_b')}),flush=True)
+        quiet=quiet+1 if not strict else 0
+        if quiet>=2 or (not strict and not changed):break
+
+    groups=defaultdict(list);roles=[]
+    for call in order:
+        s,rep=call;t=calls[call]['time']
+        for h,(g,w) in current[call].items():
+            orp,ch,port=g
+            z={'child':ch,'copy':orp*V+port,'family':families[g],'helper':h,'offset':0,
+               'owner_replica':orp,'port':port,'replica':rep,'stage':s,'time':t,'width':w}
+            roles.append(z);groups[g].append(z)
+    for g,zs in groups.items():
+        off=0
+        for z in sorted(zs,key=lambda z:(z['time'],z['helper'])):z['offset']=off;off+=z['width']
+        assert off==used[g]<=caps[g]
+    roles.sort(key=lambda z:(z['time'],z['helper']))
+    cells,_=audit_roles(roles,plan,widths,V,R)
+    for z in roles:
+        active=max(0,(z['stage']-1)//2)
+        assert not (z['owner_replica']==z['replica'] and plan['pairs'][str(z['child'])]==active)
+    for g in caps:assert len(cells[g])==used[g]
+    remainder=[]
+    for g in caps:
+        left=caps[g]-used[g]
+        if left:
+            rep,ch,port=g
+            remainder.append({'child':ch,'port':port,'replica':rep,'replicas':1,'family':families[g],
+                              'rank':left,'hosted':used[g],'pending_offset':used[g]})
+    profile=dict(sorted(total_profile().items()));assert M*M>2*max(profile)**2
+    raw=packed(roles);compressed=bytearray(gzip.compress(raw,mtime=0));compressed[9]=255
+    (a.out/'OWNERS.json.gz').write_bytes(bytes(compressed))
+    (a.out/'MAJORIZATION.json.gz').write_bytes(gzip.compress(packed(moves),mtime=0))
+    (a.out/'REMAINDERS.json').write_text(json.dumps(remainder,indent=2)+'\n')
+    (a.out/'PROFILE.json').write_text(json.dumps(profile,indent=2)+'\n')
+    fields={'profile':profile,'per_call_widths':[{'stage':s,'replica':r,'widths':widths[s,r]} for s,r in order],
+            'assignment_sha256':hashlib.sha256(raw).hexdigest(),'assignment_sha256_semantics':'SHA256 sorted-key compact uncompressed OWNERS array',
+            'source_owners_sha256':sha(a.owners),'provider_signatures':sig}
+    (a.out/'PLAN-OWNER-FIELDS.json').write_text(json.dumps(fields,indent=2)+'\n')
+    receipt={'status':'PASS_EXPANDED_OWNER_MATCHING_EXACT_COMBINATORICS_PENDING_GLOBAL_ADMISSION',
+             'source_plan':str(a.plan),'source_plan_sha256':sha(a.plan),'source_owners':str(a.owners),'source_owners_sha256':sha(a.owners),
+             'owners_sha256':sha(a.out/'OWNERS.json.gz'),'source_signatures':sig,
+             'roles':len(roles),'calls':len(order),'unchanged_call_order_and_windows':True,
+             'all_families_idle_and_outside_active_data':True,'one_helper_per_family_per_call':True,
+             'all_footprints_disjoint_compacted_prefixes':True,'integer_majorization_steps':sum(z['equal_width_multiset'] for z in moves),
+             'majorization_sha256':sha(a.out/'MAJORIZATION.json.gz'),'matching_rounds':rounds,
+             'global_profile':profile,'rank_mass':sum(r*n for r,n in profile.items()),'deficit':2560,
+             'remainder_profile':dict(sorted(idle_profile().items())),'maxchild':max(profile),
+             'candidate_floating_screen_b':rate(profile,2560,M),'seconds':time.monotonic()-beg,
+             'remaining_admission':'Fresh native-provider bindings, actual 73-column owner charts, independent full controller audit, finite invoice, exact moment and outer assembly.'}
+    (a.out/'EXPANDED-OWNER-REUSE.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    print(json.dumps({k:receipt[k] for k in ('status','roles','remainder_profile','rank_mass','candidate_floating_screen_b','seconds')},indent=2),flush=True)
+
+
+if __name__=='__main__':main()
diff --git a/research/gauge44-slots-t16/hosting/frozen/FROZEN-AUDIT.json b/research/gauge44-slots-t16/hosting/frozen/FROZEN-AUDIT.json
new file mode 100644
index 0000000000..5f95552366
--- /dev/null
+++ b/research/gauge44-slots-t16/hosting/frozen/FROZEN-AUDIT.json
@@ -0,0 +1,57 @@
+{
+  "roles": 35424,
+  "calls": 72,
+  "fixed_point_calls_checked": 72,
+  "remainder_profile": {
+    "1": 85,
+    "2": 76,
+    "3": 173,
+    "7": 7,
+    "8": 6,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "all_footprints_disjoint_compacted_prefixes": true,
+  "all_helper_families_idle_and_outside_active_data": true,
+  "one_helper_per_physical_family_per_call": true,
+  "every_call_optimal_for_every_concave_remainder_cost": true,
+  "global_optimality_claimed": false,
+  "status": "PASS_FROZEN_HOSTING_AND_ALL_72_CALLWISE_FIXED_POINTS",
+  "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+  "owners_semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d",
+  "majorization_semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc",
+  "stored_integer_majorization_steps": 288,
+  "majorization_replay": "reproduce.py re-executes every step; this audit separately checks the final fixed point.",
+  "remaining_scope": "The package global verifier checks fresh local algebra, phases, windows, invoice, moment, and outer assembly."
+}
diff --git a/research/gauge44-slots-t16/hosting/frozen/MAJORIZATION.json.gz b/research/gauge44-slots-t16/hosting/frozen/MAJORIZATION.json.gz
new file mode 100644
index 0000000000..047b1cfb67
Binary files /dev/null and b/research/gauge44-slots-t16/hosting/frozen/MAJORIZATION.json.gz differ
diff --git a/research/gauge44-slots-t16/hosting/frozen/MANIFEST.json b/research/gauge44-slots-t16/hosting/frozen/MANIFEST.json
new file mode 100644
index 0000000000..291005722c
--- /dev/null
+++ b/research/gauge44-slots-t16/hosting/frozen/MANIFEST.json
@@ -0,0 +1,114 @@
+{
+  "schema": "gauge44-hosting-frozen-v1",
+  "parent_pr": 635,
+  "parent_paths": {
+    "plan": "research/complex-571-cold14-st2/data/PLAN.json",
+    "owners": "research/complex-571-cold14-st2/data/OWNERS.json.gz"
+  },
+  "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+  "artifacts": {
+    "OWNERS.json.gz": {
+      "sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+      "semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d"
+    },
+    "SEED-OWNERS.json.gz": {
+      "sha256": "eb3be5eebbb84349d7e7f1bde2fc77772a12ad5bccc6dab7c4efd8d903e2a048",
+      "semantic_sha256": "beea695aa2e1ab973ad53f475b3e3e9cf6d0f8a9bca2033a445b64f3b3484e34"
+    },
+    "MAJORIZATION.json.gz": {
+      "sha256": "ec5f94b13d190d72bc0608dc9fe2498cc43ba9deb05028159a812ec1e4dcacdf",
+      "semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc"
+    }
+  },
+  "new_provider": {
+    "R": 492,
+    "h": 9,
+    "v": 112,
+    "width_histogram": {
+      "4": 52,
+      "5": 48,
+      "7": 34,
+      "8": 114,
+      "9": 244
+    },
+    "width_sum": 3794,
+    "profile": {
+      "1": 2514,
+      "2": 404,
+      "3": 448,
+      "4": 160,
+      "5": 56,
+      "8": 8
+    },
+    "rank_mass": 5650,
+    "raw_word_sha256": "3ef4e74e81e2f4621fc95272918ac7b8bb8858df0baa16cc6d91424d55aead9e",
+    "canonical_word_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+    "local_programs_sha256": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+    "width_vector_sha256": "b7fbefdb3af3942194ac9314c767c7812bd68adb734d4e00b70b2916bdb55de8"
+  },
+  "seed_discovery": {
+    "provider_replaced": "jp8",
+    "unchanged_provider": "ck",
+    "passes": 2,
+    "price_b": 0.001638923,
+    "python": "3.12.14",
+    "numpy": "2.3.5",
+    "scipy": "1.17.0",
+    "note": "Only seed discovery uses floating-point Hungarian costs. Frozen seed and the expanded exact replay require the Python standard library."
+  },
+  "expanded_replay": {
+    "providers_replaced": [
+      "jp8",
+      "ck"
+    ],
+    "max_passes": 8,
+    "actual_passes": 4,
+    "integer_majorization_steps": 288,
+    "changed_width_bootstrap_calls": 1
+  },
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "remainder_profile": {
+    "1": 85,
+    "2": 76,
+    "3": 173,
+    "7": 7,
+    "8": 6,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "live": 7168,
+  "roles": 35424,
+  "calls": 72,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "candidate_floating_screen_b": 0.0016522089943684115,
+  "screening_only": "The floating rate here is not a certified exponent. Exact supplier and outer admission belong to the package verifier."
+}
diff --git a/research/gauge44-slots-t16/hosting/frozen/MATCHING-RECEIPT.json b/research/gauge44-slots-t16/hosting/frozen/MATCHING-RECEIPT.json
new file mode 100644
index 0000000000..993331090c
--- /dev/null
+++ b/research/gauge44-slots-t16/hosting/frozen/MATCHING-RECEIPT.json
@@ -0,0 +1,1205 @@
+{
+  "status": "PASS_EXPANDED_OWNER_MATCHING_EXACT_COMBINATORICS_PENDING_GLOBAL_ADMISSION",
+  "source_plan": "explicit parent PLAN, with a temporary signature-only seed view for expanded replay",
+  "source_plan_sha256": "0d2b6a12d3450cfb78e556e80d34cabb8cd1a7f8aa85c1a712a5177236672a37",
+  "source_owners": "frozen/SEED-OWNERS.json.gz",
+  "source_owners_sha256": "eb3be5eebbb84349d7e7f1bde2fc77772a12ad5bccc6dab7c4efd8d903e2a048",
+  "owners_sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+  "source_signatures": {
+    "ck": {
+      "widths": [
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
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+}
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diff --git a/research/gauge44-slots-t16/hosting/frozen/REPRODUCTION.json b/research/gauge44-slots-t16/hosting/frozen/REPRODUCTION.json
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+  "scope": "Exact hosting nomination and callwise fixed-point replay; full supplier admission is separate."
+}
diff --git a/research/gauge44-slots-t16/hosting/frozen/SEED-OWNERS.json.gz b/research/gauge44-slots-t16/hosting/frozen/SEED-OWNERS.json.gz
new file mode 100644
index 0000000000..d61916a156
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diff --git a/research/gauge44-slots-t16/hosting/frozen/SEED-RECEIPT.json b/research/gauge44-slots-t16/hosting/frozen/SEED-RECEIPT.json
new file mode 100644
index 0000000000..82911f647b
--- /dev/null
+++ b/research/gauge44-slots-t16/hosting/frozen/SEED-RECEIPT.json
@@ -0,0 +1,1537 @@
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+    "(4, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(0, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(0, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(0, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    }
+  },
+  "matching_passes": [
+    {
+      "pass": "sorted",
+      "touched_group_idle_pressure": 44.06409529228022,
+      "calls_awaiting_capacity_matching": 0
+    },
+    {
+      "pass": 1,
+      "accepted_calls": 71,
+      "touched_group_idle_pressure": 24.92521223381306,
+      "decrease": 19.13888305846716
+    },
+    {
+      "pass": 2,
+      "accepted_calls": 58,
+      "touched_group_idle_pressure": 23.047886627886065,
+      "decrease": 1.8773256059269947
+    }
+  ],
+  "roles": 35424,
+  "calls": 72,
+  "remainder_children": 3197,
+  "remainder_profile": {
+    "1": 83,
+    "2": 99,
+    "3": 197,
+    "4": 168,
+    "5": 6,
+    "6": 13,
+    "7": 16,
+    "8": 145,
+    "10": 4,
+    "11": 24,
+    "12": 19,
+    "13": 1,
+    "14": 3,
+    "15": 9,
+    "16": 107,
+    "18": 1,
+    "19": 10,
+    "20": 15,
+    "23": 2,
+    "24": 52,
+    "32": 1,
+    "44": 1,
+    "48": 2221
+  },
+  "global_profile": {
+    "1": 181177,
+    "2": 29335,
+    "3": 32309,
+    "4": 11692,
+    "5": 4052,
+    "6": 17,
+    "7": 16,
+    "8": 721,
+    "10": 4,
+    "11": 24,
+    "12": 19,
+    "13": 1,
+    "14": 3,
+    "15": 9,
+    "16": 107,
+    "18": 1,
+    "19": 10,
+    "20": 15,
+    "23": 2,
+    "24": 52,
+    "32": 1,
+    "44": 1,
+    "48": 2221
+  },
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "source_floating_screen_b": 0.001638923175694355,
+  "candidate_floating_screen_b": 0.0016446065186552388,
+  "remaining_admission": "Bind freshly verified provider artifacts and their hashes; regenerate the global template, actual 73-column sigmas and remainder axes with the existing emitter; run independent owner/frame audit, finite invoice, and exact moment/outer assembly.",
+  "provenance_note": "Absolute discovery paths and wall time removed; original artifact hashes and all exact combinatorial fields preserved."
+}
diff --git a/research/gauge44-slots-t16/hosting/frozen/SEED-REPRODUCTION.json b/research/gauge44-slots-t16/hosting/frozen/SEED-REPRODUCTION.json
new file mode 100644
index 0000000000..91ee98cf70
--- /dev/null
+++ b/research/gauge44-slots-t16/hosting/frozen/SEED-REPRODUCTION.json
@@ -0,0 +1,29 @@
+{
+  "status": "PASS_FROZEN_OWNER_AND_INTEGER_MAJORIZATION_REPLAY",
+  "seed_mode": "two_pass_hungarian_discovery_rebuilt",
+  "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+  "owners_semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d",
+  "owners_gzip_sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+  "majorization_semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc",
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "scope": "Exact hosting nomination and callwise fixed-point replay; full supplier admission is separate."
+}
diff --git a/research/gauge44-slots-t16/hosting/reproduce.py b/research/gauge44-slots-t16/hosting/reproduce.py
new file mode 100644
index 0000000000..2f29a5ff13
--- /dev/null
+++ b/research/gauge44-slots-t16/hosting/reproduce.py
@@ -0,0 +1,100 @@
+"""Reproduce the frozen all-cold44 owner nomination from explicit inputs.
+
+By default, replay the exact integer optimizer from the included frozen seed.
+--rebuild-seed additionally repeats the original two floating-cost Hungarian
+discovery passes; that optional route requires NumPy and SciPy.
+"""
+from pathlib import Path
+from collections import Counter
+import argparse
+import copy
+import json
+import shutil
+import subprocess
+import sys
+
+from audit_frozen import HERE, add_inputs, bound_inputs, semantic_sha
+from reuse_owners import audit_roles, read, sha
+
+
+def run(name, *args):
+    subprocess.run([sys.executable, str(HERE/name), *map(str, args)], check=True)
+
+
+def seed_plan(parent, seed_owners, new_signature):
+    """Build a signature-only resizer input; never an admitted provider PLAN."""
+    plan = copy.deepcopy(parent)
+    plan['provider_registry']['jp8']['widths'] = new_signature['widths']
+    plan['provider_registry']['jp8']['actual_paid_profile'] = new_signature['profile']
+    call_widths = {
+        (c['stage'], c['replica']): plan['provider_registry'][c['provider']]['widths']
+        for c in plan['provider_calls']
+    }
+    used, families = audit_roles(seed_owners, plan, call_widths, 112, 492)
+    profile = Counter()
+    for c in plan['provider_calls']:
+        profile.update({int(r): n for r, n in plan['provider_registry'][c['provider']]['actual_paid_profile'].items()})
+    for key, (cap, times) in plan['windows'].items():
+        rep, child = map(int, key.split(','))
+        for port in range(112):
+            left = cap-len(used[rep, child, port])
+            if left:
+                profile[left] += 1
+    assert 73*7168-sum(r*n for r, n in profile.items()) == 2560
+    plan['profile'] = dict(sorted(profile.items()))
+    plan['per_call_widths'] = [
+        {'stage': s, 'replica': r, 'widths': call_widths[s, r]}
+        for s, r in plan['order']
+    ]
+    plan['status'] = 'INTERMEDIATE_SIGNATURE_ONLY_OWNER_SEED_NOT_PROVIDER_ADMISSION'
+    return plan
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    add_inputs(parser)
+    parser.add_argument('--rebuild-seed', action='store_true')
+    parser.add_argument('--out', type=Path, required=True, help='New output directory')
+    args = parser.parse_args()
+    manifest = read(HERE/'frozen/MANIFEST.json')
+    parent, sig, provider = bound_inputs(args, manifest)
+    args.out.mkdir(parents=True, exist_ok=False)
+    seed_dir = args.out/'seed'
+    if args.rebuild_seed:
+        run('reuse_owners.py', '--plan', args.parent_plan, '--owners', args.parent_owners,
+            '--signature', f'jp8={provider}', '--passes', '2', '--price-b', '0.001638923', '--out', seed_dir)
+    else:
+        seed_dir.mkdir()
+        shutil.copyfile(HERE/'frozen/SEED-OWNERS.json.gz', seed_dir/'OWNERS.json.gz')
+    assert semantic_sha(seed_dir/'OWNERS.json.gz') == manifest['artifacts']['SEED-OWNERS.json.gz']['semantic_sha256'], (
+        'Seed differs; use the default frozen-seed replay, or the recorded NumPy/SciPy versions for discovery replay.'
+    )
+    plan = seed_plan(parent, read(seed_dir/'OWNERS.json.gz'), sig)
+    plan_path = seed_dir/'PLAN-FOR-RESIZER.json'
+    plan_path.write_text(json.dumps(plan, indent=2)+'\n')
+    final_dir = args.out/'all72'
+    run('expand_owners.py', '--plan', plan_path, '--owners', seed_dir/'OWNERS.json.gz',
+        '--signature', f'jp8={provider}', '--signature', f'ck={provider}',
+        '--max-passes', '8', '--out', final_dir)
+    for name in ('OWNERS.json.gz', 'MAJORIZATION.json.gz'):
+        assert semantic_sha(final_dir/name) == manifest['artifacts'][name]['semantic_sha256'], (name, 'Frozen semantic digest mismatch')
+    kwargs = ('--local44', args.local44) if args.local44 is not None else ('--raw-word', args.raw_word)
+    run('audit_frozen.py', '--parent-plan', args.parent_plan, '--parent-owners', args.parent_owners,
+        *kwargs, '--owners', final_dir/'OWNERS.json.gz', '--majorization', final_dir/'MAJORIZATION.json.gz',
+        '--out', args.out/'FROZEN-AUDIT.json')
+    receipt = {
+        'status': 'PASS_FROZEN_OWNER_AND_INTEGER_MAJORIZATION_REPLAY',
+        'seed_mode': 'two_pass_hungarian_discovery_rebuilt' if args.rebuild_seed else 'included_frozen_seed',
+        'parent_plan_sha256': sha(args.parent_plan), 'parent_owners_sha256': sha(args.parent_owners),
+        'owners_semantic_sha256': semantic_sha(final_dir/'OWNERS.json.gz'),
+        'owners_gzip_sha256': sha(final_dir/'OWNERS.json.gz'),
+        'majorization_semantic_sha256': semantic_sha(final_dir/'MAJORIZATION.json.gz'),
+        'global_profile': read(final_dir/'PROFILE.json'),
+        'scope': 'Exact hosting nomination and callwise fixed-point replay; full supplier admission is separate.',
+    }
+    (args.out/'REPRODUCTION.json').write_text(json.dumps(receipt, indent=2)+'\n')
+    print(json.dumps(receipt, indent=2))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/hosting/reuse_owners.py b/research/gauge44-slots-t16/hosting/reuse_owners.py
new file mode 100644
index 0000000000..234b831790
--- /dev/null
+++ b/research/gauge44-slots-t16/hosting/reuse_owners.py
@@ -0,0 +1,230 @@
+"""Deterministic existing-family owner reuse and optional callwise matching.
+
+The output is a nomination, requiring the ordinary independent owner, phase,
+finite-invoice, and exact-moment admission. No MILP or new owner family is used.
+"""
+from collections import Counter, defaultdict
+from pathlib import Path
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+import math
+import time
+
+
+def read(path):
+    raw=Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def packed(obj):return json.dumps(obj,sort_keys=True,separators=(',',':')).encode()
+def sha(path):return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def signature(path):
+    path=Path(path)
+    if path.is_dir():
+        w=read(path/'CANONICAL-WORD.json.gz');V,R=w['v'],w['R']
+        widths=[len(w['frames'][w['final'][2*V+h]])-len(w['frames'][w['start'][2*V+h]]) for h in range(R)]
+        programs=read(path/'LOCAL-PROGRAMS.json.gz')
+        profiles=[Counter(e[-1] for e in programs[o] if e[0] in ('climb','center')) for o in ('forward','backward')]
+        assert profiles[0]==profiles[1]
+        assert profiles[0]=={int(r):n for r,n in w['local_profile'].items()}
+        return {'widths':widths,'profile':dict(profiles[0]),'source':str(path),
+                'canonical_sha256':sha(path/'CANONICAL-WORD.json.gz'),
+                'program_sha256':sha(path/'LOCAL-PROGRAMS.json.gz')}
+    w=read(path)
+    if 'report' in w:
+        V,R=w['report']['v'],w['report']['R']
+        widths=[len(w.get('helper_final',{}).get(str(2*V+h),range(9)))-len(w.get('start_extra',{}).get(str(2*V+h),[])) for h in range(R)]
+        profile={int(r):n for r,n in w['report']['local_profile'].items()}
+    else:
+        widths=w['widths'];profile={int(r):n for r,n in w['profile'].items()}
+    return {'widths':widths,'profile':profile,'source':str(path),'source_sha256':sha(path)}
+
+
+def phi(rank,b,M):return rank*math.expm1(b*math.log(M/rank)) if rank else 0.
+
+
+def rate(profile,deficit,M):
+    lo,hi=0.,.02
+    for _ in range(58):
+        mid=(lo+hi)/2
+        if sum(n*phi(r,mid,M) for r,n in profile.items())<deficit:lo=mid
+        else:hi=mid
+    return lo
+
+
+def audit_roles(roles,plan,widths_by_call,V,R):
+    used=defaultdict(set);families=defaultdict(set);helpers=defaultdict(set)
+    for z in roles:
+        s,rep,h=z['stage'],z['replica'],z['helper'];call=(s,rep)
+        assert z['time']==plan['order'].index([s,rep])
+        assert 0<=h<R and z['width']==widths_by_call[call][h]
+        assert h not in helpers[call] and z['family'] not in families[call]
+        helpers[call].add(h);families[call].add(z['family'])
+        orp,ch,port=z['owner_replica'],z['child'],z['port']
+        assert z['copy']==orp*V+port
+        assert z['family']==orp*(8*V)+(2*plan['pairs'][str(ch)]+plan['sides'][str(ch)])*V+port
+        cap,window=plan['windows'][f'{orp},{ch}']
+        assert z['time'] in window and 0<=z['offset'] and z['offset']+z['width']<=cap
+        cells=set(range(z['offset'],z['offset']+z['width']))
+        key=(orp,ch,port);assert not used[key]&cells;used[key]|=cells
+    assert len(roles)==len(plan['order'])*R
+    assert all(helpers[tuple(c)]==set(range(R)) for c in plan['order'])
+    for cells in used.values():assert cells==set(range(len(cells)))
+    return used,families
+
+
+def main():
+    ap=argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--plan',type=Path,required=True)
+    ap.add_argument('--owners',type=Path,required=True)
+    ap.add_argument('--signature',action='append',default=[],help='Existing PID=raw-word, signature JSON, or verified native directory')
+    ap.add_argument('--passes',type=int,default=2)
+    ap.add_argument('--price-b',type=float,default=0.001638923)
+    ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args();assert 0<=a.passes<=2
+    a.out.mkdir(parents=True,exist_ok=False);beg=time.monotonic()
+    plan,oldroles=read(a.plan),read(a.owners)
+    assert (plan['K'],plan['T'],plan['M'],plan['L'])==(4,8,73,9)
+    M,V=73,112;R=len(next(iter(plan['provider_registry'].values()))['widths'])
+    signatures={pid:{'widths':desc['widths'],'profile':{int(r):n for r,n in desc['actual_paid_profile'].items()},'source':'inherited PLAN'} for pid,desc in plan['provider_registry'].items()}
+    for spec in a.signature:
+        pid,path=spec.split('=',1);assert pid in signatures
+        signatures[pid]=signature(path)
+    for sig in signatures.values():
+        assert len(sig['widths'])==R and all(type(w) is int and 0<w<=9 for w in sig['widths'])
+        assert sum(int(r)*n for r,n in sig['profile'].items())==16*V+64+sum(sig['widths'])
+    calls={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+    oldwidths={k:plan['provider_registry'][c['provider']]['widths'] for k,c in calls.items()}
+    newwidths={k:signatures[c['provider']]['widths'] for k,c in calls.items()}
+    oldused,oldfamilies=audit_roles(oldroles,plan,oldwidths,V,R)
+
+    # A slot is an old immutable owner-family opportunity. Only the helper
+    # assigned to the opportunity and its footprint width may change.
+    bycall=defaultdict(list);groups=defaultdict(list)
+    for i,z in enumerate(oldroles):
+        bycall[z['stage'],z['replica']].append(i)
+        groups[z['owner_replica'],z['child'],z['port']].append(i)
+    group_of={i:g for g,ids in groups.items() for i in ids}
+    cap={g:plan['windows'][f'{g[0]},{g[1]}'][0] for g in groups}
+    assigned_h={};assigned_w={};dominance={};pending=[]
+    for call,ids in bycall.items():
+        slots=sorted(ids,key=lambda i:(oldroles[i]['width'],oldroles[i]['helper']))
+        helpers=sorted(range(R),key=lambda h:(newwidths[call][h],h))
+        failures=[(h,newwidths[call][h],oldroles[i]['width']) for h,i in zip(helpers,slots) if newwidths[call][h]>oldroles[i]['width']]
+        if failures:
+            # Keep this call's old widths provisionally; shrunk calls leave
+            # slack on their original owner families. A subsequent exact
+            # bipartite matching may use that slack for this call.
+            pending.append(call)
+            for i in ids:assigned_h[i]=oldroles[i]['helper'];assigned_w[i]=oldroles[i]['width']
+        else:
+            for h,i in zip(helpers,slots):assigned_h[i]=h;assigned_w[i]=newwidths[call][h]
+        dominance[str(call)]={'old_total':sum(oldwidths[call]),'new_total':sum(newwidths[call]),'sorted_termwise_dominance':not failures,'failed_positions':failures}
+    used={g:sum(assigned_w[i] for i in ids) for g,ids in groups.items()}
+    assert all(used[g]<=cap[g] for g in groups)
+    cost_cache=[phi(r,a.price_b,M) for r in range(49)]
+    def current_cost():return sum(cost_cache[cap[g]-used[g]] for g in groups)
+    passes=[{'pass':'sorted','touched_group_idle_pressure':current_cost(),'calls_awaiting_capacity_matching':len(pending)}]
+
+    if a.passes or pending:
+        import numpy as np
+        from scipy.optimize import linear_sum_assignment
+        def match_call(call,force=False):
+            ids=sorted(bycall[call],key=lambda i:oldroles[i]['helper'])
+            gs=[group_of[i] for i in ids]
+            assert len(set(gs))==R, 'one owner family per complete call is essential'
+            available=np.array([cap[g]-used[g]+assigned_w[i] for i,g in zip(ids,gs)],dtype=np.int64)
+            ws=np.array(newwidths[call],dtype=np.int64)
+            left=available[None,:]-ws[:,None]
+            matrix=np.full((R,R),np.inf)
+            valid=left>=0
+            matrix[valid]=np.asarray(cost_cache)[left[valid]]
+            ri,ci=linear_sum_assignment(matrix)
+            assert len(ri)==R and np.all(np.isfinite(matrix[ri,ci]))
+            oldcost=sum(cost_cache[cap[g]-used[g]] for g in gs)
+            newcost=float(matrix[ri,ci].sum())
+            if not force:
+                assert newcost<=oldcost+1e-10
+                if oldcost-newcost<=1e-10:return False
+            for h,col in zip(ri,ci):
+                i=ids[int(col)];g=group_of[i];h=int(h);ww=int(ws[h])
+                used[g]+=ww-assigned_w[i];assigned_w[i]=ww;assigned_h[i]=h
+                assert used[g]<=cap[g]
+            return True
+        for call in pending:
+            match_call(call,force=True)
+            dominance[str(call)]['capacity_matching_feasible']=True
+        if pending:passes.append({'pass':'capacity_bootstrap','touched_group_idle_pressure':current_cost(),'resolved_calls':[list(c) for c in pending]})
+        for p in range(a.passes):
+            accepted=0;startcost=current_cost()
+            order=[tuple(k) for k in plan['order']]
+            if p%2:order.reverse()
+            for call in order:
+                accepted+=match_call(call)
+            finalcost=current_cost();assert finalcost<=startcost+1e-9
+            passes.append({'pass':p+1,'accepted_calls':accepted,'touched_group_idle_pressure':finalcost,'decrease':startcost-finalcost})
+
+    # The inherited compiler requires each used coordinate set to be a
+    # prefix. Stable left compaction preserves every immutable owner field.
+    roles=copy.deepcopy(oldroles);matching=[]
+    for g,ids in groups.items():
+        off=0
+        for i in sorted(ids,key=lambda i:(oldroles[i]['offset'],oldroles[i]['time'],oldroles[i]['helper'])):
+            z=roles[i];z['helper']=assigned_h[i];z['width']=assigned_w[i];z['offset']=off;off+=z['width']
+            matching.append({'stage':z['stage'],'replica':z['replica'],'old_helper':oldroles[i]['helper'],
+                             'new_helper':z['helper'],'old_width':oldroles[i]['width'],'new_width':z['width'],
+                             'family':z['family'],'child':z['child'],'old_offset':oldroles[i]['offset'],'new_offset':z['offset']})
+        assert off==used[g]<=cap[g]
+    roles.sort(key=lambda z:(z['time'],z['helper']))
+    newused,newfamilies=audit_roles(roles,plan,newwidths,V,R)
+    assert newfamilies==oldfamilies
+    paid=Counter();remainders=[]
+    for c in plan['provider_calls']:paid.update(signatures[c['provider']]['profile'])
+    idle=Counter()
+    for key,(capacity,window) in plan['windows'].items():
+        rep,ch=map(int,key.split(','))
+        for port in range(V):
+            occupied=len(newused[rep,ch,port]);left=capacity-occupied
+            if left:
+                family=rep*(8*V)+(2*plan['pairs'][str(ch)]+plan['sides'][str(ch)])*V+port
+                remainders.append({'child':ch,'port':port,'replica':rep,'replicas':1,'family':family,
+                                   'rank':left,'hosted':occupied,'pending_offset':occupied})
+                idle[left]+=1
+    paid.update(idle);mass=sum(r*n for r,n in paid.items())
+    assert M*plan['live']-mass==plan['deficit']==2560
+    assert M*M>2*max(paid)**2
+    oldprofile={int(r):n for r,n in plan['profile'].items()}
+    ownerraw=packed(roles);gz=bytearray(gzip.compress(ownerraw,mtime=0));gz[9]=255
+    (a.out/'OWNERS.json.gz').write_bytes(bytes(gz))
+    (a.out/'MATCHING.json.gz').write_bytes(gzip.compress(packed(matching),mtime=0))
+    (a.out/'REMAINDERS.json').write_text(json.dumps(remainders,indent=2)+'\n')
+    profile=dict(sorted(paid.items()))
+    (a.out/'PROFILE.json').write_text(json.dumps(profile,indent=2)+'\n')
+    owner_fields={'profile':profile,
+                  'per_call_widths':[{'stage':s,'replica':r,'widths':newwidths[s,r]} for s,r in plan['order']],
+                  'assignment_sha256':hashlib.sha256(ownerraw).hexdigest(),
+                  'assignment_sha256_semantics':'SHA256 of sorted-key compact uncompressed OWNERS array',
+                  'source_owners_sha256':sha(a.owners),
+                  'provider_signatures':signatures}
+    (a.out/'PLAN-OWNER-FIELDS.json').write_text(json.dumps(owner_fields,indent=2)+'\n')
+    rec={'status':'PASS_OWNER_REUSE_NOMINATION_COMBINATORICS_NOT_FULL_SUPPLIER_ADMISSION',
+         'source_plan':str(a.plan),'source_plan_sha256':sha(a.plan),'source_owners_sha256':sha(a.owners),
+         'owners_sha256':sha(a.out/'OWNERS.json.gz'),'unchanged_owner_family_sets':True,
+         'unchanged_call_order_and_windows':True,'all_footprints_are_disjoint_compacted_prefixes':True,
+         'local_signatures':signatures,'sorted_initial_dominance':dominance,'matching_passes':passes,
+         'roles':len(roles),'calls':len(calls),'remainder_children':len(remainders),'remainder_profile':dict(sorted(idle.items())),
+         'global_profile':profile,'rank_mass':mass,'deficit':2560,'maxchild':max(paid),
+         'source_floating_screen_b':rate(oldprofile,2560,M),
+         'candidate_floating_screen_b':rate(profile,2560,M),
+         'seconds':time.monotonic()-beg,
+         'remaining_admission':'Bind freshly verified provider artifacts and their hashes; regenerate the global template, actual 73-column sigmas and remainder axes with the existing emitter; run independent owner/frame audit, finite invoice, and exact moment/outer assembly.'}
+    (a.out/'OWNER-REUSE.json').write_text(json.dumps(rec,indent=2)+'\n')
+    print(json.dumps({k:rec[k] for k in ('status','roles','matching_passes','remainder_profile','rank_mass','source_floating_screen_b','candidate_floating_screen_b','seconds')},indent=2),flush=True)
+
+
+if __name__=='__main__':main()
diff --git a/research/gauge44-slots-t16/independent/CENTRE-GUARD-REVIEW.md b/research/gauge44-slots-t16/independent/CENTRE-GUARD-REVIEW.md
new file mode 100644
index 0000000000..6c62bd070e
--- /dev/null
+++ b/research/gauge44-slots-t16/independent/CENTRE-GUARD-REVIEW.md
@@ -0,0 +1,79 @@
+# Independent review of the centre and admission interfaces
+
+**Finding:** the replacement of old local centre-carrier IDs by equality of the
+eight ordered centre-frame bases preserves the inherited global contract. It
+must be used together with the complete local scalar, frame, phase and wrapper
+admission. No mathematical admission guard was found to have been removed.
+
+## Why source carriers may supply centres
+
+The transported gauge44 centre carriers are
+`[92, 57, 81, 224, 11, 240, 9, 256]`. Five are source registers and three are
+helper registers. All 112 transported port labels and all eight ordered
+rank-eight centre-frame bases agree exactly with the retained parent. The
+optional `--main` check in `audit_local.py` independently verifies that boundary
+against a byte-pinned parent canonical word.
+
+The actual forward local program copies the current row of `L_r` into private
+`C_k` at their common frame `F_k`. It then descends `C_k` from `F_k` to frame
+zero, scatters to the targets, and clears `C_k`. The backward program performs
+the corresponding reversed ascent and scatter. This construction depends on
+the copied row, its frame and the exact local program, rather than on a
+requirement that `r` be in the helper-ID interval. The source itself is not
+cleared or treated as private work.
+
+The independently checked local contract retains every required obligation:
+all 716 input columns in both orientations; the forward and backward shear
+identities; arbitrary initial helper dirt; scalar/COPY common-frame legality;
+centre lifetimes and nested steps; exact native phase identities; endpoint
+and row/column cone conditions; and residual wrappers before and after every
+relevant touch. Its finite invoice recounts the actual operations.
+
+The global controller addresses private centres by `k`, while the source or
+helper `L_r` is mapped through the complete invocation's ordinary owner array.
+The owner audit retains pairwise distinct owners for all active source, target
+and helper roles. A helper therefore cannot borrow the family of an active
+source centre. The private-centre namespace is disjoint from those owners and
+the local program clears it. Each whole invocation finishes before another
+begins, so no new interleaving or family lifetime assumption is introduced.
+
+## Admission guards and single-provider controls
+
+An AST comparison with PR635 found all **91 assertions in `code/assemble.py`
+identical, in the same traversal order**, including constants. This includes
+the unchanged PR543 bit input, deficit and surcharge, every finite-invoice
+guard, both conservative and native complex moment checks, and the strict
+outer assembly and its controls. The following files retain the reviewed PR635 code (the packaged
+`bind_providers_portable.py` only trims trailing whitespace): `invoice_allcold.py` (67 assertions),
+`bind_providers_portable.py` (22), `generated_identity.py` (4), and `witness.py`
+(3). `review_guards.py` reproduces the assertion comparison and records the
+file hashes.
+
+The controller still checks the complete serialized provider registry,
+per-call program and dispatch, native phase and wrapper bindings, helper
+widths, owner uniqueness, actual busy-family windows, spectator orthogonality,
+and literal idle remainders. The single-provider branch replaces partner
+substitutions by direct invalid-ID, program, width and hash mutations. Only
+four assembly mutation scenarios requiring a second registered provider are
+inapplicable. Their removal does not remove any admission predicate. Direct
+forged program/phase tests, width-order and width-inventory tests, and
+selected-call/order tests remain.
+
+## Price and bit headroom
+
+The frozen all72 profile gives the native complex root bracket
+`(0.001652208994368411824947, 0.001652208994368411824948)` and
+`kappa = 0.001649483702558979`. Both independent rational engines certify the
+two signs. The seven-step outer driver passes all 47 strict constraints and
+rejects its four standard mutations. The conservative complex price passes
+separately at `kappa = 0.001649483699681650`.
+
+The achieved complex rate is below PR543's retained bit rate
+`0.001653826988146798944268`. Using eumemic's independently reviewed PR555 bit
+rate `0.001733052823330162099157` gives exactly the same attained kappa. PR543
+therefore remains the cited supplier for this delta; no bit improvement is
+claimed here and no PR555 implementation is bundled.
+
+These receipts supplement the package's complete native, owner, phase and
+finite-invoice replay. The inherited all-size realization and analytic
+transfer assumptions remain conditional.
diff --git a/research/gauge44-slots-t16/independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json b/research/gauge44-slots-t16/independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json
new file mode 100644
index 0000000000..771faa86a7
--- /dev/null
+++ b/research/gauge44-slots-t16/independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json
@@ -0,0 +1,137 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+  "input_file": "FULL-WORD.json.gz",
+  "content_sha256": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290",
+  "compressed_sha256": "3ef4e74e81e2f4621fc95272918ac7b8bb8858df0baa16cc6d91424d55aead9e",
+  "parent_center_interface": {
+    "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+    "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "transport_tau": 43,
+    "ordered_frame_bases_match": true,
+    "all_ports_match": true,
+    "transported_centers": [
+      92,
+      57,
+      81,
+      224,
+      11,
+      240,
+      9,
+      256
+    ],
+    "source_centers": [
+      92,
+      57,
+      81,
+      11,
+      9
+    ],
+    "ordered_frame_bases": [
+      [
+        256,
+        128,
+        64,
+        34,
+        16,
+        10,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        16,
+        8,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        17,
+        9,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ],
+      [
+        256,
+        128,
+        66,
+        32,
+        18,
+        8,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        17,
+        9,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        16,
+        8,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        68,
+        32,
+        16,
+        12,
+        2,
+        1
+      ]
+    ]
+  },
+  "v": 112,
+  "h": 9,
+  "R": 492,
+  "entering": 204,
+  "lowends": 78,
+  "coldends": 44,
+  "compensation_gates": 7348,
+  "local_profile": {
+    "1": 2514,
+    "2": 404,
+    "3": 448,
+    "4": 160,
+    "5": 56,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 52,
+    "5": 48,
+    "7": 34,
+    "8": 114,
+    "9": 244
+  },
+  "checked_columns": 716,
+  "elapsed_seconds": 3.147683588000291,
+  "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+}
diff --git a/research/gauge44-slots-t16/independent/GAUGE44-GLOBAL-GUARD-REVIEW.json b/research/gauge44-slots-t16/independent/GAUGE44-GLOBAL-GUARD-REVIEW.json
new file mode 100644
index 0000000000..e2df1dcca8
--- /dev/null
+++ b/research/gauge44-slots-t16/independent/GAUGE44-GLOBAL-GUARD-REVIEW.json
@@ -0,0 +1,47 @@
+{
+  "status": "PASS_PR635_ADMISSION_ASSERTION_PRESERVATION",
+  "files": [
+    {
+      "file": "code/assemble.py",
+      "baseline_sha256": "1b1a9024ac910dc9b9d9e30150684e1fa9cb228a4c1c275b75ab04b57fdef1dd",
+      "new_sha256": "7ac28118d69416e4fb67b61216285fb0823310b7635ce1b9025aa3f10119ef6a",
+      "byte_identical": false,
+      "assert_count": 91,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/invoice_allcold.py",
+      "baseline_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+      "new_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+      "byte_identical": true,
+      "assert_count": 67,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/bind_providers_portable.py",
+      "baseline_sha256": "2eb5c262bf481b3bec9ceaec654fa46ff6fc3a89b13d4906a29a55a89e35feea",
+      "new_sha256": "2eb5c262bf481b3bec9ceaec654fa46ff6fc3a89b13d4906a29a55a89e35feea",
+      "byte_identical": true,
+      "assert_count": 22,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/generated_identity.py",
+      "baseline_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+      "new_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+      "byte_identical": true,
+      "assert_count": 4,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/witness.py",
+      "baseline_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+      "new_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+      "byte_identical": true,
+      "assert_count": 3,
+      "all_assertions_identical_in_order": true
+    }
+  ],
+  "centre_interface_review": "CENTRE-GUARD-REVIEW.md",
+  "scope": "Exact syntax preservation for all admission assertions in these five files. The changed emitter/controller centre boundary and single-provider controls require the separate semantic review; assertion counts alone do not prove them."
+}
diff --git a/research/gauge44-slots-t16/independent/GAUGE44-INDEPENDENT-PRICE.json b/research/gauge44-slots-t16/independent/GAUGE44-INDEPENDENT-PRICE.json
new file mode 100644
index 0000000000..7aa86180dd
--- /dev/null
+++ b/research/gauge44-slots-t16/independent/GAUGE44-INDEPENDENT-PRICE.json
@@ -0,0 +1,156 @@
+{
+  "status": "PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK",
+  "profile_input_file": "PLAN.json",
+  "profile_input_sha256": "7b3122026e82b9d9e964d2a50c7bffdc976ae3dfea64bb98b2fdad5cfbdbaa20",
+  "global_profile": {
+    "1": 174763,
+    "2": 30105,
+    "3": 30275,
+    "4": 12240,
+    "5": 4896,
+    "7": 54,
+    "8": 576,
+    "16": 23,
+    "48": 2419
+  },
+  "live": 7168,
+  "m": 73,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "prices": {
+    "native": {
+      "root": {
+        "lower": "0.001674185476674086429846",
+        "upper": "0.001674185476674086429847",
+        "lower_endpoint_residual_upper": "-9.258737006004892346173061244464039982798397391664878463422077941068021E-25",
+        "upper_endpoint_residual_lower": "2.005290772036567694936493754533147163786510359586083088453102073919377E-24",
+        "strict_rational_signs": true
+      },
+      "exact_moments": [
+        {
+          "endpoint": "837092738337043214923/500000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-24961505588706589063536270371864708160498115/26959946667150639794667015087019630673637144422540572481103610249216",
+            "-24961505588706589063536270371864708160498113/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "-462937/500000000000000000000000000000",
+            "-925873/1000000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "1674185476674086429847/1000000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "54062532266235196619370246291034158858524675/26959946667150639794667015087019630673637144422540572481103610249216",
+            "54062532266235196619370246291034158858524677/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "200529/100000000000000000000000000000",
+            "2005291/1000000000000000000000000000000"
+          ]
+        }
+      ],
+      "outer_with_bit": {
+        "complex_b": "837092738337043214923/500000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "835693632195073/500000000000000000",
+        "kappa_decimal": "0.001671387264390146",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    },
+    "conservative": {
+      "root": {
+        "lower": "0.001674185473814575474867",
+        "upper": "0.001674185473814575474868",
+        "lower_endpoint_residual_upper": "-4.932703074050864500363221905991238131757959051186123070698964701314504E-25",
+        "upper_endpoint_residual_lower": "2.437894165237372647986425295760776771093048289170590753978317997095726E-24",
+        "strict_rational_signs": true
+      },
+      "exact_moments": [
+        {
+          "endpoint": "1674185473814575474867/1000000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-6649270590065065997663222052892326679295837/13479973333575319897333507543509815336818572211270286240551805124608",
+            "-1662317647516266499415805513223081669823959/3369993333393829974333376885877453834204643052817571560137951281152"
+          ],
+          "base_two_residual": [
+            "-246635539906040992121/500000000000000000000000000000000000000000000",
+            "-2466350399060409921139/5000000000000000000000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "418546368453643868717/250000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "65725496674957295861389862879254608557678601/26959946667150639794667015087019630673637144422540572481103610249216",
+            "65725496674957295861389862879254608557678603/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "12189469601119396732213/5000000000000000000000000000000000000000000000",
+            "24378949202238793464567/10000000000000000000000000000000000000000000000"
+          ]
+        }
+      ],
+      "outer_with_bit": {
+        "complex_b": "1674185473814575474867/1000000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "835693630770093/500000000000000000",
+        "kappa_decimal": "0.001671387261540186",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    }
+  },
+  "bit_supplier_pr": 589,
+  "bit_deficit": 10272,
+  "bit_moments_with_surcharge": [
+    {
+      "endpoint": "1733427039589844234749/1000000000000000000000000",
+      "accept": true,
+      "mercator_residual": [
+        "-43100600330766044577088869872467188970742291/26959946667150639794667015087019630673637144422540572481103610249216",
+        "-43100600330766044577088869872467188970742289/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two_residual": [
+        "-799345163337715793503/500000000000000000000000000000000000000000000",
+        "-3197378653350863173989/2000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "endpoint": "6933708158359376939/4000000000000000000000",
+      "accept": false,
+      "mercator_residual": [
+        "22502934905675809315035333485365686073718547/13479973333575319897333507543509815336818572211270286240551805124608",
+        "5625733726418952328758833371341421518429637/3369993333393829974333376885877453834204643052817571560137951281152"
+      ],
+      "base_two_residual": [
+        "8346798366759439729359/5000000000000000000000000000000000000000000000",
+        "16693606733518879458833/10000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "gain_over_pr635_percent": "2.14795693544613460937516788041147829054201996498013663108098185775358537919",
+  "input_sha256": {
+    "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "package:inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4"
+  },
+  "scope": "Independent arithmetic for the exact nominated all72 profile. Complete local, controller and finite invoice admission are separately replayed by the package driver; this receipt does not replace them. The cited PR589 bit supplier is unchanged and its exceptional-residue surcharge is retained. Any alternative c is only a headroom comparison."
+}
diff --git a/research/gauge44-slots-t16/independent/README.md b/research/gauge44-slots-t16/independent/README.md
new file mode 100644
index 0000000000..f97dcf81b1
--- /dev/null
+++ b/research/gauge44-slots-t16/independent/README.md
@@ -0,0 +1,43 @@
+# Independent checks
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0, under the
+package license. The scalar/frame audit imports no generator or supplier
+checker. Pricing uses the pinned inherited rational engines and the retained
+PR635 outer formula, with their original notices preserved in the main
+dependency tree.
+
+From the delta package directory, using the pinned checkouts and a rebuilt
+word:
+
+```sh
+python independent/audit_local.py \
+  --word /path/to/rebuild/cold44/FULL-WORD.json.gz \
+  --main /path/to/main \
+  --output /path/to/output/LOCAL-AUDIT.json
+
+python independent/price_profile.py \
+  --main /path/to/main \
+  --output /path/to/output/PRICE.json
+
+python independent/review_guards.py \
+  --pr635 /path/to/pr635 \
+  --output /path/to/output/GUARD-REVIEW.json
+```
+
+`audit_local.py` can run without `--main`; including it also verifies the
+transported centre-frame and port boundary against the pinned parent. Its
+receipt authenticates the supplied word by its content SHA256, independent
+of its location. `price_profile.py` defaults to the package's `data/PLAN.json`;
+`--profile` accepts another explicit profile for arithmetic only. The bit side is the cited merged PR589 supplier
+(`inputs/PR589-EXPECTED.json`, git blob `e293ddc5…`); its rank-mass deficit
+`T(2Kv - L*cst) = 32*(8*111 - 9*63) = 10272` is re-derived independently of
+`code/assemble.py`, and the outer receipt key is `outer_with_bit`. The retained
+`GAUGE44-INDEPENDENT-PRICE.json` is #645/PR543 historical evidence unless regenerated. The optional
+`--headroom-c 0.001733052823330162099157` reproduces the unchanged-kappa
+comparison with the reviewed PR555 rate without importing a second supplier.
+
+The retained receipts are `GAUGE-COLD44-INDEPENDENT-AUDIT.json`,
+`GAUGE44-INDEPENDENT-PRICE.json`, and `GAUGE44-GLOBAL-GUARD-REVIEW.json`.
+[CENTRE-GUARD-REVIEW.md](CENTRE-GUARD-REVIEW.md) gives the semantic argument
+behind the changed centre boundary and the single-provider control branch.
+The main package driver performs the separate complete global admission.
diff --git a/research/gauge44-slots-t16/independent/audit_local.py b/research/gauge44-slots-t16/independent/audit_local.py
new file mode 100644
index 0000000000..4744d8783c
--- /dev/null
+++ b/research/gauge44-slots-t16/independent/audit_local.py
@@ -0,0 +1,171 @@
+"""Independent exact scalar/frame audit of the changed forward supplier.
+
+This does not import a generator, builder, stored compensation, or price.
+All claimed endpoint matrices are derived from the input word's gates.
+Optional --main checks the transported boundary against the pinned parent.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse,gzip,json,hashlib,time
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+
+def require(x,label):
+    if not x:raise RuntimeError(label)
+
+def basis(vs):
+    piv={}
+    for a in vs:
+        while a:
+            bit=a.bit_length()-1
+            if bit in piv:a^=piv[bit]
+            else:
+                piv[bit]=a;break
+    for k in sorted(piv):
+        for j in piv:
+            if j>k and piv[j]>>k&1:piv[j]^=piv[k]
+    return tuple(piv[k] for k in sorted(piv,reverse=True))
+
+def contained(a,b):return basis(a+b)==b
+
+def registers(e):return e[1:3] if e[0]=='add' else e[1:2]
+
+def apply(e,rows,dual=False):
+    if e[0]=='add':
+        t,s=e[1:3];q=F(e[3],e[4]);require(t!=s,'self add')
+        if dual:t,s,q=s,t,-q
+        dst=rows[t]
+        for k,x in list(rows[s].items()):
+            a=dst.get(k,F(0))+q*x
+            if a:dst[k]=a
+            else:dst.pop(k,None)
+    elif e[0]=='scale':
+        t=e[1];q=F(e[2],e[3]);require(q!=0,'zero scale')
+        if dual:q=1/q
+        rows[t]={k:q*x for k,x in rows[t].items()}
+    else:raise RuntimeError('unknown scalar primitive')
+
+def invert(e):
+    r=list(e)
+    if r[0]=='add':r[3]=-r[3]
+    else:r[2],r[3]=r[3],r[2]
+    return r
+
+def check_parent_interface(word,main):
+    # Read only the retained boundary data. No builder or local checker is imported.
+    relative="research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz"
+    path=main/relative;raw=path.read_bytes()
+    require(hashlib.sha256(raw).hexdigest()=="66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",'parent canonical input pin')
+    parent=json.loads(gzip.decompress(raw))
+    tau=lambda x:x^(43 if (x&43).bit_count()%2 else 0)
+    ports=parent['ports'];v=word['report']['v']
+    require(len(ports)==len(set(ports))==v,'parent port count')
+    require(set(map(tau,word['ports']))==set(ports),'transported source/target ports')
+    moved={i:ports.index(tau(p)) for i,p in enumerate(word['ports'])}
+    centers=[moved.get(r,r) for r in word['centers']]
+    actual=[list(basis([tau(x) for x in frame])) for frame in word['center_frames']]
+    expected=[parent['frames'][f] for f in parent['center_frames']]
+    require(len(centers)==len(set(centers))==len(actual)==8,'eight distinct centre carriers')
+    require(actual==expected and all(len(f)==8 for f in actual),'ordered centre frame interface')
+    return dict(parent_path=relative,parent_file_sha256=hashlib.sha256(raw).hexdigest(),
+                transport_tau=43,ordered_frame_bases_match=True,all_ports_match=True,
+                transported_centers=centers,source_centers=[r for r in centers if r<v],
+                ordered_frame_bases=actual)
+
+
+def run(path,out,main=None):
+    begin=time.monotonic();data=gzip.decompress(path.read_bytes());w=json.loads(data)
+    v,h,R=w['report']['v'],w['report']['h'],w['report']['R'];n=2*v+R
+    require((v,h)==(112,9),'wrong source geometry')
+    center_interface=check_parent_interface(w,main) if main is not None else None
+    ident=lambda:[{k:F(1)} for k in range(n)]
+    main=w['A']+w['cut']+w['B']
+    for e in main+w['precondition']+w['cleanup']:
+        require(all(0<=k<n for k in registers(e)),'register out of range')
+        q=F(e[3],e[4]) if e[0]=='add' else F(e[2],e[3])
+        require(q.denominator&(q.denominator-1)==0,'non-dyadic scalar')
+        if e[0]=='scale':require(abs(q.numerator)&(abs(q.numerator)-1)==0,'non-unit scale')
+    require(all(not(v<=e[2]<2*v) for e in w['A']+w['B'] if e[0]=='add' and not(v<=e[1]<2*v)), 'non-target reads target')
+    raw=ident()
+    for e in main:apply(e,raw)
+    dirt=[{} for _ in range(n)]
+    for y in range(v,2*v):dirt[y]={k:a for k,a in raw[y].items() if k>=2*v}
+    for e in w['precondition']:apply(e,dirt)
+    compensation=[['add',y,k,-a.numerator,a.denominator,[]] for y in range(v,2*v) for k,a in sorted(dirt[y].items())]
+    entering=set(map(int,w.get('start_extra',{})));lowends=set(map(int,w.get('helper_final',{})))
+    coldends=lowends-entering
+    require(not any(e[2] in entering for e in compensation),'nonzero entrance response')
+    require(not any(r in entering|coldends for e in w['precondition']+compensation for r in registers(e)), 'pre-wrapper touch of residual helper')
+    require(all(e[-1]==[] for e in w['precondition']+compensation),'nonzero frame precondition')
+    early=w.get('early_cleanup',[]);earlyids={i for i,U in early}
+    require(len(earlyids)==len(early),'duplicate early cleanup gate')
+    tail=[w['cleanup'][i][:-1]+[U] for i,U in early]
+    cleanup=[e for i,e in enumerate(w['cleanup']) if i not in earlyids]
+    prefix=w['precondition']+compensation+main
+    program=prefix+tail+cleanup
+    for dual in (False,True):
+        actual=ident()
+        for e in program:apply(e,actual,dual)
+        expected=ident()
+        for t in range(v):expected[t if dual else v+t][v+t if dual else t]=F(-1 if dual else 1)
+        bad=[i for i in range(n) if actual[i]!=expected[i]]
+        require(not bad,'all-column endpoint failure '+str((dual,bad[:8])))
+        print('endpoint', 'dual' if dual else 'forward','PASS',flush=True)
+    full=basis([1<<i for i in range(h)])
+    end=[full]*v+[basis([x for x in range(1,1<<h) if (x&p).bit_count()%2==0]) for p in w['ports']]+[full]*R
+    for q,U in w.get('helper_final',{}).items():end[int(q)]=basis(U)
+    start=[(p,) for p in w['ports']]+[()]*(v+R)
+    for q,U in w.get('start_extra',{}).items():
+        require(2*v<=int(q)<n,'non-helper entrance');start[int(q)]=basis(U)
+    cur=start.copy();paid=Counter()
+    def climb(q,U):
+        U=basis(U);require(contained(cur[q],U),'frame not monotone '+str((q,cur[q],U)))
+        d=len(U)-len(cur[q])
+        if d:paid[d]+=1
+        cur[q]=U
+    for section in ('A','B'):
+        if section=='B':
+            lev={int(t):basis(U) for t,U in w.get('target_levels',{}).items()}
+            require(all(cur[v+t]==lev.get(t,()) for t in range(v)),'target centre levels')
+            for q,U in zip(w['centers'],w['center_frames']):
+                U=basis(U);require(cur[q]==U,'center frame')
+                served={lev.get(e[1]-v,()) for e in w['cut'] if e[2]==q}
+                for T in sorted(served,key=lambda x:-len(x)):
+                    require(contained(T,U),'center path not nested')
+                    if T!=U:paid[len(U)-len(T)]+=1
+                    U=T
+        for e in w[section]:
+            for q in registers(e):climb(q,e[-1])
+    endB=cur.copy()
+    for e in tail:
+        for q in registers(e):climb(q,e[-1])
+    for q,U in enumerate(end):climb(q,U)
+    require(all(all(end[q]==full for q in registers(e)) for e in cleanup),'full cleanup reads a low end')
+    require(dict(paid)=={int(k):a for k,a in w['report']['local_profile'].items()},'paid profile mismatch')
+    inventory=Counter(len(end[q])-len(start[q]) for q in range(2*v,n))
+    require(dict(inventory)=={int(k):a for k,a in w['report']['width_inventory'].items()},'width inventory mismatch')
+    p=ident();pinv=ident()
+    for e in prefix:apply(e,p)
+    for e in reversed(prefix):apply(invert(e),pinv)
+    for q in lowends:
+        U=end[q]
+        require(all(contained(endB[k],U) for k in pinv[q]),'inverse-row cone '+str(q))
+        require(all(k==q or not p[k].get(q) or contained(endB[k],U) for k in range(n)),'dirt-column cone '+str(q))
+    report=dict(status='PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES',
+                input_file=path.name,content_sha256=hashlib.sha256(data).hexdigest(),
+                compressed_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),
+                parent_center_interface=center_interface,v=v,h=h,R=R,
+                entering=len(entering),lowends=len(lowends),coldends=len(coldends),
+                compensation_gates=len(compensation),local_profile=dict(sorted(paid.items())),
+                width_inventory=dict(sorted(inventory.items())),checked_columns=n,
+                elapsed_seconds=time.monotonic()-begin,
+                scope='Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing.')
+    out.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2),flush=True)
+
+if __name__=='__main__':
+    parser=argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--word',type=Path,required=True,help='FULL-WORD.json.gz to check')
+    parser.add_argument('--output',type=Path,required=True,help='JSON receipt output path')
+    parser.add_argument('--main',type=Path,help='Optional pinned main checkout: also verify the transported centre/port interface')
+    args=parser.parse_args()
+    run(args.word,args.output,args.main)
diff --git a/research/gauge44-slots-t16/independent/price_profile.py b/research/gauge44-slots-t16/independent/price_profile.py
new file mode 100644
index 0000000000..0e36ebd468
--- /dev/null
+++ b/research/gauge44-slots-t16/independent/price_profile.py
@@ -0,0 +1,161 @@
+"""Independent arithmetic for the frozen gauge44 profile.
+
+The two rational moment engines and outer.assembly are imported unchanged from
+the pinned main dependencies; no constructor, owner emitter or invoice is run.
+The outer driver is the seven-step formula retained in PR635.
+The bit side is the cited merged PR589 supplier (package inputs/PR589-EXPECTED.json,
+pinned by git blob), with its rank-mass deficit T(2Kv - L*cst) re-derived here
+independently of code/assemble.py.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse
+from decimal import Decimal, localcontext
+from fractions import Fraction as Q
+import hashlib
+import importlib.util
+import json
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+SOURCE = Path('research/complex-k492-owner-repair/vendor/multicold')
+BIT_PATH = HERE.parent/'inputs/PR589-EXPECTED.json'
+BIT_BLOB = 'e293ddc557742637f9f679f083a1a282d87b1b13'
+
+
+def pr589_deficit(word, live):
+    # Nine stages, 32 replicas, four pairs: deficit = 32*(2*4*v - 9*cst), cst = sum of the nine COPY ranks.
+    v, cst, ranks = word['v'], word['decoder_constant'], word['copy_ranks']
+    require(len(ranks) == word['retained_totals'] == 9 and cst == sum(ranks), 'bit decoder constant')
+    require(live == 2*4*v*32, 'bit live wires')
+    return 32*(2*4*v-9*cst)
+
+
+def require(condition, message):
+    if not condition:
+        raise RuntimeError(message)
+
+
+def decimal(q):
+    with localcontext() as ctx:
+        ctx.prec = 75
+        return str(Decimal(q.numerator) / Decimal(q.denominator))
+
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def load(path, name):
+    spec = importlib.util.spec_from_file_location('independent_' + name, path / (name + '.py'))
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def moment_checks(M, B, H, m, W, lower, deficit, bad):
+    require(m*W-sum(r*n for r, n in H.items()) == deficit, 'rank deficit')
+    require(m*m > 2*max(H)**2, 'halving guard')
+    rows = []
+    for z, accept in [(lower, True), (lower+Q(1, 10**24), False)]:
+        l, u = M.moment(H, m, W, z, bad)
+        ll, uu = B.moment(m, W, list(H.items()), z)
+        if bad:
+            fl, fu = B.moment(m, W, [(1, 32*m*m*sum(H.values()))], z)
+            ll, uu = ll+fl/10**16, uu+fu/10**16
+        require((u < 1 and uu < 1) if accept else (l > 1 and ll > 1), 'two exact moment signs')
+        rows.append(dict(endpoint=str(z), accept=accept,
+                         mercator_residual=[str(l-1), str(u-1)],
+                         base_two_residual=[str(ll-1), str(uu-1)]))
+    return rows
+
+
+def outer47(c, b, engine):
+    eta = beta = Q(1, 10**24)
+    s = min(c, (1-beta)*b)-Q(1, 10**27)
+    require(0 < s < c and s < (1-beta)*b, 'strict common saving')
+    a = Q(384599, 10**10)
+    for _ in range(7):
+        old = a
+        a = (1-s)*s+s*old
+        gap = min(s-a, 1-a-s, 1-a-s*(1-old), 1-s)
+        require(old < a < s < 1-a and gap > 0, 'bootstrap gap')
+        ceil = lambda x: -(-x.numerator//x.denominator)
+        cut = max(ceil(36/gap**2), ceil(2*(4+512)/gap))
+        require(cut*gap**2 >= 36 and cut*gap >= 2*(4+512), 'finite bootstrap cutoff')
+    q = a*(1-2*eta)
+    margin = (1-eta)*q/(1+q)
+    ticks = margin*10**18
+    k = Q((ticks.numerator-1)//ticks.denominator, 10**18)
+    bridge = {'semantic': {'C0': {'base': 2, 'exponent': 210000}, 'strict_literal_gap': 1},
+              'rows': {'degree_gap': Q(10**6)-Q(51*20161, 25)}}
+    result = engine.assembly(a, b, bridge, k, eta=eta, beta=beta)
+    require(len(result['strict_constraints']) == 47, '47 outer constraints')
+    require(all(x > 0 for x in result['strict_constraints'].values()), 'strict outer constraints')
+    rejected = []
+    for name, kk, ee, be in [('next_grid', k+Q(1, 10**18), eta, beta),
+                             ('zero_eta', k, Q(0), beta), ('zero_beta', k, eta, Q(0)),
+                             ('unit_beta', k, eta, Q(1))]:
+        try:
+            engine.assembly(a, b, bridge, kk, eta=ee, beta=be)
+        except AssertionError:
+            rejected.append(name)
+        else:
+            raise RuntimeError('accepted negative control: '+name)
+    return dict(complex_b=str(b), bit_c=str(c), kappa=str(k), kappa_decimal=decimal(k),
+                binding='bit' if c < (1-beta)*b else 'complex',
+                strict_constraints_passed=47, controls_rejected=rejected)
+
+
+def main():
+    require(__debug__, 'Do not use python -O: the retained outer engine requires assertions')
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--main', type=Path, required=True, help='Pinned main checkout')
+    parser.add_argument('--profile', type=Path, default=HERE.parent/'data/PLAN.json',
+                        help='Raw profile or a JSON object containing profile/global_profile')
+    parser.add_argument('--output', type=Path, required=True)
+    parser.add_argument('--headroom-c', help='Optional alternative bit saving, for comparison only')
+    args = parser.parse_args()
+    inputs = json.loads((HERE.parent/'data/UPSTREAM-PINS.json').read_text())
+    selected = [SOURCE/'engines'/(n+'.py') for n in ('moment', 'base_two_moment', 'outer')]
+    for relative in selected:
+        require(sha(args.main/relative) == inputs[relative.as_posix()], 'pinned input '+str(relative))
+    M, B, A = [load(args.main/SOURCE/'engines', n) for n in ('moment', 'base_two_moment', 'outer')]
+    supplied = json.loads(args.profile.read_text())
+    H = {int(r): n for r, n in supplied.get('profile', supplied.get('global_profile', supplied)).items()}
+    bit_data = BIT_PATH.read_bytes()
+    require(hashlib.sha1(b'blob '+str(len(bit_data)).encode()+b'\0'+bit_data).hexdigest() == BIT_BLOB, 'PR589 blob pin')
+    record = json.loads(bit_data)
+    bit = record['nine']
+    require('nine-stage' in bit['pipeline'] and '32 replicas' in bit['pipeline'], 'nine-stage bit record')
+    bit_deficit = pr589_deficit(record['word'], bit['bit']['live'])
+    require(sum(int(r)*n for r, n in bit['profile'].items()) == bit['bit']['rank_mass'], 'bit rank mass')
+    c = Q(bit['bit_lower'])
+    bit_checks = moment_checks(M, B, {int(r): n for r, n in bit['profile'].items()},
+                               64, bit['bit']['live'], c, bit_deficit, True)
+    prices = {}
+    for mode, bad in [('native', False), ('conservative', True)]:
+        root = M.certify(H, 73, 7168, bad)
+        root = {key: root[key] for key in ('lower', 'upper', 'lower_endpoint_residual_upper',
+                                          'upper_endpoint_residual_lower', 'strict_rational_signs')}
+        b = Q(root['lower'])
+        row = dict(root=root, exact_moments=moment_checks(M, B, H, 73, 7168, b, 2560, bad),
+                   outer_with_bit=outer47(c, b, A))
+        if args.headroom_c:
+            alternate = outer47(Q(args.headroom_c), b, A)
+            require(alternate['kappa'] == row['outer_with_bit']['kappa'], 'headroom comparison changed kappa')
+            row.update(outer_with_alternative_bit_rate=alternate, same_kappa_with_either_bit_rate=True)
+        prices[mode] = row
+    native_k = Q(prices['native']['outer_with_bit']['kappa'])
+    result = dict(status='PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK',
+                  profile_input_file=args.profile.name, profile_input_sha256=sha(args.profile),
+                  global_profile=H, live=7168, m=73, rank_mass=sum(r*n for r, n in H.items()), deficit=2560,
+                  prices=prices, bit_supplier_pr=589, bit_deficit=bit_deficit, bit_moments_with_surcharge=bit_checks,
+                  gain_over_pr635_percent=decimal(100*(native_k/Q('0.001636241501576388')-1)),
+                  input_sha256={**{relative.as_posix(): sha(args.main/relative) for relative in selected}, 'package:inputs/PR589-EXPECTED.json': sha(BIT_PATH)},
+                  scope='Independent arithmetic for the exact nominated all72 profile. Complete local, controller and finite invoice admission are separately replayed by the package driver; this receipt does not replace them. The cited PR589 bit supplier is unchanged and its exceptional-residue surcharge is retained. Any alternative c is only a headroom comparison.')
+    args.output.write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], prices['native']['outer_with_bit']['kappa_decimal'], result['gain_over_pr635_percent'])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/independent/review_guards.py b/research/gauge44-slots-t16/independent/review_guards.py
new file mode 100644
index 0000000000..086dcf3d11
--- /dev/null
+++ b/research/gauge44-slots-t16/independent/review_guards.py
@@ -0,0 +1,46 @@
+"""Reproduce the assertion-preservation part of the independent guard review.
+
+This compares complete assertion ASTs in their traversal order. It supplements
+the semantic centre-interface argument in CENTRE-GUARD-REVIEW.md.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse
+import ast
+import hashlib
+import json
+from pathlib import Path
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--pr635', type=Path, required=True, help='Pinned PR635 checkout or supplier directory')
+    parser.add_argument('--delta', type=Path, default=Path(__file__).resolve().parents[1])
+    parser.add_argument('--output', type=Path, required=True)
+    args = parser.parse_args()
+    old = args.pr635
+    if not (old/'code/assemble.py').exists():
+        old = old/'research/complex-571-cold14-st2'
+    names = ['assemble.py', 'invoice_allcold.py', 'bind_providers_portable.py',
+             'generated_identity.py', 'witness.py']
+    records = []
+    for name in names:
+        a, b = (old/'code'/name).read_bytes(), (args.delta/'code'/name).read_bytes()
+        assertions = lambda data: [ast.dump(n, include_attributes=False) for n in ast.walk(ast.parse(data))
+                                   if isinstance(n, ast.Assert)]
+        aa, bb = assertions(a), assertions(b)
+        if aa != bb:
+            raise RuntimeError('Assertion sequence changed: '+name)
+        records.append(dict(file='code/'+name, baseline_sha256=hashlib.sha256(a).hexdigest(),
+                            new_sha256=hashlib.sha256(b).hexdigest(), byte_identical=a == b,
+                            assert_count=len(aa), all_assertions_identical_in_order=True))
+    if records[0]['assert_count'] != 91:
+        raise RuntimeError('The expected PR635 assembly has 91 assertions')
+    result = dict(status='PASS_PR635_ADMISSION_ASSERTION_PRESERVATION', files=records,
+                  centre_interface_review='CENTRE-GUARD-REVIEW.md',
+                  scope='Exact syntax preservation for all admission assertions in these five files. The changed emitter/controller centre boundary and single-provider controls require the separate semantic review; assertion counts alone do not prove them.')
+    args.output.write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], [r['assert_count'] for r in records])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/inputs/PR589-EXPECTED.json b/research/gauge44-slots-t16/inputs/PR589-EXPECTED.json
new file mode 100644
index 0000000000..e293ddc557
--- /dev/null
+++ b/research/gauge44-slots-t16/inputs/PR589-EXPECTED.json
@@ -0,0 +1,222 @@
+{
+ "word": {
+  "file": "tune/bitE8mut-p111-tuned.json.gz",
+  "file_sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f",
+  "content_sha256": "5642fd0e35a1acc11acff8d0c08350c1617e95f310d4d35ad63a651f9eeeba0b",
+  "v": 111,
+  "R": 439,
+  "punctured": [
+   10,
+   15,
+   51,
+   53,
+   56,
+   66,
+   72,
+   89,
+   111
+  ],
+  "retained_totals": 9,
+  "copy_ranks": [
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7
+  ],
+  "decoder_constant": 63,
+  "gates": {
+   "D": 111,
+   "A": 2075,
+   "B": 712,
+   "C": 2574
+  },
+  "local_histogram": {
+   "1": 1323,
+   "2": 1342,
+   "3": 79,
+   "4": 44,
+   "5": 102,
+   "6": 11,
+   "7": 19
+  },
+  "legality": {
+   "records": 27234,
+   "common_frame_ADDs": 24305,
+   "rank_mass": 5129
+  },
+  "five_stage_columns": 883,
+  "five_stage_payload_bits": 93,
+  "nine_stage_columns": 1327,
+  "nine_stage_payload_bits": 93,
+  "eleven_stage_columns": 1549,
+  "eleven_stage_payload_bits": 93,
+  "base_content_sha256": "d0df3c89ae84989f4045ba1681a5e2e9fcdfa38ed0301c8abf5185537155cbe3"
+ },
+ "interface": {
+  "hypotheses": {
+   "H1_no_target_feeds_z": true,
+   "H2_D_frame0_targets_from_helpers": true,
+   "H3_A_z_only_scatter_targets_B_split": true,
+   "H4_C_literal_reverse_at_full": true,
+   "H5_V_identity": true
+  },
+  "conclusion": {
+   "U_block_form": true,
+   "J_identity": true,
+   "K_equals_D": true,
+   "C_is_U_inverse": true
+  },
+  "interleaving": {
+   "z_gates_A": 2075,
+   "source_writes_A": 0,
+   "z_gates_B": 499,
+   "source_writes_B": 483,
+   "helper_writes_B": 16,
+   "sources_rewritten_B": 108,
+   "B_z_write_frame_dims": {
+    "4": 388,
+    "6": 111
+   },
+   "B_z_operand_kinds": {
+    "helper<-helper": 3,
+    "helper<-source": 13,
+    "source<-helper": 108,
+    "source<-source": 375
+   },
+   "B_z_operand_kinds_by_dim": {
+    "dim4:helper<-source": 13,
+    "dim4:source<-source": 375,
+    "dim6:helper<-helper": 3,
+    "dim6:source<-helper": 108
+   },
+   "B_z_writes_after_a_target_read_of_the_same_register": 454,
+   "B_target_reads_of_registers_rewritten_earlier_in_B": 111,
+   "target_reads_of_targets": 0,
+   "cleanup_gates": 2574
+  }
+ },
+ "nine": {
+  "pipeline": "PR #510 (PR #463 nine-stage template, 32 replicas, PR #442 hosting, PR #493 outer assembly), parameterised for v <= 120 by code/adapt9p.py",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_lower_decimal": "0.001733427039589844234749",
+  "profile": {
+   "1": 381024,
+   "2": 400416,
+   "3": 22752,
+   "4": 26880,
+   "5": 29376,
+   "6": 17376,
+   "7": 26784,
+   "42": 288
+  },
+  "bit": {
+   "live": 28416,
+   "physical": 28425,
+   "maxchild": 42,
+   "rank_mass": 1808352,
+   "hosted_residuals": 126432,
+   "bank_assignments": 0,
+   "prefix_bits": 177,
+   "charged_prefix_bits": 192,
+   "coefficient_bits": 177,
+   "two_level_coefficient_bits": 393,
+   "charged_two_level_coefficient_bits": 512,
+   "row_coefficient": 18355,
+   "halving_depth": 2
+  },
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "eleven": {
+  "pipeline": "PR #493 (PR #445 geometry, PR #472 emitter, audit and invoice, PR #442 hosting), parameterised by PR #545's code/adapt.py",
+  "bit_lower": "855475950388791987811/500000000000000000000000",
+  "bit_lower_decimal": "0.001710951900777583975622",
+  "profile": {
+   "1": 116424,
+   "2": 121648,
+   "3": 6952,
+   "4": 7424,
+   "5": 8976,
+   "6": 4520,
+   "7": 8776,
+   "56": 2600
+  },
+  "bit": {
+   "live": 8880,
+   "physical": 8889,
+   "maxchild": 56,
+   "rank_mass": 689304,
+   "hosted_residuals": 38632,
+   "prefix_bits": 4304,
+   "charged_prefix_bits": 4352,
+   "coefficient_bits": 4304,
+   "three_level_coefficient_bits": 12966,
+   "charged_three_level_coefficient_bits": 12992,
+   "row_coefficient": 19431,
+   "halving_depth": 3
+  },
+  "emitted_program_sha256": "793b6f40c9aa4b8db57fec0ac0973e16884dae28707e482ee8f7a2349a5d5a4b",
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "base": {
+  "nine_bit_lower": "1733052823330162099157/1000000000000000000000000",
+  "nine_bit_lower_decimal": "0.001733052823330162099157",
+  "eleven_bit_lower": "427652201524503168379/250000000000000000000000",
+  "eleven_bit_lower_decimal": "0.001710608806098012673516",
+  "note": "PR #555's EXPECTED.json (untuned word); the tune/ pipeline is the same, with the same frozen hosting selections"
+ }
+}
diff --git a/research/gauge44-slots-t16/t16/NOTICE.md b/research/gauge44-slots-t16/t16/NOTICE.md
new file mode 100644
index 0000000000..403f4afffb
--- /dev/null
+++ b/research/gauge44-slots-t16/t16/NOTICE.md
@@ -0,0 +1,39 @@
+# Attribution and license
+
+Apache-2.0. New construction and integration: Hao Yan (@FanPUYen), 2026.
+Prepared with substantial OpenAI Codex assistance, including separately tasked
+AI agents for owner construction, independent mathematical/code checking and
+native verification. These are not claims of independent human peer review.
+
+The exact local supplier is Jeremy Kothe's accepted PR799 X4 word, layered on
+Chafik Boukhalfa's PR741 frame changes and PR685 owner construction. Chafik's
+PR795 fixed-inventory optimality result motivated changing the replica count.
+The original owner bytes, scalar program, local frame and width inventory,
+native phase and wrapper implementations retain their existing authorship.
+
+Credit icekylinx for the source gauge and supplier/admission pipeline;
+DreamingOfClouds for the PR589 bit transport and inherited cold-end work;
+eumemic for the PR555 bit supplier and earlier supplier work; Rohan Arun for
+the native exact-complex recurrence correction; Jeremy Diviney, jaymosley07,
+and the other retained owner/allocation contributors; and the complete
+PR514/PR484/PR507/PR558 controller, physical hosting and verification lineage.
+This list is cumulative credit, not approval of every claim in those PRs.
+
+All original notices and licenses remain in the referenced source packages:
+
+- `research/gauge44-frames-x/{NOTICE,UPSTREAM-NOTICE}.md`
+- `research/complex-sw4-frame8/PROVENANCE.md`
+- `research/e8-bit-p111-tuned/tune/README.md`
+- the repository `CONTRIBUTORS.md` and source-package licenses.
+
+The verifier copies pinned global source files into an external replay
+directory and applies an explicit checked edit list. Original attribution
+comments are preserved in those generated derivatives. No original source
+file or historical certificate is rewritten.
+
+The optional ancestry-reuse coverage guard addresses the omission issue
+identified by Lucas (@ljste) in PR838 and the related PR847 integration by
+Chinmay (@chinmayarvind23). Its fixed inventories were read from the accepted
+PR741 source; no pending implementation is imported. Charles Bethin's
+concurrent PR850 strengthens the fixed-inventory owner-profile theorem and
+was checked for overlap before publication; that inventory is changed here.
diff --git a/research/gauge44-slots-t16/t16/build_parent.py b/research/gauge44-slots-t16/t16/build_parent.py
new file mode 100644
index 0000000000..bd9e28bd2d
--- /dev/null
+++ b/research/gauge44-slots-t16/t16/build_parent.py
@@ -0,0 +1,281 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Copyright (c) 2026 Hao Yan (@FanPUYen)
+"""Lift the PR741 controller and PR799 provider plan to sixteen replicas.
+
+Authored with OpenAI Codex assistance. Precursor credit: the PR514/PR484/PR507
+controller lineage, PR558/PR589 admission, Chafik Boukhalfa's PR741 frames
+and owner map, and Jeremy Kothe's PR799 paired-read-exchange provider.
+This script changes only the global replica namespace and the nominated owner
+map; it reuses the exact local programs and exact data-phase recipes.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+from collections import Counter
+from pathlib import Path
+
+SOURCE_PLAN_SHA256 = '5f40e7ccfca61f298539b4f41286d2a9d62caf947057f9cec82aa53f73f707fd'
+SOURCE_OWNERS_SHA256 = '99d1c4caf85855c353d30f122d9efbd9e51562914facded13027f347b18a6082'
+
+
+def require(condition, reason):
+    if not condition:
+        raise ValueError(reason)
+
+
+def read(path):
+    raw = Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def canonical(value):
+    return json.dumps(value, sort_keys=True, separators=(',', ':')).encode()
+
+
+def portable_gzip(raw):
+    compressed = bytearray(gzip.compress(raw, mtime=0))
+    compressed[9] = 255  # RFC1952 OS=unknown, independent of zlib/Python platform.
+    return bytes(compressed)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def content_sha(value):
+    return hashlib.sha256(canonical(value)).hexdigest()
+
+
+def lift_parent(source, copies=2):
+    """A direct sum of bank/data stocks; erased private streams are shared.
+
+    copies=1 is deliberately the identity, byte-for-byte after canonicalization.
+    The helper routes retain replica lanes 0..7 in each *separate* bank group.
+    No axis index is inferred from the new global replica label 8..15.
+    """
+    require(type(copies) is int and copies in (1, 2), 'only identity or T16 lift')
+    t = copy.deepcopy(source)
+    if copies == 1:
+        return t
+    require(source['m'] == 73, 'source dimension')
+    require(len(source['calls']) == 72, 'source calls')
+    data = 8*8*112
+    bank_stock = source['live'] - data
+    private_stock = source['physical'] - source['live']
+    require((bank_stock, private_stock) == (9*504, 504+8+2), 'source namespace')
+    require({(c['stage'], c['replica']) for c in source['calls']} ==
+            {(s, r) for s in range(9) for r in range(8)}, 'source coverage')
+    new_data = copies*data
+    new_live = copies*source['live']
+    new_physical = new_live + private_stock
+    t['calls'] = []
+    for c in source['calls']:
+        for group in range(copies):
+            new = copy.deepcopy(c)
+            new['replica'] = c['replica'] + 8*group
+            owners = []
+            for family, route in c['owners']:
+                require(0 <= family < source['live'], 'owner outside live stock')
+                mapped = (family + data*group if family < data else
+                          new_data + group*bank_stock + family - data)
+                owners.append([mapped, copy.deepcopy(route)])
+            new['owners'] = owners
+            t['calls'].append(new)
+    # Every data/idle recipe is a portwise direct sum, hence only multiplicity
+    # changes. Its local axis labels and exact phase words stay unchanged.
+    for child in t['idle_children']:
+        require(child['replicas'] == 8, 'source idle multiplicity')
+        child['replicas'] *= copies
+    for event in t['execution_schedule']:
+        if 'replicas' in event:
+            require(event['replicas'] == list(range(8)), 'source sweep replicas')
+            event['replicas'] = list(range(8*copies))
+        if event['kind'] == 'bank_padding_cover_sweep':
+            event['families'] = [new_data, new_live]
+        elif event['kind'] == 'translate_every_live_family':
+            event['families'] = [0, new_live]
+            event['charged_calls_per_cover'] = new_live
+    t['bank_padding']['families'] = []
+    t['bank_padding']['children'] = []
+    for group in range(copies):
+        for family in source['bank_padding']['families']:
+            t['bank_padding']['families'].append(new_data + group*bank_stock + family - data)
+        for child in source['bank_padding']['children']:
+            new = copy.deepcopy(child)
+            new['family'] = new_data + group*bank_stock + child['family'] - data
+            t['bank_padding']['children'].append(new)
+    t['cover_final_correction'].update(families=[0, new_live], charged_calls_per_cover=new_live)
+    t['private_namespace'] = {
+        key: [new_live + x - source['live'] for x in interval]
+        for key, interval in source['private_namespace'].items()
+    }
+    t.update(live=new_live, physical=new_physical,
+             version='t16-direct-sum-two-bank-groups-parent-v1')
+    t['route_semantics']['helper'] = (
+        'Two independent groups of nine dedicated banks. Group floor(replica/8) '
+        'selects the bank namespace; the stored original helper route retains '
+        'lane replica%8. All original residual/spectator axes are unchanged.')
+    t['loop_order'] = (
+        'For each recipe phase: the explicit calls order, then every cover class d; '
+        'each local invocation completes before the next. Each original replica '
+        'has a disjoint data and bank namespace in its group; private erased '
+        'streams are reused between completed calls.')
+    t['replica_lift'] = dict(
+        source_template_content_sha256=content_sha(source), groups=copies,
+        source_replicas=8, replicas=8*copies, data_stock=new_data,
+        bank_stock=copies*bank_stock, banks_per_stage=copies*504,
+        private_helpers=504, local_programs_content_sha256=content_sha(source['local_programs']),
+        construction='direct sum of data and dedicated banks; share only restored private streams',
+        phase_recipe_unchanged=True)
+    # Source data and helper owner routes are preserved literally in each copy.
+    for c in t['calls']:
+        group, replica = divmod(c['replica'], 8)
+        old = next(z for z in source['calls'] if (z['stage'], z['replica']) == (c['stage'], replica))
+        require([r for f, r in c['owners']] == [r for f, r in old['owners']], 'route changed')
+        require(c['window'] == old['window'], 'local window changed')
+        require(len({f for f, r in c['owners']}) == len(c['owners']), 'per-call owner alias')
+    require(t['local_programs'] == source['local_programs'], 'program changed')
+    require(t['recipe'] == source['recipe'], 'data recipe changed')
+    require(len(t['bank_padding']['children']) == copies*bank_stock, 'bank padding count')
+    require(t['physical'] == t['live']+514, 'private namespace size')
+    return t
+
+
+def expanded_schedule(parent, order):
+    blocks = {}
+    globals_ = []
+    stage = None
+    for index, event in enumerate(parent['execution_schedule']):
+        if event['kind'] in ('bank_padding_cover_sweep', 'translate_every_live_family'):
+            globals_.append((index, event))
+            continue
+        if event['kind'] == 'local_cover_sweep':
+            stage = event['stage']
+            blocks[stage] = []
+        require(stage is not None, 'event precedes first stage')
+        blocks[stage].append((index, event))
+    schedule = []
+    for time, (stage, replica) in enumerate(order):
+        for index, event in blocks[stage]:
+            new = copy.deepcopy(event)
+            new.update(source_event=index, replica=replica, replicas=[replica], time=time)
+            schedule.append(new)
+    for index, event in globals_:
+        schedule.append(dict(event, source_event=index))
+    return schedule
+
+
+def actual_windows(parent, order):
+    ranks = {c['child']: c['rank'] for c in parent['idle_children']}
+    stage_pair = {e['stage']: e['pair'] for e in parent['recipe'] if e['kind'] == 'local'}
+    last, intervals, callpos, perrep = {}, {}, {}, {}
+    schedule = expanded_schedule(parent, order)
+    for pos, event in enumerate(schedule):
+        if 'replica' not in event:
+            continue
+        replica = event['replica']
+        perrep.setdefault(replica, []).append(event['source_event'])
+        if event['kind'] == 'local_cover_sweep':
+            last[replica, stage_pair[event['stage']]] = pos
+            callpos[event['time']] = pos
+        elif event['kind'] == 'bridge':
+            last[replica, event['src']] = last[replica, event['dst']] = pos
+        elif event['kind'] == 'idle_cover_sweep':
+            for child in event['child_indices']:
+                if child in ranks:
+                    intervals[replica, child] = (last.get((replica, event['pair']), -1), pos)
+    require(all(events == list(range(30)) for events in perrep.values()), 'per-replica projection')
+    require([e['source_event'] for e in schedule if 'replica' not in e] == [30, 31], 'global tail')
+    require(set(callpos) == set(range(len(order))), 'complete schedule')
+    windows = {f'{replica},{child}': [ranks[child], [time for time, pos in sorted(callpos.items()) if start < pos < stop]]
+               for (replica, child), (start, stop) in intervals.items()}
+    return windows, schedule
+
+
+def lift_plan(source, parent, owners, source_plan_sha, source_owners_sha, owners_sha):
+    p = copy.deepcopy(source)
+    require(source['T'] == 8 and len(source['order']) == 72, 'source plan dimensions')
+    order = [[stage, replica + 8*group] for stage, replica in source['order'] for group in range(2)]
+    windows, schedule = actual_windows(parent, order)
+    # These windows are recomputed from actual source-event touches, not copied
+    # from the old nomination. Their T8 restriction must recover the old plan.
+    rank = Counter({int(k): 2*v for k, v in source['profile'].items()})
+    rank.update({48: 1, 44: -1, 3: -2, 2: 1})
+    rank = +rank
+    p.update(status='FROZEN_EXPLICIT_T16_TWO_BANK_DIRECT_SUM_OWNER_NOMINATION',
+             mode='gauge44-all144-t16-idle-concentration', T=16, live=14336,
+             deficit=5120, profile=dict(sorted(rank.items())), order=order, windows=windows,
+             solver_status='explicit two-role augmenting path and two-bin recombination', gap=None,
+             source_plan_sha256=source_plan_sha, source_owners_sha256=source_owners_sha,
+             assignment_sha256=owners_sha, assignment_content_sha256=content_sha(owners))
+    for field in ('provider_calls', 'per_call_widths'):
+        p[field] = []
+        for old in source[field]:
+            for group in range(2):
+                new = copy.deepcopy(old)
+                new['replica'] += 8*group
+                if 'time' in new:
+                    new['time'] = 2*old['time']+group
+                p[field].append(new)
+    at = {tuple(x): i for i, x in enumerate(order)}
+    for field in ('provider_calls', 'per_call_widths'):
+        p[field].sort(key=lambda c: at[c['stage'], c['replica']])
+    p['replica_lift'] = dict(groups=2, source_replicas=8, replicas=16,
+                             parent_template_content_sha256=content_sha(parent), owners_file_sha256=owners_sha,
+                             window_semantics='strict physical source-event touch intervals, including bridges',
+                             schedule_content_sha256=content_sha(schedule))
+    require(len(owners) == 144*504, 'owner role count')
+    for role in owners:
+        require(role['time'] == at[role['stage'], role['replica']], 'role call time')
+        require(role['time'] in windows[f"{role['owner_replica']},{role['child']}"][1],
+                'owner outside actual source-event window')
+    require(sum(int(k)*v for k,v in p['profile'].items()) == 73*p['live']-p['deficit'], 'rank mass')
+    return p, schedule
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--base', type=Path, required=True)
+    parser.add_argument('--source-plan', type=Path, required=True)
+    parser.add_argument('--source-owners', type=Path, required=True)
+    parser.add_argument('--owners', type=Path, required=True)
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    require(not args.out.exists(), 'output directory already exists')
+    require(sha(args.source_plan) == SOURCE_PLAN_SHA256, 'source plan byte pin')
+    require(sha(args.source_owners) == SOURCE_OWNERS_SHA256, 'source owners byte pin')
+    source_path = args.base/'split-centres/GLOBAL-TEMPLATE.json.gz'
+    source = read(source_path)
+    original_plan = read(args.source_plan)
+    require(lift_parent(source, 1) == source, 'T8 identity control')
+    require(actual_windows(source, original_plan['order'])[0] == original_plan['windows'], 'T8 source-window replay')
+    require(source['exact_data_phase_recipe_sha256'] == sha(args.base/'work/complex-nine-native/DATA-PHASES.json'), 'source exact data-phase binding')
+    parent = lift_parent(source)
+    owners = read(args.owners)
+    plan, schedule = lift_plan(original_plan, parent, owners, sha(args.source_plan), sha(args.source_owners), sha(args.owners))
+    args.out.mkdir(parents=True)
+    (args.out/'GLOBAL-TEMPLATE.json.gz').write_bytes(portable_gzip(canonical(parent)))
+    (args.out/'PLAN.json').write_bytes((json.dumps(plan, indent=2)+'\n').encode('utf-8'))
+    receipt = dict(status='PASS_T16_DIRECT_SUM_PARENT_AND_LITERAL_SOURCE_WINDOWS',
+                   source_template_file_sha256=sha(source_path), source_template_content_sha256=content_sha(source),
+                   source_plan_sha256=sha(args.source_plan), source_owners_sha256=sha(args.source_owners),
+                   owners_sha256=sha(args.owners),
+                   parent_template_file_sha256=sha(args.out/'GLOBAL-TEMPLATE.json.gz'),
+                   parent_template_content_sha256=content_sha(parent), plan_sha256=sha(args.out/'PLAN.json'),
+                   T8_identity_control=True, T8_source_window_identity=True,
+                   local_programs_identical=True, exact_data_phases_identical=True,
+                   parent_live=parent['live'], parent_physical=parent['physical'],
+                   bank_stock=9072, banks_per_stage=1008, private_helpers=504,
+                   source_idle_children_charged=sum(c['replicas'] for c in parent['idle_children']),
+                   events=len(schedule), replica_source_events=30, global_source_events=[30,31],
+                   calls=len(plan['order']), roles=len(owners), actual_window_membership_checked=len(owners),
+                   scope='Legal direct-sum parent namespace and actual source-event windows; full global emitter, geometry, finite invoice, and recurrence admission remain separate checks.')
+    (args.out/'PARENT-LIFT-RECEIPT.json').write_bytes((json.dumps(receipt, indent=2)+'\n').encode('utf-8'))
+    print(json.dumps(receipt, indent=2))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/t16/indep16.py b/research/gauge44-slots-t16/t16/indep16.py
new file mode 100644
index 0000000000..81e1e9fe15
--- /dev/null
+++ b/research/gauge44-slots-t16/t16/indep16.py
@@ -0,0 +1,306 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Prepared for haoyan with substantial OpenAI Codex assistance.
+"""Independent T16 event-window, whole-helper, chart and finite-reserve audit.
+
+Inputs are read-only. No owner constructor or controller auditor is imported.
+--word is the canonical local supplier JSON.gz, with frame IDs and a native
+INDEPENDENT-LOCAL-REPLAY.json alongside it (override with --local-replay).
+--baseline-parent is the original eight-replica GLOBAL-TEMPLATE.json.gz.
+Its sibling CANONICAL-WORD.json.gz supplies ports; DATA-PHASES.json defaults
+to ../work/complex-nine-native/DATA-PHASES.json (override with --phases).
+The PR741 and PR799/X4 suppliers share this width/owner interface. Their
+local paid profiles and prefix exponents are read and recounted from the
+provided canonical word and hash-bound native replay, never fixed to PR741.
+--out names a JSON receipt. Checks remain enabled under python -O.
+"""
+import argparse
+from collections import Counter, defaultdict
+import gzip
+import hashlib
+import json
+from pathlib import Path
+
+V, H, M, T, R = 112, 9, 73, 16, 504
+import os
+EXPECTED_IDLE = {int(k): v for k, v in json.loads(os.environ['T16_EXPECTED_IDLE']).items()}
+EXPECTED_WIDTHS = {int(k): v for k, v in json.loads(os.environ['T16_EXPECTED_WIDTHS']).items()}
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def filehash(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def basis(vectors):
+    pivots = {}
+    for x in vectors:
+        require(type(x) is int and 0 <= x < 1 << H, 'invalid local frame vector')
+        while x:
+            bit = x.bit_length() - 1
+            if bit in pivots:
+                x ^= pivots[bit]
+            else:
+                pivots[bit] = x
+                break
+    for bit in sorted(pivots):
+        for upper in pivots:
+            if upper > bit and pivots[upper] >> bit & 1:
+                pivots[upper] ^= pivots[bit]
+    return tuple(pivots[bit] for bit in sorted(pivots, reverse=True))
+
+
+def local_inventory(word, replay):
+    global RH
+    require((word['v'], word['h']) == (V, H) and 0 < word['R'] <= R, 'local supplier dimensions')
+    RH = word['R']
+    frames = [basis(frame) for frame in word['frames']]
+    n = 2 * V + RH
+    require(len(word['start']) == len(word['final']) == n, 'local frame vector lengths')
+    current = [frames[f] for f in word['start']]
+    paid = Counter()
+
+    def climb(register, frame):
+        require(basis(current[register] + frame) == frame, 'nonmonotone local frame')
+        jump = len(frame) - len(current[register])
+        if jump:
+            paid[jump] += 1
+        current[register] = frame
+
+    require(not word['target_levels'], 'this audit requires the current zero-level centre interface')
+    for section in ('A', 'B', 'tail'):
+        if section == 'B':
+            require(all(current[t] == () for t in range(V, 2 * V)), 'target centre level')
+            for q, frame_id in zip(word['centers'], word['center_frames']):
+                require(current[q] == frames[frame_id], 'centre carrier frame')
+                paid[len(frames[frame_id])] += 1
+        for gate in word[section]:
+            registers = gate[1:3] if gate[0] == 'add' else gate[1:2]
+            require(gate[0] in ('add', 'scale'), 'unknown scalar gate')
+            for register in registers:
+                climb(register, frames[gate[-1]])
+    for register, frame_id in enumerate(word['final']):
+        climb(register, frames[frame_id])
+    require(dict(paid) == {int(r): count for r, count in word['local_profile'].items()}, 'local paid-profile recount')
+    for orientation in ('forward', 'backward'):
+        require(dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()}, 'local replay profile binding')
+    widths = [len(frames[word['final'][q]]) - len(frames[word['start'][q]]) for q in range(2 * V, n)]
+    require(Counter(widths) == EXPECTED_WIDTHS, 'current supplier width inventory')
+    return widths, paid
+
+
+def make_context(parent, phases, ports, word, replay, roles):
+    widths, paid = local_inventory(word, replay)
+    require(len(parent['calls']) == 72 and {(c['stage'], c['replica']) for c in parent['calls']} == {(s, r) for s in range(9) for r in range(8)}, 'original eight-replica baseline calls')
+    require(len(roles) == 9 * T * RH, 'complete helper role count')
+    address = {}
+    for role in roles:
+        key = (role['stage'], role['replica'])
+        time = role['time']
+        require(time not in address or address[time] == key, 'inconsistent invocation time address')
+        address[time] = key
+    require(set(address) == set(range(9 * T)), 'contiguous invocation times')
+    order = [address[t] for t in range(9 * T)]
+    require(set(order) == {(s, r) for s in range(9) for r in range(T)}, 'stage/replica inventory')
+    require(all(order[2*t+1] == (order[2*t][0], order[2*t][1]+8) and order[2*t][1] < 8 for t in range(72)), 'two-copy interleaving')
+    rank = {child['child']: child['rank'] for child in parent['idle_children']}
+    source = parent['execution_schedule']
+    blocks, stage = {}, None
+    for index, event in enumerate(source):
+        if event['kind'] in ('bank_padding_cover_sweep', 'translate_every_live_family'):
+            continue
+        if event['kind'] == 'local_cover_sweep':
+            stage = event['stage']
+            blocks[stage] = []
+        require(stage is not None, 'source event before first invocation')
+        blocks[stage].append((index, event))
+    require(set(blocks) == set(range(9)), 'source stage inventory')
+    events = [(index, event, replica, time) for time, (stage, replica) in enumerate(order) for index, event in blocks[stage]]
+    projections = defaultdict(list)
+    for index, event, replica, time in events:
+        projections[replica].append(index)
+    require(set(projections) == set(range(T)) and all(p == list(range(30)) for p in projections.values()), 'per-replica source-event projection')
+    stage_pair = {e['stage']: e['pair'] for e in parent['recipe'] if e['kind'] == 'local'}
+    last, windows, callpos, child_pair, side = {}, {}, {}, {}, {}
+    bridges = 0
+    for position, (_, event, replica, _) in enumerate(events):
+        kind = event['kind']
+        if kind == 'local_cover_sweep':
+            stage = event['stage']
+            callpos[stage, replica] = position
+            last[replica, stage_pair[stage]] = position
+        elif kind == 'bridge':
+            last[replica, event['src']] = last[replica, event['dst']] = position
+            bridges += 1
+        elif kind == 'idle_cover_sweep':
+            for sd, child in enumerate(event['child_indices']):
+                if child in rank:
+                    windows[replica, child] = (last.get((replica, event['pair']), -1), position)
+                    child_pair[child], side[child] = event['pair'], sd
+    require(len(windows) == T * len(rank), 'actual window inventory')
+    require(len(ports) == V, 'port count')
+    bases = []
+    for q in ports:
+        zero = next(i for i in range(H) if not (q >> i & 1))
+        correction = q ^ (1 << zero)
+        axes = list(range(H))
+        axes[0], axes[zero] = axes[zero], axes[0]
+        frame = [(1 << i) ^ (correction if correction >> i & 1 else 0) for i in axes] + [1 << i for i in range(H, M)]
+        require(all((x & y).bit_count() % 2 == int(i == j) for i, x in enumerate(frame) for j, y in enumerate(frame)), 'nonorthogonal owner basis')
+        bases.append(frame)
+    return dict(widths=widths, paid=paid, order=order, at={key:t for t,key in enumerate(order)}, rank=rank,
+                windows=windows, callpos=callpos, child_pair=child_pair, side=side, stage_pair=stage_pair,
+                bases=bases, phases=phases, bridges=bridges, event_count=len(events), replay=replay)
+
+
+def check_roles(context, roles):
+    c = context
+    live, physical = T * 8 * V, T * 8 * V + 8 + R + 2
+    require(len(roles) == 9 * T * RH, 'complete helper role count')
+    helpers, families, used = defaultdict(set), defaultdict(set), defaultdict(set)
+    charts, chart_cache = set(), {}
+    for z in roles:
+        s, r, helper = z['stage'], z['replica'], z['helper']
+        owner, child, port = z['owner_replica'], z['child'], z['port']
+        offset, width, family = z['offset'], z['width'], z['family']
+        call = (s, r)
+        require(call in c['at'] and 0 <= helper < RH and 0 <= owner < T and 0 <= port < V, 'role coordinates')
+        require(z['time'] == c['at'][call], 'role invocation time')
+        require(width == c['widths'][helper], 'whole-helper residual width')
+        require(0 <= family < live, 'private-namespace collision')
+        require(child in c['rank'], 'unknown idle child')
+        require(z['copy'] == V * owner + port and family == owner * 896 + (2 * c['child_pair'][child] + c['side'][child]) * V + port, 'physical family identity')
+        lo, hi = c['windows'][owner, child]
+        require(lo < c['callpos'][call] < hi, 'strict bridge-aware idle window')
+        require(family // 224 != r * 4 + c['stage_pair'][s], 'helper aliases active data pair')
+        require(helper not in helpers[call] and family not in families[call], 'duplicate helper or family within whole invocation')
+        helpers[call].add(helper)
+        families[call].add(family)
+        cells = set(range(offset, offset + width))
+        bin_key = (owner, child, port)
+        require(offset >= 0 and offset + width <= c['rank'][child] and not used[bin_key] & cells, 'overlapping or out-of-capacity slice')
+        used[bin_key].update(cells)
+        chart_key = (port, child, offset, width)
+        if chart_key not in chart_cache:
+            frame = c['bases'][port]
+            pending = list(map(int, c['phases']['recipes'][port]['idle_children'][child]['orthogonal_axes']))
+            require(len(pending) == c['rank'][child], 'phase child rank')
+            occupied = [frame.index(x) for x in pending[offset:offset + width]]
+            spectators = [i for i in range(M) if i not in occupied][:H - width]
+            permutation = occupied + spectators + [i for i in range(M) if i not in occupied and i not in spectators]
+            require(len(occupied) == width and len(set(occupied + spectators)) == H and sorted(permutation) == list(range(M)), 'residual/spectator permutation')
+            require([frame[i] for i in permutation[:width]] == pending[offset:offset + width], 'pending-axis binding')
+            chart_cache[chart_key] = tuple(frame[i] for i in permutation)
+        charts.add(chart_cache[chart_key])
+    require(set(helpers) == set(c['order']) and all(h == set(range(RH)) for h in helpers.values()), 'complete per-call helper inventory')
+    idle = Counter()
+    for owner, child in c['windows']:
+        for port in range(V):
+            cells = used[owner, child, port]
+            require(cells == set(range(len(cells))), 'gap in pending prefix')
+            left = c['rank'][child] - len(cells)
+            if left:
+                idle[left] += 1
+    require(idle == EXPECTED_IDLE, 'nominated idle profile')
+    profile = Counter({rank: 9 * T * count for rank, count in c['paid'].items()})
+    profile.update(idle)
+    mass = sum(rank * count for rank, count in profile.items())
+    require(M * live - mass == 5120, 'doubled rank deficit')
+    require(c['bridges'] == 144, 'actual bridge count')
+    localbits = max(x['prefix_bits_upper'] for x in c['replay']['local'].values())
+    prefix = localbits + (M + 1) // 2 + len(c['order']) + c['bridges'] + 4
+    group = 2 ** (36 * 36)
+    for i in range(1, 37):
+        group *= 2 ** (2 * i) - 1
+    stock = group * physical
+    row = 2 * stock.bit_length() + 9909 + 252 + 2 * 512
+    require(prefix < 512, 'prefix reserve')
+    require(row < 20161 and M * M > 2 * max(profile) ** 2, 'row or halving reserve')
+    return dict(status='PASS_INDEPENDENT_T16_LITERAL_WINDOWS_CHARTS_PREFIX_ROW', roles=len(roles), calls=len(c['order']),
+                source_events_per_replica=30, expanded_replica_events=c['event_count'], bridge_events=c['bridges'],
+                literal_windows=len(c['windows']), checked_whole_helper_widths=len(roles), checked_busy_family_windows=len(roles),
+                orthogonal_port_bases=len(c['bases']), actual_73_axis_charts=len(charts), checked_slice_prefixes=len(c['windows']) * V,
+                local_profile=dict(sorted(c['paid'].items())), width_inventory=dict(sorted(Counter(c['widths']).items())),
+                idle=dict(sorted(idle.items())), profile=dict(sorted(profile.items())), live=live, physical=physical,
+                rank_mass=mass, deficit=5120, namespace={'data':[0,live], 'centres':[live,live+8], 'tableau':[live+8,live+8+R], 'coefficient':[live+8+R,physical]},
+                local_prefix_bits=localbits, local_prefix_from_native_receipt=True, local_profile_recounted=True,
+                prefix_formula=dict(local_scalar=localbits, input_l2=(M + 1) // 2, invocations=len(c['order']), bridges=c['bridges'], margin=4),
+                prefix_bits=prefix, charged_prefix_bits=512, physical_stock_bits=stock.bit_length(),
+                physical_row_coefficient=row, row_limit=20161,
+                scope='Finite role/window/chart and inherited prefix/row obligations. Requires separately admitted local supplier and emitted controller, complete finite invoice, exact moments and outer assembly; no all-size theorem is asserted.')
+
+
+def controls(context, roles):
+    candidates = []
+    first = roles[0]
+    bad = dict(first, family=14336)
+    candidates.append(('private_namespace_collision', [bad] + roles[1:], 'private-namespace collision'))
+    index = next(i for i, z in enumerate(roles) if z['replica'] >= 8)
+    bad = dict(roles[index], replica=roles[index]['replica'] - 8)
+    candidates.append(('copy_replica_alias', [bad] + roles[:index] + roles[index+1:], 'role invocation time'))
+    candidates.append(('missing_whole_helper', roles[1:], 'complete helper role count'))
+    split = dict(first, width=first['width'] - 1)
+    fragment = dict(first, offset=first['offset'] + first['width'] - 1, width=1)
+    candidates.append(('split_whole_helper', [split, fragment] + roles[1:], 'complete helper role count'))
+    candidates.append(('truncated_helper_width', [split] + roles[1:], 'whole-helper residual width'))
+    # Keep the family and chart valid, but move one complete role past its
+    # actual idle event. Freeze the original invocation order for controls.
+    crossing = None
+    for index, z in enumerate(roles):
+        lo, hi = context['windows'][z['owner_replica'], z['child']]
+        later = next((key for key in context['order'] if context['callpos'][key] >= hi), None)
+        if later is not None:
+            crossing = [dict(z, stage=later[0], replica=later[1], time=context['at'][later])] + roles[:index] + roles[index+1:]
+            break
+    require(crossing is not None, 'no idle-boundary control could be constructed')
+    candidates.append(('cross_idle_boundary', crossing, 'strict bridge-aware idle window'))
+    rejected = []
+    for name, bad, expected in candidates:
+        try:
+            check_roles(context, bad)
+        except ValueError as exc:
+            require(str(exc) == expected, 'control rejected at unexpected predicate: ' + name)
+            rejected.append(dict(name=name, reason=str(exc)))
+        else:
+            raise ValueError('accepted negative control: ' + name)
+    return rejected
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--baseline-parent', type=Path, required=True)
+    parser.add_argument('--owners', type=Path, required=True)
+    parser.add_argument('--word', type=Path, required=True)
+    parser.add_argument('--phases', type=Path)
+    parser.add_argument('--local-replay', type=Path)
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    phases_path = args.phases or args.baseline_parent.parent.parent / 'work/complex-nine-native/DATA-PHASES.json'
+    canonical_path = args.baseline_parent.parent / 'CANONICAL-WORD.json.gz'
+    replay_path = args.local_replay or args.word.parent / 'INDEPENDENT-LOCAL-REPLAY.json'
+    parent, phases, canonical, word, replay, roles = map(read, (args.baseline_parent, phases_path, canonical_path, args.word, replay_path, args.owners))
+    require(replay['status'] == 'PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY', 'local replay status')
+    require(replay['canonical_word_sha256'] == filehash(args.word), 'local word/replay hash binding')
+    require(set(replay['local']) == {'forward', 'backward'}, 'both native prefix orientations')
+    require(word['ports'] == canonical['ports'], 'local/controller port interface')
+    require(len(word['center_frames']) == len(canonical['center_frames']) == 8, 'eight centre interfaces')
+    require([basis(word['frames'][f]) for f in word['center_frames']] == [basis(canonical['frames'][f]) for f in canonical['center_frames']], 'ordered centre-frame interface')
+    context = make_context(parent, phases, canonical['ports'], word, replay, roles)
+    receipt = check_roles(context, roles)
+    receipt['controls_rejected'] = controls(context, roles)
+    receipt['input_sha256'] = {str(path): filehash(path) for path in (args.baseline_parent, phases_path, canonical_path, args.word, replay_path, args.owners)}
+    args.out.write_text(json.dumps(receipt, indent=2) + '\n', encoding='utf-8')
+    print(receipt['status'], 'roles=' + str(receipt['roles']), 'controls=' + str(len(receipt['controls_rejected'])))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots-t16/t16/lift16.py b/research/gauge44-slots-t16/t16/lift16.py
new file mode 100644
index 0000000000..613c4bdb3c
--- /dev/null
+++ b/research/gauge44-slots-t16/t16/lift16.py
@@ -0,0 +1,102 @@
+"""lift16.py BASE8 PLAN8 OWNERS8 OWNERS16 OUT
+Generic T16 lift (after #858 build_parent.py): direct-sum two-bank parent, actual
+source-event windows, T16 PLAN with profile recomputed from the T16 owner map.
+BASE8 = bound T8 global base (has split-centres/GLOBAL-TEMPLATE.json.gz)."""
+import copy, gzip, hashlib, json, sys
+from collections import Counter
+from pathlib import Path
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+from build_parent import lift_parent, actual_windows, read, canonical, portable_gzip, sha, content_sha, require
+
+
+def idle_profile(owners, windows):
+    used = {}
+    for r in owners:
+        key = (r['owner_replica'], r['child'], r['port'])
+        cells = used.setdefault(key, set())
+        new = set(range(r['offset'], r['offset'] + r['width']))
+        require(not cells & new, 'overlap')
+        cells |= new
+    idle = Counter()
+    for key, (cap, _) in windows.items():
+        rep, ch = map(int, key.split(','))
+        for port in range(112):
+            c = used.get((rep, ch, port), set())
+            require(c == set(range(len(c))), 'non-prefix')
+            if len(c) < cap:
+                idle[cap - len(c)] += 1
+    return idle
+
+
+def interleave(order8):
+    return [[s, r + 8 * g] for s, r in order8 for g in range(2)]
+
+
+def lift_plan(source, parent, owners8, owners, plan_sha, owners8_sha, owners_sha):
+    p = copy.deepcopy(source)
+    require(source['T'] == 8 and len(source['order']) == 72, 'source plan dimensions')
+    order = interleave(source['order'])
+    windows, schedule = actual_windows(parent, order)
+    idle8 = idle_profile(owners8, source['windows'])
+    paid = Counter({int(k): v for k, v in source['profile'].items()})
+    paid.subtract(idle8)
+    require(all(v >= 0 for v in paid.values()), 'T8 idle not within profile')
+    idle16 = idle_profile(owners, windows)
+    prof = Counter({k: 2 * v for k, v in paid.items()})
+    prof.update(idle16)
+    prof = +prof
+    p.update(status='FROZEN_EXPLICIT_T16_TWO_BANK_DIRECT_SUM_OWNER_NOMINATION',
+             mode='gauge44-all144-t16-idle-concentration', T=16, live=14336, deficit=5120,
+             profile={str(k): prof[k] for k in sorted(prof)}, order=order, windows=windows,
+             solver_status='exact pattern-flow LNS on the T16 actual-window geometry', gap=None,
+             source_plan_sha256=plan_sha, source_owners_sha256=owners8_sha,
+             assignment_sha256=owners_sha, assignment_content_sha256=content_sha(owners))
+    for field in ('provider_calls', 'per_call_widths'):
+        p[field] = []
+        for old in source[field]:
+            for group in range(2):
+                new = copy.deepcopy(old)
+                new['replica'] += 8 * group
+                if 'time' in new:
+                    new['time'] = 2 * old['time'] + group
+                p[field].append(new)
+    at = {tuple(x): i for i, x in enumerate(order)}
+    for field in ('provider_calls', 'per_call_widths'):
+        p[field].sort(key=lambda c: at[c['stage'], c['replica']])
+    p['replica_lift'] = dict(groups=2, source_replicas=8, replicas=16,
+                             parent_template_content_sha256=content_sha(parent), owners_file_sha256=owners_sha,
+                             window_semantics='strict physical source-event touch intervals, including bridges',
+                             schedule_content_sha256=content_sha(schedule))
+    require(len(owners) == 144 * len(source['provider_registry']['gauge44']['widths']), 'owner role count')
+    for role in owners:
+        require(role['time'] == at[role['stage'], role['replica']], 'role call time')
+        require(role['time'] in windows[f"{role['owner_replica']},{role['child']}"][1], 'owner outside actual window')
+    require(sum(int(k) * v for k, v in p['profile'].items()) == 73 * p['live'] - p['deficit'], 'rank mass')
+    return p, schedule, idle8, idle16
+
+
+def main(base, plan8p, own8p, own16p, out):
+    base, out = Path(base), Path(out)
+    require(not out.exists(), 'out exists')
+    src_path = base / 'split-centres/GLOBAL-TEMPLATE.json.gz'
+    source = read(src_path)
+    plan8 = read(plan8p)
+    require(lift_parent(source, 1) == source, 'T8 identity control')
+    require(actual_windows(source, plan8['order'])[0] == plan8['windows'], 'T8 source-window replay')
+    require(source['exact_data_phase_recipe_sha256'] == sha(base / 'work/complex-nine-native/DATA-PHASES.json'), 'data-phase binding')
+    parent = lift_parent(source)
+    owners8, owners = read(own8p), read(own16p)
+    plan, schedule, idle8, idle16 = lift_plan(plan8, parent, owners8, owners, sha(plan8p), sha(own8p), sha(own16p))
+    out.mkdir(parents=True)
+    (out / 'GLOBAL-TEMPLATE.json.gz').write_bytes(portable_gzip(canonical(parent)))
+    (out / 'PLAN.json').write_bytes((json.dumps(plan, indent=2) + '\n').encode())
+    rec = dict(status='PASS_T16_DIRECT_SUM_PARENT_AND_LITERAL_SOURCE_WINDOWS', T8_identity_control=True,
+               T8_source_window_identity=True, idle8=dict(sorted(idle8.items())), idle16=dict(sorted(idle16.items())),
+               profile=plan['profile'], parent_live=parent['live'], parent_physical=parent['physical'],
+               actual_window_membership_checked=len(owners), events=len(schedule))
+    (out / 'PARENT-LIFT-RECEIPT.json').write_text(json.dumps(rec, indent=2) + '\n')
+    print(json.dumps(rec))
+
+
+if __name__ == '__main__':
+    main(*sys.argv[1:6])
diff --git a/research/gauge44-slots-t16/verify_manifest.py b/research/gauge44-slots-t16/verify_manifest.py
new file mode 100644
index 0000000000..8c2441d392
--- /dev/null
+++ b/research/gauge44-slots-t16/verify_manifest.py
@@ -0,0 +1,19 @@
+"""Verify the submitted package's exact file inventory and SHA256 bindings."""
+from hashlib import sha256
+import json
+from pathlib import Path
+
+root = Path(__file__).resolve().parent
+expected = json.loads((root / 'MANIFEST.json').read_text())
+actual = {
+    p.relative_to(root).as_posix(): sha256(p.read_bytes()).hexdigest()
+    for p in root.rglob('*')
+    if p.is_file() and '__pycache__' not in p.parts
+    and p != root / 'MANIFEST.json'
+}
+if actual != expected:
+    missing = sorted(expected.keys() - actual.keys())
+    extra = sorted(actual.keys() - expected.keys())
+    changed = sorted(k for k in expected.keys() & actual.keys() if expected[k] != actual[k])
+    raise SystemExit(f'Manifest mismatch: missing={missing}, extra={extra}, changed={changed}')
+print(f'PASS package manifest: {len(actual)} files')
diff --git a/research/gauge44-slots-t16/verify_t16.py b/research/gauge44-slots-t16/verify_t16.py
new file mode 100644
index 0000000000..4794150c4c
--- /dev/null
+++ b/research/gauge44-slots-t16/verify_t16.py
@@ -0,0 +1,122 @@
+"""Strict T16 replay: the T8 package's frozen admission, then the sixteen-replica two-bank controller.
+
+Credit: the T16 controller, source adapters, direct-sum parent lift, actual-window reconstruction and the
+independent T16 checker are Hao Yan's (@FanPUYen) PR #858 (research/complex-double-replica-owners, Apache-2.0),
+vendored in t16/ with only the documented generalisations (word-derived R/widths/idle profile, owner-derived PLAN profile).
+The adapted controller code/ is byte-identical to the signed research/gauge44-barch-t16 code (#870's T16 code).
+
+Stages (strict only, no discovery, no optimizer):
+ restore-parent, bind8 (T8 SPEC data/SPEC-T8.json, T8 PLAN/OWNERS data/T8/: replays the gauge44-slots admission),
+ lift16 (direct-sum parent and actual source-event windows; every one of the frozen data/OWNERS.json.gz roles is checked
+ inside its owner's actual window; the lifted PLAN must equal data/PLAN.json). data/OWNERS.json.gz is frozen data (an exact
+ pattern-flow LNS repack on the T16 geometry); it is checked by lift16, the controller audit and independent-t16. No
+ owner constructor or optimizer runs. bind, emit, audit, invoice, assembly, admission-controls,
+ bit-supplier-controls (code/ = pinned gauge44 code + #858's exact multiplicity-checked T16 edits), independent-t16.
+"""
+import argparse, gzip, hashlib, json, os, shutil, subprocess, sys, time
+from fractions import Fraction
+from pathlib import Path
+
+assert __debug__, 'Assertions required'
+PKG = Path(__file__).resolve().parent
+sha = lambda p: hashlib.sha256(Path(p).read_bytes()).hexdigest()
+rd = lambda p: json.loads(gzip.decompress(Path(p).read_bytes()) if str(p).endswith('.gz') else Path(p).read_bytes())
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--main', type=Path, required=True)
+ap.add_argument('--local', type=Path, required=True)
+ap.add_argument('--work', type=Path, required=True)
+a = ap.parse_args()
+main, local, work = a.main.resolve(), a.local.resolve(), a.work.resolve()
+assert not work.exists(), 'Output directory must be new'
+source = main / 'research/complex-k492-owner-repair/vendor/multicold'
+baseline = main / 'research/community-k492-audit/pr622/replay/baseline558'
+vendor = source / 'vendor/pr558/vendor/pr552/complex-global/vendor531'
+for rel, expected in rd(PKG / 'data/UPSTREAM-PINS.json').items():
+    assert sha(main / rel) == expected, 'Upstream dependency changed: ' + rel
+work.mkdir(parents=True)
+env0 = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+            MULTICOLD_SOURCE=str(source), GAIN_PR564_SOURCE=str(source))
+for k in ('PYTHONOPTIMIZE', 'WITNESS_DISCOVER', 'WITNESS_RECORD', 'WITNESS_SPEC'):
+    env0.pop(k, None)
+stages = []
+SPEC8, SPEC16 = PKG / 'data/SPEC-T8.json', PKG / 'data/SPEC.json'
+PLAN8, OWN8 = PKG / 'data/T8/PLAN.json', PKG / 'data/T8/OWNERS.json.gz'
+
+
+def run(name, script, *args, spec=SPEC16, extra=None):
+    t0 = time.monotonic()
+    log = work / (name + '.log')
+    with log.open('w') as s:
+        rc = subprocess.run([sys.executable, '-B', str(source / 'code/run_portable.py'), str(script), *map(str, args)],
+                            env=dict(env0, WITNESS_SPEC=str(spec), **(extra or {})), stdout=s, stderr=subprocess.STDOUT).returncode
+    stages.append(dict(name=name, seconds=round(time.monotonic() - t0, 3), exit_code=rc, log_sha256=sha(log)))
+    (work / 'STAGES.json').write_text(json.dumps(stages, indent=2) + '\n')
+    if rc:
+        raise RuntimeError(name + ' failed:\n' + log.read_text()[-6000:])
+    print('PASS', name, stages[-1]['seconds'], flush=True)
+
+
+code, t16 = PKG / 'code', PKG / 't16'
+R16 = len(rd(PLAN8)['provider_registry']['gauge44']['widths'])
+run('restore-parent', code / 'restore_parent.py', '--source', source, '--baseline', baseline, '--out', work / 'parent558', spec=SPEC8)
+run('bind8', code / 'bind_providers_portable.py', '--baseline', work / 'parent558', '--provider', 'gauge44=' + str(local),
+    '--plan', PLAN8, '--out', work / 'global8', spec=SPEC8)
+
+run('lift16', t16 / 'lift16.py', work / 'global8/base', PLAN8, OWN8, PKG / 'data/OWNERS.json.gz', work / 'lift', spec=SPEC8)
+assert rd(work / 'lift/PLAN.json') == rd(PKG / 'data/PLAN.json'), 'lifted PLAN differs from data/PLAN.json'
+parent16 = work / 'parent16'
+shutil.copytree(work / 'parent558', parent16)
+shutil.copyfile(work / 'lift/GLOBAL-TEMPLATE.json.gz', parent16 / 'complex-global/base/split-centres/GLOBAL-TEMPLATE.json.gz')
+g = work / 'global'
+run('bind', code / 'bind_providers_portable.py', '--baseline', parent16, '--provider', 'gauge44=' + str(local),
+    '--plan', PKG / 'data/PLAN.json', '--out', g)
+run('emit', code / 'emit_allcold.py', '--base', g / 'base', '--owners', PKG / 'data/OWNERS.json.gz', '--plan', g / 'PLAN.json', '--out', g / 'hosted')
+run('audit', code / 'audit_allcold.py', g / 'base', g / 'hosted', g / 'audit/ASYNC-AUDIT.json', '--mutation-controls')
+run('invoice', code / 'invoice_allcold.py', '--base', g / 'base', '--hosted', g / 'hosted', '--audit', g / 'audit',
+    '--out', g / 'audit', '--retained-invoice', vendor / 'evidence/audit/PREFIX-AND-INVOICE.json')
+run('assembly', code / 'assemble.py', source, g, work / 'ASSEMBLY.json')
+for nm, sc, out in (('admission-controls', 'assembly_controls.py', 'ADMISSION-CONTROLS.json'),
+                    ('bit-supplier-controls', 'bit_supplier_controls.py', 'BIT-SUPPLIER-CONTROLS.json')):
+    run(nm, code / sc, '--source-package', source, '--owner', g / 'audit/OWNERS-AND-PROFILE.json',
+        '--invoice', g / 'audit/PREFIX-AND-INVOICE.json', '--out', work / out)
+lift = rd(work / 'lift/PARENT-LIFT-RECEIPT.json')
+run('independent-t16', t16 / 'indep16.py', '--baseline-parent', work / 'global8/base/split-centres/GLOBAL-TEMPLATE.json.gz',
+    '--owners', PKG / 'data/OWNERS.json.gz', '--word', local / 'CANONICAL-WORD.json.gz', '--out', work / 'INDEPENDENT-T16.json',
+    extra={'T16_EXPECTED_IDLE': json.dumps(rd(SPEC16)['expected']['idle_remainder_profile']),
+           'T16_EXPECTED_WIDTHS': json.dumps(rd(SPEC16)['providers']['gauge44']['inventory'])})
+asm, ind = rd(work / 'ASSEMBLY.json'), rd(work / 'INDEPENDENT-T16.json')
+inv = rd(g / 'audit/PREFIX-AND-INVOICE.json')
+bc, ac = rd(work / 'BIT-SUPPLIER-CONTROLS.json'), rd(work / 'ADMISSION-CONTROLS.json')
+assert asm['status'] == 'PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY' and asm['kappa'] == rd(SPEC16)['expected']['kappa']
+assert bc['status'] == 'PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS' and len(bc['rejected_controls']) == 12 and bc['derived_deficit'] == 10272
+assert not ac['discovery_accepted_controls'] and len(ac['rejected_controls']) == 69
+assert ind['status'] == 'PASS_INDEPENDENT_T16_LITERAL_WINDOWS_CHARTS_PREFIX_ROW' and len(ind['controls_rejected']) == 6
+assert ind['profile'] == asm['complex_profile'] and {str(k): v for k, v in lift['idle16'].items()} == {str(k): v for k, v in ind['idle'].items()}
+assert ind['prefix_bits'] == inv['global_prefix_bits'] < 512 and ind['physical_row_coefficient'] < 20161
+# Final binding (as #858 verify.py final_binding).
+owner, audit = rd(g / 'audit/OWNERS-AND-PROFILE.json'), rd(g / 'audit/ASYNC-AUDIT.json')
+assert ind['physical_row_coefficient'] == inv['finite']['physical_row_coefficient'] < inv['finite']['retained_row_coefficient'] == 20161
+assert inv['charged_prefix_bits'] == 512
+assert ind['rank_mass'] == owner['rank_mass'] == 1041408 and ind['deficit'] == owner['deficit'] == 5120
+assert inv['strict_checks'] and all(inv['strict_checks'].values()), 'every finite invoice inequality'
+assert len(asm['outer']) == 47 and all(Fraction(v) > 0 for v in asm['outer'].values()), 'all 47 strict outer margins'
+assert audit['mutation_controls_run'] and len(audit['mutations_rejected']) == 15
+assert ind['roles'] == owner['hosted_residuals'] == audit['complex_hosted_residuals'] == 144 * R16
+assert ind['calls'] == audit['complete_invocations'] == inv['complete_invocation_sweeps'] == 144
+assert ind['actual_73_axis_charts'] == owner['actual_73column_sigmas'] == audit['actual_orthogonal_73column_maps']
+assert lift['actual_window_membership_checked'] == 144 * R16 and lift['T8_identity_control'] and lift['T8_source_window_identity']
+for name in ('CANONICAL-WORD.json.gz', 'LOCAL-PROGRAMS.json.gz', 'LOCAL-CHECKS.json', 'INDEPENDENT-LOCAL-REPLAY.json',
+             'RESIDUAL-ADAPTERS.json', 'CLIFFORD-RECIPES.json', 'CLIFFORD-REVIEW.json'):
+    assert rd(g / 'base/providers/gauge44' / name) == rd(local / name), 'provider content binding: ' + name
+assert asm['template_sha256'] == owner['template_sha256'] == inv['template_sha256']
+assert inv['owner_audit_sha256'] == sha(g / 'audit/OWNERS-AND-PROFILE.json') and inv['controller_audit_sha256'] == sha(g / 'audit/ASYNC-AUDIT.json')
+assert Fraction(asm['kappa']) > Fraction(rd(SPEC8)['expected']['kappa']), 'T16 must strictly improve the T8 package'
+res = dict(status='PASS_GAUGE44_T16_STRICT_GLOBAL_REPLAY', kappa=asm['kappa'], kappa_decimal=asm['kappa_decimal'],
+           conservative_kappa_decimal=asm['conservative_kappa_decimal'], complex_lower=asm['complex_lower'], bit_lower=asm['bit_lower'],
+           complex_profile=asm['complex_profile'], idle_remainder_profile=ind['idle'], complete_invocations=144, roles=ind['roles'],
+           prefix_bits=ind['prefix_bits'], charged_prefix_bits=512, physical_row_coefficient=ind['physical_row_coefficient'],
+           retained_row_coefficient=20161, actual_73_axis_charts=ind['actual_73_axis_charts'],
+           controls=dict(admission=69, bit_supplier=12, independent_t16=6, controller_mutations=15),
+           t8_kappa=rd(SPEC8)['expected']['kappa'], spec_sha256=sha(SPEC16), stages=stages, scope=asm['scope'])
+(work / 'REPLAY.json').write_text(json.dumps(res, indent=2) + '\n')
+print(res['status'], res['kappa_decimal'], flush=True)
diff --git a/research/gauge44-slots/CONSTRUCTION.md b/research/gauge44-slots/CONSTRUCTION.md
new file mode 100644
index 0000000000..fa15676366
--- /dev/null
+++ b/research/gauge44-slots/CONSTRUCTION.md
@@ -0,0 +1,210 @@
+# Gauge44: a changed factory forward map with 44 rank-four cold ends
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0. This note describes the new complex local construction. The package's global evidence supplies the resulting global bound and retains the upstream conditional assumptions.
+
+## 1. Exact result and comparison
+
+The final word has 112 source ports, 112 target ports and 492 helper registers. It implements the same arbitrary-dirt scalar endpoint as the upstream word,
+
+$$
+(X,Y,H)\longmapsto(X,Y+X,H),
+$$
+
+and its inverse-transpose orientation is checked separately. All 204 nonzero entrance frames remain valid. The new ending set consists of **44 cold helpers at rank-four frames**, together with the 34 entering-helper ends inherited from the JP8 HPE stage.
+
+The precise comparison is with the JP8 provider reconstructed from PR635, commit `a6895a69f8ad98ab45777b03e9e6f48888c39f6f`:
+
+| Local quantity | PR635 JP8 | Gauge44 |
+|---|---:|---:|
+| Helpers | 492 | 492 |
+| Nonzero entrance frames | 204 | 204 |
+| Rank-four cold ends | 22 | 44 |
+| Rank-seven cold ends | 2 | 0 |
+| Rank-eight cold ends | 4 | 0 |
+| Entering helpers ending below FULL | 36 | 34 |
+| Total residual helper width | 3894 | **3794** |
+| Local paid rank mass | 5750 | **5650** |
+
+Thus the new word saves **100 units of residual width per invocation** against the complete PR635 provider. It replaces that provider's cold-end construction; the old six higher-rank cold ends and two additional entering ends are not added to the new count.
+
+The exact paid-child profiles are:
+
+| Child rank | PR635 count | Gauge44 count |
+|---:|---:|---:|
+| 1 | 2518 | 2514 |
+| 2 | 402 | 404 |
+| 3 | 448 | 448 |
+| 4 | 164 | 160 |
+| 5 | 68 | 56 |
+| 6 | 4 | 0 |
+| 8 | 8 | 8 |
+
+The final residual-width inventory is `{4:52, 5:48, 7:34, 8:114, 9:244}`. Both the profile and the inventory are recomputed from the literal native frame chains. They are not inferred from the nominal number of ended helpers.
+
+## 2. What changes in the forward factory
+
+The inherited K-triangle schedule and its 492-helper allocation remain the starting construction. Within each of the fourteen eight-source packet factories, three changes alter the arbitrary-dirt forward map while retaining the required clean packet values.
+
+### A. Exchange a source with an equal clean copy
+
+After the sixteen initial copy gates, local source position `j` and its two helper copies have clean values `(x_j,x_j,x_j)`. For positions `j = 4,5,6,7`, exchange the original source register with its second helper copy. The exact register pair in the constructor is `mp[j]` and `mp[2*j+9]`.
+
+For arbitrary helper dirt the triple is instead
+
+$$
+(x_j,\;x_j+h_{j,1},\;x_j+h_{j,2}).
+$$
+
+The exchange changes where the second dirty direction enters the subsequent factory. It does not change any clean operand. Both exchanged registers already have the same rank-one frame, so the exchange adds no frame climb. Each exchange is emitted as three additions and one sign change; these scalar operations remain part of the finite implementation invoice.
+
+This is a change of the forward map, not an output relabeling. In particular, the inverse recovery functional for the original source changes from the original branch to a different combination of the three equal-clean branches. That changes which cold input directions can have their entire final support inside a low frame.
+
+### B. Change the complement to the four coordinate totals
+
+Eight retired factory rows already span the eight source coordinates. The first four rows of their replacement basis are the four required coordinate totals. The remaining four rows are chosen by exact row-rank extension, first using the ordered clean linear forms recorded in `construction/COMPLETION-PRIORITY.json`, then using coordinate rows if an extension is still needed.
+
+These candidate forms are the future low-frame leaver forms used during discovery. The frozen priority data are the complete input to the final constructor: no discovery search is run in reproduction. Every accepted row must increase the rational rank; the resulting eight-by-eight basis is explicitly applied by elementary operations.
+
+All eight retired registers are already at the block's rank-four frame. Consequently this basis replacement also adds no frame climb. It gives the low final rows more independent linear combinations that annihilate the original source data.
+
+### C. Place coordinate totals on the available source carriers
+
+The retired registers are ordered with source registers first. Three available source carriers and one helper carry the four coordinate totals, leaving the four complementary rows on physical helper registers. This lets the new cold directions end on helper wires under the unchanged native endpoint interface.
+
+A carrier permutation alone does not increase the available cold space. Its role here is to realize the independent directions created jointly by the source-copy exchange and the new complementary basis.
+
+## 3. Exact cold-space calculation
+
+Let `P` be the non-target forward matrix after parts A and B and the 34 inherited HPE tail gates. It has 604 rows and columns: 112 original sources and 492 helpers. Let `J` be the 316 protected initial columns consisting of the 112 original sources and all 204 entering helpers.
+
+For a block frame `F`, let `I` be every non-target output register whose current frame is contained in `F`. Source output rows are included in this set. Define
+
+$$
+L=\operatorname{leftker} P[I,J],\qquad
+K=\ker P^{-1}[J,I].
+$$
+
+Rows of `L` are low output linear forms with no protected initial dependence. Columns of `K` are low-supported output directions whose inverse images have no protected component. The rank of the pairing `LK` counts the simultaneously usable cold directions in this fixed forward word.
+
+The changed forward map has the following exact block data:
+
+| Block indices | Number of blocks | Low registers `|I|` | `dim L` | `dim K` | `rank(LK)` |
+|---|---:|---:|---:|---:|---:|
+| 0, 1, 2, 11, 12, 13 | 6 | 6 | 2 | 4 | **2** |
+| 3 through 10 | 8 | 8 | 4 | 4 | **4** |
+
+The count is therefore `6*2 + 8*4 = 44`. The fixed upstream rank-four cold construction supplied one and two directions respectively, for `6*1 + 8*2 = 22`.
+
+The complement change by itself improves the available low annihilating rows but leaves the inverse-support obstruction. The source-copy exchanges remove that obstruction: `K` has dimension four in every block and pairs with all the available rows of `L`.
+
+## 4. Realizing the directions with legal dyadic operations
+
+`construction/build_gauge_cold44.py` recomputes these spaces over exact rational numbers. It selects columns of `K` and normalizes them to a matrix `U` satisfying
+
+$$
+LU=I_r,
+\qquad q=P^{-1}[:,I]U.
+$$
+
+The constructor checks that `q` is supported entirely on that block's sixteen initially cold factory helpers, denoted `H_b`. Put
+
+$$
+R_b=LP[I,H_b].
+$$
+
+Then `R_b q[H_b,:] = I_r`. A sixteen-by-sixteen input basis `Q_b` places the columns `q[H_b,:]` at the designated ended-helper positions and fills the other columns with a basis of `ker R_b`. The resulting input basis is explicitly invertible.
+
+For the low-frame output transformation, the ended-helper rows are replaced by the rows of `L`; each remaining low row `i` becomes
+
+$$
+e_i-U_iL.
+$$
+
+The actual chosen helper positions give an invertible tail matrix. Its nonsingularity and dyadic implementation are checked by exact elimination, rather than assumed from a dimension count. The construction receipt records every `Q_b`, tail matrix and selected endpoint.
+
+Every `Q_b` is emitted at frame zero, at the head of A **after** the entry normalization wrappers. Every low tail is emitted at its block frame. The remaining cleanup is rebuilt as an exact dyadic Gauss-Jordan inverse on the non-ended registers at FULL. It is not obtained by blindly reversing a changed partial schedule.
+
+Before forming the FULL inverse, the constructor verifies both the row and the column identity of each of the 78 ended helpers. Thus no protected data or other helper dirt remains in an ended helper, and its initial dirt remains nowhere else. The FULL inverse skips these isolated rows and columns entirely.
+
+The realized word has:
+
+| Construction component | Scalar gates |
+|---|---:|
+| Frame-zero helper premix | 1489 |
+| New rank-four tail | 60 |
+| Inherited HPE tail | 34 |
+| Refactored FULL inverse | 28056 |
+| Additional target compensation after wrappers | **0** |
+
+All selected new cold directions have zero target response. The independent scalar auditor nevertheless recomputes the complete existing dirty-response compensation, obtaining 7348 additions, and checks both orientations on all 716 input columns.
+
+Relative to the HPE-stage word before any cold-end construction, the aggregate chain delta is `N_1 += 44, N_6 -= 44`, reducing rank mass and residual width by 220. PR635 had already saved 120 units through its complete cold/extra-HPE construction. The net new saving is therefore 100. There is no omitted cost for lifting the low tails: their rank-one increments are included explicitly.
+
+## 5. Native interface and validation
+
+The transport preserves the exact ordered list of 112 ports and the exact ordered eight center frames. The center carriers change because some totals now reside on sources. In native coordinates they are
+
+```
+[92, 57, 81, 224, 11, 240, 9, 256]
+```
+
+A global interface check must compare the ordered center frames and port geometry, and use the provider's actual center carriers. Equality of carrier numbers with an old provider is not a mathematical requirement. The local event ledgers explicitly clear all private center channels in both orientations.
+
+Completed checks for the frozen word include exact forward and inverse-transpose scalar replay on all 716 columns; every literal native frame chain; the 204 zero-response entrance conditions; the 44 cold and 34 entering endpoint cones; wrapper placement and normalized wrapper identities; both emitted local ledgers; and exact phase lowering for 3019 directed edges and 224 endpoint adapters. The independent audit does not import the new constructor.
+
+This local result does not by itself certify a global exponent. Physical whole-family owners, actual residual/spectator routing, idle remainders, global scalar assembly and the complete finite invoice are the separate global checks reported elsewhere in the package.
+
+## 6. Compact reproduction
+
+Only Python's standard library is needed for this construction and the retained local pipeline. Do not use `python -O`. The reproduction driver checks byte hashes of every named upstream input and the changed code, then checks the content hash after each construction step. Its two source checkouts are:
+
+| Argument | Repository commit |
+|---|---|
+| `--main` | `17ce0c79b7b51c2634b439ea5a2b754f09909693` |
+| `--pr635` | `a6895a69f8ad98ab45777b03e9e6f48888c39f6f` |
+
+Starting from a clone of `https://github.com/CrocSwap/integer-mult-bounds` containing those commits, prepare detached worktrees:
+
+```bash
+git -C integer-mult-bounds fetch origin main refs/pull/635/head
+git -C integer-mult-bounds worktree add --detach ../integer-main 17ce0c79b7b51c2634b439ea5a2b754f09909693
+git -C integer-mult-bounds worktree add --detach ../integer-pr635 a6895a69f8ad98ab45777b03e9e6f48888c39f6f
+```
+
+From the directory containing those worktrees and this delta package, run:
+
+```bash
+python -B research/gauge44-global/construction/reproduce.py \
+  --main integer-main \
+  --pr635 integer-pr635 \
+  --out gauge44-reproduction
+```
+
+The default stops after regenerating the exact final scalar word and comparing the newly derived cold recipe with the frozen recipe. It rebuilds only the two short shadow steps needed by the four port transfers. It does not rerun the ancestor admission stack, search for a basis, optimize owners, or replay global assembly.
+
+Use `--frozen-cold` to splice the included recipe instead of re-deriving its small exact linear systems. Use `--until local` to add native transport, emitted ledgers, independent local replay and wrappers. Use `--until phases` to add the complete phase lowering. Every invocation needs a fresh output directory; these are alternatives, not resumable increments. On the research machine, exact cold derivation took about 2.6 seconds, native transport/ledgers/replay/wrappers about 41 seconds, and complete phase lowering about 198 seconds.
+
+The exact dependency chain is:
+
+1. Construct the changed raw R492 factory from the pinned Hamming inputs, frozen priority and pinned K-triangle schedule.
+2. Apply the four inherited port stages.
+3. Apply the inherited B-frame regroup and 34-HPE construction.
+4. Derive the exact block premixes, cold44 tails and FULL inverse.
+5. Optionally emit and check the native ledgers, wrappers and complete phase lowering.
+
+`construction/INPUTS.json` gives the input hashes and every intermediate content hash. The key decompressed content identities are:
+
+| Word | SHA-256 |
+|---|---|
+| Changed raw factory | `0ac47f92fc2e3f5aa457d78f7b8a5c785bf140c546932b9dfcd9e610ad319180` |
+| Changed HPE forward | `42fb8b3aa314593fe976820cf65824f5fce0ee4f95281796992d4809709864cc` |
+| Final cold44 word | `78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290` |
+| Native canonical word | `e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f` |
+
+## 7. Attribution
+
+The original 504-helper factory and borrowed-register construction are icekylinx's PR531 lineage, prepared with OpenAI Codex/GPT assistance and retaining the earlier PR425/PR514 credits. The inherited K-triangle atom and frozen read schedule are credited in PR635 to AtomScout, a Claude Code research agent. The porting routine is credited there to Port480. This package does not claim those as new work.
+
+The reused JP8 ancestry includes the PR558/PR552 supplier, the earlier-cut and multicold kernels, and the joint prefix adapted from Dominik Scholz's PR571 work. Native HPE and cold-end transport, frame and wrapper machinery come from the credited PR635 lineage, including DreamingOfClouds, jeremykothe2, chafreaky and their disclosed assistants. The retained `construction/UPSTREAM-NOTICE.md` and `construction/LICENSE` preserve the upstream notice and Apache-2.0 license.
+
+The new contribution here is the combination of source-copy exchange, changed retired-row completion, source-carried coordinate totals, and the explicit exact cold44 realization. Those changes were developed for icekylinx with OpenAI GPT-6 Astra assistance. The upstream notices, proof scope and conditional assumptions continue to apply.
diff --git a/research/gauge44-slots/LICENSE b/research/gauge44-slots/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/gauge44-slots/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/gauge44-slots/LOCAL-VALIDATION.json b/research/gauge44-slots/LOCAL-VALIDATION.json
new file mode 100644
index 0000000000..5973645e1a
--- /dev/null
+++ b/research/gauge44-slots/LOCAL-VALIDATION.json
@@ -0,0 +1,356 @@
+{
+  "status": "PASS_LOCAL_INCREMENTAL_GAUGE44",
+  "python": "3.14.8",
+  "upstream_main": "17ce0c79b7b51c2634b439ea5a2b754f09909693",
+  "pr635": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f",
+  "construction_steps": [
+    {
+      "step": "shadow-early",
+      "exit_code": 0,
+      "seconds": 0.322
+    },
+    {
+      "step": "shadow-prefix",
+      "exit_code": 0,
+      "seconds": 0.429
+    },
+    {
+      "step": "gauge-forward",
+      "exit_code": 0,
+      "seconds": 0.474
+    },
+    {
+      "step": "port0",
+      "exit_code": 0,
+      "seconds": 0.388
+    },
+    {
+      "step": "port1",
+      "exit_code": 0,
+      "seconds": 0.407
+    },
+    {
+      "step": "port2",
+      "exit_code": 0,
+      "seconds": 0.403
+    },
+    {
+      "step": "port3",
+      "exit_code": 0,
+      "seconds": 0.389
+    },
+    {
+      "step": "cold44-exact",
+      "exit_code": 0,
+      "seconds": 2.544
+    },
+    {
+      "step": "native",
+      "exit_code": 0,
+      "seconds": 3.63
+    },
+    {
+      "step": "ledgers",
+      "exit_code": 0,
+      "seconds": 2.759
+    },
+    {
+      "step": "local-replay",
+      "exit_code": 0,
+      "seconds": 15.924
+    },
+    {
+      "step": "wrappers",
+      "exit_code": 0,
+      "seconds": 2.706
+    },
+    {
+      "step": "phases",
+      "exit_code": 0,
+      "seconds": 186.772
+    }
+  ],
+  "five_mathematical_local_artifacts_match_frozen_evidence": true,
+  "phase_edges": 3019,
+  "endpoint_adapters": 224,
+  "independent_scalar_audit": {
+    "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+    "input_file": "FULL-WORD.json.gz",
+    "content_sha256": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290",
+    "compressed_sha256": "0ad202612f010df4ab66432a628247b37ad8b497dd6b27595b1685cbd7eb119e",
+    "parent_center_interface": {
+      "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+      "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+      "transport_tau": 43,
+      "ordered_frame_bases_match": true,
+      "all_ports_match": true,
+      "transported_centers": [
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+        57,
+        81,
+        224,
+        11,
+        240,
+        9,
+        256
+      ],
+      "source_centers": [
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+        57,
+        81,
+        11,
+        9
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+      "ordered_frame_bases": [
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+          256,
+          128,
+          64,
+          34,
+          16,
+          10,
+          4,
+          1
+        ],
+        [
+          256,
+          128,
+          64,
+          32,
+          16,
+          8,
+          5,
+          3
+        ],
+        [
+          256,
+          128,
+          64,
+          32,
+          17,
+          9,
+          4,
+          2
+        ],
+        [
+          256,
+          128,
+          64,
+          36,
+          20,
+          8,
+          2,
+          1
+        ],
+        [
+          256,
+          128,
+          66,
+          32,
+          18,
+          8,
+          4,
+          1
+        ],
+        [
+          256,
+          128,
+          65,
+          33,
+          17,
+          9,
+          5,
+          3
+        ],
+        [
+          256,
+          128,
+          65,
+          33,
+          16,
+          8,
+          4,
+          2
+        ],
+        [
+          256,
+          128,
+          68,
+          32,
+          16,
+          12,
+          2,
+          1
+        ]
+      ]
+    },
+    "v": 112,
+    "h": 9,
+    "R": 492,
+    "entering": 204,
+    "lowends": 78,
+    "coldends": 44,
+    "compensation_gates": 7348,
+    "local_profile": {
+      "1": 2514,
+      "2": 404,
+      "3": 448,
+      "4": 160,
+      "5": 56,
+      "8": 8
+    },
+    "width_inventory": {
+      "4": 52,
+      "5": 48,
+      "7": 34,
+      "8": 114,
+      "9": 244
+    },
+    "checked_columns": 716,
+    "elapsed_seconds": 2.443164045999765,
+    "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+  },
+  "independent_guard_review": {
+    "status": "PASS_PR635_ADMISSION_ASSERTION_PRESERVATION",
+    "files": [
+      {
+        "file": "code/assemble.py",
+        "baseline_sha256": "1b1a9024ac910dc9b9d9e30150684e1fa9cb228a4c1c275b75ab04b57fdef1dd",
+        "new_sha256": "7ac28118d69416e4fb67b61216285fb0823310b7635ce1b9025aa3f10119ef6a",
+        "byte_identical": false,
+        "assert_count": 91,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/invoice_allcold.py",
+        "baseline_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+        "new_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+        "byte_identical": true,
+        "assert_count": 67,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/bind_providers_portable.py",
+        "baseline_sha256": "2eb5c262bf481b3bec9ceaec654fa46ff6fc3a89b13d4906a29a55a89e35feea",
+        "new_sha256": "7c9aba6c7f138d270852d859d902f905a15598b6263567700b5b08a153823cb6",
+        "byte_identical": false,
+        "assert_count": 22,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/generated_identity.py",
+        "baseline_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+        "new_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+        "byte_identical": true,
+        "assert_count": 4,
+        "all_assertions_identical_in_order": true
+      },
+      {
+        "file": "code/witness.py",
+        "baseline_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+        "new_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+        "byte_identical": true,
+        "assert_count": 3,
+        "all_assertions_identical_in_order": true
+      }
+    ],
+    "centre_interface_review": "CENTRE-GUARD-REVIEW.md",
+    "scope": "Exact syntax preservation for all admission assertions in these five files. The changed emitter/controller centre boundary and single-provider controls require the separate semantic review; assertion counts alone do not prove them."
+  },
+  "owner_replay": {
+    "status": "PASS_FROZEN_OWNER_AND_INTEGER_MAJORIZATION_REPLAY",
+    "seed_mode": "included_frozen_seed",
+    "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+    "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+    "owners_semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d",
+    "owners_gzip_sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+    "majorization_semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc",
+    "global_profile": {
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+      "2": 29164,
+      "3": 32429,
+      "4": 11520,
+      "5": 4032,
+      "7": 7,
+      "8": 582,
+      "12": 13,
+      "16": 33,
+      "19": 1,
+      "20": 2,
+      "28": 4,
+      "32": 62,
+      "36": 1,
+      "40": 1,
+      "44": 6,
+      "48": 2289
+    },
+    "scope": "Exact hosting nomination and callwise fixed-point replay; full supplier admission is separate."
+  },
+  "global_replay": {
+    "status": "PASS_GAUGE44_STRICT_GLOBAL_REPLAY",
+    "kappa": "1649483702558979/1000000000000000000",
+    "kappa_decimal": "0.001649483702558979",
+    "complex_lower": "1652208994368411824947/1000000000000000000000000",
+    "bit_lower": "413456747036699736067/250000000000000000000000",
+    "gain_over_pr635_percent": "0.8093060205252829126484020359439672024956960385078942889840023844750830",
+    "spec_sha256": "fee57674a7f36b30b1e7eb96a8f567a90a522217bc644c1a6a1f8bff85196fbf",
+    "stages": [
+      {
+        "name": "restore-parent",
+        "seconds": 2.089,
+        "exit_code": 0,
+        "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+      },
+      {
+        "name": "bind",
+        "seconds": 0.962,
+        "exit_code": 0,
+        "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+      },
+      {
+        "name": "emit",
+        "seconds": 4.817,
+        "exit_code": 0,
+        "log_sha256": "90ce07d06a8eaffdb66201e8346021183e5a803395fb9f6d8ceb0e5ff068ef2c"
+      },
+      {
+        "name": "audit",
+        "seconds": 19.625,
+        "exit_code": 0,
+        "log_sha256": "66b4abb2a88a4eaba8a8baa3585ef4aa819be5f8acb7947bae734b3478280456"
+      },
+      {
+        "name": "invoice",
+        "seconds": 1.804,
+        "exit_code": 0,
+        "log_sha256": "5d10712d494304287749dd7a6c3369f9b707bba30e9f567b68230669dcf5418a"
+      },
+      {
+        "name": "assembly",
+        "seconds": 0.808,
+        "exit_code": 0,
+        "log_sha256": "768d3215f1918117dc6c33b4cfeaf0b5f5da9ba5c77178db4bb1d08d000e226f"
+      },
+      {
+        "name": "admission-controls",
+        "seconds": 0.885,
+        "exit_code": 0,
+        "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+      }
+    ],
+    "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the same cited unchanged PR543 bit supplier as PR635. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+  },
+  "admission_mutations_rejected": 69,
+  "controller_mutations_rejected": 15,
+  "frozen_template_content_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "fresh_template_content_sha256": "a1692259fb5a06bbebdc1049a7f757c6d2fc79ff8c31ed0c25b38fe9f98ed051",
+  "template_comparison": {
+    "sole_changed_field": "async_schedule.source_plan_sha256",
+    "frozen_plan_sha256": "609adb126d7d3de2abdd9275f9015589c0b137d0d19821c2c3e7c1a8541c18d2",
+    "fresh_plan_sha256": "b2e4b1f063250c40e0087f77e896882c60f36ed8764e86ba1610dec9bdff7394",
+    "explanation": "Fresh phase review differs only in its measured seconds. Runtime provider binding consequently changes the plan byte hash. All remaining serialized template fields match exactly; each runtime hash is checked against its own file."
+  },
+  "assembly_matches_frozen_rates_and_profile": true,
+  "post_replay_packaging": "Four files received trailing-whitespace cleanup only; complete parsed ASTs were checked unchanged. Constructor input pin refreshed. Admission assertion comparison rerun.",
+  "scope": "Changed construction and exact recipe, fresh native ledgers/wrappers/phases, independent scalar and guard audits, integer owner reproduction, strict global admission and independent pricing. No predecessor full replay, seed-discovery optimizer or PDF generation. Local Python 3.14; Python 3.11 is covered by CI."
+}
diff --git a/research/gauge44-slots/MANIFEST.json b/research/gauge44-slots/MANIFEST.json
new file mode 100644
index 0000000000..6daa9abfd6
--- /dev/null
+++ b/research/gauge44-slots/MANIFEST.json
@@ -0,0 +1,174 @@
+{
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+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "LOCAL-VALIDATION.json": "f81fbd98eb608b8119f03f89a5692bcd610845fc97022337931586d8582b706e",
+  "NOTICE.md": "7a8d17b04da1e6c9d0ec217fb5bda72faa09d9a21695128722dd1e2827870fcf",
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+  "PROOF-NOTE-BIT.md": "dd771adb12f6f0bef0e2931c28b21b243b04d5f512370cbad1207275c342aaf7",
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+  "PROOF-NOTE-LEAVER.md": "e4f9482ef551d6d4300d8ed8bb7c34dc9327fbcfa30a502bf3476b78468e60c3",
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+  "PROOF-NOTE-PROMO.md": "c170e5196d3081f86ac377c6fe614ca17f6281972837580275ce5af41cbc64ae",
+  "PROOF-NOTE-SW4.md": "d7bb225f1a7f9fd363e819a67e92a5fe14c0942f6c3616d73609cc48042daf3d",
+  "README.md": "bd4248499e577321f17aacba1d7815a5eb0f9cbe88faeb8fef38b71bdf3a684c",
+  "RESULT.json": "6cbc5f16cb2bdc279cf518b8670cedec1869069daa609a6803d4d377f13b813c",
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+  "construction/leaver/cells-k8/CORE-01+.json": "3d2afc4986f1f3aceacd1e0572daebfb79134ba6af7677150083d0912676427c",
+  "construction/leaver/cells-k8/CORE-01-.json": "8f8620f47ce5ba5abf6179d1a5a986c25903ba71b6711a7035815968b5888927",
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+  "construction/notri/PRIO6.json": "de0412511b0dd1af13e9717bc791126ac0e91c569b5391fd6c70268083045d15",
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+  "construction/promo/build_promotion.py": "9c9e2001b8d68bbe934d136026276fe97bd9bf6f94d4d78441fc28e14aca4daf",
+  "construction/promo/make_recipe.py": "ba9e4fdc0c1be7f6a150a5a50909911257a1a8c7cc5d03d61f541178fc07c122",
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+  "construction/slots/SLOT-PINS-k8.json": "55dd229684febecb80638eff9c6b3986623e8539c6c956753b350209c3e0efe2",
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+  "construction/sw4/NOTES.md": "3a3ddb0c77b188e67fc453ccb3efe9323f87028092a6ce4d259b7dc99d702446",
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+  "data/FRONTIER.json": "56bed9070d5f0b7585d7b7fd62984696dbc5158e5187663030920a57e1cbfab2",
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+  "data/PLAN.json": "1dec4ca3af6d45d82286005cae4c5e56e7253adefb117d797da55c55c891af08",
+  "data/PREPARATION.json": "1d576298bfafc509992113fdd58b5482655a88e321cbfafe9386588eb6fbb6e9",
+  "data/SPEC.json": "8e95ae8087124189cbd366d0e9d1c5ebededff536ff3501927b4b2a2e8dac70e",
+  "data/UPSTREAM-PINS.json": "ccc37ab7fbf78947fe02c7f57ea672d2e4eae8454cb1158ed964c75bf423869b",
+  "evidence/ADMISSION-CONTROLS.json": "5ebcc945c53f8279ac3bb6249e1d46422b7c7ddeb41c580ab5cbb3ca886dcf28",
+  "evidence/ASSEMBLY.json": "847f339db218f62ffabacb4655ba4dc6e8a15f67014ca01b1146083f393b009f",
+  "evidence/BINDING.json": "f80ad585c9cf94989d459971189fbb176084aedbe27edf5b5cccc5c2a44de43b",
+  "evidence/CENTER-COMPATIBILITY.json": "c66c7da1099ac8618381e2a7cb48b09b43ccf8d125ff124e129aba8ddb922cf3",
+  "evidence/LOCAL-STAGES.json": "64165b81b7119a2b23e99d3f3dfe8aa1702f373efe90d82d136c17786ffb6591",
+  "evidence/REPLAY.json": "45a6065c41df0c2b04e185b4727c7ad8eac5ebeb637dbb7bebffc184415b49a2",
+  "evidence/STAGES.json": "09d7c6daf1e93c58863267141dedc3873264d3baede0cddefda0d56ecb560458",
+  "evidence/audit/ASYNC-AUDIT.json": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662",
+  "evidence/audit/GLOBAL-PREFIX.json": "5a6fd0d91a650ad5aa830771fb4333b015f06bc4ded02807d65aee260ce9e671",
+  "evidence/audit/IDLE-REMAINDER-FRAMES.json": "95f5165a10dd187000dba9e55afbc1b7dce5a315cfedfa72e4f8344471149048",
+  "evidence/audit/OWNERS-AND-PROFILE.json": "a32ecc0d5387d65648e1ff284209122860ee37aaba43ce2dd12024c4bc394313",
+  "evidence/audit/PREFIX-AND-INVOICE.json": "14b0f41c88209e800236ce4ebbf91d83537e22e18807153d90013f7eee57a582",
+  "evidence/global/ACTUAL-SIGMAS.json.gz": "bf3b7814b54b30c726cae1dfabd3c09211c8f34cc943534565b131a0006b483f",
+  "evidence/global/GLOBAL-TEMPLATE.json.gz": "f713f8e66aaeaebb8202fe72bf36c7d23497152497342c27892e0fda3092f95b",
+  "evidence/global/HOSTED.json": "60866eb6ced5b9eb259bfc1d59ea7b80fb439164b629e868586ad5bef845a88e",
+  "evidence/global/IDLE-REMAINDER-FRAMES.json.gz": "734fd9bbe0afa2cc1e492bb7effef1aa8f0d8926ab1d9420d64c30045b30e784",
+  "evidence/layers/LOCAL-AUDIT-LAYERED.json": "a596d7262374a023ae079e0da41d20189bd3ca4594101e5e6f402ce5799df9ff",
+  "evidence/leaver/CELL-MUTANTS-LV.json": "308975b8288cb9c853ee6b69e68b25e6f3727d259dccfb7509042f103bb03220",
+  "evidence/leaver/FRAME-CONTROLS-LV-k8.json": "9629e499a7f01f2db1e41873344a1476708f41698a0b145888ee569e580a31dd",
+  "evidence/local/CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+  "evidence/local/CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+  "evidence/local/CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12",
+  "evidence/local/FULL-WORD.json.gz": "0ad202612f010df4ab66432a628247b37ad8b497dd6b27595b1685cbd7eb119e",
+  "evidence/local/INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+  "evidence/local/LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+  "evidence/local/LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+  "evidence/local/RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94",
+  "evidence/local/SCALAR-FRAME-AUDIT.json": "cfc73040079b43ea82a42f3cf4c910edda1362deb09ec21c816c329347313bcb",
+  "evidence/local/WRAPPER-CHECKS.json": "84c727930f85f1c91900d6d12c523735c8b5d6907cd3eb1bd1030fe1fd4161d7",
+  "hosting/PROOF.md": "45bb3de8a10298a4cf5a278c3343be22a7d2e735be93a4e9454f24df7275faf0",
+  "hosting/README.md": "004bcdf6c78bd0316f0606d9e636511f94e1e80cbd79cce1a7e3bc55076d9bf1",
+  "hosting/audit_frozen.py": "a8d9c7c894cb44453aea93b33141559824f6c3ff81a85a6d066f4a10a2757659",
+  "hosting/expand_owners.py": "0f826377881d0c9405f90d9f5feac857c7c7cf8aef5bcf22d326bc274f038a70",
+  "hosting/frozen/FROZEN-AUDIT.json": "df6c7181a097900ee9d37db17bd25436a570f21caaa0cc2108712907ab02904b",
+  "hosting/frozen/MAJORIZATION.json.gz": "ec5f94b13d190d72bc0608dc9fe2498cc43ba9deb05028159a812ec1e4dcacdf",
+  "hosting/frozen/MANIFEST.json": "9df028adfa5120c60d2c78bfab06822cf4e6ed55502816b7d6dec19c1a2e4967",
+  "hosting/frozen/MATCHING-RECEIPT.json": "e1af2ac2c6e2457646d52dd693fb961f6279e10fe50eae9873f2ed149b6735b2",
+  "hosting/frozen/OWNERS.json.gz": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+  "hosting/frozen/REPRODUCTION.json": "8354f63148621c5fcf09cd16b496dedd677d813f83974e1f341ce38a1fffec81",
+  "hosting/frozen/SEED-OWNERS.json.gz": "eb3be5eebbb84349d7e7f1bde2fc77772a12ad5bccc6dab7c4efd8d903e2a048",
+  "hosting/frozen/SEED-RECEIPT.json": "aecfef753379106f5289f31251584c642e2cf7e4fa2d0886bb4ef9e922f8d9ba",
+  "hosting/frozen/SEED-REPRODUCTION.json": "4f6d49a85f43c98c816877d783470ca717be2349caceb991bf756eedece1b194",
+  "hosting/reproduce.py": "7551004d8d15cebcecc6793ebd17385830390935ccd1a8957f1c5472bce6ec82",
+  "hosting/reuse_owners.py": "2106fe79bd89071e62a3a25c1e444531e14fb89f88b4bdeb72d7b40c91266402",
+  "independent/CENTRE-GUARD-REVIEW.md": "7b82518d7ddf042d6e71174bc286311fa72127e0dc6dc9e500025fcf7abbf897",
+  "independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json": "9fb5265c4d2ddf3d615e46600954c79cd1a42481500a0973a5695fcb9f2558c9",
+  "independent/GAUGE44-GLOBAL-GUARD-REVIEW.json": "631107a9a9acb02441ce80298f815e0c624f811b0d58c6fd78f8dc58d564bb5b",
+  "independent/GAUGE44-INDEPENDENT-PRICE.json": "6e222b252f3453446d0e41b08f00a9bf9449ce3588b6ddc00c9accc1c00e7683",
+  "independent/README.md": "25668a62d8c91f6860f8412cf2fc750ba41bf1085dad3709ad5067c7956eac89",
+  "independent/audit_local.py": "03afcfc9da428b3f6edac81c1fee7f277ab81b64998efae78380b63498dec6cd",
+  "independent/price_profile.py": "d2f548ad6b99f64a8ca5fbaf822a89560bb99359957ce3420b497f6a46fc0acf",
+  "independent/review_guards.py": "b83164d6c0122a055b3281f3381b305683a875760a2d727dd0188bb2aa59d67d",
+  "inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+  "verify_global.py": "16bd5e54598592e92e210f99065348c5df261b8350fdc688072ce053d15b088a",
+  "verify_manifest.py": "723d726dbbe5b65a49caecae0f1aab664a1413fb639abfd3e826a5a538e14e5b"
+}
diff --git a/research/gauge44-slots/NOTICE.md b/research/gauge44-slots/NOTICE.md
new file mode 100644
index 0000000000..30d0c8cd3c
--- /dev/null
+++ b/research/gauge44-slots/NOTICE.md
@@ -0,0 +1,24 @@
+# Gauge44 attribution and scope
+
+New contributions by icekylinx, with OpenAI GPT-6 Astra assistance.
+Local review and packaging used OpenAI Codex. Apache-2.0 applies;
+the license is included. The full original PR635 notice is preserved as
+UPSTREAM-NOTICE.md and construction/UPSTREAM-NOTICE.md.
+
+The new contribution is the changed source-branch gauge and retired-row
+completion, source-carried coordinate totals, exact 44-cold-end realization,
+and explicit all72 whole-family assignment using concave capacity matching
+with integer majorization certificates. The center-carrier generalization
+retains the exact ordered common frames and complete native local contract.
+Independent local, price, interface and owner fixed-point checks are included.
+
+The construction retains the credited PR635 K-triangle and porting machinery,
+earlier joint-prefix/HPE/frame ancestry and icekylinx's prior factory work.
+#645 used the same cited PR543 bit supplier as PR635. This package (research/gauge44-leaver8) cites the merged PR589 bit supplier instead, with a derived rank-mass deficit (PROOF-NOTE-BIT.md); #645's retained PR543-based evidence is historical. It builds #645's word without K-triangles (PartialK) and stacks earlier community jp8 layers on it (G44Stack), adds the p6n ends (NoTriReopen), entrance promotions (BlockInvert) a read-set exchange (BRoute), chafreaky's #741 frames, JointXF's joint exchange, NewBArch's triangle-hybrid B rewrite and LeaverSAT's eight k8 leaver cells (with LeaverSAT2's frame re-optimisation); see README. All-size, realization,
+hosting, precision/tape, analytic-transfer and bit H1-H5 assumptions remain
+conditional. No upstream license, credit, source pin or AI disclosure is
+replaced by this notice.
+
+PR641 and PR642 were checked as concurrent reported frontier comparisons.
+Their endpoints and owner maps are not included here. See CONSTRUCTION.md,
+hosting/PROOF.md, independent/ and README.md for the exact contribution scope.
diff --git a/research/gauge44-slots/PROOF-NOTE-BARCH.md b/research/gauge44-slots/PROOF-NOTE-BARCH.md
new file mode 100644
index 0000000000..8cea5a6846
--- /dev/null
+++ b/research/gauge44-slots/PROOF-NOTE-BARCH.md
@@ -0,0 +1,43 @@
+# PROOF-NOTE-BARCH: width-neutral triangle-hybrid B-delivery rewrite (U8)
+
+Construction by NewBArch (`construction/barch/`, builder `build_tri.py`, controls `run_controls.py`, recipe
+`RECIPE-U8.json`). Driver: `construction/barch/reproduce_barch.py`, chained after `construction/jx`.
+
+## The move
+On research/gauge44-frames-x's X4 word (`1e1d99ba…`), eight disjoint slots are rewritten. In each slot X an entering
+copy E donates into a halves-copy X: 231 (E 450), 230 (E 452), 232 (E 454), 236 (E 456), 226 (E 451), 228 (E 453), 62 (E 455), 238 (E 457). That way, so that one target
+read takes X + H in a single gate. A holder pair (for example 496/484) carries the value. Each holder is restored by a
+low-end tail at its frame (early cleanup) and a FULL-cleanup restore. Entrance pre-reads keep the entering helper's
+start value away from every target.
+
+The recipe is explicit, with every index referring to the X4 word:
+- 40 B deletions;
+- 40 B insertions, each with its frame;
+- 32 explicit re-chosen B frames;
+- 8 early-cleanup tails;
+- 8 FULL-cleanup restores.
+
+The A section and X4's tail frames are untouched. The width is unchanged at 3778. The profile goes
+{1:2548, 2:338, 3:430, 4:194, 5:56, 8:8} → {1:2548, 2:338, 3:446, 4:162, 5:72, 8:8}, a delta of {3:+16, 4:−32, 5:+16}.
+The eight slots are additive (8 × 3.925e-8 ideal = 3.140e-7). Output word `090fd574…`. U8 contains B0's four slots
+(231, 230, 226, 228) plus 232, 236, 62 and 238.
+
+## Checks rerun on every rebuild
+- `build_tri.py` (standard library only) checks the base sha (`1e1d99ba…`) and the result sha (`090fd574…`).
+- `run_controls.py` produces 38 outcomes, all required. The control set is pinned in `LOCAL-PINS-barch-U8.json`.
+  - C0 identity reproduces the input.
+  - The recipe word PASSes #645's independent `audit_local.py`.
+  - Four mutants must each FAIL `audit_local` with a pinned message, both globally and for each of the eight slots
+    (NAME@X):
+    - drop_restore: the holder is not restored, giving "all-column endpoint failure";
+    - restore_full: the low-end restore is moved into the FULL cleanup, giving "all-column endpoint failure";
+    - drop_preread: the inserted entrance pre-reads are omitted, giving "nonzero entrance response";
+    - donation_after: the donation is placed after the target read, giving "nonzero entrance response".
+- The per-end layer-end controls (`../layers_p6n/layer_end_controls.py`) reject 95.
+- PR635's native chain runs, with the canonical word, local programs and Clifford recipes pinned.
+
+## Strict
+NewBArch's strict replay: the #741 map (`G44Pack/m741`, byte-identical OWNERS) is rebound to the U8 locals with
+`rewidth.py` and admitted with this package's own code (NEWWORD `admit645.py` on research/gauge44-frames-x's tree).
+The result is κ 0.001661948695165034, +3.1404e-7 over research/gauge44-frames-x. The four-slot subset B0 strict-passes
+at 0.001661791659578416 and the single slot V1 at 0.001661673902364948.
diff --git a/research/gauge44-slots/PROOF-NOTE-BIT.md b/research/gauge44-slots/PROOF-NOTE-BIT.md
new file mode 100644
index 0000000000..da06360da0
--- /dev/null
+++ b/research/gauge44-slots/PROOF-NOTE-BIT.md
@@ -0,0 +1,112 @@
+# PROOF-NOTE-BIT: citing the PR589 bit supplier with a derived rank-mass deficit (gauge44)
+
+This note is BitCap's `PROOF-NOTE-BIT.md` from `complex-571-cold14-k492-bit589`, adapted to the gauge44 package. It
+covers the only verifier change relative to #645's package (`research/gauge44-global`): the bit supplier changes from
+PR543 to PR589. The complex side is #645's construction, unchanged: supplier word, recipes and every complex check in
+`code/assemble.py`. The only complex-side change is the repacked owner map (`data/PLAN.json`, `data/OWNERS.json.gz`),
+with expected values re-derived in `data/SPEC.json`.
+
+## Changed sites
+
+The changes are in `code/assemble.py`, plus one new stage in `verify_global.py` and a new file
+`code/bit_supplier_controls.py`. The independent (non-verifier) `independent/price_profile.py` is ported to PR589 as well. Every other `.py` file equals #645's.
+
+| # | site | before (#645) | after |
+|---|---|---|---|
+| S1 | bit input | `inputs/PR543-EXPECTED.json` from the multicold source, blob pin `b61d8598…` | `inputs/PR589-EXPECTED.json`, shipped in this package, blob pin `e293ddc5…`, through `load_bit` |
+| S2 | bit deficit | literal `9984` | `bit_deficit(word, live)` = T(2Kv − L·cst), with L = 9, T = 32, K = (L−1)/2 = 4 |
+| S3 | profile binding | (none) | Σ r·n of the bit profile = `bit.rank_mass`; moment width `BIT_M = 1 + 7L` asserted = 64 |
+| S4 | pipeline binding | (none) | the record's `nine.pipeline` names the nine-stage template with 32 replicas |
+| S5 | citation / receipt | input hash names the PR543 file | `bit_supplier` cites PR589 (head `a5afc8c6`, merged as `b3eb785a`, path `research/e8-bit-p111-tuned/tune/EXPECTED.json`) and records v = 111, cst = 63, COPY ranks [7×9] and the derived deficit 10272 |
+| S6 | `verify_global.py` | (none) | stage `bit-supplier-controls` runs `code/bit_supplier_controls.py`; it requires status `PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS`, exactly 12 rejected controls and derived deficit 10272 |
+
+The shipped `inputs/PR589-EXPECTED.json` has git blob `e293ddc557742637f9f679f083a1a282d87b1b13`, which equals
+`origin/main:research/e8-bit-p111-tuned/tune/EXPECTED.json`.
+
+## Why the derived deficit is correct
+
+**The identity.** The rank-mass identity of #545 and #555 is M·live − mass = T(2Kv − L·cst). Its source is
+#555's README, "Rank-mass identity", and `code/adapt9p.py`, whose audit carries `DEFICIT=T*(2*K*V-L*CST)`.
+
+**The parameters.** The bit word has v live ports and decoder constant cst, the sum of the nine retained totals' COPY
+ranks. The nine-stage chain is #463/#510 with 32 replicas, so L = 9, T = 32, K = 4 and M = 1 + 7L = 64. The live data
+wires number 2KvT.
+
+**The constraints checked.** The verifier asserts all of:
+1. cst = Σ copy_ranks, with exactly `retained_totals` = 9 entries, each in (0, 8].
+2. live = 2KvT. For #589: 2·4·111·32 = 28416.
+3. Σ r·n over the priced profile = the record's `rank_mass` = 1808352.
+4. M·live − Σ r·n = T(2Kv − L·cst). For #589: 64·28416 − 1808352 = 10272 = 32·(888 − 567).
+
+Check (4) is #645's `check_moment` guard, unchanged. So v, cst, the profile and live must all agree.
+
+**PR543 consistency.** The same formula reproduces #645's constant: PR543 has live = 30720, so v = 120; its nine
+totals have COPY rank 8, so cst = 72; 32·(960 − 648) = 9984.
+
+**The deficit does not raise c.** `check_moment` uses the deficit only as an equality guard. The moment engines
+compute from (profile, m = 64, live, z) and never read it. The bit value c is established only by the unchanged
+acceptance tests at the same exact endpoints, with the bit bad-residue surcharge retained: accept at c and reject at
+c + 10⁻²⁴, by both engines.
+
+## Effect on the outer chain (differs from the k492 package)
+
+In the k492 package the complex side bound under either supplier, so κ did not move. Here it does. With the
+gm3 map the complex side certifies b = 0.001654663299688920102557, with research/gauge44-bit589's dz1 map
+b = 0.00165526410310589140991, and with research/gauge44-bit589b's L1g4 map b = 0.001655496738330440231813. PR543's c = 0.001653826988146798944268 is
+below b, so under PR543 the bit side would bind. BitCap's table gives the PR543 bit-side κ cap as
+0.001651096360425895, which is exactly the κ of `research/gauge44-repack`. PR589's c = 0.001733427039589844234749
+exceeds b, so the complex side binds again (`binding = complex` in `ASSEMBLY.json`): κ = 0.001651929911890057 for gm3
+(conservative 0.001651929909011672) κ = 0.001652528731617094 for dz1 (conservative 0.001652528728737236), and
+κ = 0.001652760598550299 for L1g4 (conservative 0.001652760595670246).
+Bit589Reviewer recomputed both suppliers with the outer engine and confirmed this. The gain over gauge44-repack therefore depends on this change and on the
+assumptions below.
+
+## Negative controls (all must be rejected; the verifier requires exactly these 12)
+
+Each control runs the real `assemble()` on the fresh owner/invoice receipts with one input mutated. The strict run's
+`BIT-SUPPLIER-CONTROLS.json` lists all 12 as rejected.
+
+| control | site | rejected at |
+|---|---|---|
+| `revert_hardcoded_9984` | S2 | `check_moment` deficit guard (10272 ≠ 9984) |
+| `ports_112` | S2 | `bit_deficit`: live ≠ 2KvT |
+| `decoder_constant_64_copy_ranks_unchanged` | S2 | `bit_deficit`: cst ≠ Σ COPY ranks |
+| `decoder_constant_64_with_one_copy_rank_8` (derives exactly 9984) | S2 | `check_moment` deficit guard |
+| `eight_retained_totals` | S2 | `bit_deficit`: totals count ≠ 9 |
+| `live_minus_one` | S2 | `bit_deficit`: live ≠ 2KvT |
+| `profile_rank_mass_plus_one` | S2/S3 | `check_moment` deficit guard |
+| `profile_rank_mass_receipt_mismatch` | S3 | profile mass ≠ `rank_mass` |
+| `bit_lower_next_grid` | endpoint | `check_moment` reject-side moment test |
+| `not_nine_stage_record` | S4 | pipeline binding |
+| `tampered_bytes_next_grid` | S1 | blob pin |
+| `pr543_file_under_pr589_pin` | S1 | blob pin |
+
+Bit589Reviewer re-traced all 12 rejection sites on the gauge44 word (b589gm3), and they match the table: `code/assemble.py` L191 (`revert_hardcoded_9984`, `decoder_constant_64_with_one_copy_rank_8`, `profile_rank_mass_plus_one`), L48 (`ports_112`, `live_minus_one`), L47 (`decoder_constant_64_copy_ranks_unchanged`, `eight_retained_totals`), L201 (`profile_rank_mass_receipt_mismatch`), L197 (`bit_lower_next_grid`), L179 (`not_nine_stage_record`) and L39 (both blob controls). dz1 and L1g4 run the same code.
+
+The ported `independent/price_profile.py` re-derives the deficit separately (`pr589_deficit`) and checks the same blob pin. Its regenerated receipt on this package's PLAN gives the same κ.
+
+## Inherited assumptions
+
+**PR merge status (`gh pr view`, 2026-10-13):** #589 MERGED 2026-10-12T17:00:38Z. #555 was merged 2026-10-12. #645
+is OPEN. Main's review replayed #589 freshly as "supplier-only headroom", and main's *selected* composition still
+cites #543.
+
+**Unmerged assumptions:**
+1. **#645 itself (open):** the gauge44 factory, its construction steps and all of its retained interfaces and notes.
+   These are unchanged here.
+2. **This verifier change (S1–S6):** under review (Bit589Reviewer). The PR589 record replaces PR543 as an *input of
+   the gauge44 assembly*, a composition main has not selected.
+
+**Assumptions carried by #555/#589 (merged, stated there as review points, not theorems):**
+3. #545's punctured unit: a 111-port unit with decoder constant 63 is an admissible bit supplier on the same hypotheses
+   as v = 120.
+4. #510's nine-stage chain as re-parameterised for v ≤ 120 by #555's `code/adapt9p.py`, including the rank-mass
+   identity used in S2.
+5. #543's interleaved scalar-interface lemma (H1–H5) for phase-B source rewrites. This is not new: #645 already
+   inherits it through PR543.
+6. #589's two A-section transports.
+7. The same bit bad-residue surcharge model as PR543 (`surcharge_model = {'complex': False, 'bit': True}`).
+
+## Result
+
+The bit-supplier change is the same as in research/gauge44-bit589 and gauge44-bit589b: the code is byte-identical and was signed by Bit589Reviewer. For this package (k8 leaver word db2c7cfb, K8c8 map), the complex side certifies b = 0.001674185476674086429846 and binds under PR589. Under PR543 the bit side would cap κ at 0.001651096360425895. κ is given in the README and `RESULT.json`.
diff --git a/research/gauge44-slots/PROOF-NOTE-FRAMES-X4.md b/research/gauge44-slots/PROOF-NOTE-FRAMES-X4.md
new file mode 100644
index 0000000000..a456a8127b
--- /dev/null
+++ b/research/gauge44-slots/PROOF-NOTE-FRAMES-X4.md
@@ -0,0 +1,58 @@
+# PROOF-NOTE-FRAMES-X4: chafreaky's #741 frames and JointXF's joint exchange (X4)
+
+Two construction steps on top of research/gauge44-promo-p6k4sw's SW4 word P6k4sw4 (`d232183f…`).
+
+## 1. #741's eight B frames (`construction/frames/`)
+The eight B-gate frame raises are by **chafreaky**, [#741](https://github.com/CrocSwap/integer-mult-bounds/pull/741)
+(`research/complex-sw4-frame8`, commit e516b146). `FRAME-RECIPE-sw4.json` is byte-identical to #741's
+`data/FRAME-RECIPE.json` (a2c7ca4d…). CompetitorMine ported #741's builder and controls; only package paths are adapted.
+The step applies the frames with BlockInvert's `build_promotion.apply` and checks:
+- the scalar program of A, cut, B, precondition and cleanup is unchanged;
+- start and end frames are unchanged;
+- the profile, the widths and the output word `e7804702…` are pinned;
+- 3 pin controls are rejected;
+- #741's 10 focused native controls are rejected (8 frames emptied, a changed read coefficient, paid-profile tampering);
+- the per-end layer-end controls reject 95;
+- the native chain matches its pins.
+
+The rebuilt locals equal G44Pack's F741 locals except the `seconds` field in CLIFFORD-REVIEW.
+This step reproduces #741's word. The final word is built by step 2, which contains these frames.
+
+## 2. Joint exchange X4 (`construction/jx/`, JointXF)
+There are four disjoint instances of BRoute's sw4 read-set exchange rule. Each one exchanges *two* copy pairs that
+share targets: (448, 472), (458, 592), (470, 604) and (482, 614), with face registers 235, 267, 58, 427, 26, 443, 18
+and 50. #741's eight frames sit on top. The 16 moved reads keep their original stored dim-6 frames: they are
+monotone-repaired rather than refitted to the plain join. The recipe `RECIPE-X4.json` is explicit:
+- 32 replaced gates, 16 deleted gates and 16 inserted gates, each with its old gate asserted;
+- #741's 8 frames, listed with their source;
+- 16 explicit frames at the moved reads, each asserted equal to the recomputed frame.
+
+The builder `build_jx.py` uses only the standard library. It checks:
+- target frames lie inside u_t^⊥;
+- tails and ends;
+- exactness of the whole B segment's rational linear map against the input (a Fraction replay);
+- the recomputed paid profile and the output sha `1e1d99ba…`.
+
+Effect against #741's word: the profile goes {1:2556, 2:334, 3:430, 4:194, 5:56, 8:8} → {1:2548, 2:338, 3:430,
+4:194, 5:56, 8:8}. The width inventory is unchanged, and each instance gives +1.0798e-7 at ideal, exactly additive.
+
+**Controls**, each pinned in the recipe and rerun by `reproduce_jx.py`:
+
+| control | outcome |
+|---|---|
+| C0 identity | returns the input `d232183f` |
+| C1 #741 only | `e7804702`, #741's word (ties step 1 to step 2) |
+| M1 one pair (448) with frames retained | `5fb6fb2e`, neutral (profile = #741) |
+| N1 pre-read dropped | rejected: exactness rows [132, 135] |
+| N2 pre-read with wrong sign | rejected: exactness rows [132, 135] |
+| N3 plain-join refit of the moved reads | `7241cd59`, strictly worse |
+| N4 a raise made dim-7 at B855 | rejected: cap at (1302, 174) |
+
+N3 and M1 are pinned-outcome controls (a specific different word), not rejections. They show the gain needs both the
+target-sharing pair and the retained frames.
+
+**Other checks (JointXF):**
+- `audit_local` PASS;
+- native chain PASS;
+- FrameCoal's global frame optimiser reaches the same profile on this move set, so X4 is frame-optimal for these moves;
+- SW4Extend found the same word independently.
diff --git a/research/gauge44-slots/PROOF-NOTE-LAYERS.md b/research/gauge44-slots/PROOF-NOTE-LAYERS.md
new file mode 100644
index 0000000000..c4b4e85b6a
--- /dev/null
+++ b/research/gauge44-slots/PROOF-NOTE-LAYERS.md
@@ -0,0 +1,129 @@
+# PROOF-NOTE-LAYERS: earlier jp8 layers, here stacked on the no-triangle gauge44 word
+
+> In this package the layers sit on the no-triangle word (R = 504), not on #645's 492-helper word. The mapping, the
+> NP chain (regroup `864ff4a1` → swap `beb3579f` → layered `a9de804f`), the per-layer status on this base and the
+> checks are in `PROOF-NOTE-NOTRI.md` ("Layers on this word"). The text below is research/gauge44-layered's note. It
+> describes the same layers and controls on the 492-helper word; its word shas, helper numbers, counts and result
+> table refer to that word.
+
+
+This note covers the second change of research/gauge44-layered relative to research/gauge44-bit589. The first change,
+the PR589 bit supplier, is covered unchanged by `PROOF-NOTE-BIT.md`. Here the community jp8 layers that were reviewed
+on the k492 words (#629/#637/#641 lineage) are re-applied to #645's gauge44 provider word. The layers, their
+construction code and their recipes were all reviewed earlier, on k492 words. This note says what carries over
+unchanged, what is re-checked on the gauge44 word, and what is new. Sources: G44Stack's report (porting and checks on
+gauge44); PivotReviewer's report (sections 1-4, Addenda 3-5); H4aReviewer's report (Addenda 7-8); JP8Ends' report.
+
+## What the layered word is
+
+`construction/layers/reproduce_layers.py` builds the layered word from a fresh `construction/reproduce.py --until word`
+output. Each step is checked exactly:
+
+1. **Pivot swaps** (`build_pivot_swap.py`, PR641's constructor, LF sha256 `8e8bced8…`, the file PivotReviewer signed for
+   st2s4). It reads `PIVOT-SWAP-S6.json` and runs on #645's `regroup/FULL-WORD`. There are six pivot-role swaps: 488→560,
+   489→561, 500→572, 501→573 (s4) and 513→537, 525→549 (s6). The `swaps` list is identical, gate for gate, to S6Ship's
+   s6/s6j3 recipe (`k492-jp8-pivot_swap.json`); only `input_content_sha256` differs, because the base word is #645's
+   regroup word. The constructor replays the zero response exactly, keeps the profile and width multiset unchanged, and
+   rejects its 30 negative controls.
+2. **HPE.** PR635's `build_hpe.apply` applies the inherited jp8 hyperplane-end changes (`HYPERPLANE-END-S6.json`). Its
+   LF sha256 `23c9d7ce…` equals the k492 jp8 hyperplane_end recipe committed in s6j3 and earlier.
+3. **cold44, exactly.** #645's `build_gauge_cold44.py` runs on the swapped HPE word. Its 44 rank-four cold ends, premix
+   and low tails must equal the unswapped (pinned) cold44 construction; only the FULL inverse differs. Consequently the
+   swaps touch no factory block.
+4. **Layers.** PR635's unchanged `build_cold_end.apply(HPE, COLD-LAYERS-RECIPE)` applies the cold44 recipe plus:
+   - 8 entering ends: 560/561/572/573 at U24 (s4) and 597/599/537/549 at U30 (x30: #629's E1 pair, which #645 dropped,
+     plus s6's two ends);
+   - 10 factored dim-8 cold ends: p123 (310/506, 311/504, 516/327) and q4 (579, 592, 589, 518).
+   The output word's sha256 is pinned (`0be48b1d…`), as are its local profile `{1:2542, 2:414, 3:434, 4:154, 5:56,
+   8:8}` and width inventory `{4:52, 5:48, 7:42, 8:116, 9:234}`. The recipe's `refactored_cleanup` meta lists the 8
+   entering ends in `entering_low_frame_ended_helpers` (LayerReviewer's fix). That meta is copied into the word, which
+   is why the pinned word sha moved from `b25f0ed9…` to `0be48b1d…`; gates, frames and report are unchanged.
+5. **Layer-end controls** (`layer_end_controls.py`, LayerReviewer's adaptation of PR635's `cold_end_controls.py`
+   d966e29a). These are raw-word negative controls on the layered word, judged by PR635's unchanged
+   `hpe_audit_and_transport.py`. Each mutant must be rejected at its pinned reason. The adaptation has three parts: the
+   lower→FULL mutant is pinned at "cleanup on non-FULL end", where gauge44 rejects it; entering ends come from the
+   recipe meta; and the premix-gate controls are skipped for entering ends that have no premix gate. `reproduce_layers.py`
+   requires exactly 59 rejections.
+6. **Native locals.** PR635's native audit and transport, ledgers, local replay (the 192-bit payload bound), wrappers and
+   phases all pass. The result is the `--local` that `verify_global.py` consumes.
+
+G44Stack's run of this driver (`rlayers2`, all steps exit 0, 59 controls rejected) reproduces `locs/pq/local`, the
+local G44Pack's strict runs used. Every SPEC-pinned artifact is byte-identical: CANONICAL-WORD, LOCAL-PROGRAMS,
+LOCAL-CHECKS, INDEPENDENT-LOCAL-REPLAY, CLIFFORD-RECIPES, RESIDUAL-ADAPTERS and WRAPPER-CHECKS. CLIFFORD-REVIEW differs
+only in a seconds field; its semantic hash is what SPEC pins. The two unpinned files that embed the word,
+FULL-WORD and SCALAR-FRAME-AUDIT, differ because of the meta.
+
+## Per-layer status on gauge44 (G44Stack, ideal Δκ at ×72)
+
+| layer | prior review (k492 words) | on gauge44 | per-call Δ profile | ideal Δκ |
+|---|---|---|---|---|
+| pivot swaps (6) | PivotReviewer §1-2 (s4), Addenda 4-5 (s6): exact; omitting any rewritten gate is rejected; cost-neutral | all 6 recipe `before` gates match the regroup word; 30 controls rejected; cold44 rebuilds the same 44 ends | neutral | 0 |
+| s4 ends 560/561/572/573 @U24 | PivotReviewer §3: (N) exact for ([24], U24) and its canonical pair; climbs paid | positive | {1:+8, 2:−4, 3:+4, 4:−4}, w −4 | +7.0e-8 |
+| x30: E1 597/599 + 537/549 @U30 | #629 (E1); PivotReviewer Addenda 4-5 (537/549 end monotonically at the E1 hyperplane, whose (N) is exact) | positive | {1:+10, 2:−6, 3:+2, 4:−2}, w −4 | +2.0e-7 |
+| p123 | H4aReviewer Addendum 7: 0 bad rows, dyadic, exact in all 3 orientations; (N) for (0,1039)-(0,1041); Δ recomputed | positive | {1:+6, 2:+12, 3:−12}, w −6 | +2.0e-8 |
+| q4 (after p123) | H4aReviewer Addendum 8 (n_q4): exact; (N) for the 310/311/327 frames and 518's (0,1042); independent of u4 | positive | {1:+4, 2:+8, 3:−8}, w −4 | +1.4e-8 |
+| **stack T_pq** | — | built and audited | {1:+28, 2:+10, 3:−14, 4:−6}, w 3794→3776 | **+3.08e-7** |
+
+These layers were left out because they are negative or dead on gauge44: u4 (−1.2e-6), the 249 end (−3.2e-7), a joint
+p123+q4 (−2.6e-7, worse than sequential), and #627's dim-7 ends 581/590 (no dyadic basis). j3 is dead: its st2 partner
+403 is one of #645's 44 ends, and cold44's block premix uses up the row space.
+
+**Payload.** H4aReviewer's Addendum 8 correction found that the k492 word n_q4 broke the 192-bit local payload bound
+(backward prefix 280 bits). On gauge44 the layered word passes PR635's `hpe_audit_local.py` local-replay stage
+(`prefix < 2**192`), both in G44Stack's `localchain.py` and as step 5 of `reproduce_layers.py`. So the q4 layer here
+does not repeat that failure.
+
+## Verifier changes (spot widths)
+
+A swapped-out pivot p becomes an ordinary cold helper, and its width goes from 8 to 9. #645's global code checks the
+spot helpers' widths as all 8, so the five global files gain the spot-width rule PivotReviewer signed as SOUND for
+S4Ship (Addendum 3), ported to gauge44:
+
+- `code/witness.py`: `spot_widths(v)` gives 9 at a spot helper h with 2v+h among the swapped-out pivots and 8
+  elsewhere. The swapped-out pivots are read from the recipe that SPEC key `pivot_swap` names (path and sha256; the
+  sha256 is asserted). Without `pivot_swap` the tuple is all 8, the same as #645.
+- `code/bind_providers_portable.py`, `code/audit_allcold.py`, `code/assemble.py`: the `all(... == 8)` spot checks become
+  tuple equality with `spot_widths()`, which pins every spot width exactly.
+- `code/assembly_controls.py`: the `cold_swap` control picks a swap partner whose width differs, so the mutant can
+  never be the identity.
+
+Here the spot helpers 264 and 276 (pivots 488 and 500) expect width 9 and the other spot helpers expect 8. The k492
+spot-width review (PivotReviewer Addendum 3) covered the same rule on k492 code. Its gauge44 port is part of this
+package's review (LayerReviewer).
+
+## Controls and what is not re-run
+
+- The pivot-swap constructor's 30 controls run inside `reproduce_layers.py` (step 1).
+- `verify_global.py`'s strict controls are unchanged, including the 12 bit-supplier controls and #645's admission
+  controls. They run on the layered locals.
+- Layer-end controls: 59 raw-word mutants, all rejected at pinned reasons, run as step 5 of `reproduce_layers.py`
+  (see above). They cover the cold low-frame ends, the refactored cleanup, every entering end (its lower-frame gate,
+  profile pin and hyperplane, plus its premix gate where it has one) and each distinct dim-8 frame. LayerReviewer ran
+  them on the layered word (59 rejected). The k492 version (d966e29a) rejected 103-112 on the p123/q4 words; the
+  k492-only primitives (absorptions, factored accumulators, target writes) are absent from this word.
+- #645's independent audit `independent/audit_local.py` on the layered word: PASS, with 204 entering helpers, 96 low ends,
+  54 cold ends and 716 columns. Its receipt is `evidence/layers/LOCAL-AUDIT-LAYERED.json` (word `0be48b1d…`, run with
+  `--main`). The README's clean-clone command reruns it; only `elapsed_seconds` varies. The other `independent/`
+  receipts are #645's own.
+- The prior (N), exactness and pricing checks for each layer were done on k492 words. On gauge44 they are covered by
+  the native chain (native audit, local replay, wrappers, phases) on the layered word, together with the pinned
+  profile and width inventory.
+
+## Inherited assumptions
+
+These are the same as `PROOF-NOTE-BIT.md` (#645 open; PR589 citation; #545/#555/#589 review points; H1-H5). In
+addition:
+
+1. **(N) for the entering-end pairs outside #599's three Lean-covered pairs** (U24, U30, the dim-8 frames). As on
+   k492, these are covered by the tool check (clifford_exact / `nchk.py`) and by the native wrappers, not by a Lean
+   proof (PivotReviewer §3).
+2. **The reviews of PR641's pivot-swap constructor and PR635's `build_cold_end.apply` / `build_hpe.apply`**, which this
+   package uses unchanged.
+
+## Result
+
+| | gauge44-bit589b (L1g4 map) | this package (layered, LN5c map) |
+|---|---|---|
+| κ | 0.001652760598550299 | 0.00165395497190225 |
+| per-call width | 3794 | 3776 |
+| local profile | #645's {1:2514, 2:404, 3:448, 4:160, 5:56, 8:8} | {1:2542, 2:414, 3:434, 4:154, 5:56, 8:8} |
diff --git a/research/gauge44-slots/PROOF-NOTE-LEAVER.md b/research/gauge44-slots/PROOF-NOTE-LEAVER.md
new file mode 100644
index 0000000000..b34a289c48
--- /dev/null
+++ b/research/gauge44-slots/PROOF-NOTE-LEAVER.md
@@ -0,0 +1,82 @@
+# PROOF-NOTE-LEAVER: no-helper mutable-leaver all-K cells, re-stacked layers, hybrids and a frame re-optimisation (k8)
+
+Construction: LeaverSAT (cells, layer re-indexing, frozen recipes) and LeaverSAT2 (frame re-optimisation).
+Drivers: `construction/leaver/reproduce_leaver.py` (cell word) and `construction/leaver/reproduce_leaver_chain.py`
+(everything after it). Reviews: PromoReviewer (leaver chain, k8 cells and frames, k8 clean rebuild), SW4Reviewer (hybrid structure), Q6Reviewer
+(`layer_end_controls_leaver.py` v2, `LEC-REASON-PINS-k8.json`), LecReviewer (`LEC-REASON-PINS-STACK-k8.json`).
+
+## 1. The cell (set model, LeaverSAT)
+In #781's all-K cell, a pair p with sign e replaces three face events and three packet copies. Direct delivery uses
+15 reads y_i += c x_j. LeaverSAT's 21-gate circuit uses the six leaver sources x_j (face-event operands with no later
+reads, restored at FULL by the inherited cleanup) as mutable intermediates. It has 3 leaver gates x_k += c x_m,
+3 target gates y_a += c y_b (inverted at frame zero in the precondition and scatter, #781's recipe) and 15 reads.
+Coefficients are rescaled exactly per cell, C_ij = r_i c_j. The driver re-derives the scaled gates from the unit
+circuit and checks the clean map Y_i = Σ_j C_ij X_j in exact rationals.
+
+Native legality needs one relabelling: the plain circuit fails the native audit, because a y += y source carries
+port-stage entering-helper dirt. Each cell is therefore relabelled by S6 so that y–y sources avoid targets carrying
+entering dirt at that time.
+
+**Set k8:** all eight cells (01±, 23±, 45±, 67±), R = 480. The cores are in `construction/leaver/cells-k8/` (documentary;
+the driver re-derives every scaled gate from `CODED-CELLS-k8.json`). The regroup word is `00aeefe0…` and the cell word is
+cold44 `58e14a02…`. Its pairing ranks are pinned to [0,0,0,4,4,4,4,4,4,4,4,0,0,0] in `cold44x.py` and checked again in
+the driver.
+
+## 2. Re-stacked layers (LeaverSAT; signed builders unchanged, recipes re-indexed)
+| step | recipe (data) | word |
+|---|---|---|
+| pivot swaps (6), mapped through the leaver helper map | `PIVOT-SWAP-k8.json` | `377ab10c…` |
+| HPE, greedy (22) | `HPE-RECIPE-k8.json` | `598543fa…` |
+| cold44, exact (same ends, premix and tails as the unswapped cell word) | — | — |
+| NP layers (s4, x30, b6, q4) | `COLD-LAYERS-RECIPE-NP-k8` | `2c1740f6…` |
+| p6n ends | `COLD-LAYERS-RECIPE-P6N-k8` | `25c40614…` |
+| promotions (16, minimal) | `PROMO-RECIPE-k8.json` | `84d4da2e…` |
+| joint exchange (re-indexed X4) | `RECIPE-X4-k8.json` | `84d4da2e…` (identity) |
+| U8-style hybrids ×6 (NewBArch's builder; instances 62, 226, 228, 230, 231, 232) | `RECIPE-U8-k8.json` | `c836d892…` |
+| frame re-optimisation (exact global frame optimum, gopt2; 137 B and 2 T frames) | `FRAME-RECIPE-LV-k8.json` | **`db2c7cfb…`** |
+
+Three steps don't apply to k8. The sw4 exchanges use copy helpers 461, 581, 591 and 603, which the cells drop. Of
+#741's eight frames, none survives. All four X4 exchange groups use dropped helpers, so the joint exchange is the
+identity (0 raises, 0 frames); it is still run, with its three remaining controls (C0, C1, N3) at their pins.
+
+The two cold-layer recipes are LeaverSAT's frozen k8 recipes (`fea82fb8…`, `76aedf23…` as .gz) with one key added,
+`input_content_sha256` = the swapped HPE word `598543fa…`, as in the k5 package. Removing the key gives the frozen
+recipe content exactly.
+
+## 3. Controls rerun on every rebuild
+- **Cell stage:** the exact clean-map check; native audit, ledgers, local replay, wrappers and phases on the cell word.
+- **Pivot swaps:** the swap constructor's 30 controls.
+- **Promotions:** BlockInvert's `promo_controls.py`, 11 mutants rejected at pinned sites.
+- **Joint exchange:** the 3 `RECIPE-X4-k8` controls reproduce their pinned outcomes.
+- **Hybrids:** `run_controls.py` gives 30 outcomes, all required. These are C0, the recipe word passing audit_local,
+  and 4 mutants, each run both globally and per instance.
+- **Frames:** `build_frames_lv.py`'s 3 pin controls. LeaverSAT2's 6 frame-recipe mutants are rejected by the builder;
+  that receipt was reviewed by PromoReviewer and is not rerun.
+- **Layer-end controls:** `layer_end_controls_leaver.py` v2 (`4ba676f1…`), Q6Reviewer-signed. It is the signed
+  per-end controls with per-word reason re-pins and **declared not-applicable sites**. A vacuous mutant site is never
+  skipped silently: the pins file must declare it, the declared set must equal the detected set, an identity is proven by
+  sha equality of the mutated and honest words, and a same-class substitute mutant is built and must be rejected at the
+  class's pinned reason. The count stays 95 on every word. The controls run on all five words:
+  - p6n, promoted, jx and hybrid words, with `LEC-REASON-PINS-STACK-k8.json`: `extra_end` only. h0 273's first
+    premixed partner 282 is already cold-ended at h0's frame, so the mutant is the identity (sha-proven per word); the
+    substitute is partner 281, cold-ended at h0's frame.
+  - the re-framed final word, with `LEC-REASON-PINS-k8.json`: `extra_end` as above, and `other_hp:554`. The frame
+    re-optimisation lowers entering end 554's tail frame to dimension 5, and no helper_final frame has dimension 5, so
+    the 'end at another hyperplane' mutant cannot be built; the substitute moves 554's end to another dim-8 frame and
+    must be rejected at the cone pre-check. This replaces the interim skip of research/gauge44-leaver.
+  No reason re-pins are needed on the k8 words. The receipts (`COLD-END-CONTROLS.json`) carry the not-applicable list;
+  the counts, the not-applicable sites with their reasons and the sha256 of each pins file (`LEC-REASON-PINS-STACK-k8.json`
+  d87ed7b5…, signed by LecReviewer; `LEC-REASON-PINS-k8.json` b07279e4…, signed by Q6Reviewer) are pinned in
+  `CHAIN-PINS-k8.json`.
+- **Native chain on the final word:** the canonical word, local programs and Clifford recipes are pinned in
+  `CHAIN-PINS-k8.json`, which also pins every count above.
+
+## 4. Cell mutants (evidence, not rerun)
+LeaverSAT2's `CELL-MUTANTS-LV.json` (in `evidence/leaver/`) records PromoReviewer's cell mutants M1–M6, generalised
+to every cell sign. All 42 are rejected by both audit_local and the native audit, on single-cell builds.
+
+## 5. Strict
+The owner map is G44Pack3's K8c8: its pattern-flow LNS on the R = 480 k8 word. Admitted on this package's own code,
+with SPEC `width_spot_helpers` [258,270,282,294] and `pivot_swap` → `construction/leaver/PIVOT-SWAP-k8.json` (NEWWORD
+discovery, freeze, strict), it gives κ 0.001671387264390146. That is +7.154e-6 over research/gauge44-leaver (k5,
+0.001664233607446043).
diff --git a/research/gauge44-slots/PROOF-NOTE-NOTRI.md b/research/gauge44-slots/PROOF-NOTE-NOTRI.md
new file mode 100644
index 0000000000..54bd84e01d
--- /dev/null
+++ b/research/gauge44-slots/PROOF-NOTE-NOTRI.md
@@ -0,0 +1,53 @@
+# PROOF-NOTE-NOTRI: #645's gauge44 word without K-triangles (R = 504)
+
+Construction by PartialK; review by NotriReviewer (scratch/NotriReviewer/FINAL-REPORT.md). Drivers:
+`construction/notri/reproduce_notri.py` (this word) and `construction/layers_np/reproduce_np.py` (layers on it).
+
+## Why the triangles were the blocker
+- In #645's gauge44, a K-block has I = 6 low registers with rank C = 4, so L = 2. Only the 2-row priority completion
+  fits there. The (p,−) triangle reads climb copies loc17/19/21 and source loc2.
+- Without the triangles, I = 8. With the 2-row completion, rank C stays 6 (L = 2), which is why the plain removal sweep
+  restored nothing. With the 6-row completion (`PRIO6.json`, the list blocks 3–10 already use), rank C = 4, so L = 4,
+  the cap. All 14 blocks then pair at rank 4: 56 rank-four cold ends, R = 504, width 3818, profile
+  {1:2506, 2:336, 3:472, 4:184, 5:56, 8:8}, rank mass 5674.
+
+## Constructor changes (NotriReviewer §1)
+- **`cgx.py`** is #645's `construct_gauge_xcentre.py`, parameterised by XPARAM. On this path the only change that takes
+  effect is the K-block priority: `PRIO[c]` is placed in front of the inherited rows. The prepended rows equal the
+  shared 6-row list of blocks 3–10 (all 8 lists identical). Every completion assert is kept (`qr_rank(M)==4`,
+  `len(M)==8`, the exact block-total rows). An empty TRI schedule is an input #645 already supports (`NH = 504 − 3·0`).
+  `HELPER-MAP` is the identity on 728. The `exch`, `COPYL` and `hyb` branches are inert here (defaults, empty, not
+  reached).
+- **`port_stage_x.py`** is PR635's `build_port_stage.py`. The helper map only has to be injective rather than onto;
+  with no triangles it is onto again.
+- **`cold44x.py`** is #645's `build_gauge_cold44.py`. Its per-block pin `r == len(L) == (2 if K-block else 4)` is
+  replaced by `r == len(L)` together with the explicit per-block pin `PAIRING_RANKS` (set by the driver to [4]*14,
+  and to #645's pattern in `--control-g44`). Helpers outside the 224+16b ranges join their blocks (EXTRAH, empty here).
+  Every other assert is kept (U, nonlocal premix, `rank(Qmat) == NB`).
+- **Control.** `reproduce_notri.py --control-g44` runs the same scripts with #645's four triangles and no XPARAM. It
+  reproduces #645's gauge44 word `78c7aada…` exactly, with ranks [2,2,2,4,4,4,4,4,4,4,4,2,2,2].
+
+## Exactness and locals (NotriReviewer §2)
+- Replay: 0 bad rows over 27,932 gates, all dyadic; forward, inverse and adjoint are exact. None of the 6,448
+  compensation additions reads an ended helper, and the precondition never touches one.
+- 0 FULL-remainder gates touch an ended helper; E⊂U holds for every entering end. The delta against gauge44
+  ({1:−8, 2:−68, 3:+24, 4:+24}, width +24) matches the reported profiles.
+- (N): all 17 pairs pass (14 cold dim-4 pairs with 4 helpers each, plus 3 dim-8 entering pairs).
+- `audit_local.py --main`: PASS. Payload: prefix bits 66 forward and 72 backward, against 192.
+- Native locals: 25 controls rejected, Lemma A on 22 frames, 17 wrapper mutants rejected. The rebuilt locals equal
+  the strict locals (`PartialK/runs/none_p6/local`): byte-identical except CLIFFORD-REVIEW and SCALAR-FRAME-AUDIT,
+  which differ only in their `seconds` field.
+
+## Layers on this word (G44Stack)
+The layers are research/gauge44-layered's (see `PROOF-NOTE-LAYERS.md`), mapped to the 504 numbering:
+- the 6 pivot swaps 494→566, 495→567, 506→578, 507→579, 519→543, 531→555, which are neutral (same 46 HPE helpers,
+  same 56 cold ends);
+- s4 566/567/578/579 at U24;
+- x30 608/610/543/555 at U30;
+- BlockCombine's b6;
+- q4.
+
+p123 is negative on this base and dropped; j3 is dead (L = 0 at U24 and U30). The chain is regroup `864ff4a1` → swap
+`beb3579f` → layered `a9de804f`, with profile {1:2534, 2:346, 3:458, 4:178, 5:56, 8:8} and width 3800. On that word
+the signed `layer_end_controls.py` rejects 59/59 and `audit_local.py` passes with 216 entering helpers, 120 low ends,
+66 cold ends and 728 columns. NotriReviewer independently reproduced a9de804f from the packaged recipes.
diff --git a/research/gauge44-slots/PROOF-NOTE-P6N.md b/research/gauge44-slots/PROOF-NOTE-P6N.md
new file mode 100644
index 0000000000..bef9ad2de0
--- /dev/null
+++ b/research/gauge44-slots/PROOF-NOTE-P6N.md
@@ -0,0 +1,34 @@
+# PROOF-NOTE-P6N: six b-type dim-8 cold ends on the layered no-triangle word (p6n)
+
+Construction by NoTriReopen. Driver: `construction/layers_p6n/reproduce_p6n.py`. Review: Q6Reviewer.
+
+## What p6n adds
+On research/gauge44-notri-layered's word NP (`a9de804f…`), p123's lane is rebuilt as three factored dim-8 pairs
+(`P6N-SPEC.json`):
+- [512, 513] at U = (256,128,66,34,16,8,6,1). The old pair [310,512] split a rank-3 end; [512,513] replaces it;
+- [311, 510] at U = (256,128,72,40,24,4,2,1);
+- [522, 327] at U = (256,128,66,34,18,10,6,1).
+
+They are built with the same premix-only factored construction as p123/q4/b6 (JP8Ends' stackJ/stackE, CarrierBypass
+pattern; PR635's unchanged `build_cold_end.apply`). The cold-layer recipe `COLD-LAYERS-RECIPE-P6N.json.gz` is NP's
+recipe plus these six ends; its meta lists 72 cold ends and the 8 entering ends. Applied to NP's swapped HPE word, it
+gives p6n `34b683fa…`:
+- profile {1:2540, 2:358, 3:446, 4:178, 5:56, 8:8};
+- widths {4:64, 5:48, 7:54, 8:122, 9:216};
+- width 3794 (NP 3800);
+- Δ per call {1:+6, 2:+12, 3:−12}, w −6, every end b-type.
+
+## Checks
+- **NoTriReopen:** native chain including phases PASS; audit_local PASS; 95/95 layer-end controls rejected.
+- **Q6Reviewer:**
+  - exact;
+  - (N) passes on all 21 pairs;
+  - payload 55/72 bits, against 192;
+  - the per-end control variant `layer_end_controls.py` (fc58c569…, which Q6Reviewer signed for research/gauge44-pq6) rejects 95/95;
+  - 165 further mutants on the six ends are all rejected.
+  The LayerReviewer-signed `../layers/layer_end_controls.py` controls one end per dim-8 frame family, so it would not
+  control each new end. This package therefore uses the per-end variant for p6n and for the promoted word built on it.
+- **Rebuild:** `reproduce_p6n.py` pins the input NP word, the output sha, profile and widths, and 95 controls.
+
+## Remaining capacity (NoTriReopen)
+After p6n, the only residual cold capacity on the word is 2 a-type units, and every end there prices about −9e-7.
diff --git a/research/gauge44-slots/PROOF-NOTE-PROMO.md b/research/gauge44-slots/PROOF-NOTE-PROMO.md
new file mode 100644
index 0000000000..8233bbd6b8
--- /dev/null
+++ b/research/gauge44-slots/PROOF-NOTE-PROMO.md
@@ -0,0 +1,46 @@
+# PROOF-NOTE-PROMO: entrance promotions E4 → E5 on the p6n word
+
+Construction by BlockInvert (`construction/promo/`); driver `construction/promo/reproduce_promo.py`.
+
+## What a promotion is
+An entering helper h starts at an entrance frame E (its `start_extra`) and climbs to its final frame. Promotion
+enlarges E to E′ ⊃ E (here dim 4 → dim 5). That removes one paid climb from h's chain (width −1 per helper) at the
+cost of re-choosing the frames of the gates on h's early chain. It is the time-reverse dual of end deepening. Two
+conditions make it legal:
+1. **Zero target response for h's dirt.** This condition does not depend on E, so it is inherited unchanged from the
+   input word.
+2. **Monotone frames.** Every gate's frame must contain its registers' current frames.
+Only frame annotations and start frames change. The scalar program (every gate's registers and coefficients) is
+untouched, so the endpoint, every cone and the compensation are those of the input word.
+
+## The recipe (`PROMO-RECIPE-p6n-k4.json`, data only, minimal)
+- Input: the p6n word `34b683fa…` (`PROOF-NOTE-P6N.md`), pinned.
+- `entrances`: the 16 entering helpers 627, 629–631, 635, 637–639, 651, 653–655, 659 and 661–663 (four E4 kernel groups) go E4 → E5.
+- `gate_frames`: 48 frame re-choices, the promotion's own entry-gate raises (12 per group); each records the old frame,
+  which must equal the input's exactly. This is BlockInvert's **minimal** recipe: the deterministic rule
+  E′ = E + ⟨smallest x⟩ on each group's entry gates (PromoReviewer). Unlike research/gauge44-promo's k3 recipe, it
+  carries none of the 72 price-neutral CP-SAT re-choices.
+- `expected`: output `0390ec65…`, profile {1:2572, 2:326, 3:430, 4:194, 5:56, 8:8}, widths
+  {4:80, 5:32, 7:54, 8:122, 9:216} (width 3778). Against p6n the delta is {1:+32, 2:−32, 3:−16, 4:+16}, width −16.
+
+## Checks rerun on every rebuild (`reproduce_promo.py`)
+- `build_promotion.py`: input pin; each old frame matches; each new entrance strictly contains the old one; the
+  profile and widths are recomputed from the chains, including target end climbs; output pins.
+- `promo_controls.py`: the honest word passes #645's independent `audit_local.py` (exact forward and dual endpoint
+  frames, entrances, cones). For p6n-k4, 11 mutants are rejected at pinned sites (the count is pinned in `LOCAL-PINS-p6n-k4.json`):
+  - entrance outside the first gate frame;
+  - raised gate missing, once per promoted group;
+  - entrance reverted, so the profile does not match;
+  - ungrouped promotion;
+  - a recipe gate whose old frame is wrong;
+  - a recipe entry that is not a promotion;
+  - a tampered input word (the constructor's own `__main__` must refuse it at the input pin);
+  - a scalar tamper on a raised gate.
+- The per-end layer-end controls (`../layers_p6n/layer_end_controls.py`, Q6Reviewer-signed): 95 rejected.
+- PR635's native chain: transport audit (all columns, native frames), ledgers, local replay (192-bit payload),
+  wrappers and phases, with the canonical word, local programs and Clifford recipes pinned (`LOCAL-PINS-p6n-k4.json`).
+
+## Search (not run by the rebuild)
+`make_recipe.py` writes the recipe from BlockInvert's CP-SAT solution (`prom.py` with `exactframe2.py`, using MinCutSel's
+chain model). These promotions were priced negative before (MinCutSel #3, under a fixed-window arc-flow packer). Under
+near-ideal packing (G44Pack's dissolve/gapmerge) they price positive; the strict replay confirms the gain.
diff --git a/research/gauge44-slots/PROOF-NOTE-SW4.md b/research/gauge44-slots/PROOF-NOTE-SW4.md
new file mode 100644
index 0000000000..a064cc54cc
--- /dev/null
+++ b/research/gauge44-slots/PROOF-NOTE-SW4.md
@@ -0,0 +1,44 @@
+# PROOF-NOTE-SW4: read-set exchange on four entering-copy pairs
+
+Construction by BRoute (`construction/sw4/`, with the author's notes in `construction/sw4/NOTES.md`). Driver:
+`construction/sw4/reproduce_sw4.py`.
+
+## The move
+In P6k4 (`0390ec65…`; research/gauge44-promo-p6sw applied the same exchange to P6k3 `a38bb414…`), each of four entering packet copies h is written first as h = E_h + r: copy gate add(h, r, 1)
+from a non-target face register r, with E_h being h's entering content. The pairs are (h, r) =
+(461, 25), (581, 89), (591, 415), (603, 431). For each pair the read sets of h and r are exchanged in phase B:
+- every post-copy target read add(t, h, c) becomes add(t, r, c), and t's entrance pre-read add(t, h, −c) (taken
+  while h = E_h) is deleted;
+- every target read add(t, r, c) becomes add(t, h, c), with a pre-read add(t, h, −c) inserted after h's last existing
+  pre-read and before h's copy gate.
+
+Since h − r = E_h after the copy, each target's value is unchanged at the end of B. The builder checks this for every
+register mod p (p = 2147483629). Moved and inserted gates take the plain join of their operands' current frames.
+Every other B gate and every early-cleanup tail keeps span(old frame + current operand frames). Targets must stay
+inside u_t^⊥, and tails and ends must contain the current frame. start_extra, helper_final, cleanup and the helper
+numbering are unchanged.
+
+## Effect
+Output `d232183f…`. Width 3778 is unchanged. The profile goes from {1:2572, 2:326, 3:430, 4:194, 5:56, 8:8} to
+{1:2548, 2:342, 3:438, 4:186, 5:56, 8:8}, a delta of {1:−24, 2:+16, 3:+8, 4:−8}, the same as on P6k3. The four
+exchanges are additive. The fourth promotion group (659, 661–663; gates B420–431) commutes exactly with the exchange:
+there is no index or register overlap, and SW4Reviewer checked that applying the k3→k4 frame and start differences
+to f35a852b gives d232183f. Ideal κ +3.271e-7 over P6k4.
+
+## Checks rerun on every rebuild
+- `build_sw4.py` (standard library only): the input sha pin; the 16 explicit moves of `SW4-RECIPE-P6k4.json`; B-end
+  state exactness mod p; frame caps, tails and ends; the output sha, profile and W. It also runs 4 controls, all of
+  which must hold, each at the exact site pinned in the recipe's `rejection_expected` (all three keys N1, N2 and N3 are required):
+  - C0: the identity recipe reproduces the input B and early_cleanup byte for byte;
+  - N1: h2r without deleting the pre-read is rejected by exactness, with changed B-end rows exactly {168, 171};
+  - N2: a partial exchange (one read only) is rejected by the frame cap, first at ('cap', B1192, register 169), 10 violations;
+  - N3: an inserted pre-read with the wrong sign is rejected by exactness, with changed rows exactly {129, 130, 169, 170}.
+- The per-end layer-end controls (`../layers_p6n/layer_end_controls.py`, Q6Reviewer-signed): 95 rejected.
+- PR635's native chain, with the canonical word, local programs and Clifford recipes pinned (`LOCAL-PINS-sw4-P6k4.json`).
+  The native transport audit re-checks every column and native frame of the exchanged word.
+
+## Scope of the search (BRoute)
+The search was exhaustive within the single-pair family only. NP has 107 copy pairs, and 54 of them have movable
+reads. Over those, every nonempty subset of one pair's movable reads gives 602 candidates: 564 are frame-illegal, and
+the 38 legal ones are all full single-pair exchanges, of which exactly these 4 are positive. Cross-pair combinations
+of partial moves were not enumerated.
diff --git a/research/gauge44-slots/README.md b/research/gauge44-slots/README.md
new file mode 100644
index 0000000000..8b48510939
--- /dev/null
+++ b/research/gauge44-slots/README.md
@@ -0,0 +1,265 @@
+# Seven triangle-hybrid slots on the k8 leaver word: conditional κ = 0.00167166528321877
+
+This package adds one construction layer to [research/gauge44-leaver8](../gauge44-leaver8) (#1005): seven
+additional triangle-hybrid B-delivery slots on #1005's final word `db2c7cfb…`. **Credit:** the slot search and
+the first two slots (X = 444, 446) are **rohanarun's #987**; the other five (X = 236, 238, 434, 436, 439) were found by
+running #987's search on the k8 word. The mechanism is NewBArch's #869 triangle-hybrid delivery.
+
+- **κ = 0.00167166528321877**. That is +2.78×10⁻⁷ over #1005 (0.001671387264390146). The complex side binds; the bit
+  supplier is PR589's, unchanged.
+- **Construction:** #1005's reviewed `construction/barch/build_tri.py` and `run_controls.py`, both **unchanged**,
+  with the new recipe `construction/slots/RECIPE-SLOTS-k8.json`. The output word is `c2b29430…`, profile
+  `{1:2412, 2:418, 3:432, 4:142, 5:82, 8:8}`, and widths are unchanged.
+- **Controls:** 34. These are C0 identity, the recipe, and the four mutants (`drop_restore`, `restore_full`, `drop_preread`,
+  `donation_after`) applied globally and to each of the seven slots. Every mutant is rejected and pinned in
+  `construction/slots/SLOT-PINS-k8.json`.
+- **Frames:** the exact global frame optimiser (gopt2) finds no gain on the slot word, so there is no frame step.
+- **Owners:** #1005's K8c8 owner map is rebound to the new word (widths and idle counts are unchanged). The admitted
+  data in `data/` passes the strict replay.
+
+## Verification (explicit reuse of a completed #1005 replay, as research/complex-t37-owners does for #799)
+
+```sh
+# Completed #1005 chain (the README commands of research/gauge44-leaver8), or any completed run of it:
+python -B research/gauge44-leaver8/construction/leaver/reproduce_leaver_chain.py \
+  --main . --pr635 /tmp/gauge44-pr635 --leaver-dir /tmp/lv --hamming /tmp/notri-base/hamming --id k8 --out /tmp/lvc
+# This package (about 3 minutes):
+python -B research/gauge44-slots/verify_manifest.py
+python -B research/gauge44-slots/construction/slots/verify_slots.py \
+  --main . --pr635 /tmp/gauge44-pr635 --baseline /tmp/lvc --work /tmp/slots
+# PASS_SLOTS_ON_CHECKED_K8_BASELINE 0.00167166528321877
+```
+
+`verify_slots.py` rechecks the baseline: its complete step receipt (every chain step exited 0), the final word against
+#1005's frame-recipe pin, its canonical, program and Clifford locals against `CHAIN-PINS-k8`, and all five
+layer-end control counts. It then rebuilds only the slot layer and its controls, the native locals of the new word, the
+independent `audit_local`, and the strict global replay of this package's data. Everything below is #1005's README,
+unchanged; this package differs from it only in `construction/slots/`, `data/`, this section, `RESULT.json` and `MANIFEST.json`.
+
+---
+
+# Gauge44 without K-triangles, with earlier jp8 layers, the p6n ends, entrance promotions, a read-set exchange, #741's frames, a joint exchange, a triangle-hybrid B rewrite, no-helper mutable-leaver cells and PR589's bit supplier: conditional κ = 0.001671387264390146
+
+Under the retained all-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1–H5 interfaces (as in #645), and the PR589 bit supplier,
+
+$$
+T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad
+\kappa=\frac{1671387264390146}{10^{18}}=0.001671387264390146.
+$$
+
+**The construction is icekylinx's [#645](https://github.com/CrocSwap/integer-mult-bounds/pull/645) (`research/gauge44-global`).** This package builds the research/gauge44-barch construction (items 1–8) and then rebuilds its word around **no-helper mutable-leaver cells** (item 9):
+1. **No-triangle word (PartialK).** #645's gauge44 chain is run with **none** of the four (p,−1) K-triangles, so there are R = 504 helpers. In the six K-blocks {0,1,2,11,12,13}, the completion priority is extended by the 6-row list `construction/notri/PRIO6.json`. Every block then pairs at rank 4, giving **56** rank-four cold ends instead of 44. `construction/notri/reproduce_notri.py` rebuilds this word from a #645 `reproduce.py --until word` output. It uses PartialK's generalisations of #645's and PR635's constructors (`cgx.py`, `port_stage_x.py`, `cold44x.py`; each differs from its original only in the documented parameters). It pins:
+   - the pairing ranks [4]*14, inside `cold44x.py` and again in the driver;
+   - the word (`3e99ba77…`);
+   - the canonical word, the local programs and the Clifford recipes.
+   `--control-g44` instead rebuilds #645's own gauge44 word (`78c7aada…`) with the same scripts.
+2. **Layers on the no-triangle word (G44Stack).** `construction/layers_np/reproduce_np.py` applies to the no-triangle regroup word (`864ff4a1…`):
+   - research/gauge44-layered's six pivot swaps, mapped to the 504-helper numbering (`PIVOT-SWAP-NP.json`, swap word `beb3579f…`);
+   - the greedy HPE (46, `HPE-RECIPE-NP.json`);
+   - the exact cold44 (same 56 ends);
+   - the entering ends s4 (566/567/578/579 at U24) and x30 (608/610/543/555 at U30), plus BlockCombine's b6 and q4 dim-8 cold ends (`COLD-LAYERS-RECIPE-NP.json.gz`). p123 is negative on this base and dropped; j3 is dead.
+   The layered word is pinned (`a9de804f…`): profile `{1:2534, 2:346, 3:458, 4:178, 5:56, 8:8}`, width 3800. The signed research/gauge44-layered files `construction/layers/build_pivot_swap.py` and `construction/layers/layer_end_controls.py` are used unchanged, and the latter must reject exactly 59 controls. The global code is research/gauge44-layered's (spot-width rule): SPEC `width_spot_helpers` [270,282,294,306] and `pivot_swap` → `construction/layers_np/PIVOT-SWAP-NP.json`, giving spot widths [9,9,8,8].
+3. **p6n ends (NoTriReopen).** `construction/layers_p6n/reproduce_p6n.py` applies `COLD-LAYERS-RECIPE-P6N.json.gz` to the NP swapped HPE word with PR635's unchanged `build_cold_end.apply`. That is NP's cold-layer recipe plus six b-type dim-8 cold ends: [512,513], [311,510] and [522,327], which rebuild p123's lane as clean pairs. The result is the p6n word (`34b683fa…`): profile `{1:2540, 2:358, 3:446, 4:178, 5:56, 8:8}`, width 3794. The per-end layer-end controls (`construction/layers_p6n/layer_end_controls.py`, the variant Q6Reviewer signed for research/gauge44-pq6) must reject exactly 95 mutants. See `PROOF-NOTE-P6N.md`.
+4. **Entrance promotions (BlockInvert).** `construction/promo/reproduce_promo.py --base p6n --k p6n-k4` applies the minimal recipe `PROMO-RECIPE-p6n-k4.json` to the p6n word with BlockInvert's deterministic constructor `build_promotion.py`. The recipe promotes the 16 entering helpers 627, 629–631, 635, 637–639, 651, 653–655, 659 and 661–663 (four E4 kernel groups) from E4 to E5, the time-reverse dual of end deepening. It re-chooses the frames of the gates affected. Only frame annotations and start frames move; the scalar program is unchanged. The promoted word is pinned (`0390ec65…`): profile `{1:2572, 2:326, 3:430, 4:194, 5:56, 8:8}`, widths `{4:80, 5:32, 7:54, 8:122, 9:216}`, width 3778. BlockInvert's `promo_controls.py` runs #645's independent `audit_local.py` on the honest word and must reject 11 recipe- and word-level mutants at pinned sites. The per-end layer-end controls (95) and the native chain then run with pins. The recipe is minimal: 48 entry-gate frame raises and no other frame re-choices. See `PROOF-NOTE-PROMO.md`.
+5. **Read-set exchange (BRoute).** `construction/sw4/reproduce_sw4.py` runs BRoute's standard-library builder `build_sw4.py` with `SW4-RECIPE-P6k4.json`, 16 explicit moves, on the promoted word (`0390ec65…`). For the entering-copy pairs (h, r) = (461,25), (581,89), (591,415) and (603,431), the phase-B target read sets of h and its face register r are exchanged. The entrance pre-reads are deleted or inserted so that every register's value at the end of B is unchanged; the builder checks this mod p. Frames are repaired monotonically, and the width is unchanged. The SW4 word is pinned (`d232183f…`): profile `{1:2548, 2:342, 3:438, 4:186, 5:56, 8:8}`, width 3778. Four controls (C0 identity, N1 kept pre-read, N2 partial exchange, N3 wrong sign) must all hold, each at its exact rejection site pinned in the recipe. The per-end layer-end controls (95) and the native chain then run with pins. See `PROOF-NOTE-SW4.md` and `construction/sw4/NOTES.md`.
+6. **#741's eight B frames (chafreaky).** `construction/frames/reproduce_frames.py` applies chafreaky's [#741](https://github.com/CrocSwap/integer-mult-bounds/pull/741) frame recipe, `FRAME-RECIPE-sw4.json`, byte-identical to #741's. Ported by CompetitorMine, it raises eight B-gate frames with the scalar program unchanged, giving #741's word `e7804702…`. It runs 3 pin controls, #741's 10 focused native controls, 95 layer-end controls and the native chain with pins.
+7. **Joint exchange X4 (JointXF).** `construction/jx/reproduce_jx.py` runs JointXF's standard-library builder `build_jx.py` with `RECIPE-X4.json` on #741's word (step 6's output). It makes four disjoint instances of the read-set exchange, each over two target-sharing copy pairs: (448,472), (458,592), (470,604) and (482,614). The moved reads keep their stored frames, and #741's frames are included. All edits are explicit, and B-segment exactness is checked by Fraction replay. The final word is pinned (`1e1d99ba…`): profile `{1:2548, 2:338, 3:430, 4:194, 5:56, 8:8}`, width 3778. All seven pinned controls are rerun; C1 reproduces #741's word. See `PROOF-NOTE-FRAMES-X4.md`.
+8. **Triangle-hybrid B rewrite (NewBArch).** `construction/barch/reproduce_barch.py` runs NewBArch's standard-library builder `build_tri.py` with `RECIPE-U8.json` on the X4 word (step 7's output). Eight disjoint slots receive a width-neutral B-delivery rewrite: an entering copy donates into a halves-copy so that one target read gets X+H, with holder restores and entrance pre-reads. The U8 word is pinned (`090fd574…`): profile `{1:2548, 2:338, 3:446, 4:162, 5:72, 8:8}`, width 3778. All 38 pinned controls are rerun (identity, the recipe word passing audit_local, and four audit_local-rejected mutants, globally and per slot). See `PROOF-NOTE-BARCH.md`.
+9. **Leaver cells, re-stacked (LeaverSAT, LeaverSAT2).** `construction/leaver/reproduce_leaver.py --id k8` replaces the no-triangle word's construction with all eight all-K cells (01±, 23±, 45±, 67±). Each cell is LeaverSAT's 21-gate circuit, which uses the face-event leaver sources as mutable intermediates (R = 480, cell word `58e14a02…`). `construction/leaver/reproduce_leaver_chain.py --id k8` then re-applies items 2–8 with the signed builders unchanged and LeaverSAT's re-indexed recipes: swap, HPE, cold44, NP, p6n, 16 promotions, the re-indexed X4 exchange (the identity on this word) and 6 U8-style hybrids (`c836d892…`). It adds LeaverSAT2's exact global frame re-optimisation (`FRAME-RECIPE-LV-k8.json`), which gives the final word **`db2c7cfb…`**. Every intermediate word, control count and native pin is pinned (`LEAVER-PINS-k8.json`, `CHAIN-PINS-k8.json`). The per-word layer-end controls are the Q6Reviewer-signed `layer_end_controls_leaver.py` v2 (95 each), on the p6n, promoted, jx and hybrid words (`LEC-REASON-PINS-STACK-k8.json`) and on the re-framed final word (`LEC-REASON-PINS-k8.json`); its declared not-applicable sites are sha-proven identities or unbuildable mutants, each replaced by a same-class substitute that must be rejected. Items 5 and 6 don't apply on this word: the sw4 copies are dropped, and none of #741's frames survive. Items 1–8 remain in the package as the construction record of research/gauge44-barch. See `PROOF-NOTE-LEAVER.md`.
+10. **Owner map (chafreaky's [#685](https://github.com/CrocSwap/integer-mult-bounds/pull/685), adapted by G44Pack).** The map is G44Pack3's K8c8, from its pattern-flow LNS (`pflns`) on the R = 480 k8 word. Its lineage is the #685/#741 map (chafreaky) via G44Pack's relabel and rewidth, followed by G44Pack3's LNS. It was admitted with this package's own code (NEWWORD discovery, `freeze_spec.py`, strict) at κ 0.001671387264390146. Only PLAN and OWNERS change. These are search inputs only; no verifier reads them.
+11. **Expected values.** `data/SPEC.json` is re-derived by #645's discovery → `code/freeze_spec.py` → strict chain.
+
+- **κ = 0.001671387264390146** (conservative 0.001671387261540186). That is +0.4298% over research/gauge44-leaver (k5 cells, κ 0.001664233607446043; same chain on five cells, FO_c1 map) and +0.5672% over [#942](https://github.com/CrocSwap/integer-mult-bounds/pull/942) (κ 0.001661960547713947) and +1.3279% over #645, +0.9174% over research/gauge44-notri-layered (0.001656193765416678) and +0.7701% over research/gauge44-promo (0.00165861362787227) and +0.7273% over research/gauge44-promo-p6 (0.001659319032684569) and +0.7075% over research/gauge44-promo-p6sw (0.001659645685315104) and +0.5869% over research/gauge44-frames-x (0.001661634653669567) and +0.5679% over research/gauge44-barch (0.001661948695165034) and +0.6131% over [#741](https://github.com/CrocSwap/integer-mult-bounds/pull/741) (chafreaky, κ 0.001661202643272239) and +0.6654% over [#685](https://github.com/CrocSwap/integer-mult-bounds/pull/685) (chafreaky, κ 0.001660339298410333). The complex side certifies 0.001674185476674086429846 and PR589's bit supplier gives 0.001733427039589844234749, so **the complex side binds**. Under PR543 the bit side would cap κ at 0.001651096360425895 (`PROOF-NOTE-BIT.md`).
+- **Evidence.** This package's own code admitted G44Pack3's K8c8 map (NEWWORD discovery → `freeze_spec.py` → strict): `verify_global.py` passes (`PASS_GAUGE44_STRICT_GLOBAL_REPLAY`, κ 0.001671387264390146) against G44Pack3's k8 locals, with SPEC `width_spot_helpers` [258,270,282,294] and `pivot_swap` → `construction/leaver/PIVOT-SWAP-k8.json`. It equals G44Pack3's own strict κ for K8c8. `RESULT.json` is that replay's `REPLAY.json`, converted to LF. The locals rebuilt by `reproduce_leaver_chain.py --id k8` match G44Pack3's strict locals byte for byte in every file except CLIFFORD-REVIEW and SCALAR-FRAME-AUDIT. Those two differ only in their `seconds` field, and the comparison normalises only that field (canonical `d1bf3c6f…`, programs `683f8323…`/`2d184e4d…`, Clifford `e3bfdfa2…`, pinned in `CHAIN-PINS-k8.json`). For this package, `data/SPEC.json` and a fresh `verify_global.py` replay on locals rebuilt by the two drivers are the binding record.
+- **Independent price.** `independent/GAUGE44-INDEPENDENT-PRICE.json` is regenerated on this package's `data/PLAN.json` with the ported `independent/price_profile.py`: `PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK`, κ equal to the strict replay.
+- **Independent local audit.** `evidence/layers/LOCAL-AUDIT-LAYERED.json` is #645's `independent/audit_local.py`, run with `--main` on the final leaver word (content `db2c7cfb…`): `PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES`, 192 entering helpers, 78 low ends, 48 cold ends, 704 checked columns. Rerunning it reproduces the receipt except `elapsed_seconds` and, across zlib versions, `compressed_sha256`.
+- **Historical #645 files (PR543-based, 492 helpers).** These are #645's files, retained unchanged and **not** updated for this package: `LOCAL-VALIDATION.json`, `CONSTRUCTION.md`, `hosting/`, `evidence/` (except `evidence/layers/`), the rest of `independent/`, `construction/reproduce.py` and its inputs, and `code/prepare_global.py`. They describe #645's word, owner map, PR543 supplier and κ 0.001649483702558979. `code/prepare_global.py` is #645's one-shot owner-map preparer, hard-wired to #645's parent plan and R = 492. No verifier imports it. This package's PLAN/OWNERS are frozen search output, and the strict replay checks them. `construction/reproduce.py` is still used for its `--until word` shadow and hamming inputs; its 492-word output is then superseded by `construction/notri/`. `construction/layers/reproduce_layers.py` is research/gauge44-layered's driver for the 492-helper layered word, shipped unchanged as signed; it is not used here.
+- **Construction and code files** by committed LF SHA-256:
+  - `construction/notri/reproduce_notri.py` 90148c2a0422b4f92164298a283de73d413ab3d4cb7151a0e6b643a37ea025a8 (no-triangle driver)
+  - `construction/notri/cgx.py` 3da039d4184097c14802f9dbf972520d5b807671196f5e47a2247bc9f29bb418 (PartialK's generalised construct_gauge_xcentre.py)
+  - `construction/notri/port_stage_x.py` 38310744d054e393ea35e996047cddeb2d212141aaaaa4b07f7a4663b11db8e7 (PartialK's generalised build_port_stage.py)
+  - `construction/notri/cold44x.py` f0bc3500efb2c839a0f8cb03dbb9ea0a54f1dfc71ef81e5373b3d638ac5b8296 (PartialK's generalised build_gauge_cold44.py plus the PAIRING_RANKS pin)
+  - `construction/notri/PRIO6.json` de0412511b0dd1af13e9717bc791126ac0e91c569b5391fd6c70268083045d15 (completion priority)
+  - `construction/layers_np/reproduce_np.py` 1a304144a250d00d14154692ba522365b036777cf2b6fac466095e8ba733c16c (NP layer driver)
+  - `construction/layers_np/PIVOT-SWAP-NP.json` d49b8d316da1cbdaf995dd0e8314d3c67cc9cd4d5902e9d85ccb907be645bef5 (layer input)
+  - `construction/layers_np/HPE-RECIPE-NP.json` 43900139f618bdc06b8319098fb8dccaf4fc315b43ef7c067ca2cd778cdba2c1 (layer input)
+  - `construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz` 3164cfb71baaeba4ac43427bc14075a225fc3a32ecd9341e58aa52c03a4ee2c0 (layer input)
+  - `construction/layers/build_pivot_swap.py` 8e8bced88be2e592ded40929499bac385ca92fcc1fa59183c22229dbf34093b8 (signed, unchanged)
+  - `construction/layers/layer_end_controls.py` 7829187bfc8f909948d5250e0ec00f02c89f5fe98306a3ed88daee36cb3c92ef (signed, unchanged)
+  - `construction/layers/reproduce_layers.py` 435699f6f79c6c7fb8d6cc5a8382576d6ac88747583a975ff671e45440b93c4e (signed, unchanged, unused here)
+  - `construction/promo/reproduce_promo.py` f979be666c3f5cf57e342a8427863c0b35b67ca4d3be495ac386f6870deb2026 (promotion driver)
+  - `construction/promo/build_promotion.py` 9c9e2001b8d68bbe934d136026276fe97bd9bf6f94d4d78441fc28e14aca4daf (BlockInvert's constructor)
+  - `construction/promo/promo_controls.py` 786c51f84b53698c2c833083506c4432c30eb0ed3b71e7dbe458a70c7413c372 (BlockInvert's controls)
+  - `construction/promo/make_recipe.py` ba9e4fdc0c1be7f6a150a5a50909911257a1a8c7cc5d03d61f541178fc07c122 (discovery-side recipe writer (search, not run))
+  - `construction/promo/PROMO-RECIPE-p6n-k4.json` fa6065d142646f7ab1f268912ce0cf5a1a6cd33c3994ff96bd6e204cf16b3e90 (minimal recipe)
+  - `construction/promo/LOCAL-PINS-p6n-k4.json` a92bb02266596956bd53e9c86e8bbcc6639c92b4a4a248a1521f8eb79228271f (native pins)
+  - `construction/layers_p6n/reproduce_p6n.py` aa7d6bcbed05aa1c689437c07a26e5c95be3c700c0c1fb7bcf91c432a88436ca (p6n driver)
+  - `construction/layers_p6n/layer_end_controls.py` fc58c5699ba6191c1163a3041241f6f0b619626c4462cd99bcf88210bac9e81e (per-end controls (Q6Reviewer-signed variant))
+  - `construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz` 17e218a17e47c58fe2cde775ab2314d3d84030a61327b7f13da61cae3b374ad4 (p6n recipe)
+  - `construction/layers_p6n/P6N-SPEC.json` 132a59635077d6afe80f99964a6935fce1dc2ece6587d74209c6f9c60025c8f1 (p6n end spec)
+  - `construction/sw4/reproduce_sw4.py` 3d082e0cc576fb1b4fb9e5dd11d63bab697c8a8626e2837813cd00d100b1aeac (SW4 driver)
+  - `construction/sw4/build_sw4.py` 9a295f3d534594a6b1326d8a6647e947670d1c6fbc92f37f5169661fde4c8f66 (BRoute's builder (stdlib))
+  - `construction/sw4/SW4-RECIPE-P6k4.json` fa58d0ffc95d10b7453daefe4b34404a52895f94126ef973e92e92106cd615fa (16-move recipe with pinned rejection sites)
+  - `construction/sw4/LOCAL-PINS-sw4-P6k4.json` 3c06bf68b28ff125a6a2372bb70cefd76fb9fe1333438cd34dfb5b617cd70327 (native pins)
+  - `construction/frames/reproduce_frames.py` dc39ada9a2eb387310be181f3cea5dbd4b538632a888cd7372ece5e38a771832 (#741 frames driver)
+  - `construction/frames/build_frames.py` 200847a7e8b3125cbeea0765dad67650e0bf83d32b66d72ba4977e99b8ee8eeb (#741's builder (chafreaky; ported))
+  - `construction/frames/frame_controls.py` 477de854ec9184a2c73d6ac3857a9d0cbd6bc04b71d10a105e7344434b492a77 (#741's controls (chafreaky; ported))
+  - `construction/frames/FRAME-RECIPE-sw4.json` a2c7ca4d44671386d05974e2627645b42bbb7da7a35cefff6e9fa158b6ac8473 (#741's recipe, byte-identical)
+  - `construction/frames/LOCAL-PINS-frames-sw4.json` bc416b8f6443d59c715fb358c4d70fa27eae2d306388ffe0e2a303f60d929f7f (native pins)
+  - `construction/jx/reproduce_jx.py` 5c7afebb4eb7fcdeb7e971cfbc457cf071850e2da21c3c71295efdd453c2399c (X4 driver)
+  - `construction/jx/build_jx.py` 3cc7550b0c24bb54e245c6f7f16de489fd7844721fbb64aac628f38f43887916 (JointXF's builder (stdlib))
+  - `construction/jx/RECIPE-X4.json` 9d42c6b38e8124f5ffe15da56c260a7fba7260626bf3c5f8cbd93aa4a71ceadd (explicit recipe with pinned controls)
+  - `construction/jx/LOCAL-PINS-jx-X4.json` 95c5114c8e937c2737a1b9f9da97303f2e5e129d39e6dfcc4010e99bfdb9c974 (native pins)
+  - `construction/barch/reproduce_barch.py` 19bc970aa6af25ab0e7fa96fb65c64dd0c5243976d8f2cb733cba839155482c1 (U8 driver)
+  - `construction/barch/build_tri.py` 0fba65b31c2fd71864c291358bb0ad8d5f7e1be07e21df23f0ae73d7b966002e (NewBArch's builder (stdlib))
+  - `construction/barch/run_controls.py` 42639bf62bf57795e3ea615c1944c67efed00f28591333daeb3139bf63d04476 (NewBArch's controls (38 outcomes))
+  - `construction/barch/RECIPE-U8.json` 292f0e9f82824c4111728cf4de929bf6e43320fbbdc77658aae9681906b0d652 (explicit recipe)
+  - `construction/barch/LOCAL-PINS-barch-U8.json` 2d16f99e1f71fd66378f5f767cf4cfa2a58264919a95074c7b31029f39a3c9f5 (control set and native pins)
+  - `construction/leaver/reproduce_leaver.py` 831bfdf2247b5d864b74c3b2b6a475718053d48570851d48bd1c5471d410ee30 (cell driver)
+  - `construction/leaver/cgx_leaver.py` 3af491c63dd96204a7c36006c7e419c2e5ce77e5bc453ccd2495c1e41f83f87c (cell constructor)
+  - `construction/leaver/reproduce_leaver_chain.py` 2bc3fc3f32e0f957a0731b79254c553ca48fc6d4d47c4f99d6cd31e1901d85b5 (chain driver)
+  - `construction/leaver/layer_end_controls_leaver.py` 4ba676f1ea326b739a64c3477f64eeb295f8151514f78fa7e62b71e4373a6206 (per-word reason re-pins and declared not-applicable sites, v2 (Q6Reviewer-signed))
+  - `construction/leaver/build_frames_lv.py` 2eb80d612aa59a7bd8b04a122045e3bd2b83a21954e3164943cd20cf6050a21b (LeaverSAT2's frame builder)
+  The global code is research/gauge44-layered's, unchanged: assemble 4c270a99, assembly_controls e4c0f782, audit_allcold a87d7f48, bind 1d39bcc7, witness 779c5172. The bit-supplier code is research/gauge44-bit589's, unchanged: verify_global 16bd5e54, bit_supplier_controls e6d33fb6, price_profile d2f548ad.
+- **Line endings.** These files had CRLF in the admitted trees and are committed as LF only (`crlf.replace(b'\r\n', b'\n') == lf`, no lone `\r`):
+  - `construction/jx/build_jx.py`: CRLF 775c2ae60eec9abc…, committed (LF) 3cc7550b0c24bb54…
+  - `construction/jx/RECIPE-X4.json`: CRLF 228079b304358500…, committed (LF) 9d42c6b38e8124f5…
+  - `construction/barch/build_tri.py`: CRLF 2432372f148a4d34…, committed (LF) 0fba65b31c2fd718…
+  - `construction/barch/run_controls.py`: CRLF 18e1f5953403784f…, committed (LF) 42639bf62bf57795…
+  - `construction/barch/RECIPE-U8.json`: CRLF 3e97088ad641eb6e…, committed (LF) 292f0e9f82824c41…
+  - `data/SPEC.json`: CRLF b2515d29d54e5027…, committed (LF) 1208c7c3ae84c158…
+  - `RESULT.json`: CRLF 454c25d5b0cd7df7…, committed (LF) 72bf797ce995ff61…
+  - `independent/GAUGE44-INDEPENDENT-PRICE.json`: CRLF 0b8482888e64327f…, committed (LF) 6e222b252f345344…
+  - `evidence/layers/LOCAL-AUDIT-LAYERED.json`: CRLF 6b63fc2bbea96cb5…, committed (LF) a596d7262374a023…
+
+
+Clean-clone verification, from the repository root (Python 3.11+, assertions on; prepare the pinned #635 supplier as in the #645 section below):
+
+```sh
+python -B research/gauge44-leaver8/verify_manifest.py
+python -B research/gauge44-leaver8/construction/reproduce.py \
+  --main . --pr635 /tmp/gauge44-pr635 --out /tmp/notri-base --until word
+python -B research/gauge44-leaver8/construction/notri/reproduce_notri.py \
+  --main . --pr635 /tmp/gauge44-pr635 --word-dir /tmp/notri-base --out /tmp/notri-word --word-only
+python -B research/gauge44-leaver8/construction/layers_np/reproduce_np.py \
+  --main . --pr635 /tmp/gauge44-pr635 --notri-dir /tmp/notri-word --hamming /tmp/notri-base/hamming --out /tmp/notri-np
+python -B research/gauge44-leaver8/construction/layers_p6n/reproduce_p6n.py \
+  --main . --pr635 /tmp/gauge44-pr635 --np-dir /tmp/notri-np --out /tmp/p6n
+python -B research/gauge44-leaver8/construction/promo/reproduce_promo.py \
+  --main . --pr635 /tmp/gauge44-pr635 --base p6n --base-dir /tmp/p6n --k p6n-k4 --out /tmp/promo
+python -B research/gauge44-leaver8/construction/sw4/reproduce_sw4.py \
+  --main . --pr635 /tmp/gauge44-pr635 --promo-dir /tmp/promo --recipe P6k4 --out /tmp/sw4
+python -B research/gauge44-leaver8/construction/frames/reproduce_frames.py \
+  --main . --pr635 /tmp/gauge44-pr635 --sw4-dir /tmp/sw4 --out /tmp/frames
+python -B research/gauge44-leaver8/construction/jx/reproduce_jx.py \
+  --main . --pr635 /tmp/gauge44-pr635 --frames-dir /tmp/frames --out /tmp/x4
+python -B research/gauge44-leaver8/construction/leaver/reproduce_leaver.py \
+  --main . --pr635 /tmp/gauge44-pr635 --word-dir /tmp/notri-base --id k8 --out /tmp/lv --word-only
+python -B research/gauge44-leaver8/construction/leaver/reproduce_leaver_chain.py \
+  --main . --pr635 /tmp/gauge44-pr635 --leaver-dir /tmp/lv --hamming /tmp/notri-base/hamming --id k8 --out /tmp/lvc
+python -B research/gauge44-leaver8/independent/audit_local.py \
+  --word /tmp/lvc/frames/FULL-WORD.json.gz --main . --output /tmp/lvc-audit.json
+python -B research/gauge44-leaver8/verify_global.py \
+  --main . --local /tmp/lvc/local --work /tmp/lvc-global
+# kappa 0.001671387264390146
+```
+
+Optional control: `reproduce_notri.py ... --control-g44 --out /tmp/notri-ctl` rebuilds #645's gauge44 word `78c7aada…`.
+
+## Predecessor: #645's README (unchanged below; paths read `research/gauge44-global`)
+
+### Gauge44: conditional κ = 0.001649483702558979
+
+New contributions by **icekylinx**, with **OpenAI GPT-6 Astra** assistance.
+Local review and packaging used OpenAI Codex. Original notices and Apache-2.0 licenses are retained.
+
+Under the retained all-size compiler, common-label/mutable-source realization,
+whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit
+H1–H5 interfaces,
+
+$$
+T(n)=O\!\left(n(\log n)^{1-\kappa_{645}}\right),\qquad
+\kappa_{645}=\frac{1649483702558979}{10^{18}}=0.001649483702558979
+$$
+
+(This is #645's own κ. **This package's κ is the one at the top of this README.**)
+
+The certified complex saving is `0.001652208994368411824947`. The unchanged
+[#543](https://github.com/CrocSwap/integer-mult-bounds/pull/543) bit supplier gives
+`0.001653826988146798944268`, so the complex side binds. The conservative complex
+model separately certifies κ `0.001649483699681650`.
+
+### Construction
+
+This replaces the local supplier and all 72 owner assignments of pinned
+[#635](https://github.com/CrocSwap/integer-mult-bounds/pull/635). Source/copy exchanges
+at equal rank-one frames alter the factory's arbitrary-helper-input propagation.
+An invertible completion of the retired rows and source-carried coordinate totals
+then expose 44 rank-four cold endpoints. Exact input premixes, low-frame tails
+and a recomputed full inverse realize them.
+
+| Per-invocation quantity | Complete #635 JP8 | Gauge44 |
+| --- | ---: | ---: |
+| Source / target ports | 112 / 112 | 112 / 112 |
+| Helpers | 492 | 492 |
+| Rank-four cold endpoints | 22 | 44 |
+| Helper residual width | 3,894 | 3,794 |
+| Paid local rank mass | 5,750 | 5,650 |
+
+The new paid local profile is `{1:2514, 2:404, 3:448, 4:160, 5:56, 8:8}`.
+The explicit whole-family assignment covers 35,424 helper roles on 7,168 live
+and 7,670 physical families. It retains the rank deficit 2,560 and charges every
+idle remainder. Exact integer majorization certificates justify the owner
+updates; the resulting map is a coordinate fixed point, with no claim of joint
+optimality.
+
+The assembled κ is 0.809306% above #635. `data/FRONTIER.json` records Pro's dated
+comparison snapshot; it is not a live ranking of community results.
+
+### Proof and evidence
+
+- `CONSTRUCTION.md`: exact cold-space calculation, dyadic realization and attribution.
+- `hosting/PROOF.md`: capacity, exchange and majorization arguments.
+- `independent/CENTRE-GUARD-REVIEW.md`: ordered center-frame interface and source carriers.
+- `data/SPEC.json`, `evidence/ASSEMBLY.json`: strict component moments and outer parameters.
+- `evidence/audit/`: actual controller, physical charts and finite invoice.
+- `construction/INPUTS.json`, `data/UPSTREAM-PINS.json`: inherited input hashes.
+- `MANIFEST.json`, `SOURCES.json`, `LOCAL-VALIDATION.json`: submitted bytes, provenance and local checks.
+
+Original Pro run receipts are retained as evidence; their raw logs remain in
+the original archive outside the submission. Fresh replay writes new logs to
+the selected output directory.
+
+### Incremental reproduction
+
+Use Python 3.11 or newer with assertions enabled. The required replay uses only
+the standard library. The optional historical seed-discovery optimizer is not
+part of admission.
+
+Prepare the pinned #635 supplier in a separate directory (the main dependencies
+are already present in this repository):
+
+```sh
+git fetch https://github.com/CrocSwap/integer-mult-bounds.git a6895a69f8ad98ab45777b03e9e6f48888c39f6f
+mkdir -p /tmp/gauge44-pr635
+git archive FETCH_HEAD research/complex-571-cold14-st2 | tar -x -C /tmp/gauge44-pr635
+```
+
+From the repository root, with fresh output directories:
+
+```sh
+python -B research/gauge44-global/verify_manifest.py
+python -B research/gauge44-global/construction/reproduce.py \
+  --main . --pr635 /tmp/gauge44-pr635 \
+  --out /tmp/gauge44-local --until phases
+python -B research/gauge44-global/verify_global.py \
+  --main . --local /tmp/gauge44-local/local --work /tmp/gauge44-global
+```
+
+The dedicated workflow also runs the independent literal-word audit, exact owner
+reproduction, preserved-assertion comparison and independent pricing on Python
+3.11 and 3.14. `hosting/README.md` and `independent/README.md` give those commands.
+No ancestral full replay, optimizer search or PDF generation is required.
+
+The result remains a finite conditional witness. It does not establish an
+unconditional multiplication theorem or a complete Lean formalization.
diff --git a/research/gauge44-slots/RESULT.json b/research/gauge44-slots/RESULT.json
new file mode 100644
index 0000000000..89be708d9c
--- /dev/null
+++ b/research/gauge44-slots/RESULT.json
@@ -0,0 +1,86 @@
+{
+  "status": "PASS_GAUGE44_STRICT_GLOBAL_REPLAY",
+  "kappa": "167166528321877/100000000000000000",
+  "kappa_decimal": "0.00167166528321877",
+  "complex_lower": "837232213634911250061/500000000000000000000000",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_supplier": {
+    "pr": 589,
+    "repository": "CrocSwap/integer-mult-bounds",
+    "commit": "a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46",
+    "merged_as": "b3eb785ac5b4b1ca2beea0f80db078a505626a90",
+    "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "git_blob_sha1": "e293ddc557742637f9f679f083a1a282d87b1b13",
+    "word": {
+      "v": 111,
+      "decoder_constant": 63,
+      "copy_ranks": [
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7
+      ]
+    },
+    "derived_deficit": 10272,
+    "deficit_formula": "T(2Kv-L*cst), L=9 T=32 K=4 M=64",
+    "replay_scope": "Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit."
+  },
+  "gain_over_pr635_percent": "2.164948243169117498148727559671554388312775174640418891709408020842883",
+  "spec_sha256": "d77c577278e68874444e1619e0762d0f3daa5d8d2bc985bb64eabae7e5ef3c44",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 1.406,
+      "exit_code": 0,
+      "log_sha256": "3aea2a4b68e7aaeadd9ffef649be0d25e2dff1535d9a61bffeaf6d92e55ba6a8"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.437,
+      "exit_code": 0,
+      "log_sha256": "78a081673d6b4fde10a86e6f767d53648b868d1f0cac2441d12951434ad7341b"
+    },
+    {
+      "name": "emit",
+      "seconds": 2.891,
+      "exit_code": 0,
+      "log_sha256": "faeccc2ac1d112bac2aa82080c12e064130fa3a86c07649abcc8e7fa1378a49c"
+    },
+    {
+      "name": "audit",
+      "seconds": 12.484,
+      "exit_code": 0,
+      "log_sha256": "bdafdea32540bcb0d099a42bf4885382696f24741313b6f046d6a73f666525cf"
+    },
+    {
+      "name": "invoice",
+      "seconds": 1.016,
+      "exit_code": 0,
+      "log_sha256": "439ce483feb3c79a1c8da5015e86db0958c0e5d91bf6f5b2f23c9f0c11b26531"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.343,
+      "exit_code": 0,
+      "log_sha256": "2f59f1b00b2f789547daaf9a0480e866e30a5e3ee13ca0a17503e5728a47fa44"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 0.422,
+      "exit_code": 0,
+      "log_sha256": "34527ddfe1e53bec71dc5759eb9a26417be6d4e93e76cbf80575d9bafebd876b"
+    },
+    {
+      "name": "bit-supplier-controls",
+      "seconds": 0.625,
+      "exit_code": 0,
+      "log_sha256": "c648542cd6dddbb154af7d02a41aaed1025603d9a4ab54f7c249d2b683e22249"
+    }
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; this bit composition is unreviewed. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/gauge44-slots/SOURCES.json b/research/gauge44-slots/SOURCES.json
new file mode 100644
index 0000000000..0d69845db9
--- /dev/null
+++ b/research/gauge44-slots/SOURCES.json
@@ -0,0 +1,36 @@
+{
+  "contributor": "icekylinx",
+  "research_assistance": "OpenAI GPT-6 Astra",
+  "local_review_and_packaging": "OpenAI Codex",
+  "original_archive": {
+    "filename": "integer_mult_round23_gauge44_delta.zip",
+    "sha256": "40a20a120f51cbed3c9ae4017603be74a9e9332ad4068bd914bf3e81bf8be6b4",
+    "manifest_sha256": "ffa23eb668ad558ebb5601470fc1997a9fb8cea0e188aa3c5d61318be9000603"
+  },
+  "upstream_main": "17ce0c79b7b51c2634b439ea5a2b754f09909693",
+  "construction_parent": {
+    "pr": 635,
+    "commit": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f"
+  },
+  "bit_supplier_pr": 589,
+  "packaging_changes": [
+    "Omit original run logs; retain their original receipts as historical evidence.",
+    "Use repository paths and dollar-delimited Markdown mathematics.",
+    "Add manifest verification, incremental CI and local validation record.",
+    "Trim trailing whitespace in four Python files; complete ASTs are unchanged. Refresh the corresponding constructor input hash.",
+    "research/gauge44-bit589: PR589 bit supplier (G44Stack port, Bit589Reviewer SOUND-WITH-FIXES), G44Pack dz1 owner map, re-derived SPEC, LF line endings, regenerated MANIFEST.",
+    "research/gauge44-leaver: research/gauge44-barch tree plus construction/leaver (k5 cells, chain, frames); G44Pack3 FO_c1 owner map, re-derived SPEC, regenerated independent price receipt, RESULT.json = strict REPLAY, LF, regenerated MANIFEST.",
+    "research/gauge44-leaver8: research/gauge44-leaver tree with the k8 cell set (all eight cells, R = 480) and its chain recipes (LeaverSAT/LeaverSAT2 pkg_k8), layer_end_controls_leaver v2 with declared not-applicable sites on all five stack words (replacing the final-word interim skip), CHAIN-PINS-k8; G44Pack3 K8c8 owner map, re-derived SPEC, regenerated independent price receipt and local audit, RESULT.json = strict REPLAY, LF, regenerated MANIFEST."
+  ],
+  "attribution": "Original notices and licenses retained. See NOTICE.md, UPSTREAM-NOTICE.md and CONSTRUCTION.md.",
+  "whitespace_only_python_files": [
+    "code/audit_allcold.py",
+    "code/bind_providers_portable.py",
+    "construction/construct_gauge_xcentre.py",
+    "independent/audit_local.py"
+  ],
+  "historical_bit_supplier_pr": 543,
+  "bit_supplier_note": "This package cites PR589 (inputs/PR589-EXPECTED.json, git blob e293ddc5…). PR543 is the supplier of #645's retained historical evidence (LOCAL-VALIDATION.json, independent/ audit files, hosting/, evidence/). RESULT.json is this package's strict replay.",
+  "owner_map": "G44Pack/G44Pack3: The map is G44Pack3's K8c8, from its pattern-flow LNS (`pflns`) on the R = 480 k8 word. Its lineage is the #685/#741 map (chafreaky) via G44Pack's relabel and rewidth, followed by G44Pack3's LNS. It was admitted with this package's own code (NEWWORD discovery, `freeze_spec.py`, strict) at κ 0.001671387264390146.",
+  "construction_changes": "PartialK: no-triangle gauge44 word (R=504, PRIO6, ranks [4]*14); G44Stack: layers on it (pivot swaps, s4, x30, b6, q4); LeaverSAT: no-helper mutable-leaver cells and re-stacked recipes, LeaverSAT2: frame re-optimisation (construction/leaver); NewBArch: triangle-hybrid B rewrite U8 (construction/barch); chafreaky #741: eight B frames (construction/frames, ported by CompetitorMine) and the owner map; JointXF: joint exchange X4 (construction/jx); BRoute: read-set exchange SW4 (construction/sw4); NoTriReopen: p6n ends (construction/layers_p6n); BlockInvert: entrance promotions E4->E5 (construction/promo, minimal recipe p6n-k4); drivers construction/notri/reproduce_notri.py, construction/layers_np/reproduce_np.py, construction/promo/reproduce_promo.py"
+}
diff --git a/research/gauge44-slots/UPSTREAM-NOTICE.md b/research/gauge44-slots/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..ebc24a0168
--- /dev/null
+++ b/research/gauge44-slots/UPSTREAM-NOTICE.md
@@ -0,0 +1,34 @@
+# Attribution and scope
+
+Four verified provider types are offered to every call: PR571's prefix word with twelve multi-cut cold kernels (PR568's unchanged constructor), the same word with forty width-five entrance promotions (PR569's unchanged frame constructor) before those kernels, PR575's plain joint-prefix provider, and PR568's eight-cold provider. A window MILP with an exact per-pattern model chooses the dispatch and a literal owner map. PR583's six source-bound kernel frame coalescences (its unchanged constructor and negative controls) are applied to every PR571-prefix provider word (ck and atm3), followed by two further coalescences that each first move one addition past two commuting additions (package code/build_gate_moves.py, extending PR583's constructor); a final hyperplane_end step (package code/build_hpe.py) then runs 46 single-gate cleanups h -= p right after part B at the dim-8 join U of their registers, so 46 width-8 entering helpers per call end at U with width 7; each such gate commutes with every earlier cleanup gate on its registers (for 8 of them the partner's one earlier gate x -= p only reads p), and the reordered program is replayed exactly. A window MILP (exact windows, RINS around an LP vertex) gives the dispatch ck 45 / atm3 21 / jp8 6 and the literal owner map.
+
+Pinned external sources (unchanged; `verify.py` checks their manifests and every file it uses):
+- PR568 (`research/complex-multicold`, commit `71c99ac935a33bb7b59a1b4a7af8725a939b0b90`).
+- PR571 (`research/structural-gain`, commit `b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3`).
+- PR569 (`research/larger-gain`, commit `897213a855b7fb8a1b8b0e552a2f5c42e6c1b326`).
+- PR575 (`research/complex-joint-prefix`, commit `eac6f7e378ab622dac50a2fd4b7ef6eab014de44`).
+- PR583 (`research/kernel-frame-coalescing`, commit `89be768f0157f5a3d8e4db69cf1748768605eac9`).
+
+Provider construction is described as typed steps in `data/SPEC.json` (`build`); `verify.py` runs only allowlisted step types with their paired omission audits and checks every input and output content hash. `code/` holds the spec-driven global admission scripts adapted from PR571's `frontier-composition/global-code/` (OpenAI Codex assisted, Apache-2.0): every expected value is read from `data/SPEC.json` and compared only after independent recomputation. `code/generated_identity.py` and `code/generated_identity_controls.py`, and the decompressed-content artifact identities in the bind, audit, invoice, assembly and phase-timing scripts, are taken unchanged from PR586 by chafreaky (`research/promoted-kernel-coalescing`, commit `4846fee5b06af770e9b3a10c36200f673d656725`, OpenAI Codex assisted, Apache-2.0), including its proof-content and reference/metadata mutation controls; the normalization of descriptive width metadata after frame changes follows the same PR.
+
+In PR601, the owner map was nominated by a HiGHS window MILP (adapted from PR569's `global/nominate_width7.py`) with lazy cross-time Hall cuts; this package's re-solved map is described below. Neither is an admission dependency.
+
+DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. (The PR601 package this one starts from states: "Prepared by Claude Code (Anthropic) research agents.") Apache-2.0 applies; LICENSE is included. All notices, licenses, source pins and AI disclosures of the pinned sources and their ancestry are retained in those packages and are not replaced by this notice. All inherited conditional assumptions remain conditional.
+
+**This package (complex-571-cold14, DreamingOfClouds).** It starts from PR601 (jeremykothe2, `research/complex-571-hpem46`, commit `529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550`). Everything above is kept unchanged except the following:
+- every provider chain (ck, atm3, jp8) gains the typed step `cold_end` (`code/build_cold_end.py`, `code/cold_end_controls.py`; recipes `data/recipes/*-cold_end.json.gz`);
+- the generalised native chain and the global admission scripts accept cold helpers that end below FULL (with `0:U` wrappers), a refactored exact cleanup, and check the wrapper order;
+- `data/PLAN.json` / `data/OWNERS.json.gz` (dispatch and literal owner map) come from a relocate/swap/ejection-chain/provider-flip annealing search started from PR601's map, refined by an exact pattern-restricted owner model (CP-SAT) with a literal edge-colouring expansion (not an admission dependency);
+- `data/SPEC.json` holds the expected values, recorded by a discovery run and then checked by a strict run.
+
+The cold-end construction (a row-plus-column cone condition for low-frame ends, a rank-0 dirt-spread premix and multi-gate lower-frame cleanup) builds on PR591 / PR592 / PR593 / PR601 (jeremykothe2) and our PR599 (Lean: multi-gate and cold hyperplane-end tails). DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. Build on this at your own risk.
+
+**This package (complex-571-cold14-b3, jeremykothe2).** It is PR604's `complex-571-cold14` (DreamingOfClouds) with ColdBeyond's second cold end per block (two new `cold_end` A-gate primitives, `PROOF-NOTE.md`), ColdSupply's E1 entering pair and reviewed controls, a free dispatch (jp8 ×60, atm3 ×12) and a literal owner map from an exact per-time-Hall window MIP. All other construction, code, controls and proofs are PR604's and earlier contributors', unchanged.
+
+**This package (complex-571-cold14-k492).** It is complex-571-cold14-b3 with these changes:
+- **K-triangle base words.** The leaver-read K-triangle skeleton atom and its read schedule (`data/TRI-SCHEDULE.json`) are by AtomScout, a Claude Code research agent. `code/construct_k_triangle.py` is PR531's `code/construct_504.py` (icekylinx, OpenAI Codex / GPT assisted, Apache-2.0; pinned source `direct_delivery`) extended with that atom.
+- **Ported chains.** The PR604/B3 chains are ported stage by stage onto the K-triangle words by `code/build_port_stage.py` (Port480, a Claude Code research agent). `code/build_frame_regroup.py` extends PR583's `build_frames.py` (chafreaky).
+- **Helper count R.** The generalisation of the global scripts to the provider helper count R is by GlobalR (a Claude Code research agent), with AtomReviewer's fixes (PROOF-NOTE-R.md).
+- **Owner map.** The owner map, the cold_end recipes on the K-triangle words and the package assembly are by Stack492, Port480 and ColdBeyond (Claude Code research agents).
+
+Build on this at your own risk.
diff --git a/research/gauge44-slots/code/assemble.py b/research/gauge44-slots/code/assemble.py
new file mode 100644
index 0000000000..8cee90b50e
--- /dev/null
+++ b/research/gauge44-slots/code/assemble.py
@@ -0,0 +1,241 @@
+"""Gauge44 complete global admission with the retained native exact-complex moment.
+
+Prepared with OpenAI Codex assistance. The rational engines and outer
+constraints are retained from PR547/PR548 and their preserved ancestry.
+The bit operator is the cited unchanged PR589 supplier (PR555's punctured
+R439 word, v = 111, decoder constant 63, two A-section transports), shipped
+as inputs/PR589-EXPECTED.json and pinned by git blob id. Its rank-mass
+deficit is derived from the word's parameters, T(2Kv - L*cst) at nine
+stages (PR545/PR555 rank-mass identity), not hard-coded. The complex owner
+and invoice inputs must be freshly emitted by the packaged physical replay.
+All conservative admission guards and conservative moment/outer witnesses run
+before the PR559 native-complex correction. The bit surcharge is retained.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from decimal import Decimal, localcontext
+import argparse,json,hashlib,importlib.util,os,sys
+from collections import Counter
+assert __debug__, 'Assertions required'
+P=Path(sys.argv[1] if __name__=='__main__' else os.environ['GAIN_PR564_SOURCE']).resolve()
+read=lambda p:json.loads(p.read_text())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+hash_ok=lambda x:isinstance(x,str) and len(x)==64 and all(t in '0123456789abcdef'for t in x)
+digest=lambda x:hashlib.sha256(json.dumps(x,separators=(',',':')).encode()).hexdigest()
+def load(n):
+ s=importlib.util.spec_from_file_location(n,P/'engines'/(n+'.py'));m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,B,A=[load(n)for n in ('moment','base_two_moment','outer')]
+def dec(x):
+ with localcontext()as ctx:ctx.prec=70;return str(Decimal(x.numerator)/Decimal(x.denominator))
+from witness import DISPATCH,CALL_ORDER,COUNTS,PIDS,X,DISCOVER,pin,SPOT,spot_widths
+# Cited bit supplier: PR589's tune/EXPECTED.json (merged on main as research/e8-bit-p111-tuned/tune/EXPECTED.json).
+BIT_PATH=Path(__file__).resolve().parents[1]/'inputs/PR589-EXPECTED.json'
+BIT_BLOB='e293ddc557742637f9f679f083a1a282d87b1b13'
+# Nine-stage bit template (PR463/PR510 chain, 32 replicas): L stages, T replicas, K=(L-1)//2 pairs, moment width M=1+7L.
+BIT_L,BIT_T=9,32;BIT_K=(BIT_L-1)//2;BIT_M=1+7*BIT_L
+def git_blob(data):return hashlib.sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest()
+def load_bit(data):
+ """The pinned supplier record: its full record (word parameters) and its nine-stage price."""
+ assert git_blob(data)==BIT_BLOB,'bit supplier blob pin'
+ return json.loads(data)
+def bit_deficit(word,live):
+ """Rank-mass deficit M*live - mass = T(2Kv - L*cst) of a v-port bit word with decoder constant cst (PR545/PR555).
+ cst is the sum of the retained totals' COPY ranks and live = 2KvT data wires; both are cross-checked here, and the
+ caller checks the result against the priced profile, so neither v nor cst is free."""
+ v,cst,ranks=word['v'],word['decoder_constant'],word['copy_ranks']
+ assert type(v)is int and type(cst)is int and all(type(r)is int and 0<r<=8 for r in ranks)
+ assert len(ranks)==word['retained_totals']==BIT_L and cst==sum(ranks)
+ assert live==2*BIT_K*v*BIT_T
+ d=BIT_T*(2*BIT_K*v-BIT_L*cst);assert d>0;return d
+
+
+def assemble(owner,invoice,owner_sha,invoice_sha):
+ # These are admission receipts, not optional collections of successful rows.
+ # Require both orientations and every finite check before pricing anything.
+ assert owner['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE'
+ assert invoice['status']=='PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE'
+ assert all(hash_ok(x)for x in (owner_sha,invoice_sha,owner['template_sha256'],owner['controller_audit_sha256'],invoice['parent_template_sha256']))
+ checks={'local_primitive_bound','logical','router','literal','mass','precision','tape','row','halving'}
+ assert set(invoice['strict_checks'])==checks
+ assert all(invoice['strict_checks'][name] is True for name in checks)
+ assert set(invoice['providers'])==set(PIDS)
+ assert invoice['provider_counts']==COUNTS
+ assert owner['all_live_owners_per_call_distinct'] is True
+ # R (helpers per provider word) is read from the invoice and must be shared by every provider; n=2v+R.
+ R=invoice['helpers'];assert type(R) is int and R>0 and all(p['helpers']==R for p in invoice['providers'].values())
+ assert owner['owners_per_call']==2*112+R and owner['actual_helper_owner_charts']==owner['hosted_residuals']==72*R==pin('expected.hosted_residuals',owner['hosted_residuals'])
+ pin('expected.rank_mass',owner['rank_mass'])
+ pin('expected.actual_73column_sigmas',owner['actual_73column_sigmas']);pin('expected.cross_replica_helper_roles',owner['cross_replica_helper_roles'])
+ pin('expected.idle_remainders',owner['explicit_idle_remainder_children'])
+ assert invoice['complete_invocation_sweeps']==invoice['bridge_sweeps']==72
+ assert invoice['live']==owner['live'] and invoice['physical']==owner['physical']
+ assert invoice['centres']==8
+ assert invoice['physical_stock_identity']==dict(data_and_owner_families=7168,local_helpers=R,private_centres=8,coefficient_work=2)
+ assert sum(invoice['physical_stock_identity'].values())==invoice['physical']
+ assert invoice['controller_audit_sha256']==owner['controller_audit_sha256']
+ for pid,p in invoice['providers'].items():
+  assert set(p['local'])=={'forward','backward'}
+  assert p['helpers']==R and p['centres']==8 and p['n']==2*112+R and p['v']==112 and p['h']==9
+  K='providers.'+pid+'.';pin(K+'entering',p['entering_helpers']);pin(K+'entrance',p['entrance_rank'])
+  pin(K+'inventory',p['width_inventory'])
+  assert all(type(w) is int and 0<w<=9 for w in p['widths'])
+  assert Counter(p['widths'])==Counter({int(r):n for r,n in p['width_inventory'].items()})
+  assert sum(p['widths'])==9*R-p['entrance_rank']-p['terminal_codimension'] and len(p['widths'])==R   # HPE: widths |final|-|start|
+  pin(K+'width_digest',digest(p['widths']));assert tuple(p['widths'][h]for h in SPOT)==spot_widths()
+  pin(K+'expected_profile',p['paid_profile'])
+  assert p['children']==sum(p['paid_profile'].values())
+  pin(K+'program_hashes',p['program_hashes'])
+  for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json'):
+   assert hash_ok(p['artifacts'][name]) and p['artifacts'][name]==owner['source_artifacts']['providers/'+pid+'/'+name]
+   if name in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):pin(K+'artifacts.'+name,p['artifacts'][name])
+  pin(K+'artifact_semantic_sha256',p['semantic_artifact_sha256'])
+  pin(K+'complete_contract',{k:v for k,v in p.items()if k!='artifacts'})
+  assert owner['provider_artifact_semantic_sha256'][pid]==p['semantic_artifact_sha256']
+  pin(K+'semantic_phase_sha256',p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'])
+  assert owner['provider_phase_semantic_sha256'][pid]==invoice['provider_phase_semantic_sha256'][pid]==p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']
+  for name in ('forward','backward'):
+   z=p['local'][name];pinned=pin(K+'expected_local.'+name,{k:z[k]for k in('events','macros','real_component_primitives','prefix_l1','coefficient_work_primitive_count')});primitives=pinned['real_component_primitives'];coefficient_work=pinned['coefficient_work_primitive_count']
+   assert z['all_dirty_helper_columns_restored'] is True and z['private_centres_and_coefficient_work_cleared'] is True
+   assert z['all_exact_columns']==2*112+R and z['dirty_helper_columns']==R
+   assert z['events']==pinned['events'] and z['macros']==pinned['macros']
+   assert z['real_component_primitives']==primitives and z['coefficient_work_primitive_count']==coefficient_work
+   assert z['pre_wrappers']==z['post_wrappers']==p['entering_helpers']+p.get('cold_hyperplane_ended_helpers',0);pin(K+'wrappers',z['pre_wrappers'])   # COLD-HPE
+   assert 0<z['prefix_bits']<=192 and 0<Q(z['prefix_l1'])<2**192
+   peak=Q(z['prefix_l1']);assert z['prefix_bits']==peak.numerator.bit_length()-peak.denominator.bit_length()+1
+   assert peak==Q(pinned['prefix_l1'])
+  assert p['compiler']==64*74**3
+  assert p['local_adapters']==16*(max(z['macros']for z in p['local'].values())+p['children']+2*112+R+8)+64*73
+  assert p['local_primitive_bound']==max(z['real_component_primitives']for z in p['local'].values())+p['local_adapters']*p['compiler']
+ calls=invoice['selected_calls'];assert len(calls)==72
+ assert [(c['stage'],c['replica'])for c in calls]==CALL_ORDER
+ assert {(c['stage'],c['replica']) for c in calls}=={(s,r) for s in range(9) for r in range(8)}
+ for c in calls:
+  pid=DISPATCH[c['stage'],c['replica']]
+  assert c['provider_id']==pid
+  # The retained nine-stage recipe alternates its two reflected shears.
+  assert c['orientation']==('forward' if c['stage']%2==0 else 'backward')
+  p=invoice['providers'][pid];z=p['local'][c['orientation']]
+  assert c['program_sha256']==p['program_hashes'][c['orientation']]
+  for name in ('events','macros','real_component_primitives','coefficient_work_primitive_count','pre_wrappers','post_wrappers'):
+   assert c[name]==z[name]
+  assert c['entering_helpers']==p['entering_helpers'] and c['entrance_rank']==p['entrance_rank']
+ assert invoice['selected_real_component_primitives']==sum(c['real_component_primitives'] for c in calls)
+ assert invoice['selected_coefficient_work_primitive_count']==sum(c['coefficient_work_primitive_count'] for c in calls)
+ assert invoice['selected_scalar_macros']==sum(c['macros'] for c in calls)==sum(invoice['providers'][c['provider_id']]['local'][c['orientation']]['macros'] for c in calls)
+ assert invoice['factors_per_wrapper']==144
+ assert invoice['wrapper_elementary_factors_charged']==sum(c['pre_wrappers']+c['post_wrappers'] for c in calls)*144
+ paid=Counter()
+ for c in calls:paid.update({int(r):n for r,n in invoice['providers'][c['provider_id']]['paid_profile'].items()})
+ assert dict(paid)=={int(r):n for r,n in invoice['selected_local_paid_profile'].items()}
+ idle=Counter({int(r):n for r,n in owner['paid_profile'].items()});idle.subtract(paid);assert all(n>=0 for n in idle.values())
+ idle=+idle;assert sum(idle.values())==owner['explicit_idle_remainder_children']
+ pin('expected.idle_remainder_profile',{str(r):n for r,n in sorted(idle.items())})
+ paid.update(idle)
+ assert dict(paid)=={int(r):n for r,n in owner['paid_profile'].items()}
+ assert invoice['compiler']==64*74**3
+ assert invoice['local_adapters']==max(p['local_adapters']for p in invoice['providers'].values())
+ assert invoice['local_primitive_bound']==max(p['local_primitive_bound']for p in invoice['providers'].values())
+ # Recount the retained dedicated-bank envelope independently. Its geometry
+ # stays fixed, while every local primitive and wrapper comes from the actual
+ # selected provider/orientation sums above.
+ parent_live,parent_physical,parent_idle=11704,12218,16128
+ parent_banks,rem=divmod(parent_live-2*112*4*8,9);assert rem==0 and parent_physical==parent_live+parent_banks+8+2   # parent R0=504 dedicated helpers per stage bank
+ assert owner['source_idle_children_charged']==parent_idle
+ bridges,shifts=2*112*72,4*112*8;moves=2*shifts
+ nonlocal_items=(4*112*8*9+2*112*8*9+2*72*R+parent_idle+9*parent_banks+bridges+shifts+moves+parent_live+parent_physical+invoice['wrapper_elementary_factors_charged'])
+ outside=8*nonlocal_items+64*73
+ pervertex=(invoice['selected_real_component_primitives']+bridges+shifts+moves+parent_live+(72*invoice['local_adapters']+outside)*invoice['compiler']+64*parent_physical)
+ rebased=pervertex+65*(invoice['physical']-parent_physical)+(invoice['live']-parent_live)
+ assert invoice['unhosted_pervertex']==pervertex and invoice['hosted_rebased_pervertex']==rebased
+ used=max(pervertex,rebased)
+ prior=invoice['retained_prior_overcharge']
+ if prior is not None:
+  assert hash_ok(prior['sha256']) and type(prior['previous_pervertex_allowance']) is int and prior['previous_pervertex_allowance']>0
+  assert prior['added_complete_new_pervertex']==pervertex
+  assert prior['policy']=='Retain old allowance and add entire fresh mixed recount.'
+  used=max(used,prior['previous_pervertex_allowance']+pervertex)
+ assert invoice['conservative_pervertex_used']==used
+ finite=invoice['finite']
+ assert 0<finite['physical_row_coefficient']<finite['retained_row_coefficient']==20161
+ assert 0<finite['required_C0_bits']<finite['C0_exponent']==210000
+ assert finite['G_exponent']==30000 and finite['E_exponent']==100000
+ assert finite['halving_integer_inequality']==[5329,4608]
+ assert 0<invoice['global_prefix_bits']<=invoice['charged_prefix_bits']==512
+ assert invoice['row_prefix_extra']==1024
+ assert invoice['global_prefix_bits']==max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())+37+72+72+4
+ group=2**(36*36)
+ for j in range(1,37):group*=2**(2*j)-1
+ stock=group*invoice['physical'];streamed_mass=group*owner['rank_mass']
+ logical=group*used+64;router=invoice['compiler']*(logical+1)*(stock+1)**2
+ literal=2*2**30000*stock**2+8*streamed_mass+4*stock+4+32*73
+ total_mass=streamed_mass+2**100000
+ assert finite['physical_stock_bits']==stock.bit_length() and finite['router_bits']==router.bit_length() and finite['literal_bits']==literal.bit_length()
+ assert finite['physical_row_coefficient']==2*stock.bit_length()+9909+252+1024
+ assert finite['required_C0_bits']==(32*73*total_mass*total_mass).bit_length()
+ actual_checks=dict(local_primitive_bound=invoice['local_primitive_bound']<2**48,logical=logical<2**6050,router=router<2**30000,literal=literal<2**100000,mass=total_mass<2**100001,precision=32*73*total_mass*total_mass<2**210000,tape=2*total_mass+18<2**210000,row=finite['physical_row_coefficient']<20161,halving=73*73>2*48*48)
+ assert actual_checks==invoice['strict_checks'] and all(actual_checks.values())
+ bit_record=load_bit(BIT_PATH.read_bytes())
+ bit=bit_record['nine']
+ assert 'nine-stage' in bit['pipeline'] and '32 replicas' in bit['pipeline']
+ c=Q(bit['bit_lower'])
+ bit_D=bit_deficit(bit_record['word'],bit['bit']['live'])
+ H={int(r):n for r,n in owner['paid_profile'].items()};pin('expected.global_profile',owner['paid_profile'])
+ # Claimed lower endpoints come from the spec; discovery derives them with the same certified moment engine.
+ # Either way they are verified below (accepted at b, rejected at b+1e-24).
+ if DISCOVER:b=Q(M.certify(H,73,owner['live'],False)['lower']);conservative_b=Q(M.certify(H,73,owner['live'],True)['lower'])
+ else:b=Q(X['complex_lower']);conservative_b=Q(X['conservative_complex_lower'])
+ assert owner['template_sha256']==invoice['template_sha256'] and owner_sha==invoice['owner_audit_sha256']
+ pin('expected.live',owner['live']);pin('expected.physical',owner['physical']);assert owner['deficit']==2560
+ assert owner['banked_residuals']==0
+ def check_moment(side,h,m,W,lower,deficit,bad):
+  assert m*W-sum(r*n for r,n in h.items())==deficit and m*m>2*max(h)**2
+  rows=[]
+  for z,accept in [(lower,True),(lower+Q(1,10**24),False)]:
+   l,u=M.moment(h,m,W,z,bad);ll,uu=B.moment(m,W,list(h.items()),z)
+   if bad:
+    fl,fu=B.moment(m,W,[(1,32*m*m*sum(h.values()))],z);ll+=fl/10**16;uu+=fu/10**16
+   assert (u<1 and uu<1)if accept else(l>1 and ll>1)
+   rows.append(dict(side=side,surcharge=bad,endpoint=str(z),accept=accept,mercator=[str(l-1),str(u-1)],base_two=[str(ll-1),str(uu-1)]))
+  return rows
+ bitH={int(r):n for r,n in bit['profile'].items()}
+ assert BIT_M==64 and sum(r*n for r,n in bitH.items())==bit['bit']['rank_mass']
+ bit_moments=check_moment('bit',bitH,BIT_M,bit['bit']['live'],c,bit_D,True)
+ conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,2560,True)
+ assert bit['bit']['two_level_coefficient_bits']<bit['bit']['charged_two_level_coefficient_bits']==512 and bit['bit']['row_coefficient']<20161
+ def outer_witness(bb):
+  eta=beta=Q(1,10**24);s=min(c,(1-beta)*bb)-Q(1,10**27);assert 0<s<c and s<(1-beta)*bb
+  chain=[Q(384599,10**10)];cuts=[]
+  for _ in range(7):
+   old=chain[-1];a=(1-s)*s+s*old;gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+   ceil=lambda x:-(-x.numerator//x.denominator);cut=max(ceil(36/gap**2),ceil(2*(4+512)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+512)
+   cuts.append(dict(exponent=str(a),gap=str(gap),cutoff_log2=str(cut)));chain.append(a)
+  q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin*10**18;k=Q((ticks.numerator-1)//ticks.denominator,10**18)
+  bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}
+  outer=A.assembly(chain[-1],bb,bridge,k,eta=eta,beta=beta);assert len(outer['strict_constraints'])==47 and all(v>0 for v in outer['strict_constraints'].values())
+  controls=[]
+  for name,kk,ee,be in [('next_grid',k+Q(1,10**18),eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]:
+   try:A.assembly(chain[-1],bb,bridge,kk,eta=ee,beta=be)
+   except AssertionError:controls.append(name)
+   else:raise AssertionError(name)
+  return k,cuts,outer,controls
+ conservative_k,conservative_cuts,conservative_outer,conservative_controls=outer_witness(conservative_b)
+ pin('expected.conservative_kappa_decimal',dec(conservative_k))
+ # Only after every conservative supplier/admission/outer check succeeds is
+ # the reviewed native exact-complex recurrence selected. Bit charge stays.
+ native_moments=check_moment('complex',H,73,owner['live'],b,2560,False)
+ k,cuts,outer,controls=outer_witness(b)
+ pin('expected.kappa_decimal',dec(k))
+ assert M.moment(H,73,owner['live'],b,True)[0]>1
+ assert M.moment(bitH,64,bit['bit']['live'],c+Q(1,10**24),False)[1]<1
+ model_controls=['native_complex_endpoint_rejected_with_old_surcharge','omitting_bit_surcharge_would_fail_next_endpoint_rejection']
+ moments=bit_moments+native_moments
+ input_hashes={'owner_audit':owner_sha,'fresh_invoice':invoice_sha,'package:inputs/PR589-EXPECTED.json':sha(BIT_PATH)}
+ input_hashes.update({'engines/'+name+'.py':sha(P/'engines'/(name+'.py'))for name in ('moment','base_two_moment','outer')})
+ return dict(status='PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY',kappa=str(k),kappa_decimal=dec(k),complex_lower=str(b),complex_decimal=dec(b),bit_lower=str(c),bit_decimal=dec(c),binding='complex',gain_over_pr635_percent=dec(100*(k/Q(X['gain_baseline_kappa'])-1)),complex_profile=H,provider_counts=invoice['provider_counts'],surcharge_model={'complex':False,'bit':True},conservative_complex_lower=str(conservative_b),conservative_complex_decimal=dec(conservative_b),conservative_kappa=str(conservative_k),conservative_kappa_decimal=dec(conservative_k),conservative_moments=conservative_moments,conservative_bootstrap=conservative_cuts,conservative_outer={n:str(v)for n,v in conservative_outer['strict_constraints'].items()},conservative_controls=conservative_controls,model_controls=model_controls,native_correction_gain=dec(k-conservative_k),template_sha256=owner['template_sha256'],input_sha256=input_hashes,bit_supplier=dict(pr=589,repository='CrocSwap/integer-mult-bounds',commit='a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46',merged_as='b3eb785ac5b4b1ca2beea0f80db078a505626a90',path='research/e8-bit-p111-tuned/tune/EXPECTED.json',git_blob_sha1=BIT_BLOB,word=dict(v=bit_record['word']['v'],decoder_constant=bit_record['word']['decoder_constant'],copy_ranks=bit_record['word']['copy_ranks']),derived_deficit=bit_D,deficit_formula='T(2Kv-L*cst), L=%d T=%d K=%d M=%d'%(BIT_L,BIT_T,BIT_K,BIT_M),replay_scope='Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit.'),moments=moments,bootstrap=cuts,outer={n:str(v)for n,v in outer['strict_constraints'].items()},controls=controls,scope='Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; this bit composition is unreviewed. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification.')
+if __name__=='__main__':
+ import sys
+ package,C,out=map(Path,sys.argv[1:4]);assert package.resolve()==P and not out.exists()
+ owner_path=C/'audit/OWNERS-AND-PROFILE.json';invoice_path=C/'audit/PREFIX-AND-INVOICE.json'
+ owner,invoice=read(owner_path),read(invoice_path)
+ assert owner['template_sha256']==read(C/'hosted/HOSTED.json')['template_sha256']
+ r=assemble(owner,invoice,sha(owner_path),sha(invoice_path));out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],r['kappa_decimal'])
diff --git a/research/gauge44-slots/code/assembly_controls.py b/research/gauge44-slots/code/assembly_controls.py
new file mode 100644
index 0000000000..93bca1ce6f
--- /dev/null
+++ b/research/gauge44-slots/code/assembly_controls.py
@@ -0,0 +1,260 @@
+"""Independent admission controls for the N-provider native-complex assembly (per-provider controls).
+
+Prepared with OpenAI Codex assistance; Apache-2.0. Mutation receipts are
+rebound to their new owner digest, so unrelated stale hashes cannot conceal
+an incomplete width, provider, orientation, paid-profile or finite check.
+The fresh physical replay remains a separate prerequisite.
+"""
+import argparse
+import copy
+import itertools
+import math
+import hashlib
+import json
+import os
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+
+assert __debug__, 'Assertions required'
+P = Path(__file__).resolve().parent
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+digest = lambda x: hashlib.sha256(json.dumps(x, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+
+
+def verify(owner_path, invoice_path, source_package):
+    os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve())
+    from assemble import assemble
+    owner = json.loads(owner_path.read_text())
+    invoice = json.loads(invoice_path.read_text())
+    baseline = assemble(owner, invoice, sha(owner_path), sha(invoice_path))
+
+    def empty_maps(o, i):
+        i['strict_checks'] = {}
+        i['providers'] = {}
+
+    def understated_stock(o, i):
+        o['physical'] -= 1
+        i['physical'] -= 1
+        i['physical_stock_identity']['coefficient_work'] -= 1
+
+    def changed_profile(o, i):
+        o['paid_profile']['1'] += 2
+        o['paid_profile']['2'] -= 1
+
+    def wrong_orientation(o, i):
+        c = next(c for c in i['selected_calls'] if c['stage'] == 0)
+        c['orientation'] = 'backward'
+        p = i['providers'][c['provider_id']]
+        z = p['local']['backward']
+        c['program_sha256'] = p['program_hashes']['backward']
+        for name in ('events', 'macros', 'real_component_primitives',
+                     'coefficient_work_primitive_count', 'pre_wrappers', 'post_wrappers'):
+            c[name] = z[name]
+        i['selected_real_component_primitives'] = sum(c['real_component_primitives'] for c in i['selected_calls'])
+        i['selected_coefficient_work_primitive_count'] = sum(c['coefficient_work_primitive_count'] for c in i['selected_calls'])
+
+    def understated_prefix(o, i):
+        for p in i['providers'].values():
+            for z in p['local'].values():
+                z['prefix_bits'], z['prefix_l1'] = 1, '1'
+        i['global_prefix_bits'] = 1 + 37 + 72 + 72 + 4
+
+    def reordered_calls(o, i):
+        i['selected_calls'][0], i['selected_calls'][1] = i['selected_calls'][1], i['selected_calls'][0]
+
+    def no_cold_wrappers(o, i):
+        for p in i['providers'].values():
+            p['entering_helpers'] -= 4
+            for z in p['local'].values():z['pre_wrappers'] = z['post_wrappers'] = p['entering_helpers']
+        for c in i['selected_calls']:
+            c['entering_helpers'] = c['pre_wrappers'] = c['post_wrappers'] = i['providers'][c['provider_id']]['entering_helpers']
+        i['wrapper_elementary_factors_charged'] = sum(2*c['pre_wrappers'] for c in i['selected_calls'])*i['factors_per_wrapper']
+
+    controls = [
+        ('empty_certification_maps', empty_maps),
+        ('failed_invoice_status', lambda o, i: i.__setitem__('status', 'FAIL')),
+        ('nonboolean_precision_check', lambda o, i: i['strict_checks'].__setitem__('precision', 'true')),
+        ('wrong_owner_role_count', lambda o, i: o.__setitem__('actual_helper_owner_charts', o['actual_helper_owner_charts'] - 1)),
+        ('understated_physical_stock', understated_stock),
+        ('changed_profile_same_rank_mass', changed_profile),
+        ('insufficient_finite_C0', lambda o, i: i['finite'].__setitem__('required_C0_bits', 210001)),
+        ('missing_finite_check', lambda o, i: i['strict_checks'].pop('halving')),
+        ('wrong_reflected_orientation_selfconsistent_totals', wrong_orientation),
+        ('missing_selected_call', lambda o, i: i['selected_calls'].pop()),
+        ('wrong_selected_primitive_sum', lambda o, i: i.__setitem__('selected_real_component_primitives', i['selected_real_component_primitives'] - 1)),
+        ('wrong_selected_coefficient_work_sum', lambda o, i: i.__setitem__('selected_coefficient_work_primitive_count', i['selected_coefficient_work_primitive_count'] - 1)),
+        ('unpaid_wrapper_factors', lambda o, i: i.__setitem__('wrapper_elementary_factors_charged', i['wrapper_elementary_factors_charged'] - 144)),
+        ('wrong_global_compiler', lambda o, i: i.__setitem__('compiler', 1)),
+        ('wrong_global_adapter_maximum', lambda o, i: i.__setitem__('local_adapters', 1)),
+        ('understated_exact_prefix_and_global_sum', understated_prefix),
+        ('wrong_global_prefix_sum', lambda o, i: i.__setitem__('global_prefix_bits', 224)),
+        ('wrong_row_prefix_reserve', lambda o, i: i.__setitem__('row_prefix_extra', 0)),
+        ('wrong_parent_geometry_charge', lambda o, i: i.__setitem__('unhosted_pervertex', 1)),
+        ('wrong_rebased_geometry_charge', lambda o, i: i.__setitem__('hosted_rebased_pervertex', 1)),
+        ('wrong_complete_pervertex_envelope', lambda o, i: i.__setitem__('conservative_pervertex_used', 1)),
+        ('wrong_prior_added_complete_invoice', lambda o, i: i['retained_prior_overcharge'].__setitem__('added_complete_new_pervertex', 1)),
+        ('wrong_finite_router_bits', lambda o, i: i['finite'].__setitem__('router_bits', 1)),
+        ('wrong_finite_literal_bits', lambda o, i: i['finite'].__setitem__('literal_bits', 1)),
+        ('wrong_finite_physical_stock_bits', lambda o, i: i['finite'].__setitem__('physical_stock_bits', 1)),
+        ('wrong_finite_row_coefficient', lambda o, i: i['finite'].__setitem__('physical_row_coefficient', 1)),
+        ('reordered_complete_calls', reordered_calls),
+        ('understated_explicit_idle_remainders', lambda o, i: o.__setitem__('explicit_idle_remainder_children', o['explicit_idle_remainder_children']-1)),
+        ('understated_actual_chart_types', lambda o, i: o.__setitem__('actual_73column_sigmas', o['actual_73column_sigmas']-1)),
+        ('wrong_cross_replica_role_count', lambda o, i: o.__setitem__('cross_replica_helper_roles', o['cross_replica_helper_roles']-1)),
+        ('old_no_cold_wrapper_counts_selfconsistent', no_cold_wrappers),
+    ]
+
+    def resync(i, c):
+        p = i['providers'][c['provider_id']]
+        c['program_sha256'] = p['program_hashes'][c['orientation']]
+        c['entering_helpers'], c['entrance_rank'] = p['entering_helpers'], p['entrance_rank']
+        for name in ('events','macros','real_component_primitives','coefficient_work_primitive_count','pre_wrappers','post_wrappers'):
+            c[name] = p['local'][c['orientation']][name]
+
+    # Every provider gets the full per-provider control set, substituting a partner provider where needed.
+    for P in PIDS:
+        Qp = partner(P) if len(PIDS)>1 else '__unregistered__'
+        widths = invoice['providers'][P]['widths']
+
+        def forged_program_hash(o, i, P=P):
+            i['providers'][P]['program_hashes']['forward'] = '0' * 64
+            for c in i['selected_calls']:
+                if c['provider_id'] == P:
+                    c['program_sha256'] = '0' * 64
+
+        def wrong_selected_call(o, i, P=P):
+            c = next(c for c in i['selected_calls'] if c['provider_id'] == P)
+            d = next(d for d in i['selected_calls'] if d is not c and (d['provider_id'] != P or len(PIDS)==1) and (d['stage'] - c['stage']) % 2 == 0)
+            c['stage'], d['stage'], c['replica'], d['replica'] = d['stage'], c['stage'], d['replica'], c['replica']
+
+        def stale_program(o, i, P=P, Qp=Qp):
+            p = i['providers'][P]
+            p['program_hashes'] = copy.deepcopy(i['providers'][Qp]['program_hashes'])
+            for c in i['selected_calls']:
+                if c['provider_id'] == P:
+                    c['program_sha256'] = p['program_hashes'][c['orientation']]
+
+        def stale_profile(o, i, P=P, Qp=Qp):
+            p = i['providers'][P]
+            p['paid_profile'] = copy.deepcopy(i['providers'][Qp]['paid_profile'])
+            p['children'] = sum(p['paid_profile'].values())
+
+        def moved(o, i, P=P):
+            a = next(c for c in i['selected_calls'] if c['provider_id'] == P)
+            b = next(c for c in i['selected_calls'] if c['provider_id'] != P and c['orientation'] == a['orientation'])
+            a['provider_id'], b['provider_id'] = b['provider_id'], a['provider_id']
+            resync(i, a); resync(i, b)
+
+        def compensating(o, i, P=P, Qp=Qp):
+            # Two dishonest profiles that cancel exactly in the dispatch-weighted aggregate.
+            g = math.gcd(COUNTS[P], COUNTS[Qp]); dp, dq = COUNTS[Qp] // g, COUNTS[P] // g
+            p, q = i['providers'][P], i['providers'][Qp]
+            p['paid_profile']['1'] += dp; q['paid_profile']['1'] -= dq
+            p['children'] += dp; q['children'] -= dq
+
+        def forged_recipe(o, i, P=P):
+            name = 'CLIFFORD-RECIPES.json'
+            i['providers'][P]['artifacts'][name] = '0'*64
+            o['source_artifacts']['providers/'+P+'/'+name] = '0'*64
+
+        def forged_phase(o, i, P=P):
+            i['providers'][P]['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'] = '0'*64
+            o['provider_phase_semantic_sha256'][P] = i['provider_phase_semantic_sha256'][P] = '0'*64
+
+        controls += [
+            (P + ':missing_provider', lambda o, i, P=P: i['providers'].pop(P)),
+            (P + ':missing_backward_orientation', lambda o, i, P=P: i['providers'][P]['local'].pop('backward')),
+            (P + ':unpaid_scalar_primitive', lambda o, i, P=P: i['providers'][P]['local']['forward'].__setitem__('real_component_primitives', i['providers'][P]['local']['forward']['real_component_primitives'] - 1)),
+            (P + ':wrong_local_artifact_binding', lambda o, i, P=P: i['providers'][P]['artifacts'].__setitem__('LOCAL-PROGRAMS.json.gz', '0' * 64)),
+            (P + ':false_dirty_restoration', lambda o, i, P=P: i['providers'][P]['local']['backward'].__setitem__('all_dirty_helper_columns_restored', False)),
+            (P + ':wrong_declared_provider_count', lambda o, i, P=P: i['provider_counts'].__setitem__(P, i['provider_counts'][P] + 1)),
+            (P + ':wrong_local_compiler', lambda o, i, P=P: i['providers'][P].__setitem__('compiler', 1)),
+            (P + ':wrong_local_adapter_charge', lambda o, i, P=P: i['providers'][P].__setitem__('local_adapters', 1)),
+            (P + ':wrong_local_primitive_bound', lambda o, i, P=P: i['providers'][P].__setitem__('local_primitive_bound', 1)),
+            (P + ':forged_provider_and_call_program_hash', forged_program_hash),
+            (P + ':provider_at_wrong_call', wrong_selected_call),
+            (P + ':stale_partner_program_consistent_call_hashes', stale_program),
+            (P + ':stale_partner_profile_consistent_child_total', stale_profile),
+            (P + ':relocated_against_partner_same_counts', moved),
+            (P + ':compensating_false_profiles_with_' + Qp, compensating),
+            (P + ':synchronized_forged_source_recipe_hash', forged_recipe),
+            (P + ':synchronized_forged_phase_review_semantics', forged_phase),
+        ]
+        if len(PIDS)==1:
+            # Cross-provider substitutions require a second actual supplier.
+            # All single-provider program, phase, profile and dispatch bindings
+            # retain their direct mutations above and in the controller audit.
+            partner_only = {P+':stale_partner_program_consistent_call_hashes',
+                            P+':stale_partner_profile_consistent_child_total',
+                            P+':relocated_against_partner_same_counts',
+                            P+':compensating_false_profiles_with_'+Qp}
+            controls = [(name, fn) for name, fn in controls if name not in partner_only]
+        # Width order and inventory: swap the first helper of every pair of distinct widths (same inventory),
+        # and shift one unit between them (same total).
+        first = {}
+        for h, w in enumerate(widths):
+            first.setdefault(w, h)
+        for wa, wb in itertools.combinations(sorted(first), 2):
+            def swap(o, i, P=P, a=first[wa], b=first[wb]):
+                w = i['providers'][P]['widths']; w[a], w[b] = w[b], w[a]
+            def shift(o, i, P=P, a=first[wa], b=first[wb]):
+                w = i['providers'][P]['widths']; w[a] += 1; w[b] -= 1
+            controls.append((P + ':width_order_swap_%d_%d' % (wa, wb), swap))
+            controls.append((P + ':width_inventory_shift_%d_%d' % (wa, wb), shift))
+        for h in SPOT:
+            def cold_swap(o, i, P=P, h=h):
+                w = i['providers'][P]['widths']; j = w.index(9 if w[h] != 9 else 8); w[h], w[j] = w[j], w[h]   # never the identity
+            controls.append((P + ':cold_helper_width_swap_%d' % h, cold_swap))
+    rejected = []
+    accepted = []
+    for name, mutate in controls:
+        o, i = copy.deepcopy(owner), copy.deepcopy(invoice)
+        mutate(o, i)
+        oh = digest(o)
+        i['owner_audit_sha256'] = oh
+        try:
+            assemble(o, i, oh, digest(i))
+        except (AssertionError, KeyError):
+            rejected.append(name)
+        else:
+            # Discovery has no pinned values to reject spec-only mutations; the strict run must reject every control.
+            if not DISCOVER:
+                raise AssertionError('Invalid admission receipt accepted: ' + name)
+            accepted.append(name)
+    try:
+        assemble(owner, invoice, '0' * 64, sha(invoice_path))
+    except AssertionError:
+        rejected.append('wrong_owner_receipt_hash')
+    else:
+        raise AssertionError('Wrong owner digest accepted')
+    pin('expected.assembly_controls_rejected', len(rejected))
+    assert baseline['controls'] == ['next_grid', 'zero_eta', 'zero_beta', 'unit_beta']
+    assert baseline['conservative_controls'] == baseline['controls']
+    assert baseline['surcharge_model'] == {'complex': False, 'bit': True}
+    assert len(baseline['model_controls']) == 2
+    return dict(
+        status='PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS',
+        valid_receipt_kappa=baseline['kappa'],
+        input_sha256=baseline['input_sha256'],
+        assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'),
+        rejected_controls=rejected,
+        discovery_accepted_controls=accepted,
+        exact_outer_controls=baseline['controls'],
+        conservative_outer_controls=baseline['conservative_controls'],
+        recurrence_model_controls=baseline['model_controls'],
+        scope='Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay.',
+    )
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--source-package', type=Path, required=True)
+    ap.add_argument('--owner', type=Path, required=True)
+    ap.add_argument('--invoice', type=Path, required=True)
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    assert not a.out.exists()
+    result = verify(a.owner, a.invoice, a.source_package)
+    a.out.write_text(json.dumps(result, indent=2) + '\n')
+    print(result['status'], len(result['rejected_controls']))
diff --git a/research/gauge44-slots/code/audit_allcold.py b/research/gauge44-slots/code/audit_allcold.py
new file mode 100644
index 0000000000..c86f7b0235
--- /dev/null
+++ b/research/gauge44-slots/code/audit_allcold.py
@@ -0,0 +1,254 @@
+"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit.
+Imports no emitter, optimizer, expander, edge-coloring, or source hosting code.
+CLI: BASE HOSTED REPORT [--mutation-controls]
+Each provider is independently read from BASE/providers, never from a baseline width histogram.
+OpenAI Codex two-provider width-seven extension; retains all inherited independent controller checks.
+The exact 63 width-seven and 9 plain calls are frozen below.
+"""
+import sys,json,gzip,hashlib,copy
+assert __debug__, 'Assertions must remain enabled'
+from pathlib import Path
+from collections import Counter,defaultdict
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+from generated_identity import artifact_identities
+BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz')
+ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json')
+ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json')
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+provider_ids=PIDS
+providers={};registry={};phase_semantic_hashes={};artifact_semantic_hashes={}
+required_artifacts={'work/complex-nine-native/DATA-PHASES.json'}
+provider_files=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+ 'INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json')
+for pid in provider_ids:
+ p=BASE/'providers'/pid
+ c=read(p/'CANONICAL-WORD.json.gz');checks=read(p/'LOCAL-CHECKS.json')
+ programs=read(p/'LOCAL-PROGRAMS.json.gz');replay=read(p/'INDEPENDENT-LOCAL-REPLAY.json')
+ phase=read(p/'CLIFFORD-REVIEW.json');adapters=read(p/'RESIDUAL-ADAPTERS.json')['recipes']
+ widths=[len(c['frames'][c['final'][2*c['v']+h]])-len(c['frames'][c['start'][2*c['v']+h]])for h in range(c['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths();pin('providers.%s.inventory'%pid,{str(k):v for k,v in sorted(Counter(widths).items())})
+ canonical_sha=sha(p/'CANONICAL-WORD.json.gz');programs_sha=sha(p/'LOCAL-PROGRAMS.json.gz')
+ assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ assert replay['canonical_word_sha256']==canonical_sha and replay['local_programs_sha256']==programs_sha
+ assert replay['v']==c['v'] and replay['helpers']==c['R']
+ assert set(programs)==set(checks)==set(replay['local'])==set(replay['paid_profiles'])=={'forward','backward'}
+ for orientation,events in programs.items():
+  ck=checks[orientation];rr=replay['local'][orientation]
+  assert hashlib.sha256(json.dumps(events,sort_keys=True,separators=(',',':')).encode()).hexdigest()==ck['sha256']
+  assert ck['events']==len(events) and ck['all_columns']==2*c['v']+c['R']
+  assert ck['private_centers_cleared'] and ck['private_coefficient_stream_cleared_after_each_macro']
+  assert rr['all_exact_columns']==2*c['v']+c['R'] and rr['private_work_erased']
+  literal=Counter(e[-1]for e in events if e[0]in('climb','center'))
+  assert dict(literal)=={int(r):n for r,n in ck['paid_profile'].items()}=={int(r):n for r,n in c['local_profile'].items()}
+  assert ck['paid_profile']==replay['paid_profiles'][orientation]
+ assert phase['canonical_word_sha256']==canonical_sha and phase['recipe_sha256']==sha(p/'CLIFFORD-RECIPES.json')
+ assert phase['all_child_equalities_include_global_phase']
+ artifact_semantic_hashes[pid]=artifact_identities(p)
+ pin('providers.%s.artifact_semantic_sha256'%pid,artifact_semantic_hashes[pid])
+ phase_semantic_hashes[pid]=artifact_semantic_hashes[pid]['CLIFFORD-REVIEW.json']
+ for h,w in enumerate(widths):
+  assert 0<w<=c['h']
+  f=c['start'][2*c['v']+h];u=c['final'][2*c['v']+h]
+  # COLD-HPE: a cold helper (f == 0) may end below FULL too; its wrapper is the '0:U' recipe (E = bottom instance of #593)
+  if u!=1:   # HPE: wrapper for T_U T_E^-1, keyed 'E:U', rank |U|-|E|
+   a=adapters['%d:%d'%(f,u)]
+   assert a['frame']==f and a['terminal']==u and a['vectors']==c['frames'][f] and a['terminal_vectors']==c['frames'][u]
+   assert a['rank']==w==len(c['frames'][u])-len(c['frames'][f]) and a['entrance_rank']==len(c['frames'][f]) and a['terminal_rank']==len(c['frames'][u])<c['h']
+  elif w<c['h']:
+   a=adapters[str(f)]
+   assert a['frame']==f and a['vectors']==c['frames'][f] and a['rank']==w and a['entrance_rank']==c['h']-w
+ providers[pid]=dict(canonical=c,checks=checks,widths=widths)
+ registry[pid]=dict(local_programs=programs,canonical_word_sha256=canonical_sha,local_programs_sha256=programs_sha,
+  local_program_checks=checks,exact_local_clifford_recipe_sha256=sha(p/'CLIFFORD-RECIPES.json'),
+  residual_adapter_sha256=sha(p/'RESIDUAL-ADAPTERS.json'),
+  **{k:c[k]for k in('v','h','R','ports','centers')},widths=widths)
+ required_artifacts.update('providers/'+pid+'/'+fn for fn in provider_files)
+canon=providers[provider_ids[0]]['canonical'];V=canon['v'];R=canon['R'];N=2*V+R;CENTRES=len(canon['centers'])
+assert V==112 and canon['h']==9
+assert all(providers[p]['canonical'][k]==canon[k]for p in provider_ids for k in('v','h','R','ports'))
+# Independently compare ordered common frames; exact local carrier names remain
+# bound to each canonical word, program, phase receipt and residual adapters.
+for p in provider_ids:
+ c=providers[p]['canonical']
+ assert len(c['centers'])==len(c['center_frames'])==8
+ assert [c['frames'][f]for f in c['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+parent_canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz')
+assert [canon['frames'][f]for f in canon['center_frames']]==[parent_canon['frames'][f]for f in parent_canon['center_frames']]
+assert required_artifacts<=set(summary['source_artifacts'])
+prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=8;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=72;HOSTED=CALLS*R
+# The selected map is an input to check, not a claim from the emitter.
+
+assert len(DISPATCH)==72 and Counter(DISPATCH.values())==COUNTS
+expected_provider=lambda stage,replica:DISPATCH[stage,replica]
+
+def orthobasis(port):
+ q=canon['ports'][port];z=next(i for i in range(9)if(q>>i)&1==0);a=q^(1<<z);order=list(range(9));order[z],order[0]=order[0],order[z]
+ b=[(1<<i)^(a if a>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ assert len(b)==73 and all((x&y).bit_count()%2==int(i==j)for i,x in enumerate(b)for j,y in enumerate(b));return b
+bases=[orthobasis(p)for p in range(V)]
+
+def audit(t):
+ assert(t['live'],t['physical'])==(DATA,PHYSICAL)
+ assert t['local_providers']==registry and t['recipe']==parent['recipe']and 'each local invocation completes before the next' in t['loop_order'].lower()
+ assert not any(k in t for k in('local_programs','exact_local_clifford_recipe_sha256','residual_adapter_sha256'))
+ assert len(t['calls'])==72 and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
+ for key in('exact_data_phase_recipe_sha256','adapter_policy'):assert t[key]==parent[key]
+ assert t['exact_data_phase_recipe_sha256']==sha(BASE/'work/complex-nine-native/DATA-PHASES.json')
+ # Independently project the literal schedule onto every data replica.
+ src=parent['execution_schedule'];assert t['async_schedule']['source_schedule']==src
+ assert t['async_schedule']['source_call_order']==[[c['stage'],c['replica']]for c in parent['calls']]
+ order=[(c['stage'],c['replica'])for c in t['calls']]
+ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==72
+ all_local=[];perrep={r:[]for r in range(8)};globals_=[]
+ for e in t['execution_schedule']:
+  j=e['source_event'];old=copy.deepcopy(src[j])
+  if 'replica'in e:
+   r=e['replica'];assert 0<=r<8 and j<30;perrep[r].append(j)
+   expected=old|dict(source_event=j,replica=r,replicas=[r],time=e['time'])
+   if e['kind']=='local_cover_sweep':expected['provider_id']=expected_provider(e['stage'],r)
+   assert e==expected
+   assert 0<=e['time']<72 and order[e['time']][1]==r
+   if e['kind']=='local_cover_sweep':
+    assert order[e['time']]==(e['stage'],r);all_local.append((e['stage'],r,e['time']))
+  else:
+   globals_.append(j);expected=old|dict(source_event=j)
+   if e['kind']=='bank_padding_cover_sweep':expected['families']=[DATA,DATA]
+   if e['kind']=='translate_every_live_family':expected.update(families=[0,DATA],charged_calls_per_cover=DATA)
+   assert e==expected
+ assert all(v==list(range(30))for v in perrep.values()) and globals_==[30,31]
+ assert all_local==[(st,r,i)for i,(st,r)in enumerate(order)]
+ assert all('replica'in e for e in t['execution_schedule'][:-2])
+ assert [e['source_event']for e in t['execution_schedule'][-2:]]==[30,31]
+ # Local cover calls are indivisible; a block then runs the source events
+ # up to that replica's next local invocation.
+ block=-1
+ for e in t['execution_schedule'][:-2]:
+  if e['kind']=='local_cover_sweep':block+=1
+  assert e['time']==block
+ assert t['bank_padding']==dict(parent['bank_padding'],families=[],children=[])
+ assert t['cover_final_correction']==dict(parent['cover_final_correction'],families=[0,DATA],charged_calls_per_cover=DATA)
+ assert t['private_namespace']=={'centers':[DATA,DATA+CENTRES],'reserved_tableau':[DATA+CENTRES,DATA+CENTRES+R],'coefficient':[DATA+CENTRES+R,PHYSICAL]}
+ # Actual physical touch intervals include every individual bridge.
+ pairs={};sides={};windows={};last={};callpos={};stagepair={e['stage']:e['pair']for e in parent['recipe']if e['kind']=='local'}
+ for pos,e in enumerate(t['execution_schedule']):
+  if 'replica'not in e:continue
+  rep=e['replica']
+  if e['kind']=='local_cover_sweep':
+   pair=stagepair[e['stage']];callpos[e['stage'],rep]=pos;last[rep,pair]=pos
+  elif e['kind']=='bridge':last[rep,e['src']]=last[rep,e['dst']]=pos
+  elif e['kind']=='idle_cover_sweep':
+   for side,i in enumerate(e['child_indices']):
+    if i not in prank:continue
+    pairs[i]=e['pair'];sides[i]=side;windows[rep,i]=(last.get((rep,e['pair']),-1),pos)
+ used=defaultdict(set);roles={};paid=Counter();sigmas={};digest=hashlib.sha256();entering=0;cross=0;touches=defaultdict(list)
+ for call in t['calls']:
+  old=next(z for z in parent['calls']if(z['stage'],z['replica'])==(call['stage'],call['replica']))
+  assert {k:v for k,v in call.items()if k not in('owners','time','provider_id','local_program_sha256')}=={k:v for k,v in old.items()if k not in('owners','local_program_sha256')}
+  pid=expected_provider(call['stage'],call['replica']);assert call['provider_id']==pid
+  width=providers[pid]['widths'];checks=providers[pid]['checks']
+  assert call['local_program_sha256']==checks[call['orientation']]['sha256']
+  s,rep,pair=call['stage'],call['replica'],call['pair'];assert call['time']==t['async_schedule']['order'].index([s,rep]);own=call['owners'];assert len(own)==N and len({f for f,rt in own})==N and all(0<=f<DATA for f,rt in own)
+  assert own[:(2*V)]==old['owners'][:(2*V)]
+  for h,(family,route)in enumerate(own[(2*V):]):
+   w=width[h];typ,i,off=route[:3];ownerrep,sub=divmod(family,(8*V));fampair,sub=divmod(sub,(2*V));side,port=divmod(sub,V)
+   assert windows[ownerrep,i][0]<callpos[s,rep]<windows[ownerrep,i][1] and fampair==pairs[i] and side==sides[i] and 0<=off and off+w<=prank[i]
+   B=bases[port];pend=[int(x)for x in ph['recipes'][port]['idle_children'][i]['orthogonal_axes']];assert len(pend)==prank[i]
+   occ=[B.index(v)for v in pend[off:off+w]];sp=[j for j in range(M)if j not in occ][:9-w]
+   assert route==([3,i,off]if w==9 else[4,i,off,w,sp]);assert len(set(occ+sp))==9
+   order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert sorted(order)==list(range(M));sigma=[B[j]for j in order]
+   assert sigma[:w]==pend[off:off+w]and sigma[w:9]==[B[j]for j in sp]
+   sh=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sh]=sigma;digest.update(json.dumps([s,rep,h,family,sh],separators=(',',':')).encode()+b'\n')
+   key=(i,ownerrep,port);cells=set(range(off,off+w));assert not used[key]&cells;used[key]|=cells
+   role=(s,rep,h);assert role not in roles;roles[role]=dict(stage=s,replica=rep,helper=h,family=family,owner_replica=ownerrep,child=i,copy=ownerrep*V+port,port=port,offset=off,width=w)
+   touches[family].append((s,rep,h));entering+=w<9;cross+=rep!=ownerrep
+  for r,n in checks[call['orientation']]['paid_profile'].items():paid[int(r)]+=n
+ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(8)for h in range(R)}
+ # The frozen pooled metadata must bind the actual serialized owner maps.
+ assert len(t['hosting']['pooled_slots'])==HOSTED
+ for z in t['hosting']['pooled_slots']:
+  key=(z['stage'],z['replica'],z['helper']);assert key in roles
+  assert {k:z[k]for k in roles[key]}==roles[key]
+ assert len({(z['stage'],z['replica'],z['helper'])for z in t['hosting']['pooled_slots']})==HOSTED
+ rem={};wanted=[]
+ for old in parent['idle_children']:
+  i,port=old['child'],old['port']
+  for rep in range(T):
+   u=used[i,rep,port];assert u==set(range(len(u)));r=old['rank']-len(u)
+   if r:
+    f=rep*(8*V)+(2*pairs[i]+sides[i])*V+port;wanted.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=r,hosted=len(u),pending_offset=len(u)));paid[r]+=1
+ assert t['idle_children']==wanted
+ mass=sum(r*n for r,n in paid.items());assert73=73*DATA-mass;assert assert73==2560 and 73**2>2*max(paid)**2
+ return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=72)
+
+r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256']
+assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items())
+controls=[]
+def reject(name,mut):
+ if '--mutation-controls' not in sys.argv[4:]:return
+ q=copy.deepcopy(ct);mut(q)
+ try:audit(q)
+ except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name)
+ else:raise AssertionError('ACCEPTED '+name)
+enter=lambda q:next(o for c in q['calls']for o in c['owners'][(2*V):]if o[1][0]==4)
+reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__((2*V+1),q['calls'][0]['owners'][(2*V)]))
+reject('helper on active data family',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,q['calls'][0]['owners'][0][0]))
+reject('owner in private namespace',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,DATA))
+reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1))
+reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72))
+reject('omit idle remainder',lambda q:q['idle_children'].pop())
+reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1))
+# Single-provider dispatch still has all source/program/width binding controls.
+if len(provider_ids)==1:
+ P=provider_ids[0]
+ at_p=lambda q:next(c for c in q['calls']if c['provider_id']==P)
+ narrow=next(h for h in range(R)if providers[P]['widths'][h]<9)
+ reject(P+': wrong provider at its invocation',lambda q:at_p(q).__setitem__('provider_id','__unregistered__'))
+ reject(P+': stale per-call local program hash',lambda q:at_p(q).__setitem__('local_program_sha256','0'*64))
+ reject(P+': stale serialized provider program',lambda q:q['local_providers'][P]['local_programs']['forward'].pop())
+ reject(P+': unbound residual adapter hash',lambda q:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64))
+ reject(P+': wrong provider width registry',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,providers[P]['widths'][narrow]-1))
+ reject(P+': wrong per-call residual width',lambda q:at_p(q)['owners'][2*V+narrow][1].__setitem__(3,at_p(q)['owners'][2*V+narrow][1][3]-1))
+ reject(P+': wrong sweep provider',lambda q:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep').__setitem__('provider_id','__unregistered__'))
+ reject(P+': entering helper width silently restored to nine',lambda q:q['local_providers'][P]['widths'].__setitem__(narrow,9))
+else:
+ # Per-provider substitution controls: every provider is swapped against a partner provider.
+ for P in provider_ids:
+  Qp=partner(P)
+  at_p=lambda q,P=P:next(c for c in q['calls']if c['provider_id']==P)
+  diff=[h for h in range(R)if providers[P]['widths'][h]!=providers[Qp]['widths'][h]]
+  narrow=next(h for h in range(R)if providers[P]['widths'][h]<9)
+  reject(P+': wrong provider at its invocation',lambda q,P=P,Qp=Qp,at_p=at_p:at_p(q).__setitem__('provider_id',Qp))
+  reject(P+': stale per-call local program hash',lambda q,Qp=Qp,at_p=at_p:at_p(q).__setitem__('local_program_sha256',registry[Qp]['local_program_checks'][at_p(q)['orientation']]['sha256']))
+  reject(P+': stale serialized provider program',lambda q,P=P,Qp=Qp:q['local_providers'][P].__setitem__('local_programs',registry[Qp]['local_programs']))
+  reject(P+': unbound residual adapter hash',lambda q,P=P:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64))
+  if diff:reject(P+': partner width in provider width registry',lambda q,P=P,Qp=Qp,h=diff[0]:q['local_providers'][P]['widths'].__setitem__(h,providers[Qp]['widths'][h]))
+  reject(P+': wrong per-call residual width',lambda q,at_p=at_p,h=narrow:at_p(q)['owners'][2*V+h][1].__setitem__(3,at_p(q)['owners'][2*V+h][1][3]-1))
+  reject(P+': wrong sweep provider',lambda q,P=P,Qp=Qp:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep'and DISPATCH[e['stage'],e['replica']]==P).__setitem__('provider_id',Qp))
+  reject(P+': entering helper width silently restored to nine',lambda q,P=P,h=narrow:q['local_providers'][P]['widths'].__setitem__(h,9))
+
+report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=DATA,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,mutation_controls_run='--mutation-controls' in sys.argv[4:],provider_phase_semantic_sha256=phase_semantic_hashes,provider_artifact_semantic_sha256=artifact_semantic_hashes,widths_by_provider={pid:dict(sorted(Counter(providers[pid]['widths']).items()))for pid in provider_ids},provider_counts=dict(Counter(c['provider_id']for c in ct['calls'])),all_provider_program_phase_and_wrapper_bindings=True,scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations.')
+REPORT.parent.mkdir(parents=True,exist_ok=True)
+REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2))
+
+owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=DATA,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,hosted_residuals=HOSTED,banked_residuals=0,all_live_owners_per_call_distinct=True,owners_per_call=N,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],provider_phase_semantic_sha256=phase_semantic_hashes,provider_artifact_semantic_sha256=artifact_semantic_hashes,controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest())
+(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n')
+
+# Literal residual frames are a compact export of the already checked offsets,
+# not another global replay. Every row names its actual inherited axes.
+frames=[]
+for z in ct['idle_children']:
+ axes=list(map(int,ph['recipes'][z['port']]['idle_children'][z['child']]['orthogonal_axes']))
+ tail=axes[z['pending_offset']:]
+ assert len(tail)==z['rank']
+ frames.append(dict(z,orthogonal_axes=tail))
+frame_raw=json.dumps(frames,sort_keys=True,separators=(',',':')).encode()
+portable=bytearray(gzip.compress(frame_raw,mtime=0));portable[9]=255
+(OUT/'IDLE-REMAINDER-FRAMES.json.gz').write_bytes(bytes(portable))
+frame_receipt=dict(status='PASS_LITERAL_IDLE_REMAINDER_FRAMES',template_sha256=summary['template_sha256'],
+ uncompressed_frames_sha256=hashlib.sha256(frame_raw).hexdigest(),children=len(frames),
+ rank_profile=dict(sorted(Counter(z['rank']for z in frames).items())),
+ source_data_phase_sha256=hashlib.sha256((BASE/'work/complex-nine-native/DATA-PHASES.json').read_bytes()).hexdigest(),
+ scope='Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child.')
+(REPORT.parent/'IDLE-REMAINDER-FRAMES.json').write_text(json.dumps(frame_receipt,indent=2)+'\n')
diff --git a/research/gauge44-slots/code/bind_providers_portable.py b/research/gauge44-slots/code/bind_providers_portable.py
new file mode 100644
index 0000000000..97e28da17e
--- /dev/null
+++ b/research/gauge44-slots/code/bind_providers_portable.py
@@ -0,0 +1,67 @@
+"""Bind freshly verified plain and width-seven four-cold providers to the frozen literal owner plan.
+Prepared with OpenAI Codex assistance; Apache-2.0. All byte-stable native
+files are pinned to the plan. Only validated phase-receipt timing/serialization
+and directory fields are rebound; no dispatch, width or owner choice changes.
+"""
+import argparse,copy,gzip,hashlib,json,shutil
+from collections import Counter
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+from generated_identity import artifact_identities
+assert __debug__, 'Assertions required'
+ap=argparse.ArgumentParser(description=__doc__)
+for name in ('baseline','plan','out'):ap.add_argument('--'+name,type=Path,required=True)
+ap.add_argument('--provider',action='append',required=True,help='PID=DIR');a=ap.parse_args();assert not a.out.exists();a.out.mkdir(parents=True)
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+base=a.out/'base';shutil.copytree(a.baseline/'complex-global/base',base)
+ap2=dict(x.split('=',1)for x in a.provider);dirs={k:Path(v)for k,v in ap2.items()};assert set(dirs)==set(PIDS)
+for pid,src in dirs.items():shutil.copytree(src,base/'providers'/pid)
+pin('data.plan_sha256',sha(a.plan))
+plan=read(a.plan);original=copy.deepcopy(plan);sources={};helpers=set()   # R: helper count per provider word; all providers must agree
+assert set(plan['provider_registry'])==set(dirs)
+assert {(c['stage'],c['replica']):c['provider']for c in plan['provider_calls']}==DISPATCH,'PLAN dispatch differs from spec dispatch'
+stable=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json')
+for pid,desc in plan['provider_registry'].items():
+ d=base/'providers'/pid
+ word,program,checks,native,phase=[read(d/name)for name in('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-REVIEW.json')]
+ assert (word['v'],word['h'],len(word['centers']))==(112,9,8) and type(word['R']) is int and word['R']>0;helpers.add(word['R'])
+ assert word['ports']==desc['ports'] and word['centers']==desc['centers']
+ widths=[len(word['frames'][word['final'][r]])-len(word['frames'][word['start'][r]])for r in range(2*112,2*112+word['R'])]   # HPE: residual width |final|-|start|
+ assert tuple(widths[h]for h in SPOT)==spot_widths()
+ assert widths==desc['widths'];pin('providers.%s.inventory'%pid,{str(k):v for k,v in sorted(Counter(widths).items())})
+ assert native['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ pin('providers.%s.native_negative_controls'%pid,len(native['negative_controls_rejected']))
+ assert native['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and native['local_programs_sha256']==sha(d/'LOCAL-PROGRAMS.json.gz')
+ assert phase['status']=='PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES'
+ assert phase['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and phase['recipe_sha256']==sha(d/'CLIFFORD-RECIPES.json')
+ assert phase['all_child_equalities_include_global_phase'] is True and phase['endpoint_adapters']==224
+ pin('providers.%s.phase_edges'%pid,phase['directed_edges'])
+ assert set(program)==set(checks)=={'forward','backward'}
+ expected={int(r):n for r,n in checks['forward']['paid_profile'].items()};pin('providers.%s.expected_profile'%pid,checks['forward']['paid_profile'])
+ for orientation,events in program.items():
+  profile=Counter()
+  for e in events:
+   if e[0]=='climb':profile[e[5]]+=1
+   elif e[0]=='center':profile[e[4]]+=1
+  assert dict(profile)==expected=={int(r):n for r,n in checks[orientation]['paid_profile'].items()}=={int(r):n for r,n in native['paid_profiles'][orientation].items()}
+  assert hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest()==checks[orientation]['sha256']
+ identities=artifact_identities(d)
+ pin('providers.%s.artifact_semantic_sha256'%pid,identities)
+ assert identities==desc['artifact_semantic_sha256']
+ for name in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'):
+  assert sha(d/name)==desc['artifact_sha256'][name],(pid,name,'changed non-reference artifact')
+ for c in plan['provider_calls']:
+  if c['provider']==pid:
+   assert c['orientation']==('forward'if c['stage']%2==0 else'backward')
+   assert c['local_program_sha256']==checks[c['orientation']]['sha256']
+ desc['directory']='providers/'+pid
+ desc['artifact_sha256']={name:sha(d/name)for name in desc['artifact_sha256']}
+ sources[pid]=dict(artifact_sha256=desc['artifact_sha256'],canonical_content_sha256=hashlib.sha256(json.dumps(word,sort_keys=True,separators=(',',':')).encode()).hexdigest(),all_phase_edges=phase['directed_edges'])
+assert len(helpers)==1,'providers disagree on helper count R: %s'%sorted(helpers)
+plan['runtime_source_plan_sha256']=sha(a.plan)
+(a.out/'PLAN.json').write_text(json.dumps(plan,indent=2)+'\n')
+receipt=dict(status='PASS_FROZEN_048_ALLCOLD_DISPATCH_FRESH_PROVIDER_BINDING',source_plan_sha256=sha(a.plan),runtime_plan_sha256=sha(a.out/'PLAN.json'),providers=sources,only_rebound_fields=['provider_registry.directory','provider_registry.artifact_sha256','runtime_source_plan_sha256'])
+(a.out/'BINDING.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(receipt['status'])
diff --git a/research/gauge44-slots/code/bit_supplier_controls.py b/research/gauge44-slots/code/bit_supplier_controls.py
new file mode 100644
index 0000000000..e86b8527b4
--- /dev/null
+++ b/research/gauge44-slots/code/bit_supplier_controls.py
@@ -0,0 +1,111 @@
+"""Negative controls for the cited PR589 bit supplier and its derived rank-mass deficit.
+
+Apache-2.0. Each control mutates one input of the changed bit-supplier sites in assemble.py (the pinned record, the
+deficit derivation from the word's parameters, the profile/live binding, the claimed endpoint) and runs the unchanged
+assemble() on the fresh owner/invoice receipts. Every control must be rejected; the unmutated run must pass.
+`revert_hardcoded_9984` restores the PR543 constant the parent package hard-coded: with PR589's word it must fail.
+"""
+import argparse
+import copy
+import hashlib
+import json
+import os
+import tempfile
+from fractions import Fraction as Q
+from pathlib import Path
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+
+assert __debug__, 'Assertions required'
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def verify(owner_path, invoice_path, source_package):
+    os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve())
+    import assemble as A
+    owner = json.loads(owner_path.read_text())
+    invoice = json.loads(invoice_path.read_text())
+    args = (owner, invoice, sha(owner_path), sha(invoice_path))
+    baseline = A.assemble(*args)
+    data = A.BIT_PATH.read_bytes()
+    record = A.load_bit(data)
+    word = record['word']
+    assert A.bit_deficit(word, record['nine']['bit']['live']) == 10272 == 32 * (8 * 111 - 9 * 63)
+
+    real_load, real_deficit = A.load_bit, A.bit_deficit
+
+    def with_record(mutate):
+        def load(d):
+            r = copy.deepcopy(real_load(d)); mutate(r); return r
+        return load
+
+    def shift_profile(r):  # one rank-1 child becomes rank 2: rank mass +1, totals unchanged
+        p = r['nine']['profile']; p['1'] -= 1; p['2'] += 1; r['nine']['bit']['rank_mass'] += 1
+
+    bumped = data.replace(record['nine']['bit_lower'].encode(),
+                          str(Q(record['nine']['bit_lower']) + Q(1, 10**24)).encode(), 1)
+    assert bumped != data
+    pr543 = (source_package / 'inputs/PR543-EXPECTED.json').read_bytes()
+    controls = [
+        # deficit site: the parent's hard-coded constant, restored
+        ('revert_hardcoded_9984', dict(bit_deficit=lambda w, live: 9984)),
+        # deficit site: each word parameter perturbed alone
+        ('ports_112', dict(load_bit=with_record(lambda r: r['word'].__setitem__('v', 112)))),
+        ('decoder_constant_64_copy_ranks_unchanged', dict(load_bit=with_record(lambda r: r['word'].__setitem__('decoder_constant', 64)))),
+        # v=111, cst=64 derives 32*(888-576)=9984: consistent word, wrong for the priced profile
+        ('decoder_constant_64_with_one_copy_rank_8', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('decoder_constant', 64), r['word']['copy_ranks'].__setitem__(0, 8))))),
+        ('eight_retained_totals', dict(load_bit=with_record(lambda r: (r['word'].__setitem__('copy_ranks', [7] * 8), r['word'].__setitem__('decoder_constant', 56))))),
+        ('live_minus_one', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('live', r['nine']['bit']['live'] - 1)))),
+        # profile binding: same totals, rank mass +1
+        ('profile_rank_mass_plus_one', dict(load_bit=with_record(shift_profile))),
+        ('profile_rank_mass_receipt_mismatch', dict(load_bit=with_record(lambda r: r['nine']['bit'].__setitem__('rank_mass', r['nine']['bit']['rank_mass'] + 1)))),
+        # endpoint: the next 1e-24 grid point
+        ('bit_lower_next_grid', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('bit_lower', str(Q(r['nine']['bit_lower']) + Q(1, 10**24)))))),
+        ('not_nine_stage_record', dict(load_bit=with_record(lambda r: r['nine'].__setitem__('pipeline', r['nine']['pipeline'].replace('nine-stage', 'eleven-stage'))))),
+        # pinned-input site: tampered bytes and the parent's PR543 file under the PR589 pin
+        ('tampered_bytes_next_grid', dict(read=bumped)),
+        ('pr543_file_under_pr589_pin', dict(read=pr543)),
+    ]
+    rejected = []
+    scratch = Path(tempfile.mkdtemp(prefix='bitctl-'))
+    for name, patch in controls:
+        saved_path = A.BIT_PATH
+        try:
+            if 'read' in patch:
+                tmp = scratch / (name + '.json'); tmp.write_bytes(patch['read']); A.BIT_PATH = tmp
+            A.load_bit = patch.get('load_bit', real_load)
+            A.bit_deficit = patch.get('bit_deficit', real_deficit)
+            try:
+                A.assemble(*args)
+            except (AssertionError, KeyError):
+                rejected.append(name)
+            else:
+                raise AssertionError('Invalid bit supplier accepted: ' + name)
+        finally:
+            A.load_bit, A.bit_deficit, A.BIT_PATH = real_load, real_deficit, saved_path
+            if 'read' in patch:
+                tmp.unlink()
+    scratch.rmdir()
+    assert rejected == [n for n, _ in controls]
+    again = A.assemble(*args)
+    assert again['kappa'] == baseline['kappa'] and again['bit_lower'] == baseline['bit_lower']
+    return dict(
+        status='PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS',
+        kappa=baseline['kappa_decimal'], bit_lower=baseline['bit_lower'], bit_decimal=baseline['bit_decimal'],
+        binding=baseline['binding'], bit_supplier=baseline['bit_supplier'],
+        derived_deficit=baseline['bit_supplier']['derived_deficit'],
+        rejected_controls=rejected,
+        assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'),
+    )
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--source-package', type=Path, required=True)
+    ap.add_argument('--owner', type=Path, required=True)
+    ap.add_argument('--invoice', type=Path, required=True)
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    assert not a.out.exists()
+    result = verify(a.owner, a.invoice, a.source_package)
+    a.out.write_text(json.dumps(result, indent=2) + '\n', newline='\n')
+    print(result['status'], len(result['rejected_controls']))
diff --git a/research/gauge44-slots/code/emit_allcold.py b/research/gauge44-slots/code/emit_allcold.py
new file mode 100644
index 0000000000..8e147f80a6
--- /dev/null
+++ b/research/gauge44-slots/code/emit_allcold.py
@@ -0,0 +1,150 @@
+"""Two-provider width-seven whole-owner derivative, adapted with OpenAI Codex assistance.
+Based on PR514 and its credited PR484/507 lineage.
+CLI: --base VERIFIED_VARIANT --owners ASYNC-OWNERS.json.gz --plan ASYNC-PLAN.json --out OUT
+No optimizer or unpublished word builder runs. The frozen map explicitly names
+one whole helper per family per complete invocation, plus borrowed spectators.
+"""
+import sys,json,gzip,hashlib,copy,argparse
+from pathlib import Path
+from collections import Counter,defaultdict
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+parser=argparse.ArgumentParser(description=__doc__)
+parser.add_argument('--base',type=Path,required=True);parser.add_argument('--owners',type=Path,required=True);parser.add_argument('--plan',type=Path,required=True);parser.add_argument('--out',type=Path,required=True)
+a=parser.parse_args();BASE,MAP,PLAN,OUT=(p.resolve()for p in(a.base,a.owners,a.plan,a.out));assert not OUT.exists();OUT.mkdir(parents=True)
+class OH:
+ @staticmethod
+ def idle_basis(q):
+  z=next(i for i in range(9)if not(q>>i)&1);u=q^(1<<z);order=list(range(9));order[0],order[z]=order[z],order[0]
+  return[(1<<i)^(u if u>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ @staticmethod
+ def spectators(q,pending,off,w):
+  B=OH.idle_basis(q);occ=[B.index(v)for v in pending[off:off+w]]
+  return[j for j in range(73)if j not in occ][:9-w]
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+assert hashlib.sha256(MAP.read_bytes()).hexdigest()==SPEC['data']['owners_sha256'],'OWNERS not pinned by spec'
+plan=read(PLAN);assert plan['runtime_source_plan_sha256']==SPEC['data']['plan_sha256'],'PLAN not pinned by spec'
+call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==72;at={x:i for i,x in enumerate(call_order)}
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');t=copy.deepcopy(parent);canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');roles=read(MAP);T=8;V=canon['v'];M=73;R0=canon['R'];DATA=8*T*V;assert(V,canon['h'])==(112,9)   # R0: parent (split-centres) helper count
+assert(len(canon['start']),len(ph['recipes']))==(2*V+R0,V)
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+provider_files=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json')
+registry={};source_artifacts={'work/complex-nine-native/DATA-PHASES.json':sha(BASE/'work/complex-nine-native/DATA-PHASES.json')}
+for provider_id in sorted(plan['provider_registry']):
+ assert provider_id in PIDS
+ directory=BASE/'providers'/provider_id
+ assert all((directory/f).is_file()for f in provider_files)
+ pc=read(directory/'CANONICAL-WORD.json.gz');checks=read(directory/'LOCAL-CHECKS.json');programs=read(directory/'LOCAL-PROGRAMS.json.gz');replay=read(directory/'INDEPENDENT-LOCAL-REPLAY.json')
+ # Carrier names belong to the independently checked local program. The global
+ # controller's centre contract is the ordered eight exact common frame bases.
+ assert(pc['v'],pc['h'],pc['ports'])==(V,9,canon['ports'])
+ assert len(pc['centers'])==len(pc['center_frames'])==len(canon['centers'])==8
+ assert [pc['frames'][f]for f in pc['center_frames']]==[canon['frames'][f]for f in canon['center_frames']]
+ R=pc['R'];assert type(R)is int and R>0 and all(x['R']==R for x in registry.values()),'providers disagree on helper count R'
+ assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+ assert replay['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz')and replay['local_programs_sha256']==sha(directory/'LOCAL-PROGRAMS.json.gz')
+ widths=[len(pc['frames'][pc['final'][2*V+h]])-len(pc['frames'][pc['start'][2*V+h]])for h in range(R)]   # HPE: residual width |final|-|start|
+ assert widths==plan['provider_registry'][provider_id]['widths']
+ for name in provider_files:
+  value=sha(directory/name);assert value==plan['provider_registry'][provider_id]['artifact_sha256'][name]
+  source_artifacts[f'providers/{provider_id}/{name}']=value
+ registry[provider_id]=dict(local_programs=programs,canonical_word_sha256=sha(directory/'CANONICAL-WORD.json.gz'),local_programs_sha256=sha(directory/'LOCAL-PROGRAMS.json.gz'),local_program_checks=checks,exact_local_clifford_recipe_sha256=sha(directory/'CLIFFORD-RECIPES.json'),residual_adapter_sha256=sha(directory/'RESIDUAL-ADAPTERS.json'),v=V,h=9,R=R,ports=pc['ports'],centers=pc['centers'],widths=widths)
+assert len(roles)==72*R   # one whole-owner role per (call, provider helper)
+selected={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+assert len(selected)==72 and set(selected)==set(call_order)
+assert Counter(c['provider']for c in selected.values())==COUNTS
+per_call_widths={(c['stage'],c['replica']):c['widths']for c in plan['per_call_widths']}
+for key,c in selected.items():
+ assert c['time']==at[key] and c['provider']in registry
+ assert per_call_widths[key]==registry[c['provider']]['widths']
+for key in('local_programs','exact_local_clifford_recipe_sha256','residual_adapter_sha256'):t.pop(key)
+t['local_providers']=registry
+rank={z['child']:z['rank']for z in parent['idle_children']};side={};pairs={}
+for e in parent['execution_schedule']:
+ if e['kind']=='idle_cover_sweep':
+  for sd,ch in enumerate(e['child_indices']):side[ch]=sd;pairs[ch]=e['pair']
+bycall=defaultdict(dict);used=defaultdict(set);sigmas={};digest=hashlib.sha256();entering=0
+for z in roles:
+ s,rep,h=z['stage'],z['replica'],z['helper'];i,cp,off,w,f=z['child'],z['copy'],z['offset'],z['width'],z['family'];orp,port=divmod(cp,V)
+ assert 0<=s<9 and 0<=rep<T and 0<=h<R and w==registry[selected[s,rep]['provider']]['widths'][h] and 0<=orp<T
+ assert f==orp*(8*V)+(2*pairs[i]+side[i])*V+port
+ assert(h not in bycall[s,rep])and off>=0 and off+w<=rank[i]
+ assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1]
+ B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i]
+ occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[]
+ order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M
+ sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma
+ route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9
+ cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells
+ digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n')
+for c in t['calls']:
+ k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R))
+ c['owners']=c['owners'][:(2*V)]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==2*V+R and all(f<DATA for f,r in c['owners'])
+ pc=selected[k];provider_id=pc['provider'];assert c['orientation']==pc['orientation']
+ c['provider_id']=provider_id;c['local_program_sha256']=registry[provider_id]['local_program_checks'][c['orientation']]['sha256']
+ assert c['local_program_sha256']==pc['local_program_sha256']
+newidle=[];paid=Counter()
+for c in t['calls']:
+ for r,n in registry[c['provider_id']]['local_program_checks'][c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for old in parent['idle_children']:
+ i,port=old['child'],old['port']
+ for rep in range(T):
+  u=used[i,rep,port];assert u==set(range(len(u)));left=old['rank']-len(u)
+  if left:
+   f=rep*(8*V)+(2*pairs[i]+side[i])*V+port;newidle.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=left,hosted=len(u),pending_offset=len(u)));paid[left]+=1
+assert M*DATA-sum(r*n for r,n in paid.items())==2560
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R0+2
+# Local circuits, exact phase recipes, normalized wrappers and data routes stay
+# byte-identical; only full-family helper placement and idle remainders change.
+t.update(version='round20-R%d-asynchronous-whole-owner-v1'%R,live=DATA,physical=physical,idle_children=newidle,private_namespace={'centers':[DATA,DATA+C],'reserved_tableau':[DATA+C,DATA+C+R],'coefficient':[physical-2,physical]})
+t['hosting']=dict(rule='one-helper-per-physical-family-per-complete-invocation',max_helpers_per_physical_family_per_call=1,scope='asynchronously interleaved data replicas; each whole helper occurs once per(stage,invocation replica)',pooled_slots=roles,banks=[0]*9,owner_map_sha256=hashlib.sha256(MAP.read_bytes()).hexdigest(),idle_remainder_semantics='Each idle_children item acts once, on its explicit replica/family, at pending_offset with the stated rank; replicas=1.')
+t['route_semantics']['helper']='Whole physical family may belong to another replica; actual orthogonal port basis followed by residual/spectator coordinate permutation. Entering helpers have paid wrappers around the complete invocation; at most one helper and no active data wire uses that family in that invocation. Route[4,child,offset,width,spectators], width9 route[3,child,offset].'
+t['bank_padding']['families']=[];t['bank_padding']['children']=[];t['cover_final_correction']['families']=[0,DATA];t['cover_final_correction']['charged_calls_per_cover']=DATA
+for e in t['execution_schedule']:
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,DATA]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+# Expand the retained controller into one-replica blocks; each block consists
+# of its full local cover sweep and every following replica-local event before
+# its next local sweep. Final whole-stock correction remains after all replicas.
+blocks={};globals_=[];st=None
+for ei,e in enumerate(parent['execution_schedule']):
+ if e['kind']in('bank_padding_cover_sweep','translate_every_live_family'):
+  globals_.append((ei,e));continue
+ if e['kind']=='local_cover_sweep':st=e['stage'];blocks[st]=[]
+ assert st is not None
+ blocks[st].append((ei,e))
+new_schedule=[]
+for tm,(s,rep)in enumerate(call_order):
+ for ei,e in blocks[s]:
+  ne=copy.deepcopy(e);ne.update(replica=rep,replicas=[rep],source_event=ei,time=tm)
+  if ne['kind']=='local_cover_sweep':ne['provider_id']=selected[s,rep]['provider']
+  new_schedule.append(ne)
+for ei,e in globals_:
+ ne=copy.deepcopy(e);ne['source_event']=ei
+ if e['kind']=='bank_padding_cover_sweep':ne['families']=[DATA,DATA]
+ else:ne.update(t['cover_final_correction'])
+ new_schedule.append(ne)
+t['execution_schedule']=new_schedule
+cmap={(c['stage'],c['replica']):c for c in t['calls']}
+t['calls']=[dict(cmap[s,rep],time=tm)for tm,(s,rep)in enumerate(call_order)]
+t['loop_order']='Follow the explicit asynchronous execution_schedule. Each local invocation completes before the next, including its entire cover sweep and normalization wrappers. Per-replica source event order is preserved; each idle remainder executes before that replica next touches its family.'
+t['async_schedule']=dict(order=[list(x)for x in call_order],source_plan_sha256=hashlib.sha256(PLAN.read_bytes().replace(b'\r\n',b'\n')).hexdigest(),source_schedule=parent['execution_schedule'],source_call_order=[[c['stage'],c['replica']]for c in parent['calls']],scope='Only independent replica controllers are interleaved. Owner windows are measured on the owner replica timeline; no within-cover or within-invocation interleaving.')
+assert dict(sorted(paid.items()))=={int(k):v for k,v in plan['profile'].items()}
+assert M*M>2*max(paid)**2
+
+assert all(c['local_program_sha256']==registry[c['provider_id']]['local_program_checks'][c['orientation']]['sha256']for c in t['calls'])
+t['provider_dispatch']='For each indivisible local_cover_sweep, execute local_providers[call.provider_id].local_programs[call.orientation] with that provider residual adapters and Clifford recipes. The sweep provider_id must equal its call provider_id.'
+raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+res=dict(status='EMITTED_MIXED_PROVIDER_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE',
+ template_sha256=hashlib.sha256(raw).hexdigest(),
+ parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),
+ live=DATA,physical=physical,global_profile=dict(sorted(paid.items())),
+ rank_mass=sum(r*n for r,n in paid.items()),deficit=2560,maxchild=max(paid),
+ hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering,
+ unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(),
+ cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles),
+ asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(),
+ source_artifacts=source_artifacts,provider_counts=dict(Counter(c['provider_id']for c in t['calls'])),
+ scope='Two actual verified plain/width-seven providers dispatched per complete invocation; independent controller/spectator/normalization and complete finite invoice admission required.')
+(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2))
diff --git a/research/gauge44-slots/code/freeze_spec.py b/research/gauge44-slots/code/freeze_spec.py
new file mode 100644
index 0000000000..dd0358d396
--- /dev/null
+++ b/research/gauge44-slots/code/freeze_spec.py
@@ -0,0 +1,29 @@
+"""Freeze independently recomputed discovery values before strict replay."""
+import argparse
+import json
+from pathlib import Path
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--spec', type=Path, required=True)
+ap.add_argument('--discovery', type=Path, required=True)
+a = ap.parse_args()
+spec = json.loads(a.spec.read_text())
+for line in (a.discovery/'WITNESS-RECORD.jsonl').read_text().splitlines():
+    key, value = json.loads(line)
+    parts = key.split('.')
+    if len(parts)>3 and parts[0]=='providers' and parts[2]=='artifacts':
+        parts = parts[:3] + ['.'.join(parts[3:])]
+    target = spec
+    for part in parts[:-1]:
+        target = target.setdefault(part, {})
+    if parts[-1] in target:
+        assert target[parts[-1]]==value, 'Conflicting independent recomputations: '+key
+    target[parts[-1]] = value
+assembly = json.loads((a.discovery/'ASSEMBLY.json').read_text())
+for key in ('complex_lower','conservative_complex_lower','kappa','kappa_decimal','conservative_kappa_decimal'):
+    spec['expected'][key] = assembly[key]
+spec['expected']['assembly_controls_rejected'] = 69
+spec['expected']['provider_counts'] = {'gauge44':72}
+spec['expected']['mutations_rejected'] = 15
+a.spec.write_text(json.dumps(spec, indent=2)+'\n')
+print('Frozen exact witness for strict replay:', assembly['kappa_decimal'])
diff --git a/research/gauge44-slots/code/generated_identity.py b/research/gauge44-slots/code/generated_identity.py
new file mode 100644
index 0000000000..74a9b60479
--- /dev/null
+++ b/research/gauge44-slots/code/generated_identity.py
@@ -0,0 +1,62 @@
+"""Proof-relevant identities for generated artifacts, independent of gzip streams.
+
+Immutable source archives retain their exact byte hashes. For freshly emitted
+artifacts, gzip identity is the exact decompressed payload and JSON identity
+retains every field. Only CLIFFORD-REVIEW's root timing field is excluded.
+Literal receipt references are checked against actual files before replacing
+the three gzip references (and the phase recipe reference) with content hashes.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+import copy
+import gzip
+import hashlib
+import json
+import math
+
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+
+FILES=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+       'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json',
+       'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json')
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+def json_identity(value):
+    return hashlib.sha256(json.dumps(value,sort_keys=True,separators=(',',':'),allow_nan=False).encode('utf-8')).hexdigest()
+
+def payload_identity(path):
+    return hashlib.sha256(gzip.decompress(Path(path).read_bytes())).hexdigest()
+
+def phase_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'CLIFFORD-REVIEW.json').read_bytes())if value is None else value)
+    assert value['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz'),'stale phase canonical word reference'
+    assert value['recipe_sha256']==sha(directory/'CLIFFORD-RECIPES.json'),'stale phase recipe reference'
+    seconds=value.pop('seconds')
+    assert type(seconds)in(int,float) and math.isfinite(seconds) and seconds>=0,'invalid phase timing metadata'
+    value['canonical_word_sha256']=payload_identity(directory/'CANONICAL-WORD.json.gz')
+    value['recipe_sha256']=json_identity(json.loads((directory/'CLIFFORD-RECIPES.json').read_bytes()))
+    return value
+
+def native_value(directory,value=None):
+    directory=Path(directory)
+    value=copy.deepcopy(json.loads((directory/'INDEPENDENT-LOCAL-REPLAY.json').read_bytes())if value is None else value)
+    for field,name in [('canonical_word_sha256','CANONICAL-WORD.json.gz'),('local_programs_sha256','LOCAL-PROGRAMS.json.gz')]:
+        assert value[field]==sha(directory/name),'stale native artifact reference: '+field
+        value[field]=payload_identity(directory/name)
+    return value
+
+def artifact_identities(directory):
+    directory=Path(directory)
+    result={}
+    for name in FILES:
+        path=directory/name
+        if name.endswith('.gz'):
+            result[name]=payload_identity(path)
+        else:
+            value=phase_value(directory)if name=='CLIFFORD-REVIEW.json'else native_value(directory)if name=='INDEPENDENT-LOCAL-REPLAY.json'else json.loads(path.read_bytes())
+            result[name]=json_identity(value)
+    return result
diff --git a/research/gauge44-slots/code/invoice_allcold.py b/research/gauge44-slots/code/invoice_allcold.py
new file mode 100644
index 0000000000..b244cd5994
--- /dev/null
+++ b/research/gauge44-slots/code/invoice_allcold.py
@@ -0,0 +1,329 @@
+"""Fresh call-specific mixed-provider finite invoice.
+
+Prepared with OpenAI Codex assistance, Apache-2.0. The scalar/Horner recount
+and finite inequalities are adapted from the retained PR558 -> PR552 ->
+PR531 invoice_final.py, whose notices and sources are preserved in the package.
+Every call selects a hash-bound provider. Shared compiler reserves use maxima;
+primitive work, coefficient work, local children and wrappers are also summed
+from actual selected provider/orientation records.
+"""
+import argparse, gzip, hashlib, json
+import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent))
+from witness import *
+from generated_identity import artifact_identities
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+assert __debug__, 'Assertions required'
+
+def read(path):
+    data=path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix=='.gz' else data)
+def filehash(path): return hashlib.sha256(path.read_bytes()).hexdigest()
+def contenthash(path):
+    data=path.read_bytes()
+    return hashlib.sha256(gzip.decompress(data) if path.suffix=='.gz' else data).hexdigest()
+def programhash(events):
+    return hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest()
+
+def recount_provider(local_dir, registry):
+    cp=local_dir/'CANONICAL-WORD.json.gz'; pp=local_dir/'LOCAL-PROGRAMS.json.gz'
+    rp=local_dir/'INDEPENDENT-LOCAL-REPLAY.json'
+    w,programs,replay=read(cp),read(pp),read(rp)
+    checks=read(local_dir/'LOCAL-CHECKS.json')
+    assert set(programs)=={'forward','backward'}
+    assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY'
+    assert replay['canonical_word_sha256']==filehash(cp)==registry['canonical_word_sha256']
+    assert replay['local_programs_sha256']==filehash(pp)==registry['local_programs_sha256']
+    assert programs==registry['local_programs']
+    assert checks==registry['local_program_checks']
+    assert filehash(local_dir/'CLIFFORD-RECIPES.json')==registry['exact_local_clifford_recipe_sha256']
+    assert filehash(local_dir/'RESIDUAL-ADAPTERS.json')==registry['residual_adapter_sha256']
+    v,helpers,h,m=w['v'],w['R'],w['h'],73
+    assert (v,h)==(112,9) and type(helpers) is int and helpers>0
+    assert registry['v']==v and registry['R']==helpers and registry['h']==h
+    assert registry['ports']==w['ports'] and registry['centers']==w['centers']
+    assert replay['v']==v and replay['helpers']==helpers
+    n=2*v+helpers
+    widths = [len(w['frames'][w['final'][r]])-len(w['frames'][w['start'][r]]) for r in range(2*v, 2*v+helpers)]  # HPE: |final|-|start|
+    terminal_codim = sum(h-len(w['frames'][w['final'][r]]) for r in range(2*v, 2*v+helpers))  # HPE: 0 for FULL-ended helpers
+    ends = {r: f for r, f in enumerate(w['final']) if r >= 2*v and f != 1}
+    assert len(widths) == helpers
+    entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0}
+    entering = len(entrances)
+    wrapped = {**entrances, **{r: 0 for r in ends if r not in entrances}}   # COLD-HPE: cold hyperplane-ended helpers carry wrappers too
+    cold_ends = len(wrapped) - len(entrances)
+    assert entering == replay['entering_helpers']
+    local = {}
+    for orientation, events in programs.items():
+        # Endpoint equality and native frames were already independently
+        # replayed on all n columns in the hash-bound receipt above.
+        env = {('L', r): Q(1) for r in range(n)}
+        peak = Q(1)
+        real = macros = workops = 0
+        paid = Counter()
+        wrappers = {'pre': set(), 'post': set()}
+        for event in events:
+            tag = event[0]
+            if tag == 'climb':
+                paid[event[5]] += 1
+            elif tag == 'center':
+                paid[event[4]] += 1
+            elif tag == 'residual_adapter':
+                _, kind, register, frame, *end = event
+                assert kind in wrappers and wrapped.get(register) == frame
+                assert end == ([ends[register]] if register in ends else [])  # HPE: R_{E,U}^-1 and L_{E,U}^-1 name U
+                assert register not in wrappers[kind]
+                wrappers[kind].add(register)
+            elif tag == 'scalar':
+                macros += 1
+                scalar = event[1]
+                op, target = scalar[0], tuple(scalar[1])
+                if op == 'clear':
+                    env[target] = Q(0)
+                    count = 1
+                elif op == 'copy':
+                    env[target] = env[tuple(scalar[2])]
+                    count = 1
+                elif op == 'scale':
+                    q = Q(scalar[2], scalar[3])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert numerator and numerator & (numerator-1) == 0
+                    assert denominator & (denominator-1) == 0
+                    env[target] *= abs(q)
+                    count = abs(numerator.bit_length()-denominator.bit_length()) + int(q < 0)
+                elif op == 'add':
+                    source = tuple(scalar[2])
+                    q = Q(scalar[3], scalar[4])
+                    numerator, denominator = abs(q.numerator), q.denominator
+                    assert source != target and numerator > 0
+                    assert denominator & (denominator-1) == 0
+                    acc, count = 0, 1  # clear coefficient work
+                    for i, bit in enumerate(bin(numerator)[2:]):
+                        if i:
+                            acc *= 2
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                        if bit == '1':
+                            acc += 1
+                            count += 1
+                            peak = max(peak, acc*env[source])
+                    value = Q(acc)
+                    for _ in range(denominator.bit_length()-1):
+                        value /= 2
+                        count += 1
+                        peak = max(peak, value*env[source])
+                    assert value == abs(q)
+                    count += 2  # signed accumulation and work clear
+                    env[target] = env.get(target, Q(0)) + abs(q)*env[source]
+                    workops += count
+                else:
+                    raise AssertionError(op)
+                real += 2*count
+                peak = max(peak, env[target])
+            else:
+                assert tag in ('adapter', 'phase')
+        assert wrappers['pre'] == wrappers['post'] == set(wrapped)
+        assert all(value == 0 for register, value in env.items() if register[0] == 'C')
+        prior = replay['local'][orientation]
+        assert prior['all_exact_columns'] == n and prior['private_work_erased']
+        assert peak == Q(prior['prefix_l1_upper']) and peak < 2**prior['charged_payload_bits']
+        bits = peak.numerator.bit_length()-peak.denominator.bit_length()+1
+        assert bits == prior['prefix_bits_upper']
+        assert real == checks[orientation]['real_component_primitive_bound']
+        assert macros == checks[orientation]['scalar_macros']
+        assert dict(paid) == {int(r): count for r, count in checks[orientation]['paid_profile'].items()}
+        assert dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()}
+        local[orientation] = dict(
+            events=len(events), macros=macros, real_component_primitives=real,
+            prefix_l1=str(peak), prefix_bits=bits,
+            coefficient_work_primitive_count=workops, all_exact_columns=n,
+            dirty_helper_columns=helpers, all_dirty_helper_columns_restored=True,
+            private_centres_and_coefficient_work_cleared=True,
+            pre_wrappers=len(wrappers['pre']), post_wrappers=len(wrappers['post']),
+            endpoint_evidence='Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json')
+
+    centres = len(w['centers'])
+    children = sum(checks['forward']['paid_profile'].values())
+    assert checks['forward']['paid_profile'] == checks['backward']['paid_profile']
+    macro_bound = max(row['macros'] for row in local.values())
+    compiler = 64*(m+1)**3
+    adapters = 16*(macro_bound+children+n+centres)+64*m
+    primitive_bound = max(row['real_component_primitives'] for row in local.values())+adapters*compiler
+
+    assert widths==registry['widths']
+    artifacts={f.name:filehash(f) for f in local_dir.iterdir() if f.is_file()}
+    phase_review=read(local_dir/'CLIFFORD-REVIEW.json')
+    return dict(local=local,helpers=helpers,centres=centres,v=v,h=h,n=n,
+                entering_helpers=entering,entrance_rank=sum(len(w['frames'][f]) for f in w['start'][2*v:]),
+                terminal_codimension=terminal_codim, hyperplane_ended_helpers=len(ends),  # HPE: always reported (0 for FULL-ended words)
+                **({'cold_hyperplane_ended_helpers': cold_ends} if cold_ends else {}),  # COLD-HPE: absent without cold ends
+                width_inventory=dict(sorted(Counter(widths).items())),widths=widths,
+                local_adapters=adapters,local_primitive_bound=primitive_bound,
+                compiler=compiler,children=children,artifacts=artifacts,
+                paid_profile=checks['forward']['paid_profile'],
+                program_hashes={o:programhash(events) for o,events in programs.items()},semantic_artifact_sha256=artifact_identities(local_dir))
+
+
+def run(base, hosted, audit, out, retained_invoice=None):
+    local_dir=base/'split-centres'
+    parent=read(local_dir/'GLOBAL-TEMPLATE.json.gz')
+    template_path=hosted/'GLOBAL-TEMPLATE.json.gz'
+    template=read(template_path); summary=read(hosted/'HOSTED.json')
+    owners=read(audit/'OWNERS-AND-PROFILE.json'); control=read(audit/'ASYNC-AUDIT.json')
+    template_hash=contenthash(template_path)
+    assert template_hash==control['complex_template_sha256']==owners['template_sha256']==summary['template_sha256']
+    assert owners['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE'
+    assert template['recipe']==parent['recipe']
+    assert 'local_programs' not in template
+    assert set(template['local_providers'])==set(PIDS)
+    providers={pid:recount_provider(base/'providers'/pid,registry)
+               for pid,registry in template['local_providers'].items()}
+    for pid,p in providers.items():
+        assert owners['provider_phase_semantic_sha256'][pid]==control['provider_phase_semantic_sha256'][pid]==p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']
+        # The fresh controller admission must cite precisely these provider bytes.
+        for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json',
+                     'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json',
+                     'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json'):
+            path='providers/'+pid+'/'+name
+            assert summary['source_artifacts'][path]==p['artifacts'][name]
+            assert owners['source_artifacts'][path]==p['artifacts'][name]
+    # R is read from the provider words (all must agree); the parent dedicated-bank
+    # envelope keeps its own helper count R0 from the parent split-centres word.
+    assert len({p['helpers'] for p in providers.values()})==1,'providers disagree on helper count R'
+    v,h,m,centres=112,9,73,8
+    helpers=next(iter(providers.values()))['helpers']; n=2*v+helpers
+    assert all((p['v'],p['h'],p['centres'],p['n'])==(v,h,centres,n) for p in providers.values())
+    parent_helpers=read(local_dir/'CANONICAL-WORD.json.gz')['R']
+    stages,replicas,blocks_per_stream=9,8,4
+    call_count=len(template['calls'])
+    assert call_count==stages*replicas==control['complete_invocations']
+    assert control['one_owner_per_complete_invocation']
+    assert len({(c['stage'],c['replica']) for c in template['calls']})==call_count
+    parent_calls={(c['stage'],c['replica']):c for c in parent['calls']}
+    sweeps=[e for e in template['execution_schedule'] if e['kind']=='local_cover_sweep']
+    assert len(sweeps)==call_count
+    selected=[]; selected_paid=Counter(); provider_counts=Counter(); orientation_counts=Counter()
+    scalar=coefficient_work=macros=0; wrapper_factors=0
+    factors_per_wrapper=2*(m-1)
+    for c in template['calls']:
+        pid,orientation=c['provider_id'],c['orientation']; p=providers[pid]
+        old=parent_calls[(c['stage'],c['replica'])]
+        assert orientation==old['orientation'] and c['owners'][:2*v]==old['owners'][:2*v]
+        assert c['local_program_sha256']==p['program_hashes'][orientation]
+        r=p['local'][orientation]
+        scalar+=r['real_component_primitives']; coefficient_work+=r['coefficient_work_primitive_count']; macros+=r['macros']
+        wrapper_factors+=(r['pre_wrappers']+r['post_wrappers'])*factors_per_wrapper
+        provider_counts[pid]+=1; orientation_counts[(pid,orientation)]+=1
+        selected_paid.update({int(k):v for k,v in p['paid_profile'].items()})
+        selected.append(dict(stage=c['stage'],replica=c['replica'],provider_id=pid,orientation=orientation,
+                             program_sha256=c['local_program_sha256'],events=r['events'],macros=r['macros'],
+                             real_component_primitives=r['real_component_primitives'],
+                             coefficient_work_primitive_count=r['coefficient_work_primitive_count'],
+                             entering_helpers=p['entering_helpers'],entrance_rank=p['entrance_rank'],
+                             pre_wrappers=r['pre_wrappers'],post_wrappers=r['post_wrappers']))
+    assert provider_counts==COUNTS
+    # The sweep registry is executable: no hidden use of the historical supplier.
+    by_call={(c['stage'],c['replica']):c for c in template['calls']}
+    for e in sweeps:
+        c=by_call[(e['stage'],e['replica'])]
+        assert e['provider_id']==c['provider_id']
+    assert set(p['compiler'] for p in providers.values())=={64*(m+1)**3}
+    compiler=64*(m+1)**3
+    adapters=max(p['local_adapters'] for p in providers.values())
+    primitive_bound=max(p['local_primitive_bound'] for p in providers.values())
+    bridge_steps=sum(event['kind']=='bridge' for event in parent['recipe'])
+    bridge_sweeps=sum(event['kind']=='bridge' for event in template['execution_schedule'])
+    assert bridge_sweeps==replicas*bridge_steps
+    bridge_additions=2*v*bridge_sweeps
+    shifts=blocks_per_stream*v*replicas; moves=2*shifts
+    parent_live,parent_physical=parent['live'],parent['physical']
+    data_stock=2*v*blocks_per_stream*replicas
+    assert (parent_live-data_stock)%stages==0
+    parent_banks=(parent_live-data_stock)//stages
+    assert parent_banks>=0 and parent_physical==parent_live+parent_helpers+centres+2
+    nonlocal_items=(4*v*replicas*stages+2*v*replicas*stages+2*call_count*helpers
+        +sum(child['replicas'] for child in parent['idle_children'])+stages*parent_banks
+        +bridge_additions+shifts+moves+parent_live+parent_physical+wrapper_factors)
+    outside=8*nonlocal_items+64*m
+    parent_pervertex=(scalar+bridge_additions+shifts+moves+parent_live
+        +(call_count*adapters+outside)*compiler+64*parent_physical)
+    live,physical=template['live'],template['physical']
+    mass,profile=owners['rank_mass'],owners['paid_profile']
+    assert m*live-mass==owners['deficit']==2560
+    assert mass==sum(int(r)*count for r,count in profile.items())
+    assert physical==live+helpers+centres+2
+    assert live==owners['live'] and physical==owners['physical']
+    assert live<=parent_live and physical<=parent_physical
+    assert not template['bank_padding']['families']
+    assert owners['explicit_idle_remainder_children']<=owners['source_idle_children_charged']
+    # The old dedicated-bank geometry is only a conservative reserve envelope.
+    # Its singular program is never used as evidence for a mixed invocation.
+    rebased=parent_pervertex+65*(physical-parent_physical)+(live-parent_live)
+    used=max(rebased,parent_pervertex); retained=None; payload=512
+    if retained_invoice is not None:
+        previous=read(retained_invoice)
+        assert previous['compiler']==compiler and previous['charged_prefix_bits']==payload
+        previous_bound=previous['conservative_pervertex_used']
+        used=max(used,previous_bound+parent_pervertex)
+        retained=dict(sha256=filehash(retained_invoice),previous_pervertex_allowance=previous_bound,
+            added_complete_new_pervertex=parent_pervertex,policy='Retain old allowance and add entire fresh mixed recount.')
+    half=m//2; group=2**(half*half)
+    for i in range(1,half+1): group*=2**(2*i)-1
+    stock,streamed_mass=group*physical,group*mass
+    logical=group*used+64; router=compiler*(logical+1)*(stock+1)**2
+    g_bound,e_bound,c0=2**30000,2**100000,2**210000
+    total_mass=streamed_mass+e_bound
+    literal=2*g_bound*stock**2+8*streamed_mass+4*stock+4+32*m
+    row=2*stock.bit_length()+9909+252+2*payload
+    maxchild=max(map(int,profile))
+    inequalities=dict(local_primitive_bound=primitive_bound<2**48,
+        logical=logical<2**6050,router=router<g_bound,literal=literal<e_bound,
+        mass=total_mass<2**100001,precision=32*m*total_mass*total_mass<c0,
+        tape=2*total_mass+18<c0,row=row<20161,halving=m*m>2*maxchild*maxchild)
+    assert all(inequalities.values())
+    localbits=max(r['prefix_bits'] for p in providers.values() for r in p['local'].values())
+    input_l2_bits=(m+1)//2
+    required_prefix=localbits+input_l2_bits+call_count+bridge_sweeps+4
+    assert required_prefix<payload
+    receipt=dict(status='PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE',
+        template_sha256=template_hash,parent_template_sha256=contenthash(local_dir/'GLOBAL-TEMPLATE.json.gz'),
+        owner_audit_sha256=filehash(audit/'OWNERS-AND-PROFILE.json'),
+        controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'),
+        providers=providers,provider_phase_semantic_sha256={pid:p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json']for pid,p in providers.items()},provider_counts=dict(provider_counts),selected_calls=selected,
+        selected_local_paid_profile=dict(sorted(selected_paid.items())),
+        selected_real_component_primitives=scalar,selected_coefficient_work_primitive_count=coefficient_work,
+        selected_scalar_macros=macros,global_prefix_bits=required_prefix,charged_prefix_bits=payload,
+        complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,
+        helpers=helpers,centres=centres,live=live,physical=physical,
+        physical_stock_identity=dict(data_and_owner_families=live,local_helpers=helpers,
+                                     private_centres=centres,coefficient_work=2),
+        local_adapters=adapters,local_primitive_bound=primitive_bound,
+        wrapper_elementary_factors_charged=wrapper_factors,factors_per_wrapper=factors_per_wrapper,
+        compiler=compiler,unhosted_pervertex=parent_pervertex,hosted_rebased_pervertex=rebased,
+        conservative_pervertex_used=used,retained_prior_overcharge=retained,
+        finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),
+                    literal_bits=literal.bit_length(),physical_row_coefficient=row,
+                    retained_row_coefficient=20161,required_C0_bits=(32*m*total_mass*total_mass).bit_length(),
+                    halving_integer_inequality=[m*m,2*maxchild*maxchild],G_exponent=30000,
+                    E_exponent=100000,C0_exponent=210000),strict_checks=inequalities,
+        scope='Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. All three providers use fresh hash-bound independent all-column/frame/phase/normalization admission. Shared compiler uses conservative maxima; parent is geometry/overcharge only. All-size compiler, hosting, precision/tape and analytic transfer remain conditional.')
+    prefix=dict(status='PASS_MIXED_ASYNC_GLOBAL_PREFIX',template_sha256=template_hash,
+        global_prefix_bits=required_prefix,retained_payload_bits=payload,
+        complete_invocation_cover_sweeps=call_count,bridge_factor_two_sweeps=bridge_sweeps,
+        local_scalar_coefficient_work_prefix_bits=localbits,stream_input_sup_to_l2_bits=input_l2_bits,
+        primitive_arithmetic_margin_bits=4,controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'),
+        proof='Each selected normalized provider restores all arbitrary dirty helper columns and gives the same data shear endpoints. Actual whole-owner charts are right-translation bijections. Sum all 72 invocation and 72 bridge sweeps and take maximum local scalar/Horner prefix over all three providers and orientations. Idle children, phases, spectator endpoints and terminal translations are unitary. Retained all-size interfaces are conditional.')
+    out.mkdir(parents=True,exist_ok=True)
+    (out/'PREFIX-AND-INVOICE.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    (out/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix,indent=2)+'\n')
+    print(json.dumps({k:receipt[k] for k in ['status','provider_counts','selected_real_component_primitives',
+          'selected_coefficient_work_primitive_count','global_prefix_bits','finite','strict_checks']},indent=2))
+    return receipt
+
+if __name__=='__main__':
+    parser=argparse.ArgumentParser(description=__doc__)
+    for name in ('base','hosted','audit','out'):parser.add_argument('--'+name,type=Path,required=True)
+    parser.add_argument('--retained-invoice',type=Path)
+    args=parser.parse_args()
+    run(args.base,args.hosted,args.audit,args.out,args.retained_invoice)
diff --git a/research/gauge44-slots/code/prepare_global.py b/research/gauge44-slots/code/prepare_global.py
new file mode 100644
index 0000000000..655c9470f6
--- /dev/null
+++ b/research/gauge44-slots/code/prepare_global.py
@@ -0,0 +1,124 @@
+"""Bind a frozen explicit owner map to exact native local artifacts.
+
+This preparer nominates a witness. The separate serialized controller audit,
+finite invoice, two exact moment engines and strict pinned replay admit it.
+Apache-2.0; prepared with OpenAI assistance. See NOTICE.md.
+"""
+import argparse
+from collections import Counter, defaultdict
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+from generated_identity import artifact_identities, FILES
+
+assert __debug__, 'Assertions required'
+
+
+def read(path):
+    raw = Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def dump(path, value):
+    Path(path).write_text(json.dumps(value, indent=2) + '\n')
+
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--parent', type=Path, required=True)
+ap.add_argument('--owners', type=Path, required=True)
+ap.add_argument('--local', type=Path, required=True)
+ap.add_argument('--data', type=Path, required=True)
+args = ap.parse_args()
+args.data.mkdir(parents=True, exist_ok=True)
+parent_path = args.parent / 'data/PLAN.json'
+assert sha(parent_path) == '258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda'
+plan = read(parent_path)
+word = read(args.local / 'CANONICAL-WORD.json.gz')
+checks = read(args.local / 'LOCAL-CHECKS.json')
+assert (word['v'], word['h'], word['R']) == (112, 9, 492)
+widths = [len(word['frames'][word['final'][224+h]]) -
+          len(word['frames'][word['start'][224+h]]) for h in range(492)]
+profile = {int(k): v for k, v in word['local_profile'].items()}
+assert profile == {1: 2514, 2: 404, 3: 448, 4: 160, 5: 56, 8: 8}
+assert Counter(widths) == {4: 52, 5: 48, 7: 34, 8: 114, 9: 244}
+assert sum(widths) == 3794
+owners = read(args.owners)
+assert len(owners) == 72 * 492
+order = [tuple(x) for x in plan['order']]
+times = {x: i for i, x in enumerate(order)}
+used, call_helpers, call_families = defaultdict(set), defaultdict(set), defaultdict(set)
+for z in owners:
+    key = (z['stage'], z['replica'])
+    h, i, rep, port = z['helper'], z['child'], z['owner_replica'], z['port']
+    assert key in times and 0 <= h < 492 and 0 <= rep < 8 and 0 <= port < 112
+    assert z['time'] == times[key] and h not in call_helpers[key]
+    assert z['family'] not in call_families[key]
+    call_helpers[key].add(h)
+    call_families[key].add(z['family'])
+    cap, allowed = plan['windows'][f'{rep},{i}']
+    assert z['time'] in allowed and z['width'] == widths[h]
+    assert z['copy'] == rep * 112 + port
+    assert z['family'] == rep * 896 + (2*plan['pairs'][str(i)] + plan['sides'][str(i)])*112 + port
+    assert 0 <= z['offset'] and z['offset'] + z['width'] <= cap
+    cells = set(range(z['offset'], z['offset'] + z['width']))
+    group = (i, rep, port)
+    assert not used[group] & cells
+    used[group].update(cells)
+assert set(call_helpers) == set(order)
+assert all(hs == set(range(492)) for hs in call_helpers.values())
+idle = Counter()
+for key, (cap, _) in plan['windows'].items():
+    rep, i = map(int, key.split(','))
+    for port in range(112):
+        cells = used[i, rep, port]
+        assert cells == set(range(len(cells)))
+        left = cap - len(cells)
+        if left:
+            idle[left] += 1
+global_profile = Counter({r: 72*n for r, n in profile.items()}) + idle
+assert sum(r*n for r, n in global_profile.items()) == 520704
+assert 73*7168 - sum(r*n for r, n in global_profile.items()) == 2560
+pid = 'gauge44'
+for c in plan['provider_calls']:
+    c['provider'] = pid
+    c['local_program_sha256'] = checks[c['orientation']]['sha256']
+for c in plan['per_call_widths']:
+    c['widths'] = widths
+artifacts = {name: sha(args.local / name) for name in FILES}
+identities = artifact_identities(args.local)
+plan['provider_registry'] = {pid: dict(
+    directory='providers/' + pid, artifact_sha256=artifacts,
+    ports=word['ports'], centers=word['centers'], widths=widths,
+    actual_paid_profile=word['local_profile'],
+    orientation_program_sha256={k: v['sha256'] for k, v in checks.items()},
+    artifact_semantic_sha256=identities)}
+plan.update(status='FROZEN_EXPLICIT_GAUGE44_WHOLE_OWNER_NOMINATION',
+            mode='gauge44-all72', profile=dict(sorted(global_profile.items())),
+            solver_status='deterministic-capacity-matching', gap=None,
+            source_plan_sha256=sha(parent_path),
+            source_owners_sha256=sha(args.parent / 'data/OWNERS.json.gz'),
+            assignment_sha256=sha(args.owners))
+target_owners = args.data / 'OWNERS.json.gz'
+if args.owners.resolve() != target_owners.resolve():
+    shutil.copyfile(args.owners, target_owners)
+dump(args.data / 'PLAN.json', plan)
+spec = dict(schema='witness-spec/1', name='gauge44-all72',
+            data=dict(plan_sha256=sha(args.data / 'PLAN.json'), owners_sha256=sha(target_owners)),
+            dispatch=[[s, r, pid] for s in range(9) for r in range(8)],
+            call_order=plan['order'], width_spot_helpers=[264, 276, 288, 300],
+            providers={pid: {}}, expected=dict(gain_baseline_kappa='0.001636241501576388'))
+dump(args.data / 'SPEC.json', spec)
+dump(args.data / 'PREPARATION.json', dict(
+    status='PASS_EXPLICIT_MAP_AND_FRESH_PROVIDER_NOMINATION',
+    parent_plan_sha256=sha(parent_path), source_owners_sha256=sha(args.owners),
+    global_profile=dict(sorted(global_profile.items())), idle_profile=dict(sorted(idle.items())),
+    roles=len(owners), rank_mass=520704, deficit=2560,
+    remaining='Independent emitted-controller audit, fresh finite invoice, exact moments and outer assembly.'))
+print('Prepared all72 gauge44 candidate:', dict(sorted(global_profile.items())))
diff --git a/research/gauge44-slots/code/restore_parent.py b/research/gauge44-slots/code/restore_parent.py
new file mode 100644
index 0000000000..21135f898a
--- /dev/null
+++ b/research/gauge44-slots/code/restore_parent.py
@@ -0,0 +1,67 @@
+"""Materialize the omitted generated PR558 parent, then require its reviewed hash.
+
+The integrated review contains the native inputs and INTEGRATION.json but
+omits GLOBAL-TEMPLATE.json.gz. This is only the deterministic template
+binding from the inherited prepare_supplier_base.py; no old circuit or
+phase calculation is rerun. The whole exact payload must match the review.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+assert __debug__, 'Assertions required'
+ap=argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--source',type=Path,required=True)
+ap.add_argument('--baseline',type=Path,required=True)
+ap.add_argument('--out',type=Path,required=True)
+a=ap.parse_args()
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+assert not a.out.exists()
+base=a.out/'complex-global/base'
+shutil.copytree(a.baseline/'complex-global/base',base)
+d=base/'split-centres'
+parent=a.source/'vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz'
+old=read(parent);can=read(d/'CANONICAL-WORD.json.gz')
+checks=read(d/'LOCAL-CHECKS.json');programs=read(d/'LOCAL-PROGRAMS.json.gz')
+v,h,r=can['v'],can['h'],can['R'];c=len(can['centers']);m,t,l,k=73,8,9,4
+assert(v,h,r,c)==(112,9,504,8)
+widths=[h-len(can['frames'][f])for f in can['start'][2*v:]]
+data=2*k*t*v;live=data+l*r;physical=live+r+c+2
+word=copy.deepcopy(old)
+word.update(version='round20-new-supplier-dedicated-bank-parent-v1',live=live,physical=physical,local_programs=programs)
+word['private_namespace']={'centers':[live,live+c],'reserved_tableau':[live+c,live+c+r],'coefficient':[physical-2,physical]}
+for call in word['calls']:
+ s,rep=call['stage'],call['replica'];owners=copy.deepcopy(call['owners'][:2*v])
+ for helper,w in enumerate(widths):
+  route=[2,rep]if w==9 else[2,rep*w,w,list(range(t*w,t*w+9-w))]
+  owners.append([data+s*r+helper,route])
+ call['owners']=owners;call['local_program_sha256']=checks[call['orientation']]['sha256']
+children=[]
+for s in range(l):
+ for helper,w in enumerate(widths):
+  axes=list(range(t*w,m))
+  children.append(dict(family=data+s*r+helper,rank=len(axes),axis_indices=axes,orthogonal_axes=[1<<j for j in axes]))
+word['bank_padding']={'families':list(range(data,live)),'children':children,
+ 'semantics':'Each listed complement frame is applied once after the eight disjoint residual blocks of that dedicated bank. The final hosted derivative has empty families and children.'}
+word['cover_final_correction'].update(families=[0,live],charged_calls_per_cover=live)
+for i,e in enumerate(word['execution_schedule']):
+ if e['kind']=='bank_padding_cover_sweep':word['execution_schedule'][i]={'kind':'bank_padding_cover_sweep','families':[data,live],'children_source':'bank_padding.children'}
+ elif e['kind']=='translate_every_live_family':e.update(word['cover_final_correction'])
+word['exact_data_phase_recipe_sha256']=sha(base/'work/complex-nine-native/DATA-PHASES.json')
+word['exact_local_clifford_recipe_sha256']=sha(d/'CLIFFORD-RECIPES.json')
+word['residual_adapter_sha256']=sha(d/'RESIDUAL-ADAPTERS.json')
+word['supplier_substitution']={'parent_template_sha256':sha(parent),
+ 'old_canonical_word_sha256':sha(a.baseline/'complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz'),
+ 'new_canonical_word_sha256':sha(d/'CANONICAL-WORD.json.gz'),
+ 'exact_same_ports':True,'data_contract':'The same ordered 112 data ports and both complete-invocation identity-shear orientations feed the unchanged nine-stage controller. No old local program or helper profile is reused.'}
+word['route_semantics']['helper']='Dedicated family DATA+stage*R+helper; one helper per bank per complete invocation. Width-nine route[2,replica] uses axes9*replica..9*replica+8. Width-w entering route[2,w*replica,w,spectators] uses the disjoint residual block and paid normalization wrappers; spectator axes start at8*w, beyond all residual blocks.'
+raw=json.dumps(word,sort_keys=True,separators=(',',':')).encode()
+expected=read(d/'INTEGRATION.json')['global_template_sha256']
+assert hashlib.sha256(raw).hexdigest()==expected=='7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3'
+(d/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+print('PASS_EXACT_REVIEWED_PARENT_TEMPLATE_RESTORED',expected)
diff --git a/research/gauge44-slots/code/witness.py b/research/gauge44-slots/code/witness.py
new file mode 100644
index 0000000000..c5c7fbc114
--- /dev/null
+++ b/research/gauge44-slots/code/witness.py
@@ -0,0 +1,55 @@
+"""Spec loader: spec values are EXPECTED values, compared only after independent recomputation.
+WITNESS_DISCOVER=1 runs the same recomputation without comparing pinned values (pin() records only);
+it is used once to produce outputs for generate_spec.py, after which the strict run must pass.
+"""
+import json,os
+from collections import Counter
+from pathlib import Path
+SPEC=json.loads(Path(os.environ['WITNESS_SPEC']).read_text())
+DISCOVER=os.environ.get('WITNESS_DISCOVER')=='1'
+X=SPEC.get('expected',{})
+PROVIDERS=SPEC.get('providers',{})
+DISPATCH={(s,r):p for s,r,p in SPEC['dispatch']}
+CALL_ORDER=[tuple(x)for x in SPEC['call_order']]
+# width-8 spot helpers: PR558's helpers 270, 282, 294, 306, or their images under a K-triangle word's 504 -> R helper map
+# (verify.py checks the spec value against the constructor's HELPER-MAP.json)
+SPOT=tuple(SPEC.get('width_spot_helpers',(270,282,294,306)))
+# A pivot swap moves a kernel family's pivot role p -> x; the old pivot p becomes an ordinary cold helper and its width
+# goes 8 -> 9 (construction/layers, PR641 PROOF-NOTE-PIVOT). Expected spot widths are derived from the package's pinned
+# pivot-swap recipe (path and sha256 in the spec), not from free data: 9 at a swapped-out pivot, 8 otherwise.
+_PKG=Path(os.environ['WITNESS_SPEC']).resolve().parents[1]
+def _old_pivots():
+ ps=SPEC.get('pivot_swap')
+ if not ps:return frozenset()
+ raw=(_PKG/ps['recipe']).read_bytes();import hashlib
+ assert hashlib.sha256(raw).hexdigest()==ps['sha256'],'pivot-swap recipe pin'
+ return frozenset(s['pivot']for s in json.loads(raw)['swaps'])
+OLD_PIVOTS=_old_pivots()
+def spot_widths(v=112):
+ """Expected residual widths at the spot helpers (helper indices) of the gauge44 provider."""
+ return tuple(9 if 2*v+h in OLD_PIVOTS else 8 for h in SPOT)
+PIDS=tuple(sorted(set(DISPATCH.values())))
+COUNTS=dict(Counter(DISPATCH.values()))
+assert DISCOVER or set(PROVIDERS)==set(PIDS),'spec providers differ from dispatch providers'
+def lookup(key):
+ """Dotted spec path; a segment may itself contain dots when it names a file (split at most once per known file suffix)."""
+ v=SPEC;parts=key.split('.')
+ while parts:
+  for n in range(len(parts),0,-1):
+   k='.'.join(parts[:n])
+   if isinstance(v,dict) and k in v:v=v[k];parts=parts[n:];break
+  else:raise KeyError('spec has no key %s'%key)
+ return v
+def pin(key,got):
+ """Strict mode: got must equal the spec value at dotted key; the failure names the key."""
+ if DISCOVER:
+  if os.environ.get('WITNESS_RECORD'):   # discovery bookkeeping only: append (key, value) for the spec writer
+   with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10))
+  return got
+ want=lookup(key)
+ assert got==want,'SPEC MISMATCH %s: expected %s got %s'%(key,json.dumps(want)[:400],json.dumps(got,default=str)[:400])
+ return got
+def partner(pid):
+ """A different provider for substitution controls (next in sorted order)."""
+ assert len(PIDS)>1
+ return PIDS[(PIDS.index(pid)+1)%len(PIDS)]
diff --git a/research/gauge44-slots/construction/COLD44-RECIPE.json.gz b/research/gauge44-slots/construction/COLD44-RECIPE.json.gz
new file mode 100644
index 0000000000..6f59d88920
Binary files /dev/null and b/research/gauge44-slots/construction/COLD44-RECIPE.json.gz differ
diff --git a/research/gauge44-slots/construction/COMPLETION-PRIORITY.json b/research/gauge44-slots/construction/COMPLETION-PRIORITY.json
new file mode 100644
index 0000000000..e0df30aeef
--- /dev/null
+++ b/research/gauge44-slots/construction/COMPLETION-PRIORITY.json
@@ -0,0 +1,746 @@
+{
+  "0,1,2,3": {
+    "rows": [
+      [
+        "1",
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+        "1",
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+        "0",
+        "0",
+        "0"
+      ]
+    ],
+    "registers": [
+      64,
+      67
+    ]
+  },
+  "0,1,4,5": {
+    "rows": [
+      [
+        "1",
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+      ]
+    ],
+    "registers": [
+      32,
+      35
+    ]
+  },
+  "0,1,6,7": {
+    "rows": [
+      [
+        "1",
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+        "0",
+        "0",
+        "0"
+      ]
+    ],
+    "registers": [
+      24,
+      27
+    ]
+  },
+  "0,2,4,6": {
+    "rows": [
+      [
+        "1",
+        "0",
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+        "1",
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+        "0",
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+      ],
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+      [
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+      ],
+      [
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+    ],
+    "registers": [
+      16,
+      18,
+      19,
+      297,
+      301,
+      303
+    ]
+  },
+  "0,2,5,7": {
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+        "1",
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+        "1/2",
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+      [
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+      ],
+      [
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+        "1/2",
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+      ],
+      [
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+        "1/2",
+        "-1/2",
+        "0",
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+        "1/2"
+      ]
+    ],
+    "registers": [
+      40,
+      42,
+      43,
+      313,
+      317,
+      319
+    ]
+  },
+  "0,3,4,7": {
+    "rows": [
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+        "0",
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+        "1",
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+        "0",
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+      [
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+        "0",
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+      ],
+      [
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+        "0",
+        "-1/2",
+        "1/2",
+        "0"
+      ],
+      [
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+        "0",
+        "0",
+        "1/2",
+        "-1/2",
+        "0",
+        "0",
+        "1/2"
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+    ],
+    "registers": [
+      72,
+      74,
+      75,
+      329,
+      333,
+      335
+    ]
+  },
+  "0,3,5,6": {
+    "rows": [
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+        "0",
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+      ],
+      [
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+      ],
+      [
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+        "1/2",
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+      ],
+      [
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+        "0",
+        "0",
+        "1/2",
+        "-1/2",
+        "0",
+        "0",
+        "1/2"
+      ]
+    ],
+    "registers": [
+      112,
+      114,
+      115,
+      345,
+      349,
+      351
+    ]
+  },
+  "1,2,4,7": {
+    "rows": [
+      [
+        "1",
+        "0",
+        "0",
+        "1",
+        "0",
+        "0",
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+      ],
+      [
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+        "-1/2",
+        "1/2",
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+        "0",
+        "-1/2",
+        "1/2",
+        "0"
+      ],
+      [
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+        "0",
+        "0",
+        "1/2",
+        "0",
+        "0",
+        "0",
+        "0"
+      ],
+      [
+        "0",
+        "0",
+        "0",
+        "0",
+        "1",
+        "0",
+        "0",
+        "1"
+      ],
+      [
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+        "0",
+        "0",
+        "0",
+        "0",
+        "-1/2",
+        "1/2",
+        "0"
+      ],
+      [
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+        "0",
+        "0",
+        "1/2",
+        "-1/2",
+        "0",
+        "0",
+        "1/2"
+      ]
+    ],
+    "registers": [
+      8,
+      10,
+      11,
+      361,
+      365,
+      367
+    ]
+  },
+  "1,2,5,6": {
+    "rows": [
+      [
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+        "0",
+        "0",
+        "1",
+        "0",
+        "0",
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+      [
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+      [
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+      [
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+      ],
+      [
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+        "1/2",
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+      ],
+      [
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+        "1/2",
+        "-1/2",
+        "0",
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+      ]
+    ],
+    "registers": [
+      48,
+      50,
+      51,
+      377,
+      381,
+      383
+    ]
+  },
+  "1,3,4,6": {
+    "rows": [
+      [
+        "1",
+        "0",
+        "0",
+        "1",
+        "0",
+        "0",
+        "0",
+        "0"
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diff --git a/research/gauge44-slots/construction/INPUTS.json b/research/gauge44-slots/construction/INPUTS.json
new file mode 100644
index 0000000000..2b12294b58
--- /dev/null
+++ b/research/gauge44-slots/construction/INPUTS.json
@@ -0,0 +1,65 @@
+{
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+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
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+      "research/complex-571-cold14-st2/data/TRI-SCHEDULE.json": "94da9d5575f5b237097a77ac7dd09aff594322dd9c35138bfd34ffc5e1a7a51e",
+      "research/complex-571-cold14-st2/data/recipes/k492-jp8-frame_regroup.json": "9bd347334de643f29865290be1ed37289f9cae6cd339547ac89b45fa7aaee65a",
+      "research/complex-571-cold14-st2/data/recipes/k492-jp8-hyperplane_end.json": "e4d4dfd83d0c64cb0a8ee8c8bbd95d0510ee68699859e568fe201cd6f8d250c1"
+    },
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+      "COMPLETION-PRIORITY.json": "0274ffca1725e7460aaf7b672bc1248aa6dfdec11e5f0fec91af18b829f8ba47",
+      "build_gauge_cold44.py": "ec730a4d3ff12fb058780718b1d5a7afe61243c532679ef347a5a48e2af0a3bb",
+      "construct_gauge_xcentre.py": "d8d295566ef2399af2da0707a4adc83e07aa26d2344c01a66bd0ca7684cf9217",
+      "reproduce.py": "047bb9b3536b0b16bb08a21cd9fd80404ca9d022345f1aeab34b21dffc281c92"
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+    "raw": "0ac47f92fc2e3f5aa457d78f7b8a5c785bf140c546932b9dfcd9e610ad319180",
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+    "cold44": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290"
+  },
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+  "canonical_content_sha256": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+  "local_program_sha256": {
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+}
diff --git a/research/gauge44-slots/construction/LICENSE b/research/gauge44-slots/construction/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/gauge44-slots/construction/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
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+      "Work" shall mean the work of authorship, whether in Source or
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+      (an example is provided in the Appendix below).
+
+      "Derivative Works" shall mean any work, whether in Source or Object
+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
+      the Work and Derivative Works thereof.
+
+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
+      to that Work or Derivative Works thereof, that is intentionally
+      submitted to Licensor for inclusion in the Work by the copyright owner
+      or by an individual or Legal Entity authorized to submit on behalf of
+      the copyright owner. For the purposes of this definition, "submitted"
+      means any form of electronic, verbal, or written communication sent
+      to the Licensor or its representatives, including but not limited to
+      communication on electronic mailing lists, source code control systems,
+      and issue tracking systems that are managed by, or on behalf of, the
+      Licensor for the purpose of discussing and improving the Work, but
+      excluding communication that is conspicuously marked or otherwise
+      designated in writing by the copyright owner as "Not a Contribution."
+
+      "Contributor" shall mean Licensor and any individual or Legal Entity
+      on behalf of whom a Contribution has been received by Licensor and
+      subsequently incorporated within the Work.
+
+   2. Grant of Copyright License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      copyright license to reproduce, prepare Derivative Works of,
+      publicly display, publicly perform, sublicense, and distribute the
+      Work and such Derivative Works in Source or Object form.
+
+   3. Grant of Patent License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      (except as stated in this section) patent license to make, have made,
+      use, offer to sell, sell, import, and otherwise transfer the Work,
+      where such license applies only to those patent claims licensable
+      by such Contributor that are necessarily infringed by their
+      Contribution(s) alone or by combination of their Contribution(s)
+      with the Work to which such Contribution(s) was submitted. If You
+      institute patent litigation against any entity (including a
+      cross-claim or counterclaim in a lawsuit) alleging that the Work
+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
+      granted to You under this License for that Work shall terminate
+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
+      Work or Derivative Works thereof in any medium, with or without
+      modifications, and in Source or Object form, provided that You
+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
+          attribution notices from the Source form of the Work,
+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
+          distribution, then any Derivative Works that You distribute must
+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
+          pertain to any part of the Derivative Works, in at least one
+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
+          documentation, if provided along with the Derivative Works; or,
+          within a display generated by the Derivative Works, if and
+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
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+      PARTICULAR PURPOSE. You are solely responsible for determining the
+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
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+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
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+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
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+   9. Accepting Warranty or Additional Liability. While redistributing
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+   You may obtain a copy of the License at
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diff --git a/research/gauge44-slots/construction/NOTICE.md b/research/gauge44-slots/construction/NOTICE.md
new file mode 100644
index 0000000000..16b0507070
--- /dev/null
+++ b/research/gauge44-slots/construction/NOTICE.md
@@ -0,0 +1,9 @@
+# Construction delta notice
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+
+`construct_gauge_xcentre.py` modifies PR635's credited `construct_k_triangle.py`, which in turn extends icekylinx's PR531/PR514/PR425 factory lineage. Its original source comments are retained. The K-triangle schedule and the upstream porting, JP8 frame, kernel and HPE procedures are reused from the pinned source checkouts and are not new contributions of this delta.
+
+The new source-copy exchanges, complementary factory basis, carrier assignment, exact cold44 constructor and compact reproduction driver are described in `../CONSTRUCTION.md`.
+
+`UPSTREAM-NOTICE.md` is the complete unmodified notice from the pinned PR635 package. `LICENSE` is that package's Apache-2.0 license. All further notices and source credits of the referenced upstream packages remain applicable and are retained in the source checkouts rather than vendored again here.
diff --git a/research/gauge44-slots/construction/REBUILD-CHECKS.json b/research/gauge44-slots/construction/REBUILD-CHECKS.json
new file mode 100644
index 0000000000..0801f35da7
--- /dev/null
+++ b/research/gauge44-slots/construction/REBUILD-CHECKS.json
@@ -0,0 +1,51 @@
+{
+  "status": "PASS_COMPACT_SCALAR_REPRODUCTION_AND_FROZEN_RECIPE_SPLICE",
+  "steps": [
+    {
+      "step": "shadow-early",
+      "exit_code": 0,
+      "seconds": 0.355
+    },
+    {
+      "step": "shadow-prefix",
+      "exit_code": 0,
+      "seconds": 0.511
+    },
+    {
+      "step": "gauge-forward",
+      "exit_code": 0,
+      "seconds": 0.527
+    },
+    {
+      "step": "port0",
+      "exit_code": 0,
+      "seconds": 0.468
+    },
+    {
+      "step": "port1",
+      "exit_code": 0,
+      "seconds": 0.636
+    },
+    {
+      "step": "port2",
+      "exit_code": 0,
+      "seconds": 0.474
+    },
+    {
+      "step": "port3",
+      "exit_code": 0,
+      "seconds": 0.497
+    },
+    {
+      "step": "cold44-exact",
+      "exit_code": 0,
+      "seconds": 2.754
+    }
+  ],
+  "constructor_seconds": 6.222,
+  "word_content_sha256": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290",
+  "all_step_input_and_output_pins_checked": true,
+  "regenerated_recipe_equals_frozen_recipe": true,
+  "frozen_splice_matches_exact_constructor": true,
+  "scope": "One portable scalar reconstruction from pinned main and PR635 inputs; existing native and independent mathematical receipts accompany the package separately."
+}
diff --git a/research/gauge44-slots/construction/UPSTREAM-NOTICE.md b/research/gauge44-slots/construction/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..ebc24a0168
--- /dev/null
+++ b/research/gauge44-slots/construction/UPSTREAM-NOTICE.md
@@ -0,0 +1,34 @@
+# Attribution and scope
+
+Four verified provider types are offered to every call: PR571's prefix word with twelve multi-cut cold kernels (PR568's unchanged constructor), the same word with forty width-five entrance promotions (PR569's unchanged frame constructor) before those kernels, PR575's plain joint-prefix provider, and PR568's eight-cold provider. A window MILP with an exact per-pattern model chooses the dispatch and a literal owner map. PR583's six source-bound kernel frame coalescences (its unchanged constructor and negative controls) are applied to every PR571-prefix provider word (ck and atm3), followed by two further coalescences that each first move one addition past two commuting additions (package code/build_gate_moves.py, extending PR583's constructor); a final hyperplane_end step (package code/build_hpe.py) then runs 46 single-gate cleanups h -= p right after part B at the dim-8 join U of their registers, so 46 width-8 entering helpers per call end at U with width 7; each such gate commutes with every earlier cleanup gate on its registers (for 8 of them the partner's one earlier gate x -= p only reads p), and the reordered program is replayed exactly. A window MILP (exact windows, RINS around an LP vertex) gives the dispatch ck 45 / atm3 21 / jp8 6 and the literal owner map.
+
+Pinned external sources (unchanged; `verify.py` checks their manifests and every file it uses):
+- PR568 (`research/complex-multicold`, commit `71c99ac935a33bb7b59a1b4a7af8725a939b0b90`).
+- PR571 (`research/structural-gain`, commit `b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3`).
+- PR569 (`research/larger-gain`, commit `897213a855b7fb8a1b8b0e552a2f5c42e6c1b326`).
+- PR575 (`research/complex-joint-prefix`, commit `eac6f7e378ab622dac50a2fd4b7ef6eab014de44`).
+- PR583 (`research/kernel-frame-coalescing`, commit `89be768f0157f5a3d8e4db69cf1748768605eac9`).
+
+Provider construction is described as typed steps in `data/SPEC.json` (`build`); `verify.py` runs only allowlisted step types with their paired omission audits and checks every input and output content hash. `code/` holds the spec-driven global admission scripts adapted from PR571's `frontier-composition/global-code/` (OpenAI Codex assisted, Apache-2.0): every expected value is read from `data/SPEC.json` and compared only after independent recomputation. `code/generated_identity.py` and `code/generated_identity_controls.py`, and the decompressed-content artifact identities in the bind, audit, invoice, assembly and phase-timing scripts, are taken unchanged from PR586 by chafreaky (`research/promoted-kernel-coalescing`, commit `4846fee5b06af770e9b3a10c36200f673d656725`, OpenAI Codex assisted, Apache-2.0), including its proof-content and reference/metadata mutation controls; the normalization of descriptive width metadata after frame changes follows the same PR.
+
+In PR601, the owner map was nominated by a HiGHS window MILP (adapted from PR569's `global/nominate_width7.py`) with lazy cross-time Hall cuts; this package's re-solved map is described below. Neither is an admission dependency.
+
+DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. (The PR601 package this one starts from states: "Prepared by Claude Code (Anthropic) research agents.") Apache-2.0 applies; LICENSE is included. All notices, licenses, source pins and AI disclosures of the pinned sources and their ancestry are retained in those packages and are not replaced by this notice. All inherited conditional assumptions remain conditional.
+
+**This package (complex-571-cold14, DreamingOfClouds).** It starts from PR601 (jeremykothe2, `research/complex-571-hpem46`, commit `529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550`). Everything above is kept unchanged except the following:
+- every provider chain (ck, atm3, jp8) gains the typed step `cold_end` (`code/build_cold_end.py`, `code/cold_end_controls.py`; recipes `data/recipes/*-cold_end.json.gz`);
+- the generalised native chain and the global admission scripts accept cold helpers that end below FULL (with `0:U` wrappers), a refactored exact cleanup, and check the wrapper order;
+- `data/PLAN.json` / `data/OWNERS.json.gz` (dispatch and literal owner map) come from a relocate/swap/ejection-chain/provider-flip annealing search started from PR601's map, refined by an exact pattern-restricted owner model (CP-SAT) with a literal edge-colouring expansion (not an admission dependency);
+- `data/SPEC.json` holds the expected values, recorded by a discovery run and then checked by a strict run.
+
+The cold-end construction (a row-plus-column cone condition for low-frame ends, a rank-0 dirt-spread premix and multi-gate lower-frame cleanup) builds on PR591 / PR592 / PR593 / PR601 (jeremykothe2) and our PR599 (Lean: multi-gate and cold hyperplane-end tails). DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. Build on this at your own risk.
+
+**This package (complex-571-cold14-b3, jeremykothe2).** It is PR604's `complex-571-cold14` (DreamingOfClouds) with ColdBeyond's second cold end per block (two new `cold_end` A-gate primitives, `PROOF-NOTE.md`), ColdSupply's E1 entering pair and reviewed controls, a free dispatch (jp8 ×60, atm3 ×12) and a literal owner map from an exact per-time-Hall window MIP. All other construction, code, controls and proofs are PR604's and earlier contributors', unchanged.
+
+**This package (complex-571-cold14-k492).** It is complex-571-cold14-b3 with these changes:
+- **K-triangle base words.** The leaver-read K-triangle skeleton atom and its read schedule (`data/TRI-SCHEDULE.json`) are by AtomScout, a Claude Code research agent. `code/construct_k_triangle.py` is PR531's `code/construct_504.py` (icekylinx, OpenAI Codex / GPT assisted, Apache-2.0; pinned source `direct_delivery`) extended with that atom.
+- **Ported chains.** The PR604/B3 chains are ported stage by stage onto the K-triangle words by `code/build_port_stage.py` (Port480, a Claude Code research agent). `code/build_frame_regroup.py` extends PR583's `build_frames.py` (chafreaky).
+- **Helper count R.** The generalisation of the global scripts to the provider helper count R is by GlobalR (a Claude Code research agent), with AtomReviewer's fixes (PROOF-NOTE-R.md).
+- **Owner map.** The owner map, the cold_end recipes on the K-triangle words and the package assembly are by Stack492, Port480 and ColdBeyond (Claude Code research agents).
+
+Build on this at your own risk.
diff --git a/research/gauge44-slots/construction/barch/LOCAL-PINS-barch-U8.json b/research/gauge44-slots/construction/barch/LOCAL-PINS-barch-U8.json
new file mode 100644
index 0000000000..4028b95c0e
--- /dev/null
+++ b/research/gauge44-slots/construction/barch/LOCAL-PINS-barch-U8.json
@@ -0,0 +1,50 @@
+{
+ "word": "U8",
+ "barch_controls": [
+  "C0_identity",
+  "recipe",
+  "drop_restore",
+  "restore_full",
+  "drop_preread",
+  "donation_after",
+  "drop_restore@231",
+  "restore_full@231",
+  "drop_preread@231",
+  "donation_after@231",
+  "drop_restore@230",
+  "restore_full@230",
+  "drop_preread@230",
+  "donation_after@230",
+  "drop_restore@232",
+  "restore_full@232",
+  "drop_preread@232",
+  "donation_after@232",
+  "drop_restore@236",
+  "restore_full@236",
+  "drop_preread@236",
+  "donation_after@236",
+  "drop_restore@226",
+  "restore_full@226",
+  "drop_preread@226",
+  "donation_after@226",
+  "drop_restore@228",
+  "restore_full@228",
+  "drop_preread@228",
+  "donation_after@228",
+  "drop_restore@62",
+  "restore_full@62",
+  "drop_preread@62",
+  "donation_after@62",
+  "drop_restore@238",
+  "restore_full@238",
+  "drop_preread@238",
+  "donation_after@238"
+ ],
+ "layer_controls": 95,
+ "canonical_sha256": "24db880b7dab31e6af4eec8a1aba1bbbae29cd50d9a7b77cf0e9b571b3e5ae7c",
+ "program_sha256": {
+  "forward": "83d65a63f51bd1ce7f3dd4e4d3597311e065b4775796cd87aea3e3a62689047c",
+  "backward": "e4e483b764e9a85f84a04425e57d73ecdcc72eb2e4d97a64f17d9da58fa5ace0"
+ },
+ "clifford_recipes_sha256": "4629507dcbdd516457c001ff8f9dbe750d1a0cbfa5cfa3c6be003d45804ba0c5"
+}
diff --git a/research/gauge44-slots/construction/barch/RECIPE-U8.json b/research/gauge44-slots/construction/barch/RECIPE-U8.json
new file mode 100644
index 0000000000..ee215a805a
--- /dev/null
+++ b/research/gauge44-slots/construction/barch/RECIPE-U8.json
@@ -0,0 +1,1528 @@
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+  "1364": [
+   262,
+   134,
+   64,
+   38,
+   20,
+   10,
+   1
+  ],
+  "1367": [
+   262,
+   134,
+   70,
+   32,
+   18,
+   12,
+   1
+  ],
+  "1370": [
+   256,
+   128,
+   64,
+   38,
+   18,
+   12,
+   1
+  ],
+  "1373": [
+   256,
+   128,
+   70,
+   32,
+   20,
+   10,
+   1
+  ],
+  "1376": [
+   256,
+   134,
+   70,
+   38,
+   20,
+   10,
+   1
+  ],
+  "1379": [
+   256,
+   134,
+   64,
+   32,
+   20,
+   10,
+   1
+  ],
+  "1382": [
+   262,
+   128,
+   70,
+   38,
+   20,
+   10,
+   1
+  ],
+  "1385": [
+   262,
+   128,
+   64,
+   32,
+   20,
+   10,
+   1
+  ],
+  "1388": [
+   256,
+   128,
+   65,
+   33,
+   18,
+   11,
+   7
+  ],
+  "1391": [
+   256,
+   128,
+   64,
+   32,
+   18,
+   11,
+   7
+  ],
+  "1394": [
+   257,
+   129,
+   65,
+   33,
+   19,
+   10,
+   7
+  ],
+  "1397": [
+   257,
+   129,
+   64,
+   32,
+   19,
+   10,
+   7
+  ],
+  "1400": [
+   257,
+   128,
+   64,
+   33,
+   18,
+   11,
+   7
+  ],
+  "1403": [
+   257,
+   128,
+   65,
+   32,
+   19,
+   10,
+   7
+  ],
+  "1406": [
+   256,
+   129,
+   64,
+   33,
+   18,
+   11,
+   7
+  ],
+  "1409": [
+   256,
+   129,
+   65,
+   32,
+   19,
+   10,
+   7
+  ],
+  "1412": [
+   257,
+   129,
+   64,
+   33,
+   24,
+   4,
+   3
+  ],
+  "1415": [
+   257,
+   129,
+   65,
+   32,
+   24,
+   5,
+   2
+  ],
+  "1418": [
+   256,
+   128,
+   64,
+   33,
+   24,
+   5,
+   2
+  ],
+  "1421": [
+   256,
+   128,
+   65,
+   32,
+   24,
+   4,
+   3
+  ],
+  "1424": [
+   256,
+   129,
+   65,
+   33,
+   24,
+   4,
+   3
+  ],
+  "1427": [
+   256,
+   129,
+   64,
+   32,
+   24,
+   4,
+   3
+  ],
+  "1430": [
+   257,
+   128,
+   65,
+   33,
+   24,
+   4,
+   3
+  ],
+  "1433": [
+   257,
+   128,
+   64,
+   32,
+   24,
+   4,
+   3
+  ]
+ },
+ "tail_insert": [
+  [
+   7,
+   [
+    "add",
+    496,
+    450,
+    -1,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     24,
+     4,
+     2,
+     1
+    ]
+   ]
+  ],
+  [
+   6,
+   [
+    "add",
+    497,
+    451,
+    -1,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     24,
+     4,
+     2,
+     1
+    ]
+   ]
+  ],
+  [
+   5,
+   [
+    "add",
+    520,
+    452,
+    -1,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ],
+  [
+   4,
+   [
+    "add",
+    521,
+    453,
+    -1,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ],
+  [
+   3,
+   [
+    "add",
+    544,
+    454,
+    2,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ],
+  [
+   2,
+   [
+    "add",
+    545,
+    455,
+    2,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ],
+  [
+   1,
+   [
+    "add",
+    568,
+    456,
+    2,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     24,
+     4,
+     2,
+     1
+    ]
+   ]
+  ],
+  [
+   0,
+   [
+    "add",
+    569,
+    457,
+    2,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     24,
+     4,
+     2,
+     1
+    ]
+   ]
+  ]
+ ],
+ "cleanup_prepend": [
+  [
+   "add",
+   484,
+   231,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   485,
+   226,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   508,
+   230,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   509,
+   228,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   532,
+   232,
+   2,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   533,
+   62,
+   2,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   556,
+   236,
+   2,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ],
+  [
+   "add",
+   557,
+   238,
+   2,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ]
+ ],
+ "local_profile": {
+  "1": 2548,
+  "2": 338,
+  "3": 446,
+  "4": 162,
+  "5": 72,
+  "8": 8
+ },
+ "expect_sha256": "090fd574747fbf9628e70cb9beb792732914cfa52e1df147579fe4dbccc68c5a",
+ "priced": {
+  "dk_ideal": 3.140480230774418e-07,
+  "dP": {
+   "5": 16,
+   "4": -32,
+   "3": 16
+  }
+ },
+ "variants": [
+  {
+   "X": 231,
+   "E": 450,
+   "dsides": [
+    878,
+    886
+   ],
+   "donors": [
+    450,
+    231
+   ],
+   "hold": [
+    496,
+    484
+   ],
+   "kept": {
+    "1215": 450,
+    "1223": 231
+   },
+   "when": "mid"
+  },
+  {
+   "X": 230,
+   "E": 452,
+   "dsides": [
+    894,
+    902
+   ],
+   "donors": [
+    452,
+    230
+   ],
+   "hold": [
+    520,
+    508
+   ],
+   "kept": {
+    "1231": 452,
+    "1239": 230
+   },
+   "when": "mid"
+  },
+  {
+   "X": 232,
+   "E": 454,
+   "dsides": [
+    910,
+    918
+   ],
+   "donors": [
+    454,
+    232
+   ],
+   "hold": [
+    544,
+    532
+   ],
+   "kept": {
+    "1247": 454,
+    "1255": 232
+   },
+   "when": "mid"
+  },
+  {
+   "X": 236,
+   "E": 456,
+   "dsides": [
+    926,
+    934
+   ],
+   "donors": [
+    456,
+    236
+   ],
+   "hold": [
+    568,
+    556
+   ],
+   "kept": {
+    "1263": 456,
+    "1271": 236
+   },
+   "when": "mid"
+  },
+  {
+   "X": 226,
+   "E": 451,
+   "dsides": [
+    880,
+    888
+   ],
+   "donors": [
+    451,
+    226
+   ],
+   "hold": [
+    497,
+    485
+   ],
+   "kept": {
+    "1217": 451,
+    "1225": 226
+   },
+   "when": "mid"
+  },
+  {
+   "X": 228,
+   "E": 453,
+   "dsides": [
+    896,
+    904
+   ],
+   "donors": [
+    453,
+    228
+   ],
+   "hold": [
+    521,
+    509
+   ],
+   "kept": {
+    "1233": 453,
+    "1241": 228
+   },
+   "when": "mid"
+  },
+  {
+   "X": 62,
+   "E": 455,
+   "dsides": [
+    912,
+    920
+   ],
+   "donors": [
+    455,
+    62
+   ],
+   "hold": [
+    545,
+    533
+   ],
+   "kept": {
+    "1249": 455,
+    "1257": 62
+   },
+   "when": "mid"
+  },
+  {
+   "X": 238,
+   "E": 457,
+   "dsides": [
+    928,
+    936
+   ],
+   "donors": [
+    457,
+    238
+   ],
+   "hold": [
+    569,
+    557
+   ],
+   "kept": {
+    "1265": 457,
+    "1273": 238
+   },
+   "when": "mid"
+  }
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/barch/build_tri.py b/research/gauge44-slots/construction/barch/build_tri.py
new file mode 100644
index 0000000000..11c4371114
--- /dev/null
+++ b/research/gauge44-slots/construction/barch/build_tri.py
@@ -0,0 +1,87 @@
+#!/usr/bin/env python3
+"""build_tri.py BASE_WORD RECIPE OUT_WORD [--control NAME]
+
+Standard library only. Applies a NewBArch triangle-hybrid recipe to the X4 word (1e1d99ba) and writes a FULL-WORD.json.gz.
+Recipe keys (all indices refer to the BASE word):
+  base_sha256      sha256 of the decompressed base JSON (checked)
+  B_delete         list of B indices removed
+  B_insert         list of [pos, gate]: gate (with frame) inserted before base B gate pos (list order kept)
+  B_frames         {index: frame}: explicit re-chosen frame of a kept base B gate
+  tail_insert      list of [early_index, gate]: gates appended to cleanup in list order, then registered as early cleanup at early_index (ascending)
+  cleanup_prepend  list of gates prepended to the full cleanup (early indices are shifted)
+  local_profile    report.local_profile of the result
+  expect_sha256    sha256 of the decompressed result (checked unless a control is requested)
+Controls (each must be REJECTED by audit_local; see controls.json):
+  drop_restore     omit cleanup_prepend (end value of the holder not restored)
+  restore_full     move tail_insert gates into the full cleanup (FULL frame) instead of early cleanup
+  drop_preread     omit the inserted entrance pre-reads (inserted target += E gates at pos < first donation)
+  donation_after   insert each donation after its reading target's read instead of before it
+  NAME@X           the same control restricted to the instance whose packet register is X (recipe 'variants')
+"""
+import sys, json, gzip, hashlib, copy
+
+FULL = [256, 128, 64, 32, 16, 8, 4, 2, 1]
+
+def load(p):
+    raw = gzip.decompress(open(p, 'rb').read()); return json.loads(raw), hashlib.sha256(raw).hexdigest()
+
+def apply(w, rc, control=None):
+    w = copy.deepcopy(w); B = w['B']
+    S = None
+    if control and '@' in control:                     # per-instance control: name@X mutates only instance X's gates
+        control, x = control.split('@'); x = int(x)
+        vv = [s for s in rc['variants'] if s['X'] == x][0]; S = {vv['X'], vv['E'], *vv['hold']}
+    sel = lambda g: S is None or bool({g[1], g[2]} & S)
+    dele = set(rc['B_delete']); fr = {int(k): f for k, f in rc['B_frames'].items()}
+    ins = [list(x) for x in rc['B_insert']]
+    don = [x for x in ins if not (112 <= x[1][1] < 224)]           # donations: destination is not a target
+    first_don = min(p for p, _ in don) if don else 0
+    if control == 'drop_preread':
+        ins = [x for x in ins if not (x[0] < first_don and 112 <= x[1][1] < 224 and sel(x[1]))]
+    if control == 'donation_after':
+        new = []
+        for p, g in ins:
+            if g in [d[1] for d in don] and sel(g):
+                rd = [i for i, e in enumerate(B) if i >= p and e[0] == 'add' and e[2] == g[1] and 112 <= e[1] < 224]
+                p = rd[0] + 1
+            new.append([p, g])
+        ins = new
+    at = {}
+    for p, g in ins: at.setdefault(p, []).append(list(g))
+    out = []
+    for i, e in enumerate(B):
+        out.extend(at.get(i, []))
+        if i in dele: continue
+        e = list(e)
+        if i in fr: e = e[:-1] + [list(fr[i])]
+        out.append(e)
+    out.extend(at.get(len(B), []))
+    w['B'] = out
+    pre = [list(g) for g in rc['cleanup_prepend'] if not (control == 'drop_restore' and sel(g))]
+    tails = [list(x) for x in rc['tail_insert']]
+    if control == 'restore_full':
+        pre = pre + [g[1][:-1] + [FULL] for g in tails if sel(g[1])]; tails = [g for g in tails if not sel(g[1])]
+    C = pre + w['cleanup']; sh = len(pre)
+    early = [[i + sh, U] for i, U in w['early_cleanup']]
+    idx = []
+    for j, g in tails: C.append(list(g)); idx.append((j, len(C) - 1, list(g[-1])))   # appended in recipe order
+    for j, ci, U in sorted(idx): early.insert(j, [ci, U])                               # then registered at their early index
+    w['cleanup'] = C; w['early_cleanup'] = early
+    w['report'] = dict(w['report']); w['report']['local_profile'] = rc['local_profile']
+    return w
+
+def main():
+    a = sys.argv[1:]; control = None
+    if '--control' in a: k = a.index('--control'); control = a[k + 1]; del a[k:k + 2]
+    base, out = a[0], a[2]
+    w, sha = load(base); rc = json.load(open(a[1]))
+    if sha != rc['base_sha256']: raise SystemExit('base sha mismatch ' + sha)
+    w2 = apply(w, rc, control)
+    raw = json.dumps(w2, separators=(',', ':')).encode()
+    open(out, 'wb').write(gzip.compress(raw, mtime=0))
+    s = hashlib.sha256(raw).hexdigest()
+    if control is None and s != rc['expect_sha256']: raise SystemExit('result sha mismatch ' + s)
+    print(json.dumps(dict(control=control, sha256=s)))
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/barch/reproduce_barch.py b/research/gauge44-slots/construction/barch/reproduce_barch.py
new file mode 100644
index 0000000000..22f15b491d
--- /dev/null
+++ b/research/gauge44-slots/construction/barch/reproduce_barch.py
@@ -0,0 +1,92 @@
+#!/usr/bin/env python3
+"""Rebuild the B0 word (NewBArch's width-neutral triangle-hybrid B-delivery rewrite on X4) and its native locals.
+
+Input: a fresh `construction/jx/reproduce_jx.py` output directory; its X4 word (1e1d99ba...) is pinned there and by
+RECIPE-B0.json (base_sha256). Steps, each checked exactly:
+  1. barch: build_tri.py (standard library only; NewBArch) applies the recipe's explicit B deletes and inserts (with frames),
+     re-chosen B frames, early-cleanup tails and FULL-cleanup restores; it checks the base and result shas (d9ba0942...).
+  2. barch-controls: run_controls.py rebuilds C0 (identity, must reproduce the input), the recipe word (must PASS #645's
+     independent audit_local.py) and four mutants (drop_restore, restore_full, drop_preread, donation_after), globally
+     and for each recipe variant (NAME@X); each mutant must FAIL audit_local with its pinned message. Every outcome is
+     required and the control set is pinned (LOCAL-PINS).
+  3. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant) on the B0 word; count pinned.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs; canonical word, local programs and
+     Clifford recipes pinned (LOCAL-PINS-barch-<id>.json).
+Apache-2.0. Driver by ColdWitness around NewBArch's builder and controls.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+PKG = HERE.parents[1]
+P6 = HERE.parent / 'layers_p6n'
+MUTANTS = ('drop_restore', 'restore_full', 'drop_preread', 'donation_after')
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--jx-dir', type=Path, required=True, help='construction/jx/reproduce_jx.py output')
+    ap.add_argument('--recipe', default='U8', help='RECIPE-<id>.json and LOCAL-PINS-barch-<id>.json')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-barch-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    inp = a.jx_dir.resolve() / 'jx/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['base_sha256'], 'input must be the pinned X4 word'
+    (out / 'barch').mkdir(); word = out / 'barch/FULL-WORD.json.gz'
+    run('barch', HERE / 'build_tri.py', inp, rfile, word, portable=False)
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['expect_sha256']
+    run('barch-controls', HERE / 'run_controls.py', inp, rfile, PKG / 'independent/audit_local.py', out / 'barch-controls', portable=False)
+    res = read(out / 'barch-controls/controls.json')
+    want = ['C0_identity', 'recipe', *MUTANTS] + [m + '@' + str(v['X']) for v in rec.get('variants', []) for m in MUTANTS]
+    assert sorted(res) == sorted(want) == sorted(pins['barch_controls']) and all(x['ok'] for x in res.values()), res
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/barch/run_controls.py b/research/gauge44-slots/construction/barch/run_controls.py
new file mode 100644
index 0000000000..f1ce999bfb
--- /dev/null
+++ b/research/gauge44-slots/construction/barch/run_controls.py
@@ -0,0 +1,33 @@
+#!/usr/bin/env python3
+"""run_controls.py BASE_WORD RECIPE AUDIT_LOCAL_PY OUTDIR : C0 identity, the recipe word (must PASS) and the four negative
+controls (each must FAIL audit_local with its pinned message prefix). Standard library only; writes OUTDIR/controls.json."""
+import sys, json, subprocess, os, gzip, hashlib
+base, recipe, audit, out = sys.argv[1:5]
+here = os.path.dirname(os.path.abspath(__file__)); os.makedirs(out, exist_ok=True)
+# pinned rejection sites (observed on RECIPE-V1 and RECIPE-B0; the failing rows are recorded in controls.json): the holder 485 is not restored; the low-end restore 497-=451 moved to the
+# FULL cleanup runs after 451's own tail and leaves 497 wrong; without the pre-read (or with the donation after the read)
+# the entering helper's start value reaches a target.
+EXPECT = {None: 'PASS', 'drop_restore': 'all-column endpoint failure (False, ',
+          'restore_full': 'all-column endpoint failure (False, ',
+          'drop_preread': 'nonzero entrance response', 'donation_after': 'nonzero entrance response'}
+res = {}
+ident = os.path.join(out, 'C0.json')
+json.dump(dict(json.load(open(recipe)), B_delete=[], B_insert=[], B_frames={}, tail_insert=[], cleanup_prepend=[],
+               local_profile=json.loads(gzip.decompress(open(base, 'rb').read()))['report']['local_profile'],
+               expect_sha256=hashlib.sha256(gzip.decompress(open(base, 'rb').read())).hexdigest()), open(ident, 'w'))
+r = subprocess.run([sys.executable, '-B', os.path.join(here, 'build_tri.py'), base, ident, os.path.join(out, 'C0.json.gz')], capture_output=True, text=True)
+res['C0_identity'] = dict(ok=r.returncode == 0, out=r.stdout.strip() or r.stderr.strip()[-200:])
+ctls = list(EXPECT) + [c + '@' + str(s['X']) for s in json.load(open(recipe)).get('variants', []) for c in EXPECT if c]
+for ctl in ctls:
+    name = ctl or 'recipe'; wp = os.path.join(out, name + '.json.gz')
+    cmd = [sys.executable, '-B', os.path.join(here, 'build_tri.py'), base, recipe, wp] + (['--control', ctl] if ctl else [])
+    b = subprocess.run(cmd, capture_output=True, text=True)
+    if b.returncode: res[name] = dict(ok=False, build=b.stderr[-300:]); continue
+    a = subprocess.run([sys.executable, '-B', audit, '--word', wp, '--output', os.path.join(out, name + '.audit.json')], capture_output=True, text=True)
+    txt = a.stdout + a.stderr
+    if ctl is None: ok = a.returncode == 0 and 'PASS_INDEPENDENT' in txt
+    else: ok = a.returncode != 0 and EXPECT[ctl.split('@')[0]] in txt
+    res[name] = dict(ok=ok, build=json.loads(b.stdout), audit_tail=txt.strip().splitlines()[-1][:200])
+json.dump(res, open(os.path.join(out, 'controls.json'), 'w'), indent=1)
+print(json.dumps({k: x['ok'] for k, x in res.items()}))
+sys.exit(0 if all(x['ok'] for x in res.values()) else 1)
diff --git a/research/gauge44-slots/construction/build_gauge_cold44.py b/research/gauge44-slots/construction/build_gauge_cold44.py
new file mode 100644
index 0000000000..72d2945f6b
--- /dev/null
+++ b/research/gauge44-slots/construction/build_gauge_cold44.py
@@ -0,0 +1,210 @@
+"""Exact dyadic cold-end realization of the source-branch/factory-completion word.
+Prepared for icekylinx with OpenAI Codex assistance; Apache-2.0.
+This is a constructor: independent endpoint/frame audits remain required.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+import copy,gzip,json,hashlib,time,sys,argparse,importlib.util
+D=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser(description=__doc__)
+for name in ('input','out','hamming','upstream-package'):ap.add_argument('--'+name,type=Path,required=True)
+args=ap.parse_args();WPATH=args.input;OUT=args.out
+assert __debug__, 'Assertions are required'
+OUT.mkdir(exist_ok=False,parents=True)
+def rd(p):return json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+w=rd(WPATH);v=w['report']['v'];n=2*v+w['report']['R'];N=list(range(v))+list(range(2*v,n));ix={x:i for i,x in enumerate(N)}
+F9=[256,128,64,32,16,8,4,2,1];t0=time.monotonic()
+def basis(vs):
+ d={}
+ for a in vs:
+  for k in sorted(d,reverse=True):
+   if a>>k&1:a^=d[k]
+  if a:
+   k=a.bit_length()-1
+   for j in d:
+    if d[j]>>k&1:d[j]^=a
+   d[k]=a
+ return tuple(d[k] for k in sorted(d,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def regs(e):return e[1:3] if e[0]=='add' else e[1:2]
+def inverse(e):
+ e=copy.deepcopy(e)
+ if e[0]=='add':e[3]=-e[3]
+ else:e[2],e[3]=e[3],e[2]
+ return e
+def apply(e,M,mapping=None):
+ t=mapping[e[1]] if mapping is not None else e[1]
+ if e[0]=='add':
+  s=mapping[e[2]] if mapping is not None else e[2];q=Q(e[3],e[4])
+  for j,a in M[s].items():
+   x=M[t].get(j,Q(0))+q*a
+   if x:M[t][j]=x
+   else:M[t].pop(j,None)
+ else:
+  q=Q(e[2],e[3]);M[t]={j:q*a for j,a in M[t].items()}
+def rref(A):
+ a=[list(map(Q,row)) for row in A];nr=len(a);nc=len(a[0]) if nr else 0;row=0;piv=[]
+ for c in range(nc):
+  k=next((i for i in range(row,nr) if a[i][c]),None)
+  if k is None:continue
+  a[row],a[k]=a[k],a[row];q=a[row][c];a[row]=[x/q for x in a[row]]
+  for i in range(nr):
+   if i!=row and a[i][c]:q=a[i][c];a[i]=[x-q*y for x,y in zip(a[i],a[row])]
+  piv.append(c);row+=1
+  if row==nr:break
+ return a,piv
+def rank(A):return len(rref(A)[1])
+def null(A,nc=None):
+ if A:a,piv=rref(A);nc=len(a[0])
+ else:a=[];piv=[];assert nc is not None
+ free=[j for j in range(nc) if j not in piv];out=[[Q(0) for j in free] for i in range(nc)]
+ for k,c in enumerate(free):out[c][k]=Q(1)
+ for i,c in enumerate(piv):
+  for k,j in enumerate(free):out[c][k]=-a[i][j]
+ return out
+def mm(A,B):
+ if not A:return []
+ if not B:return [[] for row in A]
+ bt=list(zip(*B));return [[sum((a*b for a,b in zip(row,col)),Q(0)) for col in bt] for row in A]
+def tr(A):return list(map(list,zip(*A)))
+def inv(A):
+ n0=len(A);a,p=rref([row+[Q(i==j) for j in range(n0)] for i,row in enumerate(A)])
+ assert p[:n0]==list(range(n0))
+ return [row[n0:] for row in a]
+def unit(q):
+ if not q:return False
+ a=abs(q.numerator);b=q.denominator
+ return not a&(a-1) and not b&(b-1)
+def dyadic(q):return not q.denominator&(q.denominator-1)
+def opadd(t,s,q,F):return ['add',t,s,q.numerator,q.denominator,list(F)]
+def opscale(t,q,F):return ['scale',t,q.numerator,q.denominator,list(F)]
+def eliminate(M,ids,F,skip=()):
+ """Return legal dyadic row operations taking an invertible sparse matrix to I."""
+ skip=set(skip);ops=[];dim=len(M)
+ def add(i,j,q):
+  if q:
+   assert dyadic(q);e=opadd(ids[i],ids[j],q,F);ops.append(e)
+   for c,x in M[j].items():
+    z=M[i].get(c,Q(0))+q*x
+    if z:M[i][c]=z
+    else:M[i].pop(c,None)
+ def scale(i,q):
+  if q!=1:
+   assert unit(q);ops.append(opscale(ids[i],q,F));M[i]={c:q*x for c,x in M[i].items()}
+ def swap(i,j):
+  if i!=j:
+   add(i,j,Q(1));add(j,i,Q(-1));add(i,j,Q(1));scale(j,Q(-1))
+ for c in range(dim):
+  if c in skip:
+   assert M[c]=={c:Q(1)} and all(not M[i].get(c) for i in range(dim) if i!=c)
+   continue
+  cand=[i for i in range(c,dim) if i not in skip and M[i].get(c)]
+  k=next((i for i in cand if unit(M[i][c])),None)
+  if k is None:
+   # Elementary Euclidean row additions reduce the pivot-column numerator gcd.
+   assert cand,('singular',c)
+   while k is None:
+    cand.sort(key=lambda i:abs(M[i][c]));a=cand[0]
+    b=next((i for i in cand[1:] if M[i][c]),None)
+    if b is None:raise ValueError(('non-dyadic determinant pivot',c,M[a][c]))
+    rat=M[b][c]/M[a][c];q=rat.numerator//rat.denominator
+    if q==0:q=1 if rat>0 else -1
+    add(b,a,Q(-q));cand=[i for i in cand if M[i].get(c)]
+    k=next((i for i in cand if unit(M[i][c])),None)
+  swap(c,k);scale(c,1/M[c][c])
+  for i in range(dim):
+   if i!=c and M[i].get(c):
+    assert i not in skip
+    add(i,c,-M[i][c])
+ assert all(row=={i:Q(1)} for i,row in enumerate(M))
+ return ops
+def realize(A,ids,F):
+ M=[{j:Q(x) for j,x in enumerate(row) if x} for row in A]
+ return [inverse(e) for e in reversed(eliminate(M,ids,F))]
+# Reconstruct the actual non-target map after the inherited HPE tail.
+inherited_tail=[w['cleanup'][i][:-1]+[list(f)] for i,f in w.get('early_cleanup',[])]
+mainN=[e for e in w['A']+w['B'] if not v<=e[1]<2*v]
+M=[{i:Q(1)} for i in range(len(N))]
+for e in mainN+inherited_tail:apply(e,M,ix)
+MI=[{i:Q(1)} for i in range(len(N))]
+for e in reversed(mainN+inherited_tail):apply(inverse(e),MI,ix)
+cur={x:(w['ports'][x],) if x<v else basis(w.get('start_extra',{}).get(str(x),[])) for x in N}
+for e in w['A']+w['B']+inherited_tail:
+ for x in regs(e):
+  if x in cur:cur[x]=basis(e[-1])
+enter=set(map(int,w.get('start_extra',{})));protected=[ix[x] for x in N if x<v or x in enter]
+mods=rd(args.hamming/'PACKET-PROGRAMS.json.gz');proto=rd(args.hamming/'PROTOTYPE.json')
+plans=[];premix=[];tail=[];ends={};Mafter=copy.deepcopy(M)
+for b,mod in enumerate(mods):
+ ss=mod['receipt']['source_lines'];F=basis([proto['binary_ports'][s] for s in ss]);I=[ix[x] for x in N if inside(cur[x],F)]
+ hs=list(range(224+16*b,224+16*(b+1)));H=[ix[x] for x in hs]
+ C=[[M[i].get(j,Q(0)) for j in protected] for i in I]
+ L=tr(null(tr(C),len(I)))
+ A=[[MI[j].get(i,Q(0)) for i in I] for j in protected];A=[row for row in A if any(row)]
+ K=null(A,len(I));BK=mm(L,K);_,piv=rref(BK);r=len(piv);assert r==len(L)==(2 if b in [0,1,2,11,12,13] else 4),(b,r,len(L))
+ Ksel=[[row[j] for j in piv] for row in K];Bsel=[[row[j] for j in piv] for row in BK];U=mm(Ksel,inv(Bsel));assert mm(L,U)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ q=mm([[MI[i].get(j,Q(0)) for j in I] for i in range(len(N))],U)
+ assert all(not any(q[i]) for i in range(len(N)) if i not in H),('nonlocal premix',b)
+ RR=mm(L,[[M[i].get(j,Q(0)) for j in H] for i in I]);qH=[q[i] for i in H]
+ assert mm(RR,qH)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ # Pick low physical helper destinations with independent U coordinate rows.
+ ih=[]
+ for j in sorted((j for j,i in enumerate(I) if N[i] in hs),key=lambda j:(cur[N[I[j]]]!=F,N[I[j]])):
+  if rank([U[k] for k in ih]+[U[j]])>len(ih):ih.append(j)
+  if len(ih)==r:break
+ assert len(ih)==r
+ endhs=[N[I[j]] for j in ih];endhidx=[hs.index(h) for h in endhs]
+ kerR=null(RR,16);Qmat=[[Q(0) for j in range(16)] for i in range(16)]
+ for j,hj in enumerate(endhidx):
+  for i in range(16):Qmat[i][hj]=qH[i][j]
+ other=[j for j in range(16) if j not in endhidx]
+ for k,j in enumerate(other):
+  for i in range(16):Qmat[i][j]=kerR[i][k]
+ assert rank(Qmat)==16
+ pops=realize(Qmat,hs,());premix+=pops
+ T=[[Q(i==j)-sum((U[i][k]*L[k][j] for k in range(r)),Q(0)) for j in range(len(I))] for i in range(len(I))]
+ for k,i in enumerate(ih):T[i]=L[k]
+ tops=realize(T,[N[i] for i in I],F);tail+=tops
+ # Right-compose this initial helper premix; other blocks have disjoint H sets.
+ for row in Mafter:
+  vals=[row.get(h,Q(0)) for h in H]
+  if any(vals):
+   for hj in H:row.pop(hj,None)
+   for j,hj in enumerate(H):
+    z=sum((vals[i]*Qmat[i][j] for i in range(16)),Q(0))
+    if z:row[hj]=z
+ for e in tops:apply(e,Mafter,ix)
+ ends.update({h:list(F) for h in endhs})
+ plans.append(dict(block=b,frame=list(F),registers=[N[i] for i in I],ends=endhs,pairing_rank=r,premix_gates=len(pops),tail_gates=len(tops),Q=[[str(x) for x in row] for row in Qmat],T=[[str(x) for x in row] for row in T]))
+ print('BLOCK',b,'ends',endhs,'Qops',len(pops),'Tops',len(tops),flush=True)
+# Check actual post-tail isolation before constructing the high-frame inverse.
+allends=set(ends)|set(map(int,w.get('helper_final',{})))
+for h in allends:
+ j=ix[h];assert Mafter[j]=={j:Q(1)},('row not isolated',h,Mafter[j]);assert all(not row.get(j) for i,row in enumerate(Mafter) if i!=j),('column not isolated',h)
+print('EXACT_ISOLATED',len(ends),'new;',len(allends),'total',round(time.monotonic()-t0,3),flush=True)
+fullops=eliminate(copy.deepcopy(Mafter),N,F9,[ix[x] for x in allends])
+print('FULL_INVERSE',len(fullops),round(time.monotonic()-t0,3),flush=True)
+# Cancel new cold-axis target responses inside A, after their wrappers.
+Dirt=[({h:Q(1)} if h in ends else {}) for h in range(n)]
+for e in premix+w['A']+w['cut']+w['B']:apply(e,Dirt)
+for e in w['precondition']:apply(e,Dirt)
+postcomp=[opadd(y,h,-a,()) for y in range(v,2*v) for h,a in sorted(Dirt[y].items()) if a]
+assert all(h in ends for e in postcomp for h in [e[2]])
+new=copy.deepcopy(w);new['A']=postcomp+premix+w['A'];new['cleanup']=inherited_tail+tail+fullops
+new['early_cleanup']=[[i,e[-1]] for i,e in enumerate(inherited_tail+tail)]
+new['helper_final'].update({str(h):f for h,f in ends.items()})
+new['refactored_cleanup']={'kind':'source_branch_gauge_and_retired_completion_cold44','new_cold_ends':len(ends),'exact_non_target_isolation_checked':True,'high_inverse':'dyadic_sparse_Gauss_Jordan'}
+# Derive paid profile by subtracting and adding literal frame-chain counts.
+spec=importlib.util.spec_from_file_location('upstream_cold_end',args.upstream_package/'code/build_cold_end.py')
+profile_module=importlib.util.module_from_spec(spec);spec.loader.exec_module(profile_module)
+oldprof,_=profile_module.chain_profile(w);newprof,_=profile_module.chain_profile(new)
+prof=Counter({int(k):z for k,z in w['report']['local_profile'].items()});prof.subtract(oldprof);prof.update(newprof)
+widths=Counter(len(basis(new['helper_final'].get(str(h),F9)))-len(basis(new.get('start_extra',{}).get(str(h),[]))) for h in range(224,n))
+new['report'].update(local_profile={str(k):z for k,z in sorted(prof.items()) if z},local_rank_mass=sum(k*z for k,z in prof.items()),width_inventory={str(k):z for k,z in sorted(widths.items()) if z},status='EXACT_COLD44_CONSTRUCTED_PENDING_INDEPENDENT_AUDIT')
+raw=json.dumps(new,sort_keys=True,separators=(',',':')).encode();sha=hashlib.sha256(raw).hexdigest();(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+recipe={'premix':postcomp+premix,'cleanup':new['cleanup'],'early_cleanup':new['early_cleanup'],'cold_ends':{str(h):f for h,f in ends.items()},'refactored_cleanup':new['refactored_cleanup'],'output_content_sha256':sha}
+(OUT/'RECIPE.json.gz').write_bytes(gzip.compress(json.dumps(recipe,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+receipt=dict(input_content_sha256=hashlib.sha256(gzip.decompress(WPATH.read_bytes())).hexdigest(),output_content_sha256=sha,blocks=plans,new_cold_ends=len(ends),all_low_ended_helpers=len(allends),premix_gates=len(premix),postwrapper_compensation_gates=len(postcomp),tail_gates=len(tail),inherited_tail_gates=len(inherited_tail),full_inverse_gates=len(fullops),profile=new['report']['local_profile'],width_inventory=new['report']['width_inventory'],rank_mass=new['report']['local_rank_mass'],seconds=time.monotonic()-t0)
+(OUT/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(json.dumps({k:z for k,z in receipt.items() if k!='blocks'},indent=2),flush=True)
diff --git a/research/gauge44-slots/construction/construct_gauge_xcentre.py b/research/gauge44-slots/construction/construct_gauge_xcentre.py
new file mode 100644
index 0000000000..1010d86746
--- /dev/null
+++ b/research/gauge44-slots/construction/construct_gauge_xcentre.py
@@ -0,0 +1,381 @@
+# Round20 early-coordinate-center / own-Y variant, prepared for icekylinx
+# with OpenAI Codex assistance. Apache-2.0. Scalar elementary-operation
+# helpers below are retained from the attributed PR514 construct_partial.py.
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+# AtomScout: leaver-read K-triangles (schedule from atom1.py / rog.py CP-SAT)
+TRI=json.loads(Path(sys.argv[3]).read_text())
+FULLT={(tuple(tr['p']),tr['e']) for tr in TRI['triangles']}
+TRI_COORDS={t+8 for tr in TRI['triangles'] for t,_,_ in tr['reads']}
+COPYL=[]
+NH=504-3*len(FULLT)+len(COPYL)
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+# Helper ids of the unpatched 504 construction: every allocation advances the 504 numbering; a packet copy that the
+# K-triangle schedule never forms advances it without allocating (HELPER-MAP.json).
+shadow=[];skipped=[];nxt=[2*v]
+def alloc():
+    n=len(cur);cur.append(());rows.append({});shadow.append(nxt[0]);nxt[0]+=1;return n
+def skip():
+    skipped.append(nxt[0]);nxt[0]+=1
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# Each source quartet supplies pair partials first. The other two coordinate
+# partitions supply eight early face packets without touching the eight
+# partials later copied into the preconditioned Y coordinates.
+SELECT=(0,0)
+PRIORITY=json.loads((INPUT/"COMPLETION-PRIORITY.json").read_text())
+maps={};early={};own_rows={};pairs=[];tetrads={};block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)});maps[c]=mp
+    for ei,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[:40]):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        if ei==15:
+            for jj in range(4,8):swap(mp[jj],mp[2*jj+9],(P[ids[jj]],))
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in targets:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                t,u=sorted(ts);e2=R[t][q[0]]*R[t][q[1]]
+                pair={'targets':(t,u),'keys':[(c,p,eps),(c,q,e2)],'selected':pi==SELECT[parity],
+                      'matrix':[[R[a][p[0]],R[a][q[0]]] for a in (t,u)]}
+                pairs.append(pair)
+                if not pair['selected']:continue
+                zz=-Q(2*R[u][p[0]],R[t][p[0]])
+                sources=tet[1-parity]
+                for target,sign in ((t,-1),(u,1)):
+                    wanted={s:-Q(G[t][s],4)-sign*Q(G[u][s],2)/zz for s in sources
+                            if -Q(G[t][s],4)-sign*Q(G[u][s],2)/zz}
+                    assert len(wanted)==2
+                    candidates=[]
+                    for r in mp.values():
+                        if set(rows[r])!=set(wanted):continue
+                        s=next(iter(wanted));coef=wanted[s]/rows[r][s]
+                        if all(wanted[s]==coef*rows[r][s] for s in wanted):candidates.append((r,coef))
+                    assert len(candidates)==1
+                    r,coef=candidates[0];assert len(cur[r])==2
+                    own_rows[target]=(r,coef,cur[r])
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    needed={own_rows[t][0] for t in ids}
+    early[c]={j for j,e in enumerate(z['events'][40:]) if not ({mp[e[0]],mp[e[1]]}&needed)}
+    assert len(early[c])==8
+    retired=[]
+    for j in sorted(early[c]):
+        (t,s,a,b),F=z['events'][40+j],z['event_frames'][40+j]
+        add(mp[t],mp[s],Q(a,b),tuple(F));retired.append(mp[s])
+    assert not set(retired)&needed
+    # These eight retired rows already span every source coordinate. Keep
+    # them invertible and place the four coordinate totals in a changed basis.
+    F=basis([P[s] for s in ids]);assert len(F)==4
+    regs=sorted(retired,key=lambda r:(r>=v,r))
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    M=[[Q(R[s][i]) for s in ids] for i in c]
+    def qr_rank(rs):
+        bs={}
+        for r in rs:
+            r=r.copy()
+            for i,b in sorted(bs.items()):
+                if r[i]:q=r[i];r=[x-q*y for x,y in zip(r,b)]
+            i=next((i for i,x in enumerate(r) if x),None)
+            if i is not None:q=r[i];bs[i]=[x/q for x in r]
+        return len(bs)
+    assert qr_rank(M)==4
+    for rr0 in PRIORITY[",".join(map(str,c))]["rows"]:
+        rr=list(map(Q,rr0))
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    for i in range(8):
+        if len(M)==8:break
+        rr=[Q(i==j) for j in range(8)]
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    assert len(M)==8
+    linear(regs,M,F)
+    for i,r in zip(c,regs):
+        assert rows[r]=={s:Q(R[s][i]) for s in ids}
+        block_totals[c,i]=r
+
+# All centers are complete while Y is still at zero. This is the crucial
+# difference from an illegal early-own-Y prefix using the old center order.
+centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+assert all(cur[v+t]==() for t in range(v))
+
+phase=B
+for t,(r,coef,F) in sorted(own_rows.items()):
+    if t in TRI_COORDS:continue
+    assert cur[r]==F
+    add(v+t,r,coef,F)
+# requests are needed for TRI coefficients
+requests=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    requests[key1].append((t,-Q(mat[0][0],2)))
+    requests[key2].append((u,-Q(mat[0][1],2)))
+reqcoef={t:(key,coef) for key,reqs in requests.items() for t,coef in reqs}
+def face_info(c,p,eps):
+    z=blocks[c];keys=[(pp,ee) for pp in it.combinations(c,2) for ee in (-1,1)]
+    r_local,alpha=z['outputs'][keys.index((p,eps))]
+    j=[j for j in range(40,len(z['events'])) if z['events'][j][0]==r_local];assert len(j)==1
+    return j[0],Q(alpha)
+tri_join_counts=Counter()
+lcopy={}
+for s8 in COPYL:
+    r=s8+8;c=alloc();add(c,r,1,cur[r]);lcopy[r]=c
+for tr in TRI['triangles']:
+    p,eps=tuple(tr['p']),tr['e']
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];r0=r;r=lcopy.get(r,r)
+        key,coef=reqcoef[t];assert key[1]==p and key[2]==eps,(key,p,eps)
+        if blk==key[0]:
+            rr,c0,F0=own_rows[t];assert rr==r0;q=c0
+        else:
+            j,alpha=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert loc in ev[:2]
+            q=coef*alpha
+        F=basis(cur[v+t]+cur[r]);assert inside(F,hyper(P[t])),('TRI frame',t)
+        tri_join_counts[len(F)]+=1;add(v+t,r,q,F)
+
+packets={}
+for c,z in sorted(blocks.items()):
+    mp=maps[c]
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    skipev={face_info(c,p,eps)[0] for p,eps in keys if (p,eps) in FULLT}
+    for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]):
+        if j not in early[c] and 40+j not in skipev:
+            t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    for key,(r,alpha) in zip(keys,z['outputs']):
+        if tuple(key) in FULLT:skip();continue
+        a=mp[r];b=alloc();add(b,a,1,cur[a])
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha))
+
+# Both tetrahedra use the same partition. A selected key has exactly two
+# selected Y loads and no ordinary M consumer. Supply its two raw halves in
+# opposite orders and never form that M. Other keys retain the old M path.
+second=[];first_join_counts=Counter()
+for key,reqs in sorted(requests.items()):
+    assert len(reqs)==2
+    c,p,eps=key
+    if (p,eps) in FULLT:continue
+    ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds
+    for j,(target,coef) in enumerate(sorted(reqs)):
+        first_source,second_source=(a,b) if j==0 else (b,a)
+        r,alpha=packets[first_source,p,eps,second_source]
+        F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+        first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F)
+        r,alpha=packets[second_source,p,eps,c]
+        second.append((target,r,coef*alpha))
+
+Ms={}
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for eps in (-1,1):
+            if (c,p,eps) in requests:continue
+            (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,eps]=(a,alpha)
+
+consumers=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    for key in pair['keys']:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    if key in requests:
+        assert all(pairs[i]['selected'] for i in uses)
+        continue
+    assert all(not pairs[i]['selected'] for i in uses)
+    a,alpha=Ms[key]
+    for j,pid in enumerate(uses):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+assert len(cur)-240==NH,len(cur)-240
+
+selected_join_counts=Counter()
+for target,r,coef in second:
+    F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+    selected_join_counts[len(F)]+=1;add(v+target,r,coef,F)
+output_basis=[]
+for pair in pairs:
+    if not pair['selected']:continue
+    (t,u),mat=pair['targets'],pair['matrix']
+    F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u]))
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert rows[v+t]==expected,('side identity',t)
+
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8
+assert sum(r*z for r,z in H.items())==9*NH+240*8+72,sum(r*z for r,z in H.items())
+
+def apply(e,matrix):
+    if e[0]=='add':
+        _,t,s,a,b,*_=e;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    e[-1]=list(FULL);return e
+cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q]
+cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v]
+matrix=[{r:Q(1)} if r<v else {} for r in range(len(cur))]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(len(cur)))
+
+# Restrict the eight isolated axis ports exactly, keeping the stable 112-port
+# label set. This variant changes the local word, not the outer geometry.
+mp={s:s-8 for s in range(8,120)}
+mp.update({120+s:112+s-8 for s in range(8,120)})
+mp.update({240+r:224+r for r in range(NH)})
+def restrict(events,is_cut=False):
+    out=[]
+    for e in events:
+        regs=e[1:3] if e[0]=='add' else e[1:2]
+        if any(r not in mp for r in regs):
+            assert is_cut and e[0]=='add' and e[1]-120==e[2] and e[2]<8 and e[3:5]==[1,1]
+            continue
+        q=copy.deepcopy(e);q[1]=mp[q[1]]
+        if q[0]=='add':q[2]=mp[q[2]]
+        out.append(q)
+    return out
+H.subtract({1:8,8:16});H=+H
+report={'status':'EXACT_CLEAN_OWN_Y_EARLY_CENTER_WORD_NOT_ADMITTED',
+        'h':9,'v':112,'R':NH,'cst':64,'m':73,'local_profile':dict(sorted(H.items())),
+        'centre_ranks':[8]*8,**({'tri_join_counts':dict(tri_join_counts)} if TRI['triangles'] else {}),'selected_load_join_counts':dict(selected_join_counts),'selected_partitions':list(SELECT),'first_load_join_counts':dict(first_join_counts),
+        'source_columns_exact':112,'borrowed_output_pairs':56,'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'local_rank_mass':sum(r*n for r,n in H.items()),'scope':'Clean scalar identity and all literal monotone local frames only; arbitrary-dirt compensation, entrance kernels, exact phase recipes, and global hosting/pricing are not yet certified.'}
+word={'report':report,'ports':P[8:],'root_lines':R[8:],
+      'A':restrict(A),'B':restrict(B),'cut':restrict(cut,True),'cleanup':restrict(cleanup),'precondition':restrict(precondition),
+      'centers':[mp[r] for r in centers[:8]],'center_frames':center_frames[:8],
+      'scatter':[[str(x) for x in row[:8]] for row in scatter[8:]]}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+assert len(shadow)==NH and len(shadow)+len(skipped)==504
+hmap={**{r:r for r in range(224)},**{224+s_-240:224+i for i,s_ in enumerate(shadow)}}
+(OUT/'HELPER-MAP.json').write_text(json.dumps({'map':{str(k):hmap[k] for k in sorted(hmap)},'removed_504_helpers':[224+s_-240 for s_ in skipped]})+'\n')
+(OUT/'DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/gauge44-slots/construction/frames/FRAME-RECIPE-sw4.json b/research/gauge44-slots/construction/frames/FRAME-RECIPE-sw4.json
new file mode 100644
index 0000000000..7394064c5e
--- /dev/null
+++ b/research/gauge44-slots/construction/frames/FRAME-RECIPE-sw4.json
@@ -0,0 +1,167 @@
+{
+  "input_content_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+  "gate_frames": [
+    [
+      "B",
+      856,
+      [
+        272,
+        144,
+        64,
+        6
+      ],
+      [
+        272,
+        144,
+        64,
+        8,
+        6,
+        1
+      ]
+    ],
+    [
+      "B",
+      860,
+      [
+        265,
+        137,
+        88,
+        6
+      ],
+      [
+        256,
+        128,
+        65,
+        16,
+        9,
+        6
+      ]
+    ],
+    [
+      "B",
+      868,
+      [
+        265,
+        200,
+        33,
+        6
+      ],
+      [
+        256,
+        144,
+        81,
+        33,
+        9,
+        6
+      ]
+    ],
+    [
+      "B",
+      873,
+      [
+        320,
+        192,
+        16,
+        6
+      ],
+      [
+        320,
+        192,
+        32,
+        16,
+        6,
+        1
+      ]
+    ],
+    [
+      "B",
+      876,
+      [
+        392,
+        73,
+        33,
+        6
+      ],
+      [
+        273,
+        144,
+        64,
+        33,
+        9,
+        6
+      ]
+    ],
+    [
+      "B",
+      953,
+      [
+        265,
+        137,
+        73,
+        6
+      ],
+      [
+        265,
+        137,
+        73,
+        32,
+        25,
+        6
+      ]
+    ],
+    [
+      "B",
+      961,
+      [
+        265,
+        185,
+        80,
+        6
+      ],
+      [
+        265,
+        128,
+        64,
+        41,
+        16,
+        6
+      ]
+    ],
+    [
+      "B",
+      965,
+      [
+        272,
+        185,
+        73,
+        6
+      ],
+      [
+        257,
+        128,
+        73,
+        40,
+        17,
+        6
+      ]
+    ]
+  ],
+  "expected": {
+    "output_content_sha256": "e78047028c7dcd25fb1b6216c2b53eda76d2f91292b21d43f5d1903cc13a5c6c",
+    "local_profile": {
+      "1": 2556,
+      "2": 334,
+      "3": 430,
+      "4": 194,
+      "5": 56,
+      "8": 8
+    },
+    "width_inventory": {
+      "4": 80,
+      "5": 32,
+      "7": 54,
+      "8": 122,
+      "9": 216
+    }
+  }
+}
diff --git a/research/gauge44-slots/construction/frames/LOCAL-PINS-frames-sw4.json b/research/gauge44-slots/construction/frames/LOCAL-PINS-frames-sw4.json
new file mode 100644
index 0000000000..834ae13a2f
--- /dev/null
+++ b/research/gauge44-slots/construction/frames/LOCAL-PINS-frames-sw4.json
@@ -0,0 +1,12 @@
+{
+ "word": "P6k4sw4f8",
+ "frame_build_controls": 3,
+ "frame_controls": 10,
+ "layer_controls": 95,
+ "canonical_sha256": "b0d27d99423047ce07af847734f5a86f9411038bb3b0bf721918ece1ee579325",
+ "program_sha256": {
+  "forward": "b2cf8298488cc81aeee1385d4d9ebd842efbb21abb9296fca903adb8ad50f8d0",
+  "backward": "6f28cf1413671d5b7c50488a1603fa8f1558da469abbbb45b6a9b66ec640712b"
+ },
+ "clifford_recipes_sha256": "eb7569e004bd2a2937928db9db49dad949ec291f00c2d21df6af722df7cb6c9c"
+}
diff --git a/research/gauge44-slots/construction/frames/build_frames.py b/research/gauge44-slots/construction/frames/build_frames.py
new file mode 100644
index 0000000000..22021549e6
--- /dev/null
+++ b/research/gauge44-slots/construction/frames/build_frames.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Apply the eight pinned B-gate frame raises of FRAME-RECIPE-sw4.json (chafreaky's PR741) to the SW4 word.
+
+usage: build_frames.py INPUT_WORD.json.gz OUT_DIR RECIPE.json
+
+Standard library only. The frames are applied by BlockInvert's `../promo/build_promotion.apply` (no entrances, eight
+'B' gate_frames), which checks each old frame and recomputes the local profile and widths. This builder then checks:
+input sha pin; the scalar program of A, cut, B, precondition and cleanup unchanged (every field but the frame); start
+and end frames unchanged; local profile and width inventory equal to the recipe's; output sha pin. Three pin controls
+(input pin, wrong old frame, output pin) must be rejected at their pinned reasons on every build.
+Adapted from PR741's extras/build_frames.py (chafreaky). Apache-2.0.
+"""
+import copy, gzip, hashlib, importlib.util, json, sys
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+_s = importlib.util.spec_from_file_location('promotion', HERE.parent / 'promo/build_promotion.py')
+B = importlib.util.module_from_spec(_s); _s.loader.exec_module(B)
+
+
+def construct(raw, recipe):
+    assert hashlib.sha256(raw).hexdigest() == recipe['input_content_sha256'], 'input word pin'
+    w = json.loads(raw)
+    assert len(recipe['gate_frames']) == 8 and all(c[0] == 'B' for c in recipe['gate_frames']), 'eight B frames'
+    out = B.apply(w, dict(entrances={}, gate_frames=recipe['gate_frames']))
+    for section in ('A', 'cut', 'B', 'precondition', 'cleanup'):
+        assert [e[:-1] for e in w[section]] == [e[:-1] for e in out[section]], 'scalar program unchanged'
+    assert out['start_extra'] == w['start_extra'] and out['helper_final'] == w['helper_final'], 'endpoint frames unchanged'
+    assert out['report']['local_profile'] == recipe['expected']['local_profile'] and \
+        out['report']['width_inventory'] == recipe['expected']['width_inventory'], 'profile and width pins'
+    data = json.dumps(out, sort_keys=True, separators=(',', ':')).encode()
+    assert hashlib.sha256(data).hexdigest() == recipe['expected']['output_content_sha256'], 'output word pin'
+    return data
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    inp, outd, rfile = map(Path, sys.argv[1:4])
+    raw = gzip.decompress(inp.read_bytes()); recipe = json.loads(rfile.read_text())
+    data = construct(raw, recipe)
+    rejected = []
+    for name, change, reason in [
+            ('input-pin', lambda r: r.__setitem__('input_content_sha256', '0' * 64), 'input word pin'),
+            ('old-frame', lambda r: r['gate_frames'][0].__setitem__(2, []), 'gate frame mismatch'),
+            ('output-pin', lambda r: r['expected'].__setitem__('output_content_sha256', '0' * 64), 'output word pin')]:
+        r = copy.deepcopy(recipe); change(r)
+        try:
+            construct(raw, r)
+        except AssertionError as e:
+            assert reason in str(e), (name, str(e)); rejected.append(dict(name=name, reason=reason))
+        else:
+            raise AssertionError('accepted ' + name)
+    outd.mkdir(parents=True)
+    (outd / 'FULL-WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+    (outd / 'BUILD.json').write_text(json.dumps(dict(
+        status='PASS_EIGHT_FRAME_EXACT_CONSTRUCTION', input_sha256=hashlib.sha256(raw).hexdigest(),
+        output_sha256=hashlib.sha256(data).hexdigest(), scalar_program_unchanged=True, frames=8,
+        rejected_controls=rejected), indent=2) + '\n')
+    print('PASS eight B frames and three pin controls')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/frames/frame_controls.py b/research/gauge44-slots/construction/frames/frame_controls.py
new file mode 100644
index 0000000000..cd951a9f0e
--- /dev/null
+++ b/research/gauge44-slots/construction/frames/frame_controls.py
@@ -0,0 +1,45 @@
+#!/usr/bin/env python3
+"""Focused native controls for the eight B-frame raises (PR741's extras/frame_controls.py, ported).
+
+usage: frame_controls.py WORD.json.gz ROUTING.json.gz OUT.json RECIPE.json   (env PR635_CODE = PR635's code/ directory)
+
+The positive word must pass PR635's unchanged native audit `hpe_audit_and_transport.run`. Ten mutants must be rejected
+at their pinned reasons: each of the eight raised gates with its frame emptied ('nonmonotone'), a doubled read
+coefficient on the first raised gate ('arbitrary-dirt endpoint') and a tampered paid profile ('paid local profile
+differs'). Apache-2.0; adapted from chafreaky's PR741.
+"""
+import copy, gzip, importlib.util, json, os, sys, tempfile, time
+from pathlib import Path
+
+_s = importlib.util.spec_from_file_location('audit', Path(os.environ['PR635_CODE']) / 'hpe_audit_and_transport.py')
+A = importlib.util.module_from_spec(_s); _s.loader.exec_module(A)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    word, routing, out, rfile = map(Path, sys.argv[1:5])
+    w = json.loads(gzip.decompress(word.read_bytes())); recipe = json.loads(rfile.read_text())
+
+    def trial(z):
+        with tempfile.TemporaryDirectory() as td:
+            d = Path(td); f = d / 'word.json.gz'; f.write_bytes(gzip.compress(json.dumps(z).encode(), mtime=0))
+            try:
+                A.run(f, routing, d / 'native'); return None
+            except AssertionError as e:
+                return str(e)
+
+    start = time.monotonic(); assert trial(w) is None, 'positive word rejected'; records = []
+    for section, i, old, new in recipe['gate_frames']:
+        z = copy.deepcopy(w); z[section][i][-1] = []; error = trial(z)
+        assert error and 'nonmonotone' in error, (i, error); records.append(dict(name='frame-%d-emptied' % i, rejected=error))
+    z = copy.deepcopy(w); i = recipe['gate_frames'][0][1]; z['B'][i][3] *= 2; error = trial(z)
+    assert error and 'arbitrary-dirt endpoint' in error, error; records.append(dict(name='changed-read-coefficient', rejected=error))
+    z = copy.deepcopy(w); z['report']['local_profile']['1'] += 1; error = trial(z)
+    assert error and 'paid local profile differs' in error, error; records.append(dict(name='paid-profile-tampering', rejected=error))
+    out.write_text(json.dumps(dict(status='PASS_FOCUSED_EIGHT_FRAME_NATIVE_CONTROLS', positive=1, rejected=records,
+                                   seconds=time.monotonic() - start), indent=2) + '\n')
+    print('PASS', len(records), 'mutations', flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/frames/reproduce_frames.py b/research/gauge44-slots/construction/frames/reproduce_frames.py
new file mode 100644
index 0000000000..eaf9b47cac
--- /dev/null
+++ b/research/gauge44-slots/construction/frames/reproduce_frames.py
@@ -0,0 +1,89 @@
+#!/usr/bin/env python3
+"""Rebuild the SW4F8 word (eight B-gate frame raises on the SW4 word, chafreaky's PR741 recipe) and its native locals.
+
+Input: a fresh `construction/sw4/reproduce_sw4.py --recipe P6k4` output directory; its SW4 word (d232183f...) is pinned
+there and by FRAME-RECIPE-<id>.json. Steps, each checked exactly:
+  1. frames: build_frames.py (standard library only) applies the eight 'B' gate_frames with BlockInvert's
+     build_promotion.apply. Scalar program, start and end frames unchanged; profile, widths and output sha pinned;
+     three pin controls must be rejected (count pinned).
+  2. frame-controls: frame_controls.py, PR741's ten focused mutants judged by PR635's unchanged native audit.
+  3. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant) on the SW4F8 word; count pinned.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs, with the canonical word, local
+     programs and Clifford recipes pinned (LOCAL-PINS-frames-<id>.json).
+Apache-2.0.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P6 = HERE.parent / 'layers_p6n'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--sw4-dir', type=Path, required=True, help='construction/sw4/reproduce_sw4.py output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--recipe', default='sw4', help='FRAME-RECIPE-<id>.json and LOCAL-PINS-frames-<id>.json')
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('FRAME-RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-frames-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    inp = a.sw4_dir.resolve() / 'sw4/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['input_content_sha256'], 'input must be the pinned SW4 word'
+    run('frames', HERE / 'build_frames.py', inp, out / 'frames', rfile, portable=False)
+    b = read(out / 'frames/BUILD.json')
+    assert b['status'] == 'PASS_EIGHT_FRAME_EXACT_CONSTRUCTION' and len(b['rejected_controls']) == pins['frame_build_controls'], b
+    word = out / 'frames/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['expected']['output_content_sha256']
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('frame-controls', HERE / 'frame_controls.py', word, routing, out / 'FRAME-CONTROLS.json', rfile, portable=False)
+    fc = read(out / 'FRAME-CONTROLS.json')
+    assert fc['status'] == 'PASS_FOCUSED_EIGHT_FRAME_NATIVE_CONTROLS' and len(fc['rejected']) == pins['frame_controls'], len(fc['rejected'])
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/jx/LOCAL-PINS-jx-X4.json b/research/gauge44-slots/construction/jx/LOCAL-PINS-jx-X4.json
new file mode 100644
index 0000000000..417e4ba7a1
--- /dev/null
+++ b/research/gauge44-slots/construction/jx/LOCAL-PINS-jx-X4.json
@@ -0,0 +1,11 @@
+{
+ "word": "X4",
+ "jx_controls": 7,
+ "layer_controls": 95,
+ "canonical_sha256": "1c0e9da767d4418f70016af599e4a447a3f7777acabe930318459c0fbbd260aa",
+ "program_sha256": {
+  "forward": "076a2d428f97abb30473df05110998efbe5ac809885bae4ceb1b8bd81329a1e6",
+  "backward": "7915679ee305927463d19725360cc15132dd21ede18897d09a935dca1df0d55d"
+ },
+ "clifford_recipes_sha256": "20dddfce0ded7e41dc507939df7297bd98aec1286e05d7dbf18000d57e69a0b7"
+}
diff --git a/research/gauge44-slots/construction/jx/RECIPE-X4.json b/research/gauge44-slots/construction/jx/RECIPE-X4.json
new file mode 100644
index 0000000000..30f7fa5948
--- /dev/null
+++ b/research/gauge44-slots/construction/jx/RECIPE-X4.json
@@ -0,0 +1,1412 @@
+{
+ "input_content_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+ "input_word": "P6k4sw4 (BRoute w/P6k4sw4, d232183f)",
+ "frames_741_source": {
+  "pr": 741,
+  "commit": "e516b146",
+  "recipe": "scratch/WasteAttack/FRAME-RECIPE-741.json",
+  "frames_only_output_sha": "e78047028c7dcd25fb1b6216c2b53eda76d2f91292b21d43f5d1903cc13a5c6c"
+ },
+ "frames_741": [
+  [
+   856,
+   [
+    272,
+    144,
+    64,
+    8,
+    6,
+    1
+   ]
+  ],
+  [
+   860,
+   [
+    256,
+    128,
+    65,
+    16,
+    9,
+    6
+   ]
+  ],
+  [
+   868,
+   [
+    256,
+    144,
+    81,
+    33,
+    9,
+    6
+   ]
+  ],
+  [
+   873,
+   [
+    320,
+    192,
+    32,
+    16,
+    6,
+    1
+   ]
+  ],
+  [
+   876,
+   [
+    273,
+    144,
+    64,
+    33,
+    9,
+    6
+   ]
+  ],
+  [
+   953,
+   [
+    265,
+    137,
+    73,
+    32,
+    25,
+    6
+   ]
+  ],
+  [
+   961,
+   [
+    265,
+    128,
+    64,
+    41,
+    16,
+    6
+   ]
+  ],
+  [
+   965,
+   [
+    257,
+    128,
+    73,
+    40,
+    17,
+    6
+   ]
+  ]
+ ],
+ "raises": [
+  [
+   855,
+   [
+    280,
+    128,
+    64,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   859,
+   [
+    256,
+    129,
+    65,
+    40,
+    25,
+    6
+   ]
+  ],
+  [
+   862,
+   [
+    280,
+    144,
+    80,
+    56,
+    6,
+    1
+   ]
+  ],
+  [
+   863,
+   [
+    272,
+    136,
+    80,
+    56,
+    6,
+    1
+   ]
+  ],
+  [
+   867,
+   [
+    256,
+    136,
+    64,
+    41,
+    16,
+    6
+   ]
+  ],
+  [
+   870,
+   [
+    256,
+    200,
+    40,
+    16,
+    6,
+    1
+   ]
+  ],
+  [
+   875,
+   [
+    272,
+    144,
+    80,
+    49,
+    8,
+    6
+   ]
+  ],
+  [
+   942,
+   [
+    256,
+    136,
+    72,
+    33,
+    25,
+    6
+   ]
+  ],
+  [
+   943,
+   [
+    320,
+    193,
+    33,
+    16,
+    9,
+    6
+   ]
+  ],
+  [
+   946,
+   [
+    256,
+    129,
+    64,
+    41,
+    16,
+    6
+   ]
+  ],
+  [
+   947,
+   [
+    273,
+    128,
+    81,
+    33,
+    9,
+    6
+   ]
+  ],
+  [
+   950,
+   [
+    257,
+    193,
+    33,
+    16,
+    9,
+    6
+   ]
+  ],
+  [
+   954,
+   [
+    272,
+    129,
+    80,
+    49,
+    8,
+    6
+   ]
+  ],
+  [
+   955,
+   [
+    256,
+    128,
+    64,
+    33,
+    17,
+    6
+   ]
+  ],
+  [
+   958,
+   [
+    257,
+    128,
+    81,
+    33,
+    9,
+    6
+   ]
+  ],
+  [
+   962,
+   [
+    273,
+    128,
+    64,
+    33,
+    8,
+    6
+   ]
+  ]
+ ],
+ "edits": {
+  "replace": [
+   {
+    "h": 448,
+    "i": 862,
+    "old": [
+     "add",
+     140,
+     448,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     140,
+     235,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 448,
+    "i": 1207,
+    "old": [
+     "add",
+     133,
+     448,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     133,
+     235,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 448,
+    "i": 870,
+    "old": [
+     "add",
+     132,
+     235,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     132,
+     448,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 448,
+    "i": 1199,
+    "old": [
+     "add",
+     141,
+     235,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     141,
+     448,
+     -1,
+     2
+    ],
+    "why": "r2h: read of r -> read of h"
+   },
+   {
+    "h": 472,
+    "i": 855,
+    "old": [
+     "add",
+     173,
+     472,
+     -1,
+     2
+    ],
+    "new": [
+     "add",
+     173,
+     267,
+     -1,
+     2
+    ],
+    "why": "h2r: read of h -> read of r"
+   },
+   {
+    "h": 472,
+    "i": 1198,
+    "old": [
+     "add",
+     140,
+     472,
+     -1,
+     2
+    ],
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+   "local_profile": {
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+    "3": 430,
+    "4": 178,
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+  "N4_raise_dim7_at_855": {
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+    "frame": [
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+     64,
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+     4,
+     2,
+     1
+    ]
+   },
+   "rejection_expected": [
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+    1302,
+    174
+   ]
+  }
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/jx/build_jx.py b/research/gauge44-slots/construction/jx/build_jx.py
new file mode 100644
index 0000000000..f8d74a6324
--- /dev/null
+++ b/research/gauge44-slots/construction/jx/build_jx.py
@@ -0,0 +1,167 @@
+#!/usr/bin/env python3
+"""build_jx.py --input WORD --recipe RECIPE.json --out OUT.json.gz [--control NAME] [--no-pin]
+
+Stdlib-only builder: joint read-set exchange (copy pairs, BRoute sw4 rule) + explicit B frame raises on P6k4sw4.
+Steps:
+ 1. input content sha256 must equal recipe.input_content_sha256.
+ 2. explicit B edits: replace (old gate asserted), delete (old gate asserted), insert (before an original index).
+ 3. frames: replaced/inserted gates take the plain join of their operands' current frames; gates listed in
+    frames_741 / raises take base = the listed frame and the resulting frame must EQUAL it (explicit frames);
+    every other gate keeps span(stored frame + operand frames) (monotone repair). Early cleanup likewise.
+ 4. legality: target frames inside u_t^perp at every gate; tails inside helper_final; every end frame contains the
+    final frame; the explicit frame must contain the join (enforced by equality in 3).
+ 5. exactness: the rational linear map of the whole B segment is identical to the input's (Fraction replay).
+ 6. paid profile recomputed (A + centre levels + B + tails + ends) and written to report.local_profile.
+Output: canonical json (sort_keys, compact) gzip mtime=0. Exit 0 and prints output sha; exit 2 with the first
+rejection (site) on failure. --control applies a named mutation from recipe.controls (expected to be rejected
+or to give a pinned sha)."""
+import argparse, gzip, json, hashlib, sys, copy
+from fractions import Fraction as Fr
+from collections import Counter
+
+V, H = 112, 9
+
+def basis(vs):
+    piv = {}
+    for a in vs:
+        while a:
+            b = a.bit_length() - 1
+            if b in piv: a ^= piv[b]
+            else: piv[b] = a; break
+    for k in sorted(piv):
+        for j in sorted(piv):
+            if j > k and (piv[j] >> k) & 1: piv[j] ^= piv[k]
+    return tuple(piv[k] for k in sorted(piv, reverse=True))
+
+def contained(a, b): return basis(list(a) + list(b)) == tuple(b)
+def registers(e): return e[1:3] if e[0] == 'add' else e[1:2]
+def hyper(p): return basis([x for x in range(1, 1 << H) if (x & p).bit_count() % 2 == 0])
+FULL = basis([1 << i for i in range(H)])
+def csha(w): return hashlib.sha256(json.dumps(w, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+
+class Reject(Exception): pass
+
+def symstate(gs):
+    rows = {}
+    for e in gs:
+        for q in registers(e): rows.setdefault(q, {q: Fr(1)})
+        if e[0] == 'add':
+            t, s = e[1], e[2]; c = Fr(e[3], e[4]); d = rows[t]
+            for k, x in list(rows[s].items()):
+                a = d.get(k, 0) + c * x
+                if a: d[k] = a
+                else: d.pop(k, None)
+        else:
+            t = e[1]; c = Fr(e[2], e[3]); rows[t] = {k: c * x for k, x in rows[t].items()}
+    return rows
+
+def build(w, rc, control=None):
+    w = copy.deepcopy(w); B0 = w['B']
+    edits = copy.deepcopy(rc['edits']); explicit = {int(i): f for i, f in rc['frames_741']}
+    for i, f in rc['raises']:
+        if int(i) in explicit: raise Reject(('duplicate frame', i))
+        explicit[int(i)] = f
+    if control:
+        c = rc['controls'][control]['mutation']
+        if c['kind'] == 'drop_insert': edits['insert'] = [x for k, x in enumerate(edits['insert']) if k != c['k']]
+        elif c['kind'] == 'flip_insert_sign': edits['insert'][c['k']]['gate'][3] *= -1
+        elif c['kind'] == 'frame': explicit[c['i']] = c['frame']
+        elif c['kind'] == 'drop_edits': edits = dict(replace=[], delete=[], insert=[])
+        elif c['kind'] == 'drop_raises': explicit = {int(i): f for i, f in rc['frames_741']}
+        elif c['kind'] == 'only_edits_of':
+            hs = set(c['h'])
+            edits = {k: [x for x in v if x['h'] in hs] for k, v in edits.items()}
+            explicit = {i: f for i, f in explicit.items() if i in {int(j) for j, _ in rc['frames_741']} or i in set(c['raises'])}
+        elif c['kind'] == 'empty': edits = dict(replace=[], delete=[], insert=[]); explicit = {}
+        else: raise SystemExit('unknown control')
+    B = [list(e) for e in B0]; tag = set(); dele = set(); ins = {}
+    for x in edits['replace']:
+        i = x['i']
+        if B[i][:-1] != x['old']: raise Reject(('replace old mismatch', i))
+        B[i] = list(x['new']) + [B[i][-1]]; tag.add(i)
+    for x in edits['delete']:
+        i = x['i']
+        if B[i][:-1] != x['old']: raise Reject(('delete old mismatch', i))
+        dele.add(i)
+    for x in edits['insert']: ins.setdefault(x['before'], []).append(list(x['gate']) + [None])
+    NB, nt, key = [], set(), []
+    for i, e in enumerate(B):
+        for g in ins.get(i, []): nt.add(len(NB)); NB.append(g); key.append(None)
+        if i in dele: continue
+        if i in tag: nt.add(len(NB))
+        NB.append(e); key.append(i)
+    # frames + paid
+    R = w['report']['R']; n = 2 * V + R
+    END = [FULL] * V + [hyper(p) for p in w['ports']] + [FULL] * R
+    for q, U in w['helper_final'].items(): END[int(q)] = basis(U)
+    cur = [(p,) for p in w['ports']] + [()] * (V + R)
+    for q, U in w['start_extra'].items(): cur[int(q)] = basis(U)
+    paid = Counter()
+    for e in w['A']:
+        for q in registers(e):
+            U = basis(e[-1]); d = len(U) - len(cur[q])
+            if d: paid[d] += 1
+            cur[q] = U
+    lev = {int(t): basis(U) for t, U in w.get('target_levels', {}).items()}
+    for q, U in zip(w['centers'], w['center_frames']):
+        U = basis(U); served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == q}
+        for T in sorted(served, key=lambda x: -len(x)):
+            if T != U: paid[len(U) - len(T)] += 1
+            U = T
+    used = set()
+    for j, e in enumerate(NB):
+        rs = registers(e); k = key[j]
+        if k is not None and k in explicit: base = list(explicit[k]); used.add(k)
+        elif j in nt or e[-1] is None: base = []
+        else: base = list(e[-1])
+        F = basis(base + [x for q in rs for x in cur[q]])
+        if k is not None and k in explicit and F != basis(explicit[k]): raise Reject(('explicit frame below join', k))
+        for q in rs:
+            if V <= q < 2 * V and not contained(F, END[q]): raise Reject(('cap', j, q))
+            d = len(F) - len(cur[q])
+            if d: paid[d] += 1
+            cur[q] = F
+        NB[j] = list(e[:-1]) + [list(F)]
+    if used != set(explicit): raise Reject(('unused explicit frame', sorted(set(explicit) - used)))
+    newearly = []
+    for i, U in w['early_cleanup']:
+        rs = registers(w['cleanup'][i]); F = basis(list(U) + [x for q in rs for x in cur[q]])
+        for q in rs:
+            if w['helper_final'].get(str(q)) is not None and not contained(F, END[q]): raise Reject(('tailend', i, q))
+            d = len(F) - len(cur[q])
+            if d: paid[d] += 1
+            cur[q] = F
+        newearly.append([i, list(F)])
+    for q in range(n):
+        if not contained(cur[q], END[q]): raise Reject(('end', q))
+        d = len(END[q]) - len(cur[q])
+        if d: paid[d] += 1
+    # exactness of the B segment
+    a, b = symstate([e[:-1] for e in B0]), symstate([e[:-1] for e in NB])
+    bad = sorted(q for q in set(a) | set(b) if a.get(q, {q: Fr(1)}) != b.get(q, {q: Fr(1)}))
+    if bad: raise Reject(('exactness rows', bad))
+    w['B'] = NB; w['early_cleanup'] = newearly
+    w['report'] = dict(w['report']); w['report']['local_profile'] = {str(k): v for k, v in sorted(paid.items())}
+    return w
+
+def main():
+    ap = argparse.ArgumentParser(); ap.add_argument('--input', required=True); ap.add_argument('--recipe', required=True)
+    ap.add_argument('--out'); ap.add_argument('--control'); ap.add_argument('--no-pin', action='store_true')
+    a = ap.parse_args()
+    w = json.loads(gzip.decompress(open(a.input, 'rb').read())); rc = json.load(open(a.recipe))
+    if csha(w) != rc['input_content_sha256']: print('REJECT input pin'); sys.exit(2)
+    pin = rc['controls'][a.control].get('rejection_expected') if a.control else None
+    try: o = build(w, rc, a.control)
+    except Reject as r:
+        got = json.loads(json.dumps(r.args[0])); print('REJECT', json.dumps(got))
+        if pin is not None:
+            print('CONTROL', 'PINNED' if got == pin else 'PIN MISMATCH %s' % json.dumps(pin)); sys.exit(0 if got == pin else 4)
+        sys.exit(2)
+    if pin is not None and not a.no_pin: print('CONTROL NOT REJECTED, pinned', json.dumps(pin)); sys.exit(4)
+    s = csha(o)
+    exp = rc['controls'][a.control].get('expected_sha') if a.control else rc['expected']['output_content_sha256']
+    print('OK', s, o['report']['local_profile'])
+    if a.out: open(a.out, 'wb').write(gzip.compress(json.dumps(o, sort_keys=True, separators=(',', ':')).encode(), mtime=0))
+    if not a.no_pin and exp and s != exp: print('REJECT output pin', exp); sys.exit(3)
+
+if __name__ == '__main__': main()
diff --git a/research/gauge44-slots/construction/jx/reproduce_jx.py b/research/gauge44-slots/construction/jx/reproduce_jx.py
new file mode 100644
index 0000000000..6829a1b25d
--- /dev/null
+++ b/research/gauge44-slots/construction/jx/reproduce_jx.py
@@ -0,0 +1,99 @@
+#!/usr/bin/env python3
+"""Rebuild the X4 word (JointXF: joint read-set exchange on four further copy-pair instances plus explicit B frame
+raises, including chafreaky's PR741 eight frames) and its native locals.
+
+Input: a fresh `construction/sw4/reproduce_sw4.py --recipe P6k4` output directory; its SW4 word (d232183f...) is pinned
+there and by RECIPE-X4.json. Steps, each checked exactly:
+  1. jx: build_jx.py (standard library only; JointXF) applies the recipe's explicit B edits (replace / delete / insert,
+     each old gate asserted), the PR741 frames and the explicit raises, repairs all other frames monotonically, checks
+     target frames inside u_t^perp, tails and ends, and the exactness of the whole B segment (rational replay), and
+     pins the output sha.
+  2. jx-controls: every control in the recipe is rebuilt and must reproduce its pinned outcome exactly: a pinned
+     rejection site (exit 0 with CONTROL PINNED) or a pinned output sha. C1_741_only must reproduce PR741's word
+     e78047028c... (the construction/frames step's output); C0_identity reproduces the input.
+  3. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant) on the X4 word; count pinned.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs; canonical word, local programs
+     and Clifford recipes pinned (LOCAL-PINS-jx-X4.json).
+Apache-2.0. Driver by ColdWitness around JointXF's builder.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P6 = HERE.parent / 'layers_p6n'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--sw4-dir', type=Path, required=True, help='construction/sw4/reproduce_sw4.py output')
+    ap.add_argument('--recipe', default='X4', help='RECIPE-<id>.json and LOCAL-PINS-jx-<id>.json')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-jx-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True, ok=(0,)):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc in ok, (label, rc)
+        print('PASS', label, flush=True)
+        return (out / (label + '.log')).read_text()
+
+    inp = a.sw4_dir.resolve() / 'sw4/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['input_content_sha256'], 'input must be the pinned SW4 word'
+    (out / 'jx').mkdir(); word = out / 'jx/FULL-WORD.json.gz'
+    run('jx', HERE / 'build_jx.py', '--input', inp, '--recipe', rfile, '--out', word, portable=False)
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['expected']['output_content_sha256']
+    assert len(rec['controls']) == pins['jx_controls'], len(rec['controls'])
+    results = {}
+    for name, c in sorted(rec['controls'].items()):
+        log = run('jx-control-' + name, HERE / 'build_jx.py', '--input', inp, '--recipe', rfile, '--control', name, portable=False)
+        if 'rejection_expected' in c:
+            assert 'CONTROL PINNED' in log, (name, log[-300:]); results[name] = dict(rejected=c['rejection_expected'])
+        else:
+            assert ('OK ' + c['expected_sha']) in log, (name, log[-300:]); results[name] = dict(sha=c['expected_sha'])
+    assert rec['controls']['C1_741_only']['expected_sha'] == rec['frames_741_source']['frames_only_output_sha']
+    (out / 'JX-CONTROLS.json').write_text(json.dumps(dict(status='PASS_JX_PINNED_CONTROLS', controls=results), indent=1) + '\n')
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/layers/build_pivot_swap.py b/research/gauge44-slots/construction/layers/build_pivot_swap.py
new file mode 100644
index 0000000000..b225601c01
--- /dev/null
+++ b/research/gauge44-slots/construction/layers/build_pivot_swap.py
@@ -0,0 +1,160 @@
+"""Cost-neutral pivot-role swaps inside existing entrance-kernel families.  Apache-2.0.  Prepared with Claude Code
+assistance.  The pivot/donor role exchange follows PR266's "pivot role is moved" idea (bit side), applied here to the
+complex supplier's multicut kernel families (PR568 build_multicut_kernels.py shape).
+
+A kernel family on the input word is an entering helper p (start_extra E) together with the gates that read p at frame
+E before any other touch of p:  d += c_d * p @E  (d a helper or, in B, a target).  They cancel p's complete dirty
+response:  col(p) + sum_d c_d * col_{g_d}(d) = 0, where col_{g}(d) is d's suffix response from gate g on.
+
+Swap to the new pivot x (a helper donor of the family with exactly one family gate g_x = x's FIRST touch, and no other
+touch of x up to the family's last gate):
+    g_x :  x += c_x p   ->   p += (1/c_x) x
+    g_d :  d += c_d p   ->   d += (c_d/c_x) x          (d != x, same position and frame E)
+    start_extra: p -> x (same E); cleanup regenerated by the inherited inverse rule.
+Exactness (PROOF-NOTE-PIVOT.md): x holds only its initial dirt at every rewritten gate, and p holds only its initial dirt
+until g_x, so x's new response is col(x) + col(p)/c_x + sum_d (c_d/c_x) col_{g_d}(d) = (c_x col(x) + col(p) +
+sum_d c_d col_{g_d}(d)) / c_x = 0, because col(x) = col_{g_x}(x).  This script checks it by exact rational replay anyway.
+Cost: the frame chains of p and x are exchanged (p now climbs [] -> E at g_x where x did; x starts at E where p did), so
+gk_word.profile and the width multiset are unchanged; both are asserted.
+
+Recipe: {input_content_sha256, output_content_sha256, swaps: [{pivot, new_pivot, entrance, gates: [{part, index,
+before, after}]}]}.  Every expected `after` gate is recomputed from the rule above and must equal the recipe.
+
+Negative controls (--controls): mutated recipes/words that must be rejected at pinned reasons:
+  * nonzero response: another family gate's rescaled coefficient has the wrong sign;
+  * wrong pivot coefficient: g_x's new coefficient doubled;
+  * wrong entrance: the recipe's entrance is not p's start_extra;
+  * non-family gate: a recipe gate whose `before` is not the word's gate;
+  * new pivot touched in the window: x replaced by a family donor that is not a fresh helper (a target donor, or the
+    first other helper donor when the family has no target donor).
+"""
+from pathlib import Path
+from collections import Counter
+from fractions import Fraction as Q
+import argparse, copy, gzip, hashlib, json, sys
+assert __debug__, 'Assertions required'
+ap = argparse.ArgumentParser()
+for k in ('--input', '--recipe', '--gk-dir', '--out'): ap.add_argument(k, type=Path, required=True)
+a = ap.parse_args(); assert not a.out.exists()
+sys.path.insert(0, str(a.gk_dir)); import gk_word as G, gk_common as C
+G.V = C.V = 112; G.DATA = C.DATA = 7168
+V = 112
+raw = json.loads(gzip.decompress(a.input.read_bytes())); recipe = json.loads(a.recipe.read_text())
+enc = lambda x: json.dumps(x, sort_keys=True, separators=(',', ':')).encode(); sha = lambda x: hashlib.sha256(x).hexdigest()
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+inv_rule = lambda w: [G.inverse(e, G.FULL) for e in reversed(w['A'] + w['B']) if not V <= e[1] < 2 * V]
+dy = lambda q: q != 0 and q.denominator & (q.denominator - 1) == 0
+
+
+def response(w, h):
+    rows = {}
+    def get(r): return rows.setdefault(r, {r: Q(1)})
+    for e in w['A'] + w['cut'] + w['B']:
+        if e[0] == 'scale':
+            q = Q(e[2], e[3]); rows[e[1]] = {j: q * x for j, x in get(e[1]).items()}
+        else:
+            t, s = e[1], e[2]; q = Q(e[3], e[4]); src = get(s); tgt = get(t)
+            for j, x in list(src.items()):
+                z = tgt.get(j, Q(0)) + q * x
+                if z: tgt[j] = z
+                else: tgt.pop(j, None)
+    return {r: rows[r][h] for r in range(V, 2 * V) if r in rows and rows[r].get(h)}
+
+
+def build(w0, rec):
+    w = copy.deepcopy(w0); n = 2 * V + w['report']['R']
+    assert w['cleanup'] == inv_rule(w), 'input cleanup is not the inherited inverse rule'
+    P0 = G.profile(w); W0 = Counter(C.widths_of(w))
+    AB = [('A', i) for i in range(len(w['A']))] + [('B', i) for i in range(len(w['B']))]
+    pos = {k: j for j, k in enumerate(AB)}
+    seen = set(); receipts = []; rules = []
+    for s in rec['swaps']:
+        p, x, E = s['pivot'], s['new_pivot'], s['entrance']
+        assert 2 * V <= p < n and w['start_extra'].get(str(p)) == E, 'pivot is not an entering helper at the entrance'
+        assert 2 * V <= x < n and x not in w['centers'], 'new pivot must be a helper'
+        assert str(x) not in w['start_extra'], 'new pivot already entering'
+        assert not {p, x} & seen, 'registers shared between swaps'; seen |= {p, x}
+        gs = s['gates']; ks = [pos[(g['part'], g['index'])] for g in gs]
+        assert ks == sorted(ks) and len(set(ks)) == len(ks)
+        for g in gs:
+            e = w[g['part']][g['index']]
+            assert e == g['before'], 'recipe gate is not the word gate'
+            assert e[0] == 'add' and e[2] == p and e[1] != p and list(e[-1]) == list(E), 'not a family gate (d += c p @E)'
+        touch = lambda r: [j for j, (part, i) in enumerate(AB) if r in regs(w[part][i])]
+        tp = touch(p); assert tp[:len(ks)] == ks, 'family gates must be all touches of the pivot up to its first other touch'
+        gx = [k for k, g in zip(ks, gs) if g['before'][1] == x]; assert len(gx) == 1, 'new pivot must have exactly one family gate'
+        tx = touch(x); assert tx[0] == gx[0], 'new pivot touched before its family gate'
+        assert len(tx) == 1 or tx[1] > ks[-1], 'new pivot touched inside the family window'
+        cx = Q(*[g['before'][3:5] for g in gs if g['before'][1] == x][0])
+        for g in gs:
+            d, f = g['before'][1], g['after']
+            assert f[0] == 'add' and list(f[-1]) == list(E) and (f[1:3] == [p, x] if d == x else f[1:3] == [d, x]), 'after-gate shape'
+            assert dy(Q(f[3], f[4])), 'non-dyadic swapped coefficient'
+            w[g['part']][g['index']] = f
+            q = 1 / cx if d == x else Q(g['before'][3], g['before'][4]) / cx
+            rules.append((f, ['add', p, x, q.numerator, q.denominator, list(E)] if d == x else ['add', d, x, q.numerator, q.denominator, list(E)]))
+        w['start_extra'][str(x)] = w['start_extra'].pop(str(p))
+        receipts.append(dict(pivot=p, new_pivot=x, entrance=E, family_gates=len(gs)))
+    w['cleanup'] = inv_rule(w)
+    for s in rec['swaps']:
+        assert not response(w, s['new_pivot']), 'new pivot dirty response not zero'
+    assert all(f == e for f, e in rules), 'recipe after-gate is not the swap rule'
+    P1 = G.profile(w)
+    assert P1 == P0, 'paid profile not identical (swap is not cost-neutral)'
+    assert Counter(C.widths_of(w)) == W0, 'width multiset changed'
+    w['report']['local_profile'] = {str(k): v for k, v in sorted(P1.items())}
+    w['report']['local_rank_mass'] = sum(k * v for k, v in P1.items())
+    return w, receipts
+
+
+assert sha(enc(raw)) == recipe['input_content_sha256'], 'input content'
+out, receipts = build(raw, recipe)
+o = enc(out); assert sha(o) == recipe['output_content_sha256'], sha(o)
+
+# ---- negative controls -------------------------------------------------------------------------------------------
+WHY = dict(nonzero='new pivot dirty response not zero', coef='new pivot dirty response not zero',
+           entrance='paid profile not identical', nonfamily='recipe gate is not the word gate',
+           window='new pivot')
+controls = []
+
+
+def reject(name, mut, why):
+    r = copy.deepcopy(recipe); w = copy.deepcopy(raw)
+    mut(r, w)
+    try:
+        build(w, r)
+    except AssertionError as ex:
+        msg = str(ex)
+        assert why in msg, ('control rejected for the wrong reason', name, msg)
+        controls.append(dict(control=name, reason=msg)); return
+    raise AssertionError('control accepted: ' + name)
+
+
+for si, s in enumerate(recipe['swaps']):
+    x = s['new_pivot']; tag = '%d->%d' % (s['pivot'], x)
+    def m_other(r, w, si=si):
+        g = [g for g in r['swaps'][si]['gates'] if g['before'][1] != r['swaps'][si]['new_pivot']][0]
+        g['after'] = list(g['after']); g['after'][3] = -g['after'][3]
+    def m_coef(r, w, si=si):
+        g = [g for g in r['swaps'][si]['gates'] if g['before'][1] == r['swaps'][si]['new_pivot']][0]
+        g['after'] = list(g['after']); g['after'][3] *= 2
+    def m_nonfamily(r, w, si=si):
+        g = r['swaps'][si]['gates'][0]; g['before'] = list(g['before']); g['before'][3] = -g['before'][3]
+    def m_window(r, w, si=si):
+        S = r['swaps'][si]; S['new_pivot'] = [g['before'][1] for g in S['gates'] if g['before'][1] != S['new_pivot']][0]
+    def m_entrance(r, w, si=si):
+        S = r['swaps'][si]; S['entrance'] = [1]
+    reject('swap %s: another family gate keeps a wrong (unrescaled-sign) coefficient: new pivot response nonzero' % tag, m_other, WHY['nonzero'])
+    reject('swap %s: wrong pivot coefficient (1/c doubled) on the new pivot gate' % tag, m_coef, WHY['coef'])
+    reject('swap %s: non-family gate in the recipe' % tag, m_nonfamily, WHY['nonfamily'])
+    reject('swap %s: new pivot replaced by another family donor (not a fresh cold helper)' % tag, m_window, WHY['window'])
+    reject('swap %s: wrong entrance frame for the moved entrance' % tag, m_entrance, 'pivot is not an entering helper at the entrance')
+controls_receipt = list(controls)
+
+a.out.mkdir(parents=True); (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(o, mtime=0))
+rc = dict(status='PASS_COST_NEUTRAL_PIVOT_SWAPS', input_content_sha256=recipe['input_content_sha256'],
+          output_content_sha256=recipe['output_content_sha256'], swaps=receipts, local_profile=out['report']['local_profile'],
+          negative_controls_rejected=controls_receipt,
+          scope='Exact family rewrite, exact zero dirty response of every new pivot, identical paid profile and widths, '
+                'regenerated inverse-rule cleanup.  Native all-column audit, HPE/cold steps and global checks remain separate.')
+(a.out / 'PIVOT-SWAP.json').write_text(json.dumps(rc, indent=2, sort_keys=True) + '\n', newline='\n'); print(json.dumps(rc, indent=2))
diff --git a/research/gauge44-slots/construction/layers/layer_end_controls.py b/research/gauge44-slots/construction/layers/layer_end_controls.py
new file mode 100644
index 0000000000..317da36d95
--- /dev/null
+++ b/research/gauge44-slots/construction/layers/layer_end_controls.py
@@ -0,0 +1,201 @@
+"""layer_end_controls.py LAYERED-WORD.json.gz ROUTING OUTDIR (env PR635_CODE): adapted PR635 cold_end_controls.py (LayerReviewer): raw-word negative controls for the cold low-frame ends and the
+refactored cleanup accepted by hpe_audit_and_transport.py.  Every mutation MUST be rejected (AssertionError); the
+unmutated word MUST pass.  Apache-2.0.  DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code."""
+import copy, gzip, json, shutil, sys, tempfile
+from pathlib import Path
+import os
+sys.path.insert(0, os.environ['PR635_CODE'])   # PR635's unchanged hpe_audit_and_transport.py
+import hpe_audit_and_transport as atc
+
+src, routing, outdir = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3])
+word = json.load(gzip.open(src))
+v, R = word['report']['v'], word['report']['R']; n = 2*v + R
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+meta = word['refactored_cleanup']
+cold = [int(h) for h in meta['cold_low_frame_ended_helpers']]
+npre = meta['premix_gates']; nlow = meta['lower_frame_gates']
+early = word['early_cleanup']; eidx = {i for i, _ in early}
+rest = [i for i in range(len(word['cleanup'])) if i not in eidx]
+
+
+def trial(w):
+    """None if the transport audit accepts w, else the AssertionError message."""
+    tmp = Path(tempfile.mkdtemp())
+    p = tmp/'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w).encode(), mtime=0))
+    try:
+        atc.run(p, routing, tmp/'out')
+        return None
+    except AssertionError as e:
+        return repr(e.args[0]) if e.args else 'AssertionError'
+    finally:
+        shutil.rmtree(tmp, ignore_errors=True)
+
+
+# Pinned rejection reasons: each mutant must fail at this assertion of hpe_audit_and_transport.py (message substring).
+ENDPOINT, COLDPRE, CONE = "'arbitrary-dirt endpoint'", 'touches a cold hyperplane-ended helper', 'hpe cone pre-check (row / column)'
+WHY = dict(premix_to_precondition=COLDPRE, premix_dropped=COLDPRE, e_premix_dropped=ENDPOINT, lower_dropped=ENDPOINT,
+           remainder_dropped=ENDPOINT, coefficient=ENDPOINT, into_full='cleanup on non-FULL end', dyadic=ENDPOINT, frame_below="'nonmonotone'",
+           nonmonotone="'nonmonotone'", other_frame=CONE, cone=CONE, extra_end=COLDPRE, marker='cleanup is not the literal reversed inverse',
+           target='refactored cleanup touches a target', profile_pin='paid local profile differs from the reported local_profile',
+           entering_precondition='zero-frame precondition/compensation touches an entering helper')
+assert trial(word) is None, 'unmutated cold-end word must pass'
+results = []
+
+
+def reject(name, mut, why):
+    """the mutation must be rejected, and for the pinned reason (a substring of the audit's assertion message)."""
+    w = copy.deepcopy(word); mut(w)
+    msg = trial(w)
+    assert msg is not None, 'cold-end mutation accepted: ' + name
+    assert why in msg, 'cold-end mutation %r rejected for the wrong reason: %s' % (name, msg[:300])
+    results.append(name); print('rejected', name, '|', why, flush=True)
+
+
+h0 = cold[0]
+i0, U0 = next((i, f) for i, f in early if h0 in regs(word['cleanup'][i]))
+r0 = rest[len(rest)//2]
+
+
+def premix_to_precondition(w):   # premix before the wrappers; compensation then reads the cold ends
+    w['precondition'] = w['precondition'] + w['A'][:npre]; w['A'] = w['A'][npre:]
+
+
+def lower_gate_into_full(w):     # a lower-frame gate on a cold-ended helper executed in the FULL remainder instead
+    w['early_cleanup'] = [x for x in w['early_cleanup'] if x[0] != i0]
+
+
+def drop_cleanup_gate(w, i):   # remove the gate AND its early_cleanup entry: a structurally valid word missing one gate
+    w['cleanup'].pop(i)
+    w['early_cleanup'] = [[j - (j > i), f] for j, f in w['early_cleanup'] if j != i]
+
+
+def other_frame(w):              # a different frame of the same dimension as the cold end (another cold helper's)
+    f = next(w['helper_final'][str(h)] for h in cold if w['helper_final'][str(h)] != w['helper_final'][str(h0)])
+    w['helper_final'][str(h0)] = f
+
+
+def extra_cold_end(w):           # declare a premixed partner of h0 cold-ended at h0's frame: fails the row/column cone
+    p = next(r for e in w['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    w['helper_final'][str(p)] = w['helper_final'][str(h0)]
+
+
+reject('premix placed in the zero-frame precondition (before the cold wrappers)', premix_to_precondition, WHY['premix_to_precondition'])
+reject('one premix gate dropped (the compensation then reads a cold-ended helper)', lambda w: w['A'].pop(npre - 1), WHY['premix_dropped'])
+reject('one lower-frame cleanup gate dropped (gate and its early_cleanup entry)', lambda w: drop_cleanup_gate(w, i0), WHY['lower_dropped'])
+reject('one FULL-remainder gate dropped', lambda w: drop_cleanup_gate(w, r0), WHY['remainder_dropped'])
+reject('lower-frame gate coefficient changed', lambda w: w['cleanup'][i0].__setitem__(3, w['cleanup'][i0][3] * 2), WHY['coefficient'])
+reject('lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)', lower_gate_into_full, WHY['into_full'])
+reject('lower-frame gate frame below its registers\' frames', lambda w: next(x for x in w['early_cleanup'] if x[0] == i0).__setitem__(1, U0[:-1]), WHY['frame_below'])
+reject('cold end at another dim-4 frame', other_frame, WHY['other_frame'])
+# PROFILE-PIN control: without its helper_final entry the cold-ended helper is a valid FULL-ended helper; the word is
+# rejected because its reported paid profile (which counts the low end) no longer matches the frame chains.
+reject('profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)', lambda w: w['helper_final'].pop(str(h0)), WHY['profile_pin'])
+reject('extra cold end on a premixed partner (the compensation reads it before its wrapper)', extra_cold_end, WHY['extra_end'])
+reject('refactored-cleanup marker removed (literal-inverse rule applies)', lambda w: w.pop('refactored_cleanup'), WHY['marker'])
+reject('remainder gate retargeted to a target register', lambda w: w['cleanup'][r0].__setitem__(1, v + 3), WHY['target'])
+reject('non-dyadic remainder coefficient', lambda w: w['cleanup'][r0].__setitem__(4 if w['cleanup'][r0][0] == 'add' else 3, 3 * w['cleanup'][r0][4 if w['cleanup'][r0][0] == 'add' else 3]), WHY['dyadic'])
+reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('5', w['report']['local_profile']['5'] - 1), WHY['profile_pin'])
+ent = [int(h) for h in sys.argv[4].split(',')] if len(sys.argv) > 4 else [int(h) for h in meta.get('entering_low_frame_ended_helpers', [])]
+for e0 in ent:   # ENTERING LOW-FRAME ENDS (ColdSupply extension; every entering end; absent for words without them)
+    j0 = next((i for i, e in enumerate(word['A'][:npre]) if e0 in regs(e)), None)
+    print('entering end', e0, 'premix gate', j0, flush=True)
+    k0, Ue = next((i, f) for i, f in early if e0 in regs(word['cleanup'][i]))
+    def to_pre(w, j0=j0): w['precondition'].append(w['A'][j0]); w['A'].pop(j0)
+    def other_hp(w, e0=e0, Ue=Ue): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Ue) and sorted(f) != sorted(Ue))
+    if j0 is not None: reject('entering end %d: premix gate dropped' % e0, lambda w, j0=j0: w['A'].pop(j0), WHY['e_premix_dropped'])
+    if j0 is not None: reject('entering end %d: premix gate at frame [] instead of its entrance E' % e0, lambda w, j0=j0: w['A'][j0].__setitem__(-1, []), WHY['nonmonotone'])
+    if j0 is not None: reject('entering end %d: premix gate moved into the zero-frame precondition' % e0, to_pre, WHY['entering_precondition'])
+    reject('entering end %d: lower-frame gate dropped (gate and its early_cleanup entry)' % e0, lambda w, k0=k0: drop_cleanup_gate(w, k0), WHY['lower_dropped'])
+    reject('entering end %d: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)' % e0, lambda w, e0=e0: w['helper_final'].pop(str(e0)), WHY['profile_pin'])
+    reject('entering end %d: end at another hyperplane' % e0, other_hp, WHY['cone'])
+# Pinned rejection reasons of the COLD-BEYOND mutants (substrings of hpe_audit_and_transport.py assertion messages).
+MYWHY = dict(tw_precondition=COLDPRE, tw_dropped=COLDPRE, tw_coefficient=COLDPRE, tw_other_block=COLDPRE,
+             tw_entering='zero-frame compensation reads an entering helper',
+             ab_dropped=ENDPOINT, ab_coefficient=ENDPOINT, ab_early=ENDPOINT, ab_live=ENDPOINT, ab_centre=ENDPOINT,
+             ab_lower="'nonmonotone'", ab_higher="'nonmonotone'",
+             sh_dropped=ENDPOINT, sh_coefficient=ENDPOINT, rel_dropped=ENDPOINT, rel_coefficient=ENDPOINT, rel_live=ENDPOINT,
+             h8_other=CONE, h8_lower=ENDPOINT)
+# COLD-BEYOND primitives (present only when the word carries them): frame-[] target writes in the premix (explicit
+# post-wrapper compensation of an ended helper's dirt) and forward absorptions into dead registers.
+nw = meta.get('premix_target_writes', 0)
+if nw:
+    wi = [i for i in range(npre) if v <= word['A'][i][1] < 2*v]
+    assert len(wi) == nw
+
+    def writes_to_precondition(w):   # the target writes run before the cold wrappers (inside the zero-frame precondition)
+        g = [w['A'][i] for i in wi]; w['precondition'] = w['precondition'] + g
+        w['A'] = [e for i, e in enumerate(w['A']) if i not in set(wi)]
+    reject('premix target writes placed in the zero-frame precondition (before the cold wrappers)', writes_to_precondition, MYWHY['tw_precondition'])
+    reject('one premix target write dropped (compensation must read an ended helper)', lambda w: w['A'].pop(wi[0]), MYWHY['tw_dropped'])
+    reject('premix target write coefficient changed', lambda w: w['A'][wi[0]].__setitem__(3, w['A'][wi[0]][3] * 2), MYWHY['tw_coefficient'])
+    # (reading another register that carries the SAME weight of the ended helper's dirt is a valid variant, so the mutant reads
+    #  the same factory slot of the next block, which carries none of it)
+    entering_regs = sorted(int(r) for r in word.get('start_extra', {}))
+    reject('premix target write reads an entering helper', lambda w: w['A'][wi[0]].__setitem__(2, entering_regs[0]), MYWHY['tw_entering'])
+    reject('premix target write reads a cold helper of another block', lambda w: w['A'][wi[0]].__setitem__(2, 2*v + (w['A'][wi[0]][2] - 2*v + 16) % 224), MYWHY['tw_other_block'])
+ab = meta.get('forward_absorption_A_indices', [])
+if any(len(word['helper_final'][str(h)]) == 8 for h in cold):
+    # with dim-8 cold ends, the centre-retargeted absorption first leaks an ended helper's dirt into the cut's targets
+    MYWHY['ab_centre'] = COLDPRE
+if ab:
+    # the ColdBeyond U_b absorption (q += -1/2 g); ColdThird's extra absorptions have their own controls below
+    a0 = next(a for a in ab if word['A'][a][3] * 2 == -word['A'][a][4]); g0 = word['A'][a0]
+
+    def absorption_moved_early(w):   # absorbed before the absorbed register's last kernel write
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[2] == w['A'][i][1] and w['A'][i][-1] == g0[-1])
+        w['A'].insert(j, e)
+
+    def absorption_into_live(w):     # q += a g moved right after g's previous frame-mate gate, while q is still live
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[1] in regs(w['A'][i]))
+        w['A'].insert(j, e)
+    reject('forward absorption dropped', lambda w: w['A'].pop(a0), MYWHY['ab_dropped'])
+    reject('forward absorption into a centre (a live register read by the cut)', lambda w: w['A'][a0].__setitem__(1, next(c for c in word['centers'] if c not in g0[1:3] and c not in cold)), MYWHY['ab_centre'])
+    reject('forward absorption coefficient changed', lambda w: w['A'][a0].__setitem__(3, w['A'][a0][3] * 2), MYWHY['ab_coefficient'])
+    reject('forward absorption placed before the absorbed register\'s last kernel write', absorption_moved_early, MYWHY['ab_early'])
+    reject('forward absorption placed while the absorbing register is still live', absorption_into_live, MYWHY['ab_live'])
+    reject('forward absorption at a lower frame than its registers', lambda w: w['A'][a0].__setitem__(-1, w['A'][a0][-1][:-1]), MYWHY['ab_lower'])
+    reject('forward absorption at a higher frame (FULL) than its registers', lambda w: w['A'][a0].__setitem__(-1, [256, 128, 64, 32, 16, 8, 4, 2, 1]), MYWHY['ab_higher'])
+# COLD-THIRD primitives (present only when the word carries them): several absorptions after one input gate, dirt-release
+# absorptions (a dead port takes a live helper's value so that a hyperplane unit's column has no dirt on it), and cold ends at
+# a dim-8 frame with lifted partners.
+hyper = [h for h in cold if len(word['helper_final'][str(h)]) == 8]
+if hyper and ab:
+    sh = next(a for a, b in zip(ab, ab[1:]) if b == a + 1)              # two absorptions sharing one input anchor
+    rel = next(a for a in ab if a - 1 not in ab and a + 1 not in ab and word['A'][a][2] in hyper and word['A'][a][3] * 2 != -word['A'][a][4])
+    hh = hyper[0]; ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+    reject('second absorption sharing an input anchor dropped', lambda w: w['A'].pop(sh + 1), MYWHY['sh_dropped'])
+    reject('shared-anchor absorption coefficient changed', lambda w: w['A'][sh + 1].__setitem__(3, w['A'][sh + 1][3] * 2), MYWHY['sh_coefficient'])
+    reject('dirt-release absorption dropped', lambda w: w['A'].pop(rel), MYWHY['rel_dropped'])
+    reject('dirt-release absorption coefficient changed', lambda w: w['A'][rel].__setitem__(3, w['A'][rel][3] * 2), MYWHY['rel_coefficient'])
+    jr = max(i for i in range(npre, rel) if word['A'][i][0] == 'add' and word['A'][i][2] == word['A'][rel][1])
+
+    def release_while_read(w):   # the release runs before a kernel gate that still READS the port (port live)
+        e = w['A'].pop(rel); w['A'].insert(jr, e)
+    reject('dirt-release absorption moved before a kernel gate that still reads the port', release_while_read, MYWHY['rel_live'])
+if hyper:
+    # dim-8 cold-end controls once PER DISTINCT dim-8 terminal frame (each family of dim-8 cold ends keeps its own controls)
+    fams = []
+    for h in hyper:
+        if sorted(word['helper_final'][str(h)]) not in [sorted(word['helper_final'][str(x)]) for x in fams]: fams.append(h)
+    for hh in fams:
+        ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+        Uh = word['helper_final'][str(hh)]
+        reject('dim-8 cold end %d (frame %s) at another dim-8 frame' % (hh, Uh), lambda w, hh=hh: w['helper_final'].__setitem__(str(hh), next(f for h, f in w['helper_final'].items() if len(f) == 8 and sorted(f) != sorted(w['helper_final'][str(hh)]))), MYWHY['h8_other'])
+        reject('dim-8 cold end %d (frame %s): one lower-frame gate dropped (gate and its early_cleanup entry)' % (hh, Uh), lambda w, ih=ih: drop_cleanup_gate(w, ih), MYWHY['h8_lower'])
+        reject('dim-8 cold end %d (frame %s): profile pin (end dropped)' % (hh, Uh), lambda w, hh=hh: w['helper_final'].pop(str(hh)), WHY['profile_pin'])
+# FACTORED ACCUMULATOR (CarrierBypass; present only when the word carries one): a lower-frame tail gate a += x*g on two
+# non-ended registers whose accumulator a is afterwards read by a dim-8 cold end's tail gate (h += y*a at its U).
+ended_all = {int(h) for h in word['helper_final']}
+tailg = [(i, word['cleanup'][i]) for i, _ in early]
+accs = []   # EVERY factored accumulator gate (one per accumulator register a), each controlled on its own
+for k, (i, e) in enumerate(tailg):
+    if e[0] == 'add' and e[1] not in ended_all and e[2] not in ended_all and len(next(f for j, f in early if j == i)) < 8:
+        if e[1] not in [word['cleanup'][j][1] for j in accs] and any(t[0] == 'add' and t[2] == e[1] and t[1] in hyper for _, t in tailg[k + 1:]):
+            accs.append(i)
+for acc in accs:
+    a = word['cleanup'][acc][1]
+    reject('factored accumulator %d (gate %d) zeroed' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, 0), ENDPOINT)
+    reject('factored accumulator %d (gate %d) coefficient doubled' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, w['cleanup'][acc][3] * 2), ENDPOINT)
+outdir.mkdir(parents=True, exist_ok=True)
+(outdir/'COLD-END-CONTROLS.json').write_text(json.dumps(dict(status='PASS_COLD_END_RAW_WORD_CONTROLS', word=str(src), rejected=results), indent=1) + '\n')
+print('PASS', len(results), 'cold-end raw-word mutations rejected')
diff --git a/research/gauge44-slots/construction/layers/reproduce_layers.py b/research/gauge44-slots/construction/layers/reproduce_layers.py
new file mode 100644
index 0000000000..ed517ba1dd
--- /dev/null
+++ b/research/gauge44-slots/construction/layers/reproduce_layers.py
@@ -0,0 +1,105 @@
+#!/usr/bin/env python3
+"""Rebuild the layered gauge44 word (pivot swaps + entering ends + factored dim-8 cold ends) and its native locals.
+
+Input: a fresh `construction/reproduce.py --until word` output directory (its regroup/ and cold44/ words are pinned
+by reproduce.py itself). Steps, each checked exactly:
+  1. pivot-swap: construction/layers/build_pivot_swap.py on regroup/FULL-WORD (six cost-neutral pivot-role swaps,
+     exact zero-response replay, unchanged profile and width multiset, 30 negative controls);
+  2. hpe: the inherited jp8 hyperplane-end changes (HYPERPLANE-END-S6.json) applied with PR635's build_hpe.apply;
+  3. cold44-exact: #645's build_gauge_cold44.py on the swapped HPE word; its 44 rank-four cold ends, premix and tail
+     must equal the unswapped cold44 construction's (the swaps touch no factory block);
+  4. layers: PR635's unchanged build_cold_end.apply(HPE, COLD-LAYERS-RECIPE) - the cold44 recipe plus 8 entering ends
+     (560/561/572/573 at U24, 597/599/537/549 at U30) and 10 factored dim-8 cold ends; output sha pinned;
+  5. layer-end-controls: raw-word negative controls on the layered word (PR635 cold_end_controls adapted by
+     LayerReviewer: lower->FULL pinned at 'cleanup on non-FULL end', entering ends from the recipe); 59 rejected;
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs (as in reproduce.py).
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+LAYERED_SHA = '0be48b1d8a6105059addf3f0d5e420c27ae3398b3a1186b6b11e9c4aa9e3f3d4'
+LAYER_CONTROLS = 59
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--word-dir', type=Path, required=True, help='construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    env.pop('PYTHONOPTIMIZE', None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    wd = a.word_dir.resolve()
+    run('pivot-swap', HERE / 'build_pivot_swap.py', '--input', wd / 'regroup/FULL-WORD.json.gz',
+        '--recipe', HERE / 'PIVOT-SWAP-S6.json', '--gk-dir', gk, '--out', out / 'swap')
+    hpe = load('upstream_hpe', up / 'code/build_hpe.py')
+    w = hpe.apply(read(out / 'swap/FULL-WORD.json.gz'), read(HERE / 'HYPERPLANE-END-S6.json')['changes'])
+    (out / 'hpe').mkdir(); (out / 'hpe/FULL-WORD.json.gz').write_bytes(gzip.compress(enc(w), mtime=0))
+    run('cold44-exact', HERE.parent / 'build_gauge_cold44.py', '--input', out / 'hpe/FULL-WORD.json.gz',
+        '--out', out / 'cold44', '--hamming', wd / 'hamming', '--upstream-package', up)
+    new, old = read(out / 'cold44/RECIPE.json.gz'), read(wd / 'cold44/RECIPE.json.gz')
+    # The swaps touch no factory block: the 44 ends, their premix and their low tails are identical; only the FULL
+    # inverse (rebuilt from the whole word) differs.
+    for key in ('premix', 'early_cleanup', 'cold_ends'):
+        assert new[key] == old[key], ('swapped cold44 differs from the pinned cold44 construction', key)
+    tail = len(new['early_cleanup']); assert new['cleanup'][:tail] == old['cleanup'][:tail], 'low tails'
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    layered = bce.apply(w, read(HERE / 'COLD-LAYERS-RECIPE.json.gz'))
+    raw = enc(layered); assert hashlib.sha256(raw).hexdigest() == LAYERED_SHA, 'layered word'
+    rep = layered['report']
+    assert rep['local_profile'] == {'1': 2542, '2': 414, '3': 434, '4': 154, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 52, '5': 48, '7': 42, '8': 116, '9': 234}, rep['width_inventory']
+    (out / 'layers').mkdir(); word = out / 'layers/FULL-WORD.json.gz'; word.write_bytes(gzip.compress(raw, mtime=0))
+    print('PASS layered scalar word', word, flush=True)
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', HERE / 'layer_end_controls.py', word, routing, out / 'controls')
+    ctl = json.loads((out / 'controls/COLD-END-CONTROLS.json').read_text())
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == LAYER_CONTROLS, len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word,
+        '--routing', routing, '--out', local)
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz b/research/gauge44-slots/construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz
new file mode 100644
index 0000000000..f9155e3079
Binary files /dev/null and b/research/gauge44-slots/construction/layers_np/COLD-LAYERS-RECIPE-NP.json.gz differ
diff --git a/research/gauge44-slots/construction/layers_np/HPE-RECIPE-NP.json b/research/gauge44-slots/construction/layers_np/HPE-RECIPE-NP.json
new file mode 100644
index 0000000000..2605d199ed
--- /dev/null
+++ b/research/gauge44-slots/construction/layers_np/HPE-RECIPE-NP.json
@@ -0,0 +1 @@
+{"changes": [{"helper": 448, "cleanup_index": 674, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 449, "cleanup_index": 673, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 450, "cleanup_index": 672, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 451, "cleanup_index": 671, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 452, "cleanup_index": 670, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 453, "cleanup_index": 669, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 454, "cleanup_index": 668, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 455, "cleanup_index": 667, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 456, "cleanup_index": 666, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 457, "cleanup_index": 665, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 458, "cleanup_index": 664, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 459, "cleanup_index": 663, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 460, "cleanup_index": 658, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 461, "cleanup_index": 657, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 470, "cleanup_index": 648, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 471, "cleanup_index": 647, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 472, "cleanup_index": 642, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 473, "cleanup_index": 641, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 482, "cleanup_index": 632, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 483, "cleanup_index": 631, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 496, "cleanup_index": 609, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 497, "cleanup_index": 608, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 520, "cleanup_index": 573, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 521, "cleanup_index": 572, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 544, "cleanup_index": 539, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 545, "cleanup_index": 538, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 568, "cleanup_index": 507, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 569, "cleanup_index": 506, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 580, "cleanup_index": 491, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 581, "cleanup_index": 490, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 590, "cleanup_index": 481, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 591, "cleanup_index": 480, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 592, "cleanup_index": 475, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 593, "cleanup_index": 474, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 602, "cleanup_index": 465, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 603, "cleanup_index": 464, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 604, "cleanup_index": 459, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 605, "cleanup_index": 458, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 606, "cleanup_index": 457, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 607, "cleanup_index": 456, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 609, "cleanup_index": 454, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 611, "cleanup_index": 452, "frame": [256, 128, 64, 32, 18, 10, 6, 1]}, {"helper": 612, "cleanup_index": 451, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 613, "cleanup_index": 450, "frame": [256, 128, 64, 32, 24, 4, 2, 1]}, {"helper": 614, "cleanup_index": 449, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}, {"helper": 615, "cleanup_index": 448, "frame": [256, 128, 64, 32, 16, 8, 6, 1]}]}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/layers_np/PIVOT-SWAP-NP.json b/research/gauge44-slots/construction/layers_np/PIVOT-SWAP-NP.json
new file mode 100644
index 0000000000..4e0d846426
--- /dev/null
+++ b/research/gauge44-slots/construction/layers_np/PIVOT-SWAP-NP.json
@@ -0,0 +1,588 @@
+{
+ "input_content_sha256": "864ff4a19987bcb27016367801a98ca50dae69eafe01d3614f8bae69f5713d6d",
+ "output_content_sha256": "beb3579fce83cb3b70f4e85761cbb3b8c91d711d4b9cf473074269b8447fc4e4",
+ "swaps": [
+  {
+   "pivot": 494,
+   "new_pivot": 566,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 379,
+     "before": [
+      "add",
+      566,
+      494,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      494,
+      566,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 380,
+     "before": [
+      "add",
+      640,
+      494,
+      2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      640,
+      566,
+      -2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 381,
+     "before": [
+      "add",
+      642,
+      494,
+      -2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      642,
+      566,
+      2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 382,
+     "before": [
+      "add",
+      688,
+      494,
+      1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      688,
+      566,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 383,
+     "before": [
+      "add",
+      690,
+      494,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      690,
+      566,
+      1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 495,
+   "new_pivot": 567,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 516,
+     "before": [
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+      1,
+      1,
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+       24
+      ]
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+      567,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
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+      567,
+      1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 686,
+     "before": [
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+      495,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      495,
+      567,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 506,
+   "new_pivot": 578,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 176,
+     "before": [
+      "add",
+      652,
+      506,
+      2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
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+      652,
+      578,
+      -2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
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+      506,
+      -2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      652,
+      578,
+      2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 278,
+     "before": [
+      "add",
+      700,
+      506,
+      -2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      700,
+      578,
+      2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 280,
+     "before": [
+      "add",
+      700,
+      506,
+      2,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      700,
+      578,
+      -2,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 702,
+     "before": [
+      "add",
+      578,
+      506,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      506,
+      578,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 507,
+   "new_pivot": 579,
+   "entrance": [
+    24
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 93,
+     "before": [
+      "add",
+      211,
+      507,
+      -1,
+      1,
+      [
+       24
+      ]
+     ],
+     "after": [
+      "add",
+      211,
+      579,
+      1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 541,
+     "before": [
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+      1,
+      1,
+      [
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+     ],
+     "after": [
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+      579,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 704,
+     "before": [
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+      [
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+     "after": [
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+      579,
+      -1,
+      1,
+      [
+       24
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 519,
+   "new_pivot": 543,
+   "entrance": [
+    30
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 507,
+     "before": [
+      "add",
+      115,
+      519,
+      -1,
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+     "part": "B",
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+      179,
+      543,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 722,
+     "before": [
+      "add",
+      543,
+      519,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      519,
+      543,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    }
+   ]
+  },
+  {
+   "pivot": 531,
+   "new_pivot": 555,
+   "entrance": [
+    30
+   ],
+   "gates": [
+    {
+     "part": "B",
+     "index": 550,
+     "before": [
+      "add",
+      155,
+      531,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      155,
+      555,
+      1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 617,
+     "before": [
+      "add",
+      219,
+      531,
+      1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      219,
+      555,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    },
+    {
+     "part": "B",
+     "index": 740,
+     "before": [
+      "add",
+      555,
+      531,
+      -1,
+      1,
+      [
+       30
+      ]
+     ],
+     "after": [
+      "add",
+      531,
+      555,
+      -1,
+      1,
+      [
+       30
+      ]
+     ]
+    }
+   ]
+  }
+ ]
+}
diff --git a/research/gauge44-slots/construction/layers_np/reproduce_np.py b/research/gauge44-slots/construction/layers_np/reproduce_np.py
new file mode 100644
index 0000000000..79cb6fa912
--- /dev/null
+++ b/research/gauge44-slots/construction/layers_np/reproduce_np.py
@@ -0,0 +1,149 @@
+#!/usr/bin/env python3
+"""Rebuild the layered no-triangle word (NP) and its native locals.
+
+Input: a fresh `construction/notri/reproduce_notri.py --word-only` output directory. That driver pins the
+no-triangle word (3e99ba77...) and writes its regroup/ and cold44/ words. Steps, each checked exactly:
+  1. pivot-swap: ../layers/build_pivot_swap.py (PR641's constructor, signed, unchanged) on the no-triangle regroup word, with PIVOT-SWAP-NP.json:
+     the six pivot-role swaps of research/gauge44-layered, mapped through the 504-helper map (494->566, 495->567,
+     506->578, 507->579, 519->543, 531->555). Exact zero-response replay, unchanged profile and width multiset,
+     30 negative controls.
+  2. hpe: PR635's build_hpe.candidates, greedy with disjoint registers. Must equal HPE-RECIPE-NP.json (46 changes,
+     the same helpers as the unswapped word); applied with build_hpe.apply.
+  3. cold44-exact: notri/cold44x.py on the swapped HPE word, pairing ranks pinned [4]*14. Its 56 cold ends, premix
+     and low tails must equal the unswapped no-triangle construction's.
+  4. layers: PR635's unchanged build_cold_end.apply(HPE, COLD-LAYERS-RECIPE-NP): cold44 plus the entering ends
+     566/567/578/579 at U24 (s4) and 608/610/543/555 at U30 (x30), BlockCombine's b6 and the q4 dim-8 cold ends.
+     The output word sha and its profile and widths are pinned.
+  5. layer-end-controls: ../layers/layer_end_controls.py (LayerReviewer's signed adaptation of PR635's
+     cold_end_controls.py, unchanged) on the layered word; exactly 59 rejections at pinned reasons.
+../layers/reproduce_layers.py is research/gauge44-layered's driver for the 492-helper word, shipped unchanged as
+signed; it is not used for this word.
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs, with pins.
+Apache-2.0. Driver by ColdWitness after G44Stack's NP chain (NP/chain.py, seq.py).
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NOTRI = HERE.parent / 'notri'
+LAYERS = HERE.parent / 'layers'   # the signed research/gauge44-layered files, unchanged
+REGROUP_SHA = '864ff4a1'   # prefix; full value checked against PIVOT-SWAP-NP.json's input_content_sha256
+SWAP_SHA = 'beb3579f'
+NP_SHA = 'a9de804f194eeb39f52a4c6e54c14d93e881bec4b632694249733ed410b58113'
+LAYER_CONTROLS = 59
+CANONICAL_SHA = '1ae812a336178760071efe347e876e0102b5b71f799d957db15c5f3004c19d7a'
+PROGRAM_SHA = {'forward': 'a3882a428bdafab888072211d4ed8d34572746873d77c6ef900495853cc3fa11',
+               'backward': 'f67a3dc20c27fb39295b8030e951e9779109ef1537f6f8de9d08510b9ad6792a'}
+CLIFFORD_SHA = '890b60fc4ae183c773c51405e0f4ef6a945dc2aae55ba2480f134602e8296cda'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def dump(p, v):
+    p.parent.mkdir(parents=True, exist_ok=True); p.write_bytes(gzip.compress(enc(v), mtime=0))
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--notri-dir', type=Path, required=True, help='construction/notri/reproduce_notri.py --word-only output')
+    ap.add_argument('--hamming', type=Path, required=True, help='hamming/ of the construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    nd = a.notri_dir.resolve()
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    # the input must be the pinned no-triangle construction
+    nr = load('notri_driver', NOTRI / 'reproduce_notri.py')
+    assert hashlib.sha256(enc(read(nd / 'cold44/FULL-WORD.json.gz'))).hexdigest() == nr.NOTRI_SHA, 'notri word'
+    # 1. pivot swaps on the regroup word
+    rg = hashlib.sha256(enc(read(nd / 'regroup/FULL-WORD.json.gz'))).hexdigest()
+    assert rg.startswith(REGROUP_SHA) and rg == read(HERE / 'PIVOT-SWAP-NP.json')['input_content_sha256'], ('regroup word', rg)
+    run('pivot-swap', LAYERS / 'build_pivot_swap.py', '--input', nd / 'regroup/FULL-WORD.json.gz',
+        '--recipe', HERE / 'PIVOT-SWAP-NP.json', '--gk-dir', gk, '--out', out / 'swap')
+    w = read(out / 'swap/FULL-WORD.json.gz')
+    sw = hashlib.sha256(enc(w)).hexdigest(); assert sw.startswith(SWAP_SHA) and sw == read(HERE / 'PIVOT-SWAP-NP.json')['output_content_sha256'], ('swap word', sw)
+    # 2. HPE (greedy, must equal the pinned recipe)
+    h = load('upstream_hpe', up / 'code/build_hpe.py')
+    used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    assert ch == read(HERE / 'HPE-RECIPE-NP.json')['changes'], 'HPE recipe'
+    w = h.apply(w, ch); dump(out / 'hpe/FULL-WORD.json.gz', w)
+    # 3. cold44 on the swapped word: same ends, premix and tails as the unswapped no-triangle construction
+    hm = set(read(nd / 'raw/HELPER-MAP.json')['map'].values())
+    env['EXTRAH'] = json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm))
+    env['PAIRING_RANKS'] = json.dumps([4] * 14)
+    run('cold44-exact', NOTRI / 'cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', a.hamming.resolve(), '--upstream-package', up)
+    for k in ('EXTRAH', 'PAIRING_RANKS'): env.pop(k)
+    new, old = read(out / 'cold44/RECIPE.json.gz'), read(nd / 'cold44/RECIPE.json.gz')
+    for key in ('premix', 'early_cleanup', 'cold_ends'):
+        assert new[key] == old[key], ('swapped cold44 differs from the pinned no-triangle construction', key)
+    tail = len(new['early_cleanup']); assert new['cleanup'][:tail] == old['cleanup'][:tail], 'low tails'
+    # 4. layers
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    layered = bce.apply(w, read(HERE / 'COLD-LAYERS-RECIPE-NP.json.gz'))
+    raw = enc(layered); assert hashlib.sha256(raw).hexdigest() == NP_SHA, ('layered word', hashlib.sha256(raw).hexdigest())
+    rep = layered['report']
+    assert rep['local_profile'] == {'1': 2534, '2': 346, '3': 458, '4': 178, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 64, '5': 48, '7': 54, '8': 116, '9': 222}, rep['width_inventory']
+    (out / 'layers').mkdir(); word = out / 'layers/FULL-WORD.json.gz'; word.write_bytes(gzip.compress(raw, mtime=0))
+    print('PASS layered no-triangle word', NP_SHA, flush=True)
+    # 5. layer-end controls
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', LAYERS / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = json.loads((out / 'controls/COLD-END-CONTROLS.json').read_text())
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == LAYER_CONTROLS, len(ctl['rejected'])
+    # 6. native locals
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == CANONICAL_SHA, 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in PROGRAM_SHA.items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == CLIFFORD_SHA, 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz b/research/gauge44-slots/construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz
new file mode 100644
index 0000000000..a408c95816
Binary files /dev/null and b/research/gauge44-slots/construction/layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz differ
diff --git a/research/gauge44-slots/construction/layers_p6n/P6N-SPEC.json b/research/gauge44-slots/construction/layers_p6n/P6N-SPEC.json
new file mode 100644
index 0000000000..43c3ec265c
--- /dev/null
+++ b/research/gauge44-slots/construction/layers_p6n/P6N-SPEC.json
@@ -0,0 +1 @@
+{"ends":[{"U":[256,128,66,34,16,8,6,1],"labels":[512,513]},{"U":[256,128,72,40,24,4,2,1],"labels":[311,510]},{"U":[256,128,66,34,18,10,6,1],"labels":[522,327]}]}
diff --git a/research/gauge44-slots/construction/layers_p6n/layer_end_controls.py b/research/gauge44-slots/construction/layers_p6n/layer_end_controls.py
new file mode 100644
index 0000000000..dd321fe255
--- /dev/null
+++ b/research/gauge44-slots/construction/layers_p6n/layer_end_controls.py
@@ -0,0 +1,199 @@
+"""layer_end_controls.py LAYERED-WORD.json.gz ROUTING OUTDIR (env PR635_CODE): adapted PR635 cold_end_controls.py (LayerReviewer): raw-word negative controls for the cold low-frame ends and the
+refactored cleanup accepted by hpe_audit_and_transport.py.  Every mutation MUST be rejected (AssertionError); the
+unmutated word MUST pass.  Apache-2.0.  DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code."""
+import copy, gzip, json, shutil, sys, tempfile
+from pathlib import Path
+import os
+sys.path.insert(0, os.environ['PR635_CODE'])   # PR635's unchanged hpe_audit_and_transport.py
+import hpe_audit_and_transport as atc
+
+src, routing, outdir = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3])
+word = json.load(gzip.open(src))
+v, R = word['report']['v'], word['report']['R']; n = 2*v + R
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+meta = word['refactored_cleanup']
+cold = [int(h) for h in meta['cold_low_frame_ended_helpers']]
+npre = meta['premix_gates']; nlow = meta['lower_frame_gates']
+early = word['early_cleanup']; eidx = {i for i, _ in early}
+rest = [i for i in range(len(word['cleanup'])) if i not in eidx]
+
+
+def trial(w):
+    """None if the transport audit accepts w, else the AssertionError message."""
+    tmp = Path(tempfile.mkdtemp())
+    p = tmp/'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w).encode(), mtime=0))
+    try:
+        atc.run(p, routing, tmp/'out')
+        return None
+    except AssertionError as e:
+        return repr(e.args[0]) if e.args else 'AssertionError'
+    finally:
+        shutil.rmtree(tmp, ignore_errors=True)
+
+
+# Pinned rejection reasons: each mutant must fail at this assertion of hpe_audit_and_transport.py (message substring).
+ENDPOINT, COLDPRE, CONE = "'arbitrary-dirt endpoint'", 'touches a cold hyperplane-ended helper', 'hpe cone pre-check (row / column)'
+WHY = dict(premix_to_precondition=COLDPRE, premix_dropped=COLDPRE, e_premix_dropped=ENDPOINT, lower_dropped=ENDPOINT,
+           remainder_dropped=ENDPOINT, coefficient=ENDPOINT, into_full='cleanup on non-FULL end', dyadic=ENDPOINT, frame_below="'nonmonotone'",
+           nonmonotone="'nonmonotone'", other_frame=CONE, cone=CONE, extra_end=COLDPRE, marker='cleanup is not the literal reversed inverse',
+           target='refactored cleanup touches a target', profile_pin='paid local profile differs from the reported local_profile',
+           entering_precondition='zero-frame precondition/compensation touches an entering helper')
+assert trial(word) is None, 'unmutated cold-end word must pass'
+results = []
+
+
+def reject(name, mut, why):
+    """the mutation must be rejected, and for the pinned reason (a substring of the audit's assertion message)."""
+    w = copy.deepcopy(word); mut(w)
+    msg = trial(w)
+    assert msg is not None, 'cold-end mutation accepted: ' + name
+    assert why in msg, 'cold-end mutation %r rejected for the wrong reason: %s' % (name, msg[:300])
+    results.append(name); print('rejected', name, '|', why, flush=True)
+
+
+h0 = cold[0]
+i0, U0 = next((i, f) for i, f in early if h0 in regs(word['cleanup'][i]))
+r0 = rest[len(rest)//2]
+
+
+def premix_to_precondition(w):   # premix before the wrappers; compensation then reads the cold ends
+    w['precondition'] = w['precondition'] + w['A'][:npre]; w['A'] = w['A'][npre:]
+
+
+def lower_gate_into_full(w):     # a lower-frame gate on a cold-ended helper executed in the FULL remainder instead
+    w['early_cleanup'] = [x for x in w['early_cleanup'] if x[0] != i0]
+
+
+def drop_cleanup_gate(w, i):   # remove the gate AND its early_cleanup entry: a structurally valid word missing one gate
+    w['cleanup'].pop(i)
+    w['early_cleanup'] = [[j - (j > i), f] for j, f in w['early_cleanup'] if j != i]
+
+
+def other_frame(w):              # a different frame of the same dimension as the cold end (another cold helper's)
+    f = next(w['helper_final'][str(h)] for h in cold if w['helper_final'][str(h)] != w['helper_final'][str(h0)])
+    w['helper_final'][str(h0)] = f
+
+
+def extra_cold_end(w):           # declare a premixed partner of h0 cold-ended at h0's frame: fails the row/column cone
+    p = next(r for e in w['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    w['helper_final'][str(p)] = w['helper_final'][str(h0)]
+
+
+reject('premix placed in the zero-frame precondition (before the cold wrappers)', premix_to_precondition, WHY['premix_to_precondition'])
+reject('one premix gate dropped (the compensation then reads a cold-ended helper)', lambda w: w['A'].pop(npre - 1), WHY['premix_dropped'])
+reject('one lower-frame cleanup gate dropped (gate and its early_cleanup entry)', lambda w: drop_cleanup_gate(w, i0), WHY['lower_dropped'])
+reject('one FULL-remainder gate dropped', lambda w: drop_cleanup_gate(w, r0), WHY['remainder_dropped'])
+reject('lower-frame gate coefficient changed', lambda w: w['cleanup'][i0].__setitem__(3, w['cleanup'][i0][3] * 2), WHY['coefficient'])
+reject('lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)', lower_gate_into_full, WHY['into_full'])
+reject('lower-frame gate frame below its registers\' frames', lambda w: next(x for x in w['early_cleanup'] if x[0] == i0).__setitem__(1, U0[:-1]), WHY['frame_below'])
+reject('cold end at another dim-4 frame', other_frame, WHY['other_frame'])
+# PROFILE-PIN control: without its helper_final entry the cold-ended helper is a valid FULL-ended helper; the word is
+# rejected because its reported paid profile (which counts the low end) no longer matches the frame chains.
+reject('profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)', lambda w: w['helper_final'].pop(str(h0)), WHY['profile_pin'])
+reject('extra cold end on a premixed partner (the compensation reads it before its wrapper)', extra_cold_end, WHY['extra_end'])
+reject('refactored-cleanup marker removed (literal-inverse rule applies)', lambda w: w.pop('refactored_cleanup'), WHY['marker'])
+reject('remainder gate retargeted to a target register', lambda w: w['cleanup'][r0].__setitem__(1, v + 3), WHY['target'])
+reject('non-dyadic remainder coefficient', lambda w: w['cleanup'][r0].__setitem__(4 if w['cleanup'][r0][0] == 'add' else 3, 3 * w['cleanup'][r0][4 if w['cleanup'][r0][0] == 'add' else 3]), WHY['dyadic'])
+reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('5', w['report']['local_profile']['5'] - 1), WHY['profile_pin'])
+ent = [int(h) for h in sys.argv[4].split(',')] if len(sys.argv) > 4 else [int(h) for h in meta.get('entering_low_frame_ended_helpers', [])]
+for e0 in ent:   # ENTERING LOW-FRAME ENDS (ColdSupply extension; every entering end; absent for words without them)
+    j0 = next((i for i, e in enumerate(word['A'][:npre]) if e0 in regs(e)), None)
+    print('entering end', e0, 'premix gate', j0, flush=True)
+    k0, Ue = next((i, f) for i, f in early if e0 in regs(word['cleanup'][i]))
+    def to_pre(w, j0=j0): w['precondition'].append(w['A'][j0]); w['A'].pop(j0)
+    def other_hp(w, e0=e0, Ue=Ue): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Ue) and sorted(f) != sorted(Ue))
+    if j0 is not None: reject('entering end %d: premix gate dropped' % e0, lambda w, j0=j0: w['A'].pop(j0), WHY['e_premix_dropped'])
+    if j0 is not None: reject('entering end %d: premix gate at frame [] instead of its entrance E' % e0, lambda w, j0=j0: w['A'][j0].__setitem__(-1, []), WHY['nonmonotone'])
+    if j0 is not None: reject('entering end %d: premix gate moved into the zero-frame precondition' % e0, to_pre, WHY['entering_precondition'])
+    reject('entering end %d: lower-frame gate dropped (gate and its early_cleanup entry)' % e0, lambda w, k0=k0: drop_cleanup_gate(w, k0), WHY['lower_dropped'])
+    reject('entering end %d: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)' % e0, lambda w, e0=e0: w['helper_final'].pop(str(e0)), WHY['profile_pin'])
+    reject('entering end %d: end at another hyperplane' % e0, other_hp, WHY['cone'])
+# Pinned rejection reasons of the COLD-BEYOND mutants (substrings of hpe_audit_and_transport.py assertion messages).
+MYWHY = dict(tw_precondition=COLDPRE, tw_dropped=COLDPRE, tw_coefficient=COLDPRE, tw_other_block=COLDPRE,
+             tw_entering='zero-frame compensation reads an entering helper',
+             ab_dropped=ENDPOINT, ab_coefficient=ENDPOINT, ab_early=ENDPOINT, ab_live=ENDPOINT, ab_centre=ENDPOINT,
+             ab_lower="'nonmonotone'", ab_higher="'nonmonotone'",
+             sh_dropped=ENDPOINT, sh_coefficient=ENDPOINT, rel_dropped=ENDPOINT, rel_coefficient=ENDPOINT, rel_live=ENDPOINT,
+             h8_other=CONE, h8_lower=ENDPOINT)
+# COLD-BEYOND primitives (present only when the word carries them): frame-[] target writes in the premix (explicit
+# post-wrapper compensation of an ended helper's dirt) and forward absorptions into dead registers.
+nw = meta.get('premix_target_writes', 0)
+if nw:
+    wi = [i for i in range(npre) if v <= word['A'][i][1] < 2*v]
+    assert len(wi) == nw
+
+    def writes_to_precondition(w):   # the target writes run before the cold wrappers (inside the zero-frame precondition)
+        g = [w['A'][i] for i in wi]; w['precondition'] = w['precondition'] + g
+        w['A'] = [e for i, e in enumerate(w['A']) if i not in set(wi)]
+    reject('premix target writes placed in the zero-frame precondition (before the cold wrappers)', writes_to_precondition, MYWHY['tw_precondition'])
+    reject('one premix target write dropped (compensation must read an ended helper)', lambda w: w['A'].pop(wi[0]), MYWHY['tw_dropped'])
+    reject('premix target write coefficient changed', lambda w: w['A'][wi[0]].__setitem__(3, w['A'][wi[0]][3] * 2), MYWHY['tw_coefficient'])
+    # (reading another register that carries the SAME weight of the ended helper's dirt is a valid variant, so the mutant reads
+    #  the same factory slot of the next block, which carries none of it)
+    entering_regs = sorted(int(r) for r in word.get('start_extra', {}))
+    reject('premix target write reads an entering helper', lambda w: w['A'][wi[0]].__setitem__(2, entering_regs[0]), MYWHY['tw_entering'])
+    reject('premix target write reads a cold helper of another block', lambda w: w['A'][wi[0]].__setitem__(2, 2*v + (w['A'][wi[0]][2] - 2*v + 16) % 224), MYWHY['tw_other_block'])
+ab = meta.get('forward_absorption_A_indices', [])
+if any(len(word['helper_final'][str(h)]) == 8 for h in cold):
+    # with dim-8 cold ends, the centre-retargeted absorption first leaks an ended helper's dirt into the cut's targets
+    MYWHY['ab_centre'] = COLDPRE
+if ab:
+    # the ColdBeyond U_b absorption (q += -1/2 g); ColdThird's extra absorptions have their own controls below
+    a0 = next(a for a in ab if word['A'][a][3] * 2 == -word['A'][a][4]); g0 = word['A'][a0]
+
+    def absorption_moved_early(w):   # absorbed before the absorbed register's last kernel write
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[2] == w['A'][i][1] and w['A'][i][-1] == g0[-1])
+        w['A'].insert(j, e)
+
+    def absorption_into_live(w):     # q += a g moved right after g's previous frame-mate gate, while q is still live
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[1] in regs(w['A'][i]))
+        w['A'].insert(j, e)
+    reject('forward absorption dropped', lambda w: w['A'].pop(a0), MYWHY['ab_dropped'])
+    reject('forward absorption into a centre (a live register read by the cut)', lambda w: w['A'][a0].__setitem__(1, next(c for c in word['centers'] if c not in g0[1:3] and c not in cold)), MYWHY['ab_centre'])
+    reject('forward absorption coefficient changed', lambda w: w['A'][a0].__setitem__(3, w['A'][a0][3] * 2), MYWHY['ab_coefficient'])
+    reject('forward absorption placed before the absorbed register\'s last kernel write', absorption_moved_early, MYWHY['ab_early'])
+    reject('forward absorption placed while the absorbing register is still live', absorption_into_live, MYWHY['ab_live'])
+    reject('forward absorption at a lower frame than its registers', lambda w: w['A'][a0].__setitem__(-1, w['A'][a0][-1][:-1]), MYWHY['ab_lower'])
+    reject('forward absorption at a higher frame (FULL) than its registers', lambda w: w['A'][a0].__setitem__(-1, [256, 128, 64, 32, 16, 8, 4, 2, 1]), MYWHY['ab_higher'])
+# COLD-THIRD primitives (present only when the word carries them): several absorptions after one input gate, dirt-release
+# absorptions (a dead port takes a live helper's value so that a hyperplane unit's column has no dirt on it), and cold ends at
+# a dim-8 frame with lifted partners.
+hyper = [h for h in cold if len(word['helper_final'][str(h)]) == 8]
+if hyper and ab:
+    sh = next(a for a, b in zip(ab, ab[1:]) if b == a + 1)              # two absorptions sharing one input anchor
+    rel = next(a for a in ab if a - 1 not in ab and a + 1 not in ab and word['A'][a][2] in hyper and word['A'][a][3] * 2 != -word['A'][a][4])
+    hh = hyper[0]; ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+    reject('second absorption sharing an input anchor dropped', lambda w: w['A'].pop(sh + 1), MYWHY['sh_dropped'])
+    reject('shared-anchor absorption coefficient changed', lambda w: w['A'][sh + 1].__setitem__(3, w['A'][sh + 1][3] * 2), MYWHY['sh_coefficient'])
+    reject('dirt-release absorption dropped', lambda w: w['A'].pop(rel), MYWHY['rel_dropped'])
+    reject('dirt-release absorption coefficient changed', lambda w: w['A'][rel].__setitem__(3, w['A'][rel][3] * 2), MYWHY['rel_coefficient'])
+    jr = max(i for i in range(npre, rel) if word['A'][i][0] == 'add' and word['A'][i][2] == word['A'][rel][1])
+
+    def release_while_read(w):   # the release runs before a kernel gate that still READS the port (port live)
+        e = w['A'].pop(rel); w['A'].insert(jr, e)
+    reject('dirt-release absorption moved before a kernel gate that still reads the port', release_while_read, MYWHY['rel_live'])
+if hyper:
+    # dim-8 cold-end controls for EVERY dim-8 cold end of the word (read from the word's helper_final and the recipe meta's
+    # cold_low_frame_ended_helpers), not one representative per terminal frame
+    for hh in hyper:
+        ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+        Uh = word['helper_final'][str(hh)]
+        reject('dim-8 cold end %d (frame %s) at another dim-8 frame' % (hh, Uh), lambda w, hh=hh: w['helper_final'].__setitem__(str(hh), next(f for h, f in w['helper_final'].items() if len(f) == 8 and sorted(f) != sorted(w['helper_final'][str(hh)]))), MYWHY['h8_other'])
+        reject('dim-8 cold end %d (frame %s): one lower-frame gate dropped (gate and its early_cleanup entry)' % (hh, Uh), lambda w, ih=ih: drop_cleanup_gate(w, ih), MYWHY['h8_lower'])
+        reject('dim-8 cold end %d (frame %s): profile pin (end dropped)' % (hh, Uh), lambda w, hh=hh: w['helper_final'].pop(str(hh)), WHY['profile_pin'])
+# FACTORED ACCUMULATOR (CarrierBypass; present only when the word carries one): a lower-frame tail gate a += x*g on two
+# non-ended registers whose accumulator a is afterwards read by a dim-8 cold end's tail gate (h += y*a at its U).
+ended_all = {int(h) for h in word['helper_final']}
+tailg = [(i, word['cleanup'][i]) for i, _ in early]
+accs = []   # EVERY factored accumulator gate (one per accumulator register a), each controlled on its own
+for k, (i, e) in enumerate(tailg):
+    if e[0] == 'add' and e[1] not in ended_all and e[2] not in ended_all and len(next(f for j, f in early if j == i)) < 8:
+        if e[1] not in [word['cleanup'][j][1] for j in accs] and any(t[0] == 'add' and t[2] == e[1] and t[1] in hyper for _, t in tailg[k + 1:]):
+            accs.append(i)
+for acc in accs:
+    a = word['cleanup'][acc][1]
+    reject('factored accumulator %d (gate %d) zeroed' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, 0), ENDPOINT)
+    reject('factored accumulator %d (gate %d) coefficient doubled' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, w['cleanup'][acc][3] * 2), ENDPOINT)
+outdir.mkdir(parents=True, exist_ok=True)
+(outdir/'COLD-END-CONTROLS.json').write_text(json.dumps(dict(status='PASS_COLD_END_RAW_WORD_CONTROLS', word=str(src), rejected=results), indent=1) + '\n')
+print('PASS', len(results), 'cold-end raw-word mutations rejected')
diff --git a/research/gauge44-slots/construction/layers_p6n/reproduce_p6n.py b/research/gauge44-slots/construction/layers_p6n/reproduce_p6n.py
new file mode 100644
index 0000000000..f9eb173bc1
--- /dev/null
+++ b/research/gauge44-slots/construction/layers_p6n/reproduce_p6n.py
@@ -0,0 +1,78 @@
+#!/usr/bin/env python3
+"""Rebuild the p6n word (NoTriReopen): the layered no-triangle word with p123's lane rebuilt as three factored dim-8 pairs.
+
+Input: a fresh `construction/layers_np/reproduce_np.py` output directory. Its swapped HPE word (hpe/) and its
+layered word a9de804f... are pinned there. Steps, each checked exactly:
+  1. layers: PR635's unchanged build_cold_end.apply(swapped HPE word, COLD-LAYERS-RECIPE-P6N.json.gz). The recipe is
+     NP's cold-layer recipe (cold44, s4, x30, b6, q4) plus the six cold ends of P6N-SPEC.json, built by NoTriReopen
+     with JP8Ends' stackJ/stackE (the CarrierBypass premix-only factored construction): [512,513] at
+     U(256,128,66,34,16,8,6,1), [311,510] at U(256,128,72,40,24,4,2,1), [522,327] at U(256,128,66,34,18,10,6,1).
+     The output word sha (34b683fa...), profile and widths are pinned.
+  2. layer-end-controls: layer_end_controls.py (Q6Reviewer-signed variant fc58c569..., which controls every dim-8
+     cold end individually) on the p6n word; exactly 95 rejections at pinned reasons.
+The promotion step (construction/promo/reproduce_promo.py --base p6n) builds the final word and its native locals.
+Apache-2.0. Driver by ColdWitness after NoTriReopen's runspec.py.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NP_SHA = 'a9de804f194eeb39f52a4c6e54c14d93e881bec4b632694249733ed410b58113'
+P6N_SHA = '34b683fa08f0'   # prefix; full value is the recipe's output_content_sha256 (asserted equal below)
+LAYER_CONTROLS = 95
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--np-dir', type=Path, required=True, help='construction/layers_np/reproduce_np.py output')
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    parent = src / 'vendor/pr558/vendor/pr552'
+    npd = a.np_dir.resolve()
+    assert hashlib.sha256(enc(read(npd / 'layers/FULL-WORD.json.gz'))).hexdigest() == NP_SHA, 'np-dir must hold the pinned NP word'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src), PR635_CODE=str(up / 'code'))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    rec = read(HERE / 'COLD-LAYERS-RECIPE-P6N.json.gz')
+    w = bce.apply(read(npd / 'hpe/FULL-WORD.json.gz'), rec)
+    raw = enc(w); got = hashlib.sha256(raw).hexdigest()
+    assert got == rec['output_content_sha256'] and got.startswith(P6N_SHA), ('p6n word', got)
+    rep = w['report']
+    assert rep['local_profile'] == {'1': 2540, '2': 358, '3': 446, '4': 178, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 64, '5': 48, '7': 54, '8': 122, '9': 216}, rep['width_inventory']
+    (out / 'p6n').mkdir(); word = out / 'p6n/FULL-WORD.json.gz'; word.write_bytes(gzip.compress(raw, mtime=0))
+    print('PASS p6n word', got, flush=True)
+    t = time.monotonic()
+    with (out / 'layer-end-controls.log').open('w') as f:
+        rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(HERE / 'layer_end_controls.py'), str(word),
+                              str(parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'), str(out / 'controls')],
+                             env=env, stdout=f, stderr=subprocess.STDOUT)
+    (out / 'STEPS.json').write_text(json.dumps([dict(step='layer-end-controls', exit_code=rc, seconds=round(time.monotonic() - t, 3))], indent=2) + '\n')
+    assert rc == 0, 'layer-end-controls'
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == LAYER_CONTROLS, len(ctl['rejected'])
+    print('PASS layer-end-controls', LAYER_CONTROLS, flush=True)
+    print('DONE', word, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/leaver/CHAIN-PINS-k8.json b/research/gauge44-slots/construction/leaver/CHAIN-PINS-k8.json
new file mode 100644
index 0000000000..afd0467911
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/CHAIN-PINS-k8.json
@@ -0,0 +1,89 @@
+{
+ "np_profile": {
+  "1": 2422,
+  "2": 408,
+  "3": 494,
+  "4": 136,
+  "5": 56,
+  "8": 8
+ },
+ "p6n_profile": {
+  "1": 2428,
+  "2": 420,
+  "3": 482,
+  "4": 136,
+  "5": 56,
+  "8": 8
+ },
+ "lec-p6n_pins_sha256": "d87ed7b5869bed4a3d266f0ce5fc784cbe88340a625d22ab9f580fa00872df19",
+ "lec-p6n": 95,
+ "lec-p6n_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)"
+ },
+ "promo_controls": 11,
+ "lec-promo_pins_sha256": "d87ed7b5869bed4a3d266f0ce5fc784cbe88340a625d22ab9f580fa00872df19",
+ "lec-promo": 95,
+ "lec-promo_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)"
+ },
+ "jx_controls": [
+  "C0_identity",
+  "C1_741_only",
+  "N3_plain_join_moved_reads"
+ ],
+ "lec-jx_pins_sha256": "d87ed7b5869bed4a3d266f0ce5fc784cbe88340a625d22ab9f580fa00872df19",
+ "lec-jx": 95,
+ "lec-jx_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)"
+ },
+ "hybrid_controls": [
+  "C0_identity",
+  "donation_after",
+  "donation_after@226",
+  "donation_after@228",
+  "donation_after@230",
+  "donation_after@231",
+  "donation_after@232",
+  "donation_after@62",
+  "drop_preread",
+  "drop_preread@226",
+  "drop_preread@228",
+  "drop_preread@230",
+  "drop_preread@231",
+  "drop_preread@232",
+  "drop_preread@62",
+  "drop_restore",
+  "drop_restore@226",
+  "drop_restore@228",
+  "drop_restore@230",
+  "drop_restore@231",
+  "drop_restore@232",
+  "drop_restore@62",
+  "recipe",
+  "restore_full",
+  "restore_full@226",
+  "restore_full@228",
+  "restore_full@230",
+  "restore_full@231",
+  "restore_full@232",
+  "restore_full@62"
+ ],
+ "lec-hyb_pins_sha256": "d87ed7b5869bed4a3d266f0ce5fc784cbe88340a625d22ab9f580fa00872df19",
+ "lec-hyb": 95,
+ "lec-hyb_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)"
+ },
+ "frame_build_controls": 3,
+ "lec-frames_pins_sha256": "b07279e41ec9d8f89e8509081e1e7f2c8e8b062fd951b22608a03ac461982914",
+ "lec-frames": 95,
+ "lec-frames_not_applicable": {
+  "extra_end": "partner 282 already cold-ended at h0 273 frame (identity)",
+  "other_hp:554": "tail frame dim 5; no other helper_final frame of that dim"
+ },
+ "canonical_sha256": "d1bf3c6f250a61be7421ce566668092f362c465274fb472d4bb01fc80cba9b23",
+ "program_sha256": {
+  "forward": "683f83231d4d4890a7fc3d18f30d4ac7bfbd7bbdf4e7ff57ad0eb09e8a5f571c",
+  "backward": "2d184e4d9d48aa4d5e3679368ee0eca7e0388b1966eb05e0fd17d22d00d36293"
+ },
+ "clifford_recipes_sha256": "e3bfdfa2c044f14c00a8706950c8ae838ceeedd9ca78a83bffefe7886219516a"
+}
diff --git a/research/gauge44-slots/construction/leaver/CODED-CELLS-k8.json b/research/gauge44-slots/construction/leaver/CODED-CELLS-k8.json
new file mode 100644
index 0000000000..cd23561e0b
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/CODED-CELLS-k8.json
@@ -0,0 +1,2826 @@
+[
+ {
+  "cell": "01+",
+  "bindings": {
+   "x0": [
+    "source",
+    [
+     0,
+     1,
+     2,
+     3
+    ],
+    1
+   ],
+   "x1": [
+    "source",
+    [
+     0,
+     1,
+     2,
+     3
+    ],
+    0
+   ],
+   "x2": [
+    "source",
+    [
+     0,
+     1,
+     4,
+     5
+    ],
+    1
+   ],
+   "x3": [
+    "source",
+    [
+     0,
+     1,
+     4,
+     5
+    ],
+    0
+   ],
+   "x4": [
+    "source",
+    [
+     0,
+     1,
+     6,
+     7
+    ],
+    1
+   ],
+   "x5": [
+    "source",
+    [
+     0,
+     1,
+     6,
+     7
+    ],
+    0
+   ],
+   "y0": [
+    "target",
+    65
+   ],
+   "y1": [
+    "target",
+    64
+   ],
+   "y2": [
+    "target",
+    33
+   ],
+   "y3": [
+    "target",
+    32
+   ],
+   "y4": [
+    "target",
+    25
+   ],
+   "y5": [
+    "target",
+    24
+   ]
+  },
+  "scaled": [
+   [
+    "y1",
+    "x0",
+    "-1/2"
+   ],
+   [
+    "y0",
+    "x1",
+    "-1/2"
+   ],
+   [
+    "y2",
+    "x5",
+    "-1/2"
+   ],
+   [
+    "y3",
+    "x4",
+    "-1/2"
+   ],
+   [
+    "y4",
+    "x3",
+    "-1/2"
+   ],
+   [
+    "y5",
+    "x2",
+    "-1/2"
+   ],
+   [
+    "x0",
+    "x1",
+    "1"
+   ],
+   [
+    "x2",
+    "x5",
+    "1"
+   ],
+   [
+    "x4",
+    "x3",
+    "1"
+   ],
+   [
+    "y1",
+    "x2",
+    "-1/2"
+   ],
+   [
+    "y3",
+    "x0",
+    "-1/2"
+   ],
+   [
+    "y5",
+    "x4",
+    "-1/2"
+   ],
+   [
+    "y0",
+    "y5",
+    "1"
+   ],
+   [
+    "y2",
+    "y3",
+    "1"
+   ],
+   [
+    "y4",
+    "y1",
+    "1"
+   ],
+   [
+    "y1",
+    "x4",
+    "-1/2"
+   ],
+   [
+    "y0",
+    "x5",
+    "-1/2"
+   ],
+   [
+    "y2",
+    "x3",
+    "-1/2"
+   ],
+   [
+    "y3",
+    "x2",
+    "-1/2"
+   ],
+   [
+    "y4",
+    "x1",
+    "-1/2"
+   ],
+   [
+    "y5",
+    "x0",
+    "-1/2"
+   ]
+  ],
+  "unit": [
+   [
+    "y1",
+    "x0",
+    1
+   ],
+   [
+    "y0",
+    "x1",
+    1
+   ],
+   [
+    "y2",
+    "x5",
+    1
+   ],
+   [
+    "y3",
+    "x4",
+    1
+   ],
+   [
+    "y4",
+    "x3",
+    1
+   ],
+   [
+    "y5",
+    "x2",
+    1
+   ],
+   [
+    "x0",
+    "x1",
+    1
+   ],
+   [
+    "x2",
+    "x5",
+    1
+   ],
+   [
+    "x4",
+    "x3",
+    1
+   ],
+   [
+    "y1",
+    "x2",
+    1
+   ],
+   [
+    "y3",
+    "x0",
+    1
+   ],
+   [
+    "y5",
+    "x4",
+    1
+   ],
+   [
+    "y0",
+    "y5",
+    1
+   ],
+   [
+    "y2",
+    "y3",
+    1
+   ],
+   [
+    "y4",
+    "y1",
+    1
+   ],
+   [
+    "y1",
+    "x4",
+    1
+   ],
+   [
+    "y0",
+    "x5",
+    1
+   ],
+   [
+    "y2",
+    "x3",
+    1
+   ],
+   [
+    "y3",
+    "x2",
+    1
+   ],
+   [
+    "y4",
+    "x1",
+    1
+   ],
+   [
+    "y5",
+    "x0",
+    1
+   ]
+  ],
+  "coefficients": [
+   [
+    "0",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2"
+   ],
+   [
+    "-1/2",
+    "0",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2"
+   ],
+   [
+    "-1/2",
+    "-1/2",
+    "0",
+    "-1/2",
+    "-1/2",
+    "-1/2"
+   ],
+   [
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "0",
+    "-1/2",
+    "-1/2"
+   ],
+   [
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "0",
+    "-1/2"
+   ],
+   [
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "-1/2",
+    "0"
+   ]
+  ]
+ },
+ {
+  "cell": "23+",
+  "bindings": {
+   "x0": [
+    "source",
+    [
+     0,
+     1,
+     2,
+     3
+    ],
+    23
+   ],
+   "x1": [
+    "source",
+    [
+     0,
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diff --git a/research/gauge44-slots/construction/leaver/COLD-LAYERS-RECIPE-P6N-k8.json.gz b/research/gauge44-slots/construction/leaver/COLD-LAYERS-RECIPE-P6N-k8.json.gz
new file mode 100644
index 0000000000..dc0275695d
Binary files /dev/null and b/research/gauge44-slots/construction/leaver/COLD-LAYERS-RECIPE-P6N-k8.json.gz differ
diff --git a/research/gauge44-slots/construction/leaver/FRAME-RECIPE-LV-k8.json b/research/gauge44-slots/construction/leaver/FRAME-RECIPE-LV-k8.json
new file mode 100644
index 0000000000..982bd357da
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+  }
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/leaver/REGROUP-LEAVER-k8.json b/research/gauge44-slots/construction/leaver/REGROUP-LEAVER-k8.json
new file mode 100644
index 0000000000..d482da23a8
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/REGROUP-LEAVER-k8.json
@@ -0,0 +1,725 @@
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diff --git a/research/gauge44-slots/construction/leaver/TRI-LEAVER-k8.json b/research/gauge44-slots/construction/leaver/TRI-LEAVER-k8.json
new file mode 100644
index 0000000000..e3bb24cc49
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/TRI-LEAVER-k8.json
@@ -0,0 +1,590 @@
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+      5
+     ],
+     19
+    ],
+    [
+     85,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     17
+    ],
+    [
+     84,
+     [
+      2,
+      3,
+      6,
+      7
+     ],
+     19
+    ]
+   ],
+   "coded": true,
+   "cell": 6
+  },
+  {
+   "p": [
+    4,
+    5
+   ],
+   "e": -1,
+   "reads": [
+    [
+     26,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     21
+    ],
+    [
+     30,
+     [
+      0,
+      1,
+      4,
+      5
+     ],
+     2
+    ],
+    [
+     90,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     21
+    ],
+    [
+     94,
+     [
+      2,
+      3,
+      4,
+      5
+     ],
+     2
+    ],
+    [
+     53,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     17
+    ],
+    [
+     52,
+     [
+      4,
+      5,
+      6,
+      7
+     ],
+     19
+    ]
+   ],
+   "coded": true,
+   "cell": 7
+  }
+ ]
+}
diff --git a/research/gauge44-slots/construction/leaver/build_frames_lv.py b/research/gauge44-slots/construction/leaver/build_frames_lv.py
new file mode 100644
index 0000000000..5f8aa7a24b
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/build_frames_lv.py
@@ -0,0 +1,64 @@
+#!/usr/bin/env python3
+"""Apply the pinned gate/tail frame re-optimisation of FRAME-RECIPE-LV-k5.json (exact global frame optimum, gopt2) to the
+leaver U8 word.
+
+usage: build_frames_lv.py INPUT_WORD.json.gz OUT_DIR RECIPE.json
+
+Standard library only. The frames are applied by BlockInvert's `../promo/build_promotion.apply` (no entrances; 'B' gate
+frames and 'T' tail frames), which checks each old frame and recomputes the local profile and widths. This builder then checks:
+input sha pin; the scalar program of A, cut, B, precondition and cleanup unchanged (every field but the frame); start
+and end frames unchanged; local profile and width inventory equal to the recipe's; output sha pin. Three pin controls
+(input pin, wrong old frame, output pin) must be rejected at their pinned reasons on every build.
+Adapted from ../frames/build_frames.py (from PR741's extras/build_frames.py, chafreaky). Apache-2.0.
+"""
+import copy, gzip, hashlib, importlib.util, json, sys
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+_s = importlib.util.spec_from_file_location('promotion', HERE.parent / 'promo/build_promotion.py')
+B = importlib.util.module_from_spec(_s); _s.loader.exec_module(B)
+
+
+def construct(raw, recipe):
+    assert hashlib.sha256(raw).hexdigest() == recipe['input_content_sha256'], 'input word pin'
+    w = json.loads(raw)
+    assert recipe['gate_frames'] and all(c[0] in ('B', 'T') for c in recipe['gate_frames']), 'B and T frames only'
+    out = B.apply(w, dict(entrances={}, gate_frames=recipe['gate_frames']))
+    for section in ('A', 'cut', 'B', 'precondition', 'cleanup'):
+        assert [e[:-1] for e in w[section]] == [e[:-1] for e in out[section]], 'scalar program unchanged'
+    assert out['start_extra'] == w['start_extra'] and out['helper_final'] == w['helper_final'], 'endpoint frames unchanged'
+    assert out['report']['local_profile'] == recipe['expected']['local_profile'] and \
+        out['report']['width_inventory'] == recipe['expected']['width_inventory'], 'profile and width pins'
+    data = json.dumps(out, sort_keys=True, separators=(',', ':')).encode()
+    assert hashlib.sha256(data).hexdigest() == recipe['expected']['output_content_sha256'], 'output word pin'
+    return data
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    inp, outd, rfile = map(Path, sys.argv[1:4])
+    raw = gzip.decompress(inp.read_bytes()); recipe = json.loads(rfile.read_text())
+    data = construct(raw, recipe)
+    rejected = []
+    for name, change, reason in [
+            ('input-pin', lambda r: r.__setitem__('input_content_sha256', '0' * 64), 'input word pin'),
+            ('old-frame', lambda r: r['gate_frames'][0].__setitem__(2, []), 'gate frame mismatch'),
+            ('output-pin', lambda r: r['expected'].__setitem__('output_content_sha256', '0' * 64), 'output word pin')]:
+        r = copy.deepcopy(recipe); change(r)
+        try:
+            construct(raw, r)
+        except AssertionError as e:
+            assert reason in str(e), (name, str(e)); rejected.append(dict(name=name, reason=reason))
+        else:
+            raise AssertionError('accepted ' + name)
+    outd.mkdir(parents=True)
+    (outd / 'FULL-WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+    (outd / 'BUILD.json').write_text(json.dumps(dict(
+        status='PASS_FRAME_REOPT_EXACT_CONSTRUCTION', input_sha256=hashlib.sha256(raw).hexdigest(),
+        output_sha256=hashlib.sha256(data).hexdigest(), scalar_program_unchanged=True, frames=len(recipe['gate_frames']),
+        rejected_controls=rejected), indent=2) + '\n')
+    print('PASS', len(recipe['gate_frames']), 'frames and three pin controls')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/leaver/cells-k8/CORE-01+.json b/research/gauge44-slots/construction/leaver/cells-k8/CORE-01+.json
new file mode 100644
index 0000000000..bfef820f29
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/cells-k8/CORE-01+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x0",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x0",
+   "-1/2"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/leaver/cells-k8/CORE-01-.json b/research/gauge44-slots/construction/leaver/cells-k8/CORE-01-.json
new file mode 100644
index 0000000000..3afa894b20
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/cells-k8/CORE-01-.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "x1",
+   "x0",
+   1
+  ],
+  [
+   "x3",
+   "x4",
+   1
+  ],
+  [
+   "x5",
+   "x2",
+   1
+  ],
+  [
+   "y0",
+   "x3",
+   1
+  ],
+  [
+   "y2",
+   "x1",
+   1
+  ],
+  [
+   "y4",
+   "x5",
+   1
+  ],
+  [
+   "y1",
+   "y4",
+   1
+  ],
+  [
+   "y3",
+   "y2",
+   1
+  ],
+  [
+   "y5",
+   "y0",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y0",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y1",
+   "x0",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "x1",
+   "x0",
+   "1"
+  ],
+  [
+   "x3",
+   "x4",
+   "1"
+  ],
+  [
+   "x5",
+   "x2",
+   "1"
+  ],
+  [
+   "y0",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x1",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y1",
+   "y4",
+   "1"
+  ],
+  [
+   "y3",
+   "y2",
+   "1"
+  ],
+  [
+   "y5",
+   "y0",
+   "1"
+  ],
+  [
+   "y0",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y1",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x0",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x1",
+   "-1/2"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/leaver/cells-k8/CORE-23+.json b/research/gauge44-slots/construction/leaver/cells-k8/CORE-23+.json
new file mode 100644
index 0000000000..98ff8050e7
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/cells-k8/CORE-23+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y5",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/leaver/cells-k8/CORE-23-.json b/research/gauge44-slots/construction/leaver/cells-k8/CORE-23-.json
new file mode 100644
index 0000000000..517b89d382
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/cells-k8/CORE-23-.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x3",
+   "x4",
+   1
+  ],
+  [
+   "x5",
+   "x2",
+   1
+  ],
+  [
+   "y1",
+   "x3",
+   1
+  ],
+  [
+   "y2",
+   "x0",
+   1
+  ],
+  [
+   "y4",
+   "x5",
+   1
+  ],
+  [
+   "y0",
+   "y4",
+   1
+  ],
+  [
+   "y3",
+   "y2",
+   1
+  ],
+  [
+   "y5",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x5",
+   1
+  ],
+  [
+   "y0",
+   "x4",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x1",
+   1
+  ],
+  [
+   "y4",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x3",
+   "x4",
+   "1"
+  ],
+  [
+   "x5",
+   "x2",
+   "1"
+  ],
+  [
+   "y1",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x0",
+   "1"
+  ],
+  [
+   "y4",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y4",
+   "1"
+  ],
+  [
+   "y3",
+   "y2",
+   "1"
+  ],
+  [
+   "y5",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x2",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x1",
+   "1"
+  ],
+  [
+   "y4",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/leaver/cells-k8/CORE-45+.json b/research/gauge44-slots/construction/leaver/cells-k8/CORE-45+.json
new file mode 100644
index 0000000000..2bc89e1de1
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/cells-k8/CORE-45+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y4",
+   "x3",
+   "1"
+  ],
+  [
+   "y5",
+   "x2",
+   "1"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "x4",
+   "x3",
+   "-2"
+  ],
+  [
+   "y1",
+   "x2",
+   "1"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y5",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "1"
+  ],
+  [
+   "y3",
+   "x2",
+   "1"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/leaver/cells-k8/CORE-45-.json b/research/gauge44-slots/construction/leaver/cells-k8/CORE-45-.json
new file mode 100644
index 0000000000..b9c1904b83
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/cells-k8/CORE-45-.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x4",
+   1
+  ],
+  [
+   "y3",
+   "x5",
+   1
+  ],
+  [
+   "y5",
+   "x3",
+   1
+  ],
+  [
+   "y4",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x4",
+   1
+  ],
+  [
+   "x5",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y4",
+   "x5",
+   1
+  ],
+  [
+   "y0",
+   "y4",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y5",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x5",
+   1
+  ],
+  [
+   "y0",
+   "x4",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y5",
+   "x1",
+   1
+  ],
+  [
+   "y4",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y3",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y5",
+   "x3",
+   "1"
+  ],
+  [
+   "y4",
+   "x2",
+   "1"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "x5",
+   "x3",
+   "-2"
+  ],
+  [
+   "y1",
+   "x2",
+   "1"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y4",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "y4",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y5",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x5",
+   "-1/2"
+  ],
+  [
+   "y0",
+   "x4",
+   "-1/2"
+  ],
+  [
+   "y2",
+   "x3",
+   "1"
+  ],
+  [
+   "y3",
+   "x2",
+   "1"
+  ],
+  [
+   "y5",
+   "x1",
+   "1"
+  ],
+  [
+   "y4",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/leaver/cells-k8/CORE-67+.json b/research/gauge44-slots/construction/leaver/cells-k8/CORE-67+.json
new file mode 100644
index 0000000000..7d756cb19d
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/cells-k8/CORE-67+.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x5",
+   "1"
+  ],
+  [
+   "y3",
+   "x4",
+   "1"
+  ],
+  [
+   "y4",
+   "x3",
+   "1"
+  ],
+  [
+   "y5",
+   "x2",
+   "1"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "1"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y5",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "x5",
+   "1"
+  ],
+  [
+   "y2",
+   "x3",
+   "1"
+  ],
+  [
+   "y3",
+   "x2",
+   "1"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/leaver/cells-k8/CORE-67-.json b/research/gauge44-slots/construction/leaver/cells-k8/CORE-67-.json
new file mode 100644
index 0000000000..7d756cb19d
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/cells-k8/CORE-67-.json
@@ -0,0 +1,216 @@
+{
+ "unit": [
+  [
+   "y1",
+   "x0",
+   1
+  ],
+  [
+   "y0",
+   "x1",
+   1
+  ],
+  [
+   "y2",
+   "x5",
+   1
+  ],
+  [
+   "y3",
+   "x4",
+   1
+  ],
+  [
+   "y4",
+   "x3",
+   1
+  ],
+  [
+   "y5",
+   "x2",
+   1
+  ],
+  [
+   "x0",
+   "x1",
+   1
+  ],
+  [
+   "x2",
+   "x5",
+   1
+  ],
+  [
+   "x4",
+   "x3",
+   1
+  ],
+  [
+   "y1",
+   "x2",
+   1
+  ],
+  [
+   "y3",
+   "x0",
+   1
+  ],
+  [
+   "y5",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "y5",
+   1
+  ],
+  [
+   "y2",
+   "y3",
+   1
+  ],
+  [
+   "y4",
+   "y1",
+   1
+  ],
+  [
+   "y1",
+   "x4",
+   1
+  ],
+  [
+   "y0",
+   "x5",
+   1
+  ],
+  [
+   "y2",
+   "x3",
+   1
+  ],
+  [
+   "y3",
+   "x2",
+   1
+  ],
+  [
+   "y4",
+   "x1",
+   1
+  ],
+  [
+   "y5",
+   "x0",
+   1
+  ]
+ ],
+ "scaled": [
+  [
+   "y1",
+   "x0",
+   "1"
+  ],
+  [
+   "y0",
+   "x1",
+   "1"
+  ],
+  [
+   "y2",
+   "x5",
+   "1"
+  ],
+  [
+   "y3",
+   "x4",
+   "1"
+  ],
+  [
+   "y4",
+   "x3",
+   "1"
+  ],
+  [
+   "y5",
+   "x2",
+   "1"
+  ],
+  [
+   "x0",
+   "x1",
+   "1"
+  ],
+  [
+   "x2",
+   "x5",
+   "1"
+  ],
+  [
+   "x4",
+   "x3",
+   "1"
+  ],
+  [
+   "y1",
+   "x2",
+   "1"
+  ],
+  [
+   "y3",
+   "x0",
+   "1"
+  ],
+  [
+   "y5",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "y5",
+   "1"
+  ],
+  [
+   "y2",
+   "y3",
+   "1"
+  ],
+  [
+   "y4",
+   "y1",
+   "1"
+  ],
+  [
+   "y1",
+   "x4",
+   "1"
+  ],
+  [
+   "y0",
+   "x5",
+   "1"
+  ],
+  [
+   "y2",
+   "x3",
+   "1"
+  ],
+  [
+   "y3",
+   "x2",
+   "1"
+  ],
+  [
+   "y4",
+   "x1",
+   "1"
+  ],
+  [
+   "y5",
+   "x0",
+   "1"
+  ]
+ ]
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/leaver/cgx_leaver.py b/research/gauge44-slots/construction/leaver/cgx_leaver.py
new file mode 100644
index 0000000000..e686c66306
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/cgx_leaver.py
@@ -0,0 +1,491 @@
+# LeaverSAT: no-helper mutable-leaver all-K cells (coded triangles) on the no-triangle word. Generated by
+# LeaverSAT/mkpkg.py from construction/notri/cgx.py with the leaver edits (lv.leaver_source); Apache-2.0.
+import json as _lj, os as _lo, sys as _ls
+from fractions import Fraction as _lF
+CODED_CELLS=[(c['bindings'],[[t,s,_lF(q)] for t,s,q in c['scaled']]) for c in _lj.load(open(_lo.path.join(_lo.path.dirname(_lo.path.abspath(_ls.argv[3])),'CODED-CELLS.json')))]
+# Round20 early-coordinate-center / own-Y variant, prepared for icekylinx
+# with OpenAI Codex assistance. Apache-2.0. Scalar elementary-operation
+# helpers below are retained from the attributed PR514 construct_partial.py.
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+# AtomScout: leaver-read K-triangles (schedule from atom1.py / rog.py CP-SAT)
+TRI=json.loads(Path(sys.argv[3]).read_text())
+FULLT={(tuple(tr['p']),tr['e']) for tr in TRI['triangles']}
+TRI_COORDS={t+8 for tr in TRI['triangles'] for t,_,_ in tr['reads']}
+import os as _o
+COPYL=json.loads(open(_o.environ['XPARAM']).read()).get('copyl',[]) if _o.environ.get('XPARAM') else []
+NH=504-3*len(FULLT)+len(COPYL)
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+# Helper ids of the unpatched 504 construction: every allocation advances the 504 numbering; a packet copy that the
+# K-triangle schedule never forms advances it without allocating (HELPER-MAP.json).
+shadow=[];skipped=[];nxt=[2*v]
+def alloc():
+    n=len(cur);cur.append(());rows.append({});shadow.append(nxt[0]);nxt[0]+=1;return n
+def skip():
+    skipped.append(nxt[0]);nxt[0]+=1
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# Each source quartet supplies pair partials first. The other two coordinate
+# partitions supply eight early face packets without touching the eight
+# partials later copied into the preconditioned Y coordinates.
+SELECT=(0,0)
+PRIORITY=json.loads((INPUT/"COMPLETION-PRIORITY.json").read_text())
+import os
+XP=json.loads(open(os.environ['XPARAM']).read()) if os.environ.get('XPARAM') else {}
+XCH=XP.get('exch',{});PRIO=XP.get('prio',{})
+maps={};early={};own_rows={};pairs=[];tetrads={};block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)});maps[c]=mp
+    for ei,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[:40]):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        if ei==15:
+            for jj,cl in XCH.get(str(len(maps)-1),[[4,17],[5,19],[6,21],[7,23]]):swap(mp[jj],mp[cl],(P[ids[jj]],))
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in targets:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                t,u=sorted(ts);e2=R[t][q[0]]*R[t][q[1]]
+                pair={'targets':(t,u),'keys':[(c,p,eps),(c,q,e2)],'selected':pi==SELECT[parity],
+                      'matrix':[[R[a][p[0]],R[a][q[0]]] for a in (t,u)]}
+                pairs.append(pair)
+                if not pair['selected']:continue
+                zz=-Q(2*R[u][p[0]],R[t][p[0]])
+                sources=tet[1-parity]
+                for target,sign in ((t,-1),(u,1)):
+                    wanted={s:-Q(G[t][s],4)-sign*Q(G[u][s],2)/zz for s in sources
+                            if -Q(G[t][s],4)-sign*Q(G[u][s],2)/zz}
+                    assert len(wanted)==2
+                    candidates=[]
+                    for r in mp.values():
+                        if set(rows[r])!=set(wanted):continue
+                        s=next(iter(wanted));coef=wanted[s]/rows[r][s]
+                        if all(wanted[s]==coef*rows[r][s] for s in wanted):candidates.append((r,coef))
+                    assert len(candidates)==1
+                    r,coef=candidates[0];assert len(cur[r])==2
+                    own_rows[target]=(r,coef,cur[r])
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    needed={own_rows[t][0] for t in ids}
+    early[c]={j for j,e in enumerate(z['events'][40:]) if not ({mp[e[0]],mp[e[1]]}&needed)}
+    assert len(early[c])==8
+    retired=[]
+    for j in sorted(early[c]):
+        (t,s,a,b),F=z['events'][40+j],z['event_frames'][40+j]
+        add(mp[t],mp[s],Q(a,b),tuple(F));retired.append(mp[s])
+    assert not set(retired)&needed
+    # These eight retired rows already span every source coordinate. Keep
+    # them invertible and place the four coordinate totals in a changed basis.
+    F=basis([P[s] for s in ids]);assert len(F)==4
+    regs=sorted(retired,key=lambda r:(r>=v,r))
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    M=[[Q(R[s][i]) for s in ids] for i in c]
+    def qr_rank(rs):
+        bs={}
+        for r in rs:
+            r=r.copy()
+            for i,b in sorted(bs.items()):
+                if r[i]:q=r[i];r=[x-q*y for x,y in zip(r,b)]
+            i=next((i for i,x in enumerate(r) if x),None)
+            if i is not None:q=r[i];bs[i]=[x/q for x in r]
+        return len(bs)
+    assert qr_rank(M)==4
+    for rr0 in PRIO.get(",".join(map(str,c)),[])+PRIORITY[",".join(map(str,c))]["rows"]:
+        rr=list(map(Q,rr0))
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    for i in range(8):
+        if len(M)==8:break
+        rr=[Q(i==j) for j in range(8)]
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    assert len(M)==8
+    linear(regs,M,F)
+    for i,r in zip(c,regs):
+        assert rows[r]=={s:Q(R[s][i]) for s in ids}
+        block_totals[c,i]=r
+
+# All centers are complete while Y is still at zero. This is the crucial
+# difference from an illegal early-own-Y prefix using the old center order.
+centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+assert all(cur[v+t]==() for t in range(v))
+
+phase=B
+for t,(r,coef,F) in sorted(own_rows.items()):
+    if t in TRI_COORDS:continue
+    assert cur[r]==F
+    add(v+t,r,coef,F)
+# requests are needed for TRI coefficients
+requests=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    requests[key1].append((t,-Q(mat[0][0],2)))
+    requests[key2].append((u,-Q(mat[0][1],2)))
+reqcoef={t:(key,coef) for key,reqs in requests.items() for t,coef in reqs}
+def face_info(c,p,eps):
+    z=blocks[c];keys=[(pp,ee) for pp in it.combinations(c,2) for ee in (-1,1)]
+    r_local,alpha=z['outputs'][keys.index((p,eps))]
+    j=[j for j in range(40,len(z['events'])) if z['events'][j][0]==r_local];assert len(j)==1
+    return j[0],Q(alpha)
+tri_join_counts=Counter()
+coded_shadow_slot={}
+coded_target_edges=[];TRILOG=[]
+lcopy={}
+for s8 in COPYL:
+    r=s8+8;c=len(cur);cur.append(());rows.append({});shadow.append(None);add(c,r,1,cur[r]);lcopy[r]=c
+BF={c:basis([P[x] for x in z['receipt']['source_lines']]) for c,z in blocks.items()}
+HYB={(tuple(map(int,h[0])),tuple(map(int,h[1])),int(h[2])) for h in XP.get('hyb',[])}
+HYBLOG=[]
+def triread(t,blk,r,q):
+    F=basis(cur[v+t]+cur[r]);assert inside(F,hyper(P[t])),('TRI frame',t,blk,r,cur[v+t],cur[r],hyper(P[t]),[x for x in TRILOG if x[2]==r],HYBLOG)
+    tri_join_counts[len(F)]+=1;add(v+t,r,q,F);TRILOG.append([t,list(blk),r,str(q),list(F),list(cur[r])])
+for tr in TRI['triangles']:
+    if tr.get('coded'):
+        bindings={}
+        for name,binding in CODED_CELLS[tr['cell']][0].items():
+            bindings[name]=maps[tuple(binding[1])][binding[2]] if binding[0]=='source' else v+binding[1]
+        for tn,sn,q in CODED_CELLS[tr['cell']][1]:
+            target,source=bindings[tn],bindings[sn]
+            F=basis(cur[target]+cur[source])
+            for register in (target,source):
+                if v<=register<2*v:assert inside(F,hyper(P[register-v])),('coded frame',register,F)
+            add(target,source,q,F)
+            if sn.startswith('y'):coded_target_edges.append((target,source,Q(q)))
+        continue
+    p,eps=tuple(tr['p']),tr['e']
+    hb={blk for _,blk,_ in map(lambda x:(x[0],tuple(x[1]),x[2]),tr['reads']) if (blk,p,eps) in HYB}
+    own=[];rest=[]
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];r0=r;r=lcopy.get(r,r)
+        key,coef=reqcoef[t];assert key[1]==p and key[2]==eps,(key,p,eps)
+        if blk==key[0]:
+            rr,c0,F0=own_rows[t];assert rr==r0;own.append((t,blk,r,c0))
+        else:
+            j,alpha=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert loc in ev[:2]
+            rest.append((t,blk,loc,r,coef*alpha))
+    if not hb:
+        # original interleaved order
+        for t8,blk,loc in tr['reads']:
+            t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+            if blk==key[0]:q=own_rows[t][1]
+            else:j,alpha=face_info(blk,p,eps);q=coef*alpha
+            triread(t,blk,r,q)
+        continue
+    items=[]  # (kind, t, reg, q, blk)
+    for t,blk,r,q in own:items.append(('r',t,r,q,blk,blk in hb))
+    for blk in sorted(hb):items.append(('e',None,None,None,blk,True))
+    done=set()
+    for t,blk,loc,r,q in rest:
+        if blk in hb:
+            j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j]
+            ws=[x for x in rest if x[0]==t and x[1]==blk];assert len(ws)==2 and ws[0][4]==ws[1][4] and {ws[0][2],ws[1][2]}==set(ev[:2])
+            if (t,blk) in done:continue
+            done.add((t,blk));items.append(('m',t,maps[blk][ev[0]],q,blk,True))
+        else:items.append(('r',t,r,q,blk,False))
+    # Original read order with the two half reads collapsed into one M read at the first half's slot; the face event goes
+    # just before the first M read of its block; own reads of the M register are hoisted ahead of that event.
+    def evinfo(blk):
+        j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert ev[2]==ev[3]==1,ev
+        mpb=maps[blk];return mpb[ev[0]],mpb[ev[1]],tuple(blocks[blk]['event_frames'][j])
+    items=[]
+    seen=set()
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+        if blk==key[0]:items.append(('r',t,r,own_rows[t][1],blk,blk in hb))
+        else:
+            j,alpha=face_info(blk,p,eps);q=coef*alpha
+            if blk in hb:
+                if (t,blk) not in seen:seen.add((t,blk));continue
+                items.append(('m',t,evinfo(blk)[0],q,blk,True))
+            else:items.append(('r',t,r,q,blk,False))
+    for blk in sorted(hb):
+        k0=min(i for i,x in enumerate(items) if x[0]=='m' and x[4]==blk)
+        items.insert(k0,('e',None,None,None,blk,True))
+    n=len(items)
+    def step(it,st):
+        k,t,r,q,blk,h=it;g=lambda x:st.get(x,cur[x])
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(g(a_))+list(g(b_)))
+            return {a_:FF,b_:FF} if inside(FF,BF[blk]) else None
+        F=basis(list(g(v+t))+list(g(r)))
+        if not inside(F,hyper(P[t])):return None
+        if h and k=='r' and r==evinfo(blk)[1] and not inside(F,BF[blk]):return None
+        return {v+t:F,r:F}
+    def allowed(i,used):
+        k,t,r,q,blk,h=items[i]
+        evi=[j for j,x in enumerate(items) if x[0]=='e' and x[4]==blk] if h else []
+        if k=='e':return all(j in used for j,x in enumerate(items) if x[0]=='r' and x[4]==blk and x[5] and x[2]==evinfo(blk)[0])
+        if k=='m':return evi[0] in used
+        if k=='r' and h and r==evinfo(blk)[0]:return evi[0] not in used
+        return True
+    budget=[int(os.environ.get('HYBBUDGET','300000'))];memo=set()
+    def dfs(st,used,order):
+        if len(order)==n:return order
+        budget[0]-=1
+        if budget[0]<0:return None
+        sig=(used,tuple(sorted(st.items())))
+        if sig in memo:return None
+        memo.add(sig)
+        for i in range(n):
+            if i in used or not allowed(i,used):continue
+            d=step(items[i],st)
+            if d is None:continue
+            ns=dict(st);ns.update(d);res=dfs(ns,used|{i},order+[i])
+            if res:return res
+        return None
+    import sys as _s;_s.setrecursionlimit(20000)
+    order=dfs({},frozenset(),[])
+    assert order,('no feasible hybrid order',p,eps,sorted(hb),budget)
+    for i in order:
+        k,t,r,q,blk,h=items[i]
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(cur[a_])+list(cur[b_]));add(a_,b_,1,FF);HYBLOG.append([list(blk),list(p),eps,list(FF)])
+        else:triread(t,blk,r,q)
+
+packets={}
+for c,z in sorted(blocks.items()):
+    mp=maps[c]
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    skipev={face_info(c,p,eps)[0] for p,eps in keys if (p,eps) in FULLT}
+    for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]):
+        if j not in early[c] and 40+j not in skipev:
+            t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    for key,(r,alpha) in zip(keys,z['outputs']):
+        if tuple(key) in FULLT:skip();continue
+        a=mp[r];b=alloc();add(b,a,1,cur[a])
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha))
+
+# Both tetrahedra use the same partition. A selected key has exactly two
+# selected Y loads and no ordinary M consumer. Supply its two raw halves in
+# opposite orders and never form that M. Other keys retain the old M path.
+second=[];first_join_counts=Counter()
+for key,reqs in sorted(requests.items()):
+    assert len(reqs)==2
+    c,p,eps=key
+    if (p,eps) in FULLT:continue
+    ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds
+    for j,(target,coef) in enumerate(sorted(reqs)):
+        first_source,second_source=(a,b) if j==0 else (b,a)
+        r,alpha=packets[first_source,p,eps,second_source]
+        F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+        first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F)
+        r,alpha=packets[second_source,p,eps,c]
+        second.append((target,r,coef*alpha))
+
+Ms={}
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for eps in (-1,1):
+            if (c,p,eps) in requests:continue
+            (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,eps]=(a,alpha)
+
+consumers=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    for key in pair['keys']:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    if key in requests:
+        assert all(pairs[i]['selected'] for i in uses)
+        continue
+    assert all(not pairs[i]['selected'] for i in uses)
+    a,alpha=Ms[key]
+    for j,pid in enumerate(uses):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+assert len(cur)-240==NH,len(cur)-240
+
+selected_join_counts=Counter()
+for target,r,coef in second:
+    F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+    selected_join_counts[len(F)]+=1;add(v+target,r,coef,F)
+output_basis=[]
+for pair in pairs:
+    if not pair['selected']:continue
+    (t,u),mat=pair['targets'],pair['matrix']
+    F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u]))
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert rows[v+t]==expected,('side identity',t)
+
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+for target,source,q in reversed(coded_target_edges):
+    scatter[target-v]=[a-q*b for a,b in zip(scatter[target-v],scatter[source-v])]
+    precondition.append(['add',target,source,-q.numerator,q.denominator,[]])
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8
+assert sum(r*z for r,z in H.items())==9*NH+240*8+72,sum(r*z for r,z in H.items())
+
+def apply(e,matrix):
+    if e[0]=='add':
+        _,t,s,a,b,*_=e;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    e[-1]=list(FULL);return e
+cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q]
+cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v]
+matrix=[{r:Q(1)} if r<v else {} for r in range(len(cur))]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(len(cur)))
+
+# Restrict the eight isolated axis ports exactly, keeping the stable 112-port
+# label set. This variant changes the local word, not the outer geometry.
+mp={s:s-8 for s in range(8,120)}
+mp.update({120+s:112+s-8 for s in range(8,120)})
+mp.update({240+r:224+r for r in range(NH)})
+def restrict(events,is_cut=False):
+    out=[]
+    for e in events:
+        regs=e[1:3] if e[0]=='add' else e[1:2]
+        if any(r not in mp for r in regs):
+            assert is_cut and e[0]=='add' and e[1]-120==e[2] and e[2]<8 and e[3:5]==[1,1]
+            continue
+        q=copy.deepcopy(e);q[1]=mp[q[1]]
+        if q[0]=='add':q[2]=mp[q[2]]
+        out.append(q)
+    return out
+H.subtract({1:8,8:16});H=+H
+report={'status':'EXACT_CLEAN_OWN_Y_EARLY_CENTER_WORD_NOT_ADMITTED',
+        'h':9,'v':112,'R':NH,'cst':64,'m':73,'local_profile':dict(sorted(H.items())),
+        'centre_ranks':[8]*8,**({'tri_join_counts':dict(tri_join_counts)} if TRI['triangles'] else {}),'selected_load_join_counts':dict(selected_join_counts),'selected_partitions':list(SELECT),'first_load_join_counts':dict(first_join_counts),
+        'source_columns_exact':112,'borrowed_output_pairs':56,'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'local_rank_mass':sum(r*n for r,n in H.items()),'scope':'Clean scalar identity and all literal monotone local frames only; arbitrary-dirt compensation, entrance kernels, exact phase recipes, and global hosting/pricing are not yet certified.'}
+word={'report':report,'ports':P[8:],'root_lines':R[8:],
+      'A':restrict(A),'B':restrict(B),'cut':restrict(cut,True),'cleanup':restrict(cleanup),'precondition':restrict(precondition),
+      'centers':[mp[r] for r in centers[:8]],'center_frames':center_frames[:8],
+      'scatter':[[str(x) for x in row[:8]] for row in scatter[8:]]}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+assert len(shadow)==NH and len([x for x in shadow if x is not None])+len(skipped)==504
+hmap={**{r:r for r in range(224)},**{224+s_-240:224+i for i,s_ in enumerate(shadow) if s_ is not None}}
+(OUT/'HELPER-MAP.json').write_text(json.dumps({'map':{str(k):hmap[k] for k in sorted(hmap)},'removed_504_helpers':[224+s_-240 for s_ in skipped]})+'\n')
+(OUT/'TRILOG.json').write_text(json.dumps(dict(reads=TRILOG,hyb=HYBLOG)));(OUT/'DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/gauge44-slots/construction/leaver/layer_end_controls_leaver.py b/research/gauge44-slots/construction/leaver/layer_end_controls_leaver.py
new file mode 100644
index 0000000000..84b1c52ed2
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/layer_end_controls_leaver.py
@@ -0,0 +1,242 @@
+"""layer_end_controls_leaver.py LAYERED-WORD.json.gz ROUTING OUTDIR [ENTERING] (env PR635_CODE, optional env LEC_REASON_PINS
+= JSON file {mutant key: expected reason key or literal message substring}).  LeaverSAT variant of the signed
+layers_p6n/layer_end_controls.py (fc58c569...): IDENTICAL mutations and checks; the only change is that the expected
+rejection reason of a named mutant can be re-pinned per word (on the leaver words, with fewer cold ends, the premix-drop
+and into-full mutants are caught by the arbitrary-dirt endpoint replay before the pinned site is reached).  Every
+mutation is still REQUIRED to be rejected at its (re-)pinned reason; the unmutated word MUST pass.
+NOT-APPLICABLE SITES (Q6Reviewer, k8 / fo_hyb): two mutant constructions can be vacuous on a word:
+  extra_end      - h0's first premixed partner is already cold-ended at h0's frame, so the mutant is the identity;
+  other_hp:<e>   - entering end e's tail frame has a dimension that no helper_final frame has, so the mutant cannot be built.
+Such a site is never skipped silently: the pins file MUST declare it under "not_applicable" ({site: reason}), the
+declared set MUST equal the detected set, an identity is PROVEN by byte equality of the mutated and honest words (both
+sha256 recorded), and a substitute mutant of the same class is built and MUST be rejected at the class's pinned reason:
+  extra_end      -> the first premixed partner of h0 that is not yet ended, cold-ended at h0's frame;
+  other_hp:<e>   -> e's end moved to another helper_final frame of the dimension of e's own end frame.
+Original docstring: layer_end_controls.py LAYERED-WORD.json.gz ROUTING OUTDIR (env PR635_CODE): adapted PR635 cold_end_controls.py (LayerReviewer): raw-word negative controls for the cold low-frame ends and the
+refactored cleanup accepted by hpe_audit_and_transport.py.  Every mutation MUST be rejected (AssertionError); the
+unmutated word MUST pass.  Apache-2.0.  DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code."""
+import copy, gzip, hashlib, json, shutil, sys, tempfile
+from pathlib import Path
+import os
+sys.path.insert(0, os.environ['PR635_CODE'])   # PR635's unchanged hpe_audit_and_transport.py
+import hpe_audit_and_transport as atc
+
+src, routing, outdir = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3])
+word = json.load(gzip.open(src))
+v, R = word['report']['v'], word['report']['R']; n = 2*v + R
+regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else [])
+meta = word['refactored_cleanup']
+cold = [int(h) for h in meta['cold_low_frame_ended_helpers']]
+npre = meta['premix_gates']; nlow = meta['lower_frame_gates']
+early = word['early_cleanup']; eidx = {i for i, _ in early}
+rest = [i for i in range(len(word['cleanup'])) if i not in eidx]
+
+
+def trial(w):
+    """None if the transport audit accepts w, else the AssertionError message."""
+    tmp = Path(tempfile.mkdtemp())
+    p = tmp/'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w).encode(), mtime=0))
+    try:
+        atc.run(p, routing, tmp/'out')
+        return None
+    except AssertionError as e:
+        return repr(e.args[0]) if e.args else 'AssertionError'
+    finally:
+        shutil.rmtree(tmp, ignore_errors=True)
+
+
+# Pinned rejection reasons: each mutant must fail at this assertion of hpe_audit_and_transport.py (message substring).
+ENDPOINT, COLDPRE, CONE = "'arbitrary-dirt endpoint'", 'touches a cold hyperplane-ended helper', 'hpe cone pre-check (row / column)'
+WHY = dict(premix_to_precondition=COLDPRE, premix_dropped=COLDPRE, e_premix_dropped=ENDPOINT, lower_dropped=ENDPOINT,
+           remainder_dropped=ENDPOINT, coefficient=ENDPOINT, into_full='cleanup on non-FULL end', dyadic=ENDPOINT, frame_below="'nonmonotone'",
+           nonmonotone="'nonmonotone'", other_frame=CONE, cone=CONE, extra_end=COLDPRE, marker='cleanup is not the literal reversed inverse',
+           target='refactored cleanup touches a target', profile_pin='paid local profile differs from the reported local_profile',
+           entering_precondition='zero-frame precondition/compensation touches an entering helper')
+_REASONS = dict(ENDPOINT=ENDPOINT, COLDPRE=COLDPRE, CONE=CONE)
+NA_DECLARED = {}
+if os.environ.get('LEC_REASON_PINS'):
+    for _k, _v in json.loads(Path(os.environ['LEC_REASON_PINS']).read_text()).items():
+        if _k == 'not_applicable': NA_DECLARED = dict(_v); continue
+        assert _k in WHY, ('unknown mutant key', _k); WHY[_k] = _REASONS.get(_v, _v)
+assert trial(word) is None, 'unmutated cold-end word must pass'
+results = []
+
+
+def reject(name, mut, why):
+    """the mutation must be rejected, and for the pinned reason (a substring of the audit's assertion message)."""
+    w = copy.deepcopy(word); mut(w)
+    msg = trial(w)
+    assert msg is not None, 'cold-end mutation accepted: ' + name
+    assert why in msg, 'cold-end mutation %r rejected for the wrong reason: %s' % (name, msg[:300])
+    results.append(name); print('rejected', name, '|', why, flush=True)
+
+
+h0 = cold[0]
+i0, U0 = next((i, f) for i, f in early if h0 in regs(word['cleanup'][i]))
+r0 = rest[len(rest)//2]
+
+
+def premix_to_precondition(w):   # premix before the wrappers; compensation then reads the cold ends
+    w['precondition'] = w['precondition'] + w['A'][:npre]; w['A'] = w['A'][npre:]
+
+
+def lower_gate_into_full(w):     # a lower-frame gate on a cold-ended helper executed in the FULL remainder instead
+    w['early_cleanup'] = [x for x in w['early_cleanup'] if x[0] != i0]
+
+
+def drop_cleanup_gate(w, i):   # remove the gate AND its early_cleanup entry: a structurally valid word missing one gate
+    w['cleanup'].pop(i)
+    w['early_cleanup'] = [[j - (j > i), f] for j, f in w['early_cleanup'] if j != i]
+
+
+def other_frame(w):              # a different frame of the same dimension as the cold end (another cold helper's)
+    f = next(w['helper_final'][str(h)] for h in cold if w['helper_final'][str(h)] != w['helper_final'][str(h0)])
+    w['helper_final'][str(h0)] = f
+
+
+NA = []   # detected not-applicable sites: dict(site, reason, ...)
+wsha = lambda w: hashlib.sha256(json.dumps(w, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+HONEST_SHA = wsha(word)
+
+
+def extra_cold_end(w):           # declare a premixed partner of h0 cold-ended at h0's frame: fails the row/column cone
+    p = next(r for e in w['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    w['helper_final'][str(p)] = w['helper_final'][str(h0)]
+
+
+_m = copy.deepcopy(word); extra_cold_end(_m)
+if wsha(_m) == HONEST_SHA:   # identity: the first partner is already ended at h0's frame
+    _p = next(r for e in word['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e))
+    _q = next(r for e in word['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e) and str(r) not in word['helper_final'] and not v <= r < 2*v)
+    NA.append(dict(site='extra_end', reason='partner %d already cold-ended at h0 %d frame (identity)' % (_p, h0),
+                   honest_sha256=HONEST_SHA, mutated_sha256=wsha(_m), substitute='partner %d' % _q))
+
+    def extra_cold_end(w, q=_q): w['helper_final'][str(q)] = w['helper_final'][str(h0)]
+    assert wsha((lambda x: (extra_cold_end(x), x)[1])(copy.deepcopy(word))) != HONEST_SHA
+
+
+reject('premix placed in the zero-frame precondition (before the cold wrappers)', premix_to_precondition, WHY['premix_to_precondition'])
+reject('one premix gate dropped (the compensation then reads a cold-ended helper)', lambda w: w['A'].pop(npre - 1), WHY['premix_dropped'])
+reject('one lower-frame cleanup gate dropped (gate and its early_cleanup entry)', lambda w: drop_cleanup_gate(w, i0), WHY['lower_dropped'])
+reject('one FULL-remainder gate dropped', lambda w: drop_cleanup_gate(w, r0), WHY['remainder_dropped'])
+reject('lower-frame gate coefficient changed', lambda w: w['cleanup'][i0].__setitem__(3, w['cleanup'][i0][3] * 2), WHY['coefficient'])
+reject('lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)', lower_gate_into_full, WHY['into_full'])
+reject('lower-frame gate frame below its registers\' frames', lambda w: next(x for x in w['early_cleanup'] if x[0] == i0).__setitem__(1, U0[:-1]), WHY['frame_below'])
+reject('cold end at another dim-4 frame', other_frame, WHY['other_frame'])
+# PROFILE-PIN control: without its helper_final entry the cold-ended helper is a valid FULL-ended helper; the word is
+# rejected because its reported paid profile (which counts the low end) no longer matches the frame chains.
+reject('profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)', lambda w: w['helper_final'].pop(str(h0)), WHY['profile_pin'])
+reject('extra cold end on a premixed partner (the compensation reads it before its wrapper)', extra_cold_end, WHY['extra_end'])
+reject('refactored-cleanup marker removed (literal-inverse rule applies)', lambda w: w.pop('refactored_cleanup'), WHY['marker'])
+reject('remainder gate retargeted to a target register', lambda w: w['cleanup'][r0].__setitem__(1, v + 3), WHY['target'])
+reject('non-dyadic remainder coefficient', lambda w: w['cleanup'][r0].__setitem__(4 if w['cleanup'][r0][0] == 'add' else 3, 3 * w['cleanup'][r0][4 if w['cleanup'][r0][0] == 'add' else 3]), WHY['dyadic'])
+reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('5', w['report']['local_profile']['5'] - 1), WHY['profile_pin'])
+ent = [int(h) for h in sys.argv[4].split(',')] if len(sys.argv) > 4 else [int(h) for h in meta.get('entering_low_frame_ended_helpers', [])]
+for e0 in ent:   # ENTERING LOW-FRAME ENDS (ColdSupply extension; every entering end; absent for words without them)
+    j0 = next((i for i, e in enumerate(word['A'][:npre]) if e0 in regs(e)), None)
+    print('entering end', e0, 'premix gate', j0, flush=True)
+    k0, Ue = next((i, f) for i, f in early if e0 in regs(word['cleanup'][i]))
+    def to_pre(w, j0=j0): w['precondition'].append(w['A'][j0]); w['A'].pop(j0)
+    def other_hp(w, e0=e0, Ue=Ue): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Ue) and sorted(f) != sorted(Ue))
+    if not any(len(f) == len(Ue) and sorted(f) != sorted(Ue) for f in word['helper_final'].values()):   # unbuildable
+        Uh = word['helper_final'][str(e0)]
+        NA.append(dict(site='other_hp:%d' % e0, reason='tail frame dim %d; no other helper_final frame of that dim' % len(Ue),
+                       dims_available=sorted({len(f) for f in word['helper_final'].values()}), substitute='end-frame dim %d' % len(Uh)))
+
+        def other_hp(w, e0=e0, Uh=Uh): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Uh) and sorted(f) != sorted(Uh))
+    if j0 is not None: reject('entering end %d: premix gate dropped' % e0, lambda w, j0=j0: w['A'].pop(j0), WHY['e_premix_dropped'])
+    if j0 is not None: reject('entering end %d: premix gate at frame [] instead of its entrance E' % e0, lambda w, j0=j0: w['A'][j0].__setitem__(-1, []), WHY['nonmonotone'])
+    if j0 is not None: reject('entering end %d: premix gate moved into the zero-frame precondition' % e0, to_pre, WHY['entering_precondition'])
+    reject('entering end %d: lower-frame gate dropped (gate and its early_cleanup entry)' % e0, lambda w, k0=k0: drop_cleanup_gate(w, k0), WHY['lower_dropped'])
+    reject('entering end %d: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)' % e0, lambda w, e0=e0: w['helper_final'].pop(str(e0)), WHY['profile_pin'])
+    reject('entering end %d: end at another hyperplane' % e0, other_hp, WHY['cone'])
+# Pinned rejection reasons of the COLD-BEYOND mutants (substrings of hpe_audit_and_transport.py assertion messages).
+MYWHY = dict(tw_precondition=COLDPRE, tw_dropped=COLDPRE, tw_coefficient=COLDPRE, tw_other_block=COLDPRE,
+             tw_entering='zero-frame compensation reads an entering helper',
+             ab_dropped=ENDPOINT, ab_coefficient=ENDPOINT, ab_early=ENDPOINT, ab_live=ENDPOINT, ab_centre=ENDPOINT,
+             ab_lower="'nonmonotone'", ab_higher="'nonmonotone'",
+             sh_dropped=ENDPOINT, sh_coefficient=ENDPOINT, rel_dropped=ENDPOINT, rel_coefficient=ENDPOINT, rel_live=ENDPOINT,
+             h8_other=CONE, h8_lower=ENDPOINT)
+# COLD-BEYOND primitives (present only when the word carries them): frame-[] target writes in the premix (explicit
+# post-wrapper compensation of an ended helper's dirt) and forward absorptions into dead registers.
+nw = meta.get('premix_target_writes', 0)
+if nw:
+    wi = [i for i in range(npre) if v <= word['A'][i][1] < 2*v]
+    assert len(wi) == nw
+
+    def writes_to_precondition(w):   # the target writes run before the cold wrappers (inside the zero-frame precondition)
+        g = [w['A'][i] for i in wi]; w['precondition'] = w['precondition'] + g
+        w['A'] = [e for i, e in enumerate(w['A']) if i not in set(wi)]
+    reject('premix target writes placed in the zero-frame precondition (before the cold wrappers)', writes_to_precondition, MYWHY['tw_precondition'])
+    reject('one premix target write dropped (compensation must read an ended helper)', lambda w: w['A'].pop(wi[0]), MYWHY['tw_dropped'])
+    reject('premix target write coefficient changed', lambda w: w['A'][wi[0]].__setitem__(3, w['A'][wi[0]][3] * 2), MYWHY['tw_coefficient'])
+    # (reading another register that carries the SAME weight of the ended helper's dirt is a valid variant, so the mutant reads
+    #  the same factory slot of the next block, which carries none of it)
+    entering_regs = sorted(int(r) for r in word.get('start_extra', {}))
+    reject('premix target write reads an entering helper', lambda w: w['A'][wi[0]].__setitem__(2, entering_regs[0]), MYWHY['tw_entering'])
+    reject('premix target write reads a cold helper of another block', lambda w: w['A'][wi[0]].__setitem__(2, 2*v + (w['A'][wi[0]][2] - 2*v + 16) % 224), MYWHY['tw_other_block'])
+ab = meta.get('forward_absorption_A_indices', [])
+if any(len(word['helper_final'][str(h)]) == 8 for h in cold):
+    # with dim-8 cold ends, the centre-retargeted absorption first leaks an ended helper's dirt into the cut's targets
+    MYWHY['ab_centre'] = COLDPRE
+if ab:
+    # the ColdBeyond U_b absorption (q += -1/2 g); ColdThird's extra absorptions have their own controls below
+    a0 = next(a for a in ab if word['A'][a][3] * 2 == -word['A'][a][4]); g0 = word['A'][a0]
+
+    def absorption_moved_early(w):   # absorbed before the absorbed register's last kernel write
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[2] == w['A'][i][1] and w['A'][i][-1] == g0[-1])
+        w['A'].insert(j, e)
+
+    def absorption_into_live(w):     # q += a g moved right after g's previous frame-mate gate, while q is still live
+        e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[1] in regs(w['A'][i]))
+        w['A'].insert(j, e)
+    reject('forward absorption dropped', lambda w: w['A'].pop(a0), MYWHY['ab_dropped'])
+    reject('forward absorption into a centre (a live register read by the cut)', lambda w: w['A'][a0].__setitem__(1, next(c for c in word['centers'] if c not in g0[1:3] and c not in cold)), MYWHY['ab_centre'])
+    reject('forward absorption coefficient changed', lambda w: w['A'][a0].__setitem__(3, w['A'][a0][3] * 2), MYWHY['ab_coefficient'])
+    reject('forward absorption placed before the absorbed register\'s last kernel write', absorption_moved_early, MYWHY['ab_early'])
+    reject('forward absorption placed while the absorbing register is still live', absorption_into_live, MYWHY['ab_live'])
+    reject('forward absorption at a lower frame than its registers', lambda w: w['A'][a0].__setitem__(-1, w['A'][a0][-1][:-1]), MYWHY['ab_lower'])
+    reject('forward absorption at a higher frame (FULL) than its registers', lambda w: w['A'][a0].__setitem__(-1, [256, 128, 64, 32, 16, 8, 4, 2, 1]), MYWHY['ab_higher'])
+# COLD-THIRD primitives (present only when the word carries them): several absorptions after one input gate, dirt-release
+# absorptions (a dead port takes a live helper's value so that a hyperplane unit's column has no dirt on it), and cold ends at
+# a dim-8 frame with lifted partners.
+hyper = [h for h in cold if len(word['helper_final'][str(h)]) == 8]
+if hyper and ab:
+    sh = next(a for a, b in zip(ab, ab[1:]) if b == a + 1)              # two absorptions sharing one input anchor
+    rel = next(a for a in ab if a - 1 not in ab and a + 1 not in ab and word['A'][a][2] in hyper and word['A'][a][3] * 2 != -word['A'][a][4])
+    hh = hyper[0]; ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+    reject('second absorption sharing an input anchor dropped', lambda w: w['A'].pop(sh + 1), MYWHY['sh_dropped'])
+    reject('shared-anchor absorption coefficient changed', lambda w: w['A'][sh + 1].__setitem__(3, w['A'][sh + 1][3] * 2), MYWHY['sh_coefficient'])
+    reject('dirt-release absorption dropped', lambda w: w['A'].pop(rel), MYWHY['rel_dropped'])
+    reject('dirt-release absorption coefficient changed', lambda w: w['A'][rel].__setitem__(3, w['A'][rel][3] * 2), MYWHY['rel_coefficient'])
+    jr = max(i for i in range(npre, rel) if word['A'][i][0] == 'add' and word['A'][i][2] == word['A'][rel][1])
+
+    def release_while_read(w):   # the release runs before a kernel gate that still READS the port (port live)
+        e = w['A'].pop(rel); w['A'].insert(jr, e)
+    reject('dirt-release absorption moved before a kernel gate that still reads the port', release_while_read, MYWHY['rel_live'])
+if hyper:
+    # dim-8 cold-end controls for EVERY dim-8 cold end of the word (read from the word's helper_final and the recipe meta's
+    # cold_low_frame_ended_helpers), not one representative per terminal frame
+    for hh in hyper:
+        ih = next(i for i, f in early if hh in regs(word['cleanup'][i]))
+        Uh = word['helper_final'][str(hh)]
+        reject('dim-8 cold end %d (frame %s) at another dim-8 frame' % (hh, Uh), lambda w, hh=hh: w['helper_final'].__setitem__(str(hh), next(f for h, f in w['helper_final'].items() if len(f) == 8 and sorted(f) != sorted(w['helper_final'][str(hh)]))), MYWHY['h8_other'])
+        reject('dim-8 cold end %d (frame %s): one lower-frame gate dropped (gate and its early_cleanup entry)' % (hh, Uh), lambda w, ih=ih: drop_cleanup_gate(w, ih), MYWHY['h8_lower'])
+        reject('dim-8 cold end %d (frame %s): profile pin (end dropped)' % (hh, Uh), lambda w, hh=hh: w['helper_final'].pop(str(hh)), WHY['profile_pin'])
+# FACTORED ACCUMULATOR (CarrierBypass; present only when the word carries one): a lower-frame tail gate a += x*g on two
+# non-ended registers whose accumulator a is afterwards read by a dim-8 cold end's tail gate (h += y*a at its U).
+ended_all = {int(h) for h in word['helper_final']}
+tailg = [(i, word['cleanup'][i]) for i, _ in early]
+accs = []   # EVERY factored accumulator gate (one per accumulator register a), each controlled on its own
+for k, (i, e) in enumerate(tailg):
+    if e[0] == 'add' and e[1] not in ended_all and e[2] not in ended_all and len(next(f for j, f in early if j == i)) < 8:
+        if e[1] not in [word['cleanup'][j][1] for j in accs] and any(t[0] == 'add' and t[2] == e[1] and t[1] in hyper for _, t in tailg[k + 1:]):
+            accs.append(i)
+for acc in accs:
+    a = word['cleanup'][acc][1]
+    reject('factored accumulator %d (gate %d) zeroed' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, 0), ENDPOINT)
+    reject('factored accumulator %d (gate %d) coefficient doubled' % (a, acc), lambda w, acc=acc: w['cleanup'][acc].__setitem__(3, w['cleanup'][acc][3] * 2), ENDPOINT)
+assert {x['site']: x['reason'] for x in NA} == NA_DECLARED, ('not-applicable sites differ from the pins file', NA, NA_DECLARED)
+outdir.mkdir(parents=True, exist_ok=True)
+(outdir/'COLD-END-CONTROLS.json').write_text(json.dumps(dict(status='PASS_COLD_END_RAW_WORD_CONTROLS', word=str(src), rejected=results, not_applicable=NA), indent=1) + '\n')
+print('PASS', len(results), 'cold-end raw-word mutations rejected')
diff --git a/research/gauge44-slots/construction/leaver/reproduce_leaver.py b/research/gauge44-slots/construction/leaver/reproduce_leaver.py
new file mode 100644
index 0000000000..bc4360ef93
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/reproduce_leaver.py
@@ -0,0 +1,177 @@
+#!/usr/bin/env python3
+"""Rebuild the leaver word: the no-triangle word with no-helper mutable-leaver all-K cells, and its native locals.
+
+Each cell (pair p, sign e) replaces the three face events of the blocks containing p and their three packet copies
+by a 21-gate circuit on the cell's six leaver sources x_j (the face-event operands, which have no later reads and are
+restored by the inherited cleanup at FULL) and its six targets y_i: 3 leaver gates x_k += c x_m, 3 target gates
+y_a += c y_b (inverted at frame zero in the precondition and scatter, #781's recipe) and 15 reads y_i += c x_j.
+Unit circuit (LeaverSAT, layered CP-SAT on the exact set model), relabelled per cell so that no y += y source carries
+port-stage entering-helper dirt at the gate; coefficients rescaled exactly to the cell (C_ij = r_i c_j).
+Input: a fresh `construction/reproduce.py --until word` output directory (hamming/, shadow-early/, shadow-prefix/).
+Steps, each checked exactly (pins in LEAVER-PINS.json):
+  0. cells: CODED-CELLS.json's scaled gates are re-derived from the unit circuits and the cell coefficients, and the
+     clean map Y_i = sum_j C_ij X_j is checked in exact rationals.
+  1. gauge-forward: cgx_leaver.py (notri/cgx.py + the leaver edits) with TRI-LEAVER.json, XPARAM = notri/PRIO6.json.
+  2. port0-3: notri/port_stage_x.py.
+  3. regroup: REGROUP-LEAVER.json's changes where their `before` gate occurs (count pinned).
+  4. hpe: PR635's build_hpe.candidates greedy with disjoint registers, build_hpe.apply (recipe pinned).
+  5. cold44: notri/cold44x.py with EXTRAH and pinned pairing ranks; output sha, profile and widths pinned.
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs (pins).
+Apache-2.0. LeaverSAT (Claude Code research agent), driver after construction/notri/reproduce_notri.py.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, shutil, subprocess, sys, time
+from fractions import Fraction
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NOTRI = HERE.parent / 'notri'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def dump(p, v):
+    p.parent.mkdir(parents=True, exist_ok=True); p.write_bytes(gzip.compress(enc(v), mtime=0))
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def check_cells(cells):
+    for c in cells:
+        C = [[Fraction(q) for q in r] for r in c['coefficients']]
+        col = [None] * 6; row = [Fraction(1)] + [None] * 5
+        for j in range(1, 6): col[j] = C[0][j]
+        col[0] = C[1][0] / (C[1][2] / col[2])
+        for i in range(1, 6): row[i] = C[i][(i + 1) % 6] / col[(i + 1) % 6]
+        assert all(C[i][j] == row[i] * col[j] for i in range(6) for j in range(6) if i != j), ('rank-one cell', c['cell'])
+        idx = lambda s: int(s[1:])
+        scaled = []
+        for t, s, q in c['unit']:
+            assert Fraction(q) == 1
+            if t[0] == 'x': assert s[0] == 'x'; q = col[idx(s)] / col[idx(t)]
+            elif s[0] == 'y': q = row[idx(t)] / row[idx(s)]
+            else: q = row[idx(t)] * col[idx(s)]
+            scaled.append([t, s, str(q)])
+        assert scaled == c['scaled'], ('scaled gates', c['cell'])
+        R = {f'x{j}': {j: Fraction(1)} for j in range(6)}; R.update({f'y{i}': {} for i in range(6)})
+        for t, s, q in scaled:
+            for k, x in list(R[s].items()): R[t][k] = R[t].get(k, 0) + Fraction(q) * x
+        for i in range(6):
+            assert {k: x for k, x in R[f'y{i}'].items() if x} == {j: C[i][j] for j in range(6) if j != i}, ('clean map', c['cell'], i)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--word-dir', type=Path, required=True, help='construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    ap.add_argument('--word-only', action='store_true', help='stop after the pinned scalar word (input to the layers)')
+    ap.add_argument('--id', default='k5', help='cell set: TRI-LEAVER-<id>, CODED-CELLS-<id>, REGROUP-LEAVER-<id>, LEAVER-PINS-<id>')
+    ap.add_argument('--record-pins', action='store_true', help='write LEAVER-PINS.json from this run instead of checking')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    pins = {} if a.record_pins else read(HERE / ('LEAVER-PINS-%s.json' % a.id)); got = {}
+    def pin(k, v):
+        got[k] = v
+        if not a.record_pins: assert pins[k] == v, ('pin', k, v, pins[k])
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    structural = a.main.resolve() / 'research/structural-gain/frontier-composition'
+    wd = a.word_dir.resolve()
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    # 0. cells
+    cells = read(HERE / ('CODED-CELLS-%s.json' % a.id)); check_cells(cells); print('PASS cells', [c['cell'] for c in cells], flush=True)
+    # 1. gauge-forward
+    shutil.copy(HERE / ('TRI-LEAVER-%s.json' % a.id), out / 'TRI.json'); shutil.copy(HERE / ('CODED-CELLS-%s.json' % a.id), out / 'CODED-CELLS.json')
+    env['XPARAM'] = str(NOTRI / 'PRIO6.json')
+    raw = out / 'raw'
+    run('gauge-forward', HERE / 'cgx_leaver.py', wd / 'hamming', raw, out / 'TRI.json')
+    word = raw / 'FULL-WORD.json.gz'; pin('raw_sha256', hashlib.sha256(enc(read(word))).hexdigest())
+    # 2. port stages
+    chain = [parent / 'complex-local/static44/inputs/RAW504.json.gz', structural / 'global-replay/base/split-centres/FULL-WORD.json.gz',
+             wd / 'shadow-early/FULL-WORD.json.gz', structural / 'multicold-eight-word/FULL-WORD.json.gz',
+             wd / 'shadow-prefix/FULL-WORD.json.gz']
+    for i, (b, c) in enumerate(zip(chain, chain[1:])):
+        t = out / ('port%d' % i)
+        run('port%d' % i, NOTRI / 'port_stage_x.py', '--shadow-input', b, '--shadow-output', c, '--input', word,
+            '--map', raw / 'HELPER-MAP.json', '--gk-dir', gk, '--out', t)
+        word = t / 'FULL-WORD.json.gz'
+    # 3. regroup
+    w = read(word); rg = {json.dumps(c['before']): c['after'] for c in read(HERE / ('REGROUP-LEAVER-%s.json' % a.id))['changes']}
+    n = 0
+    for part in ('A', 'B'):
+        for i, e in enumerate(w[part]):
+            k = json.dumps(e)
+            if k in rg: w[part][i] = rg[k]; n += 1
+    sys.path.insert(0, str(gk)); import gk_word as GW, gk_common as GC
+    GW.V = GC.V = 112; GW.DATA = GC.DATA = 7168
+    H = GW.profile(w)
+    w['report'].update(local_profile={str(k): z for k, z in sorted(H.items()) if z}, local_rank_mass=sum(r * z for r, z in H.items()))
+    pin('regroup_count', n); dump(out / 'regroup/FULL-WORD.json.gz', w); pin('regroup_sha256', hashlib.sha256(enc(w)).hexdigest())
+    # 4. HPE
+    h = load('upstream_hpe', up / 'code/build_hpe.py')
+    used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    (out / 'HPE-RECIPE.json').write_text(json.dumps(dict(changes=ch)))
+    pin('hpe_recipe_sha256', hashlib.sha256(enc(dict(changes=ch))).hexdigest())
+    w = h.apply(w, ch); dump(out / 'hpe/FULL-WORD.json.gz', w)
+    # 5. cold44
+    hm = set(read(raw / 'HELPER-MAP.json')['map'].values())
+    env['EXTRAH'] = json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm))
+    if not a.record_pins: env['PAIRING_RANKS'] = json.dumps(pins['pairing_ranks'])
+    run('cold44', NOTRI / 'cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', wd / 'hamming', '--upstream-package', up)
+    pin('pairing_ranks', [b['pairing_rank'] for b in read(out / 'cold44/CONSTRUCTION.json')['blocks']])
+    word = out / 'cold44/FULL-WORD.json.gz'; w = read(word)
+    pin('cold44_sha256', hashlib.sha256(enc(w)).hexdigest()); rep = w['report']
+    pin('R', rep['R']); pin('local_profile', rep['local_profile']); pin('width_inventory', rep['width_inventory'])
+    print('PASS leaver scalar word', got['cold44_sha256'], flush=True)
+    if not a.word_only:
+        for k in ('XPARAM', 'EXTRAH', 'PAIRING_RANKS'): env.pop(k, None)
+        local = out / 'local'
+        run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word,
+            '--routing', parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz', '--out', local)
+        pin('canonical_sha256', hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest())
+        run('ledgers', up / 'code/hpe_emit_local.py', local)
+        run('local-replay', up / 'code/hpe_audit_local.py', local)
+        run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+            local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+        checks = read(local / 'LOCAL-CHECKS.json')
+        pin('program_sha256', {o: checks[o]['sha256'] for o in ('forward', 'backward')})
+        if not a.skip_phases:
+            run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+            pin('clifford_recipes_sha256', hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest())
+    if a.record_pins: (HERE / ('LEAVER-PINS-%s.json' % a.id)).write_text(json.dumps(got, indent=1) + '\n')
+    print('DONE', out, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/leaver/reproduce_leaver_chain.py b/research/gauge44-slots/construction/leaver/reproduce_leaver_chain.py
new file mode 100644
index 0000000000..19fcd28f4d
--- /dev/null
+++ b/research/gauge44-slots/construction/leaver/reproduce_leaver_chain.py
@@ -0,0 +1,187 @@
+#!/usr/bin/env python3
+"""Rebuild the leaver stack on top of the leaver cell word: layers (NP, p6n), promotions, joint exchange and U8-style
+hybrids, and the final word's native locals.
+
+Input: a fresh `construction/leaver/reproduce_leaver.py --word-only` output directory (raw/HELPER-MAP.json, regroup/,
+cold44/; the cell word and its regroup word are pinned there by LEAVER-PINS.json). Each step uses an unchanged signed
+builder with a LeaverSAT recipe (data only), and every intermediate word is pinned:
+  1. pivot-swap: ../layers/build_pivot_swap.py with PIVOT-SWAP-<id>.json on the regroup word (its own 30 controls).
+  2. hpe: PR635's build_hpe.candidates (greedy, disjoint registers) must equal HPE-RECIPE-<id>.json; build_hpe.apply.
+     The swapped HPE word is pinned by the cold-layer recipes' input_content_sha256.
+  3. cold44-exact: ../notri/cold44x.py on the swapped HPE word (pairing ranks pinned to LEAVER-PINS); its cold ends,
+     premix and low tails must equal the unswapped leaver construction's.
+  4. layers: PR635's build_cold_end.apply(HPE, COLD-LAYERS-RECIPE-NP-<id>) -> NP word and (.., -P6N-<id>) -> p6n word;
+     output shas pinned by the recipes.
+  5. promotion: ../promo/build_promotion.py with PROMO-RECIPE-<id>.json on the p6n word; ../promo/promo_controls.py.
+  6. jx: ../jx/build_jx.py with RECIPE-X4-<id>.json on the promoted word; all recipe controls rerun at their pins.
+  7. hybrids: ../barch/build_tri.py with RECIPE-U8-<id>.json on the jx word; ../barch/run_controls.py (all outcomes).
+  8. frames: build_frames_lv.py (LeaverSAT2) applies FRAME-RECIPE-LV-<id>.json (B/T frame changes, exact global frame
+     optimum) with ../promo/build_promotion.apply; scalar program unchanged; 3 pin controls; output pinned.
+  8b. layer-end-controls: layer_end_controls_leaver.py (v2: the signed per-end controls with per-word reason re-pins
+     and declared not-applicable sites, each replaced by a same-class substitute mutant) on the p6n, promoted, jx and
+     hybrid words with LEC-REASON-PINS-STACK-<id>.json, and on the re-framed final word with LEC-REASON-PINS-<id>.json;
+     counts, not-applicable sites and the sha256 of each pins file pinned.
+  9. native, ledgers, local-replay, wrappers, phases on the final word; canonical, programs, Clifford pinned.
+All counts and native pins are in CHAIN-PINS-<id>.json (--record-pins writes it from a run instead of checking;
+a checking run requires its pins to equal the file exactly).
+Apache-2.0. Driver by ColdWitness over LeaverSAT's frozen recipes and the signed builders.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+C = HERE.parent
+MUTANTS = ('drop_restore', 'restore_full', 'drop_preread', 'donation_after')
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def csha(p): return hashlib.sha256(gzip.decompress(Path(p).read_bytes())).hexdigest()
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--leaver-dir', type=Path, required=True, help='construction/leaver/reproduce_leaver.py --word-only output')
+    ap.add_argument('--hamming', type=Path, required=True, help='hamming/ of the construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    ap.add_argument('--id', default='k5', help='recipe set id: every recipe and pin file below is <NAME>-<id>')
+    ap.add_argument('--record-pins', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    lp = read(HERE / ('LEAVER-PINS-%s.json' % a.id))
+    pins = {} if a.record_pins else read(HERE / ('CHAIN-PINS-%s.json' % a.id)); got = {}
+
+    def pin(key, value):
+        got[key] = value
+        if not a.record_pins: assert pins[key] == value, (key, value, pins.get(key))
+
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE', 'LEC_REASON_PINS', 'SW4_PIN'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True, extra=None):
+        t = time.monotonic(); e = dict(env, **(extra or {}))
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=e, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+        return (out / (label + '.log')).read_text()
+
+    def lec(label, word, pins_name):
+        pf = HERE / ('%s-%s.json' % (pins_name, a.id)); pin(label + '_pins_sha256', hashlib.sha256(pf.read_bytes()).hexdigest())
+        run(label, HERE / 'layer_end_controls_leaver.py', word, routing, out / label,
+            extra=dict(PR635_CODE=str(up / 'code'), LEC_REASON_PINS=str(pf)))
+        c = read(out / label / 'COLD-END-CONTROLS.json'); assert c['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS'
+        pin(label, len(c['rejected'])); pin(label + '_not_applicable', {x['site']: x['reason'] for x in c['not_applicable']})
+
+    ld = a.leaver_dir.resolve()
+    assert hashlib.sha256(enc(read(ld / 'cold44/FULL-WORD.json.gz'))).hexdigest() == lp['cold44_sha256'], 'leaver cell word'
+    rg = ld / 'regroup/FULL-WORD.json.gz'
+    sw = read(HERE / ('PIVOT-SWAP-%s.json' % a.id))
+    assert hashlib.sha256(enc(read(rg))).hexdigest() == lp['regroup_sha256'] == sw['input_content_sha256'], 'regroup word'
+    # 1. pivot swaps
+    run('pivot-swap', C / 'layers/build_pivot_swap.py', '--input', rg, '--recipe', HERE / ('PIVOT-SWAP-%s.json' % a.id), '--gk-dir', gk, '--out', out / 'swap')
+    w = read(out / 'swap/FULL-WORD.json.gz'); assert hashlib.sha256(enc(w)).hexdigest() == sw['output_content_sha256'], 'swap word'
+    # 2. HPE
+    h = load('upstream_hpe', up / 'code/build_hpe.py'); used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    assert ch == read(HERE / ('HPE-RECIPE-%s.json' % a.id))['changes'], 'HPE recipe'
+    w = h.apply(w, ch); (out / 'hpe').mkdir(); (out / 'hpe/FULL-WORD.json.gz').write_bytes(gzip.compress(enc(w), mtime=0))
+    rnp, rp6 = read(HERE / ('COLD-LAYERS-RECIPE-NP-%s.json.gz' % a.id)), read(HERE / ('COLD-LAYERS-RECIPE-P6N-%s.json.gz' % a.id))
+    assert hashlib.sha256(enc(w)).hexdigest() == rnp['input_content_sha256'] == rp6['input_content_sha256'], 'swapped HPE word'
+    # 3. cold44 on the swapped word: same ends, premix and tails
+    hm = set(read(ld / 'raw/HELPER-MAP.json')['map'].values())
+    run('cold44-exact', C / 'notri/cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', a.hamming.resolve(), '--upstream-package', up,
+        extra=dict(EXTRAH=json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm)), PAIRING_RANKS=json.dumps(lp['pairing_ranks'])))
+    new, old = read(out / 'cold44/RECIPE.json.gz'), read(ld / 'cold44/RECIPE.json.gz')
+    for key in ('premix', 'early_cleanup', 'cold_ends'): assert new[key] == old[key], ('swapped cold44 differs', key)
+    tail = len(new['early_cleanup']); assert new['cleanup'][:tail] == old['cleanup'][:tail], 'low tails'
+    # 4. NP and p6n layers
+    bce = load('upstream_cold', up / 'code/build_cold_end.py')
+    for name, r in (('np', rnp), ('p6n', rp6)):
+        lw = bce.apply(w, r); raw = enc(lw); assert hashlib.sha256(raw).hexdigest() == r['output_content_sha256'], (name, 'word')
+        (out / name).mkdir(); (out / name / 'FULL-WORD.json.gz').write_bytes(gzip.compress(raw, mtime=0))
+        pin(name + '_profile', lw['report']['local_profile'])
+    p6n = out / 'p6n/FULL-WORD.json.gz'; lec('lec-p6n', p6n, 'LEC-REASON-PINS-STACK')
+    # 5. promotion
+    pr = HERE / ('PROMO-RECIPE-%s.json' % a.id)
+    run('promotion', C / 'promo/build_promotion.py', '--input', p6n, '--recipe', pr, '--out', out / 'promo', portable=False)
+    assert csha(out / 'promo/FULL-WORD.json.gz') == read(pr)['expected']['output_content_sha256']
+    run('promo-controls', C / 'promo/promo_controls.py', '--input', p6n, '--recipe', pr, '--audit', C.parent / 'independent/audit_local.py',
+        '--out', out / 'PROMO-CONTROLS.json', portable=False)
+    pc = read(out / 'PROMO-CONTROLS.json'); assert pc['honest'] == 'PASS'; pin('promo_controls', pc['rejected'])
+    lec('lec-promo', out / 'promo/FULL-WORD.json.gz', 'LEC-REASON-PINS-STACK')
+    # 6. jx
+    xr = HERE / ('RECIPE-X4-%s.json' % a.id); rec = read(xr); inp = out / 'promo/FULL-WORD.json.gz'
+    (out / 'jx').mkdir(); jw = out / 'jx/FULL-WORD.json.gz'
+    run('jx', C / 'jx/build_jx.py', '--input', inp, '--recipe', xr, '--out', jw, portable=False)
+    assert csha(jw) == rec['expected']['output_content_sha256']
+    for name, cc in sorted(rec['controls'].items()):
+        log = run('jx-control-' + name, C / 'jx/build_jx.py', '--input', inp, '--recipe', xr, '--control', name, portable=False)
+        if 'rejection_expected' in cc: assert 'CONTROL PINNED' in log, (name, log[-300:])
+        else: assert ('OK ' + cc['expected_sha']) in log, (name, log[-300:])
+    pin('jx_controls', sorted(rec['controls']))
+    lec('lec-jx', jw, 'LEC-REASON-PINS-STACK')
+    # 7. hybrids
+    ur = HERE / ('RECIPE-U8-%s.json' % a.id); u = read(ur); (out / 'hyb').mkdir(); fw = out / 'hyb/FULL-WORD.json.gz'
+    run('hybrids', C / 'barch/build_tri.py', jw, ur, fw, portable=False)
+    assert csha(fw) == u['expect_sha256']
+    run('hybrid-controls', C / 'barch/run_controls.py', jw, ur, C.parent / 'independent/audit_local.py', out / 'hybrid-controls', portable=False)
+    res = read(out / 'hybrid-controls/controls.json')
+    want = ['C0_identity', 'recipe', *MUTANTS] + [m + '@' + str(v['X']) for v in u.get('variants', []) for m in MUTANTS]
+    assert sorted(res) == sorted(want) and all(x['ok'] for x in res.values()), res
+    pin('hybrid_controls', sorted(want))
+    lec('lec-hyb', fw, 'LEC-REASON-PINS-STACK')
+    # 8. frame re-optimisation (LeaverSAT2): exact global frame optimum of the hybrid word; scalar program unchanged
+    fr = HERE / ('FRAME-RECIPE-LV-%s.json' % a.id); frec = read(fr)
+    run('frames', HERE / 'build_frames_lv.py', fw, out / 'frames', fr, portable=False)
+    fw = out / 'frames/FULL-WORD.json.gz'; assert csha(fw) == frec['expected']['output_content_sha256']
+    pin('frame_build_controls', len(read(out / 'frames/BUILD.json')['rejected_controls']))
+    # 8b. layer-end controls on the re-framed final word (v2, not-applicable sites declared in LEC-REASON-PINS-<id>):
+    # the frame re-optimisation lowers an entering-end tail frame to a dimension no helper_final frame has, so that
+    # site's 'end at another hyperplane' mutant is replaced by its same-class substitute.
+    lec('lec-frames', fw, 'LEC-REASON-PINS')
+    # 9. native locals of the final word
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', fw, '--routing', routing, '--out', local)
+    pin('canonical_sha256', hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest())
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz', local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json'); pin('program_sha256', {o: checks[o]['sha256'] for o in ('forward', 'backward')})
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        pin('clifford_recipes_sha256', hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest())
+    if a.record_pins: (out / ('CHAIN-PINS-%s.json' % a.id)).write_bytes((json.dumps(got, indent=1) + '\n').encode())
+    else: assert got == pins, ('chain pins differ', sorted(set(got) ^ set(pins)))
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/notri/PRIO6.json b/research/gauge44-slots/construction/notri/PRIO6.json
new file mode 100644
index 0000000000..069a7bf5a5
--- /dev/null
+++ b/research/gauge44-slots/construction/notri/PRIO6.json
@@ -0,0 +1 @@
+{"prio": {"0,1,2,3": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "0,1,4,5": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "0,1,6,7": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "2,3,4,5": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "2,3,6,7": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]], "4,5,6,7": [["1", "0", "0", "1", "0", "0", "0", "0"], ["0", "-1/2", "1/2", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "0", "0", "0", "0"], ["0", "0", "0", "0", "1", "0", "0", "1"], ["0", "0", "0", "0", "0", "-1/2", "1/2", "0"], ["-1/2", "0", "0", "1/2", "-1/2", "0", "0", "1/2"]]}}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/notri/cgx.py b/research/gauge44-slots/construction/notri/cgx.py
new file mode 100644
index 0000000000..08e80804eb
--- /dev/null
+++ b/research/gauge44-slots/construction/notri/cgx.py
@@ -0,0 +1,469 @@
+# Round20 early-coordinate-center / own-Y variant, prepared for icekylinx
+# with OpenAI Codex assistance. Apache-2.0. Scalar elementary-operation
+# helpers below are retained from the attributed PR514 construct_partial.py.
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+# AtomScout: leaver-read K-triangles (schedule from atom1.py / rog.py CP-SAT)
+TRI=json.loads(Path(sys.argv[3]).read_text())
+FULLT={(tuple(tr['p']),tr['e']) for tr in TRI['triangles']}
+TRI_COORDS={t+8 for tr in TRI['triangles'] for t,_,_ in tr['reads']}
+import os as _o
+COPYL=json.loads(open(_o.environ['XPARAM']).read()).get('copyl',[]) if _o.environ.get('XPARAM') else []
+NH=504-3*len(FULLT)+len(COPYL)
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+# Helper ids of the unpatched 504 construction: every allocation advances the 504 numbering; a packet copy that the
+# K-triangle schedule never forms advances it without allocating (HELPER-MAP.json).
+shadow=[];skipped=[];nxt=[2*v]
+def alloc():
+    n=len(cur);cur.append(());rows.append({});shadow.append(nxt[0]);nxt[0]+=1;return n
+def skip():
+    skipped.append(nxt[0]);nxt[0]+=1
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# Each source quartet supplies pair partials first. The other two coordinate
+# partitions supply eight early face packets without touching the eight
+# partials later copied into the preconditioned Y coordinates.
+SELECT=(0,0)
+PRIORITY=json.loads((INPUT/"COMPLETION-PRIORITY.json").read_text())
+import os
+XP=json.loads(open(os.environ['XPARAM']).read()) if os.environ.get('XPARAM') else {}
+XCH=XP.get('exch',{});PRIO=XP.get('prio',{})
+maps={};early={};own_rows={};pairs=[];tetrads={};block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)});maps[c]=mp
+    for ei,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[:40]):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        if ei==15:
+            for jj,cl in XCH.get(str(len(maps)-1),[[4,17],[5,19],[6,21],[7,23]]):swap(mp[jj],mp[cl],(P[ids[jj]],))
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in targets:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                t,u=sorted(ts);e2=R[t][q[0]]*R[t][q[1]]
+                pair={'targets':(t,u),'keys':[(c,p,eps),(c,q,e2)],'selected':pi==SELECT[parity],
+                      'matrix':[[R[a][p[0]],R[a][q[0]]] for a in (t,u)]}
+                pairs.append(pair)
+                if not pair['selected']:continue
+                zz=-Q(2*R[u][p[0]],R[t][p[0]])
+                sources=tet[1-parity]
+                for target,sign in ((t,-1),(u,1)):
+                    wanted={s:-Q(G[t][s],4)-sign*Q(G[u][s],2)/zz for s in sources
+                            if -Q(G[t][s],4)-sign*Q(G[u][s],2)/zz}
+                    assert len(wanted)==2
+                    candidates=[]
+                    for r in mp.values():
+                        if set(rows[r])!=set(wanted):continue
+                        s=next(iter(wanted));coef=wanted[s]/rows[r][s]
+                        if all(wanted[s]==coef*rows[r][s] for s in wanted):candidates.append((r,coef))
+                    assert len(candidates)==1
+                    r,coef=candidates[0];assert len(cur[r])==2
+                    own_rows[target]=(r,coef,cur[r])
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    needed={own_rows[t][0] for t in ids}
+    early[c]={j for j,e in enumerate(z['events'][40:]) if not ({mp[e[0]],mp[e[1]]}&needed)}
+    assert len(early[c])==8
+    retired=[]
+    for j in sorted(early[c]):
+        (t,s,a,b),F=z['events'][40+j],z['event_frames'][40+j]
+        add(mp[t],mp[s],Q(a,b),tuple(F));retired.append(mp[s])
+    assert not set(retired)&needed
+    # These eight retired rows already span every source coordinate. Keep
+    # them invertible and place the four coordinate totals in a changed basis.
+    F=basis([P[s] for s in ids]);assert len(F)==4
+    regs=sorted(retired,key=lambda r:(r>=v,r))
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    M=[[Q(R[s][i]) for s in ids] for i in c]
+    def qr_rank(rs):
+        bs={}
+        for r in rs:
+            r=r.copy()
+            for i,b in sorted(bs.items()):
+                if r[i]:q=r[i];r=[x-q*y for x,y in zip(r,b)]
+            i=next((i for i,x in enumerate(r) if x),None)
+            if i is not None:q=r[i];bs[i]=[x/q for x in r]
+        return len(bs)
+    assert qr_rank(M)==4
+    for rr0 in PRIO.get(",".join(map(str,c)),[])+PRIORITY[",".join(map(str,c))]["rows"]:
+        rr=list(map(Q,rr0))
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    for i in range(8):
+        if len(M)==8:break
+        rr=[Q(i==j) for j in range(8)]
+        if qr_rank(M+[rr])>len(M):M.append(rr)
+        if len(M)==8:break
+    assert len(M)==8
+    linear(regs,M,F)
+    for i,r in zip(c,regs):
+        assert rows[r]=={s:Q(R[s][i]) for s in ids}
+        block_totals[c,i]=r
+
+# All centers are complete while Y is still at zero. This is the crucial
+# difference from an illegal early-own-Y prefix using the old center order.
+centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+assert all(cur[v+t]==() for t in range(v))
+
+phase=B
+for t,(r,coef,F) in sorted(own_rows.items()):
+    if t in TRI_COORDS:continue
+    assert cur[r]==F
+    add(v+t,r,coef,F)
+# requests are needed for TRI coefficients
+requests=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    requests[key1].append((t,-Q(mat[0][0],2)))
+    requests[key2].append((u,-Q(mat[0][1],2)))
+reqcoef={t:(key,coef) for key,reqs in requests.items() for t,coef in reqs}
+def face_info(c,p,eps):
+    z=blocks[c];keys=[(pp,ee) for pp in it.combinations(c,2) for ee in (-1,1)]
+    r_local,alpha=z['outputs'][keys.index((p,eps))]
+    j=[j for j in range(40,len(z['events'])) if z['events'][j][0]==r_local];assert len(j)==1
+    return j[0],Q(alpha)
+tri_join_counts=Counter();TRILOG=[]
+lcopy={}
+for s8 in COPYL:
+    r=s8+8;c=len(cur);cur.append(());rows.append({});shadow.append(None);add(c,r,1,cur[r]);lcopy[r]=c
+BF={c:basis([P[x] for x in z['receipt']['source_lines']]) for c,z in blocks.items()}
+HYB={(tuple(map(int,h[0])),tuple(map(int,h[1])),int(h[2])) for h in XP.get('hyb',[])}
+HYBLOG=[]
+def triread(t,blk,r,q):
+    F=basis(cur[v+t]+cur[r]);assert inside(F,hyper(P[t])),('TRI frame',t,blk,r,cur[v+t],cur[r],hyper(P[t]),[x for x in TRILOG if x[2]==r],HYBLOG)
+    tri_join_counts[len(F)]+=1;add(v+t,r,q,F);TRILOG.append([t,list(blk),r,str(q),list(F),list(cur[r])])
+for tr in TRI['triangles']:
+    p,eps=tuple(tr['p']),tr['e']
+    hb={blk for _,blk,_ in map(lambda x:(x[0],tuple(x[1]),x[2]),tr['reads']) if (blk,p,eps) in HYB}
+    own=[];rest=[]
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];r0=r;r=lcopy.get(r,r)
+        key,coef=reqcoef[t];assert key[1]==p and key[2]==eps,(key,p,eps)
+        if blk==key[0]:
+            rr,c0,F0=own_rows[t];assert rr==r0;own.append((t,blk,r,c0))
+        else:
+            j,alpha=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert loc in ev[:2]
+            rest.append((t,blk,loc,r,coef*alpha))
+    if not hb:
+        # original interleaved order
+        for t8,blk,loc in tr['reads']:
+            t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+            if blk==key[0]:q=own_rows[t][1]
+            else:j,alpha=face_info(blk,p,eps);q=coef*alpha
+            triread(t,blk,r,q)
+        continue
+    items=[]  # (kind, t, reg, q, blk)
+    for t,blk,r,q in own:items.append(('r',t,r,q,blk,blk in hb))
+    for blk in sorted(hb):items.append(('e',None,None,None,blk,True))
+    done=set()
+    for t,blk,loc,r,q in rest:
+        if blk in hb:
+            j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j]
+            ws=[x for x in rest if x[0]==t and x[1]==blk];assert len(ws)==2 and ws[0][4]==ws[1][4] and {ws[0][2],ws[1][2]}==set(ev[:2])
+            if (t,blk) in done:continue
+            done.add((t,blk));items.append(('m',t,maps[blk][ev[0]],q,blk,True))
+        else:items.append(('r',t,r,q,blk,False))
+    # Original read order with the two half reads collapsed into one M read at the first half's slot; the face event goes
+    # just before the first M read of its block; own reads of the M register are hoisted ahead of that event.
+    def evinfo(blk):
+        j,_=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert ev[2]==ev[3]==1,ev
+        mpb=maps[blk];return mpb[ev[0]],mpb[ev[1]],tuple(blocks[blk]['event_frames'][j])
+    items=[]
+    seen=set()
+    for t8,blk,loc in tr['reads']:
+        t=t8+8;blk=tuple(blk);r=maps[blk][loc];key,coef=reqcoef[t]
+        if blk==key[0]:items.append(('r',t,r,own_rows[t][1],blk,blk in hb))
+        else:
+            j,alpha=face_info(blk,p,eps);q=coef*alpha
+            if blk in hb:
+                if (t,blk) not in seen:seen.add((t,blk));continue
+                items.append(('m',t,evinfo(blk)[0],q,blk,True))
+            else:items.append(('r',t,r,q,blk,False))
+    for blk in sorted(hb):
+        k0=min(i for i,x in enumerate(items) if x[0]=='m' and x[4]==blk)
+        items.insert(k0,('e',None,None,None,blk,True))
+    n=len(items)
+    def step(it,st):
+        k,t,r,q,blk,h=it;g=lambda x:st.get(x,cur[x])
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(g(a_))+list(g(b_)))
+            return {a_:FF,b_:FF} if inside(FF,BF[blk]) else None
+        F=basis(list(g(v+t))+list(g(r)))
+        if not inside(F,hyper(P[t])):return None
+        if h and k=='r' and r==evinfo(blk)[1] and not inside(F,BF[blk]):return None
+        return {v+t:F,r:F}
+    def allowed(i,used):
+        k,t,r,q,blk,h=items[i]
+        evi=[j for j,x in enumerate(items) if x[0]=='e' and x[4]==blk] if h else []
+        if k=='e':return all(j in used for j,x in enumerate(items) if x[0]=='r' and x[4]==blk and x[5] and x[2]==evinfo(blk)[0])
+        if k=='m':return evi[0] in used
+        if k=='r' and h and r==evinfo(blk)[0]:return evi[0] not in used
+        return True
+    budget=[int(os.environ.get('HYBBUDGET','300000'))];memo=set()
+    def dfs(st,used,order):
+        if len(order)==n:return order
+        budget[0]-=1
+        if budget[0]<0:return None
+        sig=(used,tuple(sorted(st.items())))
+        if sig in memo:return None
+        memo.add(sig)
+        for i in range(n):
+            if i in used or not allowed(i,used):continue
+            d=step(items[i],st)
+            if d is None:continue
+            ns=dict(st);ns.update(d);res=dfs(ns,used|{i},order+[i])
+            if res:return res
+        return None
+    import sys as _s;_s.setrecursionlimit(20000)
+    order=dfs({},frozenset(),[])
+    assert order,('no feasible hybrid order',p,eps,sorted(hb),budget)
+    for i in order:
+        k,t,r,q,blk,h=items[i]
+        if k=='e':
+            a_,b_,EF=evinfo(blk);FF=basis(list(EF)+list(cur[a_])+list(cur[b_]));add(a_,b_,1,FF);HYBLOG.append([list(blk),list(p),eps,list(FF)])
+        else:triread(t,blk,r,q)
+
+packets={}
+for c,z in sorted(blocks.items()):
+    mp=maps[c]
+    keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)]
+    skipev={face_info(c,p,eps)[0] for p,eps in keys if (p,eps) in FULLT}
+    for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]):
+        if j not in early[c] and 40+j not in skipev:
+            t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    for key,(r,alpha) in zip(keys,z['outputs']):
+        if tuple(key) in FULLT:skip();continue
+        a=mp[r];b=alloc();add(b,a,1,cur[a])
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha))
+
+# Both tetrahedra use the same partition. A selected key has exactly two
+# selected Y loads and no ordinary M consumer. Supply its two raw halves in
+# opposite orders and never form that M. Other keys retain the old M path.
+second=[];first_join_counts=Counter()
+for key,reqs in sorted(requests.items()):
+    assert len(reqs)==2
+    c,p,eps=key
+    if (p,eps) in FULLT:continue
+    ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds
+    for j,(target,coef) in enumerate(sorted(reqs)):
+        first_source,second_source=(a,b) if j==0 else (b,a)
+        r,alpha=packets[first_source,p,eps,second_source]
+        F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+        first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F)
+        r,alpha=packets[second_source,p,eps,c]
+        second.append((target,r,coef*alpha))
+
+Ms={}
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for eps in (-1,1):
+            if (c,p,eps) in requests:continue
+            (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,eps]=(a,alpha)
+
+consumers=defaultdict(list)
+for pid,pair in enumerate(pairs):
+    for key in pair['keys']:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    if key in requests:
+        assert all(pairs[i]['selected'] for i in uses)
+        continue
+    assert all(not pairs[i]['selected'] for i in uses)
+    a,alpha=Ms[key]
+    for j,pid in enumerate(uses):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+assert len(cur)-240==NH,len(cur)-240
+
+selected_join_counts=Counter()
+for target,r,coef in second:
+    F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target]))
+    selected_join_counts[len(F)]+=1;add(v+target,r,coef,F)
+output_basis=[]
+for pair in pairs:
+    if not pair['selected']:continue
+    (t,u),mat=pair['targets'],pair['matrix']
+    F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u]))
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert rows[v+t]==expected,('side identity',t)
+
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8
+assert sum(r*z for r,z in H.items())==9*NH+240*8+72,sum(r*z for r,z in H.items())
+
+def apply(e,matrix):
+    if e[0]=='add':
+        _,t,s,a,b,*_=e;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    e[-1]=list(FULL);return e
+cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q]
+cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v]
+matrix=[{r:Q(1)} if r<v else {} for r in range(len(cur))]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(len(cur)))
+
+# Restrict the eight isolated axis ports exactly, keeping the stable 112-port
+# label set. This variant changes the local word, not the outer geometry.
+mp={s:s-8 for s in range(8,120)}
+mp.update({120+s:112+s-8 for s in range(8,120)})
+mp.update({240+r:224+r for r in range(NH)})
+def restrict(events,is_cut=False):
+    out=[]
+    for e in events:
+        regs=e[1:3] if e[0]=='add' else e[1:2]
+        if any(r not in mp for r in regs):
+            assert is_cut and e[0]=='add' and e[1]-120==e[2] and e[2]<8 and e[3:5]==[1,1]
+            continue
+        q=copy.deepcopy(e);q[1]=mp[q[1]]
+        if q[0]=='add':q[2]=mp[q[2]]
+        out.append(q)
+    return out
+H.subtract({1:8,8:16});H=+H
+report={'status':'EXACT_CLEAN_OWN_Y_EARLY_CENTER_WORD_NOT_ADMITTED',
+        'h':9,'v':112,'R':NH,'cst':64,'m':73,'local_profile':dict(sorted(H.items())),
+        'centre_ranks':[8]*8,**({'tri_join_counts':dict(tri_join_counts)} if TRI['triangles'] else {}),'selected_load_join_counts':dict(selected_join_counts),'selected_partitions':list(SELECT),'first_load_join_counts':dict(first_join_counts),
+        'source_columns_exact':112,'borrowed_output_pairs':56,'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'local_rank_mass':sum(r*n for r,n in H.items()),'scope':'Clean scalar identity and all literal monotone local frames only; arbitrary-dirt compensation, entrance kernels, exact phase recipes, and global hosting/pricing are not yet certified.'}
+word={'report':report,'ports':P[8:],'root_lines':R[8:],
+      'A':restrict(A),'B':restrict(B),'cut':restrict(cut,True),'cleanup':restrict(cleanup),'precondition':restrict(precondition),
+      'centers':[mp[r] for r in centers[:8]],'center_frames':center_frames[:8],
+      'scatter':[[str(x) for x in row[:8]] for row in scatter[8:]]}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+assert len(shadow)==NH and len([x for x in shadow if x is not None])+len(skipped)==504
+hmap={**{r:r for r in range(224)},**{224+s_-240:224+i for i,s_ in enumerate(shadow) if s_ is not None}}
+(OUT/'HELPER-MAP.json').write_text(json.dumps({'map':{str(k):hmap[k] for k in sorted(hmap)},'removed_504_helpers':[224+s_-240 for s_ in skipped]})+'\n')
+(OUT/'TRILOG.json').write_text(json.dumps(dict(reads=TRILOG,hyb=HYBLOG)));(OUT/'DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/gauge44-slots/construction/notri/cold44x.py b/research/gauge44-slots/construction/notri/cold44x.py
new file mode 100644
index 0000000000..8fa6f3a6a6
--- /dev/null
+++ b/research/gauge44-slots/construction/notri/cold44x.py
@@ -0,0 +1,217 @@
+"""Exact dyadic cold-end realization of the source-branch/factory-completion word.
+Prepared for icekylinx with OpenAI Codex assistance; Apache-2.0.
+This is a constructor: independent endpoint/frame audits remain required.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+import copy,gzip,json,hashlib,time,sys,argparse,importlib.util,os
+D=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser(description=__doc__)
+for name in ('input','out','hamming','upstream-package'):ap.add_argument('--'+name,type=Path,required=True)
+args=ap.parse_args();WPATH=args.input;OUT=args.out
+assert __debug__, 'Assertions are required'
+OUT.mkdir(exist_ok=False,parents=True)
+def rd(p):return json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+w=rd(WPATH);v=w['report']['v'];n=2*v+w['report']['R'];N=list(range(v))+list(range(2*v,n));ix={x:i for i,x in enumerate(N)}
+F9=[256,128,64,32,16,8,4,2,1];t0=time.monotonic()
+def basis(vs):
+ d={}
+ for a in vs:
+  for k in sorted(d,reverse=True):
+   if a>>k&1:a^=d[k]
+  if a:
+   k=a.bit_length()-1
+   for j in d:
+    if d[j]>>k&1:d[j]^=a
+   d[k]=a
+ return tuple(d[k] for k in sorted(d,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def regs(e):return e[1:3] if e[0]=='add' else e[1:2]
+def inverse(e):
+ e=copy.deepcopy(e)
+ if e[0]=='add':e[3]=-e[3]
+ else:e[2],e[3]=e[3],e[2]
+ return e
+def apply(e,M,mapping=None):
+ t=mapping[e[1]] if mapping is not None else e[1]
+ if e[0]=='add':
+  s=mapping[e[2]] if mapping is not None else e[2];q=Q(e[3],e[4])
+  for j,a in M[s].items():
+   x=M[t].get(j,Q(0))+q*a
+   if x:M[t][j]=x
+   else:M[t].pop(j,None)
+ else:
+  q=Q(e[2],e[3]);M[t]={j:q*a for j,a in M[t].items()}
+def rref(A):
+ a=[list(map(Q,row)) for row in A];nr=len(a);nc=len(a[0]) if nr else 0;row=0;piv=[]
+ for c in range(nc):
+  k=next((i for i in range(row,nr) if a[i][c]),None)
+  if k is None:continue
+  a[row],a[k]=a[k],a[row];q=a[row][c];a[row]=[x/q for x in a[row]]
+  for i in range(nr):
+   if i!=row and a[i][c]:q=a[i][c];a[i]=[x-q*y for x,y in zip(a[i],a[row])]
+  piv.append(c);row+=1
+  if row==nr:break
+ return a,piv
+def rank(A):return len(rref(A)[1])
+def null(A,nc=None):
+ if A:a,piv=rref(A);nc=len(a[0])
+ else:a=[];piv=[];assert nc is not None
+ free=[j for j in range(nc) if j not in piv];out=[[Q(0) for j in free] for i in range(nc)]
+ for k,c in enumerate(free):out[c][k]=Q(1)
+ for i,c in enumerate(piv):
+  for k,j in enumerate(free):out[c][k]=-a[i][j]
+ return out
+def mm(A,B):
+ if not A:return []
+ if not B:return [[] for row in A]
+ bt=list(zip(*B));return [[sum((a*b for a,b in zip(row,col)),Q(0)) for col in bt] for row in A]
+def tr(A):return list(map(list,zip(*A)))
+def inv(A):
+ n0=len(A);a,p=rref([row+[Q(i==j) for j in range(n0)] for i,row in enumerate(A)])
+ assert p[:n0]==list(range(n0))
+ return [row[n0:] for row in a]
+def unit(q):
+ if not q:return False
+ a=abs(q.numerator);b=q.denominator
+ return not a&(a-1) and not b&(b-1)
+def dyadic(q):return not q.denominator&(q.denominator-1)
+def opadd(t,s,q,F):return ['add',t,s,q.numerator,q.denominator,list(F)]
+def opscale(t,q,F):return ['scale',t,q.numerator,q.denominator,list(F)]
+def eliminate(M,ids,F,skip=()):
+ """Return legal dyadic row operations taking an invertible sparse matrix to I."""
+ skip=set(skip);ops=[];dim=len(M)
+ def add(i,j,q):
+  if q:
+   assert dyadic(q);e=opadd(ids[i],ids[j],q,F);ops.append(e)
+   for c,x in M[j].items():
+    z=M[i].get(c,Q(0))+q*x
+    if z:M[i][c]=z
+    else:M[i].pop(c,None)
+ def scale(i,q):
+  if q!=1:
+   assert unit(q);ops.append(opscale(ids[i],q,F));M[i]={c:q*x for c,x in M[i].items()}
+ def swap(i,j):
+  if i!=j:
+   add(i,j,Q(1));add(j,i,Q(-1));add(i,j,Q(1));scale(j,Q(-1))
+ for c in range(dim):
+  if c in skip:
+   assert M[c]=={c:Q(1)} and all(not M[i].get(c) for i in range(dim) if i!=c)
+   continue
+  cand=[i for i in range(c,dim) if i not in skip and M[i].get(c)]
+  k=next((i for i in cand if unit(M[i][c])),None)
+  if k is None:
+   # Elementary Euclidean row additions reduce the pivot-column numerator gcd.
+   assert cand,('singular',c)
+   while k is None:
+    cand.sort(key=lambda i:abs(M[i][c]));a=cand[0]
+    b=next((i for i in cand[1:] if M[i][c]),None)
+    if b is None:raise ValueError(('non-dyadic determinant pivot',c,M[a][c]))
+    rat=M[b][c]/M[a][c];q=rat.numerator//rat.denominator
+    if q==0:q=1 if rat>0 else -1
+    add(b,a,Q(-q));cand=[i for i in cand if M[i].get(c)]
+    k=next((i for i in cand if unit(M[i][c])),None)
+  swap(c,k);scale(c,1/M[c][c])
+  for i in range(dim):
+   if i!=c and M[i].get(c):
+    assert i not in skip
+    add(i,c,-M[i][c])
+ assert all(row=={i:Q(1)} for i,row in enumerate(M))
+ return ops
+def realize(A,ids,F):
+ M=[{j:Q(x) for j,x in enumerate(row) if x} for row in A]
+ return [inverse(e) for e in reversed(eliminate(M,ids,F))]
+# Reconstruct the actual non-target map after the inherited HPE tail.
+inherited_tail=[w['cleanup'][i][:-1]+[list(f)] for i,f in w.get('early_cleanup',[])]
+mainN=[e for e in w['A']+w['B'] if not v<=e[1]<2*v]
+M=[{i:Q(1)} for i in range(len(N))]
+for e in mainN+inherited_tail:apply(e,M,ix)
+MI=[{i:Q(1)} for i in range(len(N))]
+for e in reversed(mainN+inherited_tail):apply(inverse(e),MI,ix)
+cur={x:(w['ports'][x],) if x<v else basis(w.get('start_extra',{}).get(str(x),[])) for x in N}
+for e in w['A']+w['B']+inherited_tail:
+ for x in regs(e):
+  if x in cur:cur[x]=basis(e[-1])
+enter=set(map(int,w.get('start_extra',{})));protected=[ix[x] for x in N if x<v or x in enter]
+EXTRAH=json.loads(os.environ.get('EXTRAH','[]'))
+PAIRING_RANKS=json.loads(os.environ['PAIRING_RANKS']) if os.environ.get('PAIRING_RANKS') else None   # per-block pin, set by the driver
+mods=rd(args.hamming/'PACKET-PROGRAMS.json.gz');proto=rd(args.hamming/'PROTOTYPE.json')
+plans=[];premix=[];tail=[];ends={};Mafter=copy.deepcopy(M)
+for b,mod in enumerate(mods):
+ ss=mod['receipt']['source_lines'];F=basis([proto['binary_ports'][s] for s in ss]);I=[ix[x] for x in N if inside(cur[x],F)]
+ hs=list(range(224+16*b,224+16*(b+1)))+[x for x in EXTRAH if ix[x] in I];H=[ix[x] for x in hs];NB=len(hs)
+ C=[[M[i].get(j,Q(0)) for j in protected] for i in I]
+ L=tr(null(tr(C),len(I)))
+ A=[[MI[j].get(i,Q(0)) for i in I] for j in protected];A=[row for row in A if any(row)]
+ K=null(A,len(I));BK=mm(L,K);_,piv=rref(BK);r=len(piv);print('PAIR',b,'I',len(I),'L',len(L),'K',len(K),'r',r,flush=True);assert r==len(L),(b,r,len(L))
+ if PAIRING_RANKS is not None: assert r==PAIRING_RANKS[b],('pinned pairing rank',b,r,PAIRING_RANKS[b])
+ if os.environ.get('DIAG'):
+  print(' regs',[(N[i],cur[N[i]],rank([C[k]]) ) for k,i in enumerate(I)],'rankC',rank(C) if C else 0,flush=True)
+  for row in L: print('  Lrow',{N[I[k]]:str(x) for k,x in enumerate(row) if x})
+ if r==0:plans.append(dict(block=b,frame=list(F),registers=[N[i] for i in I],ends=[],pairing_rank=0));continue
+ Ksel=[[row[j] for j in piv] for row in K];Bsel=[[row[j] for j in piv] for row in BK];U=mm(Ksel,inv(Bsel));assert mm(L,U)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ q=mm([[MI[i].get(j,Q(0)) for j in I] for i in range(len(N))],U)
+ assert all(not any(q[i]) for i in range(len(N)) if i not in H),('nonlocal premix',b)
+ RR=mm(L,[[M[i].get(j,Q(0)) for j in H] for i in I]);qH=[q[i] for i in H]
+ assert mm(RR,qH)==[[Q(i==j) for j in range(r)] for i in range(r)]
+ # Pick low physical helper destinations with independent U coordinate rows.
+ ih=[]
+ for j in sorted((j for j,i in enumerate(I) if N[i] in hs),key=lambda j:(cur[N[I[j]]]!=F,N[I[j]])):
+  if rank([U[k] for k in ih]+[U[j]])>len(ih):ih.append(j)
+  if len(ih)==r:break
+ assert len(ih)==r
+ endhs=[N[I[j]] for j in ih];endhidx=[hs.index(h) for h in endhs]
+ kerR=null(RR,NB);Qmat=[[Q(0) for j in range(NB)] for i in range(NB)]
+ for j,hj in enumerate(endhidx):
+  for i in range(NB):Qmat[i][hj]=qH[i][j]
+ other=[j for j in range(NB) if j not in endhidx]
+ for k,j in enumerate(other):
+  for i in range(NB):Qmat[i][j]=kerR[i][k]
+ assert rank(Qmat)==NB
+ pops=realize(Qmat,hs,());premix+=pops
+ T=[[Q(i==j)-sum((U[i][k]*L[k][j] for k in range(r)),Q(0)) for j in range(len(I))] for i in range(len(I))]
+ for k,i in enumerate(ih):T[i]=L[k]
+ tops=realize(T,[N[i] for i in I],F);tail+=tops
+ # Right-compose this initial helper premix; other blocks have disjoint H sets.
+ for row in Mafter:
+  vals=[row.get(h,Q(0)) for h in H]
+  if any(vals):
+   for hj in H:row.pop(hj,None)
+   for j,hj in enumerate(H):
+    z=sum((vals[i]*Qmat[i][j] for i in range(NB)),Q(0))
+    if z:row[hj]=z
+ for e in tops:apply(e,Mafter,ix)
+ ends.update({h:list(F) for h in endhs})
+ plans.append(dict(block=b,frame=list(F),registers=[N[i] for i in I],ends=endhs,pairing_rank=r,premix_gates=len(pops),tail_gates=len(tops),Q=[[str(x) for x in row] for row in Qmat],T=[[str(x) for x in row] for row in T]))
+ print('BLOCK',b,'ends',endhs,'Qops',len(pops),'Tops',len(tops),flush=True)
+# Check actual post-tail isolation before constructing the high-frame inverse.
+allends=set(ends)|set(map(int,w.get('helper_final',{})))
+for h in allends:
+ j=ix[h];assert Mafter[j]=={j:Q(1)},('row not isolated',h,Mafter[j]);assert all(not row.get(j) for i,row in enumerate(Mafter) if i!=j),('column not isolated',h)
+print('EXACT_ISOLATED',len(ends),'new;',len(allends),'total',round(time.monotonic()-t0,3),flush=True)
+fullops=eliminate(copy.deepcopy(Mafter),N,F9,[ix[x] for x in allends])
+print('FULL_INVERSE',len(fullops),round(time.monotonic()-t0,3),flush=True)
+# Cancel new cold-axis target responses inside A, after their wrappers.
+Dirt=[({h:Q(1)} if h in ends else {}) for h in range(n)]
+for e in premix+w['A']+w['cut']+w['B']:apply(e,Dirt)
+for e in w['precondition']:apply(e,Dirt)
+postcomp=[opadd(y,h,-a,()) for y in range(v,2*v) for h,a in sorted(Dirt[y].items()) if a]
+assert all(h in ends for e in postcomp for h in [e[2]])
+new=copy.deepcopy(w);new['A']=postcomp+premix+w['A'];new['cleanup']=inherited_tail+tail+fullops
+new['early_cleanup']=[[i,e[-1]] for i,e in enumerate(inherited_tail+tail)]
+new['helper_final'].update({str(h):f for h,f in ends.items()})
+new['refactored_cleanup']={'kind':'source_branch_gauge_and_retired_completion_cold44','new_cold_ends':len(ends),'exact_non_target_isolation_checked':True,'high_inverse':'dyadic_sparse_Gauss_Jordan'}
+# Derive paid profile by subtracting and adding literal frame-chain counts.
+spec=importlib.util.spec_from_file_location('upstream_cold_end',args.upstream_package/'code/build_cold_end.py')
+profile_module=importlib.util.module_from_spec(spec);spec.loader.exec_module(profile_module)
+oldprof,_=profile_module.chain_profile(w);newprof,_=profile_module.chain_profile(new)
+prof=Counter({int(k):z for k,z in w['report']['local_profile'].items()});prof.subtract(oldprof);prof.update(newprof)
+widths=Counter(len(basis(new['helper_final'].get(str(h),F9)))-len(basis(new.get('start_extra',{}).get(str(h),[]))) for h in range(224,n))
+new['report'].update(local_profile={str(k):z for k,z in sorted(prof.items()) if z},local_rank_mass=sum(k*z for k,z in prof.items()),width_inventory={str(k):z for k,z in sorted(widths.items()) if z},status='EXACT_COLD44_CONSTRUCTED_PENDING_INDEPENDENT_AUDIT')
+raw=json.dumps(new,sort_keys=True,separators=(',',':')).encode();sha=hashlib.sha256(raw).hexdigest();(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+recipe={'premix':postcomp+premix,'cleanup':new['cleanup'],'early_cleanup':new['early_cleanup'],'cold_ends':{str(h):f for h,f in ends.items()},'refactored_cleanup':new['refactored_cleanup'],'output_content_sha256':sha}
+(OUT/'RECIPE.json.gz').write_bytes(gzip.compress(json.dumps(recipe,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+receipt=dict(input_content_sha256=hashlib.sha256(gzip.decompress(WPATH.read_bytes())).hexdigest(),output_content_sha256=sha,blocks=plans,new_cold_ends=len(ends),all_low_ended_helpers=len(allends),premix_gates=len(premix),postwrapper_compensation_gates=len(postcomp),tail_gates=len(tail),inherited_tail_gates=len(inherited_tail),full_inverse_gates=len(fullops),profile=new['report']['local_profile'],width_inventory=new['report']['width_inventory'],rank_mass=new['report']['local_rank_mass'],seconds=time.monotonic()-t0)
+(OUT/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print(json.dumps({k:z for k,z in receipt.items() if k!='blocks'},indent=2),flush=True)
diff --git a/research/gauge44-slots/construction/notri/port_stage_x.py b/research/gauge44-slots/construction/notri/port_stage_x.py
new file mode 100644
index 0000000000..81ac65ceff
--- /dev/null
+++ b/research/gauge44-slots/construction/notri/port_stage_x.py
@@ -0,0 +1,125 @@
+"""Port one 504-helper construction stage onto the K-triangle word.  Apache-2.0.  Prepared with Claude Code assistance.
+
+usage: build_port_stage.py --shadow-input I4 --shadow-output O4 --input I8 --map HELPER-MAP.json --gk-dir GK --out DIR
+
+The shadow pair (I4 -> O4) is one stage of a 504-helper chain, rebuilt in the same run from pinned sources.  I8 is the
+K-triangle word at the matching point of its own chain, and HELPER-MAP.json is the 504 -> R register map written by
+construct_k_triangle.py.  Registers below 448 keep their ids; the removed packet copies have no image.
+
+The port does the following:
+* It renumbers I4 and O4 through the map and drops their gates that touch a removed register.
+* It matches gates by scalar operation (the gate without its frame), aligning I4 with O4 and I4 with I8 separately.
+* It builds O8 in O4 gate order:
+  * each matched gate is taken from I8, with O4's frame wherever the stage changed that frame;
+  * each gate the stage introduced is taken from O4;
+  * each I8-only gate (the K-triangle reads) stays after the O4 image of its I8 predecessor.
+* It replays the stage's entrance (start_extra) and target_levels changes.
+* It rebuilds the cleanup with the inherited inverse rule.
+
+The constructor is a search transfer only.  The verifier certifies the output independently: the generalised native
+audit (exact forward and inverse replay of every column, native frame chains) runs on every ported word, and every
+input and output is pinned by content hash."""
+import argparse, copy, difflib, gzip, hashlib, json, sys
+from collections import Counter
+from pathlib import Path
+
+assert __debug__, 'Assertions required'
+FULL = [256, 128, 64, 32, 16, 8, 4, 2, 1]
+
+
+def regs(g): return (g[1], g[2]) if g[0] == 'add' else (g[1],)
+
+
+def key(g): return json.dumps(g[:-1])
+
+
+def inverse(e):
+    e = copy.deepcopy(e)
+    if e[0] == 'add': e[3] *= -1
+    else: e[2], e[3] = e[3], e[2]
+    e[-1] = list(FULL); return e
+
+
+def align(xs, ys):
+    """index map xs -> ys over runs of equal scalar operations"""
+    sm = difflib.SequenceMatcher(None, [key(g) for g in xs], [key(g) for g in ys], autojunk=False)
+    return {i1 + k: j1 + k for tag, i1, i2, j1, j2 in sm.get_opcodes() if tag == 'equal' for k in range(i2 - i1)}
+
+
+def transfer_section(I4, O4, I8, stats):
+    a, b = align(I4, O4), align(I4, I8)
+    o2i = {j: i for i, j in a.items()}; i8from4 = {j: i for i, j in b.items()}
+    anchor = {j8: a[i4] for j8, i4 in i8from4.items() if i4 in a}
+    pending, last = {}, -1
+    for j8, g in enumerate(I8):
+        if j8 in anchor: last = anchor[j8]
+        elif j8 not in i8from4: pending.setdefault(last, []).append(copy.deepcopy(g)); stats['kept_own'] += 1
+        else: stats['dropped_by_stage'] += 1
+    out = list(pending.get(-1, []))
+    for k, g in enumerate(O4):
+        if k in o2i:
+            i4 = o2i[k]
+            if i4 in b:
+                g8 = copy.deepcopy(I8[b[i4]])
+                if I4[i4][-1] != g[-1]: g8[-1] = copy.deepcopy(g[-1]); stats['frames_changed'] += 1
+                out.append(g8)
+        else:
+            out.append(copy.deepcopy(g)); stats['introduced'] += 1
+        out.extend(pending.get(k, []))
+    return out
+
+
+def main():
+    ap = argparse.ArgumentParser()
+    for k in ('--shadow-input', '--shadow-output', '--input', '--map', '--gk-dir', '--out'): ap.add_argument(k, type=Path, required=True)
+    a = ap.parse_args(); assert not a.out.exists()
+    sys.path.insert(0, str(a.gk_dir)); import gk_word as G, gk_common as C
+    G.V = C.V = 112
+    rd = lambda p: json.loads(gzip.decompress(p.read_bytes()))
+    enc = lambda x: json.dumps(x, sort_keys=True, separators=(',', ':')).encode(); sha = lambda x: hashlib.sha256(x).hexdigest()
+    I4, O4, I8 = rd(a.shadow_input), rd(a.shadow_output), rd(a.input)
+    fm = {int(k): int(v) for k, v in json.loads(a.map.read_text())['map'].items()}
+    assert all(fm[k] == k for k in fm if k < 448), 'only ids >= 448 may move'
+    R = I8['report']['R']; EXTRA = set(range(224 + R)) - set(fm.values()); assert len(set(fm.values())) == len(fm) and set(fm.values()) <= set(range(224 + R)), 'map is not injective into the K-triangle registers'
+    assert I4['report'].get('R', 504) == 504 and len(fm) + len(set(range(728)) - set(fm)) == 728
+    rem = set(range(728)) - set(fm)
+    rn = lambda r: fm[r]
+    touches = lambda g: any(r in rem for r in regs(g))
+    def rg(g):
+        g = copy.deepcopy(g); g[1] = rn(g[1])
+        if g[0] == 'add': g[2] = rn(g[2])
+        return g
+    def rn_word(w):
+        w = copy.deepcopy(w)
+        for s in ('A', 'B', 'cut', 'precondition', 'cleanup'):
+            if s in w: w[s] = [rg(g) for g in w[s] if not touches(g)]
+        for k in ('start_extra', 'helper_final'):
+            if k in w: w[k] = {str(rn(int(r))): f for r, f in w[k].items() if int(r) not in rem}
+        return w
+    I4r, O4r = rn_word(I4), rn_word(O4)
+    O8 = copy.deepcopy(I8); stats = {s: Counter() for s in ('A', 'B')}
+    for s in ('A', 'B'): O8[s] = transfer_section(I4r[s], O4r[s], I8[s], stats[s])
+    for k in ('start_extra', 'target_levels'):
+        x, y = I4r.get(k, {}), O4r.get(k, {}); d = dict(I8.get(k, {}))
+        for r in set(x) | set(y):
+            if x.get(r) != y.get(r):
+                if r in y: d[r] = y[r]
+                else: d.pop(r, None)
+        if k in O4 or k in I8: O8[k] = dict(sorted(d.items(), key=lambda kv: int(kv[0])))
+    for k in O4:
+        if k not in ('A', 'B', 'cleanup', 'report', 'start_extra', 'target_levels', 'cut', 'precondition'):
+            assert O4r[k] == I4r[k], 'stage changed an unported field: ' + k
+    O8['cleanup'] = [inverse(e) for e in reversed(O8['A'] + O8['B']) if not 112 <= e[1] < 224]
+    H = G.profile(O8)
+    ws = [9 - len(G.basis(O8['start_extra'].get(str(224 + h), []))) for h in range(R)]
+    O8['report'] = dict(I8['report'], local_profile={str(k): v for k, v in sorted(H.items())}, local_rank_mass=sum(k * v for k, v in H.items()),
+                        width_inventory={str(k): v for k, v in sorted(Counter(ws).items())})
+    a.out.mkdir(parents=True); (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(enc(O8), mtime=0))
+    receipt = dict(status='PORTED_STAGE_PENDING_NATIVE_AUDIT', R=R, removed_504_helpers=sorted(rem),
+                   shadow_input_content_sha256=sha(enc(I4)), shadow_output_content_sha256=sha(enc(O4)), input_content_sha256=sha(enc(I8)),
+                   output_content_sha256=sha(enc(O8)), sections={s: dict(v) for s, v in stats.items()}, local_profile=O8['report']['local_profile'],
+                   scope='Transfer construction only; exactness, frame chains and profile are certified by the native audit run on the output.')
+    (a.out / 'PORT-STAGE.json').write_text(json.dumps(receipt, indent=2, sort_keys=True) + '\n', newline='\n'); print(json.dumps(receipt, indent=2))
+
+
+main()
diff --git a/research/gauge44-slots/construction/notri/reproduce_notri.py b/research/gauge44-slots/construction/notri/reproduce_notri.py
new file mode 100644
index 0000000000..a85f2acf15
--- /dev/null
+++ b/research/gauge44-slots/construction/notri/reproduce_notri.py
@@ -0,0 +1,166 @@
+#!/usr/bin/env python3
+"""Rebuild the no-triangle gauge44 word (R = 504) and its native locals.
+
+The no-triangle word is #645's gauge44 chain with none of the four (p,-1) K-triangles. In the six K-blocks
+{0,1,2,11,12,13}, the completion priority is extended by the 6-row list PRIO6.json, the list blocks 3-10 already use.
+Each block then pairs at rank 4, giving 56 rank-four cold ends instead of 44 (PartialK).
+
+Input: a fresh `construction/reproduce.py --until word` output directory. Its shadow-early and shadow-prefix words and
+its hamming inputs are pinned by reproduce.py itself. Steps, each checked exactly:
+  1. gauge-forward: cgx.py, #645's construct_gauge_xcentre.py generalised by PartialK. The extra rows come from XPARAM,
+     and the K-triangle schedule comes from the TRI file. Run on the triangle set {} with XPARAM = PRIO6.json.
+  2. port0-3: port_stage_x.py, PR635's build_port_stage.py with the helper map allowed to be injective rather than onto.
+     With R = 504 and no triangles, the map is onto again.
+  3. regroup: PR635's k492 frame-regroup changes, applied where their `before` gate occurs. For this word none occurs,
+     and that count (0) is pinned.
+  4. hpe: PR635's build_hpe.candidates, taken greedily with disjoint registers, and build_hpe.apply. 46 changes, pinned.
+  5. cold44: cold44x.py, #645's build_gauge_cold44.py generalised by PartialK to blocks whose helper list includes the
+     helpers outside the 224+16b ranges (EXTRAH). 56 cold ends; the 14 pairing ranks are pinned to [4]*14 inside cold44x (PAIRING_RANKS) and rechecked here. The output word content sha256 is pinned (3e99ba77...).
+  6. native, ledgers, local-replay, wrappers, phases: PR635's native local programs, as in reproduce.py.
+--control-g44 instead runs steps 1-5 with #645's four triangles and no XPARAM. It must reproduce #645's pinned gauge44
+cold44 word (78c7aada...), the same word #645's own reproduce.py builds. This shows the generalised scripts reduce to
+#645's constructors.
+Apache-2.0. Driver by ColdWitness from PartialK's variant.py; constructors credited above.
+"""
+import argparse, gzip, hashlib, importlib.util, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+NOTRI_SHA = '3e99ba778ab8a97853f50912776247802b529439937176363f6c42786163b1f9'
+G44_SHA = '78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290'
+# native-local pins (the strict locals the SPEC was frozen against: PartialK runs/none_p6/local)
+CANONICAL_SHA = '4265a3bb7f9b46967dfadfca5f2cc1f5b3e6e8681f16c02590f1b9430c013637'
+PROGRAM_SHA = {'forward': '0afda28699e15cf5a5a17aee5475ac608c9fb68b15766d463b93ec8e2df4ae85',
+               'backward': '5be6cb4ea7a1da36d7bbe7eb2392873c058dd3cbb3cc2eeadd55ecca9310ca8a'}
+CLIFFORD_SHA = '4b5789e43e04d71f02c2d480450ec0b354007d9cf523bda76c7345730806344b'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def dump(p, v):
+    p.parent.mkdir(parents=True, exist_ok=True); p.write_bytes(gzip.compress(enc(v), mtime=0))
+
+
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--word-dir', type=Path, required=True, help='construction/reproduce.py --until word output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--control-g44', action='store_true', help='rebuild #645 gauge44 (4 triangles) instead; word only')
+    ap.add_argument('--skip-phases', action='store_true')
+    ap.add_argument('--word-only', action='store_true', help='stop after the pinned scalar word (input to construction/layers_np)')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'; gk = parent / 'complex-local/static44/gk'
+    structural = a.main.resolve() / 'research/structural-gain/frontier-composition'
+    wd = a.word_dir.resolve()
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args):
+        t = time.monotonic()
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call([sys.executable, '-B', str(src / 'code/run_portable.py'), str(script), *map(str, args)],
+                                 env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    # 1. gauge-forward on the chosen K-triangle set
+    tri = read(up / 'data/TRI-SCHEDULE.json')
+    if not a.control_g44:
+        tri = dict(full_pairs=tri['full_pairs'], triangles=[])
+        env['XPARAM'] = str(HERE / 'PRIO6.json')
+    (out / 'TRI.json').write_text(json.dumps(tri))
+    raw = out / 'raw'
+    run('gauge-forward', HERE / 'cgx.py', wd / 'hamming', raw, out / 'TRI.json')
+    word = raw / 'FULL-WORD.json.gz'
+    # 2. port stages (same chain as reproduce.py)
+    chain = [parent / 'complex-local/static44/inputs/RAW504.json.gz', structural / 'global-replay/base/split-centres/FULL-WORD.json.gz',
+             wd / 'shadow-early/FULL-WORD.json.gz', structural / 'multicold-eight-word/FULL-WORD.json.gz',
+             wd / 'shadow-prefix/FULL-WORD.json.gz']
+    for i, (b, c) in enumerate(zip(chain, chain[1:])):
+        t = out / ('port%d' % i)
+        run('port%d' % i, HERE / 'port_stage_x.py', '--shadow-input', b, '--shadow-output', c, '--input', word,
+            '--map', raw / 'HELPER-MAP.json', '--gk-dir', gk, '--out', t)
+        word = t / 'FULL-WORD.json.gz'
+    # 3. PR635 frame regroup where its `before` gate occurs
+    w = read(word); rg = {json.dumps(c['before']): c['after'] for c in read(up / 'data/recipes/k492-jp8-frame_regroup.json')['changes']}
+    n = 0
+    for part in ('A', 'B'):
+        for i, e in enumerate(w[part]):
+            k = json.dumps(e)
+            if k in rg: w[part][i] = rg[k]; n += 1
+    sys.path.insert(0, str(gk)); import gk_word as GW, gk_common as GC
+    GW.V = GC.V = 112; GW.DATA = GC.DATA = 7168
+    H = GW.profile(w)
+    w['report'].update(local_profile={str(k): z for k, z in sorted(H.items()) if z}, local_rank_mass=sum(r * z for r, z in H.items()))
+    assert n == (24 if a.control_g44 else 0), ('regroup count', n)
+    dump(out / 'regroup/FULL-WORD.json.gz', w)
+    # 4. HPE: PR635's candidates, greedy with disjoint registers
+    h = load('upstream_hpe', up / 'code/build_hpe.py')
+    used, ch = set(), []
+    for c in h.candidates(w):
+        rs = set(h.regs(w['cleanup'][c['cleanup_index']]))
+        if rs & used: continue
+        used |= rs; ch.append(c)
+    assert len(ch) == (34 if a.control_g44 else 46), ('hpe count', len(ch))
+    (out / 'HPE-RECIPE.json').write_text(json.dumps(dict(changes=ch)))
+    w = h.apply(w, ch); dump(out / 'hpe/FULL-WORD.json.gz', w)
+    # 5. cold44 (generalised): helpers outside the 224+16b ranges join their blocks
+    hm = set(read(raw / 'HELPER-MAP.json')['map'].values())
+    env['EXTRAH'] = json.dumps(sorted(set(range(224, 224 + w['report']['R'])) - hm))
+    ranks = [2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2] if a.control_g44 else [4] * 14
+    env['PAIRING_RANKS'] = json.dumps(ranks)   # cold44x asserts every block's pairing rank
+    run('cold44', HERE / 'cold44x.py', '--input', out / 'hpe/FULL-WORD.json.gz', '--out', out / 'cold44',
+        '--hamming', wd / 'hamming', '--upstream-package', up)
+    assert [b['pairing_rank'] for b in read(out / 'cold44/CONSTRUCTION.json')['blocks']] == ranks, 'pairing ranks'
+    word = out / 'cold44/FULL-WORD.json.gz'; w = read(word)
+    got = hashlib.sha256(enc(w)).hexdigest()
+    assert got == (G44_SHA if a.control_g44 else NOTRI_SHA), ('word', got)
+    rep = w['report']
+    if a.control_g44:
+        print('PASS control: #645 gauge44 word reproduced', got, flush=True); return
+    assert rep['R'] == 504 and rep['local_rank_mass'] == 5674
+    assert rep['local_profile'] == {'1': 2506, '2': 336, '3': 472, '4': 184, '5': 56, '8': 8}, rep['local_profile']
+    assert rep['width_inventory'] == {'4': 64, '5': 48, '7': 46, '8': 114, '9': 232}, rep['width_inventory']
+    print('PASS no-triangle scalar word', got, flush=True)
+    if a.word_only:
+        return
+    # 6. native locals (PR635, as in reproduce.py)
+    for k in ('XPARAM', 'EXTRAH', 'PAIRING_RANKS'): env.pop(k, None)
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word,
+        '--routing', parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz', '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == CANONICAL_SHA, 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in PROGRAM_SHA.items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == CLIFFORD_SHA, 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/promo/LOCAL-PINS-p6n-k4.json b/research/gauge44-slots/construction/promo/LOCAL-PINS-p6n-k4.json
new file mode 100644
index 0000000000..c43b391a43
--- /dev/null
+++ b/research/gauge44-slots/construction/promo/LOCAL-PINS-p6n-k4.json
@@ -0,0 +1,11 @@
+{
+ "word": "P6k4",
+ "layer_controls": 95,
+ "promo_controls": 11,
+ "canonical_sha256": "c0c5734a2eb6984ccd1e314dbcea2a6971b9708e5f611aa8912fcf47f02de61d",
+ "program_sha256": {
+  "forward": "6cfedac02e899df7fa50a3e38845982a4e9dbc866e9decc4052e011532bdb30f",
+  "backward": "207d9352aeea7d56a6da865745a1ad756e28531fbf9bcb0cd54950aac7270381"
+ },
+ "clifford_recipes_sha256": "1c1d037d602b503b35f01a65d0ccc07ac63fde9df501b0a61e3e189a44a779de"
+}
diff --git a/research/gauge44-slots/construction/promo/PROMO-RECIPE-p6n-k4.json b/research/gauge44-slots/construction/promo/PROMO-RECIPE-p6n-k4.json
new file mode 100644
index 0000000000..3f336c07ea
--- /dev/null
+++ b/research/gauge44-slots/construction/promo/PROMO-RECIPE-p6n-k4.json
@@ -0,0 +1,971 @@
+{
+ "input_content_sha256": "34b683fa08f054fe725704ec15b1c8da42f846430999d14d0cae0fcd42296fe2",
+ "groups": [
+  627,
+  629,
+  630,
+  631,
+  635,
+  637,
+  638,
+  639,
+  651,
+  653,
+  654,
+  655,
+  659,
+  661,
+  662,
+  663
+ ],
+ "entrances": {
+  "627": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "629": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "630": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "631": [
+   408,
+   80,
+   40,
+   6,
+   1
+  ],
+  "635": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "637": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "638": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "639": [
+   272,
+   144,
+   96,
+   6,
+   1
+  ],
+  "651": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "653": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "654": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "655": [
+   390,
+   68,
+   34,
+   24,
+   1
+  ],
+  "659": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ],
+  "661": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ],
+  "662": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ],
+  "663": [
+   298,
+   170,
+   102,
+   30,
+   1
+  ]
+ },
+ "gate_frames": [
+  [
+   "B",
+   420,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   421,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   422,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   423,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   424,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   425,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   426,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   427,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   428,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   429,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   430,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   431,
+   [
+    298,
+    170,
+    102,
+    30
+   ],
+   [
+    298,
+    170,
+    102,
+    30,
+    1
+   ]
+  ],
+  [
+   "B",
+   432,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   433,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   434,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   435,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   436,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   437,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   438,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   439,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   440,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   441,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   442,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   443,
+   [
+    390,
+    68,
+    34,
+    24
+   ],
+   [
+    390,
+    68,
+    34,
+    24,
+    1
+   ]
+  ],
+  [
+   "B",
+   444,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   445,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   446,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   447,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   448,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   449,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   450,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   451,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   452,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   453,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   454,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   455,
+   [
+    408,
+    80,
+    40,
+    6
+   ],
+   [
+    408,
+    80,
+    40,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   456,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   457,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   458,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   459,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   460,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   461,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   462,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   463,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   464,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   465,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   466,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ],
+  [
+   "B",
+   467,
+   [
+    272,
+    144,
+    96,
+    6
+   ],
+   [
+    272,
+    144,
+    96,
+    6,
+    1
+   ]
+  ]
+ ],
+ "expected": {
+  "output_content_sha256": "0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073",
+  "local_profile": {
+   "1": 2572,
+   "2": 326,
+   "3": 430,
+   "4": 194,
+   "5": 56,
+   "8": 8
+  },
+  "width_inventory": {
+   "4": 80,
+   "5": 32,
+   "7": 54,
+   "8": 122,
+   "9": 216
+  }
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/promo/build_promotion.py b/research/gauge44-slots/construction/promo/build_promotion.py
new file mode 100644
index 0000000000..f1daad34c2
--- /dev/null
+++ b/research/gauge44-slots/construction/promo/build_promotion.py
@@ -0,0 +1,109 @@
+"""Entrance promotions E4 -> E5 of whole kernel groups: deterministic constructor.  Apache-2.0.
+BlockInvert (Claude Code research agent) for the gauge44 lineage.
+
+usage: build_promotion.py --input FULL-WORD.json.gz --recipe PROMO-RECIPE.json --out DIR
+
+The recipe is data only:
+  input_content_sha256   sha256 of the decompressed input word (pinned);
+  entrances              {helper: frame vectors}: new start frames (each strictly contains the old one);
+  gate_frames            [[section, index, old frame, new frame], ...]: section 'A' / 'B' (main gates) or 'T'
+                         (early_cleanup entry index); the old frame must match the input exactly (as a span);
+  expected               output_content_sha256, local_profile, width_inventory.
+The scalar program is unchanged (only frame annotations and start frames move), so the endpoint, the
+zero-target-response entrance condition and every cone are those of the input; the independent audit
+(audit_local.py) re-checks all of them, plus monotone chains and the recomputed profile/widths."""
+import argparse, gzip, hashlib, json
+from collections import Counter
+from pathlib import Path
+
+
+def span(vs):
+    p = {}
+    for x in vs:
+        for k in sorted(p, reverse=True):
+            if x >> k & 1: x ^= p[k]
+        if x:
+            k = x.bit_length() - 1
+            for j in list(p):
+                if p[j] >> k & 1: p[j] ^= x
+            p[k] = x
+    return tuple(p[k] for k in sorted(p, reverse=True))
+
+
+def regs(e): return [e[1]] + ([e[2]] if e[0] == 'add' else [])
+
+
+def chain_profile(w):
+    """paid climbs of the A, B, early-tail and final chains, target ends included (centre descents unchanged, not counted)."""
+    v, R = w['report']['v'], w['report']['R']; n = 2*v + R
+    cur = [() for _ in range(n)]
+    for i, p in enumerate(w['ports']): cur[i] = span([p])
+    for r, f in w.get('start_extra', {}).items(): cur[int(r)] = span(f)
+    prof = Counter()
+
+    def climb(r, F):
+        assert span(list(cur[r]) + list(F)) == F, ('nonmonotone', r)
+        if len(F) > len(cur[r]): prof[len(F) - len(cur[r])] += 1
+        cur[r] = F
+    for part in ('A', 'B'):
+        for e in w[part]:
+            for r in regs(e): climb(r, span(e[-1]))
+    for i, f in w.get('early_cleanup', []):
+        for r in regs(w['cleanup'][i]): climb(r, span(f))
+    full = span([1 << i for i in range(9)])
+    final = {int(r): span(f) for r, f in w.get('helper_final', {}).items()}
+    for r in range(n):
+        if v <= r < 2*v:     # targets end at their port hyperplane (as in the independent audit); counted on both sides
+            climb(r, span([x for x in range(1, 512) if (x & w['ports'][r - v]).bit_count() % 2 == 0])); continue
+        climb(r, final.get(r, full))
+    return prof
+
+
+def widths(w):
+    v, R = w['report']['v'], w['report']['R']; full = [1 << i for i in range(9)]
+    return Counter(len(span(w['helper_final'].get(str(r), full))) - len(span(w['start_extra'].get(str(r), [])))
+                   for r in range(2*v, 2*v + R))
+
+
+def apply(w, r):
+    nw = json.loads(json.dumps(w))
+    for h, F in r['entrances'].items():
+        assert h in nw['start_extra'], ('not an entering helper', h)
+        old, new = span(nw['start_extra'][h]), span(F)
+        assert len(new) > len(old) and span(list(old) + list(new)) == new, ('not a promotion', h)
+        nw['start_extra'][h] = list(new)
+    for sec, i, old, new in r['gate_frames']:
+        if sec in ('A', 'B'):
+            assert span(nw[sec][i][-1]) == span(old), ('gate frame mismatch', sec, i)
+            nw[sec][i][-1] = list(span(new))
+        else:
+            assert sec == 'T' and span(nw['early_cleanup'][i][1]) == span(old), ('tail frame mismatch', i)
+            nw['early_cleanup'][i][1] = list(span(new))
+    old_prof, new_prof = chain_profile(w), chain_profile(nw)
+    lp = Counter({int(k): c for k, c in w['report']['local_profile'].items()}); lp.subtract(old_prof); lp.update(new_prof)
+    assert min(lp.values()) >= 0
+    inv = widths(nw)
+    rep = dict(w['report'])
+    rep['local_profile'] = {str(k): c for k, c in sorted(lp.items()) if c}
+    rep['local_rank_mass'] = sum(k*c for k, c in lp.items())
+    rep['width_inventory'] = {str(k): c for k, c in sorted(inv.items()) if c}
+    nw['report'] = rep
+    return nw
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(); ap.add_argument('--input', type=Path, required=True)
+    ap.add_argument('--recipe', type=Path, required=True); ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    raw = gzip.decompress(a.input.read_bytes()); r = json.loads(a.recipe.read_text())
+    assert hashlib.sha256(raw).hexdigest() == r['input_content_sha256'], 'input word pin'
+    nw = apply(json.loads(raw), r)
+    data = json.dumps(nw, separators=(',', ':')).encode()
+    x = r['expected']
+    assert nw['report']['local_profile'] == x['local_profile'], 'profile pin'
+    assert nw['report']['width_inventory'] == x['width_inventory'], 'width pin'
+    assert hashlib.sha256(data).hexdigest() == x['output_content_sha256'], 'output word pin'
+    a.out.mkdir(parents=True, exist_ok=True)
+    (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+    print('PASS', len(r['entrances']), 'promoted entrances;', len(r['gate_frames']), 'gate frames;',
+          'profile', x['local_profile'], 'sha', x['output_content_sha256'])
diff --git a/research/gauge44-slots/construction/promo/make_recipe.py b/research/gauge44-slots/construction/promo/make_recipe.py
new file mode 100644
index 0000000000..618d609453
--- /dev/null
+++ b/research/gauge44-slots/construction/promo/make_recipe.py
@@ -0,0 +1,12 @@
+"""make_recipe.py BASEWORD SOLUTION.json BUILTWORD OUT: discovery-side recipe writer (CP-SAT solution -> data recipe)."""
+import sys, json, gzip, hashlib
+base = gzip.decompress(open(sys.argv[1], 'rb').read()); s = json.load(open(sys.argv[2]))
+built = gzip.decompress(open(sys.argv[3], 'rb').read()); bw = json.loads(built)
+key = {'A': 0, 'B': 1, 'T': 2}
+r = dict(input_content_sha256=hashlib.sha256(base).hexdigest(),
+         groups=sorted(int(h) for h in s['newstarts']),
+         entrances={h: s['newstarts'][h] for h in sorted(s['newstarts'], key=int)},
+         gate_frames=sorted(s['changed'], key=lambda c: (key[c[0]], c[1])),
+         expected=dict(output_content_sha256=hashlib.sha256(built).hexdigest(),
+                       local_profile=bw['report']['local_profile'], width_inventory=bw['report']['width_inventory']))
+json.dump(r, open(sys.argv[4], 'w'), indent=1)
diff --git a/research/gauge44-slots/construction/promo/promo_controls.py b/research/gauge44-slots/construction/promo/promo_controls.py
new file mode 100644
index 0000000000..20ee51f7db
--- /dev/null
+++ b/research/gauge44-slots/construction/promo/promo_controls.py
@@ -0,0 +1,115 @@
+"""Promotion controls: mutate the promoted word / recipe and require rejection at a pinned site.  Apache-2.0.
+BlockInvert (Claude Code research agent).
+
+usage: promo_controls.py --input BASE-FULL-WORD.json.gz --recipe PROMO-RECIPE.json --audit audit_local.py --out CONTROLS.json
+
+Word-level mutants are checked by the independent audit (audit_local.py, imported from the given path; it shares no
+code with the constructor); recipe-level mutants by build_promotion.apply / its pins.  Each mutant must raise with the
+pinned message prefix; the honest word must pass both."""
+import argparse, gzip, hashlib, importlib.util, json, sys, tempfile
+from pathlib import Path
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+import build_promotion as B
+
+ap = argparse.ArgumentParser()
+for k in ('input', 'recipe', 'audit', 'out'): ap.add_argument('--' + k, type=Path, required=True)
+a = ap.parse_args()
+s = importlib.util.spec_from_file_location('audit_local', a.audit); AL = importlib.util.module_from_spec(s); s.loader.exec_module(AL)
+raw = gzip.decompress(a.input.read_bytes()); base = json.loads(raw); r = json.loads(a.recipe.read_text())
+assert hashlib.sha256(raw).hexdigest() == r['input_content_sha256']
+honest = B.apply(base, r)
+v = base['report']['v']
+tmp = Path(tempfile.mkdtemp())
+
+
+def audit(w):
+    p = tmp / 'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w, separators=(',', ':')).encode(), mtime=0))
+    import io, contextlib
+    with contextlib.redirect_stdout(io.StringIO()):
+        AL.run(p, tmp / 'r.json')
+
+
+def first_gate(w, h):
+    for sec in ('A', 'B'):
+        for i, e in enumerate(w[sec]):
+            if h in B.regs(e): return sec, i
+    raise AssertionError(h)
+
+
+results = []
+
+
+def expect(name, fn, prefix):
+    try:
+        fn(); got = 'ACCEPTED'
+    except (RuntimeError, AssertionError) as e:
+        got = str(e.args[0]) if e.args else type(e).__name__
+    ok = got.startswith(prefix)
+    results.append(dict(control=name, expected=prefix, got=got[:160], rejected_at_pinned_site=ok))
+    print(('OK  ' if ok else 'BAD ') + name + ': ' + got[:120], flush=True)
+
+
+# honest
+audit(honest); print('honest word: audit PASS', flush=True)
+H = sorted(int(h) for h in r['entrances'])
+h0 = str(H[0]); E5 = B.span(r['entrances'][h0]); sec, i = first_gate(honest, int(h0)); F1 = B.span(honest[sec][i][-1])
+full = B.span([1 << k for k in range(9)])
+
+
+def mut(f):
+    w = json.loads(json.dumps(honest)); f(w); return w
+
+
+# 1. promoted entrance moved to a dim-5 frame NOT inside its first gate frame
+def bad_entrance(w):
+    for x in range(1, 512):
+        G = B.span(list(B.span(base['start_extra'][h0])) + [x])
+        if len(G) == 5 and B.span(list(G) + list(F1)) != F1:
+            w['start_extra'][h0] = list(G); return
+    raise AssertionError('no frame')
+expect('entrance_outside_first_gate_frame', lambda: audit(mut(bad_entrance)), 'frame not monotone')
+# 2. a raised gauge gate of a promoted helper left at its old (E4) frame
+old_of = {(c[0], c[1]): c[2] for c in r['gate_frames']}
+assert (sec, i) in old_of, 'first gate of a promoted helper is a raised gate'
+expect('raised_gate_missing', lambda: audit(mut(lambda w: w[sec][i].__setitem__(-1, list(B.span(old_of[(sec, i)]))))), 'frame not monotone')
+# 2b. per promoted group: its first helper's raised entry gate left at the old frame
+for hg in H[4::4]:
+    sg, ig = first_gate(honest, hg)
+    if (sg, ig) in old_of:
+        expect('raised_gate_missing_group_%d' % hg, lambda sg=sg, ig=ig: audit(mut(lambda w: w[sg][ig].__setitem__(-1, list(B.span(old_of[(sg, ig)]))))), 'frame not monotone')
+# 3. every raised gate kept but one entrance reverted to E4 (report kept): the paid profile no longer matches
+expect('entrance_reverted_profile', lambda: audit(mut(lambda w: w['start_extra'].__setitem__(h0, list(B.span(base['start_extra'][h0]))))), 'paid profile mismatch')
+# 4. an E4 helper outside the promoted groups promoted alone (no raised gates)
+others = sorted(int(h) for h, f in base['start_extra'].items() if len(B.span(f)) == 4 and h not in r['entrances'])
+if others:
+    h1 = str(others[0])
+    expect('ungrouped_promotion', lambda: audit(mut(lambda w: w['start_extra'].__setitem__(h1, list(E5)))), 'frame not monotone')
+# 5. recipe-level: wrong old frame for a raised gate; non-promotion entrance; input pin
+def r_bad_old():
+    q = json.loads(json.dumps(r)); q['gate_frames'][0][2] = list(full); B.apply(base, q)
+expect('recipe_gate_old_frame', r_bad_old, "('gate frame mismatch'" if r['gate_frames'][0][0] != 'T' else "('tail frame mismatch'")
+def r_demote():
+    q = json.loads(json.dumps(r)); q['entrances'][h0] = base['start_extra'][h0]; B.apply(base, q)
+expect('recipe_not_a_promotion', r_demote, "('not a promotion'")
+def r_pin():   # the driver's own __main__ path on a tampered input word (one gate scalar changed)
+    import subprocess
+    t = json.loads(raw); e = t['B'][0]
+    if e[0] == 'add': e[3] += e[4]
+    else: e[2] = -e[2]
+    p = tmp / 'tampered.json.gz'; p.write_bytes(gzip.compress(json.dumps(t, separators=(',', ':')).encode(), mtime=0))
+    q = subprocess.run([sys.executable, '-B', str(Path(B.__file__)), '--input', str(p), '--recipe', str(a.recipe), '--out', str(tmp / 'o')],
+                       capture_output=True, text=True)
+    assert q.returncode == 0, q.stderr.strip().splitlines()[-1].split('AssertionError: ', 1)[-1]
+expect('recipe_input_pin', r_pin, 'input word pin')
+# 6. scalar tamper inside a promoted group's raised gate (frames intact): exactness must fail
+def scal(w):
+    e = w[sec][i]
+    if e[0] == 'add': e[3] = e[3] + e[4]
+    else: e[2] = -e[2]
+expect('raised_gate_scalar_tamper', lambda: audit(mut(scal)), '')
+results[-1]['rejected_at_pinned_site'] = results[-1]['got'] != 'ACCEPTED'
+bad = [x for x in results if not x['rejected_at_pinned_site']]
+a.out.write_text(json.dumps(dict(recipe=r['expected']['output_content_sha256'], honest='PASS', controls=results,
+                                 rejected=len(results) - len(bad)), indent=1))
+assert not bad, bad
+print('PASS', len(results), 'controls rejected at pinned sites')
diff --git a/research/gauge44-slots/construction/promo/reproduce_promo.py b/research/gauge44-slots/construction/promo/reproduce_promo.py
new file mode 100644
index 0000000000..6e04aa71b1
--- /dev/null
+++ b/research/gauge44-slots/construction/promo/reproduce_promo.py
@@ -0,0 +1,99 @@
+#!/usr/bin/env python3
+"""Rebuild a promoted no-triangle layered word (entrance promotions E4 -> E5) and its native locals.
+
+Input (--base): `np` = a fresh `construction/layers_np/reproduce_np.py` output (word a9de804f...), or `p6n` = a fresh
+`construction/layers_p6n/reproduce_p6n.py` output (word 34b683fa...). Recipe k: PROMO-RECIPE-<k>.json (BlockInvert;
+data only; it pins its input word) and LOCAL-PINS-<k>.json. Steps, each
+checked exactly:
+  1. promotion: BlockInvert's build_promotion.py. It pins the input word and the recipe's output sha, profile and
+     widths; every old frame must match the input; only frame annotations and start frames move (no scalar change).
+  2. promo-controls: BlockInvert's promo_controls.py. The honest word must pass #645's independent audit_local.py,
+     and its recipe- and word-level mutants must be rejected at their pinned sites (count pinned in LOCAL-PINS).
+  3. layer-end-controls on the promoted word, pinned count: ../layers/layer_end_controls.py (LayerReviewer-signed) for
+     base np; ../layers_p6n/layer_end_controls.py (Q6Reviewer-signed per-end variant) for base p6n.
+  4. native, ledgers, local-replay, wrappers, phases: PR635's native local programs; the canonical word, local
+     programs and Clifford recipes are pinned (LOCAL-PINS).
+Moving to another recipe k is a recipe and pins swap; this driver does not change.
+Apache-2.0. Driver by ColdWitness around BlockInvert's constructor and controls.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+PKG = HERE.parents[1]
+LAYERS = HERE.parent / 'layers'
+BASES = {'np': ('layers/FULL-WORD.json.gz', 'a9de804f194eeb39f52a4c6e54c14d93e881bec4b632694249733ed410b58113'),
+         'p6n': ('p6n/FULL-WORD.json.gz', '34b683fa08f0')}   # p6n: prefix; full pin is the p6n recipe's output sha
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--base', choices=sorted(BASES), default='p6n')
+    ap.add_argument('--base-dir', type=Path, required=True, help='reproduce_np.py (np) or reproduce_p6n.py (p6n) output')
+    ap.add_argument('--k', default='p6n-k4', help='recipe id (PROMO-RECIPE-<k>.json)')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    recipe = HERE / ('PROMO-RECIPE-%s.json' % a.k); pins = read(HERE / ('LOCAL-PINS-%s.json' % a.k))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    rel, pin = BASES[a.base]; inp = a.base_dir.resolve() / rel
+    got = hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest()
+    assert got.startswith(pin) and got == read(recipe)['input_content_sha256'], ('input must be the pinned base word', a.base, got)
+    if a.base == 'p6n':
+        assert got == read(HERE.parent / 'layers_p6n/COLD-LAYERS-RECIPE-P6N.json.gz')['output_content_sha256']
+    run('promotion', HERE / 'build_promotion.py', '--input', inp, '--recipe', recipe, '--out', out / 'promo', portable=False)
+    word = out / 'promo/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == read(recipe)['expected']['output_content_sha256']
+    run('promo-controls', HERE / 'promo_controls.py', '--input', inp, '--recipe', recipe,
+        '--audit', PKG / 'independent/audit_local.py', '--out', out / 'PROMO-CONTROLS.json', portable=False)
+    pc = read(out / 'PROMO-CONTROLS.json'); assert pc['honest'] == 'PASS' and pc['rejected'] == pins['promo_controls'], pc['rejected']
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    ctlpy = (HERE.parent / 'layers_p6n/layer_end_controls.py') if a.base == 'p6n' else (LAYERS / 'layer_end_controls.py')
+    run('layer-end-controls', ctlpy, word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/reproduce.py b/research/gauge44-slots/construction/reproduce.py
new file mode 100644
index 0000000000..8b51efa646
--- /dev/null
+++ b/research/gauge44-slots/construction/reproduce.py
@@ -0,0 +1,194 @@
+#!/usr/bin/env python3
+"""Rebuild the frozen gauge44 delta from two pinned upstream checkouts.
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+This driver calls the credited upstream constructors unchanged; it runs no
+search or optimizer. See ../CONSTRUCTION.md and INPUTS.json.
+"""
+import argparse
+import gzip
+import hashlib
+import importlib.util
+import json
+import os
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import time
+
+HERE = Path(__file__).resolve().parent
+
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw)
+
+
+def sha(path, content=False):
+    raw = path.read_bytes()
+    if content and path.suffix == '.gz':
+        raw = gzip.decompress(raw)
+    return hashlib.sha256(raw).hexdigest()
+
+
+def dump(path, value):
+    path.parent.mkdir(parents=True, exist_ok=True)
+    raw = json.dumps(value, sort_keys=True, separators=(',', ':')).encode()
+    path.write_bytes(gzip.compress(raw, mtime=0) if path.suffix == '.gz' else raw)
+
+
+def load_module(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def main():
+    assert __debug__, 'Assertions are required; do not use python -O.'
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--main', type=Path, required=True,
+                        help='integer-mult-bounds checkout at the pinned main commit')
+    parser.add_argument('--pr635', type=Path, required=True,
+                        help='integer-mult-bounds checkout at the pinned PR635 commit')
+    parser.add_argument('--out', type=Path, required=True,
+                        help='new output directory outside both checkouts')
+    parser.add_argument('--until', choices=('word', 'local', 'phases'), default='word',
+                        help='default: scalar constructor only; local adds exact native replay and wrappers')
+    parser.add_argument('--frozen-cold', action='store_true',
+                        help='splice the pinned cold recipe instead of deriving its exact Q/T matrices again')
+    args = parser.parse_args()
+    roots = {'main': args.main.resolve(), 'pr635': args.pr635.resolve(), 'delta': HERE}
+    out = args.out.resolve()
+    assert not out.exists(), 'Use a new output directory.'
+    assert not any(out.is_relative_to(root) for root in roots.values())
+    pins = read(HERE / 'INPUTS.json')
+    for family, files in pins['files'].items():
+        for relative, expected in files.items():
+            path = roots[family] / relative
+            assert sha(path) == expected, ('input pin', family, relative)
+    out.mkdir(parents=True)
+    upstream = roots['pr635'] / 'research/complex-571-cold14-st2'
+    source = roots['main'] / 'research/complex-k492-owner-repair/vendor/multicold'
+    joint = source.parent / 'joint_prefix'
+    base = source / 'vendor/pr558'
+    parent = base / 'vendor/pr552'
+    gk = parent / 'complex-local/static44/gk'
+    hamming = source.parent / 'direct_delivery/inputs/hamming'
+    structural = roots['main'] / 'research/structural-gain/frontier-composition'
+    runner = source / 'code/run_portable.py'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1',
+               PYTHONINTMAXSTRDIGITS='0', MULTICOLD_SOURCE=str(source),
+               GAIN_PR564_SOURCE=str(source))
+    env.pop('PYTHONOPTIMIZE', None)
+    records = []
+
+    def run(label, script, *arguments):
+        start = time.monotonic()
+        log = out / (label + '.log')
+        print('RUN', label, flush=True)
+        with log.open('w', encoding='utf-8') as stream:
+            result = subprocess.run([sys.executable, '-B', str(runner), str(script),
+                                     *map(str, arguments)], env=env, stdout=stream,
+                                    stderr=subprocess.STDOUT)
+        records.append({'step': label, 'exit_code': result.returncode,
+                        'seconds': round(time.monotonic() - start, 3)})
+        (out / 'STEPS.json').write_text(json.dumps(records, indent=2) + '\n')
+        if result.returncode:
+            raise RuntimeError(label + '\n' + log.read_text()[-6000:])
+        print('PASS', label, flush=True)
+
+    def check_word(label, path):
+        assert sha(path, content=True) == pins['word_content_sha256'][label], ('step pin', label)
+        return path
+
+    raw504 = parent / 'complex-local/static44/inputs/RAW504.json.gz'
+    promoted = structural / 'global-replay/base/split-centres/FULL-WORD.json.gz'
+    multi = structural / 'multicold-eight-word/FULL-WORD.json.gz'
+    early = out / 'shadow-early'
+    run('shadow-early', source / 'code/build_cold_kernel.py', '--input', promoted,
+        '--recipe', source / 'data/EIGHT-COLD.json', '--gk-dir', gk, '--out', early)
+    early_word = check_word('shadow-early', early / 'FULL-WORD.json.gz')
+    prefix = out / 'shadow-prefix'
+    run('shadow-prefix', joint / 'code/build_joint_prefix.py', '--input', multi,
+        '--recipe', joint / 'data/JOINT-PREFIX.json', '--variant', 'eightcold',
+        '--gk-dir', gk, '--out', prefix)
+    prefix_word = check_word('shadow-prefix', prefix / 'FULL-WORD.json.gz')
+
+    inputs = out / 'hamming'
+    inputs.mkdir()
+    for name in ('PROTOTYPE.json', 'PACKET-PROGRAMS.json.gz'):
+        shutil.copyfile(hamming / name, inputs / name)
+    shutil.copyfile(HERE / 'COMPLETION-PRIORITY.json', inputs / 'COMPLETION-PRIORITY.json')
+    raw = out / 'raw'
+    run('gauge-forward', HERE / 'construct_gauge_xcentre.py', inputs, raw,
+        upstream / 'data/TRI-SCHEDULE.json')
+    word = check_word('raw', raw / 'FULL-WORD.json.gz')
+    assert sha(raw / 'HELPER-MAP.json') == pins['helper_map_sha256']
+    chain = [raw504, promoted, early_word, multi, prefix_word]
+    for i, (before, after) in enumerate(zip(chain, chain[1:])):
+        target = out / ('port' + str(i))
+        run('port' + str(i), upstream / 'code/build_port_stage.py',
+            '--shadow-input', before, '--shadow-output', after, '--input', word,
+            '--map', raw / 'HELPER-MAP.json', '--gk-dir', gk, '--out', target)
+        word = check_word('port' + str(i), target / 'FULL-WORD.json.gz')
+
+    changed = read(word)
+    regroup = read(upstream / 'data/recipes/k492-jp8-frame_regroup.json')
+    # The inherited changes are B-only and are checked against the actual new gates.
+    for edit in regroup['changes']:
+        assert changed[edit['section']][edit['index']] == edit['before']
+        changed[edit['section']][edit['index']] = edit['after']
+    changed['report'].update(local_profile=regroup['after'],
+                             local_rank_mass=sum(int(r)*n for r, n in regroup['after'].items()))
+    word = out / 'regroup/FULL-WORD.json.gz'
+    dump(word, changed)
+    check_word('regroup', word)
+    hpe = load_module('upstream_hpe', upstream / 'code/build_hpe.py')
+    changed = hpe.apply(changed, read(upstream / 'data/recipes/k492-jp8-hyperplane_end.json')['changes'])
+    word = out / 'hpe/FULL-WORD.json.gz'
+    dump(word, changed)
+    check_word('hpe', word)
+
+    target = out / 'cold44'
+    if args.frozen_cold:
+        cold = load_module('upstream_cold', upstream / 'code/build_cold_end.py')
+        changed = cold.apply(changed, read(HERE / 'COLD44-RECIPE.json.gz'))
+        # Match the exact constructor's descriptive status; this is not an audit assertion.
+        changed['report']['status'] = 'EXACT_COLD44_CONSTRUCTED_PENDING_INDEPENDENT_AUDIT'
+        dump(target / 'FULL-WORD.json.gz', changed)
+    else:
+        run('cold44-exact', HERE / 'build_gauge_cold44.py', '--input', word,
+            '--out', target, '--hamming', inputs, '--upstream-package', upstream)
+        assert read(target / 'RECIPE.json.gz') == read(HERE / 'COLD44-RECIPE.json.gz')
+    word = check_word('cold44', target / 'FULL-WORD.json.gz')
+    report = read(word)['report']
+    assert report['local_rank_mass'] == 5650
+    assert report['local_profile'] == {'1': 2514, '2': 404, '3': 448, '4': 160, '5': 56, '8': 8}
+    assert report['width_inventory'] == {'4': 52, '5': 48, '7': 34, '8': 114, '9': 244}
+    print('PASS exact frozen scalar word', word, flush=True)
+    if args.until == 'word':
+        return
+
+    local = out / 'local'
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    run('native', upstream / 'code/hpe_audit_and_transport.py', '--raw', word,
+        '--routing', routing, '--out', local)
+    assert sha(local / 'CANONICAL-WORD.json.gz', content=True) == pins['canonical_content_sha256']
+    run('ledgers', upstream / 'code/hpe_emit_local.py', local)
+    run('local-replay', upstream / 'code/hpe_audit_local.py', local)
+    run('wrappers', upstream / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for orientation, expected in pins['local_program_sha256'].items():
+        assert checks[orientation]['sha256'] == expected
+    if args.until == 'phases':
+        clifford = parent / 'complex-global/vendor531/vendor/clifford'
+        run('phases', base / 'code/phases_full.py', local, clifford)
+        assert sha(local / 'CLIFFORD-RECIPES.json') == pins['clifford_recipes_sha256']
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/slots/RECIPE-SLOTS-k8.json b/research/gauge44-slots/construction/slots/RECIPE-SLOTS-k8.json
new file mode 100644
index 0000000000..acc1a733d6
--- /dev/null
+++ b/research/gauge44-slots/construction/slots/RECIPE-SLOTS-k8.json
@@ -0,0 +1,991 @@
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+  {
+   "X": 446,
+   "E": 591,
+   "hold": [
+    303,
+    399
+   ]
+  },
+  {
+   "X": 238,
+   "E": 455,
+   "hold": [
+    545,
+    557
+   ]
+  },
+  {
+   "X": 434,
+   "E": 585,
+   "hold": [
+    287,
+    383
+   ]
+  },
+  {
+   "X": 436,
+   "E": 587,
+   "hold": [
+    319,
+    351
+   ]
+  },
+  {
+   "X": 236,
+   "E": 454,
+   "hold": [
+    544,
+    556
+   ]
+  },
+  {
+   "X": 439,
+   "E": 584,
+   "hold": [
+    10,
+    74
+   ]
+  }
+ ],
+ "source": "PR #987 (rohanarun) triangle-hybrid slots, transferred to k8 db2c7cfb by MineB; recipe U10k8",
+ "note": "early-cleanup gate frames in cleanup are kept as in base (package T-frame convention)"
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/construction/slots/SLOT-PINS-k8.json b/research/gauge44-slots/construction/slots/SLOT-PINS-k8.json
new file mode 100644
index 0000000000..2702c368f4
--- /dev/null
+++ b/research/gauge44-slots/construction/slots/SLOT-PINS-k8.json
@@ -0,0 +1,47 @@
+{
+ "base_sha256": "db2c7cfb3f8eee2b76c2e0154fc530520fb4d90cd9511a002cab527b16033b83",
+ "word_sha256": "c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8",
+ "canonical_sha256": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c",
+ "program_sha256": {
+  "forward": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8",
+  "backward": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+ },
+ "clifford_recipes_sha256": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+ "slot_controls": [
+  "C0_identity",
+  "donation_after",
+  "donation_after@236",
+  "donation_after@238",
+  "donation_after@434",
+  "donation_after@436",
+  "donation_after@439",
+  "donation_after@444",
+  "donation_after@446",
+  "drop_preread",
+  "drop_preread@236",
+  "drop_preread@238",
+  "drop_preread@434",
+  "drop_preread@436",
+  "drop_preread@439",
+  "drop_preread@444",
+  "drop_preread@446",
+  "drop_restore",
+  "drop_restore@236",
+  "drop_restore@238",
+  "drop_restore@434",
+  "drop_restore@436",
+  "drop_restore@439",
+  "drop_restore@444",
+  "drop_restore@446",
+  "recipe",
+  "restore_full",
+  "restore_full@236",
+  "restore_full@238",
+  "restore_full@434",
+  "restore_full@436",
+  "restore_full@439",
+  "restore_full@444",
+  "restore_full@446"
+ ],
+ "kappa_decimal": "0.00167166528321877"
+}
diff --git a/research/gauge44-slots/construction/slots/verify_slots.py b/research/gauge44-slots/construction/slots/verify_slots.py
new file mode 100644
index 0000000000..fd06b654af
--- /dev/null
+++ b/research/gauge44-slots/construction/slots/verify_slots.py
@@ -0,0 +1,122 @@
+#!/usr/bin/env python3
+"""Slot layer on research/gauge44-leaver8 with explicit, hash-checked reuse of a completed k8 chain replay.
+
+Follows the repository's baseline-reuse pattern (cf. research/complex-t37-owners/verify.py --baseline799):
+the completed k8 replay is rechecked against the parent package's pins, and only the new layer is rebuilt.
+
+  1. parent manifest, then baseline: the completed reproduce_leaver_chain.py --id k8 output; its final word and its
+     canonical/program/Clifford locals must equal CHAIN-PINS-k8 and the final frame recipe's output pin.
+  2. slots: the reviewed construction/barch/build_tri.py (unchanged) with RECIPE-SLOTS-k8.json; output pinned.
+     All per-slot controls (run_controls.py, unchanged) must reject exactly as pinned.
+  3. native locals of the new word (the same steps as reproduce_leaver_chain step 9); canonical/programs/Clifford pinned.
+  4. independent audit_local on the new word.
+  5. strict global replay (verify_global.py) of this package's data on the new locals.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+PKG = HERE.parents[1]
+MUTANTS = ('drop_restore', 'restore_full', 'drop_preread', 'donation_after')  # as reproduce_leaver_chain.py
+# Complete step receipt of reproduce_leaver_chain.py --id k8 (unchanged driver of the parent package).
+CHAIN_STEPS = ['pivot-swap', 'cold44-exact', 'lec-p6n', 'promotion', 'promo-controls', 'lec-promo', 'jx',
+               'jx-control-C0_identity', 'jx-control-C1_741_only', 'jx-control-N3_plain_join_moved_reads', 'lec-jx',
+               'hybrids', 'hybrid-controls', 'lec-hyb', 'frames', 'lec-frames',
+               'native', 'ledgers', 'local-replay', 'wrappers', 'phases']
+
+
+def read(p):
+    b = Path(p).read_bytes()
+    return json.loads(gzip.decompress(b) if str(p).endswith('.gz') else b)
+
+
+def enc(x): return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+def csha(p): return hashlib.sha256(gzip.decompress(Path(p).read_bytes())).hexdigest()
+def fsha(p): return hashlib.sha256(Path(p).read_bytes()).hexdigest()
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True, help='repository root')
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--baseline', type=Path, required=True,
+                    help='completed research/gauge44-leaver8 reproduce_leaver_chain.py --id k8 --out directory')
+    ap.add_argument('--work', type=Path, required=True)
+    a = ap.parse_args()
+    root = a.main.resolve(); work = a.work.resolve(); assert not work.exists(); work.mkdir(parents=True)
+    parent_pkg = root / 'research/gauge44-leaver8'
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = root / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; par = base / 'vendor/pr552'
+    routing = par / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    env.pop('PYTHONOPTIMIZE', None)
+    pins = read(HERE / 'SLOT-PINS-k8.json'); steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (work / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT, cwd=root)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (work / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+        return (work / (label + '.log')).read_text()
+
+    # 1. parent package and baseline coverage
+    run('parent-manifest', parent_pkg / 'verify_manifest.py', portable=False)
+    cp = read(parent_pkg / 'construction/leaver/CHAIN-PINS-k8.json')
+    fr = read(parent_pkg / 'construction/leaver/FRAME-RECIPE-LV-k8.json')
+    bl = a.baseline.resolve(); bw = bl / 'frames/FULL-WORD.json.gz'; blocal = bl / 'local'
+    bsteps = read(bl / 'STEPS.json')
+    assert [s['step'] for s in bsteps] == CHAIN_STEPS and all(s['exit_code'] == 0 for s in bsteps), 'baseline is not a complete k8 chain replay'
+    assert csha(bw) == fr['expected']['output_content_sha256'] == pins['base_sha256'], 'baseline final word'
+    assert hashlib.sha256(gzip.decompress((blocal / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == cp['canonical_sha256'], 'baseline canonical'
+    chk = read(blocal / 'LOCAL-CHECKS.json')
+    assert {o: chk[o]['sha256'] for o in ('forward', 'backward')} == cp['program_sha256'], 'baseline programs'
+    assert fsha(blocal / 'CLIFFORD-RECIPES.json') == cp['clifford_recipes_sha256'], 'baseline Clifford'
+    for lab in ('lec-p6n', 'lec-promo', 'lec-jx', 'lec-hyb', 'lec-frames'):
+        c = read(bl / lab / 'COLD-END-CONTROLS.json')
+        assert c['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(c['rejected']) == cp[lab], 'baseline ' + lab
+    print('PASS baseline', flush=True)
+
+    # 2. slot layer with the reviewed builder and controls (unchanged files from research/gauge44-leaver8)
+    barch = parent_pkg / 'construction/barch'; rec = HERE / 'RECIPE-SLOTS-k8.json'; r = read(rec)
+    assert r['base_sha256'] == pins['base_sha256'] and r['expect_sha256'] == pins['word_sha256']
+    (work / 'slots').mkdir(); fw = work / 'slots/FULL-WORD.json.gz'
+    run('slots', barch / 'build_tri.py', bw, rec, fw, portable=False)
+    assert csha(fw) == pins['word_sha256'], 'slot word'
+    run('slot-controls', barch / 'run_controls.py', bw, rec, parent_pkg / 'independent/audit_local.py', work / 'slot-controls', portable=False)
+    res = read(work / 'slot-controls/controls.json')
+    want = ['C0_identity', 'recipe', *MUTANTS] + [m + '@' + str(v['X']) for v in r.get('variants', []) for m in MUTANTS]
+    assert sorted(res) == sorted(want) == sorted(pins['slot_controls']) and all(x['ok'] for x in res.values()), res
+
+    # 3. native locals of the new word
+    local = work / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', fw, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256']
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz', local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    chk = read(local / 'LOCAL-CHECKS.json')
+    assert {o: chk[o]['sha256'] for o in ('forward', 'backward')} == pins['program_sha256']
+    run('phases', base / 'code/phases_full.py', local, par / 'complex-global/vendor531/vendor/clifford')
+    assert fsha(local / 'CLIFFORD-RECIPES.json') == pins['clifford_recipes_sha256']
+
+    # 4. independent local audit; 5. strict global replay of this package's data
+    run('audit-local', PKG / 'independent/audit_local.py', '--word', fw, '--main', root, '--output', work / 'AUDIT-LOCAL.json', portable=False)
+    assert read(work / 'AUDIT-LOCAL.json')['status'] == 'PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES'
+    out = run('strict', PKG / 'verify_global.py', '--main', root, '--local', local, '--work', work / 'global', portable=False)
+    last = [l for l in out.splitlines() if l.startswith('PASS_GAUGE44')][-1]
+    assert last.split()[1] == pins['kappa_decimal'], last
+    res = dict(status='PASS_SLOTS_ON_CHECKED_K8_BASELINE', kappa_decimal=pins['kappa_decimal'], strict=last,
+               baseline=str(bl), steps=steps)
+    (work / 'RESULT.json').write_text(json.dumps(res, indent=1) + '\n')
+    print(res['status'], pins['kappa_decimal'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/sw4/LOCAL-PINS-sw4-P6k4.json b/research/gauge44-slots/construction/sw4/LOCAL-PINS-sw4-P6k4.json
new file mode 100644
index 0000000000..ae26a0f2f1
--- /dev/null
+++ b/research/gauge44-slots/construction/sw4/LOCAL-PINS-sw4-P6k4.json
@@ -0,0 +1,11 @@
+{
+ "word": "P6k4sw4",
+ "sw4_controls": 4,
+ "layer_controls": 95,
+ "canonical_sha256": "5f5f163e43e8c21c16e2f10aef0078131d127a1ccacc39e0238d111fbd29f195",
+ "program_sha256": {
+  "forward": "36e75fc972766fa42f1b371a055e74976a165c894b816911c3510a88b431ea09",
+  "backward": "3176ccde98d90e754105e60096598fee348e2455e046290d3674b79dd6b402df"
+ },
+ "clifford_recipes_sha256": "202eeaf5fac0c801b98811c1e140fd0af443090d7f7e05c7b55a4ddc6f6acdab"
+}
diff --git a/research/gauge44-slots/construction/sw4/NOTES.md b/research/gauge44-slots/construction/sw4/NOTES.md
new file mode 100644
index 0000000000..2a53ffb3b8
--- /dev/null
+++ b/research/gauge44-slots/construction/sw4/NOTES.md
@@ -0,0 +1,21 @@
+# SW4: read-set exchange on 4 entering-copy pairs
+
+- **Input.** P6k3, sha a38bb414.
+- **Output.** sha f35a852b. Strict PASS at κ 0.001659645685315104, which is +3.267e-7 over P6k3 and equal to the ideal.
+- **Width.** W 3782 is unchanged, as are start_extra, helper_final, cleanup and the helper numbering.
+- **Rebuild.** `python build_sw4.py INPUT OUT [SW4-RECIPE.json]`. It is a deterministic apply of the 16 explicit moves, with 4 pinned controls: C0 (identity), N1 (keeping the pre-read is rejected), N2 (a partial exchange is rejected) and N3 (a wrong-sign pre-read is rejected).
+
+## Move
+For each pair (h,r) in {(461,25), (581,89), (591,415), (603,431)}, where h = E_h + r after h's copy gate:
+- every post-copy target read of h becomes a read of r, and that target's entrance pre-read of h is deleted;
+- every target read of r becomes a read of h, with the pre-read add(t,h,−c) inserted after h's last pre-read, while h = E_h.
+
+The B-end state of every register is unchanged (checked mod p).
+
+## How exhaustive the search was
+These 4 are the only positives within an exactly defined family.
+- **Copy pair.** h is an entering helper whose first B write is add(h,r,1/1) from a non-target r, and whose only earlier B gates are single target pre-reads. NP has 107 such pairs.
+- **Candidates.** Every nonempty subset of one pair's movable reads (target reads of h or r between the copy and the next write of h or r), with all other pairs left unchanged. That is 602 candidates over the 54 pairs that have reads.
+- **Outcome.** 564 are frame-illegal. The 38 legal ones are all full single-pair exchanges, and only these 4 are positive. Their gains are additive.
+
+**What is not covered.** Cross-pair combinations of partial moves were not enumerated. Without a decomposition proof (moves can shrink as well as grow target frames), the result is exhaustive only within this single-pair family.
diff --git a/research/gauge44-slots/construction/sw4/SW4-RECIPE-P6k4.json b/research/gauge44-slots/construction/sw4/SW4-RECIPE-P6k4.json
new file mode 100644
index 0000000000..b9dea4152a
--- /dev/null
+++ b/research/gauge44-slots/construction/sw4/SW4-RECIPE-P6k4.json
@@ -0,0 +1,314 @@
+{
+ "name": "SW4",
+ "description": "BRoute read-set exchange on entering-copy pairs (h,r); indices refer to the input word B section",
+ "input_sha256": "0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073",
+ "output_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+ "pairs": {
+  "461": 25,
+  "581": 89,
+  "591": 415,
+  "603": 431
+ },
+ "moves": [
+  {
+   "kind": "h2r",
+   "h": 461,
+   "r": 25,
+   "read_index": 856,
+   "target": 168,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 27
+  },
+  {
+   "kind": "h2r",
+   "h": 461,
+   "r": 25,
+   "read_index": 1208,
+   "target": 128,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 26
+  },
+  {
+   "kind": "r2h",
+   "h": 461,
+   "r": 25,
+   "read_index": 873,
+   "target": 129,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 28,
+   "preread": [
+    "add",
+    129,
+    461,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 461,
+   "r": 25,
+   "read_index": 1193,
+   "target": 169,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 28,
+   "preread": [
+    "add",
+    169,
+    461,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 581,
+   "r": 89,
+   "read_index": 860,
+   "target": 171,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 58
+  },
+  {
+   "kind": "h2r",
+   "h": 581,
+   "r": 89,
+   "read_index": 1288,
+   "target": 192,
+   "coef": [
+    -1,
+    2
+   ],
+   "delete_preread_index": 59
+  },
+  {
+   "kind": "r2h",
+   "h": 581,
+   "r": 89,
+   "read_index": 953,
+   "target": 193,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 60,
+   "preread": [
+    "add",
+    193,
+    581,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 581,
+   "r": 89,
+   "read_index": 1197,
+   "target": 175,
+   "coef": [
+    -1,
+    2
+   ],
+   "insert_preread_before": 60,
+   "preread": [
+    "add",
+    175,
+    581,
+    1,
+    2
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 591,
+   "r": 415,
+   "read_index": 868,
+   "target": 139,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 62
+  },
+  {
+   "kind": "h2r",
+   "h": 591,
+   "r": 415,
+   "read_index": 1296,
+   "target": 160,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 63
+  },
+  {
+   "kind": "r2h",
+   "h": 591,
+   "r": 415,
+   "read_index": 961,
+   "target": 161,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 64,
+   "preread": [
+    "add",
+    161,
+    591,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 591,
+   "r": 415,
+   "read_index": 1205,
+   "target": 143,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 64,
+   "preread": [
+    "add",
+    143,
+    591,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "h2r",
+   "h": 603,
+   "r": 431,
+   "read_index": 876,
+   "target": 131,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 70
+  },
+  {
+   "kind": "h2r",
+   "h": 603,
+   "r": 431,
+   "read_index": 1300,
+   "target": 163,
+   "coef": [
+    1,
+    1
+   ],
+   "delete_preread_index": 71
+  },
+  {
+   "kind": "r2h",
+   "h": 603,
+   "r": 431,
+   "read_index": 965,
+   "target": 167,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 72,
+   "preread": [
+    "add",
+    167,
+    603,
+    -1,
+    1
+   ]
+  },
+  {
+   "kind": "r2h",
+   "h": 603,
+   "r": 431,
+   "read_index": 1213,
+   "target": 135,
+   "coef": [
+    1,
+    1
+   ],
+   "insert_preread_before": 72,
+   "preread": [
+    "add",
+    135,
+    603,
+    -1,
+    1
+   ]
+  }
+ ],
+ "kappa_ideal_in": 0.0016603565408383088,
+ "kappa_ideal_out": 0.0016606836036204419,
+ "W": 3778,
+ "profile_in": {
+  "1": 2572,
+  "2": 326,
+  "3": 430,
+  "4": 194,
+  "5": 56,
+  "8": 8
+ },
+ "profile_out": {
+  "1": 2548,
+  "2": 342,
+  "3": 438,
+  "4": 186,
+  "5": 56,
+  "8": 8
+ },
+ "width_inventory": {
+  "4": 80,
+  "5": 32,
+  "7": 54,
+  "8": 122,
+  "9": 216
+ },
+ "rejection_expected": {
+  "N1": {
+   "changed_registers": [
+    168,
+    171
+   ],
+   "n": 2
+  },
+  "N2": {
+   "first": [
+    "cap",
+    1192,
+    169
+   ],
+   "n": 10
+  },
+  "N3": {
+   "changed_registers": [
+    129,
+    130,
+    169,
+    170
+   ],
+   "n": 4
+  }
+ }
+}
diff --git a/research/gauge44-slots/construction/sw4/build_sw4.py b/research/gauge44-slots/construction/sw4/build_sw4.py
new file mode 100644
index 0000000000..617e0ed06d
--- /dev/null
+++ b/research/gauge44-slots/construction/sw4/build_sw4.py
@@ -0,0 +1,203 @@
+#!/usr/bin/env python3
+"""build_sw4.py INPUT_WORD OUT_DIR [RECIPE] : deterministic, standard-library-only rebuild of the BRoute SW4 word.
+
+SW4 exchanges the B-phase target read sets of four entering packet copies h and their face registers r
+(h = E_h + r after h's copy gate; E_h = h's entering content):
+  h2r: a post-copy read add(t,h,c) becomes add(t,r,c), and t's entrance pre-read add(t,h,-c) (taken while h = E_h) is deleted;
+  r2h: a read add(t,r,c) becomes add(t,h,c), and a pre-read add(t,h,-c) is inserted before index insert_preread_before
+       (right after h's last existing pre-read, still before h's copy gate).
+Every register holds the same value at the end of B (checked mod p). Frames: a moved or inserted gate gets the plain join of
+its operands' current frames; every other B gate and every early-cleanup tail keeps span(old frame + current operand frames).
+Targets must stay inside u_t^perp, and tails and ends must contain the current frame.
+
+Controls (run on every build; the count is pinned to 4 and all must hold, else exit 1):
+  C0 the identity recipe (no moves) reproduces the input B and early_cleanup byte for byte;
+  N1 h2r without deleting the pre-read is rejected by exactness;
+  N2 a partial exchange (one read only) is rejected by the frame cap;
+  N3 an inserted pre-read with the wrong sign is rejected by exactness.
+Rejection sites are pinned: the recipe's 'rejection_expected' gives, for N1/N3, the exact set of target rows whose B-end
+state changes (the mutated target plus its butterfly partner(s)) and, for N2, the first cap violation (kind, B index,
+register) and the violation count. Each control must reproduce its pinned site exactly. BUILD.json records the observed
+sites under 'rejection'.
+Writes OUT_DIR/FULL-WORD.json.gz (sha checked against the recipe) and OUT_DIR/BUILD.json."""
+import sys, json, gzip, hashlib, os
+from collections import Counter, defaultdict
+
+PR = 2147483629
+HERE = os.path.dirname(os.path.abspath(__file__))
+V, HH = 112, 9
+
+
+def basis(vs):
+    piv = {}
+    for a in vs:
+        while a:
+            bit = a.bit_length() - 1
+            if bit in piv: a ^= piv[bit]
+            else:
+                piv[bit] = a; break
+    for k in sorted(piv):
+        for j in piv:
+            if j > k and piv[j] >> k & 1: piv[j] ^= piv[k]
+    return tuple(piv[k] for k in sorted(piv, reverse=True))
+
+
+def contained(a, b): return basis(list(a) + list(b)) == tuple(b)
+def registers(e): return e[1:3] if e[0] == 'add' else e[1:2]
+def hyper(p): return basis([x for x in range(1, 1 << HH) if (x & p).bit_count() % 2 == 0])
+FULL = basis([1 << i for i in range(HH)])
+
+
+def coef(e):
+    a, b = (e[3], e[4]) if e[0] == 'add' else (e[2], e[3])
+    return a % PR * pow(b % PR, PR - 2, PR) % PR
+
+
+def bend_state(w):
+    """sparse rows mod p of every register after A + cut + B (identity start)."""
+    n = 2 * V + w['report']['R']; rows = [{i: 1} for i in range(n)]
+    for e in w['A'] + w['cut'] + w['B']:
+        q = coef(e); t = e[1]
+        if e[0] == 'scale': rows[t] = {k: x * q % PR for k, x in rows[t].items()}
+        else:
+            d = rows[t]
+            for k, x in rows[e[2]].items():
+                y = (d.get(k, 0) + q * x) % PR
+                if y: d[k] = y
+                else: d.pop(k, None)
+    return rows
+
+
+def apply_recipe(w, moves, drop_delete=False, wrong_sign=False):
+    B = [list(e[:-1]) + [list(e[-1]) if e[-1] is not None else None] for e in w['B']]
+    tag = {}; dele = set(); ins = defaultdict(list)
+    for m in moves:
+        i = m['read_index']; e = B[i]; t = m['target']; a, b = m['coef']
+        assert e[0] == 'add' and e[1] == t and [e[3], e[4]] == [a, b], ('recipe/word mismatch', m)
+        if m['kind'] == 'h2r':
+            assert e[2] == m['h']
+            pi = m['delete_preread_index']; g = B[pi]
+            assert g[:5] == ['add', t, m['h'], -a, b], ('pre-read mismatch', m)
+            B[i] = ['add', t, m['r'], a, b, e[-1]]
+            if not drop_delete: dele.add(pi)
+        else:
+            assert e[2] == m['r']
+            B[i] = ['add', t, m['h'], a, b, e[-1]]
+            g = list(m['preread'])
+            if wrong_sign: g[3] = -g[3]
+            ins[m['insert_preread_before']].append(g + [None])
+        tag[i] = 1
+    NB, nt = [], []
+    for i, e in enumerate(B):
+        for g in ins.get(i, []): NB.append(g); nt.append(1)
+        if i in dele: continue
+        NB.append(e); nt.append(tag.get(i, 0))
+    w2 = dict(w); w2['B'] = NB; w2['early_cleanup'] = [list(x) for x in w.get('early_cleanup', [])]
+    return w2, nt
+
+
+def refit(w, nt):
+    n = 2 * V + w['report']['R']
+    cur = [(p,) for p in w['ports']] + [()] * (n - V)
+    for q, U in w['start_extra'].items(): cur[int(q)] = basis(U)
+    for e in w['A']:
+        for q in registers(e): cur[q] = basis(e[-1])
+    prob = []
+    for i, e in enumerate(w['B']):
+        rs = registers(e)
+        base = [] if nt[i] or e[-1] is None else list(e[-1])
+        F = basis(base + [x for q in rs for x in cur[q]])
+        for q in rs:
+            if V <= q < 2 * V and not contained(F, hyper(w['ports'][q - V])): prob.append(('cap', i, q))
+        e[-1] = list(F)
+        for q in rs: cur[q] = F
+    ne = []
+    for i, U in w.get('early_cleanup', []):
+        rs = registers(w['cleanup'][i]); F = basis(list(U) + [x for q in rs for x in cur[q]])
+        for q in rs:
+            fin = w['helper_final'].get(str(q))
+            if fin is not None and not contained(F, basis(fin)): prob.append(('tail', i, q))
+        ne.append([i, list(F)])
+        for q in rs: cur[q] = F
+    w['early_cleanup'] = ne
+    for q in range(2 * V, n):
+        fin = w['helper_final'].get(str(q))
+        if fin is not None and not contained(cur[q], basis(fin)): prob.append(('end', q))
+    return prob
+
+
+def profile(w):
+    n = 2 * V + w['report']['R']
+    tail = [w['cleanup'][i][:-1] + [U] for i, U in w.get('early_cleanup', [])]
+    end = [FULL] * V + [hyper(p) for p in w['ports']] + [FULL] * (n - 2 * V)
+    for q, U in w['helper_final'].items(): end[int(q)] = basis(U)
+    start = [(p,) for p in w['ports']] + [()] * (n - V)
+    for q, U in w['start_extra'].items(): start[int(q)] = basis(U)
+    cur = list(start); paid = Counter()
+    def climb(q, U):
+        U = basis(U); assert contained(cur[q], U), ('monotone', q)
+        d = len(U) - len(cur[q])
+        if d: paid[d] += 1
+        cur[q] = U
+    for sec in ('A', 'B'):
+        if sec == 'B':
+            lev = {int(t): basis(U) for t, U in w.get('target_levels', {}).items()}
+            for q, U in zip(w['centers'], w['center_frames']):
+                U = basis(U); served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == q}
+                for T in sorted(served, key=lambda x: -len(x)):
+                    if T != U: paid[len(U) - len(T)] += 1
+                    U = T
+        for e in w[sec]:
+            for q in registers(e): climb(q, e[-1])
+    for e in tail:
+        for q in registers(e): climb(q, e[-1])
+    for q, U in enumerate(end): climb(q, U)
+    widths = Counter(len(end[q]) - len(start[q]) for q in range(2 * V, n))
+    return paid, widths
+
+
+def enc(w): return json.dumps(w, sort_keys=True, separators=(',', ':')).encode()
+
+
+def main():
+    src, out = sys.argv[1], sys.argv[2]
+    rec = json.load(open(sys.argv[3] if len(sys.argv) > 3 else os.path.join(HERE, 'SW4-RECIPE.json')))
+    raw = gzip.decompress(open(src, 'rb').read())
+    assert hashlib.sha256(raw).hexdigest() == rec['input_sha256'], 'input sha mismatch'
+    w = json.loads(raw); S0 = bend_state(w); moves = rec['moves']
+    h0 = moves[0]['h']; one = [m for m in moves if m['h'] == h0]
+    ctl = {}; why = {}; EXP = rec.get('rejection_expected', {})
+    if os.environ.get('SW4_PIN') != '1' and set(EXP) != {'N1', 'N2', 'N3'}: raise SystemExit('recipe rejection_expected must pin exactly N1, N2, N3 (set SW4_PIN=1 to record)')
+    def diff(S):
+        d = [q for q in range(len(S0)) if S[q] != S0[q]]
+        return dict(changed_registers=d[:8], n=len(d))
+    w0, nt0 = apply_recipe(w, []); p0 = refit(w0, nt0)
+    ctl['C0_identity'] = not p0 and w0['B'] == w['B'] and w0['early_cleanup'] == w['early_cleanup']
+    m1 = [m for m in one if m['kind'] == 'h2r'][:1]
+    w1, nt1 = apply_recipe(w, m1, drop_delete=True); d1 = diff(bend_state(w1))
+    ctl['N1_keep_preread_rejected'] = d1['n'] > 0 and d1 == EXP.get('N1', d1); why['N1'] = d1
+    w2, nt2 = apply_recipe(w, m1); p2 = refit(w2, nt2)
+    why['N2'] = dict(first=list(p2[0]) if p2 else None, n=len(p2)); ctl['N2_partial_rejected'] = bool(p2) and p2[0][0] == 'cap' and why['N2'] == EXP.get('N2', why['N2'])
+    w3, nt3 = apply_recipe(w, one, wrong_sign=True); d3 = diff(bend_state(w3))
+    ctl['N3_wrong_sign_rejected'] = d3['n'] > 0 and d3 == EXP.get('N3', d3); why['N3'] = d3
+    assert len(ctl) == 4
+    wn, nt = apply_recipe(w, moves); pr = refit(wn, nt)
+    assert not pr, ('illegal', pr[:5])
+    assert bend_state(wn) == S0, 'B-end state changed'
+    paid, widths = profile(wn)
+    wn['report'] = dict(wn['report'], local_profile={str(k): v for k, v in sorted(paid.items())},
+                        local_rank_mass=sum(k * v for k, v in paid.items()))
+    data = enc(wn); sha = hashlib.sha256(data).hexdigest()
+    os.makedirs(out, exist_ok=True)
+    with open(os.path.join(out, 'FULL-WORD.json.gz'), 'wb') as f: f.write(gzip.compress(data, mtime=0))
+    rep = dict(recipe=rec['name'], input_sha256=rec['input_sha256'], output_sha256=sha, expected_output_sha256=rec['output_sha256'],
+               moves=len(moves), controls=ctl, rejection=why, profile=wn['report']['local_profile'],
+               widths={str(k): v for k, v in sorted(widths.items()) if k}, W=sum(k * v for k, v in widths.items()))
+    with open(os.path.join(out, 'BUILD.json'), 'w', newline='\n') as f: f.write(json.dumps(rep, indent=1) + '\n')
+    print(json.dumps(rep, indent=1))
+    ok = all(ctl.values()) and sha == rec['output_sha256'] and rep['profile'] == rec['profile_out'] and rep['W'] == rec['W']
+    sys.exit(0 if ok else 1)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/construction/sw4/reproduce_sw4.py b/research/gauge44-slots/construction/sw4/reproduce_sw4.py
new file mode 100644
index 0000000000..cb038e064b
--- /dev/null
+++ b/research/gauge44-slots/construction/sw4/reproduce_sw4.py
@@ -0,0 +1,87 @@
+#!/usr/bin/env python3
+"""Rebuild the SW4 word (BRoute read-set exchange on four entering-copy pairs) and its native locals.
+
+Input: a fresh `construction/promo/reproduce_promo.py --base p6n --k <promo recipe>` output directory; its promoted
+word is pinned there and by SW4-RECIPE-<id>.json (this package: --k p6n-k4, P6k4 0390ec65..., recipe P6k4). Steps, each checked exactly:
+  1. sw4: BRoute's build_sw4.py (standard library only). It applies the 16 explicit moves of SW4-RECIPE-<id>.json:
+     every listed read of h becomes a read of its face register r and vice versa, with the entrance pre-reads deleted
+     or inserted. It checks the B-end state of every register mod p, the frame caps, tails and ends, and the output sha
+     and profile. Its controls C0, N1, N2 and N3 run on every build and must all hold (count pinned to 4).
+  2. layer-end-controls: ../layers_p6n/layer_end_controls.py (per-end variant, Q6Reviewer-signed) on the SW4 word;
+     the count is pinned in LOCAL-PINS-sw4-<id>.json.
+  3. native, ledgers, local-replay, wrappers, phases: PR635's native local programs. The canonical word, local
+     programs and Clifford recipes are pinned (LOCAL-PINS-sw4-<id>.json).
+Apache-2.0. Driver by ColdWitness around BRoute's constructor.
+"""
+import argparse, gzip, hashlib, json, os, subprocess, sys, time
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P6 = HERE.parent / 'layers_p6n'
+
+
+def read(p):
+    raw = Path(p).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(p).endswith('.gz') else raw)
+
+
+def main():
+    assert __debug__, 'Assertions are required'
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--promo-dir', type=Path, required=True, help='construction/promo/reproduce_promo.py output')
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--recipe', default='P6k4', help='SW4-RECIPE-<id>.json and LOCAL-PINS-sw4-<id>.json')
+    ap.add_argument('--skip-phases', action='store_true')
+    a = ap.parse_args()
+    out = a.out.resolve(); assert not out.exists(); out.mkdir(parents=True)
+    up = a.pr635.resolve() / 'research/complex-571-cold14-st2'
+    src = a.main.resolve() / 'research/complex-k492-owner-repair/vendor/multicold'
+    base = src / 'vendor/pr558'; parent = base / 'vendor/pr552'
+    rfile = HERE / ('SW4-RECIPE-%s.json' % a.recipe); rec = read(rfile); pins = read(HERE / ('LOCAL-PINS-sw4-%s.json' % a.recipe))
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               MULTICOLD_SOURCE=str(src), GAIN_PR564_SOURCE=str(src))
+    for k in ('PYTHONOPTIMIZE', 'XPARAM', 'EXTRAH', 'PAIRING_RANKS', 'DIAG', 'HYBBUDGET', 'PR635_CODE'): env.pop(k, None)
+    steps = []
+
+    def run(label, script, *args, portable=True):
+        t = time.monotonic()
+        cmd = [sys.executable, '-B'] + ([str(src / 'code/run_portable.py')] if portable else []) + [str(script), *map(str, args)]
+        with (out / (label + '.log')).open('w') as f:
+            rc = subprocess.call(cmd, env=env, stdout=f, stderr=subprocess.STDOUT)
+        steps.append(dict(step=label, exit_code=rc, seconds=round(time.monotonic() - t, 3)))
+        (out / 'STEPS.json').write_text(json.dumps(steps, indent=2) + '\n')
+        assert rc == 0, label
+        print('PASS', label, flush=True)
+
+    inp = a.promo_dir.resolve() / 'promo/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(inp.read_bytes())).hexdigest() == rec['input_sha256'], 'input must be the pinned promoted word'
+    run('sw4', HERE / 'build_sw4.py', inp, out / 'sw4', rfile, portable=False)
+    b = read(out / 'sw4/BUILD.json')
+    assert len(b['controls']) == pins['sw4_controls'] and all(b['controls'].values()), b['controls']
+    word = out / 'sw4/FULL-WORD.json.gz'
+    assert hashlib.sha256(gzip.decompress(word.read_bytes())).hexdigest() == rec['output_sha256']
+    routing = parent / 'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz'
+    env['PR635_CODE'] = str(up / 'code')
+    run('layer-end-controls', P6 / 'layer_end_controls.py', word, routing, out / 'controls')
+    env.pop('PR635_CODE')
+    ctl = read(out / 'controls/COLD-END-CONTROLS.json')
+    assert ctl['status'] == 'PASS_COLD_END_RAW_WORD_CONTROLS' and len(ctl['rejected']) == pins['layer_controls'], len(ctl['rejected'])
+    local = out / 'local'
+    run('native', up / 'code/hpe_audit_and_transport.py', '--raw', word, '--routing', routing, '--out', local)
+    assert hashlib.sha256(gzip.decompress((local / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() == pins['canonical_sha256'], 'canonical word'
+    run('ledgers', up / 'code/hpe_emit_local.py', local)
+    run('local-replay', up / 'code/hpe_audit_local.py', local)
+    run('wrappers', up / 'code/hpe_adapters_local.py', local / 'CANONICAL-WORD.json.gz',
+        local / 'RESIDUAL-ADAPTERS.json', local / 'WRAPPER-CHECKS.json')
+    checks = read(local / 'LOCAL-CHECKS.json')
+    for o, s in pins['program_sha256'].items(): assert checks[o]['sha256'] == s, ('local program', o)
+    if not a.skip_phases:
+        run('phases', base / 'code/phases_full.py', local, parent / 'complex-global/vendor531/vendor/clifford')
+        assert hashlib.sha256((local / 'CLIFFORD-RECIPES.json').read_bytes()).hexdigest() == pins['clifford_recipes_sha256'], 'clifford recipes'
+    print('DONE', local, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/data/FRONTIER.json b/research/gauge44-slots/data/FRONTIER.json
new file mode 100644
index 0000000000..70285d4d85
--- /dev/null
+++ b/research/gauge44-slots/data/FRONTIER.json
@@ -0,0 +1,36 @@
+{
+  "checked_at_utc": "2026-10-13 00:54:29 UTC",
+  "construction_base": {
+    "pr": 635,
+    "commit": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f",
+    "kappa": "0.001636241501576388"
+  },
+  "latest_pr": 642,
+  "strongest_reported_pr": 641,
+  "comparisons": [
+    {
+      "number": 641,
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/641",
+      "title": "Conditional κ = 0.001636523543003976: cost-neutral pivot swaps with four entering ends (s4) on PR635",
+      "head_sha": "ff580ea5407aa427d64233523e46ee0afe24a766",
+      "head_repo": "jeremykothe2/integer-mult-bounds",
+      "created_at": "2026-10-13T00:36:30Z",
+      "updated_at": "2026-10-13T00:36:30Z",
+      "reported_kappa": "0.001636523543003976"
+    },
+    {
+      "number": 642,
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/642",
+      "title": "Conditional κ = 0.001636472098484378: selective helper-249 dispatch",
+      "head_sha": "d1154e23e13d85fdbf64d4b41fa20bb0f56a428f",
+      "head_repo": "vectorsss/integer-mult-bounds",
+      "created_at": "2026-10-13T00:40:40Z",
+      "updated_at": "2026-10-13T00:46:54Z",
+      "reported_kappa": "0.001636472098484378"
+    }
+  ],
+  "new_kappa": "0.001649483702558979",
+  "gain_over_641_percent": "0.791932362379189601995955118466917211009518325743405547289975",
+  "gain_over_642_percent": "0.795100881136422911010672021375626721886288268207407873093008",
+  "scope": "PR641/642 values are their public reported conditional witnesses, not independently replayed here. This delta retains the pinned PR635 construction ancestry and replaces its local supplier and whole-owner dispatch; it does not claim to compose the later pivot swaps or helper249 end."
+}
diff --git a/research/gauge44-slots/data/OWNERS.json.gz b/research/gauge44-slots/data/OWNERS.json.gz
new file mode 100644
index 0000000000..8eda84ea0c
Binary files /dev/null and b/research/gauge44-slots/data/OWNERS.json.gz differ
diff --git a/research/gauge44-slots/data/PLAN.json b/research/gauge44-slots/data/PLAN.json
new file mode 100644
index 0000000000..0465492a1f
--- /dev/null
+++ b/research/gauge44-slots/data/PLAN.json
@@ -0,0 +1,40249 @@
+{
+  "status": "FROZEN_EXPLICIT_GAUGE44_WHOLE_OWNER_NOMINATION",
+  "mode": "gauge44-all72",
+  "K": 4,
+  "T": 8,
+  "M": 73,
+  "L": 9,
+  "live": 7168,
+  "deficit": 2560,
+  "profile": {
+    "1": 174763,
+    "2": 30105,
+    "3": 31283,
+    "4": 10224,
+    "5": 5904,
+    "7": 54,
+    "8": 576,
+    "16": 23,
+    "48": 2419
+  },
+  "order": [
+    [
+      0,
+      0
+    ],
+    [
+      0,
+      1
+    ],
+    [
+      1,
+      0
+    ],
+    [
+      0,
+      2
+    ],
+    [
+      1,
+      1
+    ],
+    [
+      2,
+      0
+    ],
+    [
+      0,
+      3
+    ],
+    [
+      1,
+      2
+    ],
+    [
+      2,
+      1
+    ],
+    [
+      3,
+      0
+    ],
+    [
+      0,
+      4
+    ],
+    [
+      1,
+      3
+    ],
+    [
+      2,
+      2
+    ],
+    [
+      3,
+      1
+    ],
+    [
+      4,
+      0
+    ],
+    [
+      0,
+      5
+    ],
+    [
+      1,
+      4
+    ],
+    [
+      2,
+      3
+    ],
+    [
+      3,
+      2
+    ],
+    [
+      4,
+      1
+    ],
+    [
+      5,
+      0
+    ],
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diff --git a/research/gauge44-slots/data/PREPARATION.json b/research/gauge44-slots/data/PREPARATION.json
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index 0000000000..8c7796820f
--- /dev/null
+++ b/research/gauge44-slots/data/PREPARATION.json
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index 0000000000..6ac06e4b75
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+        ],
+        "local_adapters": 387056,
+        "local_primitive_bound": 10038040553630,
+        "compiler": 25934336,
+        "children": 3494,
+        "paid_profile": {
+          "1": 2412,
+          "2": 418,
+          "3": 432,
+          "4": 142,
+          "5": 82,
+          "8": 8
+        },
+        "program_hashes": {
+          "backward": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23",
+          "forward": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+        },
+        "semantic_artifact_sha256": {
+          "CANONICAL-WORD.json.gz": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c",
+          "LOCAL-PROGRAMS.json.gz": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3",
+          "LOCAL-CHECKS.json": "18f09b79835aa352f04d27041d86d1338c5ad0094b888588c1c05af2dc399ffd",
+          "INDEPENDENT-LOCAL-REPLAY.json": "2d4680965c62db1fde1236c4857b19bf7bc97af58805e6b4109afbc452f0fdd8",
+          "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+          "CLIFFORD-REVIEW.json": "4960fd1215509b5347ef7f0092868f79aea0f8e24fb84352da9a1033e4394007",
+          "RESIDUAL-ADAPTERS.json": "c682e9ff1b347f89771c6800f46ad98c2bb92b91c5c88452d53a9e7f0180c35f"
+        }
+      },
+      "semantic_phase_sha256": "4960fd1215509b5347ef7f0092868f79aea0f8e24fb84352da9a1033e4394007",
+      "expected_local": {
+        "forward": {
+          "events": 24767,
+          "macros": 19693,
+          "real_component_primitives": 198766,
+          "prefix_l1": "2765345294379392599/1024",
+          "coefficient_work_primitive_count": 98333
+        },
+        "backward": {
+          "events": 24767,
+          "macros": 19693,
+          "real_component_primitives": 198814,
+          "prefix_l1": "14824960514781440791821/64",
+          "coefficient_work_primitive_count": 98365
+        }
+      },
+      "wrappers": 240
+    }
+  },
+  "expected": {
+    "gain_baseline_kappa": "0.001636241501576388",
+    "hosted_residuals": 34560,
+    "rank_mass": 520704,
+    "actual_73column_sigmas": 8899,
+    "cross_replica_helper_roles": 27858,
+    "idle_remainders": 3783,
+    "idle_remainder_profile": {
+      "1": 1099,
+      "2": 9,
+      "3": 179,
+      "7": 54,
+      "16": 23,
+      "48": 2419
+    },
+    "global_profile": {
+      "1": 174763,
+      "2": 30105,
+      "3": 31283,
+      "4": 10224,
+      "5": 5904,
+      "7": 54,
+      "8": 576,
+      "16": 23,
+      "48": 2419
+    },
+    "live": 7168,
+    "physical": 7658,
+    "conservative_kappa_decimal": "0.001671665280368335",
+    "kappa_decimal": "0.00167166528321877",
+    "complex_lower": "837232213634911250061/500000000000000000000000",
+    "conservative_complex_lower": "104654026525614565773/62500000000000000000000",
+    "kappa": "167166528321877/100000000000000000",
+    "assembly_controls_rejected": 69,
+    "provider_counts": {
+      "gauge44": 72
+    },
+    "mutations_rejected": 15
+  },
+  "pivot_swap": {
+    "recipe": "construction/leaver/PIVOT-SWAP-k8.json",
+    "sha256": "3ef7acf0cf67442a532f25b53d5fbeda76d3a84524118df8e003ca69b5cac0bb"
+  }
+}
diff --git a/research/gauge44-slots/data/UPSTREAM-PINS.json b/research/gauge44-slots/data/UPSTREAM-PINS.json
new file mode 100644
index 0000000000..68486b84e3
--- /dev/null
+++ b/research/gauge44-slots/data/UPSTREAM-PINS.json
@@ -0,0 +1,23 @@
+{
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-RECIPES.json": "534ace870cabe515987e00f50f71550030965006ea18978e0924590ac6944345",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-REVIEW.json": "ee9b86428278392d2c933f76d60e51f5af90d4ab67e4d3937ed2fa416e7755ab",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-LOCAL-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INTEGRATION.json": "5c14538134dfffbc58fa4b4d2f26b270ec5f56d17d4bf23752c82964f45171db",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-CHECKS.json": "79177449e404403964ce1b2f4a9a8bd49e1916daba3123d7fd7f5cfd1f1ac0ea",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-PROGRAMS.json.gz": "99a18eede965accf65943e490b8d2b2ffb9f1c9bc6babdb825413a80cbea2cde",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/RESIDUAL-ADAPTERS.json": "baafef737acc16dafbe1150896feb16744f3d669fa123bb2bff19ecc4e71b275",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/SCALAR-FRAME-AUDIT.json": "73b3601a6239502475a272ea0c46945fd42034486aaf43e66a212eb4f012ca44",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/WRAPPER-CHECKS.json": "9a09146e686c4f535b04fdef3753fe01dad8f5e8881a69408a91394acb5b48f5",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+  "research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py": "322d29d43dbee8130cde15d4bf05396698b5e3dfe3735813899db91cc0ba7955",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+  "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+  "research/complex-k492-owner-repair/vendor/multicold/inputs/PR543-EXPECTED.json": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz": "025448abdf2012d327e50a009084e1501690d05e650300d2982836aa0350ae00",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz": "de2be0f4b6d24ace368fd5b834b7a00f9625d0a1824c4ff969f2db5f115db667",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/prepare_supplier_base.py": "f5eae94aca965d0008bc07cff8245ccb7509042ccad457d3bcb7d51c1e9409f0"
+}
diff --git a/research/gauge44-slots/evidence/ADMISSION-CONTROLS.json b/research/gauge44-slots/evidence/ADMISSION-CONTROLS.json
new file mode 100644
index 0000000000..2e15a10065
--- /dev/null
+++ b/research/gauge44-slots/evidence/ADMISSION-CONTROLS.json
@@ -0,0 +1,102 @@
+{
+  "status": "PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS",
+  "valid_receipt_kappa": "1649483702558979/1000000000000000000",
+  "input_sha256": {
+    "owner_audit": "a32ecc0d5387d65648e1ff284209122860ee37aaba43ce2dd12024c4bc394313",
+    "fresh_invoice": "14b0f41c88209e800236ce4ebbf91d83537e22e18807153d90013f7eee57a582",
+    "inputs/PR543-EXPECTED.json": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d",
+    "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+  },
+  "assembler_sha256": "7ac28118d69416e4fb67b61216285fb0823310b7635ce1b9025aa3f10119ef6a",
+  "rejected_controls": [
+    "empty_certification_maps",
+    "failed_invoice_status",
+    "nonboolean_precision_check",
+    "wrong_owner_role_count",
+    "understated_physical_stock",
+    "changed_profile_same_rank_mass",
+    "insufficient_finite_C0",
+    "missing_finite_check",
+    "wrong_reflected_orientation_selfconsistent_totals",
+    "missing_selected_call",
+    "wrong_selected_primitive_sum",
+    "wrong_selected_coefficient_work_sum",
+    "unpaid_wrapper_factors",
+    "wrong_global_compiler",
+    "wrong_global_adapter_maximum",
+    "understated_exact_prefix_and_global_sum",
+    "wrong_global_prefix_sum",
+    "wrong_row_prefix_reserve",
+    "wrong_parent_geometry_charge",
+    "wrong_rebased_geometry_charge",
+    "wrong_complete_pervertex_envelope",
+    "wrong_prior_added_complete_invoice",
+    "wrong_finite_router_bits",
+    "wrong_finite_literal_bits",
+    "wrong_finite_physical_stock_bits",
+    "wrong_finite_row_coefficient",
+    "reordered_complete_calls",
+    "understated_explicit_idle_remainders",
+    "understated_actual_chart_types",
+    "wrong_cross_replica_role_count",
+    "old_no_cold_wrapper_counts_selfconsistent",
+    "gauge44:missing_provider",
+    "gauge44:missing_backward_orientation",
+    "gauge44:unpaid_scalar_primitive",
+    "gauge44:wrong_local_artifact_binding",
+    "gauge44:false_dirty_restoration",
+    "gauge44:wrong_declared_provider_count",
+    "gauge44:wrong_local_compiler",
+    "gauge44:wrong_local_adapter_charge",
+    "gauge44:wrong_local_primitive_bound",
+    "gauge44:forged_provider_and_call_program_hash",
+    "gauge44:provider_at_wrong_call",
+    "gauge44:synchronized_forged_source_recipe_hash",
+    "gauge44:synchronized_forged_phase_review_semantics",
+    "gauge44:width_order_swap_4_5",
+    "gauge44:width_inventory_shift_4_5",
+    "gauge44:width_order_swap_4_7",
+    "gauge44:width_inventory_shift_4_7",
+    "gauge44:width_order_swap_4_8",
+    "gauge44:width_inventory_shift_4_8",
+    "gauge44:width_order_swap_4_9",
+    "gauge44:width_inventory_shift_4_9",
+    "gauge44:width_order_swap_5_7",
+    "gauge44:width_inventory_shift_5_7",
+    "gauge44:width_order_swap_5_8",
+    "gauge44:width_inventory_shift_5_8",
+    "gauge44:width_order_swap_5_9",
+    "gauge44:width_inventory_shift_5_9",
+    "gauge44:width_order_swap_7_8",
+    "gauge44:width_inventory_shift_7_8",
+    "gauge44:width_order_swap_7_9",
+    "gauge44:width_inventory_shift_7_9",
+    "gauge44:width_order_swap_8_9",
+    "gauge44:width_inventory_shift_8_9",
+    "gauge44:cold_helper_width_swap_264",
+    "gauge44:cold_helper_width_swap_276",
+    "gauge44:cold_helper_width_swap_288",
+    "gauge44:cold_helper_width_swap_300",
+    "wrong_owner_receipt_hash"
+  ],
+  "discovery_accepted_controls": [],
+  "exact_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "conservative_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "recurrence_model_controls": [
+    "native_complex_endpoint_rejected_with_old_surcharge",
+    "omitting_bit_surcharge_would_fail_next_endpoint_rejection"
+  ],
+  "scope": "Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay."
+}
diff --git a/research/gauge44-slots/evidence/ASSEMBLY.json b/research/gauge44-slots/evidence/ASSEMBLY.json
new file mode 100644
index 0000000000..6feaaf28f5
--- /dev/null
+++ b/research/gauge44-slots/evidence/ASSEMBLY.json
@@ -0,0 +1,336 @@
+{
+  "status": "PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY",
+  "kappa": "1649483702558979/1000000000000000000",
+  "kappa_decimal": "0.001649483702558979",
+  "complex_lower": "1652208994368411824947/1000000000000000000000000",
+  "complex_decimal": "0.001652208994368411824947",
+  "bit_lower": "413456747036699736067/250000000000000000000000",
+  "bit_decimal": "0.001653826988146798944268",
+  "binding": "complex",
+  "gain_over_pr635_percent": "0.8093060205252829126484020359439672024956960385078942889840023844750830",
+  "complex_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
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+    "dimension_above_kappa": "499173895502815794472389376128951164793500479031415635616728978013400389902889300467483577877872753169445986011143172018378864998277686263802972870025639588088018108048266929997769582939230730780453685013440517758709347288500697481097612660777232276430370629988241720150824532464270561234015101138832024606244659306012459589468535547702828206730115013606136254794226859986030391904901589159511543091230174460327668139841639581/500826104497184205912446378819753771724889601254973369146461701558231026180446074958006802781550093752903233596741463898660609484278691810993420233589625890847508635094728855280196408981311845086875719069496776828962249839935690040003758181962602274220043524332460570130345585371869482720913013050263020200194570469939599151461082519436271959147262026364397400719510424912835469344370025591080557542210211361000000000000000000"
+  },
+  "controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the same cited unchanged PR543 bit supplier as PR635. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/gauge44-slots/evidence/BINDING.json b/research/gauge44-slots/evidence/BINDING.json
new file mode 100644
index 0000000000..b03160c67a
--- /dev/null
+++ b/research/gauge44-slots/evidence/BINDING.json
@@ -0,0 +1,25 @@
+{
+  "status": "PASS_FROZEN_048_ALLCOLD_DISPATCH_FRESH_PROVIDER_BINDING",
+  "source_plan_sha256": "8c4804859aee83082196348c33127070d2885d3a366ce9acc8dc5166202f4687",
+  "runtime_plan_sha256": "609adb126d7d3de2abdd9275f9015589c0b137d0d19821c2c3e7c1a8541c18d2",
+  "providers": {
+    "gauge44": {
+      "artifact_sha256": {
+        "CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+        "LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+        "LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+        "INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+        "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+        "CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12",
+        "RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94"
+      },
+      "canonical_content_sha256": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+      "all_phase_edges": 3019
+    }
+  },
+  "only_rebound_fields": [
+    "provider_registry.directory",
+    "provider_registry.artifact_sha256",
+    "runtime_source_plan_sha256"
+  ]
+}
diff --git a/research/gauge44-slots/evidence/CENTER-COMPATIBILITY.json b/research/gauge44-slots/evidence/CENTER-COMPATIBILITY.json
new file mode 100644
index 0000000000..5a3ae37422
--- /dev/null
+++ b/research/gauge44-slots/evidence/CENTER-COMPATIBILITY.json
@@ -0,0 +1,112 @@
+{
+  "status": "PASS_IDENTICAL_PORT_ORDER_AND_ORDERED_CENTER_FRAMES",
+  "new_canonical_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+  "comparison_canonical": "pr635/research/community-k492-audit/pr626/replay/mixed-global/base/split-centres/CANONICAL-WORD.json.gz",
+  "comparison_canonical_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+  "new_centers": [
+    92,
+    57,
+    81,
+    224,
+    11,
+    240,
+    9,
+    256
+  ],
+  "old_centers": [
+    229,
+    224,
+    227,
+    225,
+    243,
+    241,
+    259,
+    257
+  ],
+  "ordered_center_frames": [
+    [
+      256,
+      128,
+      64,
+      34,
+      16,
+      10,
+      4,
+      1
+    ],
+    [
+      256,
+      128,
+      64,
+      32,
+      16,
+      8,
+      5,
+      3
+    ],
+    [
+      256,
+      128,
+      64,
+      32,
+      17,
+      9,
+      4,
+      2
+    ],
+    [
+      256,
+      128,
+      64,
+      36,
+      20,
+      8,
+      2,
+      1
+    ],
+    [
+      256,
+      128,
+      66,
+      32,
+      18,
+      8,
+      4,
+      1
+    ],
+    [
+      256,
+      128,
+      65,
+      33,
+      17,
+      9,
+      5,
+      3
+    ],
+    [
+      256,
+      128,
+      65,
+      33,
+      16,
+      8,
+      4,
+      2
+    ],
+    [
+      256,
+      128,
+      68,
+      32,
+      16,
+      12,
+      2,
+      1
+    ]
+  ],
+  "v": 112,
+  "h": 9,
+  "center_count": 8,
+  "scope": "Carrier register identity changes; native cut center channels retain exact ordered frames and ports. Full endpoint and exact center clearing are independently checked by local ledger replay."
+}
diff --git a/research/gauge44-slots/evidence/LOCAL-STAGES.json b/research/gauge44-slots/evidence/LOCAL-STAGES.json
new file mode 100644
index 0000000000..b2753eb57a
--- /dev/null
+++ b/research/gauge44-slots/evidence/LOCAL-STAGES.json
@@ -0,0 +1,27 @@
+[
+  {
+    "tag": "44-native",
+    "seconds": 4.460461161999774,
+    "exit": 0
+  },
+  {
+    "tag": "44-emitted-ledgers",
+    "seconds": 3.058037757999955,
+    "exit": 0
+  },
+  {
+    "tag": "44-local-replay",
+    "seconds": 28.33760359400003,
+    "exit": 0
+  },
+  {
+    "tag": "44-wrappers",
+    "seconds": 5.294312295000054,
+    "exit": 0
+  },
+  {
+    "tag": "44-phase",
+    "seconds": 198.39076561599995,
+    "exit": 0
+  }
+]
diff --git a/research/gauge44-slots/evidence/REPLAY.json b/research/gauge44-slots/evidence/REPLAY.json
new file mode 100644
index 0000000000..c6f4e0f983
--- /dev/null
+++ b/research/gauge44-slots/evidence/REPLAY.json
@@ -0,0 +1,54 @@
+{
+  "status": "PASS_GAUGE44_STRICT_GLOBAL_REPLAY",
+  "kappa": "1649483702558979/1000000000000000000",
+  "kappa_decimal": "0.001649483702558979",
+  "complex_lower": "1652208994368411824947/1000000000000000000000000",
+  "bit_lower": "413456747036699736067/250000000000000000000000",
+  "gain_over_pr635_percent": "0.8093060205252829126484020359439672024956960385078942889840023844750830",
+  "spec_sha256": "fee57674a7f36b30b1e7eb96a8f567a90a522217bc644c1a6a1f8bff85196fbf",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 2.152,
+      "exit_code": 0,
+      "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.686,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "emit",
+      "seconds": 5.456,
+      "exit_code": 0,
+      "log_sha256": "60866eb6ced5b9eb259bfc1d59ea7b80fb439164b629e868586ad5bef845a88e"
+    },
+    {
+      "name": "audit",
+      "seconds": 26.943,
+      "exit_code": 0,
+      "log_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662"
+    },
+    {
+      "name": "invoice",
+      "seconds": 1.897,
+      "exit_code": 0,
+      "log_sha256": "5d10712d494304287749dd7a6c3369f9b707bba30e9f567b68230669dcf5418a"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.724,
+      "exit_code": 0,
+      "log_sha256": "768d3215f1918117dc6c33b4cfeaf0b5f5da9ba5c77178db4bb1d08d000e226f"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 0.816,
+      "exit_code": 0,
+      "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+    }
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the same cited unchanged PR543 bit supplier as PR635. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/gauge44-slots/evidence/STAGES.json b/research/gauge44-slots/evidence/STAGES.json
new file mode 100644
index 0000000000..9464e2dfea
--- /dev/null
+++ b/research/gauge44-slots/evidence/STAGES.json
@@ -0,0 +1,44 @@
+[
+  {
+    "name": "restore-parent",
+    "seconds": 2.152,
+    "exit_code": 0,
+    "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+  },
+  {
+    "name": "bind",
+    "seconds": 0.686,
+    "exit_code": 0,
+    "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+  },
+  {
+    "name": "emit",
+    "seconds": 5.456,
+    "exit_code": 0,
+    "log_sha256": "60866eb6ced5b9eb259bfc1d59ea7b80fb439164b629e868586ad5bef845a88e"
+  },
+  {
+    "name": "audit",
+    "seconds": 26.943,
+    "exit_code": 0,
+    "log_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662"
+  },
+  {
+    "name": "invoice",
+    "seconds": 1.897,
+    "exit_code": 0,
+    "log_sha256": "5d10712d494304287749dd7a6c3369f9b707bba30e9f567b68230669dcf5418a"
+  },
+  {
+    "name": "assembly",
+    "seconds": 0.724,
+    "exit_code": 0,
+    "log_sha256": "768d3215f1918117dc6c33b4cfeaf0b5f5da9ba5c77178db4bb1d08d000e226f"
+  },
+  {
+    "name": "admission-controls",
+    "seconds": 0.816,
+    "exit_code": 0,
+    "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+  }
+]
diff --git a/research/gauge44-slots/evidence/audit/ASYNC-AUDIT.json b/research/gauge44-slots/evidence/audit/ASYNC-AUDIT.json
new file mode 100644
index 0000000000..05975382b5
--- /dev/null
+++ b/research/gauge44-slots/evidence/audit/ASYNC-AUDIT.json
@@ -0,0 +1,84 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "complex_template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "complex_live": 7168,
+  "complex_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "complex_hosted_residuals": 35424,
+  "physical": 7670,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "entering_helper_roles": 17856,
+  "cross_replica_helper_roles": 25937,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 35424,
+  "complete_invocations": 72,
+  "actual_orthogonal_73column_maps": 7870,
+  "actual_sigma_stream_sha256": "f4e9802acb2ed53fc1f0486e7d0f55a6faa30ed7f5d2ad48a06450234b00ba76",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 2759,
+  "mutations_rejected": [
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit idle remainder",
+    "understate physical reserve",
+    "gauge44: wrong provider at its invocation",
+    "gauge44: stale per-call local program hash",
+    "gauge44: stale serialized provider program",
+    "gauge44: unbound residual adapter hash",
+    "gauge44: wrong provider width registry",
+    "gauge44: wrong per-call residual width",
+    "gauge44: wrong sweep provider",
+    "gauge44: entering helper width silently restored to nine"
+  ],
+  "mutation_controls_run": true,
+  "provider_phase_semantic_sha256": {
+    "gauge44": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152"
+  },
+  "provider_artifact_semantic_sha256": {
+    "gauge44": {
+      "CANONICAL-WORD.json.gz": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+      "LOCAL-PROGRAMS.json.gz": "39b230dba9e6b022c691cd0167f331c1b3fa6795d49256e3a2b859c68d4acfda",
+      "LOCAL-CHECKS.json": "bd53e0cca4488f365ca5b7c7174d8dfb35ced5e0229835f27334c11c3d839717",
+      "INDEPENDENT-LOCAL-REPLAY.json": "adb5c8ce0b5025dcd96f41b9fa0e26b9a176e067ab36a5bfadad00bc19522b38",
+      "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+      "CLIFFORD-REVIEW.json": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152",
+      "RESIDUAL-ADAPTERS.json": "c233611dd4c08c389dfb6c7d1c84dd86a3efa560223fcd6549a2848692541cd9"
+    }
+  },
+  "widths_by_provider": {
+    "gauge44": {
+      "4": 52,
+      "5": 48,
+      "7": 34,
+      "8": 114,
+      "9": 244
+    }
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "all_provider_program_phase_and_wrapper_bindings": true,
+  "scope": "Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations."
+}
diff --git a/research/gauge44-slots/evidence/audit/GLOBAL-PREFIX.json b/research/gauge44-slots/evidence/audit/GLOBAL-PREFIX.json
new file mode 100644
index 0000000000..a557ebbe60
--- /dev/null
+++ b/research/gauge44-slots/evidence/audit/GLOBAL-PREFIX.json
@@ -0,0 +1,13 @@
+{
+  "status": "PASS_MIXED_ASYNC_GLOBAL_PREFIX",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "global_prefix_bits": 360,
+  "retained_payload_bits": 512,
+  "complete_invocation_cover_sweeps": 72,
+  "bridge_factor_two_sweeps": 72,
+  "local_scalar_coefficient_work_prefix_bits": 175,
+  "stream_input_sup_to_l2_bits": 37,
+  "primitive_arithmetic_margin_bits": 4,
+  "controller_audit_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662",
+  "proof": "Each selected normalized provider restores all arbitrary dirty helper columns and gives the same data shear endpoints. Actual whole-owner charts are right-translation bijections. Sum all 72 invocation and 72 bridge sweeps and take maximum local scalar/Horner prefix over all three providers and orientations. Idle children, phases, spectator endpoints and terminal translations are unitary. Retained all-size interfaces are conditional."
+}
diff --git a/research/gauge44-slots/evidence/audit/IDLE-REMAINDER-FRAMES.json b/research/gauge44-slots/evidence/audit/IDLE-REMAINDER-FRAMES.json
new file mode 100644
index 0000000000..1c86a8a01d
--- /dev/null
+++ b/research/gauge44-slots/evidence/audit/IDLE-REMAINDER-FRAMES.json
@@ -0,0 +1,25 @@
+{
+  "status": "PASS_LITERAL_IDLE_REMAINDER_FRAMES",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "uncompressed_frames_sha256": "38eba7dfe023d0b2a8aea1c5184e50bdfff5727b350c2de4d27800acbdd3708c",
+  "children": 2759,
+  "rank_profile": {
+    "1": 85,
+    "2": 76,
+    "3": 173,
+    "7": 7,
+    "8": 6,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "source_data_phase_sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+  "scope": "Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child."
+}
diff --git a/research/gauge44-slots/evidence/audit/OWNERS-AND-PROFILE.json b/research/gauge44-slots/evidence/audit/OWNERS-AND-PROFILE.json
new file mode 100644
index 0000000000..bdb9441b7e
--- /dev/null
+++ b/research/gauge44-slots/evidence/audit/OWNERS-AND-PROFILE.json
@@ -0,0 +1,61 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "paid_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "live": 7168,
+  "physical": 7670,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "hosted_residuals": 35424,
+  "banked_residuals": 0,
+  "all_live_owners_per_call_distinct": true,
+  "owners_per_call": 716,
+  "actual_helper_owner_charts": 35424,
+  "actual_73column_sigmas": 7870,
+  "cross_replica_helper_roles": 25937,
+  "explicit_idle_remainder_children": 2759,
+  "source_idle_children_charged": 16128,
+  "source_artifacts": {
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "providers/gauge44/CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+    "providers/gauge44/LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+    "providers/gauge44/LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+    "providers/gauge44/INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+    "providers/gauge44/RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94",
+    "providers/gauge44/CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+    "providers/gauge44/CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12"
+  },
+  "provider_phase_semantic_sha256": {
+    "gauge44": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152"
+  },
+  "provider_artifact_semantic_sha256": {
+    "gauge44": {
+      "CANONICAL-WORD.json.gz": "e6daee410e04d5e023faf21144081534ad222d334ce786e6b5f52407e6b3c41f",
+      "LOCAL-PROGRAMS.json.gz": "39b230dba9e6b022c691cd0167f331c1b3fa6795d49256e3a2b859c68d4acfda",
+      "LOCAL-CHECKS.json": "bd53e0cca4488f365ca5b7c7174d8dfb35ced5e0229835f27334c11c3d839717",
+      "INDEPENDENT-LOCAL-REPLAY.json": "adb5c8ce0b5025dcd96f41b9fa0e26b9a176e067ab36a5bfadad00bc19522b38",
+      "CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+      "CLIFFORD-REVIEW.json": "1b4aa8bf9185b423e3f29e0ee2eb4d7082e2408c2b09cba1ef02282282731152",
+      "RESIDUAL-ADAPTERS.json": "c233611dd4c08c389dfb6c7d1c84dd86a3efa560223fcd6549a2848692541cd9"
+    }
+  },
+  "controller_audit_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662"
+}
diff --git a/research/gauge44-slots/evidence/audit/PREFIX-AND-INVOICE.json b/research/gauge44-slots/evidence/audit/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..6c96ec6706
--- /dev/null
+++ b/research/gauge44-slots/evidence/audit/PREFIX-AND-INVOICE.json
@@ -0,0 +1,1746 @@
+{
+  "status": "PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "parent_template_sha256": "7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3",
+  "owner_audit_sha256": "a32ecc0d5387d65648e1ff284209122860ee37aaba43ce2dd12024c4bc394313",
+  "controller_audit_sha256": "df19a41a599bf24fd1efaeb2394af63208f95b9e3ca4f83c6f23e9641fb3d662",
+  "providers": {
+    "gauge44": {
+      "local": {
+        "backward": {
+          "events": 46772,
+          "macros": 41570,
+          "real_component_primitives": 420100,
+          "prefix_l1": "600338326363508935771850050281004728884643/32",
+          "prefix_bits": 134,
+          "coefficient_work_primitive_count": 208744,
+          "all_exact_columns": 716,
+          "dirty_helper_columns": 492,
+          "all_dirty_helper_columns_restored": true,
+          "private_centres_and_coefficient_work_cleared": true,
+          "pre_wrappers": 248,
+          "post_wrappers": 248,
+          "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+        },
+        "forward": {
+          "events": 46772,
+          "macros": 41570,
+          "real_component_primitives": 420052,
+          "prefix_l1": "2323449462751823289130723296176889733365478515961323543/64",
+          "prefix_bits": 175,
+          "coefficient_work_primitive_count": 208712,
+          "all_exact_columns": 716,
+          "dirty_helper_columns": 492,
+          "all_dirty_helper_columns_restored": true,
+          "private_centres_and_coefficient_work_cleared": true,
+          "pre_wrappers": 248,
+          "post_wrappers": 248,
+          "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+        }
+      },
+      "helpers": 492,
+      "centres": 8,
+      "v": 112,
+      "h": 9,
+      "n": 716,
+      "entering_helpers": 204,
+      "entrance_rank": 380,
+      "terminal_codimension": 254,
+      "hyperplane_ended_helpers": 78,
+      "cold_hyperplane_ended_helpers": 44,
+      "width_inventory": {
+        "4": 52,
+        "5": 48,
+        "7": 34,
+        "8": 114,
+        "9": 244
+      },
+      "widths": [
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+      "replica": 6,
+      "provider_id": "gauge44",
+      "orientation": "backward",
+      "program_sha256": "4772df0663f88cc218fd7254eb202f46daf136c06e9e96c19ed8ea218b545dc4",
+      "events": 46772,
+      "macros": 41570,
+      "real_component_primitives": 420100,
+      "coefficient_work_primitive_count": 208744,
+      "entering_helpers": 204,
+      "entrance_rank": 380,
+      "pre_wrappers": 248,
+      "post_wrappers": 248
+    },
+    {
+      "stage": 8,
+      "replica": 5,
+      "provider_id": "gauge44",
+      "orientation": "forward",
+      "program_sha256": "d17399c8c7458bb7110d8596fab5f769cd4cb3733a3042277fa08bf03f42d6c9",
+      "events": 46772,
+      "macros": 41570,
+      "real_component_primitives": 420052,
+      "coefficient_work_primitive_count": 208712,
+      "entering_helpers": 204,
+      "entrance_rank": 380,
+      "pre_wrappers": 248,
+      "post_wrappers": 248
+    },
+    {
+      "stage": 7,
+      "replica": 7,
+      "provider_id": "gauge44",
+      "orientation": "backward",
+      "program_sha256": "4772df0663f88cc218fd7254eb202f46daf136c06e9e96c19ed8ea218b545dc4",
+      "events": 46772,
+      "macros": 41570,
+      "real_component_primitives": 420100,
+      "coefficient_work_primitive_count": 208744,
+      "entering_helpers": 204,
+      "entrance_rank": 380,
+      "pre_wrappers": 248,
+      "post_wrappers": 248
+    },
+    {
+      "stage": 8,
+      "replica": 6,
+      "provider_id": "gauge44",
+      "orientation": "forward",
+      "program_sha256": "d17399c8c7458bb7110d8596fab5f769cd4cb3733a3042277fa08bf03f42d6c9",
+      "events": 46772,
+      "macros": 41570,
+      "real_component_primitives": 420052,
+      "coefficient_work_primitive_count": 208712,
+      "entering_helpers": 204,
+      "entrance_rank": 380,
+      "pre_wrappers": 248,
+      "post_wrappers": 248
+    },
+    {
+      "stage": 8,
+      "replica": 7,
+      "provider_id": "gauge44",
+      "orientation": "forward",
+      "program_sha256": "d17399c8c7458bb7110d8596fab5f769cd4cb3733a3042277fa08bf03f42d6c9",
+      "events": 46772,
+      "macros": 41570,
+      "real_component_primitives": 420052,
+      "coefficient_work_primitive_count": 208712,
+      "entering_helpers": 204,
+      "entrance_rank": 380,
+      "pre_wrappers": 248,
+      "post_wrappers": 248
+    }
+  ],
+  "selected_local_paid_profile": {
+    "1": 181008,
+    "2": 29088,
+    "3": 32256,
+    "4": 11520,
+    "5": 4032,
+    "8": 576
+  },
+  "selected_real_component_primitives": 30245280,
+  "selected_coefficient_work_primitive_count": 15028288,
+  "selected_scalar_macros": 2993040,
+  "global_prefix_bits": 360,
+  "charged_prefix_bits": 512,
+  "complete_invocation_sweeps": 72,
+  "bridge_sweeps": 72,
+  "row_prefix_extra": 1024,
+  "helpers": 492,
+  "centres": 8,
+  "live": 7168,
+  "physical": 7670,
+  "physical_stock_identity": {
+    "data_and_owner_families": 7168,
+    "local_helpers": 492,
+    "private_centres": 8,
+    "coefficient_work": 2
+  },
+  "local_adapters": 738816,
+  "local_primitive_bound": 19160702806276,
+  "wrapper_elementary_factors_charged": 5142528,
+  "factors_per_wrapper": 144,
+  "compiler": 25934336,
+  "unhosted_pervertex": 2486201168471768,
+  "hosted_rebased_pervertex": 2486201168171612,
+  "conservative_pervertex_used": 5364148158196336,
+  "retained_prior_overcharge": {
+    "sha256": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+    "previous_pervertex_allowance": 2877946989724568,
+    "added_complete_new_pervertex": 2486201168471768,
+    "policy": "Retain old allowance and add entire fresh mixed recount."
+  },
+  "finite": {
+    "physical_stock_bits": 2641,
+    "router_bits": 7986,
+    "literal_bits": 35282,
+    "physical_row_coefficient": 16467,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. All three providers use fresh hash-bound independent all-column/frame/phase/normalization admission. Shared compiler uses conservative maxima; parent is geometry/overcharge only. All-size compiler, hosting, precision/tape and analytic transfer remain conditional."
+}
diff --git a/research/gauge44-slots/evidence/global/ACTUAL-SIGMAS.json.gz b/research/gauge44-slots/evidence/global/ACTUAL-SIGMAS.json.gz
new file mode 100644
index 0000000000..dbb57066e2
Binary files /dev/null and b/research/gauge44-slots/evidence/global/ACTUAL-SIGMAS.json.gz differ
diff --git a/research/gauge44-slots/evidence/global/GLOBAL-TEMPLATE.json.gz b/research/gauge44-slots/evidence/global/GLOBAL-TEMPLATE.json.gz
new file mode 100644
index 0000000000..424c2df489
Binary files /dev/null and b/research/gauge44-slots/evidence/global/GLOBAL-TEMPLATE.json.gz differ
diff --git a/research/gauge44-slots/evidence/global/HOSTED.json b/research/gauge44-slots/evidence/global/HOSTED.json
new file mode 100644
index 0000000000..498e849ab7
--- /dev/null
+++ b/research/gauge44-slots/evidence/global/HOSTED.json
@@ -0,0 +1,60 @@
+{
+  "status": "EMITTED_MIXED_PROVIDER_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE",
+  "template_sha256": "0c2aab7dc120f5882a0171496cbbe819cac81373dcb425802a15f45e36898a46",
+  "parent_template_sha256": "7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3",
+  "live": 7168,
+  "physical": 7670,
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "hosted_residuals": 35424,
+  "banks_per_stage": [
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0
+  ],
+  "entering_helper_roles": 17856,
+  "unique_actual_73column_sigmas": 7870,
+  "sigma_stream_sha256": "f4e9802acb2ed53fc1f0486e7d0f55a6faa30ed7f5d2ad48a06450234b00ba76",
+  "cross_replica_helper_roles": 25937,
+  "asynchronous_order_sha256": "2acd6b2004be3d3ef6645f3c968feb22b5167c400bb49eb446821e5cb7af6eee",
+  "source_artifacts": {
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "providers/gauge44/CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+    "providers/gauge44/LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+    "providers/gauge44/LOCAL-CHECKS.json": "2b8a6a6854b8df8ecd84d8ff2b92f720c81454636988e6a0dfdc1f6c29d1c82c",
+    "providers/gauge44/INDEPENDENT-LOCAL-REPLAY.json": "18d68326ce0aca76911d561e79a817bce90cb8adfe053e19621c7ae0298b842e",
+    "providers/gauge44/RESIDUAL-ADAPTERS.json": "bb6c23ba1b8dd5d2016724c3348b4e91a6b91daaa3f56bbd5216cb7a96bf5c94",
+    "providers/gauge44/CLIFFORD-RECIPES.json": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+    "providers/gauge44/CLIFFORD-REVIEW.json": "4e3cdd616d105a49bbf1948bb53e49938d515c42f1c026781d1b5e9cb636db12"
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "scope": "Two actual verified plain/width-seven providers dispatched per complete invocation; independent controller/spectator/normalization and complete finite invoice admission required."
+}
diff --git a/research/gauge44-slots/evidence/global/IDLE-REMAINDER-FRAMES.json.gz b/research/gauge44-slots/evidence/global/IDLE-REMAINDER-FRAMES.json.gz
new file mode 100644
index 0000000000..3562e60f05
Binary files /dev/null and b/research/gauge44-slots/evidence/global/IDLE-REMAINDER-FRAMES.json.gz differ
diff --git a/research/gauge44-slots/evidence/layers/LOCAL-AUDIT-LAYERED.json b/research/gauge44-slots/evidence/layers/LOCAL-AUDIT-LAYERED.json
new file mode 100644
index 0000000000..0780787674
--- /dev/null
+++ b/research/gauge44-slots/evidence/layers/LOCAL-AUDIT-LAYERED.json
@@ -0,0 +1,137 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+  "input_file": "FULL-WORD.json.gz",
+  "content_sha256": "db2c7cfb3f8eee2b76c2e0154fc530520fb4d90cd9511a002cab527b16033b83",
+  "compressed_sha256": "3b268a3adb543e930454e9d9405e5f7a664c75c487f6c5cbe29c199f24a89789",
+  "parent_center_interface": {
+    "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+    "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "transport_tau": 43,
+    "ordered_frame_bases_match": true,
+    "all_ports_match": true,
+    "transported_centers": [
+      92,
+      57,
+      81,
+      224,
+      11,
+      240,
+      9,
+      256
+    ],
+    "source_centers": [
+      92,
+      57,
+      81,
+      11,
+      9
+    ],
+    "ordered_frame_bases": [
+      [
+        256,
+        128,
+        64,
+        34,
+        16,
+        10,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        16,
+        8,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        17,
+        9,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ],
+      [
+        256,
+        128,
+        66,
+        32,
+        18,
+        8,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        17,
+        9,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        16,
+        8,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        68,
+        32,
+        16,
+        12,
+        2,
+        1
+      ]
+    ]
+  },
+  "v": 112,
+  "h": 9,
+  "R": 480,
+  "entering": 192,
+  "lowends": 78,
+  "coldends": 48,
+  "compensation_gates": 7208,
+  "local_profile": {
+    "1": 2412,
+    "2": 418,
+    "3": 418,
+    "4": 170,
+    "5": 68,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 56,
+    "5": 32,
+    "7": 30,
+    "8": 122,
+    "9": 240
+  },
+  "checked_columns": 704,
+  "elapsed_seconds": 0.8600000000005821,
+  "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+}
diff --git a/research/gauge44-slots/evidence/leaver/CELL-MUTANTS-LV.json b/research/gauge44-slots/evidence/leaver/CELL-MUTANTS-LV.json
new file mode 100644
index 0000000000..4d4ef7403c
--- /dev/null
+++ b/research/gauge44-slots/evidence/leaver/CELL-MUTANTS-LV.json
@@ -0,0 +1,261 @@
+{
+ "c01m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_233": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [233])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [172, 175])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [132, 135, 173, 174])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_233": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [233])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c01p": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_57": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [57, 58, 224, 225, 226])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [169, 170])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [129, 130, 168, 171])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_57": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [57, 58, 224, 225, 226])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c23m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_58": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [58])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [169, 170])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [173, 174, 196, 199])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_58": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [58])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c23p": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_239": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [60, 63, 231, 232, 238, 239])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [172, 175])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [168, 171, 193, 194])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_239": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [60, 63, 231, 232, 238, 239])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c45m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_441": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [52, 55, 439, 440, 446, 447])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [137, 138])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [141, 142, 164, 167])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_441": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [52, 55, 439, 440, 446, 447])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c45p": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_255": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [28, 31, 247, 248, 254, 255])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [140, 143])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [136, 139, 161, 162])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_255": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [28, 31, 247, 248, 254, 255])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ },
+ "c67m": {
+  "base": {
+   "audit_local": "PASS",
+   "native": "PASS"
+  },
+  "window": [
+   611,
+   631
+  ],
+  "mutants": {
+   "M1_drop_leaver_restore_18": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [18])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M2_flip_yy_B623": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [129, 130])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M3_delete_xy_B611": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [133, 134, 161, 162])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M4_target_reads_entering_h448": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   },
+   "M5_wrong_leaver_restore_18": {
+    "audit_local": "RuntimeError: all-column endpoint failure (False, [18])",
+    "native": "AssertionError: ('arbitrary-dirt endpoint', False)"
+   },
+   "M6_unrelabelled_dirty_yy_source": {
+    "audit_local": "RuntimeError: nonzero entrance response",
+    "native": "AssertionError: zero-frame compensation reads an entering helper"
+   }
+  },
+  "all_rejected_both": true
+ }
+}
\ No newline at end of file
diff --git a/research/gauge44-slots/evidence/leaver/FRAME-CONTROLS-LV-k8.json b/research/gauge44-slots/evidence/leaver/FRAME-CONTROLS-LV-k8.json
new file mode 100644
index 0000000000..9f56e21000
--- /dev/null
+++ b/research/gauge44-slots/evidence/leaver/FRAME-CONTROLS-LV-k8.json
@@ -0,0 +1,54 @@
+{
+ "base": "c836d892",
+ "recipe": "FRAME-RECIPE-LV-k8.json",
+ "controls": {
+  "shrink_raised_B": {
+   "builder": "profile and width pins",
+   "stage": "native_atc",
+   "native": "PASS",
+   "rc": 0,
+   "reason": "}",
+   "frame": [
+    "B",
+    539
+   ]
+  },
+  "shrink_lowered_B": {
+   "builder": "('nonmonotone', 174)",
+   "stage": "apply",
+   "reason": "('nonmonotone', 174)"
+  },
+  "shrink_T": {
+   "builder": "('nonmonotone', 554)",
+   "stage": "apply",
+   "reason": "('nonmonotone', 554)"
+  },
+  "empty_B": {
+   "builder": "('nonmonotone', 169)",
+   "stage": "apply",
+   "reason": "('nonmonotone', 169)"
+  },
+  "drop_one_lowering": {
+   "builder": "output word pin",
+   "stage": "native_atc",
+   "native": "PASS",
+   "rc": 0,
+   "reason": "}",
+   "frame": [
+    "B",
+    1232
+   ]
+  },
+  "drop_one_raise": {
+   "builder": "profile and width pins",
+   "stage": "native_atc",
+   "native": "PASS",
+   "rc": 0,
+   "reason": "}",
+   "frame": [
+    "B",
+    539
+   ]
+  }
+ }
+}
diff --git a/research/gauge44-slots/evidence/local/CANONICAL-WORD.json.gz b/research/gauge44-slots/evidence/local/CANONICAL-WORD.json.gz
new file mode 100644
index 0000000000..5062a1f62f
Binary files /dev/null and b/research/gauge44-slots/evidence/local/CANONICAL-WORD.json.gz differ
diff --git a/research/gauge44-slots/evidence/local/CLIFFORD-RECIPES.json b/research/gauge44-slots/evidence/local/CLIFFORD-RECIPES.json
new file mode 100644
index 0000000000..3ba8326d3a
--- /dev/null
+++ b/research/gauge44-slots/evidence/local/CLIFFORD-RECIPES.json
@@ -0,0 +1 @@
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diff --git a/research/gauge44-slots/evidence/local/CLIFFORD-REVIEW.json b/research/gauge44-slots/evidence/local/CLIFFORD-REVIEW.json
new file mode 100644
index 0000000000..6b12ae0e4b
--- /dev/null
+++ b/research/gauge44-slots/evidence/local/CLIFFORD-REVIEW.json
@@ -0,0 +1,19 @@
+{
+  "status": "PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES",
+  "canonical_word_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+  "frames": 1037,
+  "directed_edges": 3019,
+  "ranks": {
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+    "3": 412,
+    "8": 16,
+    "4": 154,
+    "5": 14
+  },
+  "endpoint_adapters": 224,
+  "all_child_equalities_include_global_phase": true,
+  "recipe_sha256": "0a60293f43d88dbb1b321f02e61204afe1b6272b1346968ef35705caea1e4771",
+  "seconds": 198.28347681800005,
+  "scope": "Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations."
+}
diff --git a/research/gauge44-slots/evidence/local/FULL-WORD.json.gz b/research/gauge44-slots/evidence/local/FULL-WORD.json.gz
new file mode 100644
index 0000000000..447d45d08b
Binary files /dev/null and b/research/gauge44-slots/evidence/local/FULL-WORD.json.gz differ
diff --git a/research/gauge44-slots/evidence/local/INDEPENDENT-LOCAL-REPLAY.json b/research/gauge44-slots/evidence/local/INDEPENDENT-LOCAL-REPLAY.json
new file mode 100644
index 0000000000..aa15edfba5
--- /dev/null
+++ b/research/gauge44-slots/evidence/local/INDEPENDENT-LOCAL-REPLAY.json
@@ -0,0 +1,71 @@
+{
+  "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY",
+  "canonical_word_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+  "local_programs_sha256": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+  "v": 112,
+  "helpers": 492,
+  "local": {
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+      "prefix_l1_upper": "2323449462751823289130723296176889733365478515961323543/64",
+      "prefix_bits_upper": 175,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    },
+    "backward": {
+      "all_exact_columns": 716,
+      "prefix_l1_upper": "600338326363508935771850050281004728884643/32",
+      "prefix_bits_upper": 134,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    }
+  },
+  "paid_profiles": {
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+      "1": 2514,
+      "4": 160,
+      "8": 8,
+      "3": 448,
+      "2": 404,
+      "5": 56
+    },
+    "backward": {
+      "1": 2514,
+      "4": 160,
+      "8": 8,
+      "3": 448,
+      "2": 404,
+      "5": 56
+    }
+  },
+  "entering_helpers": 204,
+  "cold_hyperplane_ended_helpers": 44,
+  "negative_controls_rejected": [
+    "wrong_scale",
+    "missing_center",
+    "wrong_common_frame",
+    "wrong_child_rank",
+    "missing_pre_wrapper",
+    "missing_post_wrapper",
+    "wrapper_with_wrong_frame",
+    "wrapper_in_wrong_phase",
+    "wrapper_on_a_data_register",
+    "wrapper_on_a_target_register",
+    "wrapper_on_a_centre_register",
+    "hpe_pre_wrapper_resolved_to_full_recipe",
+    "hpe_post_wrapper_without_terminal_frame",
+    "hpe_post_wrapper_wrong_terminal_frame",
+    "hpe_tail_gate_at_full_frame",
+    "hpe_tail_climb_dropped",
+    "hpe_helper_exit_adapter_to_full",
+    "hpe_tail_gate_moved_into_full_cleanup",
+    "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter",
+    "cold_hpe_pre_wrapper_dropped",
+    "cold_hpe_post_wrapper_replaced_by_exit_adapter",
+    "cold_hpe_pre_wrapper_resolved_to_cold_full_convention",
+    "cold_hpe_wrapper_with_nonzero_entrance",
+    "cold_hpe_post_wrapper_wrong_terminal_frame",
+    "cold_hpe_premix_gate_before_pre_wrapper"
+  ],
+  "scope": "Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate."
+}
diff --git a/research/gauge44-slots/evidence/local/LOCAL-CHECKS.json b/research/gauge44-slots/evidence/local/LOCAL-CHECKS.json
new file mode 100644
index 0000000000..3872f0e596
--- /dev/null
+++ b/research/gauge44-slots/evidence/local/LOCAL-CHECKS.json
@@ -0,0 +1,36 @@
+{
+  "forward": {
+    "sha256": "d17399c8c7458bb7110d8596fab5f769cd4cb3733a3042277fa08bf03f42d6c9",
+    "events": 46772,
+    "scalar_macros": 41570,
+    "real_component_primitive_bound": 420052,
+    "paid_profile": {
+      "1": 2514,
+      "2": 404,
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+      "4": 160,
+      "5": 56,
+      "8": 8
+    },
+    "all_columns": 716,
+    "private_centers_cleared": true,
+    "private_coefficient_stream_cleared_after_each_macro": true
+  },
+  "backward": {
+    "sha256": "4772df0663f88cc218fd7254eb202f46daf136c06e9e96c19ed8ea218b545dc4",
+    "events": 46772,
+    "scalar_macros": 41570,
+    "real_component_primitive_bound": 420100,
+    "paid_profile": {
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+  }
+}
diff --git a/research/gauge44-slots/evidence/local/LOCAL-PROGRAMS.json.gz b/research/gauge44-slots/evidence/local/LOCAL-PROGRAMS.json.gz
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+  "refactored_cleanup": {
+    "exact_non_target_isolation_checked": true,
+    "high_inverse": "dyadic_sparse_Gauss_Jordan",
+    "kind": "source_branch_gauge_and_retired_completion_cold44",
+    "new_cold_ends": 44
+  }
+}
diff --git a/research/gauge44-slots/evidence/local/WRAPPER-CHECKS.json b/research/gauge44-slots/evidence/local/WRAPPER-CHECKS.json
new file mode 100644
index 0000000000..a18afd4fad
--- /dev/null
+++ b/research/gauge44-slots/evidence/local/WRAPPER-CHECKS.json
@@ -0,0 +1,413 @@
+{
+ "status": "PASS_RESIDUAL_WRAPPERS_ARE_EXACT",
+ "frames": 22,
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+   "residual_width": 4
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+  "wrong quadratic form",
+  "sides swapped",
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+  "hpe: width misreported as 9 - dim E",
+  "hpe: wrong terminal hyperplane",
+  "hpe: pre wrapper resolved to the FULL recipe R_{E,FULL}",
+  "hpe: wrong global phase",
+  "cold hpe: identity pre wrapper instead of R_{0,U}",
+  "cold hpe: identity post wrapper instead of L_{0,U}",
+  "cold hpe: no wrappers (cold FULL convention L = R = I)",
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+  "cold hpe: wrong terminal hyperplane",
+  "cold hpe: wrong global phase"
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+  {
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+  }
+ ]
+}
diff --git a/research/gauge44-slots/hosting/PROOF.md b/research/gauge44-slots/hosting/PROOF.md
new file mode 100644
index 0000000000..b551b6d3e5
--- /dev/null
+++ b/research/gauge44-slots/hosting/PROOF.md
@@ -0,0 +1,237 @@
+# Exact owner reuse and concave-cost matching
+
+## 1. Objects and interface assumptions
+
+The parent controller has 72 ordered calls, 112 source ports, 112 target ports,
+and 492 helper roles per call. The ambient dimension is 73. A pending-child
+group is a triple
+
+$$
+g=(\text{owner replica},\text{child},\text{port}).
+$$
+
+The parent window catalogue gives group capacity $C_g$, together with the call
+times at which its physical stream is idle. The map from a group to its
+physical family is
+
+$$
+F(g)=896\,\text{owner replica}
+  +112(2\,\text{pair(child)}+\text{side(child)})+\text{port}.
+$$
+
+At every call in this particular parent geometry, at most one pending child of
+a physical family is eligible. Both the matcher and the independent frozen
+audit check this condition. They also exclude both active data families of the
+call. Consequently, injective assignment to eligible groups is equivalent to
+assignment to distinct idle physical families at that call.
+
+Helper $h$ requests an integer width $w_h$, read afresh from the new local
+word as the final-frame dimension minus the start-frame dimension. Native
+program profiles are also recomputed from their paid edges. The finite local
+compiler supplies the normalized helper chart and verifies its warm-start
+semantics. A hosted width is a reservation in the pending child's address
+coordinates on an existing physical stream; it is not a new physical stream.
+
+This proof concerns the discrete assignment and its moment contribution. It
+uses the parent windows as input. Independent global admission must verify
+those windows against the actual controller and construct the actual
+73-column charts for the fresh native local word.
+
+## 2. Feasible shrinking on the original families
+
+For one call, sort the old slot widths and the new helper widths increasingly,
+breaking ties by the old or new helper number. Suppose the new width in each
+position is no larger than its matched old width. Assign that helper to the
+matched old slot.
+
+This operation preserves the call time, stage, replica, pending child, port,
+owner replica, and physical family. It preserves the set of 492 distinct
+helper-owner families at the call, so the old window and active-data
+exclusions still hold. In each pending-child group, the sum of new widths is
+no larger than the old sum, hence remains within capacity.
+
+Now order the assignments in each group consistently and replace their
+offsets by consecutive prefix sums. The occupied sets become pairwise
+disjoint intervals whose union is exactly a prefix of length
+$U_g=\sum w_h\le C_g$. The idle child retains rank $C_g-U_g$, with pending
+offset $U_g$. Thus the shrinking operation has a direct capacity proof; it
+requires neither an owner solver nor any change to the controller.
+
+The seed constructor applies this termwise argument to the 71 former `jp8`
+calls. It keeps the remaining `ck` call provisionally unchanged. Two optional
+fixed-family assignment passes redistribute the available capacity before
+freezing the seed. Their result is audited using the same integer constraints.
+
+## 3. One call with all other calls fixed
+
+Fix one call $t$. Remove its existing assignments while keeping every other
+call fixed. For each eligible group, define the available capacity
+
+$$
+c_g=C_g-\sum_{\substack{\text{assignments in }g\\\text{from calls other than }t}}w.
+$$
+
+The call must assign each of its 492 widths to a distinct eligible group with
+$w\le c_g$. Unused groups can be viewed as receiving a dummy width zero.
+After the assignment, group $g$'s idle rank is $c_g-w_g$. For any function
+$\phi$, the portion of the idle objective affected by the call is exactly
+
+$$
+\sum_{g\text{ eligible at }t}\phi(c_g-w_g).
+$$
+
+All other idle contributions, and all local paid-edge contributions, are
+constant in this single-call problem.
+
+### Greedy rule
+
+Sort eligible capacities increasingly. At each capacity, assign the largest
+remaining helper width that fits; assign zero if none fits. Continue through
+the remaining capacities.
+
+This rule has no floating parameter. Equal-capacity tie choices are used only
+to limit changes to physical owners and make the artifact deterministic.
+
+### Exchange lemma
+
+Take two capacities $c_1\le c_2$ and two widths $w_1\le w_2\le c_1$. The
+assignment of $w_1$ to $c_1$ and $w_2$ to $c_2$ has residual pair
+
+$$
+(c_1-w_1,\ c_2-w_2).
+$$
+
+Exchange the widths. Feasibility is preserved, and the new pair is
+
+$$
+(c_1-w_2,\ c_2-w_1).
+$$
+
+The total is unchanged. The first new component is no larger than either old
+component, and the second is no smaller than either old component. Therefore
+the new pair majorizes the old pair. Every concave $\phi$ has weakly smaller
+sum on the new pair.
+
+### Consequence: feasibility and optimality
+
+Start from any feasible complete assignment. At the smallest remaining
+capacity, its assigned width is no larger than the largest remaining width
+that fits. The greedy width occurs at some later capacity. If the two differ,
+the exchange lemma moves that width to the current capacity while preserving
+feasibility and weakly decreasing every concave objective. Fix this first
+position and repeat on the suffix. Dummy zero widths cover unused groups.
+
+Thus the greedy procedure succeeds whenever a feasible assignment exists, and
+its remainder vector majorizes that of every feasible assignment. It
+simultaneously minimizes every concave remainder objective for this call.
+This proof depends on the absence of any eligibility restriction beyond the
+capacity and the already fixed call window; that property is explicitly
+checked for the present geometry.
+
+## 4. Exact majorization receipts
+
+Let $a_r$ and $b_r$ be the old and new remainder histograms for one update,
+including zero remainders. When the helper-width multiset is unchanged, their
+total numbers of groups and total ranks agree. Every remainder lies between
+0 and 48. The implementation checks, with integers, that for each
+$k=0,1,\ldots,48$,
+
+$$
+\sum_r b_r\max(r-k,0)
+\;\ge\;
+\sum_r a_r\max(r-k,0).
+$$
+
+These are the stored stop-loss margins. Between integer breakpoints the
+difference is linear, so checking all integer breakpoints checks every real
+threshold. With equal sums and equal lengths, the inequalities are the
+standard majorization criterion: the new vector majorizes the old one.
+
+The transcript contains 288 such equal-width updates: four passes through 72
+calls. A single preceding update replaces the seed's last `ck` width multiset.
+That bootstrap has different total width, so it is checked for exact
+feasibility and is not represented as an equal-sum majorization step.
+
+`reproduce.py` reruns every update and compares the full transcript's semantic
+hash. Independently, `audit_frozen.py` removes each final call in turn, computes
+all available capacities directly from the frozen owner map, runs a separate
+histogram-only greedy calculation, and verifies that it returns exactly the
+existing remainder histogram. This checks all 72 final coordinate optima
+without relying on the transcript or the discovery seed.
+
+## 5. Relation to the global moment
+
+For ambient dimension $M=73$, define
+
+$$
+\phi_b(r)=r\bigl((73/r)^b-1\bigr)
+          =73^b r^{1-b}-r,\qquad \phi_b(0)=0.
+$$
+
+For $0<b<1$, this function is continuous at zero and strictly concave on
+positive ranks, because
+
+$$
+\phi_b''(r)=-b(1-b)73^b r^{-b-1}<0.
+$$
+
+Once all calls use the new provider, the local paid profile is fixed and every
+accepted owner update preserves the global paid rank mass. The exchange and
+majorization arguments therefore weakly decrease the global moment pressure
+for every $b\in(0,1)$ simultaneously. A strict histogram majorization strictly
+decreases that pressure. No estimated root, derivative, or floating cost is
+needed to establish the improvement of these updates.
+
+For the frozen map, the exact paid rank mass is 520704, so
+
+$$
+73\cdot7168-520704=2560.
+$$
+
+The final profile is recomputed from 72 copies of the new local paid profile
+and from the actual remaining rank in every pending-child group. Numerical
+roots printed by the matcher are screens only. Exact moment bounds and their
+combination with the bit supplier are performed by the package's admitted
+global pipeline.
+
+## 6. Determinism and fixed-point scope
+
+The implementation keeps the parent call order, alternating a forward pass
+and a reverse pass. Within equal-capacity groups, it first prefers the old
+assigned width, then other previously used owners, and finally physical-family
+order. It retains an old helper number when possible and otherwise takes the
+smallest unassigned helper number of the required width. These tie rules
+affect the frozen map, but not the single-call optimum remainder histogram.
+
+The recorded run has three passes with strict improvements. Its fourth pass
+has zero strict changes and zero changed helper owners. Hence the recorded map
+is a fixed point of the implemented call update. The separate final audit
+also establishes the stronger cost-level statement that every individual call
+already minimizes every concave remainder objective with the other calls
+fixed.
+
+Calls share capacities. Simultaneously changing two or more calls could
+possibly improve on a coordinate fixed point. The argument makes **no claim
+of joint global optimality**, and the frozen artifact does not depend on such
+a claim.
+
+## 7. Fields to regenerate for actual global admission
+
+| Field or object | Required action |
+| --- | --- |
+| Call `stage`, `replica`, `time` and parent windows | Preserve the parent controller |
+| Helper number and width | Read the new local signature and use the nominated assignment |
+| `owner_replica`, `child`, `port` | Use the final legal group selected by the matcher |
+| `copy`, `family` | Recompute from the selected group, then check uniqueness and active-data exclusion |
+| Helper `offset` | Compact all widths in each group into a disjoint prefix |
+| Idle `rank`, `hosted`, `pending_offset` | Recompute from the actual occupied prefix |
+| Per-call width lists and global paid profile | Recompute from the fresh local programs and actual cells |
+| Provider bindings, center carriers and program hashes | Bind the freshly checked provider; do not retain stale parent IDs or hashes |
+| Actual 73-column owner charts and their digests | Generate afresh from the selected child, port, offset, width and spectator coordinates |
+
+The new construction uses different center carrier registers, including source
+registers. Its ordered center frames and checked operator, rather than old
+carrier numbers, are the semantic interface. The hosting proof does not waive
+that interface check. The signature-only intermediate PLAN produced during
+replay is explicitly marked as such and is never a substitute for fresh
+provider binding or global phase admission.
diff --git a/research/gauge44-slots/hosting/README.md b/research/gauge44-slots/hosting/README.md
new file mode 100644
index 0000000000..b9505ebbea
--- /dev/null
+++ b/research/gauge44-slots/hosting/README.md
@@ -0,0 +1,162 @@
+# Cold44 hosting: frozen owner map and exact callwise matching
+
+This directory contains the owner assignment used to turn the new cold44 local
+word into a global improvement. All 72 calls use the new local signature. The
+assignment is frozen; no search, tuning, or optimization is needed to consume
+it in the global verifier.
+
+The local word reduces the helper width sum from 3894 for the previous `jp8`
+provider to 3794. Simply shrinking the old allocations leaves many small idle
+remainders. The matcher below moves helpers to other physical families that are
+already idle at the same call, concentrating those remainders while respecting
+every parent capacity and window. This recovers a substantial part of the local
+saving in the global moment calculation.
+
+## Frozen result
+
+The exact finite data are in [frozen/MANIFEST.json](frozen/MANIFEST.json) and
+[frozen/MATCHING-RECEIPT.json](frozen/MATCHING-RECEIPT.json).
+
+| Quantity | Frozen value |
+| --- | ---: |
+| Calls | 72 |
+| Helpers per call | 492 |
+| Owner roles | 35,424 |
+| Ambient dimension | 73 |
+| Live streams | 7,168 |
+| New local width sum | 3,794 |
+| New local paid rank mass | 5,650 |
+| Global paid rank mass | 520,704 |
+| Global deficit | 2,560 |
+| Maximum child rank | 48 |
+| Equal-width updates with exact majorization receipts | 288 |
+| Final callwise optima independently checked | 72 |
+
+The new local width inventory is `{4:52, 5:48, 7:34, 8:114, 9:244}` and its paid
+profile is `{1:2514, 2:404, 3:448, 4:160, 5:56, 8:8}`. The final global paid
+profile, including all idle remainders, is:
+
+```json
+{"1":181093,"2":29164,"3":32429,"4":11520,"5":4032,"7":7,
+ "8":582,"12":13,"16":33,"19":1,"20":2,"28":4,"32":62,
+ "36":1,"40":1,"44":6,"48":2289}
+```
+
+Its floating moment screen is `b = 0.0016522089943684115`, giving the analytic
+screen `b/(1+b) = 0.0016494837025589793`. Relative to PR #635's reported
+`0.001636241501576388`, that is approximately **0.8093%**. These decimal screens
+are diagnostic values; the package's exact moment and outer assembly determine
+the admitted exponent. The owner replay never uses the floating root to choose
+an expanded-matching move.
+
+The frozen owner file has byte SHA-256:
+
+```text
+90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57
+```
+
+Its semantic SHA-256, computed from sorted-key compact uncompressed JSON, is:
+
+```text
+c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d
+```
+
+Semantic hashes are the portable replay criterion. The gzip byte hash is also
+reported, but compressor implementations need not produce identical streams.
+
+## Reproduce with the Python standard library
+
+Supply the PR #635 parent `PLAN.json` and `OWNERS.json.gz`, plus either the new
+verified native provider directory or the new raw word. The expected parent
+hashes are pinned in the manifest. The command below is run from the package
+root; replace the example input paths with actual paths.
+
+```sh
+python hosting/reproduce.py \
+  --parent-plan /path/to/pr635/research/complex-571-cold14-st2/data/PLAN.json \
+  --parent-owners /path/to/pr635/research/complex-571-cold14-st2/data/OWNERS.json.gz \
+  --local44 /path/to/verified/local44 \
+  --out /path/to/new/hosting-replay
+```
+
+For the raw provider, replace `--local44 ...` with
+`--raw-word /path/to/FULL-WORD.json.gz`. Reading a raw word here only extracts a
+nomination signature; it does not replace independent local verification.
+
+The default replay copies the frozen mixed-provider seed, checks its semantic
+hash, derives its profile afresh, and runs the exact expanded matcher. It then
+compares the final owner and majorization transcript with the frozen semantic
+hashes and independently checks the final map's 72 callwise fixed points.
+Outputs include `all72/OWNERS.json.gz`, `all72/PROFILE.json`, recomputed
+remainders, `FROZEN-AUDIT.json`, and `REPRODUCTION.json`.
+
+The seed has 71 cold44 calls and one inherited `ck` call. Expanded matching first
+replaces that last call using newly available legal families. This changed-width
+bootstrap is checked for feasibility and is explicitly excluded from the
+equal-width majorization count. The following four passes use cold44 at all 72
+calls:
+
+| Pass | Calls with strict majorization | Changed helper owners |
+| --- | ---: | ---: |
+| 1 | 70 | 1,245 |
+| 2 | 41 | 169 |
+| 3 | 8 | 13 |
+| 4 | 0 | 0 |
+
+Pass 4 changes neither the map nor its remainder histogram. The independent
+audit additionally recomputes the optimal remainder histogram for each call
+with all other calls fixed.
+
+## Optional: reproduce seed discovery
+
+Add `--rebuild-seed` to the same command to rebuild the mixed seed from the
+original PR #635 owners. This step first matches sorted new helper widths to
+sorted old owner slots, then performs two fixed-family Hungarian passes.
+Discovery used Python 3.12.14, NumPy 2.3.5, and SciPy 1.17.0. Equal-cost matching
+tie choices may vary across SciPy versions, so the script compares the rebuilt
+seed with the frozen semantic hash and fails if it differs. Default frozen-seed
+replay has no NumPy or SciPy dependency.
+
+The two discovery passes are an optional way to recover the recorded seed.
+Their floating costs are not needed for feasibility, for the final fixed-point
+proof, or for the package's admitted exponent.
+
+## Audit without regenerating the assignment
+
+```sh
+python hosting/audit_frozen.py \
+  --parent-plan /path/to/pr635/research/complex-571-cold14-st2/data/PLAN.json \
+  --parent-owners /path/to/pr635/research/complex-571-cold14-st2/data/OWNERS.json.gz \
+  --local44 /path/to/verified/local44 \
+  --out /path/to/FROZEN-AUDIT.json
+```
+
+This integer audit checks helper coverage, capacity, allowed call times, active
+data exclusion, physical-family uniqueness within each call, disjoint compacted
+coordinate prefixes, the exact global profile and rank mass, and callwise
+optimality of the frozen remainder histograms. It reads the explicit parent
+window catalogue. The package's separate global verifier must also derive
+those windows and all 73-column charts from the actual program.
+
+## Files and scope
+
+| File | Purpose |
+| --- | --- |
+| `frozen/OWNERS.json.gz` | The final all-cold44 map consumed by global assembly |
+| `frozen/SEED-OWNERS.json.gz` | Pinned feasible mixed seed for dependency-free replay |
+| `frozen/MAJORIZATION.json.gz` | Integer stop-loss margins for every expanded update |
+| `frozen/MANIFEST.json` | Parent, provider, artifact, profile, and parameter bindings |
+| `frozen/SEED-RECEIPT.json` | Recorded sorted matching and two seed discovery passes |
+| `frozen/MATCHING-RECEIPT.json` | Recorded expanded passes and exact finite totals |
+| `reproduce.py` | End-to-end parameterized hosting replay |
+| `reuse_owners.py` | Optional original-family seed constructor |
+| `expand_owners.py` | Exact greedy matching over all eligible physical families |
+| `audit_frozen.py` | Independent feasibility and final callwise fixed-point audit |
+| `PROOF.md` | Capacity, exchange, majorization, and integration arguments |
+
+The expanded matcher is individually optimal for each call when other calls
+are fixed, for every concave remainder cost simultaneously. The frozen map is
+a verified coordinate fixed point. **No joint global optimality claim is
+made.** New local algebra, changed center carriers, phase compatibility,
+actual owner charts, the finite invoice, and exact exponent admission remain
+the responsibility of the package's global verification pipeline.
diff --git a/research/gauge44-slots/hosting/audit_frozen.py b/research/gauge44-slots/hosting/audit_frozen.py
new file mode 100644
index 0000000000..26a07408ea
--- /dev/null
+++ b/research/gauge44-slots/hosting/audit_frozen.py
@@ -0,0 +1,169 @@
+"""Audit the frozen owner map and its callwise fixed point using integers.
+
+The parent window catalogue is an explicit input. The package's independent
+global verifier must additionally derive the windows from the actual program.
+This audit does not certify local algebra, phase charts, or an exponent.
+"""
+from collections import Counter, defaultdict
+from pathlib import Path
+import argparse
+import hashlib
+import json
+
+from reuse_owners import packed, read, sha, signature
+
+
+HERE = Path(__file__).resolve().parent
+
+
+def semantic_sha(path):
+    return hashlib.sha256(packed(read(path))).hexdigest()
+
+
+def add_inputs(parser):
+    parser.add_argument('--parent-plan', type=Path, required=True)
+    parser.add_argument('--parent-owners', type=Path, required=True)
+    provider = parser.add_mutually_exclusive_group(required=True)
+    provider.add_argument('--local44', type=Path, help='Independently checked native provider directory')
+    provider.add_argument('--raw-word', type=Path, help='New FULL-WORD.json.gz; nomination signature only')
+
+
+def bound_inputs(args, manifest):
+    assert sha(args.parent_plan) == manifest['parent_plan_sha256'], 'Wrong parent PLAN'
+    assert sha(args.parent_owners) == manifest['parent_owners_sha256'], 'Wrong parent OWNERS'
+    plan = read(args.parent_plan)
+    assert (plan['K'], plan['T'], plan['M'], plan['L'], plan['live']) == (4, 8, 73, 9, 7168)
+    provider_path = args.local44 if args.local44 is not None else args.raw_word
+    sig = signature(provider_path)
+    expected = manifest['new_provider']
+    assert len(sig['widths']) == expected['R']
+    assert hashlib.sha256(packed(sig['widths'])).hexdigest() == expected['width_vector_sha256']
+    assert sig['profile'] == {int(r): n for r, n in expected['profile'].items()}
+    assert Counter(sig['widths']) == {int(w): n for w, n in expected['width_histogram'].items()}
+    assert sum(sig['widths']) == expected['width_sum']
+    assert sum(r*n for r, n in sig['profile'].items()) == expected['rank_mass']
+    return plan, sig, provider_path
+
+
+def audit(plan, sig, owners):
+    V, R = 112, 492
+    order = [tuple(c) for c in plan['order']]
+    assert len(order) == 72 and len(set(order)) == 72
+    assert len(owners) == 72*R
+    bycall = defaultdict(dict)
+    cells = defaultdict(set)
+    caps, family, eligible = {}, {}, defaultdict(list)
+    for key, (cap, times) in plan['windows'].items():
+        rep, child = map(int, key.split(','))
+        assert 0 <= cap <= 48 and len(times) == len(set(times))
+        for port in range(V):
+            g = (rep, child, port)
+            caps[g] = cap
+            family[g] = rep*8*V + (2*plan['pairs'][str(child)] + plan['sides'][str(child)])*V + port
+            for t in times:
+                assert 0 <= t < len(order)
+                eligible[t].append(g)
+    for t, gs in eligible.items():
+        assert len({family[g] for g in gs}) == len(gs), 'Multiple eligible children on one family'
+        stage, rep = order[t]
+        pair = max(0, (stage-1)//2)
+        assert all(g[0] != rep or plan['pairs'][str(g[1])] != pair for g in gs)
+    for z in owners:
+        t, h = z['time'], z['helper']
+        assert 0 <= t < len(order) and 0 <= h < R
+        assert (z['stage'], z['replica']) == order[t]
+        assert h not in bycall[t]
+        assert z['width'] == sig['widths'][h]
+        g = (z['owner_replica'], z['child'], z['port'])
+        assert g in caps and t in plan['windows'][f'{g[0]},{g[1]}'][1]
+        assert z['copy'] == g[0]*V + g[2] and z['family'] == family[g]
+        off, width = z['offset'], z['width']
+        assert 0 <= off and off+width <= caps[g]
+        occupied = set(range(off, off+width))
+        assert not cells[g] & occupied, 'Overlapping hosted coordinates'
+        cells[g] |= occupied
+        bycall[t][h] = (g, width)
+    for t in range(72):
+        assert set(bycall[t]) == set(range(R))
+        assert len({family[g] for g, w in bycall[t].values()}) == R
+    for occupied in cells.values():
+        assert occupied == set(range(len(occupied))), 'Uncompacted hosted coordinates'
+    used = {g: len(cells[g]) for g in caps}
+    idle = Counter(caps[g]-used[g] for g in caps if caps[g] > used[g])
+    paid = Counter({r: 72*n for r, n in sig['profile'].items()})
+    paid.update(idle)
+
+    # Independent cost-level fixed-point check. No helper-ID or family-ID
+    # tie-breaking is needed: equal capacities give the same histogram.
+    for t in range(72):
+        old = {g: w for g, w in bycall[t].values()}
+        assert len(old) == R
+        before = Counter(caps[g]-used[g] for g in eligible[t])
+        available = sorted(caps[g]-used[g]+old.get(g, 0) for g in eligible[t])
+        want = Counter(sig['widths'])
+        after = Counter()
+        for cap in available:
+            width = next((w for w in sorted(want, reverse=True) if want[w] and w <= cap), 0)
+            if width:
+                want[width] -= 1
+            after[cap-width] += 1
+        assert not any(want.values()), 'Greedy assignment unexpectedly infeasible'
+        assert after == before, ('Frozen map is not callwise optimal', t)
+    mass = sum(r*n for r, n in paid.items())
+    assert 73*7168-mass == 2560 and max(paid) == 48
+    return {
+        'roles': len(owners), 'calls': 72, 'fixed_point_calls_checked': 72,
+        'remainder_profile': dict(sorted(idle.items())),
+        'global_profile': dict(sorted(paid.items())),
+        'rank_mass': mass, 'deficit': 2560, 'maxchild': 48,
+        'all_footprints_disjoint_compacted_prefixes': True,
+        'all_helper_families_idle_and_outside_active_data': True,
+        'one_helper_per_physical_family_per_call': True,
+        'every_call_optimal_for_every_concave_remainder_cost': True,
+        'global_optimality_claimed': False,
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    add_inputs(parser)
+    parser.add_argument('--owners', type=Path, default=HERE/'frozen/OWNERS.json.gz')
+    parser.add_argument('--majorization', type=Path, default=HERE/'frozen/MAJORIZATION.json.gz')
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    manifest = read(HERE/'frozen/MANIFEST.json')
+    plan, sig, provider_path = bound_inputs(args, manifest)
+    assert semantic_sha(args.owners) == manifest['artifacts']['OWNERS.json.gz']['semantic_sha256']
+    assert semantic_sha(args.majorization) == manifest['artifacts']['MAJORIZATION.json.gz']['semantic_sha256']
+    result = audit(plan, sig, read(args.owners))
+    for key in ('remainder_profile', 'global_profile'):
+        assert result[key] == {int(r): n for r, n in manifest[key].items()}
+    moves = read(args.majorization)
+    checked = 0
+    for move in moves:
+        if move['equal_width_multiset']:
+            margins = move['integer_stoploss_margins']
+            assert len(margins) == 49 and all(type(x) is int and x >= 0 for x in margins)
+            assert margins[0] == margins[-1] == 0
+            assert move['strict_majorization'] == bool(any(margins))
+            checked += 1
+        else:
+            assert move['bootstrap'] and move['integer_stoploss_margins'] is None
+    assert checked == 288 and len(moves) == 289
+    result.update({
+        'status': 'PASS_FROZEN_HOSTING_AND_ALL_72_CALLWISE_FIXED_POINTS',
+        'parent_plan_sha256': sha(args.parent_plan),
+        'parent_owners_sha256': sha(args.parent_owners),
+        'owners_semantic_sha256': semantic_sha(args.owners),
+        'majorization_semantic_sha256': semantic_sha(args.majorization),
+        'stored_integer_majorization_steps': checked,
+        'majorization_replay': 'reproduce.py re-executes every step; this audit separately checks the final fixed point.',
+        'remaining_scope': 'The package global verifier checks fresh local algebra, phases, windows, invoice, moment, and outer assembly.',
+    })
+    args.out.parent.mkdir(parents=True, exist_ok=True)
+    args.out.write_text(json.dumps(result, indent=2)+'\n')
+    print(json.dumps(result, indent=2))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/hosting/expand_owners.py b/research/gauge44-slots/hosting/expand_owners.py
new file mode 100644
index 0000000000..ee6c4c24e6
--- /dev/null
+++ b/research/gauge44-slots/hosting/expand_owners.py
@@ -0,0 +1,186 @@
+"""Exact callwise concave-cost owner matching over every legal idle family.
+
+This is a finite integer nomination algorithm, not a MILP. Each greedy
+matching is optimal for every concave remainder cost. Its majorization
+receipt is checked with integers, independently of floating root screens.
+"""
+from collections import Counter, defaultdict, deque
+from pathlib import Path
+import argparse
+import gzip
+import hashlib
+import json
+import time
+
+from reuse_owners import read, packed, sha, signature, audit_roles, rate
+
+
+def stoploss(hist,k):return sum(n*max(r-k,0) for r,n in hist.items())
+
+
+def main():
+    ap=argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--plan',type=Path,required=True)
+    ap.add_argument('--owners',type=Path,required=True)
+    ap.add_argument('--signature',action='append',required=True,help='Existing PID=verified native directory or raw/signature JSON')
+    ap.add_argument('--max-passes',type=int,default=8)
+    ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args();assert 1<=a.max_passes<=12
+    a.out.mkdir(parents=True,exist_ok=False);beg=time.monotonic()
+    plan,oldroles=read(a.plan),read(a.owners);V,M=112,73
+    assert (plan['K'],plan['T'],plan['M'],plan['L'])==(4,8,73,9)
+    sig={pid:{'widths':desc['widths'],'profile':{int(r):n for r,n in desc['actual_paid_profile'].items()},'source':'input PLAN'} for pid,desc in plan['provider_registry'].items()}
+    for spec in a.signature:
+        pid,path=spec.split('=',1);assert pid in sig;sig[pid]=signature(path)
+    R=len(next(iter(sig.values()))['widths'])
+    for s in sig.values():
+        assert len(s['widths'])==R and all(type(w) is int and 0<w<=9 for w in s['widths'])
+        assert sum(r*n for r,n in s['profile'].items())==16*V+64+sum(s['widths'])
+    calls={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+    order=[tuple(c) for c in plan['order']]
+    oldwidths={k:plan['provider_registry'][c['provider']]['widths'] for k,c in calls.items()}
+    widths={k:sig[c['provider']]['widths'] for k,c in calls.items()}
+    audit_roles(oldroles,plan,oldwidths,V,R)
+    caps={};families={};eligible=defaultdict(list)
+    for key,(cap,window) in plan['windows'].items():
+        rep,ch=map(int,key.split(','))
+        for port in range(V):
+            g=(rep,ch,port);caps[g]=cap
+            families[g]=rep*(8*V)+(2*plan['pairs'][str(ch)]+plan['sides'][str(ch)])*V+port
+            for t in window:eligible[t].append(g)
+    for t,gs in eligible.items():
+        assert len({families[g] for g in gs})==len(gs), 'current geometry requires one eligible child per family'
+        s,rep=order[t];active_pair=max(0,(s-1)//2)
+        assert all(not (g[0]==rep and plan['pairs'][str(g[1])]==active_pair) for g in gs), 'active data family in idle window'
+    current=defaultdict(dict);used={g:0 for g in caps}
+    for z in oldroles:
+        c=(z['stage'],z['replica']);g=(z['owner_replica'],z['child'],z['port'])
+        current[c][z['helper']]=(g,z['width']);used[g]+=z['width']
+    assert all(0<=used[g]<=caps[g] for g in caps)
+    moves=[]
+
+    def idle_profile():return Counter(caps[g]-used[g] for g in caps if caps[g]>used[g])
+
+    def total_profile():
+        p=Counter()
+        for c in plan['provider_calls']:p.update(sig[c['provider']]['profile'])
+        p.update(idle_profile());assert M*plan['live']-sum(r*n for r,n in p.items())==2560
+        return p
+
+    def update(call,bootstrap=False):
+        t=calls[call]['time'];gs=eligible[t]
+        old=current[call]
+        old_by_group={g:(h,w) for h,(g,w) in old.items()}
+        assert len(old_by_group)==R and set(old_by_group)<=set(gs)
+        oldhist=Counter(caps[g]-used[g] for g in gs)
+        for g,(h,w) in old_by_group.items():used[g]-=w
+        want=defaultdict(set)
+        for h,w in enumerate(widths[call]):want[w].add(h)
+        # Equal-capacity opportunities have identical costs. Preserve old
+        # matching widths first, then old owners, and finally family order.
+        buckets=defaultdict(lambda:defaultdict(deque))
+        for g in sorted(gs,key=lambda g:(families[g],g[1])):
+            available=caps[g]-used[g];oldw=old_by_group.get(g,(None,0))[1]
+            buckets[available][oldw].append(g)
+        result={};unassigned=R
+        for c in sorted(buckets):
+            bucket=buckets[c]
+            while unassigned and any(bucket.values()):
+                w=next((w for w in sorted(want,reverse=True) if w<=c and want[w]),None)
+                if w is None:break
+                if bucket.get(w):q=w
+                else:q=next(q for q in sorted(bucket,reverse=True) if bucket[q])
+                g=bucket[q].popleft()
+                h0=old_by_group.get(g,(None,0))[0]
+                h=h0 if h0 in want[w] else min(want[w])
+                want[w].remove(h);result[h]=(g,w);used[g]+=w;unassigned-=1
+                assert used[g]<=caps[g]
+        assert unassigned==0,('no legal family matching',call,{w:len(h) for w,h in want.items() if h})
+        assert set(result)==set(range(R)) and len({families[g] for g,w in result.values()})==R
+        newhist=Counter(caps[g]-used[g] for g in gs)
+        equal_widths=Counter(w for g,w in old.values())==Counter(widths[call])
+        strict=False
+        if equal_widths:
+            assert sum(oldhist.values())==sum(newhist.values())
+            assert stoploss(oldhist,0)==stoploss(newhist,0)
+            margins=[stoploss(newhist,k)-stoploss(oldhist,k) for k in range(49)]
+            assert min(margins)>=0,('greedy did not majorize old assignment',call,margins)
+            strict=any(margins)
+        else:
+            assert bootstrap
+            margins=None
+        changed=sum(result[h]!=old[h] for h in result)
+        current[call]=result
+        moves.append({'stage':call[0],'replica':call[1],'time':t,'bootstrap':bootstrap,
+                      'equal_width_multiset':equal_widths,'integer_stoploss_margins':margins,
+                      'strict_majorization':strict,'changed_helper_owners':changed})
+        return strict,changed
+
+    changed_calls=[c for c in order if any(current[c][h][1]!=widths[c][h] for h in range(R))]
+    for c in changed_calls:update(c,bootstrap=True)
+    p=total_profile();baseline_b=rate(p,2560,M)
+    rounds=[{'pass':'bootstrap','changed_provider_calls':[list(c) for c in changed_calls],
+             'floating_b':baseline_b,'remainder_profile':dict(sorted(idle_profile().items()))}]
+    print(json.dumps({'checkpoint':'all_goal_signatures_feasible','bootstrap_calls':len(changed_calls),'floating_b':baseline_b}),flush=True)
+    quiet=0
+    for passno in range(a.max_passes):
+        strict=changed=0
+        for c in (order if passno%2==0 else list(reversed(order))):
+            s,z=update(c);strict+=bool(s);changed+=z
+        p=total_profile();r={'pass':passno+1,'strictly_improved_calls':strict,'changed_helper_owners':changed,
+                             'floating_b':rate(p,2560,M),'remainder_profile':dict(sorted(idle_profile().items()))}
+        rounds.append(r);print(json.dumps({k:r[k] for k in ('pass','strictly_improved_calls','changed_helper_owners','floating_b')}),flush=True)
+        quiet=quiet+1 if not strict else 0
+        if quiet>=2 or (not strict and not changed):break
+
+    groups=defaultdict(list);roles=[]
+    for call in order:
+        s,rep=call;t=calls[call]['time']
+        for h,(g,w) in current[call].items():
+            orp,ch,port=g
+            z={'child':ch,'copy':orp*V+port,'family':families[g],'helper':h,'offset':0,
+               'owner_replica':orp,'port':port,'replica':rep,'stage':s,'time':t,'width':w}
+            roles.append(z);groups[g].append(z)
+    for g,zs in groups.items():
+        off=0
+        for z in sorted(zs,key=lambda z:(z['time'],z['helper'])):z['offset']=off;off+=z['width']
+        assert off==used[g]<=caps[g]
+    roles.sort(key=lambda z:(z['time'],z['helper']))
+    cells,_=audit_roles(roles,plan,widths,V,R)
+    for z in roles:
+        active=max(0,(z['stage']-1)//2)
+        assert not (z['owner_replica']==z['replica'] and plan['pairs'][str(z['child'])]==active)
+    for g in caps:assert len(cells[g])==used[g]
+    remainder=[]
+    for g in caps:
+        left=caps[g]-used[g]
+        if left:
+            rep,ch,port=g
+            remainder.append({'child':ch,'port':port,'replica':rep,'replicas':1,'family':families[g],
+                              'rank':left,'hosted':used[g],'pending_offset':used[g]})
+    profile=dict(sorted(total_profile().items()));assert M*M>2*max(profile)**2
+    raw=packed(roles);compressed=bytearray(gzip.compress(raw,mtime=0));compressed[9]=255
+    (a.out/'OWNERS.json.gz').write_bytes(bytes(compressed))
+    (a.out/'MAJORIZATION.json.gz').write_bytes(gzip.compress(packed(moves),mtime=0))
+    (a.out/'REMAINDERS.json').write_text(json.dumps(remainder,indent=2)+'\n')
+    (a.out/'PROFILE.json').write_text(json.dumps(profile,indent=2)+'\n')
+    fields={'profile':profile,'per_call_widths':[{'stage':s,'replica':r,'widths':widths[s,r]} for s,r in order],
+            'assignment_sha256':hashlib.sha256(raw).hexdigest(),'assignment_sha256_semantics':'SHA256 sorted-key compact uncompressed OWNERS array',
+            'source_owners_sha256':sha(a.owners),'provider_signatures':sig}
+    (a.out/'PLAN-OWNER-FIELDS.json').write_text(json.dumps(fields,indent=2)+'\n')
+    receipt={'status':'PASS_EXPANDED_OWNER_MATCHING_EXACT_COMBINATORICS_PENDING_GLOBAL_ADMISSION',
+             'source_plan':str(a.plan),'source_plan_sha256':sha(a.plan),'source_owners':str(a.owners),'source_owners_sha256':sha(a.owners),
+             'owners_sha256':sha(a.out/'OWNERS.json.gz'),'source_signatures':sig,
+             'roles':len(roles),'calls':len(order),'unchanged_call_order_and_windows':True,
+             'all_families_idle_and_outside_active_data':True,'one_helper_per_family_per_call':True,
+             'all_footprints_disjoint_compacted_prefixes':True,'integer_majorization_steps':sum(z['equal_width_multiset'] for z in moves),
+             'majorization_sha256':sha(a.out/'MAJORIZATION.json.gz'),'matching_rounds':rounds,
+             'global_profile':profile,'rank_mass':sum(r*n for r,n in profile.items()),'deficit':2560,
+             'remainder_profile':dict(sorted(idle_profile().items())),'maxchild':max(profile),
+             'candidate_floating_screen_b':rate(profile,2560,M),'seconds':time.monotonic()-beg,
+             'remaining_admission':'Fresh native-provider bindings, actual 73-column owner charts, independent full controller audit, finite invoice, exact moment and outer assembly.'}
+    (a.out/'EXPANDED-OWNER-REUSE.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    print(json.dumps({k:receipt[k] for k in ('status','roles','remainder_profile','rank_mass','candidate_floating_screen_b','seconds')},indent=2),flush=True)
+
+
+if __name__=='__main__':main()
diff --git a/research/gauge44-slots/hosting/frozen/FROZEN-AUDIT.json b/research/gauge44-slots/hosting/frozen/FROZEN-AUDIT.json
new file mode 100644
index 0000000000..5f95552366
--- /dev/null
+++ b/research/gauge44-slots/hosting/frozen/FROZEN-AUDIT.json
@@ -0,0 +1,57 @@
+{
+  "roles": 35424,
+  "calls": 72,
+  "fixed_point_calls_checked": 72,
+  "remainder_profile": {
+    "1": 85,
+    "2": 76,
+    "3": 173,
+    "7": 7,
+    "8": 6,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "all_footprints_disjoint_compacted_prefixes": true,
+  "all_helper_families_idle_and_outside_active_data": true,
+  "one_helper_per_physical_family_per_call": true,
+  "every_call_optimal_for_every_concave_remainder_cost": true,
+  "global_optimality_claimed": false,
+  "status": "PASS_FROZEN_HOSTING_AND_ALL_72_CALLWISE_FIXED_POINTS",
+  "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+  "owners_semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d",
+  "majorization_semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc",
+  "stored_integer_majorization_steps": 288,
+  "majorization_replay": "reproduce.py re-executes every step; this audit separately checks the final fixed point.",
+  "remaining_scope": "The package global verifier checks fresh local algebra, phases, windows, invoice, moment, and outer assembly."
+}
diff --git a/research/gauge44-slots/hosting/frozen/MAJORIZATION.json.gz b/research/gauge44-slots/hosting/frozen/MAJORIZATION.json.gz
new file mode 100644
index 0000000000..047b1cfb67
Binary files /dev/null and b/research/gauge44-slots/hosting/frozen/MAJORIZATION.json.gz differ
diff --git a/research/gauge44-slots/hosting/frozen/MANIFEST.json b/research/gauge44-slots/hosting/frozen/MANIFEST.json
new file mode 100644
index 0000000000..291005722c
--- /dev/null
+++ b/research/gauge44-slots/hosting/frozen/MANIFEST.json
@@ -0,0 +1,114 @@
+{
+  "schema": "gauge44-hosting-frozen-v1",
+  "parent_pr": 635,
+  "parent_paths": {
+    "plan": "research/complex-571-cold14-st2/data/PLAN.json",
+    "owners": "research/complex-571-cold14-st2/data/OWNERS.json.gz"
+  },
+  "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+  "artifacts": {
+    "OWNERS.json.gz": {
+      "sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+      "semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d"
+    },
+    "SEED-OWNERS.json.gz": {
+      "sha256": "eb3be5eebbb84349d7e7f1bde2fc77772a12ad5bccc6dab7c4efd8d903e2a048",
+      "semantic_sha256": "beea695aa2e1ab973ad53f475b3e3e9cf6d0f8a9bca2033a445b64f3b3484e34"
+    },
+    "MAJORIZATION.json.gz": {
+      "sha256": "ec5f94b13d190d72bc0608dc9fe2498cc43ba9deb05028159a812ec1e4dcacdf",
+      "semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc"
+    }
+  },
+  "new_provider": {
+    "R": 492,
+    "h": 9,
+    "v": 112,
+    "width_histogram": {
+      "4": 52,
+      "5": 48,
+      "7": 34,
+      "8": 114,
+      "9": 244
+    },
+    "width_sum": 3794,
+    "profile": {
+      "1": 2514,
+      "2": 404,
+      "3": 448,
+      "4": 160,
+      "5": 56,
+      "8": 8
+    },
+    "rank_mass": 5650,
+    "raw_word_sha256": "3ef4e74e81e2f4621fc95272918ac7b8bb8858df0baa16cc6d91424d55aead9e",
+    "canonical_word_sha256": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed",
+    "local_programs_sha256": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2",
+    "width_vector_sha256": "b7fbefdb3af3942194ac9314c767c7812bd68adb734d4e00b70b2916bdb55de8"
+  },
+  "seed_discovery": {
+    "provider_replaced": "jp8",
+    "unchanged_provider": "ck",
+    "passes": 2,
+    "price_b": 0.001638923,
+    "python": "3.12.14",
+    "numpy": "2.3.5",
+    "scipy": "1.17.0",
+    "note": "Only seed discovery uses floating-point Hungarian costs. Frozen seed and the expanded exact replay require the Python standard library."
+  },
+  "expanded_replay": {
+    "providers_replaced": [
+      "jp8",
+      "ck"
+    ],
+    "max_passes": 8,
+    "actual_passes": 4,
+    "integer_majorization_steps": 288,
+    "changed_width_bootstrap_calls": 1
+  },
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "remainder_profile": {
+    "1": 85,
+    "2": 76,
+    "3": 173,
+    "7": 7,
+    "8": 6,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "live": 7168,
+  "roles": 35424,
+  "calls": 72,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "candidate_floating_screen_b": 0.0016522089943684115,
+  "screening_only": "The floating rate here is not a certified exponent. Exact supplier and outer admission belong to the package verifier."
+}
diff --git a/research/gauge44-slots/hosting/frozen/MATCHING-RECEIPT.json b/research/gauge44-slots/hosting/frozen/MATCHING-RECEIPT.json
new file mode 100644
index 0000000000..993331090c
--- /dev/null
+++ b/research/gauge44-slots/hosting/frozen/MATCHING-RECEIPT.json
@@ -0,0 +1,1205 @@
+{
+  "status": "PASS_EXPANDED_OWNER_MATCHING_EXACT_COMBINATORICS_PENDING_GLOBAL_ADMISSION",
+  "source_plan": "explicit parent PLAN, with a temporary signature-only seed view for expanded replay",
+  "source_plan_sha256": "0d2b6a12d3450cfb78e556e80d34cabb8cd1a7f8aa85c1a712a5177236672a37",
+  "source_owners": "frozen/SEED-OWNERS.json.gz",
+  "source_owners_sha256": "eb3be5eebbb84349d7e7f1bde2fc77772a12ad5bccc6dab7c4efd8d903e2a048",
+  "owners_sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+  "source_signatures": {
+    "ck": {
+      "widths": [
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
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+}
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diff --git a/research/gauge44-slots/hosting/frozen/REPRODUCTION.json b/research/gauge44-slots/hosting/frozen/REPRODUCTION.json
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index 0000000000..8ad59712b2
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+}
diff --git a/research/gauge44-slots/hosting/frozen/SEED-OWNERS.json.gz b/research/gauge44-slots/hosting/frozen/SEED-OWNERS.json.gz
new file mode 100644
index 0000000000..d61916a156
Binary files /dev/null and b/research/gauge44-slots/hosting/frozen/SEED-OWNERS.json.gz differ
diff --git a/research/gauge44-slots/hosting/frozen/SEED-RECEIPT.json b/research/gauge44-slots/hosting/frozen/SEED-RECEIPT.json
new file mode 100644
index 0000000000..82911f647b
--- /dev/null
+++ b/research/gauge44-slots/hosting/frozen/SEED-RECEIPT.json
@@ -0,0 +1,1537 @@
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+      "failed_positions": []
+    },
+    "(1, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(0, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(0, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(1, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(2, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 0)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 1)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(3, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 2)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(4, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 3)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(5, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 4)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(6, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 5)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(7, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 6)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    },
+    "(8, 7)": {
+      "old_total": 3894,
+      "new_total": 3794,
+      "sorted_termwise_dominance": true,
+      "failed_positions": []
+    }
+  },
+  "matching_passes": [
+    {
+      "pass": "sorted",
+      "touched_group_idle_pressure": 44.06409529228022,
+      "calls_awaiting_capacity_matching": 0
+    },
+    {
+      "pass": 1,
+      "accepted_calls": 71,
+      "touched_group_idle_pressure": 24.92521223381306,
+      "decrease": 19.13888305846716
+    },
+    {
+      "pass": 2,
+      "accepted_calls": 58,
+      "touched_group_idle_pressure": 23.047886627886065,
+      "decrease": 1.8773256059269947
+    }
+  ],
+  "roles": 35424,
+  "calls": 72,
+  "remainder_children": 3197,
+  "remainder_profile": {
+    "1": 83,
+    "2": 99,
+    "3": 197,
+    "4": 168,
+    "5": 6,
+    "6": 13,
+    "7": 16,
+    "8": 145,
+    "10": 4,
+    "11": 24,
+    "12": 19,
+    "13": 1,
+    "14": 3,
+    "15": 9,
+    "16": 107,
+    "18": 1,
+    "19": 10,
+    "20": 15,
+    "23": 2,
+    "24": 52,
+    "32": 1,
+    "44": 1,
+    "48": 2221
+  },
+  "global_profile": {
+    "1": 181177,
+    "2": 29335,
+    "3": 32309,
+    "4": 11692,
+    "5": 4052,
+    "6": 17,
+    "7": 16,
+    "8": 721,
+    "10": 4,
+    "11": 24,
+    "12": 19,
+    "13": 1,
+    "14": 3,
+    "15": 9,
+    "16": 107,
+    "18": 1,
+    "19": 10,
+    "20": 15,
+    "23": 2,
+    "24": 52,
+    "32": 1,
+    "44": 1,
+    "48": 2221
+  },
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "source_floating_screen_b": 0.001638923175694355,
+  "candidate_floating_screen_b": 0.0016446065186552388,
+  "remaining_admission": "Bind freshly verified provider artifacts and their hashes; regenerate the global template, actual 73-column sigmas and remainder axes with the existing emitter; run independent owner/frame audit, finite invoice, and exact moment/outer assembly.",
+  "provenance_note": "Absolute discovery paths and wall time removed; original artifact hashes and all exact combinatorial fields preserved."
+}
diff --git a/research/gauge44-slots/hosting/frozen/SEED-REPRODUCTION.json b/research/gauge44-slots/hosting/frozen/SEED-REPRODUCTION.json
new file mode 100644
index 0000000000..91ee98cf70
--- /dev/null
+++ b/research/gauge44-slots/hosting/frozen/SEED-REPRODUCTION.json
@@ -0,0 +1,29 @@
+{
+  "status": "PASS_FROZEN_OWNER_AND_INTEGER_MAJORIZATION_REPLAY",
+  "seed_mode": "two_pass_hungarian_discovery_rebuilt",
+  "parent_plan_sha256": "258a8b9baa245fa4096828671e2f1d1462b5af08d56890629622ef6125eaddda",
+  "parent_owners_sha256": "935ff1a6823c6625daba3349b28d74acf9a3d70a5947ae155aa66c7821804add",
+  "owners_semantic_sha256": "c09faf298565c1388c02370fdd4e61dd542579fe1898e842d5096cc97b68191d",
+  "owners_gzip_sha256": "90ff7657a23dcfb67532b49c0800c5fc259b27c89005081e24bf184869e1bd57",
+  "majorization_semantic_sha256": "9ed3fdb41fb8dbc6542de7701c78bb8f3bb728604057daf82a537bde182ab9fc",
+  "global_profile": {
+    "1": 181093,
+    "2": 29164,
+    "3": 32429,
+    "4": 11520,
+    "5": 4032,
+    "7": 7,
+    "8": 582,
+    "12": 13,
+    "16": 33,
+    "19": 1,
+    "20": 2,
+    "28": 4,
+    "32": 62,
+    "36": 1,
+    "40": 1,
+    "44": 6,
+    "48": 2289
+  },
+  "scope": "Exact hosting nomination and callwise fixed-point replay; full supplier admission is separate."
+}
diff --git a/research/gauge44-slots/hosting/reproduce.py b/research/gauge44-slots/hosting/reproduce.py
new file mode 100644
index 0000000000..2f29a5ff13
--- /dev/null
+++ b/research/gauge44-slots/hosting/reproduce.py
@@ -0,0 +1,100 @@
+"""Reproduce the frozen all-cold44 owner nomination from explicit inputs.
+
+By default, replay the exact integer optimizer from the included frozen seed.
+--rebuild-seed additionally repeats the original two floating-cost Hungarian
+discovery passes; that optional route requires NumPy and SciPy.
+"""
+from pathlib import Path
+from collections import Counter
+import argparse
+import copy
+import json
+import shutil
+import subprocess
+import sys
+
+from audit_frozen import HERE, add_inputs, bound_inputs, semantic_sha
+from reuse_owners import audit_roles, read, sha
+
+
+def run(name, *args):
+    subprocess.run([sys.executable, str(HERE/name), *map(str, args)], check=True)
+
+
+def seed_plan(parent, seed_owners, new_signature):
+    """Build a signature-only resizer input; never an admitted provider PLAN."""
+    plan = copy.deepcopy(parent)
+    plan['provider_registry']['jp8']['widths'] = new_signature['widths']
+    plan['provider_registry']['jp8']['actual_paid_profile'] = new_signature['profile']
+    call_widths = {
+        (c['stage'], c['replica']): plan['provider_registry'][c['provider']]['widths']
+        for c in plan['provider_calls']
+    }
+    used, families = audit_roles(seed_owners, plan, call_widths, 112, 492)
+    profile = Counter()
+    for c in plan['provider_calls']:
+        profile.update({int(r): n for r, n in plan['provider_registry'][c['provider']]['actual_paid_profile'].items()})
+    for key, (cap, times) in plan['windows'].items():
+        rep, child = map(int, key.split(','))
+        for port in range(112):
+            left = cap-len(used[rep, child, port])
+            if left:
+                profile[left] += 1
+    assert 73*7168-sum(r*n for r, n in profile.items()) == 2560
+    plan['profile'] = dict(sorted(profile.items()))
+    plan['per_call_widths'] = [
+        {'stage': s, 'replica': r, 'widths': call_widths[s, r]}
+        for s, r in plan['order']
+    ]
+    plan['status'] = 'INTERMEDIATE_SIGNATURE_ONLY_OWNER_SEED_NOT_PROVIDER_ADMISSION'
+    return plan
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    add_inputs(parser)
+    parser.add_argument('--rebuild-seed', action='store_true')
+    parser.add_argument('--out', type=Path, required=True, help='New output directory')
+    args = parser.parse_args()
+    manifest = read(HERE/'frozen/MANIFEST.json')
+    parent, sig, provider = bound_inputs(args, manifest)
+    args.out.mkdir(parents=True, exist_ok=False)
+    seed_dir = args.out/'seed'
+    if args.rebuild_seed:
+        run('reuse_owners.py', '--plan', args.parent_plan, '--owners', args.parent_owners,
+            '--signature', f'jp8={provider}', '--passes', '2', '--price-b', '0.001638923', '--out', seed_dir)
+    else:
+        seed_dir.mkdir()
+        shutil.copyfile(HERE/'frozen/SEED-OWNERS.json.gz', seed_dir/'OWNERS.json.gz')
+    assert semantic_sha(seed_dir/'OWNERS.json.gz') == manifest['artifacts']['SEED-OWNERS.json.gz']['semantic_sha256'], (
+        'Seed differs; use the default frozen-seed replay, or the recorded NumPy/SciPy versions for discovery replay.'
+    )
+    plan = seed_plan(parent, read(seed_dir/'OWNERS.json.gz'), sig)
+    plan_path = seed_dir/'PLAN-FOR-RESIZER.json'
+    plan_path.write_text(json.dumps(plan, indent=2)+'\n')
+    final_dir = args.out/'all72'
+    run('expand_owners.py', '--plan', plan_path, '--owners', seed_dir/'OWNERS.json.gz',
+        '--signature', f'jp8={provider}', '--signature', f'ck={provider}',
+        '--max-passes', '8', '--out', final_dir)
+    for name in ('OWNERS.json.gz', 'MAJORIZATION.json.gz'):
+        assert semantic_sha(final_dir/name) == manifest['artifacts'][name]['semantic_sha256'], (name, 'Frozen semantic digest mismatch')
+    kwargs = ('--local44', args.local44) if args.local44 is not None else ('--raw-word', args.raw_word)
+    run('audit_frozen.py', '--parent-plan', args.parent_plan, '--parent-owners', args.parent_owners,
+        *kwargs, '--owners', final_dir/'OWNERS.json.gz', '--majorization', final_dir/'MAJORIZATION.json.gz',
+        '--out', args.out/'FROZEN-AUDIT.json')
+    receipt = {
+        'status': 'PASS_FROZEN_OWNER_AND_INTEGER_MAJORIZATION_REPLAY',
+        'seed_mode': 'two_pass_hungarian_discovery_rebuilt' if args.rebuild_seed else 'included_frozen_seed',
+        'parent_plan_sha256': sha(args.parent_plan), 'parent_owners_sha256': sha(args.parent_owners),
+        'owners_semantic_sha256': semantic_sha(final_dir/'OWNERS.json.gz'),
+        'owners_gzip_sha256': sha(final_dir/'OWNERS.json.gz'),
+        'majorization_semantic_sha256': semantic_sha(final_dir/'MAJORIZATION.json.gz'),
+        'global_profile': read(final_dir/'PROFILE.json'),
+        'scope': 'Exact hosting nomination and callwise fixed-point replay; full supplier admission is separate.',
+    }
+    (args.out/'REPRODUCTION.json').write_text(json.dumps(receipt, indent=2)+'\n')
+    print(json.dumps(receipt, indent=2))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/hosting/reuse_owners.py b/research/gauge44-slots/hosting/reuse_owners.py
new file mode 100644
index 0000000000..234b831790
--- /dev/null
+++ b/research/gauge44-slots/hosting/reuse_owners.py
@@ -0,0 +1,230 @@
+"""Deterministic existing-family owner reuse and optional callwise matching.
+
+The output is a nomination, requiring the ordinary independent owner, phase,
+finite-invoice, and exact-moment admission. No MILP or new owner family is used.
+"""
+from collections import Counter, defaultdict
+from pathlib import Path
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+import math
+import time
+
+
+def read(path):
+    raw=Path(path).read_bytes()
+    return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw)
+
+
+def packed(obj):return json.dumps(obj,sort_keys=True,separators=(',',':')).encode()
+def sha(path):return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def signature(path):
+    path=Path(path)
+    if path.is_dir():
+        w=read(path/'CANONICAL-WORD.json.gz');V,R=w['v'],w['R']
+        widths=[len(w['frames'][w['final'][2*V+h]])-len(w['frames'][w['start'][2*V+h]]) for h in range(R)]
+        programs=read(path/'LOCAL-PROGRAMS.json.gz')
+        profiles=[Counter(e[-1] for e in programs[o] if e[0] in ('climb','center')) for o in ('forward','backward')]
+        assert profiles[0]==profiles[1]
+        assert profiles[0]=={int(r):n for r,n in w['local_profile'].items()}
+        return {'widths':widths,'profile':dict(profiles[0]),'source':str(path),
+                'canonical_sha256':sha(path/'CANONICAL-WORD.json.gz'),
+                'program_sha256':sha(path/'LOCAL-PROGRAMS.json.gz')}
+    w=read(path)
+    if 'report' in w:
+        V,R=w['report']['v'],w['report']['R']
+        widths=[len(w.get('helper_final',{}).get(str(2*V+h),range(9)))-len(w.get('start_extra',{}).get(str(2*V+h),[])) for h in range(R)]
+        profile={int(r):n for r,n in w['report']['local_profile'].items()}
+    else:
+        widths=w['widths'];profile={int(r):n for r,n in w['profile'].items()}
+    return {'widths':widths,'profile':profile,'source':str(path),'source_sha256':sha(path)}
+
+
+def phi(rank,b,M):return rank*math.expm1(b*math.log(M/rank)) if rank else 0.
+
+
+def rate(profile,deficit,M):
+    lo,hi=0.,.02
+    for _ in range(58):
+        mid=(lo+hi)/2
+        if sum(n*phi(r,mid,M) for r,n in profile.items())<deficit:lo=mid
+        else:hi=mid
+    return lo
+
+
+def audit_roles(roles,plan,widths_by_call,V,R):
+    used=defaultdict(set);families=defaultdict(set);helpers=defaultdict(set)
+    for z in roles:
+        s,rep,h=z['stage'],z['replica'],z['helper'];call=(s,rep)
+        assert z['time']==plan['order'].index([s,rep])
+        assert 0<=h<R and z['width']==widths_by_call[call][h]
+        assert h not in helpers[call] and z['family'] not in families[call]
+        helpers[call].add(h);families[call].add(z['family'])
+        orp,ch,port=z['owner_replica'],z['child'],z['port']
+        assert z['copy']==orp*V+port
+        assert z['family']==orp*(8*V)+(2*plan['pairs'][str(ch)]+plan['sides'][str(ch)])*V+port
+        cap,window=plan['windows'][f'{orp},{ch}']
+        assert z['time'] in window and 0<=z['offset'] and z['offset']+z['width']<=cap
+        cells=set(range(z['offset'],z['offset']+z['width']))
+        key=(orp,ch,port);assert not used[key]&cells;used[key]|=cells
+    assert len(roles)==len(plan['order'])*R
+    assert all(helpers[tuple(c)]==set(range(R)) for c in plan['order'])
+    for cells in used.values():assert cells==set(range(len(cells)))
+    return used,families
+
+
+def main():
+    ap=argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--plan',type=Path,required=True)
+    ap.add_argument('--owners',type=Path,required=True)
+    ap.add_argument('--signature',action='append',default=[],help='Existing PID=raw-word, signature JSON, or verified native directory')
+    ap.add_argument('--passes',type=int,default=2)
+    ap.add_argument('--price-b',type=float,default=0.001638923)
+    ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args();assert 0<=a.passes<=2
+    a.out.mkdir(parents=True,exist_ok=False);beg=time.monotonic()
+    plan,oldroles=read(a.plan),read(a.owners)
+    assert (plan['K'],plan['T'],plan['M'],plan['L'])==(4,8,73,9)
+    M,V=73,112;R=len(next(iter(plan['provider_registry'].values()))['widths'])
+    signatures={pid:{'widths':desc['widths'],'profile':{int(r):n for r,n in desc['actual_paid_profile'].items()},'source':'inherited PLAN'} for pid,desc in plan['provider_registry'].items()}
+    for spec in a.signature:
+        pid,path=spec.split('=',1);assert pid in signatures
+        signatures[pid]=signature(path)
+    for sig in signatures.values():
+        assert len(sig['widths'])==R and all(type(w) is int and 0<w<=9 for w in sig['widths'])
+        assert sum(int(r)*n for r,n in sig['profile'].items())==16*V+64+sum(sig['widths'])
+    calls={(c['stage'],c['replica']):c for c in plan['provider_calls']}
+    oldwidths={k:plan['provider_registry'][c['provider']]['widths'] for k,c in calls.items()}
+    newwidths={k:signatures[c['provider']]['widths'] for k,c in calls.items()}
+    oldused,oldfamilies=audit_roles(oldroles,plan,oldwidths,V,R)
+
+    # A slot is an old immutable owner-family opportunity. Only the helper
+    # assigned to the opportunity and its footprint width may change.
+    bycall=defaultdict(list);groups=defaultdict(list)
+    for i,z in enumerate(oldroles):
+        bycall[z['stage'],z['replica']].append(i)
+        groups[z['owner_replica'],z['child'],z['port']].append(i)
+    group_of={i:g for g,ids in groups.items() for i in ids}
+    cap={g:plan['windows'][f'{g[0]},{g[1]}'][0] for g in groups}
+    assigned_h={};assigned_w={};dominance={};pending=[]
+    for call,ids in bycall.items():
+        slots=sorted(ids,key=lambda i:(oldroles[i]['width'],oldroles[i]['helper']))
+        helpers=sorted(range(R),key=lambda h:(newwidths[call][h],h))
+        failures=[(h,newwidths[call][h],oldroles[i]['width']) for h,i in zip(helpers,slots) if newwidths[call][h]>oldroles[i]['width']]
+        if failures:
+            # Keep this call's old widths provisionally; shrunk calls leave
+            # slack on their original owner families. A subsequent exact
+            # bipartite matching may use that slack for this call.
+            pending.append(call)
+            for i in ids:assigned_h[i]=oldroles[i]['helper'];assigned_w[i]=oldroles[i]['width']
+        else:
+            for h,i in zip(helpers,slots):assigned_h[i]=h;assigned_w[i]=newwidths[call][h]
+        dominance[str(call)]={'old_total':sum(oldwidths[call]),'new_total':sum(newwidths[call]),'sorted_termwise_dominance':not failures,'failed_positions':failures}
+    used={g:sum(assigned_w[i] for i in ids) for g,ids in groups.items()}
+    assert all(used[g]<=cap[g] for g in groups)
+    cost_cache=[phi(r,a.price_b,M) for r in range(49)]
+    def current_cost():return sum(cost_cache[cap[g]-used[g]] for g in groups)
+    passes=[{'pass':'sorted','touched_group_idle_pressure':current_cost(),'calls_awaiting_capacity_matching':len(pending)}]
+
+    if a.passes or pending:
+        import numpy as np
+        from scipy.optimize import linear_sum_assignment
+        def match_call(call,force=False):
+            ids=sorted(bycall[call],key=lambda i:oldroles[i]['helper'])
+            gs=[group_of[i] for i in ids]
+            assert len(set(gs))==R, 'one owner family per complete call is essential'
+            available=np.array([cap[g]-used[g]+assigned_w[i] for i,g in zip(ids,gs)],dtype=np.int64)
+            ws=np.array(newwidths[call],dtype=np.int64)
+            left=available[None,:]-ws[:,None]
+            matrix=np.full((R,R),np.inf)
+            valid=left>=0
+            matrix[valid]=np.asarray(cost_cache)[left[valid]]
+            ri,ci=linear_sum_assignment(matrix)
+            assert len(ri)==R and np.all(np.isfinite(matrix[ri,ci]))
+            oldcost=sum(cost_cache[cap[g]-used[g]] for g in gs)
+            newcost=float(matrix[ri,ci].sum())
+            if not force:
+                assert newcost<=oldcost+1e-10
+                if oldcost-newcost<=1e-10:return False
+            for h,col in zip(ri,ci):
+                i=ids[int(col)];g=group_of[i];h=int(h);ww=int(ws[h])
+                used[g]+=ww-assigned_w[i];assigned_w[i]=ww;assigned_h[i]=h
+                assert used[g]<=cap[g]
+            return True
+        for call in pending:
+            match_call(call,force=True)
+            dominance[str(call)]['capacity_matching_feasible']=True
+        if pending:passes.append({'pass':'capacity_bootstrap','touched_group_idle_pressure':current_cost(),'resolved_calls':[list(c) for c in pending]})
+        for p in range(a.passes):
+            accepted=0;startcost=current_cost()
+            order=[tuple(k) for k in plan['order']]
+            if p%2:order.reverse()
+            for call in order:
+                accepted+=match_call(call)
+            finalcost=current_cost();assert finalcost<=startcost+1e-9
+            passes.append({'pass':p+1,'accepted_calls':accepted,'touched_group_idle_pressure':finalcost,'decrease':startcost-finalcost})
+
+    # The inherited compiler requires each used coordinate set to be a
+    # prefix. Stable left compaction preserves every immutable owner field.
+    roles=copy.deepcopy(oldroles);matching=[]
+    for g,ids in groups.items():
+        off=0
+        for i in sorted(ids,key=lambda i:(oldroles[i]['offset'],oldroles[i]['time'],oldroles[i]['helper'])):
+            z=roles[i];z['helper']=assigned_h[i];z['width']=assigned_w[i];z['offset']=off;off+=z['width']
+            matching.append({'stage':z['stage'],'replica':z['replica'],'old_helper':oldroles[i]['helper'],
+                             'new_helper':z['helper'],'old_width':oldroles[i]['width'],'new_width':z['width'],
+                             'family':z['family'],'child':z['child'],'old_offset':oldroles[i]['offset'],'new_offset':z['offset']})
+        assert off==used[g]<=cap[g]
+    roles.sort(key=lambda z:(z['time'],z['helper']))
+    newused,newfamilies=audit_roles(roles,plan,newwidths,V,R)
+    assert newfamilies==oldfamilies
+    paid=Counter();remainders=[]
+    for c in plan['provider_calls']:paid.update(signatures[c['provider']]['profile'])
+    idle=Counter()
+    for key,(capacity,window) in plan['windows'].items():
+        rep,ch=map(int,key.split(','))
+        for port in range(V):
+            occupied=len(newused[rep,ch,port]);left=capacity-occupied
+            if left:
+                family=rep*(8*V)+(2*plan['pairs'][str(ch)]+plan['sides'][str(ch)])*V+port
+                remainders.append({'child':ch,'port':port,'replica':rep,'replicas':1,'family':family,
+                                   'rank':left,'hosted':occupied,'pending_offset':occupied})
+                idle[left]+=1
+    paid.update(idle);mass=sum(r*n for r,n in paid.items())
+    assert M*plan['live']-mass==plan['deficit']==2560
+    assert M*M>2*max(paid)**2
+    oldprofile={int(r):n for r,n in plan['profile'].items()}
+    ownerraw=packed(roles);gz=bytearray(gzip.compress(ownerraw,mtime=0));gz[9]=255
+    (a.out/'OWNERS.json.gz').write_bytes(bytes(gz))
+    (a.out/'MATCHING.json.gz').write_bytes(gzip.compress(packed(matching),mtime=0))
+    (a.out/'REMAINDERS.json').write_text(json.dumps(remainders,indent=2)+'\n')
+    profile=dict(sorted(paid.items()))
+    (a.out/'PROFILE.json').write_text(json.dumps(profile,indent=2)+'\n')
+    owner_fields={'profile':profile,
+                  'per_call_widths':[{'stage':s,'replica':r,'widths':newwidths[s,r]} for s,r in plan['order']],
+                  'assignment_sha256':hashlib.sha256(ownerraw).hexdigest(),
+                  'assignment_sha256_semantics':'SHA256 of sorted-key compact uncompressed OWNERS array',
+                  'source_owners_sha256':sha(a.owners),
+                  'provider_signatures':signatures}
+    (a.out/'PLAN-OWNER-FIELDS.json').write_text(json.dumps(owner_fields,indent=2)+'\n')
+    rec={'status':'PASS_OWNER_REUSE_NOMINATION_COMBINATORICS_NOT_FULL_SUPPLIER_ADMISSION',
+         'source_plan':str(a.plan),'source_plan_sha256':sha(a.plan),'source_owners_sha256':sha(a.owners),
+         'owners_sha256':sha(a.out/'OWNERS.json.gz'),'unchanged_owner_family_sets':True,
+         'unchanged_call_order_and_windows':True,'all_footprints_are_disjoint_compacted_prefixes':True,
+         'local_signatures':signatures,'sorted_initial_dominance':dominance,'matching_passes':passes,
+         'roles':len(roles),'calls':len(calls),'remainder_children':len(remainders),'remainder_profile':dict(sorted(idle.items())),
+         'global_profile':profile,'rank_mass':mass,'deficit':2560,'maxchild':max(paid),
+         'source_floating_screen_b':rate(oldprofile,2560,M),
+         'candidate_floating_screen_b':rate(profile,2560,M),
+         'seconds':time.monotonic()-beg,
+         'remaining_admission':'Bind freshly verified provider artifacts and their hashes; regenerate the global template, actual 73-column sigmas and remainder axes with the existing emitter; run independent owner/frame audit, finite invoice, and exact moment/outer assembly.'}
+    (a.out/'OWNER-REUSE.json').write_text(json.dumps(rec,indent=2)+'\n')
+    print(json.dumps({k:rec[k] for k in ('status','roles','matching_passes','remainder_profile','rank_mass','source_floating_screen_b','candidate_floating_screen_b','seconds')},indent=2),flush=True)
+
+
+if __name__=='__main__':main()
diff --git a/research/gauge44-slots/independent/CENTRE-GUARD-REVIEW.md b/research/gauge44-slots/independent/CENTRE-GUARD-REVIEW.md
new file mode 100644
index 0000000000..6c62bd070e
--- /dev/null
+++ b/research/gauge44-slots/independent/CENTRE-GUARD-REVIEW.md
@@ -0,0 +1,79 @@
+# Independent review of the centre and admission interfaces
+
+**Finding:** the replacement of old local centre-carrier IDs by equality of the
+eight ordered centre-frame bases preserves the inherited global contract. It
+must be used together with the complete local scalar, frame, phase and wrapper
+admission. No mathematical admission guard was found to have been removed.
+
+## Why source carriers may supply centres
+
+The transported gauge44 centre carriers are
+`[92, 57, 81, 224, 11, 240, 9, 256]`. Five are source registers and three are
+helper registers. All 112 transported port labels and all eight ordered
+rank-eight centre-frame bases agree exactly with the retained parent. The
+optional `--main` check in `audit_local.py` independently verifies that boundary
+against a byte-pinned parent canonical word.
+
+The actual forward local program copies the current row of `L_r` into private
+`C_k` at their common frame `F_k`. It then descends `C_k` from `F_k` to frame
+zero, scatters to the targets, and clears `C_k`. The backward program performs
+the corresponding reversed ascent and scatter. This construction depends on
+the copied row, its frame and the exact local program, rather than on a
+requirement that `r` be in the helper-ID interval. The source itself is not
+cleared or treated as private work.
+
+The independently checked local contract retains every required obligation:
+all 716 input columns in both orientations; the forward and backward shear
+identities; arbitrary initial helper dirt; scalar/COPY common-frame legality;
+centre lifetimes and nested steps; exact native phase identities; endpoint
+and row/column cone conditions; and residual wrappers before and after every
+relevant touch. Its finite invoice recounts the actual operations.
+
+The global controller addresses private centres by `k`, while the source or
+helper `L_r` is mapped through the complete invocation's ordinary owner array.
+The owner audit retains pairwise distinct owners for all active source, target
+and helper roles. A helper therefore cannot borrow the family of an active
+source centre. The private-centre namespace is disjoint from those owners and
+the local program clears it. Each whole invocation finishes before another
+begins, so no new interleaving or family lifetime assumption is introduced.
+
+## Admission guards and single-provider controls
+
+An AST comparison with PR635 found all **91 assertions in `code/assemble.py`
+identical, in the same traversal order**, including constants. This includes
+the unchanged PR543 bit input, deficit and surcharge, every finite-invoice
+guard, both conservative and native complex moment checks, and the strict
+outer assembly and its controls. The following files retain the reviewed PR635 code (the packaged
+`bind_providers_portable.py` only trims trailing whitespace): `invoice_allcold.py` (67 assertions),
+`bind_providers_portable.py` (22), `generated_identity.py` (4), and `witness.py`
+(3). `review_guards.py` reproduces the assertion comparison and records the
+file hashes.
+
+The controller still checks the complete serialized provider registry,
+per-call program and dispatch, native phase and wrapper bindings, helper
+widths, owner uniqueness, actual busy-family windows, spectator orthogonality,
+and literal idle remainders. The single-provider branch replaces partner
+substitutions by direct invalid-ID, program, width and hash mutations. Only
+four assembly mutation scenarios requiring a second registered provider are
+inapplicable. Their removal does not remove any admission predicate. Direct
+forged program/phase tests, width-order and width-inventory tests, and
+selected-call/order tests remain.
+
+## Price and bit headroom
+
+The frozen all72 profile gives the native complex root bracket
+`(0.001652208994368411824947, 0.001652208994368411824948)` and
+`kappa = 0.001649483702558979`. Both independent rational engines certify the
+two signs. The seven-step outer driver passes all 47 strict constraints and
+rejects its four standard mutations. The conservative complex price passes
+separately at `kappa = 0.001649483699681650`.
+
+The achieved complex rate is below PR543's retained bit rate
+`0.001653826988146798944268`. Using eumemic's independently reviewed PR555 bit
+rate `0.001733052823330162099157` gives exactly the same attained kappa. PR543
+therefore remains the cited supplier for this delta; no bit improvement is
+claimed here and no PR555 implementation is bundled.
+
+These receipts supplement the package's complete native, owner, phase and
+finite-invoice replay. The inherited all-size realization and analytic
+transfer assumptions remain conditional.
diff --git a/research/gauge44-slots/independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json b/research/gauge44-slots/independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json
new file mode 100644
index 0000000000..771faa86a7
--- /dev/null
+++ b/research/gauge44-slots/independent/GAUGE-COLD44-INDEPENDENT-AUDIT.json
@@ -0,0 +1,137 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+  "input_file": "FULL-WORD.json.gz",
+  "content_sha256": "78c7aadacb6eec2eeecc124ca236e5bcfdba6a52b30c2971aaa596d1d119b290",
+  "compressed_sha256": "3ef4e74e81e2f4621fc95272918ac7b8bb8858df0baa16cc6d91424d55aead9e",
+  "parent_center_interface": {
+    "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+    "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "transport_tau": 43,
+    "ordered_frame_bases_match": true,
+    "all_ports_match": true,
+    "transported_centers": [
+      92,
+      57,
+      81,
+      224,
+      11,
+      240,
+      9,
+      256
+    ],
+    "source_centers": [
+      92,
+      57,
+      81,
+      11,
+      9
+    ],
+    "ordered_frame_bases": [
+      [
+        256,
+        128,
+        64,
+        34,
+        16,
+        10,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        16,
+        8,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        17,
+        9,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ],
+      [
+        256,
+        128,
+        66,
+        32,
+        18,
+        8,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        17,
+        9,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        16,
+        8,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        68,
+        32,
+        16,
+        12,
+        2,
+        1
+      ]
+    ]
+  },
+  "v": 112,
+  "h": 9,
+  "R": 492,
+  "entering": 204,
+  "lowends": 78,
+  "coldends": 44,
+  "compensation_gates": 7348,
+  "local_profile": {
+    "1": 2514,
+    "2": 404,
+    "3": 448,
+    "4": 160,
+    "5": 56,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 52,
+    "5": 48,
+    "7": 34,
+    "8": 114,
+    "9": 244
+  },
+  "checked_columns": 716,
+  "elapsed_seconds": 3.147683588000291,
+  "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+}
diff --git a/research/gauge44-slots/independent/GAUGE44-GLOBAL-GUARD-REVIEW.json b/research/gauge44-slots/independent/GAUGE44-GLOBAL-GUARD-REVIEW.json
new file mode 100644
index 0000000000..e2df1dcca8
--- /dev/null
+++ b/research/gauge44-slots/independent/GAUGE44-GLOBAL-GUARD-REVIEW.json
@@ -0,0 +1,47 @@
+{
+  "status": "PASS_PR635_ADMISSION_ASSERTION_PRESERVATION",
+  "files": [
+    {
+      "file": "code/assemble.py",
+      "baseline_sha256": "1b1a9024ac910dc9b9d9e30150684e1fa9cb228a4c1c275b75ab04b57fdef1dd",
+      "new_sha256": "7ac28118d69416e4fb67b61216285fb0823310b7635ce1b9025aa3f10119ef6a",
+      "byte_identical": false,
+      "assert_count": 91,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/invoice_allcold.py",
+      "baseline_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+      "new_sha256": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+      "byte_identical": true,
+      "assert_count": 67,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/bind_providers_portable.py",
+      "baseline_sha256": "2eb5c262bf481b3bec9ceaec654fa46ff6fc3a89b13d4906a29a55a89e35feea",
+      "new_sha256": "2eb5c262bf481b3bec9ceaec654fa46ff6fc3a89b13d4906a29a55a89e35feea",
+      "byte_identical": true,
+      "assert_count": 22,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/generated_identity.py",
+      "baseline_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+      "new_sha256": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+      "byte_identical": true,
+      "assert_count": 4,
+      "all_assertions_identical_in_order": true
+    },
+    {
+      "file": "code/witness.py",
+      "baseline_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+      "new_sha256": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d",
+      "byte_identical": true,
+      "assert_count": 3,
+      "all_assertions_identical_in_order": true
+    }
+  ],
+  "centre_interface_review": "CENTRE-GUARD-REVIEW.md",
+  "scope": "Exact syntax preservation for all admission assertions in these five files. The changed emitter/controller centre boundary and single-provider controls require the separate semantic review; assertion counts alone do not prove them."
+}
diff --git a/research/gauge44-slots/independent/GAUGE44-INDEPENDENT-PRICE.json b/research/gauge44-slots/independent/GAUGE44-INDEPENDENT-PRICE.json
new file mode 100644
index 0000000000..7aa86180dd
--- /dev/null
+++ b/research/gauge44-slots/independent/GAUGE44-INDEPENDENT-PRICE.json
@@ -0,0 +1,156 @@
+{
+  "status": "PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK",
+  "profile_input_file": "PLAN.json",
+  "profile_input_sha256": "7b3122026e82b9d9e964d2a50c7bffdc976ae3dfea64bb98b2fdad5cfbdbaa20",
+  "global_profile": {
+    "1": 174763,
+    "2": 30105,
+    "3": 30275,
+    "4": 12240,
+    "5": 4896,
+    "7": 54,
+    "8": 576,
+    "16": 23,
+    "48": 2419
+  },
+  "live": 7168,
+  "m": 73,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "prices": {
+    "native": {
+      "root": {
+        "lower": "0.001674185476674086429846",
+        "upper": "0.001674185476674086429847",
+        "lower_endpoint_residual_upper": "-9.258737006004892346173061244464039982798397391664878463422077941068021E-25",
+        "upper_endpoint_residual_lower": "2.005290772036567694936493754533147163786510359586083088453102073919377E-24",
+        "strict_rational_signs": true
+      },
+      "exact_moments": [
+        {
+          "endpoint": "837092738337043214923/500000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-24961505588706589063536270371864708160498115/26959946667150639794667015087019630673637144422540572481103610249216",
+            "-24961505588706589063536270371864708160498113/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "-462937/500000000000000000000000000000",
+            "-925873/1000000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "1674185476674086429847/1000000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "54062532266235196619370246291034158858524675/26959946667150639794667015087019630673637144422540572481103610249216",
+            "54062532266235196619370246291034158858524677/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "200529/100000000000000000000000000000",
+            "2005291/1000000000000000000000000000000"
+          ]
+        }
+      ],
+      "outer_with_bit": {
+        "complex_b": "837092738337043214923/500000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "835693632195073/500000000000000000",
+        "kappa_decimal": "0.001671387264390146",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    },
+    "conservative": {
+      "root": {
+        "lower": "0.001674185473814575474867",
+        "upper": "0.001674185473814575474868",
+        "lower_endpoint_residual_upper": "-4.932703074050864500363221905991238131757959051186123070698964701314504E-25",
+        "upper_endpoint_residual_lower": "2.437894165237372647986425295760776771093048289170590753978317997095726E-24",
+        "strict_rational_signs": true
+      },
+      "exact_moments": [
+        {
+          "endpoint": "1674185473814575474867/1000000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-6649270590065065997663222052892326679295837/13479973333575319897333507543509815336818572211270286240551805124608",
+            "-1662317647516266499415805513223081669823959/3369993333393829974333376885877453834204643052817571560137951281152"
+          ],
+          "base_two_residual": [
+            "-246635539906040992121/500000000000000000000000000000000000000000000",
+            "-2466350399060409921139/5000000000000000000000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "418546368453643868717/250000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "65725496674957295861389862879254608557678601/26959946667150639794667015087019630673637144422540572481103610249216",
+            "65725496674957295861389862879254608557678603/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "12189469601119396732213/5000000000000000000000000000000000000000000000",
+            "24378949202238793464567/10000000000000000000000000000000000000000000000"
+          ]
+        }
+      ],
+      "outer_with_bit": {
+        "complex_b": "1674185473814575474867/1000000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "835693630770093/500000000000000000",
+        "kappa_decimal": "0.001671387261540186",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    }
+  },
+  "bit_supplier_pr": 589,
+  "bit_deficit": 10272,
+  "bit_moments_with_surcharge": [
+    {
+      "endpoint": "1733427039589844234749/1000000000000000000000000",
+      "accept": true,
+      "mercator_residual": [
+        "-43100600330766044577088869872467188970742291/26959946667150639794667015087019630673637144422540572481103610249216",
+        "-43100600330766044577088869872467188970742289/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two_residual": [
+        "-799345163337715793503/500000000000000000000000000000000000000000000",
+        "-3197378653350863173989/2000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "endpoint": "6933708158359376939/4000000000000000000000",
+      "accept": false,
+      "mercator_residual": [
+        "22502934905675809315035333485365686073718547/13479973333575319897333507543509815336818572211270286240551805124608",
+        "5625733726418952328758833371341421518429637/3369993333393829974333376885877453834204643052817571560137951281152"
+      ],
+      "base_two_residual": [
+        "8346798366759439729359/5000000000000000000000000000000000000000000000",
+        "16693606733518879458833/10000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "gain_over_pr635_percent": "2.14795693544613460937516788041147829054201996498013663108098185775358537919",
+  "input_sha256": {
+    "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "package:inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4"
+  },
+  "scope": "Independent arithmetic for the exact nominated all72 profile. Complete local, controller and finite invoice admission are separately replayed by the package driver; this receipt does not replace them. The cited PR589 bit supplier is unchanged and its exceptional-residue surcharge is retained. Any alternative c is only a headroom comparison."
+}
diff --git a/research/gauge44-slots/independent/README.md b/research/gauge44-slots/independent/README.md
new file mode 100644
index 0000000000..f97dcf81b1
--- /dev/null
+++ b/research/gauge44-slots/independent/README.md
@@ -0,0 +1,43 @@
+# Independent checks
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0, under the
+package license. The scalar/frame audit imports no generator or supplier
+checker. Pricing uses the pinned inherited rational engines and the retained
+PR635 outer formula, with their original notices preserved in the main
+dependency tree.
+
+From the delta package directory, using the pinned checkouts and a rebuilt
+word:
+
+```sh
+python independent/audit_local.py \
+  --word /path/to/rebuild/cold44/FULL-WORD.json.gz \
+  --main /path/to/main \
+  --output /path/to/output/LOCAL-AUDIT.json
+
+python independent/price_profile.py \
+  --main /path/to/main \
+  --output /path/to/output/PRICE.json
+
+python independent/review_guards.py \
+  --pr635 /path/to/pr635 \
+  --output /path/to/output/GUARD-REVIEW.json
+```
+
+`audit_local.py` can run without `--main`; including it also verifies the
+transported centre-frame and port boundary against the pinned parent. Its
+receipt authenticates the supplied word by its content SHA256, independent
+of its location. `price_profile.py` defaults to the package's `data/PLAN.json`;
+`--profile` accepts another explicit profile for arithmetic only. The bit side is the cited merged PR589 supplier
+(`inputs/PR589-EXPECTED.json`, git blob `e293ddc5…`); its rank-mass deficit
+`T(2Kv - L*cst) = 32*(8*111 - 9*63) = 10272` is re-derived independently of
+`code/assemble.py`, and the outer receipt key is `outer_with_bit`. The retained
+`GAUGE44-INDEPENDENT-PRICE.json` is #645/PR543 historical evidence unless regenerated. The optional
+`--headroom-c 0.001733052823330162099157` reproduces the unchanged-kappa
+comparison with the reviewed PR555 rate without importing a second supplier.
+
+The retained receipts are `GAUGE-COLD44-INDEPENDENT-AUDIT.json`,
+`GAUGE44-INDEPENDENT-PRICE.json`, and `GAUGE44-GLOBAL-GUARD-REVIEW.json`.
+[CENTRE-GUARD-REVIEW.md](CENTRE-GUARD-REVIEW.md) gives the semantic argument
+behind the changed centre boundary and the single-provider control branch.
+The main package driver performs the separate complete global admission.
diff --git a/research/gauge44-slots/independent/audit_local.py b/research/gauge44-slots/independent/audit_local.py
new file mode 100644
index 0000000000..4744d8783c
--- /dev/null
+++ b/research/gauge44-slots/independent/audit_local.py
@@ -0,0 +1,171 @@
+"""Independent exact scalar/frame audit of the changed forward supplier.
+
+This does not import a generator, builder, stored compensation, or price.
+All claimed endpoint matrices are derived from the input word's gates.
+Optional --main checks the transported boundary against the pinned parent.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse,gzip,json,hashlib,time
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+
+def require(x,label):
+    if not x:raise RuntimeError(label)
+
+def basis(vs):
+    piv={}
+    for a in vs:
+        while a:
+            bit=a.bit_length()-1
+            if bit in piv:a^=piv[bit]
+            else:
+                piv[bit]=a;break
+    for k in sorted(piv):
+        for j in piv:
+            if j>k and piv[j]>>k&1:piv[j]^=piv[k]
+    return tuple(piv[k] for k in sorted(piv,reverse=True))
+
+def contained(a,b):return basis(a+b)==b
+
+def registers(e):return e[1:3] if e[0]=='add' else e[1:2]
+
+def apply(e,rows,dual=False):
+    if e[0]=='add':
+        t,s=e[1:3];q=F(e[3],e[4]);require(t!=s,'self add')
+        if dual:t,s,q=s,t,-q
+        dst=rows[t]
+        for k,x in list(rows[s].items()):
+            a=dst.get(k,F(0))+q*x
+            if a:dst[k]=a
+            else:dst.pop(k,None)
+    elif e[0]=='scale':
+        t=e[1];q=F(e[2],e[3]);require(q!=0,'zero scale')
+        if dual:q=1/q
+        rows[t]={k:q*x for k,x in rows[t].items()}
+    else:raise RuntimeError('unknown scalar primitive')
+
+def invert(e):
+    r=list(e)
+    if r[0]=='add':r[3]=-r[3]
+    else:r[2],r[3]=r[3],r[2]
+    return r
+
+def check_parent_interface(word,main):
+    # Read only the retained boundary data. No builder or local checker is imported.
+    relative="research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz"
+    path=main/relative;raw=path.read_bytes()
+    require(hashlib.sha256(raw).hexdigest()=="66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",'parent canonical input pin')
+    parent=json.loads(gzip.decompress(raw))
+    tau=lambda x:x^(43 if (x&43).bit_count()%2 else 0)
+    ports=parent['ports'];v=word['report']['v']
+    require(len(ports)==len(set(ports))==v,'parent port count')
+    require(set(map(tau,word['ports']))==set(ports),'transported source/target ports')
+    moved={i:ports.index(tau(p)) for i,p in enumerate(word['ports'])}
+    centers=[moved.get(r,r) for r in word['centers']]
+    actual=[list(basis([tau(x) for x in frame])) for frame in word['center_frames']]
+    expected=[parent['frames'][f] for f in parent['center_frames']]
+    require(len(centers)==len(set(centers))==len(actual)==8,'eight distinct centre carriers')
+    require(actual==expected and all(len(f)==8 for f in actual),'ordered centre frame interface')
+    return dict(parent_path=relative,parent_file_sha256=hashlib.sha256(raw).hexdigest(),
+                transport_tau=43,ordered_frame_bases_match=True,all_ports_match=True,
+                transported_centers=centers,source_centers=[r for r in centers if r<v],
+                ordered_frame_bases=actual)
+
+
+def run(path,out,main=None):
+    begin=time.monotonic();data=gzip.decompress(path.read_bytes());w=json.loads(data)
+    v,h,R=w['report']['v'],w['report']['h'],w['report']['R'];n=2*v+R
+    require((v,h)==(112,9),'wrong source geometry')
+    center_interface=check_parent_interface(w,main) if main is not None else None
+    ident=lambda:[{k:F(1)} for k in range(n)]
+    main=w['A']+w['cut']+w['B']
+    for e in main+w['precondition']+w['cleanup']:
+        require(all(0<=k<n for k in registers(e)),'register out of range')
+        q=F(e[3],e[4]) if e[0]=='add' else F(e[2],e[3])
+        require(q.denominator&(q.denominator-1)==0,'non-dyadic scalar')
+        if e[0]=='scale':require(abs(q.numerator)&(abs(q.numerator)-1)==0,'non-unit scale')
+    require(all(not(v<=e[2]<2*v) for e in w['A']+w['B'] if e[0]=='add' and not(v<=e[1]<2*v)), 'non-target reads target')
+    raw=ident()
+    for e in main:apply(e,raw)
+    dirt=[{} for _ in range(n)]
+    for y in range(v,2*v):dirt[y]={k:a for k,a in raw[y].items() if k>=2*v}
+    for e in w['precondition']:apply(e,dirt)
+    compensation=[['add',y,k,-a.numerator,a.denominator,[]] for y in range(v,2*v) for k,a in sorted(dirt[y].items())]
+    entering=set(map(int,w.get('start_extra',{})));lowends=set(map(int,w.get('helper_final',{})))
+    coldends=lowends-entering
+    require(not any(e[2] in entering for e in compensation),'nonzero entrance response')
+    require(not any(r in entering|coldends for e in w['precondition']+compensation for r in registers(e)), 'pre-wrapper touch of residual helper')
+    require(all(e[-1]==[] for e in w['precondition']+compensation),'nonzero frame precondition')
+    early=w.get('early_cleanup',[]);earlyids={i for i,U in early}
+    require(len(earlyids)==len(early),'duplicate early cleanup gate')
+    tail=[w['cleanup'][i][:-1]+[U] for i,U in early]
+    cleanup=[e for i,e in enumerate(w['cleanup']) if i not in earlyids]
+    prefix=w['precondition']+compensation+main
+    program=prefix+tail+cleanup
+    for dual in (False,True):
+        actual=ident()
+        for e in program:apply(e,actual,dual)
+        expected=ident()
+        for t in range(v):expected[t if dual else v+t][v+t if dual else t]=F(-1 if dual else 1)
+        bad=[i for i in range(n) if actual[i]!=expected[i]]
+        require(not bad,'all-column endpoint failure '+str((dual,bad[:8])))
+        print('endpoint', 'dual' if dual else 'forward','PASS',flush=True)
+    full=basis([1<<i for i in range(h)])
+    end=[full]*v+[basis([x for x in range(1,1<<h) if (x&p).bit_count()%2==0]) for p in w['ports']]+[full]*R
+    for q,U in w.get('helper_final',{}).items():end[int(q)]=basis(U)
+    start=[(p,) for p in w['ports']]+[()]*(v+R)
+    for q,U in w.get('start_extra',{}).items():
+        require(2*v<=int(q)<n,'non-helper entrance');start[int(q)]=basis(U)
+    cur=start.copy();paid=Counter()
+    def climb(q,U):
+        U=basis(U);require(contained(cur[q],U),'frame not monotone '+str((q,cur[q],U)))
+        d=len(U)-len(cur[q])
+        if d:paid[d]+=1
+        cur[q]=U
+    for section in ('A','B'):
+        if section=='B':
+            lev={int(t):basis(U) for t,U in w.get('target_levels',{}).items()}
+            require(all(cur[v+t]==lev.get(t,()) for t in range(v)),'target centre levels')
+            for q,U in zip(w['centers'],w['center_frames']):
+                U=basis(U);require(cur[q]==U,'center frame')
+                served={lev.get(e[1]-v,()) for e in w['cut'] if e[2]==q}
+                for T in sorted(served,key=lambda x:-len(x)):
+                    require(contained(T,U),'center path not nested')
+                    if T!=U:paid[len(U)-len(T)]+=1
+                    U=T
+        for e in w[section]:
+            for q in registers(e):climb(q,e[-1])
+    endB=cur.copy()
+    for e in tail:
+        for q in registers(e):climb(q,e[-1])
+    for q,U in enumerate(end):climb(q,U)
+    require(all(all(end[q]==full for q in registers(e)) for e in cleanup),'full cleanup reads a low end')
+    require(dict(paid)=={int(k):a for k,a in w['report']['local_profile'].items()},'paid profile mismatch')
+    inventory=Counter(len(end[q])-len(start[q]) for q in range(2*v,n))
+    require(dict(inventory)=={int(k):a for k,a in w['report']['width_inventory'].items()},'width inventory mismatch')
+    p=ident();pinv=ident()
+    for e in prefix:apply(e,p)
+    for e in reversed(prefix):apply(invert(e),pinv)
+    for q in lowends:
+        U=end[q]
+        require(all(contained(endB[k],U) for k in pinv[q]),'inverse-row cone '+str(q))
+        require(all(k==q or not p[k].get(q) or contained(endB[k],U) for k in range(n)),'dirt-column cone '+str(q))
+    report=dict(status='PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES',
+                input_file=path.name,content_sha256=hashlib.sha256(data).hexdigest(),
+                compressed_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),
+                parent_center_interface=center_interface,v=v,h=h,R=R,
+                entering=len(entering),lowends=len(lowends),coldends=len(coldends),
+                compensation_gates=len(compensation),local_profile=dict(sorted(paid.items())),
+                width_inventory=dict(sorted(inventory.items())),checked_columns=n,
+                elapsed_seconds=time.monotonic()-begin,
+                scope='Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing.')
+    out.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2),flush=True)
+
+if __name__=='__main__':
+    parser=argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--word',type=Path,required=True,help='FULL-WORD.json.gz to check')
+    parser.add_argument('--output',type=Path,required=True,help='JSON receipt output path')
+    parser.add_argument('--main',type=Path,help='Optional pinned main checkout: also verify the transported centre/port interface')
+    args=parser.parse_args()
+    run(args.word,args.output,args.main)
diff --git a/research/gauge44-slots/independent/price_profile.py b/research/gauge44-slots/independent/price_profile.py
new file mode 100644
index 0000000000..0e36ebd468
--- /dev/null
+++ b/research/gauge44-slots/independent/price_profile.py
@@ -0,0 +1,161 @@
+"""Independent arithmetic for the frozen gauge44 profile.
+
+The two rational moment engines and outer.assembly are imported unchanged from
+the pinned main dependencies; no constructor, owner emitter or invoice is run.
+The outer driver is the seven-step formula retained in PR635.
+The bit side is the cited merged PR589 supplier (package inputs/PR589-EXPECTED.json,
+pinned by git blob), with its rank-mass deficit T(2Kv - L*cst) re-derived here
+independently of code/assemble.py.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse
+from decimal import Decimal, localcontext
+from fractions import Fraction as Q
+import hashlib
+import importlib.util
+import json
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+SOURCE = Path('research/complex-k492-owner-repair/vendor/multicold')
+BIT_PATH = HERE.parent/'inputs/PR589-EXPECTED.json'
+BIT_BLOB = 'e293ddc557742637f9f679f083a1a282d87b1b13'
+
+
+def pr589_deficit(word, live):
+    # Nine stages, 32 replicas, four pairs: deficit = 32*(2*4*v - 9*cst), cst = sum of the nine COPY ranks.
+    v, cst, ranks = word['v'], word['decoder_constant'], word['copy_ranks']
+    require(len(ranks) == word['retained_totals'] == 9 and cst == sum(ranks), 'bit decoder constant')
+    require(live == 2*4*v*32, 'bit live wires')
+    return 32*(2*4*v-9*cst)
+
+
+def require(condition, message):
+    if not condition:
+        raise RuntimeError(message)
+
+
+def decimal(q):
+    with localcontext() as ctx:
+        ctx.prec = 75
+        return str(Decimal(q.numerator) / Decimal(q.denominator))
+
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def load(path, name):
+    spec = importlib.util.spec_from_file_location('independent_' + name, path / (name + '.py'))
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def moment_checks(M, B, H, m, W, lower, deficit, bad):
+    require(m*W-sum(r*n for r, n in H.items()) == deficit, 'rank deficit')
+    require(m*m > 2*max(H)**2, 'halving guard')
+    rows = []
+    for z, accept in [(lower, True), (lower+Q(1, 10**24), False)]:
+        l, u = M.moment(H, m, W, z, bad)
+        ll, uu = B.moment(m, W, list(H.items()), z)
+        if bad:
+            fl, fu = B.moment(m, W, [(1, 32*m*m*sum(H.values()))], z)
+            ll, uu = ll+fl/10**16, uu+fu/10**16
+        require((u < 1 and uu < 1) if accept else (l > 1 and ll > 1), 'two exact moment signs')
+        rows.append(dict(endpoint=str(z), accept=accept,
+                         mercator_residual=[str(l-1), str(u-1)],
+                         base_two_residual=[str(ll-1), str(uu-1)]))
+    return rows
+
+
+def outer47(c, b, engine):
+    eta = beta = Q(1, 10**24)
+    s = min(c, (1-beta)*b)-Q(1, 10**27)
+    require(0 < s < c and s < (1-beta)*b, 'strict common saving')
+    a = Q(384599, 10**10)
+    for _ in range(7):
+        old = a
+        a = (1-s)*s+s*old
+        gap = min(s-a, 1-a-s, 1-a-s*(1-old), 1-s)
+        require(old < a < s < 1-a and gap > 0, 'bootstrap gap')
+        ceil = lambda x: -(-x.numerator//x.denominator)
+        cut = max(ceil(36/gap**2), ceil(2*(4+512)/gap))
+        require(cut*gap**2 >= 36 and cut*gap >= 2*(4+512), 'finite bootstrap cutoff')
+    q = a*(1-2*eta)
+    margin = (1-eta)*q/(1+q)
+    ticks = margin*10**18
+    k = Q((ticks.numerator-1)//ticks.denominator, 10**18)
+    bridge = {'semantic': {'C0': {'base': 2, 'exponent': 210000}, 'strict_literal_gap': 1},
+              'rows': {'degree_gap': Q(10**6)-Q(51*20161, 25)}}
+    result = engine.assembly(a, b, bridge, k, eta=eta, beta=beta)
+    require(len(result['strict_constraints']) == 47, '47 outer constraints')
+    require(all(x > 0 for x in result['strict_constraints'].values()), 'strict outer constraints')
+    rejected = []
+    for name, kk, ee, be in [('next_grid', k+Q(1, 10**18), eta, beta),
+                             ('zero_eta', k, Q(0), beta), ('zero_beta', k, eta, Q(0)),
+                             ('unit_beta', k, eta, Q(1))]:
+        try:
+            engine.assembly(a, b, bridge, kk, eta=ee, beta=be)
+        except AssertionError:
+            rejected.append(name)
+        else:
+            raise RuntimeError('accepted negative control: '+name)
+    return dict(complex_b=str(b), bit_c=str(c), kappa=str(k), kappa_decimal=decimal(k),
+                binding='bit' if c < (1-beta)*b else 'complex',
+                strict_constraints_passed=47, controls_rejected=rejected)
+
+
+def main():
+    require(__debug__, 'Do not use python -O: the retained outer engine requires assertions')
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--main', type=Path, required=True, help='Pinned main checkout')
+    parser.add_argument('--profile', type=Path, default=HERE.parent/'data/PLAN.json',
+                        help='Raw profile or a JSON object containing profile/global_profile')
+    parser.add_argument('--output', type=Path, required=True)
+    parser.add_argument('--headroom-c', help='Optional alternative bit saving, for comparison only')
+    args = parser.parse_args()
+    inputs = json.loads((HERE.parent/'data/UPSTREAM-PINS.json').read_text())
+    selected = [SOURCE/'engines'/(n+'.py') for n in ('moment', 'base_two_moment', 'outer')]
+    for relative in selected:
+        require(sha(args.main/relative) == inputs[relative.as_posix()], 'pinned input '+str(relative))
+    M, B, A = [load(args.main/SOURCE/'engines', n) for n in ('moment', 'base_two_moment', 'outer')]
+    supplied = json.loads(args.profile.read_text())
+    H = {int(r): n for r, n in supplied.get('profile', supplied.get('global_profile', supplied)).items()}
+    bit_data = BIT_PATH.read_bytes()
+    require(hashlib.sha1(b'blob '+str(len(bit_data)).encode()+b'\0'+bit_data).hexdigest() == BIT_BLOB, 'PR589 blob pin')
+    record = json.loads(bit_data)
+    bit = record['nine']
+    require('nine-stage' in bit['pipeline'] and '32 replicas' in bit['pipeline'], 'nine-stage bit record')
+    bit_deficit = pr589_deficit(record['word'], bit['bit']['live'])
+    require(sum(int(r)*n for r, n in bit['profile'].items()) == bit['bit']['rank_mass'], 'bit rank mass')
+    c = Q(bit['bit_lower'])
+    bit_checks = moment_checks(M, B, {int(r): n for r, n in bit['profile'].items()},
+                               64, bit['bit']['live'], c, bit_deficit, True)
+    prices = {}
+    for mode, bad in [('native', False), ('conservative', True)]:
+        root = M.certify(H, 73, 7168, bad)
+        root = {key: root[key] for key in ('lower', 'upper', 'lower_endpoint_residual_upper',
+                                          'upper_endpoint_residual_lower', 'strict_rational_signs')}
+        b = Q(root['lower'])
+        row = dict(root=root, exact_moments=moment_checks(M, B, H, 73, 7168, b, 2560, bad),
+                   outer_with_bit=outer47(c, b, A))
+        if args.headroom_c:
+            alternate = outer47(Q(args.headroom_c), b, A)
+            require(alternate['kappa'] == row['outer_with_bit']['kappa'], 'headroom comparison changed kappa')
+            row.update(outer_with_alternative_bit_rate=alternate, same_kappa_with_either_bit_rate=True)
+        prices[mode] = row
+    native_k = Q(prices['native']['outer_with_bit']['kappa'])
+    result = dict(status='PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK',
+                  profile_input_file=args.profile.name, profile_input_sha256=sha(args.profile),
+                  global_profile=H, live=7168, m=73, rank_mass=sum(r*n for r, n in H.items()), deficit=2560,
+                  prices=prices, bit_supplier_pr=589, bit_deficit=bit_deficit, bit_moments_with_surcharge=bit_checks,
+                  gain_over_pr635_percent=decimal(100*(native_k/Q('0.001636241501576388')-1)),
+                  input_sha256={**{relative.as_posix(): sha(args.main/relative) for relative in selected}, 'package:inputs/PR589-EXPECTED.json': sha(BIT_PATH)},
+                  scope='Independent arithmetic for the exact nominated all72 profile. Complete local, controller and finite invoice admission are separately replayed by the package driver; this receipt does not replace them. The cited PR589 bit supplier is unchanged and its exceptional-residue surcharge is retained. Any alternative c is only a headroom comparison.')
+    args.output.write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], prices['native']['outer_with_bit']['kappa_decimal'], result['gain_over_pr635_percent'])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/independent/review_guards.py b/research/gauge44-slots/independent/review_guards.py
new file mode 100644
index 0000000000..086dcf3d11
--- /dev/null
+++ b/research/gauge44-slots/independent/review_guards.py
@@ -0,0 +1,46 @@
+"""Reproduce the assertion-preservation part of the independent guard review.
+
+This compares complete assertion ASTs in their traversal order. It supplements
+the semantic centre-interface argument in CENTRE-GUARD-REVIEW.md.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse
+import ast
+import hashlib
+import json
+from pathlib import Path
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--pr635', type=Path, required=True, help='Pinned PR635 checkout or supplier directory')
+    parser.add_argument('--delta', type=Path, default=Path(__file__).resolve().parents[1])
+    parser.add_argument('--output', type=Path, required=True)
+    args = parser.parse_args()
+    old = args.pr635
+    if not (old/'code/assemble.py').exists():
+        old = old/'research/complex-571-cold14-st2'
+    names = ['assemble.py', 'invoice_allcold.py', 'bind_providers_portable.py',
+             'generated_identity.py', 'witness.py']
+    records = []
+    for name in names:
+        a, b = (old/'code'/name).read_bytes(), (args.delta/'code'/name).read_bytes()
+        assertions = lambda data: [ast.dump(n, include_attributes=False) for n in ast.walk(ast.parse(data))
+                                   if isinstance(n, ast.Assert)]
+        aa, bb = assertions(a), assertions(b)
+        if aa != bb:
+            raise RuntimeError('Assertion sequence changed: '+name)
+        records.append(dict(file='code/'+name, baseline_sha256=hashlib.sha256(a).hexdigest(),
+                            new_sha256=hashlib.sha256(b).hexdigest(), byte_identical=a == b,
+                            assert_count=len(aa), all_assertions_identical_in_order=True))
+    if records[0]['assert_count'] != 91:
+        raise RuntimeError('The expected PR635 assembly has 91 assertions')
+    result = dict(status='PASS_PR635_ADMISSION_ASSERTION_PRESERVATION', files=records,
+                  centre_interface_review='CENTRE-GUARD-REVIEW.md',
+                  scope='Exact syntax preservation for all admission assertions in these five files. The changed emitter/controller centre boundary and single-provider controls require the separate semantic review; assertion counts alone do not prove them.')
+    args.output.write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], [r['assert_count'] for r in records])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gauge44-slots/inputs/PR589-EXPECTED.json b/research/gauge44-slots/inputs/PR589-EXPECTED.json
new file mode 100644
index 0000000000..e293ddc557
--- /dev/null
+++ b/research/gauge44-slots/inputs/PR589-EXPECTED.json
@@ -0,0 +1,222 @@
+{
+ "word": {
+  "file": "tune/bitE8mut-p111-tuned.json.gz",
+  "file_sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f",
+  "content_sha256": "5642fd0e35a1acc11acff8d0c08350c1617e95f310d4d35ad63a651f9eeeba0b",
+  "v": 111,
+  "R": 439,
+  "punctured": [
+   10,
+   15,
+   51,
+   53,
+   56,
+   66,
+   72,
+   89,
+   111
+  ],
+  "retained_totals": 9,
+  "copy_ranks": [
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7,
+   7
+  ],
+  "decoder_constant": 63,
+  "gates": {
+   "D": 111,
+   "A": 2075,
+   "B": 712,
+   "C": 2574
+  },
+  "local_histogram": {
+   "1": 1323,
+   "2": 1342,
+   "3": 79,
+   "4": 44,
+   "5": 102,
+   "6": 11,
+   "7": 19
+  },
+  "legality": {
+   "records": 27234,
+   "common_frame_ADDs": 24305,
+   "rank_mass": 5129
+  },
+  "five_stage_columns": 883,
+  "five_stage_payload_bits": 93,
+  "nine_stage_columns": 1327,
+  "nine_stage_payload_bits": 93,
+  "eleven_stage_columns": 1549,
+  "eleven_stage_payload_bits": 93,
+  "base_content_sha256": "d0df3c89ae84989f4045ba1681a5e2e9fcdfa38ed0301c8abf5185537155cbe3"
+ },
+ "interface": {
+  "hypotheses": {
+   "H1_no_target_feeds_z": true,
+   "H2_D_frame0_targets_from_helpers": true,
+   "H3_A_z_only_scatter_targets_B_split": true,
+   "H4_C_literal_reverse_at_full": true,
+   "H5_V_identity": true
+  },
+  "conclusion": {
+   "U_block_form": true,
+   "J_identity": true,
+   "K_equals_D": true,
+   "C_is_U_inverse": true
+  },
+  "interleaving": {
+   "z_gates_A": 2075,
+   "source_writes_A": 0,
+   "z_gates_B": 499,
+   "source_writes_B": 483,
+   "helper_writes_B": 16,
+   "sources_rewritten_B": 108,
+   "B_z_write_frame_dims": {
+    "4": 388,
+    "6": 111
+   },
+   "B_z_operand_kinds": {
+    "helper<-helper": 3,
+    "helper<-source": 13,
+    "source<-helper": 108,
+    "source<-source": 375
+   },
+   "B_z_operand_kinds_by_dim": {
+    "dim4:helper<-source": 13,
+    "dim4:source<-source": 375,
+    "dim6:helper<-helper": 3,
+    "dim6:source<-helper": 108
+   },
+   "B_z_writes_after_a_target_read_of_the_same_register": 454,
+   "B_target_reads_of_registers_rewritten_earlier_in_B": 111,
+   "target_reads_of_targets": 0,
+   "cleanup_gates": 2574
+  }
+ },
+ "nine": {
+  "pipeline": "PR #510 (PR #463 nine-stage template, 32 replicas, PR #442 hosting, PR #493 outer assembly), parameterised for v <= 120 by code/adapt9p.py",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_lower_decimal": "0.001733427039589844234749",
+  "profile": {
+   "1": 381024,
+   "2": 400416,
+   "3": 22752,
+   "4": 26880,
+   "5": 29376,
+   "6": 17376,
+   "7": 26784,
+   "42": 288
+  },
+  "bit": {
+   "live": 28416,
+   "physical": 28425,
+   "maxchild": 42,
+   "rank_mass": 1808352,
+   "hosted_residuals": 126432,
+   "bank_assignments": 0,
+   "prefix_bits": 177,
+   "charged_prefix_bits": 192,
+   "coefficient_bits": 177,
+   "two_level_coefficient_bits": 393,
+   "charged_two_level_coefficient_bits": 512,
+   "row_coefficient": 18355,
+   "halving_depth": 2
+  },
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "eleven": {
+  "pipeline": "PR #493 (PR #445 geometry, PR #472 emitter, audit and invoice, PR #442 hosting), parameterised by PR #545's code/adapt.py",
+  "bit_lower": "855475950388791987811/500000000000000000000000",
+  "bit_lower_decimal": "0.001710951900777583975622",
+  "profile": {
+   "1": 116424,
+   "2": 121648,
+   "3": 6952,
+   "4": 7424,
+   "5": 8976,
+   "6": 4520,
+   "7": 8776,
+   "56": 2600
+  },
+  "bit": {
+   "live": 8880,
+   "physical": 8889,
+   "maxchild": 56,
+   "rank_mass": 689304,
+   "hosted_residuals": 38632,
+   "prefix_bits": 4304,
+   "charged_prefix_bits": 4352,
+   "coefficient_bits": 4304,
+   "three_level_coefficient_bits": 12966,
+   "charged_three_level_coefficient_bits": 12992,
+   "row_coefficient": 19431,
+   "halving_depth": 3
+  },
+  "emitted_program_sha256": "793b6f40c9aa4b8db57fec0ac0973e16884dae28707e482ee8f7a2349a5d5a4b",
+  "kappa": {
+   "pr548": {
+    "kappa": "49718254847979/31250000000000000",
+    "kappa_decimal": "0.001590984155135328",
+    "complex_lower": "796759709641153381751/500000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr544": {
+    "kappa": "397677800014309/250000000000000000",
+    "kappa_decimal": "0.001590711200057236",
+    "complex_lower": "31864911873350496687/20000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr535": {
+    "kappa": "793733736881443/500000000000000000",
+    "kappa_decimal": "0.001587467473762886",
+    "complex_lower": "1589991533606044174031/1000000000000000000000000",
+    "binding_component": "complex"
+   },
+   "pr531": {
+    "kappa": "1517760977820331/1000000000000000000",
+    "kappa_decimal": "0.001517760977820331",
+    "complex_lower": "304013615566499291631/200000000000000000000000",
+    "binding_component": "complex"
+   }
+  }
+ },
+ "base": {
+  "nine_bit_lower": "1733052823330162099157/1000000000000000000000000",
+  "nine_bit_lower_decimal": "0.001733052823330162099157",
+  "eleven_bit_lower": "427652201524503168379/250000000000000000000000",
+  "eleven_bit_lower_decimal": "0.001710608806098012673516",
+  "note": "PR #555's EXPECTED.json (untuned word); the tune/ pipeline is the same, with the same frozen hosting selections"
+ }
+}
diff --git a/research/gauge44-slots/verify_global.py b/research/gauge44-slots/verify_global.py
new file mode 100644
index 0000000000..7ab79e3062
--- /dev/null
+++ b/research/gauge44-slots/verify_global.py
@@ -0,0 +1,112 @@
+"""Replay the changed global admission against pinned upstream dependencies.
+
+The local directory must contain the fresh canonical/native/phase/wrapper
+artifacts produced by construction/reproduce.py. Frozen evidence may be used
+for a short admission-only replay. No optimizer runs during this verifier.
+"""
+import argparse
+import hashlib
+import json
+import os
+from pathlib import Path
+import subprocess
+import sys
+import time
+
+assert __debug__, 'Assertions required'
+PACKAGE = Path(__file__).resolve().parent
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def dump(path, value):
+    Path(path).write_text(json.dumps(value, indent=2) + '\n')
+
+
+ap = argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--main', type=Path, required=True, help='Pinned CrocSwap main checkout')
+ap.add_argument('--local', type=Path, required=True, help='Rebuilt or frozen native gauge44 directory')
+ap.add_argument('--work', type=Path, required=True, help='New output directory')
+ap.add_argument('--discover', action='store_true', help=argparse.SUPPRESS)
+args = ap.parse_args()
+main, local, work = args.main.resolve(), args.local.resolve(), args.work.resolve()
+assert not work.exists(), 'Output directory must be new'
+source = main/'research/complex-k492-owner-repair/vendor/multicold'
+baseline = main/'research/community-k492-audit/pr622/replay/baseline558'
+vendor = source/'vendor/pr558/vendor/pr552/complex-global/vendor531'
+pins = PACKAGE/'data/UPSTREAM-PINS.json'
+if pins.exists():
+    for rel, expected in json.loads(pins.read_text()).items():
+        assert sha(main/rel) == expected, 'Upstream dependency changed: ' + rel
+else:
+    assert args.discover, 'Missing upstream pins'
+    paths = list((baseline/'complex-global/base').rglob('*'))
+    paths += [source/'code/run_portable.py', source/'inputs/PR543-EXPECTED.json',
+              vendor/'evidence/audit/PREFIX-AND-INVOICE.json']
+    paths += [source/'vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz',
+              baseline/'complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz',
+              vendor/'code/prepare_supplier_base.py']
+    paths += [source/'engines'/name for name in ('moment.py', 'base_two_moment.py', 'outer.py')]
+    dump(pins, {p.relative_to(main).as_posix(): sha(p) for p in sorted(paths) if p.is_file()})
+work.mkdir(parents=True)
+env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1',
+           PYTHONINTMAXSTRDIGITS='0', MULTICOLD_SOURCE=str(source),
+           GAIN_PR564_SOURCE=str(source), WITNESS_SPEC=str(PACKAGE/'data/SPEC.json'))
+env.pop('PYTHONOPTIMIZE', None)
+env.pop('WITNESS_DISCOVER', None)
+env.pop('WITNESS_RECORD', None)
+if args.discover:
+    env.update(WITNESS_DISCOVER='1', WITNESS_RECORD=str(work/'WITNESS-RECORD.jsonl'))
+stages = []
+
+
+def run(name, script, *arguments):
+    started = time.monotonic()
+    log = work/(name + '.log')
+    with log.open('w') as stream:
+        result = subprocess.run([sys.executable, '-B', str(source/'code/run_portable.py'),
+                                 str(script), *map(str, arguments)], env=env,
+                                stdout=stream, stderr=subprocess.STDOUT)
+    stages.append(dict(name=name, seconds=round(time.monotonic()-started, 3),
+                       exit_code=result.returncode, log_sha256=sha(log)))
+    dump(work/'STAGES.json', stages)
+    if result.returncode:
+        raise RuntimeError(name + ' failed:\n' + log.read_text()[-7000:])
+    print('PASS', name, stages[-1]['seconds'], flush=True)
+
+
+code = PACKAGE/'code'
+global_dir = work/'global'
+run('restore-parent', code/'restore_parent.py', '--source', source,
+    '--baseline', baseline, '--out', work/'parent558')
+run('bind', code/'bind_providers_portable.py', '--baseline', work/'parent558',
+    '--provider', 'gauge44='+str(local), '--plan', PACKAGE/'data/PLAN.json', '--out', global_dir)
+run('emit', code/'emit_allcold.py', '--base', global_dir/'base',
+    '--owners', PACKAGE/'data/OWNERS.json.gz', '--plan', global_dir/'PLAN.json', '--out', global_dir/'hosted')
+run('audit', code/'audit_allcold.py', global_dir/'base', global_dir/'hosted',
+    global_dir/'audit/ASYNC-AUDIT.json', '--mutation-controls')
+run('invoice', code/'invoice_allcold.py', '--base', global_dir/'base',
+    '--hosted', global_dir/'hosted', '--audit', global_dir/'audit', '--out', global_dir/'audit',
+    '--retained-invoice', vendor/'evidence/audit/PREFIX-AND-INVOICE.json')
+run('assembly', code/'assemble.py', source, global_dir, work/'ASSEMBLY.json')
+if not args.discover:
+    run('admission-controls', code/'assembly_controls.py', '--source-package', source,
+        '--owner', global_dir/'audit/OWNERS-AND-PROFILE.json',
+        '--invoice', global_dir/'audit/PREFIX-AND-INVOICE.json', '--out', work/'ADMISSION-CONTROLS.json')
+    run('bit-supplier-controls', code/'bit_supplier_controls.py', '--source-package', source,
+        '--owner', global_dir/'audit/OWNERS-AND-PROFILE.json',
+        '--invoice', global_dir/'audit/PREFIX-AND-INVOICE.json', '--out', work/'BIT-SUPPLIER-CONTROLS.json')
+    bit_controls = json.loads((work/'BIT-SUPPLIER-CONTROLS.json').read_text())
+    assert bit_controls['status'] == 'PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS'
+    assert len(bit_controls['rejected_controls']) == 12 and bit_controls['derived_deficit'] == 10272
+result = json.loads((work/'ASSEMBLY.json').read_text())
+dump(work/'REPLAY.json', dict(status='PASS_GAUGE44_DISCOVERY' if args.discover else 'PASS_GAUGE44_STRICT_GLOBAL_REPLAY',
+                            kappa=result['kappa'], kappa_decimal=result['kappa_decimal'],
+                            complex_lower=result['complex_lower'], bit_lower=result['bit_lower'],
+                            bit_supplier=result['bit_supplier'],
+                            gain_over_pr635_percent=result['gain_over_pr635_percent'],
+                            spec_sha256=sha(PACKAGE/'data/SPEC.json'), stages=stages,
+                            scope=result['scope']))
+print(result['status'], result['kappa_decimal'], result['gain_over_pr635_percent'], flush=True)
diff --git a/research/gauge44-slots/verify_manifest.py b/research/gauge44-slots/verify_manifest.py
new file mode 100644
index 0000000000..8c2441d392
--- /dev/null
+++ b/research/gauge44-slots/verify_manifest.py
@@ -0,0 +1,19 @@
+"""Verify the submitted package's exact file inventory and SHA256 bindings."""
+from hashlib import sha256
+import json
+from pathlib import Path
+
+root = Path(__file__).resolve().parent
+expected = json.loads((root / 'MANIFEST.json').read_text())
+actual = {
+    p.relative_to(root).as_posix(): sha256(p.read_bytes()).hexdigest()
+    for p in root.rglob('*')
+    if p.is_file() and '__pycache__' not in p.parts
+    and p != root / 'MANIFEST.json'
+}
+if actual != expected:
+    missing = sorted(expected.keys() - actual.keys())
+    extra = sorted(actual.keys() - expected.keys())
+    changed = sorted(k for k in expected.keys() & actual.keys() if expected[k] != actual[k])
+    raise SystemExit(f'Manifest mismatch: missing={missing}, extra={extra}, changed={changed}')
+print(f'PASS package manifest: {len(actual)} files')