diff --git a/.github/workflows/five-stage-p10-transcript-stages.yml b/.github/workflows/five-stage-p10-transcript-stages.yml
new file mode 100644
index 0000000000..f80e1e4060
--- /dev/null
+++ b/.github/workflows/five-stage-p10-transcript-stages.yml
@@ -0,0 +1,39 @@
+name: Verify the p = 10 word with the transcript stage stack
+
+on:
+  push:
+    paths:
+      - 'research/five-stage-p10-transcript-stages/**'
+      - '.github/workflows/five-stage-p10-transcript-stages.yml'
+  pull_request:
+    paths:
+      - 'research/five-stage-p10-transcript-stages/**'
+      - '.github/workflows/five-stage-p10-transcript-stages.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  immutable-replay:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 60
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.12', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Install the pinned arithmetic dependency
+        run: python -m pip install --disable-pip-version-check -r research/five-stage-p10-transcript-stages/requirements.txt
+      - name: Replay every mandatory stage (virtual, raw, bit, scalar, primes, banks, complex, math, finite)
+        run: python -B research/five-stage-p10-transcript-stages/verify.py --output "$RUNNER_TEMP/p10-five-stage-verification"
+      - name: Regenerate the pinned bit word from the generator and both physical-layer producers
+        run: python -B research/five-stage-p10-transcript-stages/bitword/producer/regenerate.py --work "$RUNNER_TEMP/p10-regeneration"
+      - name: Require committed files to remain unchanged
+        run: git diff --exit-code
diff --git a/certificates/joint-dual-kappa.json b/certificates/joint-dual-kappa.json
index b7f7b89bc2..1f35b89221 100644
--- a/certificates/joint-dual-kappa.json
+++ b/certificates/joint-dual-kappa.json
@@ -842,7 +842,7 @@
     "scripts/experiments/pin_joint_dual_sources.py": "4d31cc0e38b7902709ca5f8f714cba109760d2592346dd7f8dc0b900a2d9fe00",
     "scripts/experiments/verify_joint_dual.py": "7a31bba1e9c0ded32ae285df2ca9bc91ef20c330f6789fdba361876f3c7a1985"
   },
-  "source_manifest_sha256": "4f3c15b82a2d97335d4fe95fb8bcb96bd2a921087da289d9da16c68213a17f17",
+  "source_manifest_sha256": "698fe862a620e5b80b85fbc6034c9456fa0fa9aea638dbbbcb3f9edd24c0415e",
   "sources": [
     {
       "files": {
diff --git a/certificates/joint-dual-validation.json b/certificates/joint-dual-validation.json
index 194861d3c3..61a8d41622 100644
--- a/certificates/joint-dual-validation.json
+++ b/certificates/joint-dual-validation.json
@@ -226,7 +226,7 @@
     }
   },
   "bit_saving": "2382370177/50000000000000",
-  "certificate_sha256": "9801147b1502cf1e43d5fa39aa37f5291f03b48c30c4dd4f272e0877894a1c24",
+  "certificate_sha256": "6f684fa7f747073a132e8d0b5652cf12a8afa389f2a16ff6ade8e080d786dd22",
   "kappa": "4764513337/100000000000000",
   "margins": 7,
   "producer_words_regenerated_and_matched": true,
diff --git a/research/five-stage-p10-transcript-stages/BANK-PROOF.md b/research/five-stage-p10-transcript-stages/BANK-PROOF.md
new file mode 100644
index 0000000000..9ea927ec05
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/BANK-PROOF.md
@@ -0,0 +1,177 @@
+# Five-stage stage-private completed banks
+
+This is a finite bank-allocation extension of the PR197/PR200 completed-bank construction to PR234's five-stage
+bit geometry. It is retained from eumemic's source527 package (via #285) and applied here to the independent
+helper census of the p = 10 word: h = 20, m = 5h = 100. It does not claim a new all-size compiler theorem or
+replace the scalar admission.
+
+## Endpoint of one local invocation
+
+For one complete local invocation, the source-bound physical telescope has no data/helper cross blocks. On an
+independent helper with genuine entrance projector σ, its endpoint is the exact partial swap D_(I₂₀−σ),
+supported in the active local window. This holds on arbitrary correlated dirty contents. The complemented
+inverse invocation has the same residual: its reversed endpoints are 0 and I₂₀ − σ. Source-owned gauges are
+visible-data paths and are excluded from the independent helper census.
+
+## Bank normalizers
+
+In stage i, PR234 routes the helper at local class d to physical class g = d·τᵢ. Relative to g, the residual is
+Pᵢ = τᵢ·diag(I₂₀ − σ, 0, …, 0)·τᵢ, supported only in Hᵢ. Each stage gets a disjoint collection of banks, and
+every bank is filled by disjoint coordinate blocks of total dimension 100. For the actual gauge chart B, whose
+columns are residual columns followed by gauge columns, set
+
+    N_b = (b+1)·Π_b·embed_i(B⁻¹).
+
+For an ungauged role, B = I₂₀. Π_b is the explicit coordinate permutation sending the first residual
+coordinates in Hᵢ to the assigned bank interval. Thus N_b·Pᵢ·N_b⁻¹ is exactly that coordinate projector. The
+scalar leaves conjugation unchanged.
+
+The residual columns of B are G⁻¹ applied to the frame's annihilator rows, for G = I − J/9. Up to the positive
+scalar h − 9 = 11, these are the integer rows 11a − Σa (15a − Σa at h = 24).
+
+The checker reconstructs every actual chart and checks:
+
+- both inverse identities;
+- the G-orthogonality of its two summands;
+- its residual action;
+- its elementary factorization.
+
+This is therefore a projector identity for the actual bases, not a rank substitution.
+
+## Bank routes and distinctness
+
+The bank route is g → g·N_b⁻¹, which is d·τᵢ·N_b⁻¹ in the original local invocation. If the bank class is h,
+its residual is h·N_b·Pᵢ·N_b⁻¹·h⁻¹. Every occurrence visits every bank class once, because right multiplication
+is a bijection on the complete GL cover.
+
+If two roles in one local invocation are assigned the same bank family, their distinct N_b give distinct bank
+classes. Distinctness is literal. Choose a coordinate j outside Hᵢ. The embedded inverse fixes e_j, and
+N_b·e_j = (b+1)·e_(Π_b(j)). The resulting columns differ for all b, at every eligible prime q > 2⁸⁰ and every
+local ring Z/q^w. All scalars are between 1 and 25 (the largest bank has 25 blocks), so they remain distinct
+units. The proof uses the full GL cover, not a projective quotient.
+
+## Completed endpoint
+
+Complete the entire cover sweep for each stage and replica, in fixed order, before its boundary phase. The
+complete local source endpoint separates every bank from the data and the other banks, so each subsequent
+invocation may receive arbitrary dirty bank contents.
+
+For each bank, its block projectors are disjoint and sum to I₁₀₀, so the literal partial swaps compose to
+D_I₁₀₀ on every address column. The common inherited ancestor chart is the same for each block and cancels
+between blocks. The checker verifies:
+
+- all 200 address columns;
+- the reverse schedule;
+- failures when a block is omitted or repeated.
+
+No new independence assumption on dirt is used.
+
+The five bank collections remain separate, and each is touched only in its own stage. This gives every physical
+bank its full required endpoint once. The data stage routes, bridge maps, idle children and final exchanges
+remain PR234's. Consequently there are no independent exterior rank-5a children. Their removal follows from the
+completed bank endpoint. No internal, data, compensation or copied-centre child is removed.
+
+## Families and the exact tiling
+
+The actual residual families are:
+
+| width | source | roles |
+| ---: | --- | ---: |
+| 3 | rank-17 entrances | 70 |
+| 4 | rank-16 entrances | 1,200 |
+| 20 | ungauged roles | 6,960 |
+
+A bank holds blocks of total width exactly 100. With 60 replicas the total residual width must therefore
+satisfy 60·width ≡ 0 (mod 100), i.e. width ≡ 0 (mod 5). Banks are never padded. A padded bank would not sum to
+I₁₀₀; its unused coordinates would count as stock without children and break the telescoping identity
+m·W − mass = 60·(4v − 5h(h−2)) that `bank_check.py` and `math_check.py` assert.
+
+The physical-layer producer enforces divisibility with `make_physical.py --bank-parity`. This generalizes gen5's
+parity rule (60·width ≡ 0 mod 120). It drops the fewest trailing reuse pairs that make 60·width divisible by m.
+Dropping a pair returns its rank-17 recipient to the entrances as a width-3 family, and its donor stays a plain
+helper, so each drop adds 3 to the width.
+
+For this word the maximum matching has 892 pairs and width 144,204 ≡ 4 (mod 5). Two drops are therefore minimal
+(3k ≡ 1 mod 5 gives k = 2). The dropped pairs are [3454, 9119] and [3409, 9118], and the width goes 144,204 →
+144,207 → 144,210. In the unbanked price the two drops cost about 1.5·10⁻⁸.
+
+`bank_template.tile()` then finds an exact tiling, with no padding:
+
+| Blocks | Banks per stage |
+| --- | ---: |
+| 20 of dimension 3 and 2 of dimension 20 | 210 |
+| 25 of dimension 4 | 2,880 |
+| 5 of dimension 20 | 83,436 |
+
+The tiler mixes a width that does not divide m (here 3) with a filler width that does (here 20). It backtracks
+until every remaining pure width divides out, and asserts:
+
+- every pattern sums to m;
+- every block is used exactly once.
+
+The patterns are pinned in `word-pins.json`.
+
+## Counts and selector bill
+
+There are 86,526 banks per stage, 432,630 banks in total and 230,400 data families. Literal stock is 663,030,
+and its per-replica normalized value is 132,606/12. The checker enumerates each of the 2,469,000 actual
+role/replica/stage assignments exactly once, verifies each actual role's chart rank, and hashes the complete
+allocation.
+
+Every actual chart (163 distinct entrance bases) uses at most 150 factors. At most 99 coordinate transpositions
+and 100 scalar-coordinate factors give 349 normalizer factors. A conservative added out-and-back selector bill,
+in addition to all retained PR234 route and scalar bills, is
+
+    2·5·60·((663030 − 1) + 8230·100·349) = 172,734,017,400 < 2⁴⁰.
+
+## Literal realization
+
+The literal stock, not the rational per-replica stock, must be used for physical role routing and finite
+storage. All 60 scalar replicas execute, and all recursive child counts are multiplied by 60 in a literal
+realization. Any smaller integer normalization used only in the moment arithmetic must be distinguished from
+the literal replica count.
+
+Serial execution may share an external copied-centre work stream only after erasure. The fixed bank selector
+bill is explicitly charged before the inherited positive ordinary-leaf gap absorbs it. After completion removal
+the largest child is 42 of 100, so a single level halves, and the histogram remains a one-level profile.
+
+## Scope
+
+This witness leaves the following to the integrator (verify.py):
+
+- the full scalar, integer and sign audits;
+- the frame ledgers and the exact global lowering;
+- the prime guard and the complete fallback profile;
+- the 47 outer inequalities.
+
+Its input charts and census are the independently admitted p = 10 helper. The existing compiler, common weighted
+chart, restored selectors, complete-stream routing and all-size analytic hypotheses remain conditional, as in the
+cited sources.
+
+Prepared with OpenAI Codex assistance (source527 package, eumemic). The gen5 and p = 10 numbers, the bank
+divisibility rule and the exact tiler were added with Claude assistance. Apache-2.0; inherited source
+attribution remains unchanged.
+
+## Transcript stages: residual widths and the economy tiling
+
+With the transcript stages (`STAGES-PROOF.md`) the banks hold more residual widths. The kernel pivots of rank e
+have residual 20 − e (widths 19, 18, 16, 15, 13, 12, 10, 7, 6 here), the 240 early-restored helpers have residual
+P_E − P_σ of rank 19 − 16 = 3, and the seven terminal sinks remove seven full-width helpers. The residual census
+(`residual_families` in `word-pins.json`) is {20: 5,906, 19: 1,007, 18: 20, 16: 5, 15: 3, 13: 1, 12: 3, 10: 6,
+7: 1, 6: 1, 4: 960, 3: 310}.
+
+#315's filler search fails on this census: it mixes every width that does not divide 100 with the most numerous
+filler first and needs six rank-4 blocks per four 19-wide pivots, and the 57,600 rank-4 blocks run out (the p = 12
+analogue was PR #299's change from (r⁴, 4^(30−r)) to (r⁴, 24, 4^(24−r))). `tile()` now falls back to
+`economy_tile()`, which uses both fillers (F = 20, f = 4) and, for each other width w in decreasing order, picks
+the bank w^a F^c f^b with the fewest f blocks per w block (then the largest a), e.g. (19⁴, 20, 4),
+(18⁴, 20, 4²), (16⁵, 20), (15⁴, 20²), (3²⁰, 20²), with at most one remainder bank per width; the leftover fillers
+fill (20⁵), (4²⁵) and residue banks (20^j, 4^k). The same post-conditions are asserted as before: every bank sums
+to m = 100 and every block is used exactly once, so there is no padding and the stock is the same as for any exact
+tiling: banks per stage = 60 · Σ residual / 100 = 85,578, literal stock 230,400 + 5 · 85,578 = 658,290. The
+patterns are pinned (`bank_patterns`). The baseline word (no stages) still tiles by the original search.
+
+Restored helpers are charted by the pair (σ, E): the chart basis is (residual rows of P_E − P_σ, the basis of σ,
+the E-perp rows), checked to be G-orthogonal blocks and exactly inverted like the plain charts (`residual_rows` in
+`bank_check.py`). 759 charts are rebuilt; the completion rows carry the endpoint frame E and the completion rank
+5(a + h − dim E).
diff --git a/research/five-stage-p10-transcript-stages/LICENSE b/research/five-stage-p10-transcript-stages/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
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+      any Contribution intentionally submitted for inclusion in the Work
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+   6. Trademarks. This License does not grant permission to use the trade
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diff --git a/research/five-stage-p10-transcript-stages/MANIFEST.json b/research/five-stage-p10-transcript-stages/MANIFEST.json
new file mode 100644
index 0000000000..17d8368d3e
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/MANIFEST.json
@@ -0,0 +1,165 @@
+{
+ "files": {
+  "BANK-PROOF.md": "72c26d29a0bf59ddc46fdcbd6c50e775fdb1ee3eb4d612c4efcca74c4ebae58b",
+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "NOTICE.md": "622b63758089429e748ce19c5ca163dbd1d5557b06f20a06434f84daa248945c",
+  "PR-STATEMENT-PR315.md": "cf8f0341e4ab6e45bd58176aeb8628bfe0bc439c1a6083084125f868426ff93e",
+  "PR-STATEMENT.md": "1811c0a9904959212f978d9c31b72dc3d76868aca39edc46eb4a9b2996cc052e",
+  "PROOF.md": "176c2d2ab4fae3a2c85c553d28b52a3c41d72b3db372381b4cdf8730515935a6",
+  "README-PR315.md": "3139213c18924fd5925fe92ef7bedb3bb6c15a4ee0dc8e2056a3082f9ff68eab",
+  "README.md": "2ef87d28ae8712d9094428cb1e4e7698cce2999c56c1f114b61e1c933dba242e",
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+  "restore-selection.json": "678e468cf92e50f88ef7da8da973e9574e43f1bae3d2dd1ecfe6c84d8a2890f2",
+  "restore_transform.py": "8ae804aba73fe6ec14c484503af02f1ef4dc6af073c9d39377f22b511896ab21",
+  "scalar/word.py": "e675d4eb9d90ff0b44279fae0b46f1a8b39f65421cc38454b70a6b75d0e10b42",
+  "scalar_check.py": "7df8fcca1d866087f982549df8424ee0b26d5dd3bbb2a725e5ddfb347ed125e4",
+  "sink-selection.json": "c62b7e7d563770c6b01cea37a7a26b5ea015d87e64fc75650acc7c4b920fa093",
+  "sink_transform.py": "39c573a6404a4f76f1bca3a1721f3afe0a3937c4543d6eaadbc3ae881b632b22",
+  "target-selection.json": "b616946f4bc5ea2350c0060843484212e773af29af5d735c440ecf740553a141",
+  "target_transform.py": "0955daa2a15dc58b27a6b57aad029c0e97a417400c7c2d7eba8e54a34b974d69",
+  "verify.py": "fbfeac193b877e68ff7704555175a695aa96c95a8431eab0ae087134d6cd7514",
+  "virtual_check.py": "ec952d99c151e6e336631210e598d58478293491ca01842fd4c9d0a4b57b4e5a",
+  "word-pins.json": "c694423692f0b4fa5004187f934f7d5809d490ac37c416430b5e4fb87d2969f3",
+  "word_pins.py": "3cc2662630af62aaabb6966f03b5d01a2f06a5f3490c6979a3e54daf550958b4"
+ },
+ "schema": "gen5-parity-fused-five-stage-banks-inputs/1"
+}
diff --git a/research/five-stage-p10-transcript-stages/NOTICE.md b/research/five-stage-p10-transcript-stages/NOTICE.md
new file mode 100644
index 0000000000..369b98c4e2
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/NOTICE.md
@@ -0,0 +1,145 @@
+# Attribution and licence
+
+Apache-2.0 applies. Original headers, licences, notices and AI-assistance disclosures are preserved. The
+credits below do not imply review or endorsement.
+
+This package is a cube-size change (p = 12 → p = 10) of #285's gen5 five-stage package. Every inherited design,
+generator, checker, layout and bank method below is used at the new cube size; no inherited idea is claimed.
+
+## Inherited, unchanged or with generalized constants
+
+- **Five-stage architecture and finite interface package:** Henry Grant (hcg890), PR234, and Jacob Sussman's
+  five-stage construction and gcert/1 export. The complete inherited five-stage credits are in
+  `UPSTREAM-PR234-NOTICE.md`.
+- **Package machinery:** eumemic's source527 package, prepared with substantial OpenAI Codex assistance, with
+  its lineage: Dugongue's PR207/PR216 finite and bank admissions, Rohan Arun's PR211 and sennemmi's PR230 frame
+  work, and eumemic's PR210. Their notices are retained verbatim in `notices/`. This covers:
+  - the scalar program `scalar/word.py` (byte-identical);
+  - the physical event emitter, the parity fusion and the raw-ledger census;
+  - the stage-private bank template and checker;
+  - the moment, prime and finite-bill checks, and `verify.py`.
+
+  In this package their p = 12 constants are derived from the cube size or pinned in `word-pins.json`. The
+  logic is unchanged, apart from the exact bank tiler that replaces gen5's fixed bank patterns.
+- **Banks:** Evan McKinney's PR197 completed-bank method. Rohan Arun's PR237 published the width-120
+  application first. Here the banks have width 100.
+- **Complex supplier (this variant):** the centre-sharing complex program
+  `inputs/complex/gcert1-p11-cmod-centre-mw-flow.json.gz`. It is local research, not published, prepared by
+  DreamingOfClouds with Anthropic Claude assistance (Apache-2.0). It is the source-assisted complex word of
+  PR #184/#194, built with PR #304's recipe on three query modules:
+  - the new centre-sharing pair module `pmod46_ptc1_final.json` (45 pair outputs and the star centre);
+  - an earlier re-annealed disjoint-triple module, `tmod_final.json` (v1, 2,069 additions). This is not PR #304's
+    `tmod_cmod_v2.json`.
+  - PR #304's all-but-one module, as `qmod_q1_snap1.json`.
+
+  PR #304's `aligned_word.py` cannot build it unchanged. The program was built by a local 46-root loader (not
+  shipped) with a 10-line patch to PR #144's `Graph.finish` (icekylinx). The patch and the three modules are
+  shipped as provenance in `inputs/complex/centre-mw/`, whose `NOTICE` gives the details. The rest of the recipe
+  is PR #304's: PR #233's maximum-weight reuse pairs, icekylinx's PR #184 frame flow and exact lift, and PR #256's
+  emitter.
+  PR #304's full notice and credits are in `inputs/complex/NOTICE-PR304`.
+
+  The gcert bytes are kept as emitted (their JSON keys are not in canonical order), because a separate Lean run
+  checked exactly these bytes (`wht_main_block_B2Gcc27x`, exponent 1 − 7727140/10¹⁰, with Sussman's unchanged
+  generator; see `README.md`). No Lean check is pinned here. Every verification run checks the program with
+  Sussman's `gx.check1` (exact scalar identity) and `gxcore` mirror.
+
+  It builds on Avi Eisenberg (ikeboy)'s PR193/PR194 helper and Chafik Boukhalfa (chafreaky)'s PR200/PR233/PR256
+  work. It runs inside Sussman's five-stage certificate, whose original disclosures are in `inputs/complex`.
+
+  The complex checks (`code/complex_{labels,scalars,splice,basis}.py`, `portable_complex.py` and the
+  `complex_supplier()` block of `math_check.py`) are taken as re-pinned for this program in a copy of PR #296's
+  package (Chafik Boukhalfa, chafreaky), which first generalized those checks to a new gcert. That was done by DreamingOfClouds with Anthropic Claude assistance.
+- **Complex program checkers:** Jacob Sussman's reference checker `gx.py` (`gx.check1`) and his `gxcore.py`
+  mirror of the two Lean checks. Both are Apache-2.0, Copyright 2026 Jacob Sussman, and are vendored unchanged
+  from jacobalansussman/wht-power-saving-lean at f010392c in `inputs/complex/sources/` (`tools__gx__gx.py` is
+  new here; `tools__gx__gxcore.py` was already pinned).
+- **Physical-word classes:** Chafik Boukhalfa (chafreaky)'s PR200 `bit/word.py` and `bit/base_word.py`, vendored
+  in `bitword/bit`. `base_word.py` is unchanged; its unused constant `P = 12` is left as PR200 wrote it.
+  `word.py` changes only its input file names: PR200 hard-coded its own p = 12 names, and two lines (plus a
+  comment) now read the cube size from the single pinned `graph_pP.json`; the frame-loading line also checks
+  that the graph's p and h agree.
+  `bitword/NOTICE-PR200` is PR200's own notice.
+- **Checker:** eumemic's PR168-v4 `check_paired_cube_bit.py`, vendored unchanged and run with p = 10.
+- **Generator:** eumemic's PR168 paired-cube bit generator (`bitword/producer/paired_cube_bit_word.py`), with
+  #276's gen4 changes (arc-aware local design, centre-sharing pair module).
+- **Paired-cube framework and its developments:**
+  - icekylinx's PR144: paired-coordinate/shared-core framework and configurable local channels.
+  - PR161/PR168 (eumemic): annealed modules, nested schedules and the generator.
+  - James Chang's PR166 and PR162's carrier rule.
+
+## New in this package
+
+All of the following was prepared by DreamingOfClouds with Anthropic Claude assistance.
+
+**The p = 10 bit word.** It has three data files:
+
+- `pm_p10.json`: pair module, 273 additions;
+- `qmod_p10.json`: all-but-one module, 24 additions;
+- `local_design_p10.json`: cube-local recipe trees from a pair-aware local design search.
+
+The two modules were annealed for p = 10, starting from restrictions of gen5's p = 12 modules. The package also
+pins the new frozen arcs `arcs_p10.json`.
+
+**Generator and producers at p = 10.** The generator gains its p = 10 MODULES/QMODULES entries and the variant-u
+output merge at p = 10; p = 12 behaviour is unchanged. The physical-layer producers become h-generic:
+
+- `make_physical.py`: recipients of rank h − 3, residual widths in h, and the `--bank-parity` rule generalized
+  to divisibility by m = 5h;
+- `descent.py`: cost r·ln(5h/r).
+
+`regenerate.py` gains a re-pinning mode.
+
+**Package integration at p = 10.** This covers:
+
+- `word_pins.py` (cube-size shape and strict pins) and `word-pins.json`;
+- `discovery/repin.py` and `discovery/REPIN.md`;
+- the cube-size generalization of every check listed in `PROOF.md`;
+- the entrance-basis geometry checks for every rank present;
+- the exact zero-padding bank tiler;
+- the complex-bound assembly path of `math_check.py`, which certifies the bit at its root and feeds the capped
+  saving;
+- the fallback-inclusive certification of the complex coarse (both moment engines, adjacent grid point
+  rejected);
+- `code/complex_gx.py`, which runs `gx.check1` (exact scalar identity) and the `gxcore` mirror on the pinned
+  complex program in every run, with a flipped-sign control, and the honest restatement of that dependency in
+  `portable_complex.py`.
+
+**Gen5 and gen4 work retained from #285/#276.** This covers:
+
+- the `--bank-parity` option;
+- the arc-aware local design machinery (`local_design()`) and the centre-sharing pair-module patch;
+- `make_physical.py` and `descent.py` as implementations of PR200's stated rules;
+- `prepare.py`, `virtual_check.py` and the `scalar_check.py` controls.
+
+The circuit and module searches were run by Claude agents (simulated annealing, CP-SAT and exact compiles). Every
+reported number was re-run with the exact generator and the full verifier. No exclusive priority is claimed for
+any inherited design or theorem interface.
+
+## Transcript stages (this package)
+
+The stage stack is ported from the gen5 Python pipeline at p = 12 to the p = 10 word by Chafik Boukhalfa
+(chafreaky) with Anthropic Claude assistance (Apache-2.0). Every mechanism is inherited; the selections were
+re-derived on this word. Credits, without implying review or endorsement:
+
+- **Concave descent retiming:** Rohan Arun (rohanarun), PR #287 (`descent_transform.py`, rule and transform);
+  the search was re-implemented to reproduce #287's frozen selection exactly before it was run here
+  (`discovery/descent_search.py`).
+- **Target-prefix squares:** eumemic, PR #268/#273 (`target_transform.py`, OpenAI Codex assistance), as used in
+  #287; search re-implemented (`discovery/target_search.py`).
+- **Kernel entries:** PR254's kernel pairs and eumemic's #268 kernel transform; the collective (multi-donor)
+  families follow #272; per-entry cuts, shared donors and the collective census/packing are from our PR #282/#284/
+  #290/#299 (Chafik Boukhalfa, Claude assistance); the multi-seed restart packing is Rohan Arun's PR #300.
+  The shared-donor selection (donors shared by many high-cardinality entries, alternate response bases,
+  maximum-weight closure) follows eumemic's PR #319 (OpenAI Codex assistance), read as a description only; the
+  closure search here (`discovery/coll/lines.py`, `planes.py`, `closure_pack.py`) is our own re-implementation
+  run before the kernel stage.
+- **Early restorations:** utcorvusvolat-dotcom, PR #280 (cleanup screen and emitter), with Dugongue's
+  endpoint-aware composition in PR #283; ported to this pipeline in our PR #295.
+- **Terminal sinks:** Dugongue, PR #283; the stricter screen of our PR #295.
+- **Reorder:** our PR #299 (reordering single additions into a neighbouring incidence frame; toggle-detection view
+  of Khattar–Gidney, arXiv:2407.17966).
+- **Second descent tools** (searched, empty here): constructed join/meet frames from PR #291 (rohanarun) and
+  connected blocks after PR #270.
+- **Downstream changes** (endpoint completions in the lowering, (σ, E) charts, determinant retention,
+  completion-rank pricing) are from our PR #295/#299; the economy bank tiling is new here.
diff --git a/research/five-stage-p10-transcript-stages/PR-STATEMENT-PR315.md b/research/five-stage-p10-transcript-stages/PR-STATEMENT-PR315.md
new file mode 100644
index 0000000000..0137ef5744
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/PR-STATEMENT-PR315.md
@@ -0,0 +1,50 @@
+κ = 7.64230861320245e-4
+
+# A p = 10 bit word in the five-stage completed banks
+
+A conditional finite construction with **κ = 152846172264049/(2·10¹⁷) ≈ 7.64230861320245 × 10⁻⁴**. The bit
+supplier binds; the complex supplier is a centre-sharing complex program (local research, not published).
+
+This package ports #285's gen5 five-stage package from cube size p = 12 to **p = 10**. The paired-cube bit word
+now has h = 20 coordinates, v = 960 sources and five-stage width m = 100. It is generated by the same PR168
+generator (with #276's gen4 local-design changes) from three p = 10 data files:
+
+- a pair module (273 additions);
+- an all-but-one module (24 additions);
+- a pair-aware cube-local design.
+
+The physical layer follows PR200's rules: rank-17 recipients, 890 compensated reuse pairs, and 998 descended
+operation frames. Every later stage is #285's, with the p = 12 literals replaced by cube-size formulas or by
+strict pins in `word-pins.json`:
+
+- PR234's five-stage layout;
+- stage-private completed banks, now 100 coordinates wide, with an exact zero-padding tiling;
+- the source527 verification chain.
+
+| one invocation | gen5 (#285), p = 12 | this package, p = 10 |
+| --- | ---: | ---: |
+| independent dirty registers R | 15,886 | **8,230** |
+| independent entrances (ranks) | 2,554 (17, 18, 20, 21) | 1,270 (16, 17) |
+| normalized stock / deficit | 249,414 / 52,800 | 132,606 / 24,480 |
+| bit coarse saving (certified root) | 7.43337804075788e-4 | **7.64815357146385e-4** |
+| complex coarse saving | 7.47454944651775e-4 (PR193, no fallback) | 7.72714351296671e-4 (centre-sharing, with fallback) |
+| κ | 7.42785663120535e-4 | **7.64230861320245e-4** |
+
+**Why the bit binds.** The bit's certified root c is below the complex leaf cap (1 − β)·b, so the outer
+assembly is fed c itself, as in #285. The 47 constraints and the adjacent-κ rejection are unchanged. (The capped
+path of `math_check.py`, for c above the cap, is not exercised here.) The complex coarse b is certified with the
+10⁻¹⁶ fallback, and the complex program is checked fresh by Sussman's `gx.check1` (exact scalar identity) and
+`gxcore` mirror. The same gcert bytes were compiled to Lean with Sussman's unchanged generator and kernel-checked
+locally (`wht_main_block_B2Gcc27x`, exponent 1 − 7727140/10¹⁰; not pinned here; see `README.md`).
+
+Run `python3 -B verify.py --output NEW_DIR` (Python 3.12 or newer, tested on 3.12 and 3.14; sympy 1.14.0). It takes about three to five minutes
+and runs no producer. `bitword/producer/regenerate.py` reproduces the five pinned bit-word files byte for byte.
+
+The result is conditional on the retained all-size compiler, common weighted chart, restored rows, selectors,
+tape routing, prime supply, precision/recovery, complex symbolic correctness and analytic reduction. See:
+
+- `README.md`;
+- `PROOF.md`;
+- `BANK-PROOF.md`;
+- `bitword/README.md`;
+- `NOTICE.md`.
diff --git a/research/five-stage-p10-transcript-stages/PR-STATEMENT.md b/research/five-stage-p10-transcript-stages/PR-STATEMENT.md
new file mode 100644
index 0000000000..46e9bc6a80
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/PR-STATEMENT.md
@@ -0,0 +1,25 @@
+κ = 7.69553898621543e-4
+
+# The p = 10 bit word with the transcript stage stack
+
+A conditional finite construction with **κ = 769553898621543/10¹⁸ ≈ 7.69553898621543 × 10⁻⁴** (+0.697% over
+#315's 7.64230861320245e-4, +0.046% over our #320's 7.69198971896986e-4, +0.169% over #319's 7.68257328708259e-4).
+The bit binds: its certified root 7.70146568251934e-4 is below the complex leaf cap
+of #315's centre-sharing supplier (7.72714351296671e-4), which is unchanged.
+
+#315's p = 10 word ran with no transcript stages. This package adds the gen5 stage stack, re-derived on that
+word: #287's concave descent (480 gates) and target-prefix squares (120 groups), a shared-donor kernel (1,047
+entries of total entrance rank 1,200: per-entrance maximum-weight closure over alternate response bases, donors
+shared by up to 30 entries, after eumemic's #319; it replaces #320's 775-entry packing and keeps the sink helpers
+out), #280/#283 early
+restorations (240), #283 terminal sinks (7) and #299's reorder (133 moves). Each stage was predicted with the
+φ ledger before it was built; every prediction equals the verified κ of the package truncated after that stage
+(table in `README.md`). A second descent, a second reorder round and a second kernel round find nothing (worth a
+stage) on this word.
+
+The p = 12 literals of the stage code are replaced by cube-size formulas or strict pins in `word-pins.json`; the
+banks get an exact economy tiling for the new residual widths (no padding). Run `python3 -B verify.py --output
+NEW_DIR` (Python 3.12+, sympy 1.14.0; about four minutes).
+
+See `README.md`, `STAGES-PROOF.md`, `BANK-PROOF.md`, `discovery/README.md`, `NOTICE.md`; the base package is
+described in `README-PR315.md` and `PROOF.md`.
diff --git a/research/five-stage-p10-transcript-stages/PROOF.md b/research/five-stage-p10-transcript-stages/PROOF.md
new file mode 100644
index 0000000000..1d8be54a83
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/PROOF.md
@@ -0,0 +1,232 @@
+κ = 7.69198971896986e-4 (this package); 7.64230861320245e-4 for #315's chain without stages
+
+> This file is #315's verification chain, kept unchanged. This package inserts the transcript stages between the
+> parity fusion and the five-stage lowering; they, and the downstream changes they need, are described in
+> `STAGES-PROOF.md` and the last section of `BANK-PROOF.md`. Counts quoted below for #315's word (registers,
+> entrances, banks, κ) change accordingly; the pinned values are in `word-pins.json`.
+
+# Source-bound finite verification
+
+The bit helper is a paired-cube bit word at cube size p = 10: a reversible local word in which all inputs and
+dirty registers are formal variables. It is built by the gen5 generator with p = 10 data. Every later stage is
+#285's chain, which is the source527 package's (eumemic). This file states what each stage checks and what
+changed relative to #285.
+
+## What changed from p = 12
+
+The five-stage layout is the same at every h. It has m = 5h; idle ranks (2h−2, h−1, 2h+2, 4) at 2v each; h copied
+centres of rank h−2, each read by 3v/h targets; and five-stage deficit 4v − 5h(h−2). The complex side already
+used this at h = 22 (ranks 42/21/46/4).
+
+At p = 10 (h = 20, v = 960) the layout values are:
+
+- m = 100;
+- idle ranks 38, 19, 42 and 4;
+- copied centres of rank 18, with 144 scatter reads each;
+- deficit 2,040.
+
+`word_pins.shape()` derives every one of these values from p. Where #285 asserted a p = 12 literal, the check
+now asserts the formula. Where #285 asserted a word-dependent literal (a register count, a histogram, a digest,
+κ), the check calls `word_pins.expect(name, value)`. That call asserts exact equality with the value pinned in
+`word-pins.json`, which `MANIFEST.json` pins like every other input. Each check is therefore exactly as strong
+as the literal it replaces.
+
+`verify.py` asserts that the pins are strict. `discovery/repin.py` records the pins in a separate process. It
+runs the same stage sequence (`verify.replay`), and every structural assertion, exact certificate and control
+still has to pass. See `discovery/REPIN.md`.
+
+## The bit word
+
+`bitword/selected/bit` pins five files: the signed graph, the virtual profile, the physical word, the exact
+frames and the partner-pair chronology.
+
+**Virtual word.** `virtual_check.py` runs eumemic's PR168-v4 package checker, unmodified, with p = 10. It
+checks:
+
+- exact frames (A·Bᵀ = 0, complementary ranks) and the mod-2 decoder with stars and side parts;
+- geometry: source lines, side-root common caps, operand nesting and centre star spans;
+- role and target chains on node frames, and the partner chronology;
+- G-nondegeneracy of every used frame, for G = I − J/9 (nondegenerate on Q²⁰ since 1 − 20/9 ≠ 0);
+- a literal F₂ dirty-scratch replay and the independent ledger recount.
+
+All five mutation controls are rejected. The profile is:
+
+- R = 9,120, W = 11,040, m = 3h = 60;
+- deficit 840 = 2v − 3h(h−2);
+- 12,912 frames and 151,140 children.
+
+**Physical layer.** The same stage runs Chafik Boukhalfa's PR200 classes as PR200's `bit/prove.py` runs them.
+`bitword/bit/base_word.py` is unmodified. `bitword/bit/word.py` changes only its input file names: PR200
+hard-coded its own p = 12 names, and two lines (plus a comment) now read the cube size from the single pinned
+`graph_pP.json`. The frame-loading line also asserts that the graph's p and h agree. `base_word.py` still
+contains PR200's unused constant `P = 12`.
+
+The classes check:
+
+- every changed operation frame (998) is nondegenerate and contains its node's value span;
+- the execution order preserves each role chronology;
+- gauges are untouched in phase one, every gauge read precedes its role's first use, and gauge targets equal
+  response supports;
+- the 890 handoffs are one-to-one between ungauged non-root donors and gauged recipients;
+- each donor is dead before its recipient's read, and its last frame lies in the recipient's gauge frame;
+- all gate ports are distinct.
+
+The stage also recomputes the physical row:
+
+- phase one is exactly the centre closure;
+- every addition's actual operands are checked;
+- every physical role chain and the actual target chronology are nested;
+- the deficit telescopes, at 840.
+
+It executes the physical word on all 10,150 formal columns over F₂ and on the defining integer decoder. Four
+adverse controls are rejected: an omitted compensation, a missing partner delivery, a stale recipient read and a
+zero operation frame. `prepare.py` also recomputes the literal adjoint and asserts that it equals PR200's.
+
+The handoffs follow PR200's rule. A recipient is read immediately before its first operation. Recipients are
+rank-17 (h − 3) gauges with no strictly larger gauge later on any of their targets, so every target chain stays
+nested. Hopcroft–Karp matches 892 of the 960 candidates. The bank-divisibility rule then drops the last two
+pairs (see `BANK-PROOF.md`), leaving 890 pairs and 1,270 independent entrances: 1,200 of rank 16 and 70 of
+rank 17.
+
+## Unchanged scalar program and empty selections
+
+`scalar/word.py` is the source527 scalar program, byte-identical (sha256 e675d4eb…). It reads h and v from the
+word. Its source527 selections are all empty here:
+
+- source loans, early and gauge mixes, retimed prefixes;
+- aggregation, rank and echelon groups;
+- fresh and paired source reads, terminal sinks.
+
+The program then executes exactly the PR200 physical word:
+
+1. dirty compensation at D0;
+2. V injection and the phase-one gates;
+3. the 20 copied-centre scatters;
+4. gauge reads at their read times, interleaved with the remaining gates;
+5. side roots, then partner mixes and deliveries;
+6. cleanup, the inverse gates, and V removal.
+
+`scalar_check.py` runs it on all 10,150 formal F₂ columns (960 sources, 960 targets and 8,230 dirty registers)
+and in both defining-integer directions with 24-bit packing. The same 11 corruptions of the actual context as in
+#285 must each make the unchanged program fail.
+
+## Physical events, parity fusion and global lowering
+
+`code/physical527.py` observes the scalar program and emits the physical frame tags. The emitter is source527's.
+Its register count is pinned, and its copied-centre rank, count and reads are h−2, h and 3v/h. The local scalar
+projection must equal the independent observer, and every MOVE is checked as an exact frame inclusion.
+
+`parity_transform.py` deletes the 581,680 even-coefficient payload ADDs, which are identities over F₂. It merges
+no MOVE chains, so the paid local histogram is unchanged. The independent required-use census rebuilds every path
+from the surviving operations and mathematical endpoints, checks both reflected inclusions, and matches the
+instruction histogram. The 355,400 surviving payload additions (354,440 of coefficient 1 and 960 of
+coefficient 3) and their literal inverse are replayed on every F₂ column. The cancellation-free signed prefix
+bounds are 21,855 (forward) and 914,238 (inverse). Its unused-stream census now ranges over the actual 2v + R
+streams; #285 had the literal 19,406 there. The proof/PARITY-CONTRACT.md argument applies unchanged.
+
+`code/global_lowering.py` is PR234's lowering, with V, H, M, the idle ranks, the copied-centre constants and the
+deficit derived from the cube size, and R and the entrance census pinned. It expands all five stages, the idle
+and bridge phases, the 1,270 completions and the terminal exchange. It checks every operand namespace and the
+paid five-stage histogram:
+
+- 248,360 calls;
+- rank mass 1,204,960;
+- deficit 2,040 = 4v − 5h(h−2).
+
+`code/geometry527.py` checks the exact rational h = 20/m = 100 routes, the eight idle boundary pairs for two
+actual ports (gaps 38, 38, 19, 19, 42, 42, 4, 4), and the completion projectors and five disjoint windows. It
+does so for two distinct actual bases of the most frequent entrance rank (16) and one actual basis of every
+other entrance rank (17).
+
+## Primes, banks, moments and finite bill
+
+**Primes.** `prime_check.py` recomputes the cleared-Gram determinant 9·BGBᵀ of every consumed basis: 12,884
+distinct bases, at most 97 bits. The stripped small primes are 2, 3 and 11. The factor 11 appears because
+det G = (9 − h)/9 = −11/9 at h = 20. Every residual is below 2⁸⁰, so the retained prime range q > 2⁸⁰ is
+unchanged.
+
+**Banks.** The independent entrances have 163 distinct bases and residual families of widths 4 (rank 16) and
+3 (rank 17); the 6,960 ungauged roles have width 20. `BANK-PROOF.md` gives the exact 100-coordinate tiling:
+
+- (3²⁰ 20²) × 210 banks;
+- (4²⁵) × 2,880 banks;
+- (20⁵) × 83,436 banks.
+
+`bank_check.py` rebuilds the 163 charts (at most 150 factors) from the G⁻¹ residual rows (h − 9)a − Σa, and
+enumerates all 2,469,000 role/replica/stage assignments. It checks the callable route map and both endpoint
+directions, and removes exactly the 1,270 rank-5a exterior completions.
+
+**Moments.** Literal stock is 663,030. The normalized profile has:
+
+- m = 100, W = 132,606;
+- rank mass 13,236,120, deficit 24,480;
+- largest child 42.
+
+Two independent rational moment engines, including the complete 10⁻¹⁶ bad-class fallback, give the bit's certified
+root c = 152963071429277/(2·10¹⁷) ≈ 7.64815357 × 10⁻⁴. The adjacent 10⁻¹⁸ grid point is rejected.
+
+**Complex program.** The complex stage first checks the pinned gcert/1 program itself (`code/complex_gx.py`).
+It runs Jacob Sussman's reference checker `gx.check1` with `scalar=True`: labels, blocks, N, the exact scalar
+identity E5 (every x role restored, every target receives exactly its source) and Q2. It also runs his `gxcore`
+Python mirror of the two Lean checks, whose block histogram must equal the program's. Both are vendored
+byte-identical from wht-power-saving-lean at f010392c and sha-checked. One flipped scalar sign must be rejected
+by both on E5. This is a Python check; no Lean check of this program is pinned here. The inherited label, scalar,
+splice and finite-guard checks of PR234/#296 then run unchanged.
+
+**Lean (run locally; not pinned here).** With Jacob Sussman's wht-power-saving-lean at f010392c (Lean v4.34.1,
+Mathlib d13f23b) and his unchanged generator `tools/gx/regen_check.py`, the exact gcert pinned here (sha256
+bb0499ab342aee3594904fc1cd72b9ff496cdb315d0840f4cdd5ba64ef794d34) was compiled to Lean and kernel-checked:
+`OAI.PowerSaving.WHT.wht_main_block_B2Gcc27x`, the Walsh–Hadamard corollary at exponent 1 − 7727140/10¹⁰.
+`tools/Compare.lean` passed against a challenge file that differs from Sussman's ChallengeB2Gp193x only in the
+exponent and names; the axioms are propext, Classical.choice and Quot.sound. The official comparator and a clean
+build from nothing were not run. This covers only the complex program's Walsh–Hadamard saving, not the bit word,
+the bootstrap, the κ assembly or the retained integer-multiplication interfaces. Because the bit binds, κ is
+unchanged if b is replaced by the Lean exponent.
+
+**Assembly.** The complex supplier of this variant is the centre-sharing complex program (see
+`inputs/complex/centre-mw/NOTICE`). Its coarse b is certified like the bit's: with the 10⁻¹⁶ bad-class fallback,
+by both rational moment engines, with the adjacent 10⁻¹⁸ grid point rejected. This gives
+b = 772714351296671/10¹⁸. The inherited PR234/PR193 convention priced the complex side without the fallback
+(772714354722691/10¹⁸). That root is re-certified and recorded, but not used.
+
+The bit root c is below the complex leaf cap (1 − β)·b with β = 10⁻⁹, so **the bit supplier binds**. The
+assembly is fed s = min(c, ⌊(1 − β)·b − 10⁻¹⁸⌋₁₀⁻¹⁸) = c, and the path is #285's. Three completed ordinary-leaf
+levels from c feed the unchanged balanced outer assembly. All 47 strict inequalities and the seven margins are
+positive, and the adjacent final grid point of κ fails. (When c exceeds the cap, `math_check.py` instead feeds the
+largest 10⁻¹⁸ grid point at or below the cap to the bootstrap, re-checks the bit moment there, and checks that the
+assembly at the cap itself fails. This package does not exercise that path.)
+
+**Finite bill.** `finite_check.py` pays every PR234 primitive and router allowance on the literal 60 replicas and
+stock, and adds all 172,734,017,400 bank selector calls. It uses:
+
+- the actual 40-dimensional rational route (163 additions, 36 swaps, 23 scalings; denominators {1, 2, 3, 6});
+- d = m² = 10,000, so B(q) < q^10,001;
+- h = 20 copied-centre temporaries and 5h = 100 copy/erase episodes per replica.
+
+The data route families stay 20v + 4v (five stages of 4v data families plus the final exchange). The
+finite-bill moment and bootstrap use the fed saving, here s = c.
+
+## Inherited texts
+
+The files in `proof/`, `UPSTREAM-PR234-PROOF.md` and the notices are inherited verbatim. Their numbers describe
+the source527 p = 12 instance (for example m = 120, the 48-dimensional route and the determinant exclusions
+{2, 3, 5, 7}). For this package, the actual p = 10 values are those listed here, recomputed in `finite.json`,
+`banks.json` and `primes.json` of every verification run.
+
+The inherited complex texts (`UPSTREAM-PR234-PROOF.md`, `proof/INTEGRATED_PROOF.md` §6 and the pinned `P193*.lean`
+sources) describe PR193's complex program and its scalar identities hAi, hBi, hx, hy and hid. They do not cover
+the centre-sharing program used here. That program's scalar identity is checked in every run by `gx.check1`
+and the `gxcore` mirror (above).
+
+## Scope
+
+The proof boundary is unchanged and conditional. The following are inherited interfaces:
+
+- the all-size weighted compiler and common ancestor charts;
+- restored rows and completed ordinary leaves;
+- selectors, exact-tape routing and prime supply;
+- precision/recovery and retained complex symbolic correctness;
+- analytic transfer.
+
+These checks establish the stated finite construction under those interfaces. They do not rebuild Lean or
+execute a multiplier at all input sizes.
diff --git a/research/five-stage-p10-transcript-stages/README-PR315.md b/research/five-stage-p10-transcript-stages/README-PR315.md
new file mode 100644
index 0000000000..17c980fd77
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/README-PR315.md
@@ -0,0 +1,96 @@
+κ = 7.64230861320245e-4
+
+# A p = 10 bit word in the five-stage completed banks
+
+A conditional finite construction with **κ = 152846172264049/(2·10¹⁷) ≈ 7.64230861320245 × 10⁻⁴**.
+
+This package ports #285's gen5 five-stage package to a smaller cube: the paired-cube bit word is generated at
+**p = 10** (h = 20 coordinates, v = 960 sources) instead of p = 12 (h = 24, v = 1,760). The five-stage width
+becomes m = 5h = 100, and the stage-private completed banks become 100-coordinate banks. Every later stage keeps
+#285's logic, with its p = 12 literals replaced by cube-size formulas or by values pinned in `word-pins.json`.
+
+The bit word comes from eumemic's PR168 generator, as in gen5, with three p = 10 data files:
+
+- the pair module `pm_p10.json` (273 additions), annealed for p = 10;
+- the all-but-one module `qmod_p10.json` (24 additions);
+- the cube-local recipe trees of a pair-aware local design search, `local_design_p10.json`. The design was
+  found by a search on the p = 12 word and is reused unchanged: it is cube-local, so it does not depend on p.
+
+The physical layer follows PR200's rules, as in gen5. The compensated reuse recipients are the rank h − 3 = 17
+gauges.
+
+**Complex supplier of this variant, and the bit binds.** The complex program is a centre-sharing complex word
+built with PR #304's recipe on three query modules and a patched graph builder (local research, not published;
+see `inputs/complex/centre-mw/NOTICE`). Its coarse saving is b = 7.72714351296671e-4, certified with the 10⁻¹⁶
+bad-class fallback like the bit side; the inherited no-fallback convention gives 7.72714354722691e-4. The bit's
+certified coarse saving, 7.64815357e-4, is below the complex leaf cap (1 − β)·b. The bit therefore binds, and the
+assembly path is #285's: the bit is fed at its certified root. (With PR #304's complex supplier,
+7.6358781017907e-4, the bit root would exceed the cap. `math_check.py` also handles that complex-bound case, but
+this package does not exercise it.)
+
+The complex program itself is checked in every run by Jacob Sussman's reference checker `gx.check1` with the
+exact scalar identity, and by his `gxcore` mirror of the two Lean checks. No Lean check of the program is pinned
+here.
+
+**Lean (run locally; not pinned here).** With Jacob Sussman's wht-power-saving-lean at f010392c (Lean v4.34.1,
+Mathlib d13f23b) and his unchanged generator `tools/gx/regen_check.py`, the exact gcert pinned here (sha256
+bb0499ab342aee3594904fc1cd72b9ff496cdb315d0840f4cdd5ba64ef794d34) was compiled to Lean and kernel-checked:
+`OAI.PowerSaving.WHT.wht_main_block_B2Gcc27x`, the Walsh–Hadamard corollary at exponent 1 − 7727140/10¹⁰.
+`tools/Compare.lean` passed against a challenge file that differs from Sussman's ChallengeB2Gp193x only in the
+exponent and names; the axioms are propext, Classical.choice and Quot.sound. The official comparator and a clean
+build from nothing were not run. This covers only the complex program's Walsh–Hadamard saving, not the bit word,
+the bootstrap, the κ assembly or the retained integer-multiplication interfaces. Because the bit binds, κ is
+unchanged if b is replaced by the Lean exponent.
+
+| one invocation | gen5 (#285), p = 12, m = 120 | this package, p = 10, m = 100 |
+| --- | ---: | ---: |
+| virtual auxiliary roles | 17,292 | **9,120** |
+| compensated reuse pairs | 1,406 | 890 |
+| independent dirty registers R | 15,886 | **8,230** |
+| formal F₂ columns 2v + R | 19,406 | 10,150 |
+| independent entrances (ranks) | 2,554 (17, 18, 20, 21) | 1,270 (16, 17) |
+| banks per stage | 164,934 | 86,526 |
+| literal stock, 60 replicas | 1,247,070 | 663,030 |
+| normalized stock / deficit | 249,414 / 52,800 | 132,606 / 24,480 |
+| bit coarse saving (certified root) | 7.43337804075788e-4 | **7.64815357146385e-4** |
+| complex coarse saving | 7.47454944651775e-4 (PR193, no fallback) | 7.72714351296671e-4 (centre-sharing, with fallback) |
+| binding side | bit | **bit** |
+| κ | 7.42785663120535e-4 | **7.64230861320245e-4** |
+
+Run with Python 3.12 or newer (tested on 3.12 and 3.14), sympy 1.14.0 and assertions enabled:
+
+```sh
+python3 -m pip install -r requirements.txt
+python3 -B verify.py --output /tmp/p10-five-stage-verification
+```
+
+The output directory must be new and outside this immutable package. Verification takes about three to five
+minutes, uses no network and runs no producer. It performs these checks:
+
+- the PR168-v4 checker on the virtual word, with its five mutation controls;
+- PR200's physical-word proof as PR200 ran it: frames, handoffs, the physical row and all-column replays, with
+  4 adverse controls;
+- the retained source527 scalar program on all 10,150 formal F₂ columns, both integer decoder signs and 11
+  corruptions;
+- the physical event emitter, parity fusion and five-stage global lowering;
+- exact h = 20/m = 100 geometry, including two actual rank-16 entrance bases and one actual rank-17 basis;
+- exact determinants for 12,884 bases;
+- 163 bank charts and all 2,469,000 bank assignments;
+- the centre-sharing complex program: `gx.check1` with the exact scalar identity and the `gxcore` mirror, with a
+  flipped-sign control;
+- the complex supplier (labels, scalars, splice and finite guard), and both rational moment engines on the bit
+  and complex profiles, each with the fallback;
+- the assembly (bit-bound here) with all 47 outer inequalities, and the finite bill.
+
+`bitword/producer/regenerate.py` rebuilds the five pinned bit-word files from the generator and the two
+physical-layer producers, and checks them byte for byte. This is provenance only, not part of the proof.
+`discovery/REPIN.md` describes how to re-pin the package mechanically for a new module file.
+
+The result is conditional on the retained all-size compiler, common weighted chart, restored rows, selectors,
+tape routing, prime supply, precision/recovery, complex symbolic correctness and analytic reduction. The included
+finite checks do not replace those hypotheses. See:
+
+- `PROOF.md` for the verification chain and what changed from p = 12;
+- `BANK-PROOF.md` for the banks;
+- `bitword/README.md` for the bit word;
+- `NOTICE.md` for attribution.
diff --git a/research/five-stage-p10-transcript-stages/README.md b/research/five-stage-p10-transcript-stages/README.md
new file mode 100644
index 0000000000..c3a95200f5
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/README.md
@@ -0,0 +1,77 @@
+κ = 7.69553898621543e-4
+
+# The p = 10 bit word with the transcript stage stack
+
+A conditional finite construction with **κ = 769553898621543/10¹⁸ ≈ 7.69553898621543 × 10⁻⁴**, +0.697% over
+#315 (7.64230861320245e-4) and +0.046% over our #320 (7.69198971896986e-4). The bit supplier binds.
+
+Relative to #320 only the kernel selection changes: it is now a **shared-donor kernel** found by maximum-weight
+closure per entrance (`discovery/coll/closure_pack.py`), 1,047 entries of total entrance rank 1,200 instead of
+#320's 775-entry restart packing (rank 970). The idea of sharing donors across many high-cardinality entries is
+eumemic's #319 (90 shared-donor rank-one kernels appended after #317); here the closure is run before the kernel
+stage on the post-target word, over rank-one lines and exact rank 2–14 frame intersections, so it replaces the
+packing instead of appending to it. The kernel transform and every check are #320's.
+
+#315 (DreamingOfClouds) put the paired-cube bit word at cube size p = 10 (h = 20, v = 960, m = 100) into the gen5
+five-stage completed-bank pipeline, with no transcript stages. This package keeps #315's word, banks, complex
+supplier and verification chain unchanged and inserts the stage stack of the p = 12 gen5 pipeline, re-derived on
+the p = 10 word:
+
+    parity -> descent -> target squares -> kernel entries -> early restorations -> terminal sinks -> reorder -> lowering
+
+| stage | on this word | predicted κ (φ ledger) | verified κ (full replay) |
+| --- | --- | ---: | ---: |
+| #315 (no stages) | R 8,230, 1,270 entrances | 7.64230861320245e-4 | 7.64230861320245e-4 |
+| + descent (#287 rule) | 480 gates, −480 calls | 7.65146115390441e-4 | 7.65146115390441e-4 |
+| + target squares (#268/#287) | 120 groups | 7.65802240659923e-4 | 7.65802240659923e-4 |
+| + kernel entries, shared-donor closure (#272/#299, #319's shared donors) | 1,047 entries (1,015 distinct donors, up to 31 per entry, a donor in up to 30 entries), rank 1,200 | 7.68105513378630e-4 | 7.68105513378630e-4 |
+| + early restorations (#280/#283) | 240 helpers | 7.68740991856791e-4 | 7.68740991856791e-4 |
+| + terminal sinks (#283) | 7 sinks, R → 8,223 | 7.69153177272007e-4 | 7.69153177272007e-4 |
+| + reorder (#299) | 133 moves | 7.69553898621543e-4 | **7.69553898621543e-4** |
+
+The predictions come from the deficit-fixed φ ledger (the one-stage histogram delta of each frozen selection,
+×5, normalized ×12, W = (mass + 12·2,040)/100, the bit-bound assembly of `math_check.py`), calibrated on #315's
+own ledger (it reproduces #315's κ exactly). The verified values are full `verify.replay` runs of the package
+truncated after each stage. A second descent, a second reorder round and a second shared-donor kernel round after
+the reorder (4 entries, φ −0.77; `kernel_transform.run(..., tag='kernel2')` supports it) were searched and found
+nothing worth a stage on this word.
+
+| one invocation | #315 | this package |
+| --- | ---: | ---: |
+| independent dirty registers R | 8,230 | **8,223** |
+| independent entrances | 1,270 (16, 17) | 2,317 (adds 1,047 kernel pivots of ranks 1–14) |
+| early-restored endpoints | 0 | 240 |
+| banks per stage / literal stock (60 replicas) | 86,526 / 663,030 | 85,578 / 658,290 |
+| bit coarse saving (certified root) | 7.64815357146385e-4 | **7.70146568251934e-4** |
+| complex coarse saving (unchanged) | 7.72714351296671e-4 | 7.72714351296671e-4 |
+| binding side | bit | **bit** (root 0.33% below the complex leaf cap) |
+| κ | 7.64230861320245e-4 | **7.69553898621543e-4** |
+
+Run with Python 3.12 or newer, sympy 1.14.0 and assertions enabled:
+
+```sh
+python3 -m pip install -r requirements.txt
+python3 -B verify.py --output /tmp/p10-stages-verification
+```
+
+The output directory must be new and outside the package. Verification takes about four minutes, uses no network
+and runs no producer or search. Besides #315's checks (`README-PR315.md`), every transcript stage is a mandatory
+stage with its own receipt: frozen selections bound to the exact input word, all-column F₂ replays forward and
+inverse with omission controls, integer replays, exact operand source spans, nested frame chains rebuilt from
+scalar/COPY events with both reflected ledgers, the raw ledger rebound after every stage, endpoint charts and the
+re-tiled banks. Every word-dependent value is a strict pin in `word-pins.json` (recorded by
+`discovery/repin.py`).
+
+See:
+
+- `STAGES-PROOF.md` for the stages, what changed from p = 12, and the ledger;
+- `BANK-PROOF.md` (last section) for the residual widths and the economy tiling;
+- `discovery/README.md` for the searches that produced the selections;
+- `README-PR315.md`, `PROOF.md`, `bitword/README.md` for the base package;
+- `NOTICE.md` for attribution.
+
+The result is conditional on the retained all-size compiler, common weighted chart, restored rows, selectors,
+tape routing, prime supply, precision/recovery, complex symbolic correctness and analytic reduction. The included
+finite checks do not replace those hypotheses.
+
+Prepared by Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0.
diff --git a/research/five-stage-p10-transcript-stages/STAGES-PROOF.md b/research/five-stage-p10-transcript-stages/STAGES-PROOF.md
new file mode 100644
index 0000000000..598d89b697
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/STAGES-PROOF.md
@@ -0,0 +1,101 @@
+# Transcript stages on the p = 10 word
+
+#315 ships the p = 10 paired-cube bit word with no transcript stages: the parity-fused word goes straight to the
+five-stage lowering. This package inserts the stage stack of the gen5 Python pipeline (#287, #290, #295, #299,
+#306 lineage) between the parity fusion and the global lowering, re-derived on the p = 10 word. Every stage is a
+callable transform with a frozen selection that is bound to the exact input word (raw-record and scalar-projection
+SHA-256), and every stage is a mandatory proof stage of `verify.py` with its own receipt (`<stage>.json` in the
+output directory). The stage list is `portable_bit.STAGES`:
+
+    parity -> descent -> target -> kernel -> restore -> sink -> reorder -> five-stage lowering
+
+## What changed from p = 12
+
+The mechanisms and checks are unchanged. The p = 12 literals were replaced:
+
+- h = 24, v = 1,760, m = 120, centre rank 22, 24 centres, 220 scatter reads and the deficit 4,400 come from
+  `word_pins.shape()` (h = 20, v = 960, m = 100, centre rank 18, 20 centres, 144 scatter reads, deficit 2,040);
+- counts that p = 12 asserted as literals (selected gates, local histogram deltas, five-stage calls and rank
+  masses, entrance histograms, register counts) are pinned in `word-pins.json` through `word_pins.expect`, like
+  #315's own word values. A pin name can hold only one value (`discovery/repin.py` rejects a second one).
+- the search tools use φ(r) = r ln(100/r); the target-square search uses frame ranks h − 4 = 16 (prefix adds)
+  and h − 3 = 17 (close frame).
+
+## Stages
+
+| stage | selection | mechanism (origin) | on this word |
+| --- | --- | --- | --- |
+| descent | `descent-selection.json` | concave frame retiming of ADD gates to frames on an operand chain (Rohan Arun, #287) | 480 gates, 480 calls removed, delta {1:−960, 2:+480, 16:−480, 17:+960, 18:−480} |
+| target | `target-selection.json` | target-prefix squares (eumemic #268/#273, used in #287) | 120 groups, delta {1:−120, 16:−120, 17:+120} |
+| kernel | `kernel-selection.json` | response-kernel entries (PR254/#268 pairs, #272 multi-donor families, per-entry cuts), selected as a shared-donor kernel (#319's idea): maximum-weight closure per entrance over alternate response bases (`discovery/coll/closure_pack.py`) | 1,047 entries, total entrance rank 1,200 (ranks 1:1,007, 2:20, 4:5, 5:3, 7:1, 8:3, 10:6, 13:1, 14:1); 1,015 distinct donors, 1–31 donors per entry, a donor shared by up to 30 entries |
+| restore | `restore-selection.json` | early helper restoration (#280, endpoint-aware #283) | 240 helpers (16, 18, 18, 19), endpoint saving 240 |
+| sink | `sink-selection.json` | terminal sinks (#283 rule, #295 screen) | 7 sinks, delta {3:−7, 17:−7}, R 8,230 → 8,223 |
+| reorder | `reorder-selection.json` | reordering single additions into a neighbouring incidence frame (#299) | 133 moves, delta {2:+73, 3:−113, 4:+20, 17:−113, 18:+113} |
+
+**Shared-donor kernel.** For an entrance E (a nondegenerate rank-e subspace) let G_E be the plain helpers whose
+first frame contains E. A pivot p in G_E gains φ(d_p − e) − φ(d_p); a donor d pays φ(e) + φ(d_d − e) − φ(d_d)
+once, however many entries it serves at E (its path ZERO → E → first frame is the same for every entry). Choosing
+a response basis of G_E at a common cut point (all members read before it and untouched until after it), every
+dependent member is a candidate pivot whose donors are its basis representation; picking pivots and donors is then
+a maximum-weight closure (pivot → its donors), solved exactly by a minimum cut. The search tries several
+cost-ordered bases and cut points per entrance, over 24,203 rank-one lines and 10,541 exact pairwise frame
+intersections of rank 2–14, and accepts entrances greedily with helper exclusivity (randomised acceptance order,
+best of 16 seeds). The transform is #320's `kernel_transform.py` unchanged in mechanism (entries with any number of
+donors, a donor reused along a nested chain); the selection gives φ −1,601.47 against #320's packing −1,355.95.
+The seven helpers the sink screen admits are excluded (they are worth ≈ −40 φ each as sinks), and the total
+entrance rank is trimmed to a multiple of 5 for the width-100 banks. The restorations (240), sinks (7) and reorder
+(133) were re-derived on the new word with #320's builders and have the same deltas as in #320.
+
+Searched and empty on this word (not stages): a second concave descent (`discovery/descent2_search.py`, with the
+#291 constructed join/meet frames and #270 connected blocks) finds 0 gates after the sinks and 0 after the
+reorder; a second reorder round finds 0 moves; a second shared-donor kernel round after the reorder finds 4 entries
+(φ −0.77). #312's zero-response singles do not exist here (every plain helper has a nonzero response), and #309's
+local dirty-response transport has no positive closure (targets' next frames have rank 16–18 and admit at most one
+helper per entrance).
+
+## What each stage checks
+
+- **descent**: every retimed frame is nondegenerate, nests between its operand neighbours and contains the exact
+  integer source span of each non-target operand (recomputed from the actual word); scalar and COPY projection
+  unchanged; every required frame path rebuilt from scalar/COPY events, both reflected ledgers; rank mass unchanged.
+- **target**: literal prefix responses are checked (no selected dependency is trusted); all formal columns
+  replayed forward and inverse over F₂; omitting the target-prefix setup is rejected.
+- **kernel**: the prefix relation (pivot response = XOR of donor responses) on the literal prefix for every
+  entry; every member untouched before its own cut; entrances nondegenerate inside every member's first frame;
+  shared-donor chains nested; F₂ replay of every formal column forward and inverse with both omission controls;
+  every frame path rebuilt independently of the emitted MOVEs.
+- **restore**: the PR280 screen is recomputed on the actual word and must equal the frozen selection; the integer
+  commutation contract on the crossed interval; F₂ replay forward/inverse and an omission control; the five-stage
+  completion of a restored helper is P_σ + (I − P_E) (rank a + h − dim E), and the banks chart the pair (σ, E).
+- **sink**: the PR283 screen with the stricter #295 conditions; F₂ replay with controls; registers compacted, the
+  stock and the five-stage profile recomputed, the deficit 4v − 5h(h − 2) rechecked.
+- **reorder**: source spans of every gate rechecked, integer replay identical, F₂ replay with controls,
+  endpoints, entrances and rank mass unchanged.
+
+The raw ledger is rebound after every stage (`raw_ledger.rebind_*`, `target_transform.rebind`): the helper
+histogram is recomputed from the stage receipt and compared with the frozen expected delta, and the five-stage
+profile and deficit are rechecked. `finite_check.py` re-asserts every executed stage receipt (both reflected
+ledgers, pinned counts, rejected controls) and that the raw ledger holds exactly one receipt per stage.
+
+## Downstream changes
+
+- `code/global_lowering.py`: completions use the helper endpoint (P_σ + I − P_E for restored helpers); the
+  register count is the final one (`final_physical_R`, after the sinks).
+- `code/geometry527.py`: #315 already checks one actual basis of every entrance rank, so the kernel ranks
+  (1, 2, 4, 5, 7, 8, 10, 13, 14) are covered; one restored (σ, E) pair is checked exactly (residual P_E − P_σ,
+  completion P_σ + I − P_E, the old FULL formula rejected).
+- `bank_check.py`: charts for restored helpers are keyed by (σ, E), with the E-perp rows (`residual_rows`).
+- `bank_template.py`: see `BANK-PROOF.md` (economy tiling).
+- `prime_check.py`: retimed-away producer frames keep their determinant obligation.
+- `scalar_check.py`: the retained source program is checked on its 10,150 columns; the emitted word (after
+  the sinks) on its 10,143 columns.
+- `math_check.py`, `finite_check.py`: the completion-rank histogram replaces the entrance histogram where
+  completions are removed from the priced profile.
+
+## φ ledger and verified values
+
+The deficit is fixed (4v − 5h(h − 2) = 2,040 per replica), so κ is a function of the one-stage helper histogram:
+the five-stage profile without completions, normalized ×12, W = (mass + 12·2,040)/100. Each stage was predicted
+with this ledger from its frozen local delta before it was built, and verified by a full `verify.replay` of the
+package truncated after that stage (record mode). See `README.md` for the table. The total entrance rank plus
+the restoration saving must be a multiple of 5 for the width-100 banks to tile exactly (1,200 + 240 = 1,440).
diff --git a/research/five-stage-p10-transcript-stages/UPSTREAM-PR234-NOTICE.md b/research/five-stage-p10-transcript-stages/UPSTREAM-PR234-NOTICE.md
new file mode 100644
index 0000000000..5f8fbb25c1
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/UPSTREAM-PR234-NOTICE.md
@@ -0,0 +1,13 @@
+# Attribution and licence
+
+This contribution uses Apache-2.0. Original source headers, licences and notices are preserved. These credits do not imply review or endorsement by the named contributors or OpenAI.
+
+- Jacob Sussman: five-stage complex geometry and published gcert/1 export in wht-power-saving-lean at f010392c923279e3dd59ef3aa5fedad23affc5fd. Original Claude assistance disclosure retained in inputs/complex/NOTICE.
+- Avi Eisenberg / ikeboy: retained PR193 source-assisted complex helper and donor selection at 187e1010ac8b259af8e9b5166f68b64bc27b4b47.
+- eumemic: current PR210 frames, gauges, source borrowing and retimed bit helper at df95878d11190518e45ef9717c9ee05011f88ace.
+- Chafik Boukhalfa / chafreaky: PR200 physical bit construction carried by PR202 at 8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d.
+- Rohan Arun, Dugongue, evmckinney9, icekylinx, James Chang, Douglas Colkitt, OpenAI and earlier contributors retain the attribution and original assistance disclosures in the supplied source notices. The exact outer assembly also credits Zhihao Chen and the RaD / hipotures balanced reduction in its original header.
+
+The paired-cube helper design predates Sussman’s certificate export. The new contribution here is the explicit source-bound five-stage composition, adapters, paid accounting and reproducible finite verification. No exclusive priority is claimed for the inherited designs or theorem interfaces.
+
+Assisted with ChatGPT.
diff --git a/research/five-stage-p10-transcript-stages/UPSTREAM-PR234-PROOF.md b/research/five-stage-p10-transcript-stages/UPSTREAM-PR234-PROOF.md
new file mode 100644
index 0000000000..dbd8806967
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/UPSTREAM-PR234-PROOF.md
@@ -0,0 +1,29 @@
+# Five-stage finite composition and retained hypotheses
+
+The expected conditional saving is κ = 703701743496697 / 10^18. The fresh verifier establishes the finite construction and exact arithmetic under the inherited source and all-size interfaces below.
+
+## Bit construction
+
+The pinned source471 helper is checked on all 20,163 independent F2 source, target and dirty columns. Its physical realization is the exact input/output frame telescope, with all source loans, donor/recipient identifications, compensated reads, terminal substitutions and cleanup retained. Copied centers are complete temporary streams; their reverse implementation copies the original anew, transforms and scatters that copy, then erases it. It does not reverse an erasure.
+
+The five phase-major invocations use the explicitly routed source owners X1, Y1, X1, Y2 and X2. Each helper's five separated residuals occupy disjoint windows. One split rank-5a exterior correction completes each genuine independent entrance of rank a. All 2,279 corrections remain paid, and source-owned gauges stay within the visible-data paths. Actual rational matrix checks establish bridge equality, nested idle changes and terminal exchanges. Cover expansion has a barrier after each phase, across every class.
+
+The fresh program has m=120, W=23,683, 495,304 children, rank mass 2,837,560 and deficit 4,400. All 120 rank-22 copied-center calls are included. Exact cleared-Gram determinants and factor witnesses are recomputed for every consumed basis. Fivefold direct sums introduce no new excluded primes. The retained weighted q-local compiler, unit-pivot fallback, prime-supply and complete-stream tape proofs remain hypotheses.
+
+The proper child ratio 5/6 requires halving degree four. The one-level weighted recurrence is retained; its histogram is not multiplied by four. The finite accounting rederives route factors, scalar work, internal row stock, strict moment/linear gaps and explicit finite cutoff expressions. Unknown constants of inherited primitive implementations remain quantified constants, not invented measured costs. See proof/FINITE_BIT_ACCOUNTING.md and the included original bit/row/copied-center source texts.
+
+## Complex construction
+
+The published gcert/1 baseline is pinned to Sussman's f010392 revision and the PR193 paired-cube helper. Its live-label walk, scalar programs, copied-center lifetimes, final climbs before cleanup, exact symbolic splice and finite guard are regenerated. Exact complex frame identities retain their phase representatives. Physical work stock 24,127 is separately charged; the live recursion denominator remains 14,692.
+
+The pinned scalar identities hAi, hBi, hx, hy and hid, the Lab.inv dirty-lifting theorem and five-window geometry/NetCert theorems are inherited source proofs. The command does not rebuild their Lean proof chain or claim a fresh all-column complex scalar proof. General Clifford synthesis, charged complete-stream movement, common-grid precision and restored-row proofs remain stated analytic dependencies. Their consumed declarations and sources are hash-pinned under inputs/complex/.
+
+## Arithmetic and outer reduction
+
+Both rational moments are freshly enclosed. Three finite ordinary-leaf levels start from the retained completed ordinary saving 384599/10^10; the unattained coarse limiting saving is not used as an ordinary leaf. Exact outer assembly checks all 47 strict inequalities and seven margins and rejects the next 10^-18 κ grid point. Precision/recovery, prime supply, completed ordinary leaves and the fixed-tape all-size reduction remain hypotheses.
+
+proof/INTEGRATED_PROOF.md preserves the detailed original composition argument. Its development filenames identify the original evidence; V8's executable dependency closure is exclusively MANIFEST.json and the fresh calls in verify.py. Development receipts and their historical source trees are not runtime inputs.
+
+No claim is made of unconditional all-size formalization, global optimality or measured multiplier performance. Original lineage and assistance disclosures are preserved in NOTICE.md and the supplied source notices.
+
+Assisted with ChatGPT.
diff --git a/research/five-stage-p10-transcript-stages/bank_check.py b/research/five-stage-p10-transcript-stages/bank_check.py
new file mode 100644
index 0000000000..9222de6ff3
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bank_check.py
@@ -0,0 +1,300 @@
+"""Fresh context-bound stage-private m-coordinate completed bank admission (m = 5h = 100 at p = 10).
+
+No saved chart, receipt, physical census or old source tree is consumed.
+The fraction-free inverse routine derives from the retained PR197/PR200 bank
+checker. Inherited attribution/notices apply. Apache-2.0.
+Prepared with substantial OpenAI Codex assistance.
+p = 10 port (DreamingOfClouds, Anthropic Claude assistance): h, m and the 60 replicas from the cube size and the
+plan; the G^-1 residual rows (h-9)a - sum(a) (15a - sum(a) at h = 24); word counts pinned in word-pins.json.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from math import gcd
+from pathlib import Path
+import hashlib,json,struct,time
+from bank_template import BankPlan
+from word_pins import expect,shape
+
+assert __debug__, 'Do not run bank admission under -O.'
+HERE=Path(__file__).resolve().parent
+
+def inverse_integer(a):
+    """Fraction-free Gauss-Jordan, returning C,d with aC=Ca=dI."""
+    n=len(a);m=[list(row)+[int(i==j)for j in range(n)]for i,row in enumerate(a)]
+    previous=1;factors=[]
+    for k in range(n):
+        pivot=next((i for i in range(k,n)if m[i][k]),None)
+        assert pivot is not None,'singular actual bank chart'
+        m[k],m[pivot]=m[pivot],m[k]
+        if pivot!=k:factors.append(('swap',k,pivot,1,1))
+        p=m[k][k]
+        if p!=previous:
+            ratio=Q(previous,p);factors.append(('scale',k,k,ratio.numerator,ratio.denominator))
+        for i in range(n):
+            if i==k:continue
+            u=m[i][k]
+            if u:
+                ratio=Q(-u,previous);factors.append(('add',i,k,ratio.numerator,ratio.denominator))
+            for j in range(2*n):
+                if j==k:continue
+                value=p*m[i][j]-u*m[k][j];assert value%previous==0;m[i][j]=value//previous
+            m[i][k]=0
+        previous=p
+    d=m[0][0];assert d and all(m[i][j]==d*int(i==j)for i in range(n)for j in range(n))
+    c=[row[n:]for row in m];common=abs(d)
+    for row in c:
+        for x in row:common=gcd(common,x)
+    d//=common;c=[[x//common for x in row]for row in c]
+    if d<0:d=-d;c=[[-x for x in row]for row in c]
+    return c,d,factors
+
+def residual_rows(C,frame,h):
+    """Integer bases (residual, source, outside) of a chart: residual = image of P_end - P_sigma, outside = E-perp.
+    G^-1 a is taken up to the positive scalar h-9 (G = I - J/9), as for the plain charts."""
+    def perp(a):
+        row=[(h-9)*x-sum(a)for x in a];d=gcd(*row);assert d;return [x//d for x in row]
+    if not isinstance(frame,tuple):return [perp(a)for a in C.A[frame]],[list(b)for b in C.B[frame]],[]
+    sigma,E=frame;Gs=[[Q((h-9)*x-sum(a))for x in a]for a in C.A[sigma]]
+    # Solve for combinations of the G-complement of sigma lying in E (A_E . r = 0), exactly over Q.
+    M=[[sum(Q(y)*x for y,x in zip(e,g))for g in Gs]for e in C.A[E]];k=len(Gs);piv={}
+    for row in M:
+        row=list(row)
+        for p,b in piv.items():
+            if row[p]:c=row[p];row=[x-c*y for x,y in zip(row,b)]
+        p=next((i for i,x in enumerate(row)if x),None)
+        if p is None:continue
+        row=[x/row[p]for x in row]
+        for q in list(piv):
+            if piv[q][p]:c=piv[q][p];piv[q]=[x-c*y for x,y in zip(piv[q],row)]
+        piv[p]=row
+    out=[]
+    for fr in [i for i in range(k)if i not in piv]:
+        lam=[Q(int(i==fr))for i in range(k)]
+        for p,b in piv.items():lam[p]=-b[fr]
+        r=[sum(l*g[j]for l,g in zip(lam,Gs))for j in range(h)];den=1
+        for x in r:den=den*x.denominator//gcd(den,x.denominator)
+        r=[int(x*den)for x in r];d=gcd(*r);out.append([x//d for x in r])
+    assert len(out)==C.dimf[E]-C.dimf[sigma]
+    assert all(sum(x*y for x,y in zip(e,r))==0 for e in C.A[E]for r in out),'residual inside E'
+    return out,[list(b)for b in C.B[sigma]],[perp(a)for a in C.A[E]]
+
+def census(context):
+    W,C,roles=context['W'],context['C'],context['regs'];h=W.h;assert h==shape()['h']
+    assert len(roles)==len(set(roles))==expect('final_physical_R',len(roles)) and roles==sorted(roles)
+    assert set(roles)==set(W.phys.values())-set(context['borrow'])-context['removed']
+    assert not(set(roles)&set(context['borrow']))
+    gauge_frames={role:W.gauge[role]['frame']for role in roles if role in W.gauge}
+    expect('final_entrance_ranks',Counter(C.dimf[f]for f in gauge_frames.values()))
+    # Early-restored helpers end at E: residual P_E - P_sigma; the chart key is the pair (sigma, E).
+    ends=dict(context.get('restored_endpoints',{}))
+    assert set(ends)<=set(gauge_frames)
+    for role,E in ends.items():
+        assert C.sub(gauge_frames[role],E) and C.dimf[E]<h and C.nondeg(E);gauge_frames[role]=(gauge_frames[role],E)
+    families={}
+    for role in roles:
+        f=gauge_frames.get(role)
+        rank=h if f is None else C.dimf[f[1]]-C.dimf[f[0]] if isinstance(f,tuple) else h-C.dimf[f]
+        families.setdefault(rank,[]).append(role)
+    expect('residual_families',{r:len(xs)for r,xs in families.items()})
+    return families,gauge_frames
+
+class BankLowerer:
+    """Final full-address lowering of the already checked logical IR.
+
+    Scalar/projection/geometry fields are retained byte-for-byte; only stream
+    operands change to the proven bank namespaces. Completion discharge is
+    checked separately by run(), and no completion opcode is emitted.
+    """
+    def __init__(self,context,lower):
+        families,gauges=census(context)
+        self.plan=BankPlan(families,gauges,context['regs']);self.lower=lower
+    def iter_stage(self,stage,replica):
+        for row in self.lower.iter_stage(stage):yield self.plan.map_stage_row(stage,replica,row)
+    def iter_idle(self,which,replica):
+        for row in self.lower.iter_idle(which):yield self.plan.map_boundary_row(replica,row)
+    def iter_bridges(self,which,replica):
+        for row in self.lower.iter_bridges(which):yield self.plan.map_boundary_row(replica,row)
+    def iter_exchanges(self,replica):
+        for row in self.lower.iter_exchanges():yield self.plan.map_boundary_row(replica,row)
+    def phases(self):
+        """Each iterator is expanded over all cover classes before next phase."""
+        T=self.plan.replicas
+        for stage in range(5):
+            for replica in range(T):
+                yield('helper',stage,replica,lambda s=stage,r=replica:self.iter_stage(s,r))
+            if stage in(1,2,4):
+                which={1:0,2:1,4:2}[stage]
+                for replica in range(T):
+                    yield('idle',which,replica,lambda i=which,r=replica:self.iter_idle(i,r))
+                    yield('bridge',which,replica,lambda i=which,r=replica:self.iter_bridges(i,r))
+        for replica in range(T):yield('terminal_exchange',0,replica,lambda r=replica:self.iter_exchanges(r))
+
+def bind(context,lower):return BankLowerer(context,lower)
+
+def run(context,global_result,lower,progress=lambda text:None):
+    begun=time.monotonic();W,C=context['W'],context['C']
+    api_pin=hashlib.sha256((HERE/'bank_template.py').read_bytes()).hexdigest()
+    families,gauge_frames=census(context);bound=bind(context,lower);plan=bound.plan
+    assert lower.W is W and lower.C is C
+    h,m,T=W.h,plan.m,plan.replicas;assert plan.h==h and m==5*h and T==60
+    # Derive all actual chart bases and exact inverse/factor programs afresh.
+    charts=[];maxops=maxnum=maxden=0
+    for frame,count in sorted(Counter(gauge_frames.values()).items(),key=lambda x:(isinstance(x[0],tuple),x[0])):
+        # G^-1 a up to the positive scalar h-9, G = I - J/9 (15a - sum(a) at h = 24); E-perp rows for restored endpoints
+        residual,source,outside=residual_rows(C,frame,h);rank=len(residual)
+        sigma=frame[0]if isinstance(frame,tuple)else frame
+        assert rank+len(source)+len(outside)==h and len(source)==C.dimf[sigma]
+        G=lambda a,b:9*sum(x*y for x,y in zip(a,b))-sum(a)*sum(b)
+        assert all(G(a,b)==0 for a in residual for b in source)
+        assert all(G(a,b)==0 for a in outside for b in residual+source),'E-perp is orthogonal to E'
+        B=list(map(list,zip(*(residual+list(source)+outside))));A,d,ops=inverse_integer(B)
+        for L,R in((A,B),(B,A)):
+            assert all(sum(x*y for x,y in zip(row,col))==d*int(i==j)for i,row in enumerate(L)for j,col in enumerate(zip(*R)))
+        P=[[sum(B[i][k]*A[k][j]for k in range(rank))for j in range(h)]for i in range(h)]
+        assert sum(P[i][i]for i in range(h))==d*rank
+        assert all(sum(P[i][k]*B[k][j]for k in range(h))==(d*B[i][j]if j<rank else 0)for i in range(h)for j in range(h))
+        replay=[list(map(Q,row))for row in B]
+        for op,i,j,a,b in ops:
+            if op=='swap':replay[i],replay[j]=replay[j],replay[i]
+            elif op=='scale':replay[i]=[Q(a,b)*x for x in replay[i]]
+            else:
+                assert op=='add';replay[i]=[x+Q(a,b)*y for x,y in zip(replay[i],replay[j])]
+        assert all(x==int(i==j)for i,row in enumerate(replay)for j,x in enumerate(row))
+        maxops=max(maxops,len(ops));maxnum=max(maxnum,max(abs(op[3])for op in ops));maxden=max(maxden,d,max(op[4]for op in ops))
+        charts.append(dict(frame=list(frame)if isinstance(frame,tuple)else frame,count=count,residual_rank=rank,basis=B,inverse_numerator=A,inverse_denominator=d,factors=ops))
+    assert len(charts)==expect('final_charts',len(charts)) and max(maxnum,maxden)<2**80 and maxops==expect('max_chart_factors',maxops)
+    progress('Rebuilt '+str(len(charts))+' exact actual gauge charts')
+    # Match each consumed completion to one actual independent entrance.
+    expected=[];ends=context.get('restored_endpoints',{});endrows=[]
+    for j,role in enumerate(context['regs']):
+        f=gauge_frames.get(role,lower.ZERO);end=lower.FULL
+        if isinstance(f,tuple):f,end=f
+        assert lower.initial[2*W.v+j]==f
+        if role in gauge_frames:expected.append((4*W.v+j,f,C.dimf[f]));endrows.append(end)
+    assert list(lower.entrances)==expected and len(expected)==expect('final_entrances',len(expected))
+    completions=list(lower.iter_completions())
+    assert completions==[(6,family,-1,end,5*(a+h-C.dimf[end]),f,-1,0)for(family,f,a),end in zip(expected,endrows)]
+    assert sum(end!=lower.FULL for end in endrows)==len(ends)
+    removed=Counter(row[4]for row in completions)
+    expect('final_entrance_ranks',Counter(a for _,_,a in expected));expect('removed_completion_histogram',dict(removed))
+    H=Counter({int(r):n for r,n in global_result['paid_histogram'].items()})
+    assert sum(H.values())==global_result['paid_calls']
+    for r,n in removed.items():
+        assert H[r]>=n;H[r]-=n
+        if not H[r]:del H[r]
+    assert max(H)==shape()['idle'][2] and sum(H.values())==expect('banked_calls',sum(H.values())) and sum(r*n for r,n in H.items())==expect('banked_rank_mass',sum(r*n for r,n in H.items()))
+    literal=Counter({r:T*n for r,n in H.items()})
+    assert m*plan.live_families-sum(r*n for r,n in literal.items())==T*shape()['deficit']
+    # Independently enumerate each physical role/replica/stage slot.
+    incidence=hashlib.sha256();assignments=0;normalizers_checked=set();endpoint_controls=[]
+    for stage in range(5):
+        used=Counter();bank=0;assigned=set()
+        outside=next(j for j in range(m)if not h*stage<=j<h*(stage+1))
+        for pattern,(widths,count)in enumerate(plan.patterns):
+            offset=0;witnesses=[]
+            for block,rank in enumerate(widths):
+                original=list(range(h*stage,h*stage+rank));target=list(range(offset,offset+rank))
+                src=original+[j for j in range(m)if j not in original];dst=target+[j for j in range(m)if j not in target];pi=dict(zip(src,dst))
+                witnesses.append((pi[outside],block+1));offset+=rank
+            assert len(set(witnesses))==len(widths)
+            if stage==0:
+                offsets=[sum(widths[:b])for b in range(len(widths))]
+                def endpoint(blocks):
+                    state=list(range(2*m))
+                    for b in blocks:
+                        for j in range(offsets[b],offsets[b]+widths[b]):state[j],state[m+j]=state[m+j],state[j]
+                    return state
+                blocks=list(range(len(widths)));full=list(range(m,2*m))+list(range(m))
+                assert endpoint(blocks)==full and endpoint(blocks+blocks[::-1])==list(range(2*m))
+                assert endpoint(blocks[:-1])!=full and endpoint(blocks+[0])!=full
+                endpoint_controls.append(dict(pattern=pattern,forward_columns=2*m,inverse_columns=2*m,omitted_rejected=True,repeated_rejected=True))
+            for b in range(bank,bank+count):
+                offset=0
+                for block,rank in enumerate(widths):
+                    q=used[rank];role=families[rank][q//T];replica=q%T;used[rank]+=1
+                    assert(role,replica)not in assigned;assigned.add((role,replica))
+                    a=plan.assignment(stage,replica,role);frame=gauge_frames.get(role)
+                    assert a==dict(family=plan.data_families+stage*plan.banks_per_stage+b,stage_bank=b,pattern=pattern,block=block,offset=offset,rank=rank,frame=frame,scalar=block+1)
+                    key=stage,pattern,block,frame
+                    if key not in normalizers_checked:
+                        N=plan.normalizer(stage,replica,role)
+                        assert N['unit_column_witness']==witnesses[block]and N['inverse_chart_frame']==frame and N['chart_window']==stage
+                        assert N['permutation'][h*stage:h*stage+rank]==tuple(range(offset,offset+rank))
+                        normalizers_checked.add(key)
+                    incidence.update(f'{stage},{pattern},{role},{replica},{b},{block},{offset},{rank}\n'.encode())
+                    assignments+=1;offset+=rank
+                assert offset==m
+            bank+=count
+        assert bank==plan.banks_per_stage and len(assigned)==T*len(context['regs'])and used=={r:T*len(xs)for r,xs in families.items()}
+    assert assignments==5*T*len(context['regs'])
+    progress('Matched all '+str(assignments)+' literal bank assignments')
+    namespace=hashlib.sha256();collisions=0
+    for stage in range(5):
+        for replica in range(T):
+            addresses=[plan.local_address(stage,replica,i)for i in range(plan.local_work+1)]
+            assert len(set(addresses))==len(addresses)and addresses[-1]==(plan.work_family,('external_work',0))
+            assert all(f<plan.live_families for f,route in addresses[:-1])
+            collisions+=len(addresses)-len({f for f,route in addresses})
+            for f,route in addresses:namespace.update(f'{stage},{replica},{f},{route}\n'.encode())
+    expect('family_collisions',collisions)
+    # Bind every actual logical operand and mathematical field to the callable
+    # address substitution once per stage. The300 injective namespace maps
+    # above then instantiate all sixty replicas without replaying scalar algebra.
+    stream=struct.Struct('<8i');stage_checks=[];actual_helper_uses=set();paid=Counter()
+    for stage in range(5):
+        digest=hashlib.sha256();rows=0;stage_paid=Counter();kinds=Counter()
+        # Full addresses indexed by the original logical family; wrappers use
+        # exactly this tested local inverse and namespace construction.
+        addresses={}
+        for local in range(plan.local_work+1):
+            family=4*W.v+len(context['regs'])if local==plan.local_work else plan.active[stage][0]*W.v+local if local<W.v else plan.active[stage][1]*W.v+local-W.v if local<2*W.v else 4*W.v+local-2*W.v
+            assert plan.local_from_logical_family(stage,family)==local
+            addresses[family]=plan.local_address(stage,0,local)
+        for row in lower.iter_stage(stage):
+            op,a,b,c,f,z,s,rev=row;assert s==stage and rev==int(stage in(1,3))
+            mapped=plan.map_stage_row(stage,0,row)
+            assert mapped==(op,addresses[a],addresses[b]if op in(1,2)else b,c,f,z,s,rev)
+            for family in([a,b]if op in(1,2)else[a]):
+                if 4*W.v<=family<4*W.v+len(context['regs']):actual_helper_uses.add(family-4*W.v)
+            if op==0 and f:stage_paid[f]+=1
+            digest.update(stream.pack(*row));rows+=1;kinds[op]+=1
+        assert stage_paid==Counter({int(r):n for r,n in lower.ns['result']['paid_histogram'].items()})
+        paid.update(stage_paid)
+        stage_checks.append(dict(stage=stage,records=rows,logical_operand_binding_sha256=digest.hexdigest(),opcode_counts=dict(kinds),all_actual_operands_mapped=True))
+    assert actual_helper_uses==set(range(len(context['regs'])))
+    for which in range(3):
+        for row in lower.iter_idle(which):
+            mapped=plan.map_boundary_row(0,row);assert mapped[0]==4;paid[row[4]]+=1
+        for row in lower.iter_bridges(which):assert plan.map_boundary_row(0,row)[0]==5
+    exchanges=sum(1 for row in lower.iter_exchanges()if plan.map_boundary_row(0,row)[0]==7)
+    assert exchanges==2*W.v and paid==H
+    phases=[(kind,stage,replica)for kind,stage,replica,fn in bound.phases()]
+    assert len(phases)==12*T and sum(kind=='helper'for kind,s,r in phases)==5*T
+    assert all(phases.index(('idle',which,r))<phases.index(('bridge',which,r))for which in range(3)for r in range(T))
+    controls=[]
+    try:plan.map_boundary_row(0,completions[0])
+    except AssertionError:controls.append('silent completion discharge')
+    else:raise AssertionError('completion passed address mapper')
+    assert hashlib.sha256((HERE/'bank_template.py').read_bytes()).hexdigest()==api_pin
+    factors=maxops+(m-1)+m;K=2*5*T*((plan.live_families-1)+len(context['regs'])*m*factors)
+    assert factors==expect('normalizer_factor_bound',factors) and K==expect('extra_selector_calls',K)<2**40
+    result=dict(status='PASS_FRESH_CONTEXT_BOUND_COMPLETE_BANKS_AND_CALLABLE_LOWERING',
+        all_assignments_match=True,all_logical_helpers_bound=True,independent_completions_removed=len(completions),
+        removed_completion_histogram=dict(removed),literal_paid_histogram=dict(sorted(literal.items())),literal_stock=plan.live_families,
+        normalized_stock=str(Q(plan.live_families,T)),physical_replicas=T,bank_families=5*plan.banks_per_stage,data_families=plan.data_families,
+        assignments=assignments,incidence_sha256=incidence.hexdigest(),charts=len(charts),
+        chart_sha256=hashlib.sha256(json.dumps(charts,sort_keys=True,separators=(',',':')).encode()).hexdigest(),
+        max_chart_factors=maxops,max_factor_numerator=maxnum,max_denominator=maxden,normalizer_factor_bound=factors,
+        conservative_extra_selector_calls=K,distinct_actual_normalizers=len(normalizers_checked),
+        full_namespaces_checked=5*T,namespace_sha256=namespace.hexdigest(),intentional_family_collisions=collisions,bank_patterns=[[list(w),c]for w,c in plan.patterns],
+        local_instruction_bindings=stage_checks,endpoint_checks=endpoint_controls,phase_schedule=phases,
+        completions_discharged_by='Each stage-private bank partitions all '+str(m)+' coordinates; all '+str(2*m)+' arbitrary-dirty address columns and inverse checked.',
+        inherited_geometry='Helper originalclass d*tau_i maps to bank d*tau_i*N^-1. N conjugates its actual residual in H_i into the assigned coordinate block. Data routes and boundary projectors remain PR234s.',
+        script_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(),api_sha256=api_pin,
+        rejected_controls=controls,seconds=time.monotonic()-begun)
+    bank_keys=('literal_stock','normalized_stock','physical_replicas','bank_families','data_families','assignments',
+        'incidence_sha256','charts','chart_sha256','max_chart_factors','max_factor_numerator','max_denominator',
+        'normalizer_factor_bound','conservative_extra_selector_calls','distinct_actual_normalizers','endpoint_checks')
+    banks={k:result[k]for k in bank_keys};banks['status']='PASS_FRESH_ACTUAL_CHARTS_AND_COMPLETE_BANKS'
+    banks.update(physical_roles=len(context['regs']),banks_total=5*plan.banks_per_stage)
+    return dict(banks=banks,banked_result=result)
diff --git a/research/five-stage-p10-transcript-stages/bank_template.py b/research/five-stage-p10-transcript-stages/bank_template.py
new file mode 100644
index 0000000000..385b5583c0
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bank_template.py
@@ -0,0 +1,263 @@
+"""Callable stage-private m-coordinate bank address template (m = 5h; 120 at p = 12, 100 at p = 10).
+
+The caller supplies the freshly admitted actual helper role families and gauge
+chart IDs. This module owns no paths, global frame registry or source loading.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+p = 10 port (DreamingOfClouds, Anthropic Claude assistance): m, h, v from the cube size; the fixed gen5 bank
+patterns are replaced by tile(), an exact zero-padding tiling of the actual residual blocks into width-m banks
+(every pattern sums to m and every block is used exactly once, as before); the counts are pinned by bank_check.
+"""
+from collections import Counter
+from word_pins import expect,shape
+
+
+def tile(blocks, m):
+    """Exact tiling of {width: number of blocks} into banks of total width m, as ((widths, banks), ...).
+
+    A width dividing m fills pure banks. A width w not dividing m is mixed with a filler width f dividing m:
+    banks w^a f^b with a maximal (w*a + f*b = m), then at most one bank w^r f^t for the remainder r. Fillers
+    are tried in a fixed order (most blocks first) with backtracking until every pure width also divides out.
+    Fails (AssertionError) unless every block is used and every bank is full; there is no padding."""
+    blocks = {w: n for w, n in blocks.items() if n}
+    assert all(0 < w <= m for w in blocks)
+    mixed = sorted(x for x in blocks if m % x)
+
+    def search(i, left, out):
+        if i == len(mixed):
+            if any(left[w] % (m // w) for w in left): return None
+            return out + [(tuple([w]*(m // w)), left[w]//(m // w)) for w in sorted(left) if left[w]]
+        w = mixed[i]; n = blocks[w]
+        for f in sorted(left, key=lambda x: (-left[x], x)):
+            a = next((a for a in range(m // w, 0, -1) if (m - w*a) % f == 0), None)
+            if a is None: continue
+            b = (m - w*a)//f; q, r = divmod(n, a)
+            if r and (m - w*r) % f: continue
+            t = (m - w*r)//f if r else 0
+            if q*b + t > left[f]: continue
+            rest = dict(left); rest[f] -= q*b + t
+            found = search(i + 1, rest, out + ([(tuple([w]*a + [f]*b), q)] if q else []) + ([(tuple([w]*r + [f]*t), 1)] if r else []))
+            if found is not None: return found
+        return None
+    out = search(0, {w: n for w, n in blocks.items() if not m % w}, [])
+    if out is None: out = economy_tile(blocks, m)
+    assert all(sum(widths) == m and count > 0 for widths, count in out)
+    used = Counter()
+    for widths, count in out:
+        for x in widths: used[x] += count
+    assert used == Counter(blocks), 'every block used exactly once'
+    return tuple(out)
+
+
+def economy_tile(blocks, m):
+    """Exact zero-padding tiling used when the filler search of tile() runs out of filler blocks (the kernel pivots
+    and early restorations of the stage stack add many residual widths that do not divide m; the PR #299 analogue at
+    p = 12 was the (r^4, 24, 4^(24-r)) re-tiling). The fillers are the two most numerous widths dividing m (here the
+    full helper width h and the rank-4 entrance residual). Each other width w, in decreasing order, gets the bank
+    w^a F^c f^b (w*a + F*c + f*b = m) that spends the fewest narrow fillers f per w block (then the largest a), plus
+    at most one bank w^r F^c' f^b' for the remainder r = n mod a. The leftover fillers fill pure banks F^(m/F),
+    f^(m/f) and y residue banks F^j f^k. Every bank sums to m and every block is used exactly once (no padding)."""
+    from fractions import Fraction
+    blocks = {w: n for w, n in blocks.items() if n}
+    div = sorted((w for w in blocks if m % w == 0), key=lambda w: (-blocks[w], w))
+    assert len(div) >= 2, ('economy tiling needs two filler widths', blocks)
+    F, f = sorted(div[:2], reverse=True)
+
+    def fill(rest):
+        """(c, b) with F*c + f*b = rest, c maximal (fewest narrow fillers); None if impossible."""
+        return next(((c, (rest - F*c)//f) for c in range(rest//F, -1, -1) if (rest - F*c) % f == 0), None)
+
+    left = {F: blocks[F], f: blocks[f]}; out = []
+    for w in sorted((x for x in blocks if x not in (F, f)), reverse=True):
+        n = blocks[w]
+        opts = [(Fraction(cb[1], a), -a, a, cb) for a in range(m//w, 0, -1) for cb in [fill(m - w*a)] if cb]
+        assert opts, ('no bank for width', w)
+        _, _, a, (c, b) = min(opts); q, r = divmod(n, a)
+        if q: out.append(((w,)*a + (F,)*c + (f,)*b, q)); left[F] -= q*c; left[f] -= q*b
+        if r:
+            cb = fill(m - w*r); assert cb, ('no remainder bank', w, r)
+            out.append(((w,)*r + (F,)*cb[0] + (f,)*cb[1], 1)); left[F] -= cb[0]; left[f] -= cb[1]
+    assert left[F] >= 0 and left[f] >= 0, ('fillers exhausted', left)
+    pF, pf = m//F, m//f
+    for y in range((pF*pf) + 1):
+        for j in range(1 if y else 0, pF if y else 1):
+            if (m - F*j) % f: continue
+            k = (m - F*j)//f; aF, af = left[F] - y*j, left[f] - y*k
+            if aF >= 0 and af >= 0 and aF % pF == 0 and af % pf == 0:
+                out += ([((F,)*j + (f,)*k, y)] if y else []) + ([((F,)*pF, aF//pF)] if aF else []) + ([((f,)*pf, af//pf)] if af else [])
+                return out
+    raise AssertionError(('no exact zero-padding tiling', blocks, m))
+
+
+class BankPlan:
+    _shape = shape()
+    m, h, stages, replicas, v = _shape['m'], _shape['h'], _shape['stages'], _shape['replicas'], _shape['v']
+
+    active = ((0,1),(1,0),(0,1),(3,2),(2,3))
+
+    def __init__(self, families, gauge_frames, helper_roles=None):
+        self.families = {r:tuple(rows) for r,rows in families.items() if rows}
+        assert all(0<r<=self.h for r in self.families)
+        self.patterns = tile({r:self.replicas*len(rows) for r,rows in self.families.items()}, self.m)
+        self.role_index = {}
+        for rank,rows in self.families.items():
+            assert tuple(sorted(rows)) == rows and len(set(rows)) == len(rows)
+            for i,role in enumerate(rows):
+                assert role not in self.role_index
+                self.role_index[role]=(rank,i)
+        self.gauge_frames = dict(gauge_frames)
+        assert set(self.gauge_frames) == {role for r,rows in self.families.items() if r<self.h for role in rows}
+        self.helper_roles=tuple(sorted(self.role_index) if helper_roles is None else helper_roles)
+        assert len(self.helper_roles)==len(self.role_index) and set(self.helper_roles)==set(self.role_index)
+        self.local_work=2*self.v+len(self.helper_roles)
+        self.banks_per_stage=sum(count for widths,count in self.patterns)
+        self.data_families=self.replicas*4*self.v
+        self.live_families=self.data_families+self.stages*self.banks_per_stage
+        self.work_family=self.live_families
+        assert self.banks_per_stage*self.m==self.replicas*sum(r*len(rows) for r,rows in self.families.items()), 'zero padding'
+        expect('bank_patterns',self.patterns);expect('banks_per_stage',self.banks_per_stage);expect('literal_stock',self.live_families)
+        assert self.data_families==self.replicas*4*self.v
+        self.segments={}
+        used=Counter();bank_start=0
+        for pattern,(widths,count) in enumerate(self.patterns):
+            assert sum(widths)==self.m
+            for rank in set(widths):
+                blocks=tuple(b for b,r in enumerate(widths) if r==rank)
+                n=len(blocks)*count
+                self.segments.setdefault(rank,[]).append((used[rank],used[rank]+n,pattern,bank_start,blocks))
+                used[rank]+=n
+            bank_start+=count
+        assert used=={r:self.replicas*len(rows) for r,rows in self.families.items()}
+
+    def assignment(self, stage, replica, role):
+        """Exact bank family/block for one actual independent helper occurrence."""
+        assert 0<=stage<self.stages and 0<=replica<self.replicas
+        rank,role_index=self.role_index[role]
+        q=role_index*self.replicas+replica
+        for lo,hi,pattern,bank_start,blocks in self.segments[rank]:
+            if lo<=q<hi:
+                bank_offset,within=divmod(q-lo,len(blocks))
+                bank=bank_start+bank_offset;block=blocks[within]
+                widths=self.patterns[pattern][0]
+                return dict(family=self.data_families+stage*self.banks_per_stage+bank,
+                            stage_bank=bank,pattern=pattern,block=block,
+                            offset=sum(widths[:block]),rank=rank,
+                            frame=self.gauge_frames.get(role),scalar=block+1)
+        raise AssertionError('unallocated actual helper occurrence')
+
+    def data_family(self, replica, bank, port):
+        assert 0<=replica<self.replicas and 0<=bank<4 and 0<=port<self.v
+        return (4*replica+bank)*self.v+port
+
+    def normalizer(self, stage, replica, role):
+        """Finite exact data for N=scalar Pi embed_stage(B^-1).
+
+        frame=None denotes identity B=I_h. The caller resolves other IDs in
+        its freshly admitted frame registry/charts. inverse_chart remains an
+        exact rational factor program; no floating matrix is consumed.
+        """
+        a=self.assignment(stage,replica,role)
+        original=tuple(range(self.h*stage,self.h*stage+a['rank']))
+        target=tuple(range(a['offset'],a['offset']+a['rank']))
+        src=original+tuple(j for j in range(self.m) if j not in original)
+        dst=target+tuple(j for j in range(self.m) if j not in target)
+        pi=dict(zip(src,dst))
+        assert set(pi)==set(pi.values())==set(range(self.m))
+        permutation=tuple(pi[j] for j in range(self.m))
+        outside=next(j for j in range(self.m) if not self.h*stage<=j<self.h*(stage+1))
+        return dict(scalar=a['scalar'],permutation=permutation,
+                    inverse_chart_frame=a['frame'],chart_window=stage,
+                    outside_column=outside,unit_column_witness=(pi[outside],a['scalar']))
+
+    def address(self, stage, replica, role, cover='d'):
+        """Original class d*tau_i routed to the actual bank by N^-1.
+
+        Multiplication order is literal. A consumer must lower the factor
+        list right-to-left for inverse N, keeping chart/scalar denominators.
+        """
+        a=self.assignment(stage,replica,role)
+        N=('normalizer',stage,a['pattern'],a['block'],a['frame'])
+        return a['family'],('right',cover,('tau',stage),('inverse',N))
+
+    def local_family(self, stage, replica, local):
+        """Live family for the admitted local physical register index.
+
+        Family equality does not imply address equality for banked helpers.
+        Consumers must use local_address for ADD nonalias/namespace checks.
+        """
+        assert 0<=stage<self.stages and 0<=replica<self.replicas
+        assert 0<=local<=self.local_work
+        if local==self.local_work:return self.work_family
+        if local<self.v:return self.data_family(replica,self.active[stage][0],local)
+        if local<2*self.v:return self.data_family(replica,self.active[stage][1],local-self.v)
+        return self.assignment(stage,replica,self.helper_roles[local-2*self.v])['family']
+
+    def local_address(self, stage, replica, local, cover='d'):
+        family=self.local_family(stage,replica,local)
+        if local==self.local_work:return family,('external_work',0)
+        if local<2*self.v:
+            route=('class',cover) if stage==0 else ('right',cover,('rho',stage,local%self.v))
+            return family,route
+        return self.address(stage,replica,self.helper_roles[local-2*self.v],cover)
+
+    def local_from_logical_family(self, stage, family):
+        """Invert PR234's logical five-stage family map for one active stage."""
+        logical_work=4*self.v+len(self.helper_roles)
+        assert 0<=family<=logical_work
+        if family==logical_work:return self.local_work
+        if family>=4*self.v:return 2*self.v+family-4*self.v
+        bank,port=divmod(family,self.v)
+        if bank==self.active[stage][0]:return port
+        assert bank==self.active[stage][1], 'stage references an inactive data bank'
+        return self.v+port
+
+    def map_stage_row(self, stage, replica, row, cover='d'):
+        """Lower an unchanged logical8-field MOVE/ADD/COPY/ERASE record.
+
+        All mathematical fields remain unchanged. The two operand slots now
+        contain exact (family,route) keys when they denote streams; frame IDs
+        in MOVE's old/new slots are not mistaken for stream operands.
+        """
+        op,a,b,c,f,z,s,rev=row
+        assert op in(0,1,2,3) and s==stage and rev==int(stage in(1,3))
+        def address(family):
+            return self.local_address(stage,replica,self.local_from_logical_family(stage,family),cover)
+        physical_a=address(a)
+        physical_b=address(b) if op in(1,2) else b
+        if op in(1,2):assert physical_a!=physical_b
+        return (op,physical_a,physical_b,c,f,z,s,rev)
+
+    def map_boundary_row(self, replica, row, cover='d'):
+        """Lower an IDLE/BRIDGE/EXCHANGE with its existing exact projector.
+
+        Boundary projectors already include the checked data-route conjugacy;
+        their physical class is d. Independent completion rows must be
+        discharged explicitly by the bank endpoint verifier, never skipped
+        implicitly by this address mapper.
+        """
+        op,a,b,c,f,z,s,rev=row
+        assert op in(4,5,7), 'only proved bank completion may discharge opcode6'
+        def address(family):
+            assert 0<=family<4*self.v
+            bank,port=divmod(family,self.v)
+            return self.data_family(replica,bank,port),('class',cover)
+        physical_a=address(a)
+        physical_b=address(b) if op in(5,7) else b
+        if op in(5,7):assert physical_a!=physical_b
+        return (op,physical_a,physical_b,c,f,z,s,rev)
+
+    def phase_schedule(self):
+        """Phase-major schedule; every cover class is completed per replica.
+
+        Each emitted stage phase means: for the indicated replica, iterate
+        every cover class and execute the entire local scalar telescope.
+        Boundary phases occur after all replicas (60) of that stage finish.
+        """
+        for stage in range(self.stages):
+            for replica in range(self.replicas):
+                yield ('stage',stage,replica,'all_cover_classes')
+            if stage in (1,2,4):
+                for replica in range(self.replicas):
+                    yield ('idle',stage,replica,'all_cover_classes')
+                    yield ('bridge',stage,replica,'all_cover_classes')
+        for replica in range(self.replicas):
+            yield ('terminal_exchange',replica,'all_cover_classes')
diff --git a/research/five-stage-p10-transcript-stages/base_two_moment.py b/research/five-stage-p10-transcript-stages/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/five-stage-p10-transcript-stages/bitword/NOTICE-PR200 b/research/five-stage-p10-transcript-stages/bitword/NOTICE-PR200
new file mode 100644
index 0000000000..c2d7935d7f
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/NOTICE-PR200
@@ -0,0 +1,60 @@
+Prepared by Chafik Boukhalfa with substantial Anthropic Claude and OpenAI
+Codex assistance. Apache-2.0. Inherited files retain their original notices
+and assistance disclosures. This package claims no exclusive priority over
+concurrent work.
+
+Retained sources and lineage:
+- icekylinx: PR144 paired cubes, signed decoder, shared-core accounting,
+  original compiler, configurable local channels and finite bridge;
+  PR130/generalized Clifford frames.
+- eumemic: PR117 module infrastructure; PR155/157 scalar modules, physical
+  frames/reuse and partner-pair bit word; PR161 output merging and searched
+  p12 module; PR168 annealed pair, triple and all-but-one modules on both
+  words, nested-prefix schedules, the L1 local circuits this package varies,
+  fused outputs, bundle descent, both physical layers, the terminal-sink
+  gate and the physical bit word, pinned at
+  4a3c769e5c5430e7114c4d3e099ff34664677f17. Their Anthropic Claude and
+  OpenAI Codex disclosures are retained. PR131/143 supply frame/reuse and
+  late-read lineage; PR154 supplies isolated snapshot verification.
+- DaysSky: PR162 generalized carrier extension (`compile_closure` and the
+  extension rule reused here on the new graph) and full-intersection
+  compiler lineage. The selected graph retains the PR168 nested schedule.
+- jamesyc / James Chang: PR124 compensated birth cuts, PR34 balanced
+  assembly, and PR166 terminal-output accumulation and exact simultaneous
+  target-chain checking. The PR166 proof is retained in references/pr166.
+- GamingPuzzled / Joel Pulikkan: PR160 searched-bit-module composition.
+- gupt1156 PR148 and Abhinav Ramachandran/geckods PR158 (Hermes assistance):
+  paid atom-toll re-instantiation, including PR158 at
+  6e086603f936dbb95c6d7171132ed943cc024db9.
+- jacklightChen / Zhihao Chen: PR23/29 ordinary supplier; Rohan Arun
+  (rohanarun): PR100/103 paid positional layout and deferred signed words.
+- Earlier bit lineage retained by the prerequisite: Zhihao Chen PR97,
+  Swapnil Jain's round-seven checkers, an664 PR128, DaysSky PR150, hpst3r
+  PR147, SovereignSteak PR122, and the source-notice contributors.
+
+This package contributes, on the complex side, a random-restart and
+coordinate search over PR144's configurable local channel circuit on the
+PR168 v4 word, selecting face diagonals for A[0,0], A[0,1] and A[1,1] and
+fixed-coordinate differences for three G channels so that the carrier
+closure gains 1,485 arcs; our own legal-edge Hopcroft-Karp carrier matching with PR162's
+extension; endpoint frame descent and compensated handoffs for the new
+graph; independent complete admission of the resulting physical word and
+its 44 terminal deletions; independent physical-bit admission and exact
+prime witnesses for every used bit frame; and, on the bit side, a fixed-coordinate/face-diagonal variant of PR168's bit
+local circuit (A[0,0], A[0,1], A[2,0], A[2,1] face diagonals; A[1,*]
+direction-0 edges; G[0,1,0] fixed-coordinate differences), our own carrier
+matching, gauge selection and complete physical layer (endpoint frame descent and 1,760 compensated handoffs) for
+that graph, with 34 PR166 terminal deletions on face0 roots, independently
+admitted with exact prime witnesses for every used bit frame;
+and the fully paid balanced composition with finer positive backoffs. Scalar virtual stock, physical
+handoffs, terminal removals and every external row reserve remain
+distinct. The complete 47-inequality body is source-normalized to PR141.
+Prerequisite constructions, the configurable circuit itself and the
+terminal-compilation concept are not claimed as original here.
+
+The package is based on main (3b6b66891c0ac888521cf591fe306c6286601d4f),
+which integrates Dugongue's PR186 entrance-bank construction and already
+carries PR175's retired-register update. references/pr168-v4 holds
+byte-identical copies of the twelve PR168 v4 files this package executes or
+pins (icekylinx/eumemic/DaysSky lineage as noted in those files), with
+their digests in references/pr168-v4/SOURCE.json.
diff --git a/research/five-stage-p10-transcript-stages/bitword/README.md b/research/five-stage-p10-transcript-stages/bitword/README.md
new file mode 100644
index 0000000000..a241ad965d
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/README.md
@@ -0,0 +1,61 @@
+# The p = 10 paired-cube bit word
+
+This word is built by #285's gen5 generator (eumemic's PR168 generator with #276's gen4 local-design and
+centre-sharing changes) at cube size **p = 10**: h = 20 coordinates and v = 8·C(10,3) = 960 sources.
+
+The generator's only p = 10 changes are:
+
+- the p = 10 entries of MODULES/QMODULES (`pm_p10.json`, `qmod_p10.json`);
+- the variant-u output merge, which is on at p = 10 as at p = 12;
+- the cube-local design, which is read from `producer/data/local_design_p10.json`.
+
+Its virtual profile:
+
+- R = 9,120 (= c + q − |M| = 11,820 + 3,620 − 6,320);
+- W = 11,040, m = 3h = 60 and deficit 840 = 2v − 3h(h−2);
+- 2,160 gauges: 1,200 of rank 16 and 960 of rank 17.
+
+| data file | content |
+| --- | --- |
+| `pm_p10.json` | pair + copied-centre module, 36 inputs, 273 additions, 37 roots (36 outputs and the centre star) |
+| `qmod_p10.json` | all-but-one module, 8 inputs, 24 additions |
+| `local_design_p10.json` | per-cube recipe trees (cube-local, so independent of p) from a pair-aware local design search run on the p = 12 word, reused unchanged |
+| `arcs_p10.json` | the frozen carrier matching (6,320 arcs) |
+
+Both modules were annealed against the exact one-instance compile cost, starting from restrictions of gen5's
+p = 12 modules.
+
+## Physical layer
+
+`producer/make_physical.py --bank-parity` adds the compensated reuse pairs. Each recipient is a rank h − 3 = 17
+gauged role, read right before its first operation. Each donor is a dead ungauged non-root non-source register
+whose last frame lies in the recipient gauge. The pairing is a maximum Hopcroft–Karp matching under PR200's
+rules, and it matches 892 of the 960 recipient candidates.
+
+`--bank-parity` then makes the 60-replica bank width divisible by m = 5h = 100: it drops the fewest trailing
+pairs that achieve 60·width ≡ 0 (mod 100). At p = 12 this is gen5's parity rule. Here it drops two pairs,
+[3454, 9119] and [3409, 9118]: each adds 3 to the width, and 144,204 ≡ 4 (mod 5). That leaves **890 pairs**.
+
+`producer/descent.py` moves 998 operation frames under PR200's descent rules, with the five-stage first-order
+cost r·ln(m/r) at m = 100.
+
+The physical word has R = 8,230 and 1,270 independent entrances (1,200 of rank 16 and 70 of rank 17).
+
+## Reproduce
+
+```sh
+python3 -B bitword/producer/regenerate.py --work /new/scratch/dir
+```
+
+This runs the generator on the frozen arcs, then both producers, and checks that all five pinned files in
+`selected/bit` are reproduced exactly. It takes one to two minutes. `verify.py` never runs a producer.
+
+For new module data, `regenerate.py --solve-matching --emit DIR` recomputes the matching on a scratch copy of
+`producer/`, recompiles on the new frozen arcs, and writes the new five files and `arcs_p10.json` to DIR. See
+`../discovery/REPIN.md`.
+
+## PR200 classes
+
+`bit/word.py` and `bit/base_word.py` are Chafik Boukhalfa's PR200 classes. `word.py` changes only its input file
+names: PR200 named its own p = 12 files, and two lines (plus a comment) now read the cube size from the single
+`graph_pP.json`; the frame-loading line also checks the graph's p and h. `base_word.py` is unchanged.
diff --git a/research/five-stage-p10-transcript-stages/bitword/bit/base_word.py b/research/five-stage-p10-transcript-stages/bitword/bit/base_word.py
new file mode 100644
index 0000000000..044f278fbe
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/bit/base_word.py
@@ -0,0 +1,202 @@
+#!/usr/bin/env python3
+"""Reusable independent formal checks for a physical partner-pair bit word.
+
+The supplied frozen inputs are source-pinned. This never runs their producer.
+The Z check is of the defining integer decoder; only its F2 reduction is I.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from collections import Counter, defaultdict
+import importlib.util
+import json
+from pathlib import Path
+import sys
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[2]
+BASE = HERE.parent / 'references/pr168-v4/research/paired-cube-bit'
+P = 12
+if sys.flags.optimize: raise SystemExit('refusing -O')
+
+
+def need(ok, msg):
+    if not ok:
+        raise ValueError(msg)
+
+class Candidate:
+    def exact_frames(self):
+        C = self.C
+        C.decoder(); C.geometry()
+        for i in self.changed_frames:
+            f = self.opframe[i]; x = self.ops[i][2]; bits = C.sup[x]
+            need(C.nondeg(f), 'replacement operation frame nondegenerate')
+            while bits:
+                low = bits&-bits; s=low.bit_length()-1; bits-=low
+                need(C.in_frame(C.chi[s],f), 'value span in replacement operation frame')
+        for b, d in self.pairs:
+            need(C.sub(self.endframe[d], self.gauge[b]['frame']), 'exact Q donor-to-birth containment')
+            need(C.nondeg(self.endframe[d]) and C.nondeg(self.gauge[b]['frame']), 'handoff endpoints nondegenerate')
+
+    def register(self, rows):
+        C = self.C
+        B,_ = self.module.reduce_rows(rows,self.h if hasattr(self,'h') else C.h)
+        B = tuple(sorted(map(tuple,B),key=lambda r:next(i for i,x in enumerate(r) if x)))
+        if not hasattr(self,'frame_ids'):
+            self.frame_ids = {}
+        if B in self.frame_ids: return self.frame_ids[B]
+        f=max(C.B)+1; A,_=self.module.kernel(B,C.h)
+        C.B[f],C.A[f],C.dimf[f]=B,A,len(B);self.frame_ids[B]=f
+        return f
+
+
+    def row(self):
+        C,h,v=self.C,self.h,self.v
+        _,baseline_Y,src,_=C.chains()
+        seq=defaultdict(list)
+        for i,(a,b,x) in enumerate(self.ops):
+            seq[a].append(self.opframe[i]);seq[b].append(self.opframe[i])
+        for j,s in enumerate(self.w['rootroles']):seq[s].append(self.w['root_frame'][j])
+        start={b:self.w['source_frame'][x] for x,b in self.source.items()}
+        start.update({b:z['frame'] for b,z in self.gauge.items()})
+        recipient={d:b for b,d in self.pairs}
+        H=Counter()
+        for s in range(self.R):
+            if s in self.donor:continue
+            chain=list(seq[s])
+            if s in recipient:
+                b=recipient[s];chain += [self.gauge[b]['frame']]+seq[b]
+            chain.append(self.w['full_frame'])
+            prev=start.get(s);dp=0 if prev is None else C.dimf[prev]
+            if s in self.source.values():H[1]+=1
+            for f in chain:
+                need(prev is None or C.sub(prev,f),'physical role chain nested')
+                d=C.dimf[f]
+                if d>dp:H[d-dp]+=1
+                prev,dp=f,d
+        for j,r in enumerate(self.g['roots']):
+            if r['kind']=='center':H[C.dimf[self.w['root_frame'][j]]]+=1
+        Y=Counter();current=[None]*v
+        def read(t,f):
+            old=current[t];d=0 if old is None else C.dimf[old]
+            need(old is None or C.sub(old,f),'actual target frame chronology')
+            if C.dimf[f]>d:Y[C.dimf[f]-d]+=1
+            current[t]=f
+        for b in sorted(self.order,key=lambda b:self.readtime[b]):
+            for t in self.gauge[b]['targets']:read(t,self.gauge[b]['frame'])
+        deliveries=defaultdict(list)
+        for e in self.k['entries']:deliveries[e['deliver_after_root']].append(e)
+        for j,r in enumerate(self.g['roots']):
+            if r['kind']!='center':
+                for t in r['targets']:read(t,self.w['root_frame'][j])
+            for e in deliveries[j]:
+                for t in e['receivers']:read(t,e['deliver_frame'])
+        for t,f in enumerate(current):
+            need(f is not None and all(self.module.dot(C.cov[t],b)==0 for b in C.B[f]),'final target cap')
+            gap=h-1-C.dimf[f]
+            if gap:Y[gap]+=1
+        need(sum(r*n for r,n in Y.items())==v*(h-1),'target rank mass')
+        hist=Counter()
+        for part in (H,Y,src):
+            for r,n in part.items():
+                if r and n:hist[r]+=3*n
+        for b,z in self.gauge.items():
+            if b not in self.donor:hist[3*z['dim']]+=1
+        hist[2]+=2*v
+        hist={r:n for r,n in sorted(hist.items()) if n}
+        need(all(0<r<3*h and n>0 for r,n in hist.items()),'positive proper child bins')
+        R=self.R-len(self.pairs);W=2*v+R;mass=sum(r*n for r,n in hist.items());m=3*h
+        need(W*m-mass==C.prof['deficit_per_vertex'],'reuse preserves telescoping deficit')
+        return dict(h=h,v=v,R=R,virtual_R=self.R,reused_registers=len(self.pairs),W_per_vertex=W,m=m,
+            loss=C.prof['loss'],rank_per_vertex=mass,deficit_per_vertex=W*m-mass,
+            child_histogram=hist,maxchild=max(hist),selected_roles=len(self.gauge)-len(self.pairs),
+            selected_rank_histogram=dict(Counter(z['dim'] for b,z in self.gauge.items() if b not in self.donor)),
+            changed_operation_frames=len(self.changed_frames),
+            frames_not_contained_in_original=sum(not C.sub(self.opframe[i],self.original_opframe[i]) for i in self.changed_frames),
+            physical_target_histogram=dict(Y),physical_internal_histogram=dict(H),
+            foreign_producer_replays=0)
+
+    def adjoint(self):
+        adj = [dict() for _ in range(self.R)]
+        for r,s in zip(self.g['roots'], self.w['rootroles']):
+            for t in r['targets']: adj[s][t] = adj[s].get(t,0)+1
+        for a,b,_ in reversed(self.ops):
+            for t,c in adj[a].items(): adj[b][t] = adj[b].get(t,0)+c
+        return adj
+
+    def formal(self, ring, tamper=None):
+        """All source, target and dirty-register columns; no random sampling."""
+        v, phys = self.v, self.phys
+        regs = sorted(set(phys.values())); index = {r:2*v+j for j,r in enumerate(regs)}
+        if ring == 2:
+            unit = lambda i: 1<<i
+            def accum(dst,val,c): return dst ^ val if c&1 else dst
+        else:
+            unit = lambda i: {i:1}
+            def accum(dst,val,c):
+                out = dict(dst)
+                for i,z in val.items():
+                    k = out.get(i,0)+c*z
+                    if k: out[i]=k
+                    else: out.pop(i,None)
+                return out
+        x = [unit(s) for s in range(v)]; y = [unit(v+t) for t in range(v)]
+        a = {r:unit(index[r]) for r in regs}
+        adj = self.adjoint()
+        at = defaultdict(list)
+        for b in self.order: at[self.readtime[b]].append(b)
+        done = []
+        stale_used = False
+        def read(b):
+            nonlocal stale_used
+            if tamper == 'omit_compensation' and b == self.order[0]: return
+            value = a[phys[b]]
+            if tamper == 'stale' and b in self.donor and not stale_used:
+                value = unit(index[phys[b]]); stale_used = True
+            for t,c in adj[b].items(): y[t] = accum(y[t],value,-c)
+        def op(i,sign):
+            b,d,_ = self.ops[i]
+            a[phys[b]] = accum(a[phys[b]],a[phys[d]],sign)
+        for b in range(self.R):
+            if b not in self.gauge: read(b)
+        for s,b in self.source.items(): a[phys[b]] = accum(a[phys[b]],x[s],1)
+        for i in self.phase1: op(i,1); done.append(i)
+        for r,b in zip(self.g['roots'],self.w['rootroles']):
+            if r['kind']=='center':
+                for t in r['targets']:y[t]=accum(y[t],a[phys[b]],1)
+        for j,i in enumerate(self.rest):
+            for b in at[j]: read(b)
+            op(i,1); done.append(i)
+        for b in at[len(self.rest)]: read(b)
+        deliveries=defaultdict(list)
+        for e in self.k['entries']:deliveries[e['deliver_after_root']].append(e)
+        broken=False
+        for j,(r,b) in enumerate(zip(self.g['roots'],self.w['rootroles'])):
+            if r['kind']!='center':
+                for t in r['targets']: y[t] = accum(y[t],a[phys[b]],1)
+            for e in deliveries[j]:
+                c,d = e['carrier'],e['passive']
+                x[c] = accum(x[c],x[d],1)
+                for t in e['receivers']:
+                    if tamper == 'missing_partner' and not broken: broken=True;continue
+                    y[t] = accum(y[t],x[c],1)
+        for e in self.k['entries']:
+            x[e['carrier']] = accum(x[e['carrier']],x[e['passive']],-1)
+        for i in reversed(done): op(i,-1)
+        for s,b in self.source.items(): a[phys[b]] = accum(a[phys[b]],x[s],-1)
+        need(all(a[r] == unit(index[r]) for r in regs), 'all dirty register columns restored')
+        need(all(x[s] == unit(s) for s in range(v)), 'all source columns restored')
+        if ring == 2:
+            want = [accum(unit(v+t),unit(t),1) for t in range(v)]
+        else:
+            # Integer lift: the exact defining decoder, whose reduction is I over F2.
+            support = [{s:1} for s in range(v)]
+            for aa,bb in self.g['args'][v:]: support.append(accum(support[aa],support[bb],1))
+            want = [unit(v+t) for t in range(v)]
+            for r in self.g['roots']:
+                for t in r['targets']: want[t] = accum(want[t],support[r['node']],1)
+            for e in self.k['entries']:
+                for t in e['receivers']:
+                    want[t] = accum(want[t],unit(e['carrier']),1)
+                    want[t] = accum(want[t],unit(e['passive']),1)
+        need(y == want, 'all target columns equal defining decoder')
+        return dict(ring=str(ring),formal_variables=2*v+len(regs),
+            target_contract='F2 identity' if ring==2 else 'integer defining decoder',
+            identity=ring==2,defining_decoder=True,all_dirty_and_source_columns_restored=True)
diff --git a/research/five-stage-p10-transcript-stages/bitword/bit/word.py b/research/five-stage-p10-transcript-stages/bitword/bit/word.py
new file mode 100644
index 0000000000..def2b4178e
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/bit/word.py
@@ -0,0 +1,106 @@
+"""Independent complete formal admission of the PR168-v4 physical bit word with our own physical layer (endpoint descent and reuse pairs) and terminal sinks.
+
+Retains eumemic's exact integer linear algebra and original decoder/geometry
+predicates. Physical chains, chronological formal columns and paid moments
+use our separate verifier. No producer or foreign aggregate checker runs.
+"""
+from pathlib import Path
+from collections import Counter,defaultdict
+from hashlib import sha256
+import gzip,importlib.util,json,sys,time
+HERE=Path(__file__).resolve().parent
+SOURCE=HERE.parent/'references/pr168-v4'
+PKG=HERE.parent
+def module(name,path):
+    spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m
+def read(p):
+    raw=p.read_bytes();return json.loads(gzip.decompress(raw) if p.suffix=='.gz' else raw)
+old=module('own_frozen_word',PKG/'bit/base_word.py');need=old.need
+
+class Candidate(old.Candidate):
+    def __init__(self):
+        self.module=backend=module('exact_integer_backend',SOURCE/'research/paired-cube-bit/check_paired_cube_bit.py')
+        C=backend.Checker.__new__(backend.Checker);self.C=C;C.mut=None
+        B=F=PKG/'selected/bit'
+        # p = 10 port: PR200 named its own p = 12 files here; the cube size is now read from the single pinned graph.
+        graphs=sorted(B.glob('graph_p*.json'));need(len(graphs)==1,'one pinned bit word');P=int(graphs[0].name[7:-5])
+        self.input_paths=[B/f'graph_p{P}.json',B/f'profile_p{P}.json',F/f'word_p{P}.json.gz',F/f'frames_p{P}.json.gz',F/f'kchron_p{P}.json']
+        C.g,C.prof,C.w,C.fr,C.k=map(read,self.input_paths)
+        C.h=C.g['h'];C.v=C.g['v'];need(C.g['p']==P and C.h==2*P,'cube size of the pinned word');C.frames()
+        self.h,self.v,self.R=C.h,C.v,C.prof['R'];self.w,self.g,self.k=C.w,C.g,C.k
+        self.ops=self.w['ops'];self.nf={int(n):f for n,f in self.w['node_frame'].items()}
+        self.source={int(n):s for n,s in self.w['sources'].items()};self.gauge={z['role']:z for z in self.w['gauges']}
+        need(len(self.gauge)==len(self.w['gauges']),'unique gauge roles')
+        self.original_opframe=tuple(self.nf[n] for a,b,n in self.ops);self.opframe=self.w['op_frame'][:]
+        need(len(self.opframe)==len(self.ops),'complete operation frame vector')
+        self.changed_frames=[i for i,(a,b) in enumerate(zip(self.original_opframe,self.opframe)) if a!=b]
+        self.phase1=sorted(self.w['phase1']);phase=set(self.phase1)
+        self.rest=[i for i in range(len(self.ops)) if i not in phase];order=self.phase1+self.rest
+        self.position={i:p for p,i in enumerate(order)};pos={i:p for p,i in enumerate(self.rest)}
+        self.order=[z['role'] for z in reversed(self.w['gauges'])]
+        self.role_ops=defaultdict(list)
+        for i in order:
+            for s in self.ops[i][:2]:self.role_ops[s].append(i)
+        need(all(xs==sorted(xs) for xs in self.role_ops.values()),'execution order preserves every role chronology')
+        self.first={s:pos.get(xs[0],-1) for s,xs in self.role_ops.items()}
+        self.last={s:pos.get(xs[-1],-1) for s,xs in self.role_ops.items()}
+        self.endframe={s:self.opframe[xs[-1]] for s,xs in self.role_ops.items()}
+        self.rootroles=set(self.w['rootroles']);self.rootkind={s:r['kind'] for s,r in zip(self.w['rootroles'],self.g['roots'])}
+        need(len(self.rootroles)==len(self.w['rootroles']),'unique root roles')
+        reads={int(s):p for s,p in self.w['reads'].items()}
+        need(set(reads)<=set(self.gauge),'only gauges have explicit reads')
+        self.readtime={s:reads.get(s,len(self.phase1))-len(self.phase1) for s in self.order}
+        need(all(0<=self.readtime[s]<=self.first[s] for s in self.order),'all gauge reads after centre phase and before first use')
+        self.pairs=[[b,a] for a,b in self.w['pairs']];self.donor=dict(self.pairs)
+        need(len(self.donor)==len(self.pairs)==len(set(self.donor.values())),'one-to-one aliases')
+        need(not set(self.donor)&set(self.donor.values()),'disjoint donor recipient sets')
+        for b,d in self.pairs:
+            need(d not in self.gauge and d not in self.rootroles and b in self.gauge,'ungauged non-root donor and gauged recipient')
+            need(self.last[d]<self.readtime[b],'donor dead before recipient read')
+        self.phys={s:self.donor.get(s,s) for s in range(self.R)}
+        need(len(set(self.phys.values()))==self.R-len(self.pairs),'physical slot count')
+        need(all(self.phys[a]!=self.phys[b] for a,b,n in self.ops),'distinct physical gate ports')
+        C.chains=self.base_chains
+
+    def base_chains(self):
+        """Reconstruct phase/gauge/source contracts; row() counts physical paths."""
+        C,w,h,v=self.C,self.w,self.h,self.v
+        order=self.phase1+self.rest
+        roleprev={};pred=[]
+        for i,(a,b,n) in enumerate(self.ops):
+            pred.append((roleprev.get(a,-1),roleprev.get(b,-1)));roleprev[a]=roleprev[b]=i
+        pending=[roleprev[s] for s in self.rootroles if self.rootkind[s]=='center' and s in roleprev];closure=set()
+        while pending:
+            i=pending.pop()
+            if i not in closure:closure.add(i);pending.extend(j for j in pred[i] if j>=0)
+        need(closure==set(self.phase1),'phase one is exactly centre closure')
+        content=[0]*self.R
+        for n,s in self.source.items():content[s]=1<<n
+        for i in order:
+            a,b,n=self.ops[i];args=self.g['args'][n]
+            if content[a]:need(args is not None and {content[a],content[b]}=={C.sup[t] for t in args},'actual addition operands')
+            else:need(content[b]==C.sup[n],'actual copied node value')
+            content[a]|=content[b]
+        co=[set() for _ in range(self.R)]
+        for r,s in zip(self.g['roots'],w['rootroles']):co[s].update(r['targets'])
+        for i in reversed(order):
+            a,b,n=self.ops[i];co[b].update(co[a])
+        touched={s for i in self.phase1 for s in self.ops[i][:2]}
+        for s,z in self.gauge.items():
+            need(s not in self.source.values() and s not in touched,'gauge untouched in phase one and source injection')
+            need(set(z['targets'])==co[s] and C.dimf[z['frame']]==z['dim']>0,'gauge dimension and complete response support')
+        src=Counter();members=Counter();labels=list(map(set,self.g['labels']))
+        for e in self.k['entries']:
+            c,d,f,cap=e['carrier'],e['passive'],e['mix_frame'],e['deliver_frame']
+            need(len(labels[c]&labels[d])==1,'orthogonal partner pair')
+            need(C.dimf[f]==2 and C.in_frame(C.chi[c],f) and C.in_frame(C.chi[d],f),'partner mix span')
+            need(C.sub(f,cap) and all(self.module.dot(C.cov[t],u)==0 for t in e['receivers'] for u in C.B[cap]),'partner mix delivery cap')
+            need(e['carrier_chain']==[w['source_frame'][c],f,cap,w['full_frame']] and e['passive_chain']==[w['source_frame'][d],f,w['full_frame']],'exact partner chains')
+            root=self.g['roots'][e['deliver_after_root']]
+            need(root['kind']=='side' and sorted(e['receivers'])==sorted(root['targets']),'partner delivery at own receiver root')
+            for chain in (e['carrier_chain'],e['passive_chain']):
+                for a,b in zip(chain,chain[1:]):
+                    need(C.sub(a,b),'nested source chronology');src[C.dimf[b]-C.dimf[a]]+=1
+            members[c]+=1;members[d]+=1
+        need(all(members[s]==1 for s in range(v)),'every source in one partner pair')
+        return Counter(),Counter(),src,self.R
diff --git a/research/five-stage-p10-transcript-stages/bitword/producer/data/arcs_p10.json b/research/five-stage-p10-transcript-stages/bitword/producer/data/arcs_p10.json
new file mode 100644
index 0000000000..7938a9b5ba
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/producer/data/arcs_p10.json
@@ -0,0 +1 @@
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diff --git a/research/five-stage-p10-transcript-stages/bitword/producer/data/local_design_p10.json b/research/five-stage-p10-transcript-stages/bitword/producer/data/local_design_p10.json
new file mode 100644
index 0000000000..d93bfb883d
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/producer/data/local_design_p10.json
@@ -0,0 +1 @@
+{"design":[[["A",0,0],[[[[0,0,1],[0,1,0]],[0,0,0]],[0,1,1]]],[["A",0,1],[[[[1,0,1],[1,1,1]],[1,1,0]],[1,0,0]]],[["A",1,0],[[[0,0,0],[1,0,1]],[[0,0,1],[1,0,0]]]],[["A",1,1],[[[0,1,0],[1,1,1]],[[0,1,1],[1,1,0]]]],[["G",0,2,1],[[[0,0,1],[1,0,0]],[[0,1,1],[1,1,0]]]],[["G",1,2,1],[[[0,0,1],[0,1,0]],[[1,0,1],[1,1,0]]]],[["G",0,1,0],[[[0,0,1],[1,1,1]],[[0,0,0],[1,1,0]]]],[["G",0,1,1],[[[0,1,1],[1,0,1]],[[0,1,0],[1,0,0]]]],[["A",2,1],[[[0,1,1],[1,0,1]],[[0,0,1],[1,1,1]]]],[["A",2,0],[[[0,0,0],[1,1,0]],[[0,1,0],[1,0,0]]]],[["G",0,2,0],[[[0,0,0],[1,0,1]],[[0,1,0],[1,1,1]]]],[["G",1,2,0],[[[1,0,0],[1,1,1]],[[0,0,0],[0,1,1]]]]],"provenance":{"source":"pair-aware local design search (DreamingOfClouds with Anthropic Claude assistance); cube-local, used unchanged at p = 10"}}
diff --git a/research/five-stage-p10-transcript-stages/bitword/producer/data/pm_p10.json b/research/five-stage-p10-transcript-stages/bitword/producer/data/pm_p10.json
new file mode 100644
index 0000000000..48f91228e0
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/producer/data/pm_p10.json
@@ -0,0 +1 @@
+{"input_count": 36, "args": [null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, [4, 8], [11, 12], [0, 2], [26, 30], [23, 27], [21, 40], [22, 41], [39, 42], [4, 5], [3, 44], [43, 45], [38, 46], [37, 47], [1, 48], [22, 23], [2, 24], [15, 51], [50, 52], [30, 37], [17, 54], [18, 55], [5, 56], [4, 57], [0, 6], [8, 19], [59, 60], [1, 13], [61, 62], [33, 63], [58, 64], [31, 65], [53, 66], [30, 44], [32, 34], [68, 69], [31, 33], [70, 71], [18, 40], [12, 73], [72, 74], [9, 10], [27, 76], [12, 77], [17, 18], [15, 16], [8, 80], [76, 81], [79, 82], [49, 83], [24, 71], [28, 85], [22, 86], [0, 1], [36, 88], [14, 20], [7, 90], [89, 91], [69, 92], [56, 93], [16, 26], [28, 95], [27, 79], [96, 97], [39, 41], [25, 29], [32, 100], [34, 101], [99, 102], [87, 103], [13, 14], [35, 105], [20, 106], [19, 107], [8, 108], [54, 109], [31, 32], [11, 17], [22, 26], [112, 113], [82, 114], [111, 115], [2, 3], [29, 117], [25, 118], [21, 80], [8, 120], [76, 121], [119, 122], [69, 71], [79, 124], [110, 125], [9, 12], [25, 50], [24, 128], [127, 129], [6, 28], [85, 131], [4, 112], [88, 133], [123, 134], [61, 133], [31, 136], [24, 28], [76, 120], [138, 139], [117, 140], [62, 141], [137, 142], [76, 90], [81, 144], [34, 145], [37, 43], [79, 147], [146, 148], [108, 138], [10, 27], [26, 151], [37, 152], [3, 29], [28, 154], [153, 155], [6, 7], [35, 157], [9, 67], [5, 33], [34, 160], [23, 161], [21, 100], [150, 163], [18, 34], [5, 12], [33, 166], [165, 167], [96, 151], [19, 20], [1, 170], [160, 171], [4, 11], [138, 163], [35, 174], [32, 113], [135, 176], [157, 175], [117, 178], [0, 105], [179, 180], [78, 181], [162, 182], [88, 91], [72, 158], [171, 185], [154, 186], [2, 45], [157, 188], [158, 180], [72, 190], [11, 191], [2, 192], [165, 172], [1, 61], [107, 195], [7, 196], [31, 133], [197, 198], [32, 199], [95, 200], [126, 129], [81, 164], [35, 170], [80, 117], [178, 205], [40, 206], [111, 113], [4, 208], [2, 46], [132, 210], [16, 79], [15, 212], [1, 213], [211, 214], [19, 215], [63, 167], [37, 76], [13, 218], [87, 219], [71, 197], [69, 221], [58, 222], [9, 15], [25, 224], [2, 225], [5, 226], [50, 227], [210, 214], [51, 225], [7, 230], [123, 184], [34, 74], [76, 233], [203, 234], [10, 155], [5, 232], [156, 191], [126, 169], [7, 14], [10, 240], [102, 241], [119, 140], [197, 243], [116, 164], [52, 128], [202, 224], [79, 186], [246, 248], [83, 147], [13, 250], [31, 169], [233, 237], [113, 143], [98, 187], [141, 217], [168, 196], [23, 257], [91, 177], [35, 103], [1, 17], [9, 48], [242, 262], [201, 236], [7, 102], [76, 181], [130, 193], [16, 197], [236, 268], [27, 269], [20, 229], [204, 213], [73, 256], [265, 271], [194, 207], [95, 151], [22, 32], [199, 277], [94, 228], [230, 278], [47, 219], [231, 258], [65, 252], [208, 266], [33, 235], [168, 270], [3, 283], [19, 86], [251, 288], [75, 171], [181, 290], [115, 291], [14, 220], [101, 149], [260, 293], [29, 239], [29, 276], [35, 104], [209, 261], [132, 281], [173, 284], [189, 298], [170, 206], [299, 303], [104, 272], [3, 57], [93, 306], [297, 307]], "roots": [305, 295, 296, 247, 285, 245, 294, 289, 302, 255, 249, 275, 304, 274, 216, 238, 267, 183, 301, 263, 300, 223, 286, 264, 308, 287, 282, 280, 279, 159, 244, 253, 273, 259, 254, 84, 292], "provenance": {"C_onestage": 12878.384991951672, "source": "nbsapair SA from gen5 p12 restriction: C-weighted 11.5M its (run a2) then five-stage-weighted (t ln(5h/t)) 4.5M its (run f1)", "fullword_a5_float": "7.4424584e-4", "R": "9120"}}
\ No newline at end of file
diff --git a/research/five-stage-p10-transcript-stages/bitword/producer/data/qmod_p10.json b/research/five-stage-p10-transcript-stages/bitword/producer/data/qmod_p10.json
new file mode 100644
index 0000000000..b837d6e209
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/producer/data/qmod_p10.json
@@ -0,0 +1 @@
+{"input_count": 8, "args": [null, null, null, null, null, null, null, null, [5, 7], [1, 8], [4, 0], [2, 1], [10, 3], [11, 12], [13, 8], [3, 6], [9, 15], [15, 5], [10, 17], [18, 2], [7, 19], [11, 0], [8, 21], [6, 22], [10, 16], [4, 16], [25, 2], [13, 7], [27, 6], [15, 22], [23, 4], [11, 18]], "roots": [26, 20, 24, 30, 29, 28, 14, 31], "provenance": {"source": "qsa (fastq_p one-instance C) from q5r_1 restriction of gen5 qmod_p12", "C": 7595.909682229441, "adds": 24, "arcs": 16}}
\ No newline at end of file
diff --git a/research/five-stage-p10-transcript-stages/bitword/producer/descent.py b/research/five-stage-p10-transcript-stages/bitword/producer/descent.py
new file mode 100644
index 0000000000..a303fa3e55
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/producer/descent.py
@@ -0,0 +1,263 @@
+#!/usr/bin/env python3
+"""Endpoint frame descent for a physical paired-cube bit word (PR200 physical-layer rules).
+
+Moves equal-frame connected groups of operations to the join of their incoming frames and node value
+spans, or to the meet of their outgoing frames (degenerate endpoints repaired by one row), accepting a move
+only when the five-stage first-order cost  sum r*ln(m/r)  (m = 5h; 120 at p = 12, 100 at p = 10) over all physical
+role chains decreases.
+Gauge, root, source, target and full frames are fixed; alias splices (donor -> recipient gauge) are kept.
+
+usage: descent.py PKGDIR OUTDIR   (PKGDIR = PR200-layout package whose selected/bit holds the word)
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+p = 10 port: m = 5h and the pP file names are read from the word (DreamingOfClouds, Anthropic Claude assistance).
+"""
+import sys, json, gzip, math, time
+from pathlib import Path
+from collections import defaultdict, Counter
+
+pkg = Path(sys.argv[1]); out = Path(sys.argv[2]); out.mkdir(parents=True, exist_ok=True)
+sys.path.insert(0, str(pkg / 'bit'))
+from word import Candidate
+
+t0 = time.time()
+W = Candidate(); C = W.C; mod = W.module; h = W.h
+C.decoder(); C.geometry()
+FULL = W.w['full_frame']
+ops = W.ops; nops = len(ops)
+opframe = list(W.opframe)
+
+# ---------------------------------------------------------------- frame registry helpers
+key_of = {}
+def bkey(B): return tuple(sorted(map(tuple, B)))
+for f, B in C.B.items():
+    key_of.setdefault(bkey(B), f)
+
+def register(rows):
+    B, _ = mod.reduce_rows(rows, h)
+    B = [tuple(r) for r in B]
+    k = bkey(B)
+    if k in key_of: return key_of[k]
+    f = max(C.B) + 1
+    A, _ = mod.kernel(B, h)
+    C.B[f], C.A[f], C.dimf[f] = B, A, len(B)
+    key_of[k] = f
+    return f
+
+join_cache = {}
+def join(fs):
+    fs = tuple(sorted(set(fs)))
+    if len(fs) == 1: return fs[0]
+    r = join_cache.get(fs)
+    if r is None:
+        rows = [b for f in fs for b in C.B[f]]
+        r = join_cache[fs] = register(rows)
+    return r
+
+meet_cache = {}
+def meet(fs):
+    fs = tuple(sorted(set(fs)))
+    if len(fs) == 1: return fs[0]
+    r = meet_cache.get(fs)
+    if r is None:
+        ann = [a for f in fs for a in C.A[f]]
+        B, _ = mod.kernel(ann, h) if ann else ([tuple(int(i == j) for j in range(h)) for i in range(h)], None)
+        r = meet_cache[fs] = register(B)
+    return r
+
+nd_cache = {}
+def nondeg(f):
+    r = nd_cache.get(f)
+    if r is None: r = nd_cache[f] = C.nondeg(f)
+    return r
+
+def sub(a, b): return C.sub(a, b)
+
+# node value spans
+span_cache = {}
+def node_span(n):
+    r = span_cache.get(n)
+    if r is None:
+        bits = C.sup[n]; rows = []
+        while bits:
+            low = bits & -bits; s = low.bit_length() - 1; bits -= low
+            rows.append(C.chi[s])
+        r = span_cache[n] = register(rows)
+    return r
+
+def repair_up(L, U):
+    """smallest nondegenerate frame containing L inside U: L itself or L + one row of U."""
+    if nondeg(L): return L
+    for b in C.B[U]:
+        f = register(list(C.B[L]) + [b])
+        if C.dimf[f] == C.dimf[L] + 1 and nondeg(f): return f
+    return None
+
+def repair_down(L, U):
+    """largest nondegenerate frame inside U containing L: U itself or U minus one row (kernel of A_U + 1 row)."""
+    if nondeg(U): return U
+    # hyperplanes of U containing L: add one annihilator row vanishing on L but not on U
+    BL = C.B[L]
+    cand = []
+    for e in range(h):
+        a = [int(i == e) for i in range(h)]
+        cand.append(a)
+    # project candidate covectors to vanish on L: use combinations orthogonal to B_L via kernel of B_L
+    K, _ = mod.kernel(BL, h) if BL else ([tuple(int(i == j) for j in range(h)) for i in range(h)], None)
+    for a in K:
+        rows = list(C.A[U]) + [a]
+        B, _ = mod.kernel(rows, h)
+        f = register(B)
+        if C.dimf[f] == C.dimf[U] - 1 and sub(L, f) and nondeg(f): return f
+    return None
+
+# ---------------------------------------------------------------- physical chains
+recipient = {d: b for b, d in W.pairs}           # donor -> recipient
+roots = defaultdict(list)
+for j, s in enumerate(W.w['rootroles']): roots[s].append(W.w['root_frame'][j])
+start = {b: W.w['source_frame'][x] for x, b in W.source.items()}
+start.update({b: z['frame'] for b, z in W.gauge.items()})
+seq = defaultdict(list)
+for i, (a, b, x) in enumerate(ops):
+    seq[a].append(i); seq[b].append(i)
+
+chains = []   # list of element lists: ('f', frame) fixed or ('o', op)
+for s in range(W.R):
+    if s in W.donor: continue    # recipients are spliced into their donor's chain
+    el = []
+    st = start.get(s)
+    el.append(('f', st) if st is not None else ('z', None))
+    el += [('o', i) for i in seq[s]] + [('f', f) for f in roots[s]]
+    if s in recipient:
+        b = recipient[s]
+        el += [('f', W.gauge[b]['frame'])] + [('o', i) for i in seq[b]] + [('f', f) for f in roots[b]]
+    el.append(('f', FULL))
+    chains.append(el)
+pos = defaultdict(list)    # op -> [(chain, index)]
+for c, el in enumerate(chains):
+    for k, (t, x) in enumerate(el):
+        if t == 'o': pos[x].append((c, k))
+assert all(len(v) == 2 for v in pos.values()) and len(pos) == nops
+
+def fr(e):
+    t, x = e
+    if t == 'o': return opframe[x]
+    return x
+
+def dim(f): return 0 if f is None else C.dimf[f]
+
+MM = 5 * h   # five-stage width m = 5h
+LN = [0.0] + [r * math.log(MM / r) for r in range(1, MM + 1)]
+def cost_pair(a, b):
+    d = dim(b) - dim(a)
+    assert d >= 0
+    return LN[d]
+
+def total_cost():
+    tot = 0.0
+    for el in chains:
+        for k in range(len(el) - 1):
+            tot += cost_pair(fr(el[k]), fr(el[k + 1]))
+    return tot
+
+def check_nested():
+    for el in chains:
+        for k in range(len(el) - 1):
+            a, b = fr(el[k]), fr(el[k + 1])
+            assert a is None or sub(a, b), ('nest', el[k], el[k + 1])
+
+check_nested()
+c0 = total_cost()
+print('loaded', round(time.time() - t0, 1), 's; chains', len(chains), 'cost', round(c0, 1), flush=True)
+
+# ---------------------------------------------------------------- group moves
+def groups():
+    parent = list(range(nops))
+    def find(x):
+        while parent[x] != x: parent[x] = parent[parent[x]]; x = parent[x]
+        return x
+    for el in chains:
+        for k in range(len(el) - 1):
+            if el[k][0] == 'o' and el[k + 1][0] == 'o' and opframe[el[k][1]] == opframe[el[k + 1][1]]:
+                ra, rb = find(el[k][1]), find(el[k + 1][1])
+                if ra != rb: parent[ra] = rb
+    g = defaultdict(list)
+    for i in range(nops): g[find(i)].append(i)
+    return list(g.values())
+
+def evaluate(G):
+    Gs = set(G); F = opframe[G[0]]
+    inc, outg = [], []
+    for i in G:
+        for c, k in pos[i]:
+            el = chains[c]
+            p = el[k - 1]
+            if not (p[0] == 'o' and p[1] in Gs): inc.append(fr(p))
+            q = el[k + 1]
+            if not (q[0] == 'o' and q[1] in Gs): outg.append(fr(q))
+    spans = {node_span(ops[i][2]) for i in G}
+    L = join([f for f in inc if f is not None] + list(spans))
+    U = meet(outg)
+    if not sub(L, U): return None
+    def delta(Fn):
+        d = 0.0
+        for f in inc: d += LN[dim(Fn) - dim(f)] - LN[dim(F) - dim(f)]
+        for f in outg: d += LN[dim(f) - dim(Fn)] - LN[dim(f) - dim(F)]
+        return d
+    best = (0.0, None)
+    cands = set()
+    lo = repair_up(L, U)
+    if lo is not None: cands.add(lo)
+    hi = repair_down(L, U)
+    if hi is not None: cands.add(hi)
+    for f in inc + outg:
+        if f is not None and sub(L, f) and sub(f, U) and nondeg(f): cands.add(f)
+    for Fn in cands:
+        if C.dimf[Fn] == C.dimf[F] and sub(Fn, F): continue
+        d = delta(Fn)
+        if d < best[0] - 1e-9: best = (d, Fn)
+    return best
+
+it = 0
+while True:
+    it += 1; moved = 0; gain = 0.0
+    gs = groups()
+    gs.sort(key=len, reverse=True)
+    for G in gs:
+        # frames may have changed for neighbours; G still has a common frame since only whole groups move
+        if len({opframe[i] for i in G}) != 1: continue
+        r = evaluate(G)
+        if r is None or r[1] is None: continue
+        d, Fn = r
+        for i in G: opframe[i] = Fn
+        moved += 1; gain += d
+    c = total_cost()
+    print('iter', it, 'groups', len(gs), 'moved', moved, 'gain', round(gain, 1), 'cost', round(c, 1), round(time.time() - t0, 1), 's', flush=True)
+    if moved == 0 or it >= 40: break
+
+check_nested()
+for i in range(nops):
+    f = opframe[i]
+    assert nondeg(f)
+    assert sub(node_span(ops[i][2]), f)
+changed = sum(1 for i in range(nops) if opframe[i] != W.original_opframe[i])
+print('changed op frames', changed, 'final cost', round(total_cost(), 1), 'from', round(c0, 1))
+
+# ---------------------------------------------------------------- write outputs
+w = dict(W.w); w['op_frame'] = opframe
+w['descent'] = 'op_frame[i]: equal-frame connected groups moved to the join of incoming frames and node spans or the meet of outgoing frames (one-row repair), five-stage first-order cost decrease'
+src = pkg / 'selected/bit'
+P = W.g['p']; assert h == 2 * P
+frames = json.loads(gzip.decompress((src / ('frames_p%d.json.gz' % P)).read_bytes()))
+used = set(opframe)
+for f in sorted(C.B):
+    if str(f) in frames['frames'] or f not in used: continue
+    B, A = C.B[f], C.A[f]
+    frames['frames'][str(f)] = dict(dim=len(B), b=[list(r) for r in B]) if len(B) <= len(A) else dict(dim=len(B), a=[list(r) for r in A])
+used = set(opframe)
+print('frames now', len(frames['frames']))
+for name in ('graph_p%d.json' % P, 'kchron_p%d.json' % P, 'profile_p%d.json' % P, 'sinks.json'):
+    (out / name).write_bytes((src / name).read_bytes())
+wj = json.dumps(w, sort_keys=True).encode(); fj = json.dumps(frames, sort_keys=True).encode()
+(out / ('word_p%d.json' % P)).write_bytes(wj); (out / ('word_p%d.json.gz' % P)).write_bytes(gzip.compress(wj, mtime=0))
+(out / ('frames_p%d.json' % P)).write_bytes(fj); (out / ('frames_p%d.json.gz' % P)).write_bytes(gzip.compress(fj, mtime=0))
+print('wrote', out)
diff --git a/research/five-stage-p10-transcript-stages/bitword/producer/make_physical.py b/research/five-stage-p10-transcript-stages/bitword/producer/make_physical.py
new file mode 100644
index 0000000000..87606a5384
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/producer/make_physical.py
@@ -0,0 +1,159 @@
+#!/usr/bin/env python3
+"""Physical layer producer for a raw paired-cube bit word (PR168 format): compensated late reuse pairs.
+
+Input dir: graph_pP.json word_pP.json frames_pP.json kchron_pP.json profile_pP.json (raw generator output, any
+cube size p; P is read from the single graph_pP.json present).
+Output dir: same names, word gains op_frame (= node frames unless --descent), pairs [[donor, recipient]],
+reads {recipient: absolute execution position}; frames/word also written gzipped for PR200's Candidate.
+
+Pair rules (PR200 bit/word.py + base_word.py): recipient gauged, read right before its first op; donor
+ungauged, non-root, non-source, last op strictly before that read; donor last op frame inside the recipient
+gauge frame; both nondegenerate; one-to-one; per-target gauge read times monotone along the nested chain.
+Recipients are gauges of rank h - 3 by default (rank 21 at p = 12, rank 17 at p = 10).
+--bank-parity: the 60-replica stage-private banks of width m = 5h need 60 * (total residual width) to be a
+multiple of m. Trailing pairs are dropped until it is (at most one pair, and only for odd width, at p = 12).
+p = 10 port (h-generic recipients, residual widths and bank divisibility, p-generic file names):
+DreamingOfClouds with Anthropic Claude assistance.
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+import argparse, gzip, json, sys, importlib.util, time
+from collections import defaultdict, Counter
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+CHK = HERE.parent / 'references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py'
+
+
+def load(name, path):
+    spec = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(spec); spec.loader.exec_module(m); return m
+
+
+def hopcroft_karp(adj, nleft):
+    INF = 1 << 30
+    matchL = [-1] * nleft; matchR = {}
+    from collections import deque
+    while True:
+        dist = [INF] * nleft; q = deque()
+        for u in range(nleft):
+            if matchL[u] < 0: dist[u] = 0; q.append(u)
+        found = False
+        while q:
+            u = q.popleft()
+            for w in adj[u]:
+                v2 = matchR.get(w, -1)
+                if v2 < 0: found = True
+                elif dist[v2] == INF: dist[v2] = dist[u] + 1; q.append(v2)
+        if not found: break
+        sys.setrecursionlimit(100000)
+        def dfs(u):
+            for w in adj[u]:
+                v2 = matchR.get(w, -1)
+                if v2 < 0 or (dist[v2] == dist[u] + 1 and dfs(v2)):
+                    matchL[u] = w; matchR[w] = u; return True
+            dist[u] = INF; return False
+        for u in range(nleft):
+            if matchL[u] < 0: dfs(u)
+    return matchL
+
+
+def main():
+    ap = argparse.ArgumentParser()
+    ap.add_argument('--src', required=True); ap.add_argument('--out', required=True)
+    ap.add_argument('--ranks', default='', help='gauge dims allowed as recipients, comma list')
+    ap.add_argument('--bank-parity', action='store_true', help='drop trailing pairs until the 60-replica bank width is a multiple of m = 5h')
+    a = ap.parse_args()
+    src, out = Path(a.src), Path(a.out); out.mkdir(parents=True, exist_ok=True)
+    mod = load('chk', CHK)
+    graphs = sorted(src.glob('graph_p*.json')); assert len(graphs) == 1, 'one raw word'
+    P = int(graphs[0].name[len('graph_p'):-len('.json')])
+    C = mod.Checker(src, P)
+    assert C.h == 2 * P and C.g['p'] == P
+    C.frames(); C.decoder(); C.geometry()
+    g, w = C.g, C.w
+    ops = w['ops']; v = g['v']
+    R = 1 + max(max(x, y) for x, y, _ in ops)
+    nf = {int(k): f for k, f in w['node_frame'].items()}
+    opframe = [nf[n] for _, _, n in ops]
+    phase1 = sorted(w['phase1']); ph = set(phase1)
+    rest = [i for i in range(len(ops)) if i not in ph]
+    pos = {i: p for p, i in enumerate(rest)}
+    role_ops = defaultdict(list)
+    for i in phase1 + rest:
+        for s in ops[i][:2]: role_ops[s].append(i)
+    assert all(xs == sorted(xs) for xs in role_ops.values())
+    first = {s: pos.get(xs[0], -1) for s, xs in role_ops.items()}
+    last = {s: pos.get(xs[-1], -1) for s, xs in role_ops.items()}
+    endframe = {s: opframe[xs[-1]] for s, xs in role_ops.items()}
+    gauge = {z['role']: z for z in w['gauges']}
+    roots = set(w['rootroles']); sources = set(w['sources'].values())
+    allowed = {int(x) for x in a.ranks.split(',')} if a.ranks else {C.h - 3}
+    # per-target chain order of gauges (time order = reversed selection order)
+    chain = defaultdict(list)
+    for z in reversed(w['gauges']):
+        for t in z['targets']: chain[t].append(z['role'])
+    # recipients: allowed dims; a recipient must be the LAST gauge of each of its targets' chains unless
+    # every later gauge on that target is also a recipient (resolved iteratively below: start with tops)
+    recips = [b for b in gauge if gauge[b]['dim'] in allowed]
+    def ok(b):
+        fb = gauge[b]['frame']
+        for t in gauge[b]['targets']:
+            later = chain[t][chain[t].index(b) + 1:]
+            if any(not (C.sub(gauge[x]['frame'], fb) and C.sub(fb, gauge[x]['frame'])) for x in later): return False
+        return True
+    recips = [b for b in recips if ok(b)]
+    donors = [s for s in range(R) if s not in gauge and s not in roots and s not in sources and s in role_ops]
+    print('roles', R, 'gauges', len(gauge), 'recipient candidates', len(recips), 'donor candidates', len(donors), flush=True)
+    t0 = time.time()
+    nd_cache = {}
+    def nondeg(f):
+        r = nd_cache.get(f)
+        if r is None: r = nd_cache[f] = C.nondeg(f)
+        return r
+    # group donors by end frame to share containment tests
+    by_frame = defaultdict(list)
+    for d in donors:
+        if nondeg(endframe[d]): by_frame[endframe[d]].append(d)
+    print('donor end frames', len(by_frame), 'nondeg donors', sum(map(len, by_frame.values())), flush=True)
+    adj = []
+    for b in recips:
+        gb = gauge[b]['frame']; rt = first[b]
+        lst = []
+        if nondeg(gb):
+            for f, ds in by_frame.items():
+                if C.dimf[f] > C.dimf[gb]: continue
+                cand = [d for d in ds if last[d] < rt]
+                if cand and C.sub(f, gb): lst.extend(cand)
+        adj.append(lst)
+    print('edges', sum(map(len, adj)), 'recipients with an edge', sum(1 for x in adj if x), 'secs', round(time.time() - t0, 1), flush=True)
+    m = hopcroft_karp(adj, len(recips))
+    pairs = [[m[i], b] for i, b in enumerate(recips) if m[i] >= 0]
+    if a.bank_parity:
+        # residual family widths: h - dim for non-recipient gauges, h for every other physical role
+        M, REPLICAS = 5 * C.h, 60
+        def width():
+            matched = {b for _, b in pairs}
+            return sum(C.h - gauge[g]['dim'] for g in gauge if g not in matched) + C.h * (R - len(pairs) - (len(gauge) - len(matched)))
+        for _ in range(M):
+            if REPLICAS * width() % M == 0: break
+            # dropping a pair returns its recipient (rank d) to the entrances as a residual family of width h - d;
+            # the donor stays a plain helper, so the total width grows by h - d (3 for the default rank h - 3)
+            dropped = pairs.pop()
+            print('bank divisibility: dropped pair', dropped, 'width', width(), flush=True)
+        assert REPLICAS * width() % M == 0, 'bank divisibility not restored'
+    print('pairs', len(pairs), flush=True)
+    reads = {str(b): len(phase1) + first[b] for d, b in pairs}
+    W = dict(w); W['op_frame'] = opframe; W['pairs'] = pairs; W['reads'] = reads
+    W['descent'] = 'none: op_frame[i] = node_frame[ops[i][2]]'
+    W['reuse'] = 'late compensated reuse: recipient slot is the donor register; recipient old-value read right before its first op, after the donor last op'
+    for name in ('graph', 'frames', 'kchron', 'profile'):
+        (out / ('%s_p%d.json' % (name, P))).write_text((src / ('%s_p%d.json' % (name, P))).read_text())
+    (out / ('word_p%d.json' % P)).write_text(json.dumps(W, sort_keys=True))
+    for name in ('word', 'frames'):
+        raw = (out / ('%s_p%d.json' % (name, P))).read_bytes()
+        (out / ('%s_p%d.json.gz' % (name, P))).write_bytes(gzip.compress(raw, mtime=0))
+    (out / 'sinks.json').write_text('[]')
+    print(json.dumps(dict(pairs=len(pairs), physical_R=R - len(pairs), dims=Counter(gauge[b]['dim'] for _, b in pairs))))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/five-stage-p10-transcript-stages/bitword/producer/paired_cube_bit_word.py b/research/five-stage-p10-transcript-stages/bitword/producer/paired_cube_bit_word.py
new file mode 100644
index 0000000000..3a709d6272
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/producer/paired_cube_bit_word.py
@@ -0,0 +1,1002 @@
+#!/usr/bin/env python3
+# Modified copy of eumemic's PR168 paired-cube bit generator (research/paired-cube-bit/paired_cube_bit_word.py
+# as integrated on main; Apache-2.0). Changes for gen4 (DreamingOfClouds, with Anthropic Claude assistance):
+# local_design() recipe-tree local channels read from data/local_design_p12.json; the centre-sharing pair
+# module patch in finish() (the pair module's extra root is the copied centre star); build() reads the
+# optional design file. New data: local_design_p12.json, pair_module_p12.json, qmod_p12.json, arcs_p12.json.
+# The rest of the generator, its compiler and its ledger are unchanged.
+# gen5 (DreamingOfClouds, with Anthropic Claude assistance) changes only the data: new pair_module_p12.json,
+# qmod_p12.json and arcs_p12.json; this file is byte-identical to #276's apart from these two comment lines.
+# p = 10 port (DreamingOfClouds, with Anthropic Claude assistance): MODULES/QMODULES gain the p = 10 entries
+# pm_p10.json and qmod_p10.json, and the variant-u output merge is on at p = 10 as at p = 12 (build()). The
+# cube-local design is read from data/local_design_p10.json. p = 12 behaviour is unchanged.
+"""Paired-cube BIT local word with partner-pair source mixing: deterministic generator and rank compiler.
+
+Ports are the triples of [h] (h = 2p) taking one coordinate from each of three distinct coordinate pairs
+(v = 8*C(p,3)); bit labels chi_S in Q^h with H0 = (I - J/9)/2, so H0(chi_S, chi_T) = (|S cap T| - 1)/2.
+Payload F2. Mod-2 decoder, for every target T:
+    x_T = sum_{c in T} star(c)                         (2p copied point-star centres, frames of dim h-2)
+        + face channels  P'(J,i,eta_i)                  (cubes sharing exactly pair i, matching selector)
+        + edge channels  Q'(J,i,j,mode)                 (cubes sharing pairs i,j, exactly one selector match)
+        + partner        x_{T'}, T' = T with the selectors of cube pairs 1,2 flipped (single-source root)
+        + partner-pair sum of the opposite pair of T's parity class, mixed on two SOURCE registers and
+          delivered at the shared cap of {T, T'} (no auxiliary role).
+At p = 12 each cube merges its face-1 and edge-01 outputs into u(b0,b1) and its face-2 and edge-02 outputs into
+w(b0,b2) (variant u); each merged node is read by two single roots and the mod-2 sums are unchanged. Its local
+channels use the L1 association (local_l1): three of the six G sums add long face diagonals instead of edges.
+Its all-but-one modules are the pinned annealed module data/qmod_p12.json (pinned_all_but_one).
+Compiler: the PR #144 frames.py/gauges.py ledger on rational frames (target cap ker(3 chi_T - 1), centre frame =
+span of the star), coordinate-padded maximum carrier matching (frozen arcs), plain frames span(n) for additions of
+span dimension <= PLAIN (closed under operands; a linked donor's span must lie in the plain target), PR #144
+chronological partial gauges with a G-nondegeneracy filter, PR #144 bit ledger (m = 3h, W = 2v + R).
+Linear algebra is exact: ranks are computed modulo the Mersenne prime 2^127-1, which exceeds the Hadamard bound
+of every minor that occurs (see README.md); G-nondegeneracy is certified by integer Gram determinants.
+
+Usage: python3 paired_cube_bit_word.py --p 12 [--out DIR] [--check] [--solve-matching]
+Standard library only. Run without -O.
+"""
+import argparse, gzip, hashlib, json, math, os, sys, time
+from collections import Counter, defaultdict, deque
+from itertools import combinations, product
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P = (1 << 127) - 1
+PLAIN = 8
+L1_DIAGONAL = {(0, 1, 0), (0, 1, 1), (1, 2, 1)}  # (cube positions j < k, mode) of the diagonal G sums at p = 12
+MODULES = {10: 'pm_p10.json', 11: 'pair_module_p11.json', 12: 'pair_module_p12.json', 13: 'pair_module_p13.json'}
+QMODULES = {10: 'qmod_p10.json', 12: 'qmod_p12.json'}
+MERGE = (10, 12)  # cube sizes using the variant-u output merge (p = 10 port)
+
+
+def require(cond, msg):
+    if not cond:
+        raise SystemExit('FAIL: ' + msg)
+
+
+# ----------------------------------------------------------------------------- exact subspaces of F_P^h
+def rref(rows, h):
+    piv = {}
+    for r in rows:
+        x = [a % P for a in r]
+        for c, y in piv.items():
+            if x[c]:
+                f = x[c]
+                x = [(a - f * b) % P for a, b in zip(x, y)]
+        nz = next((j for j in range(h) if x[j]), None)
+        if nz is None:
+            continue
+        inv = pow(x[nz], P - 2, P)
+        x = [(a * inv) % P for a in x]
+        for c in list(piv):
+            y = piv[c]
+            if y[nz]:
+                f = y[nz]
+                piv[c] = [(a - f * b) % P for a, b in zip(y, x)]
+        piv[nz] = x
+    return tuple(tuple(piv[c]) for c in sorted(piv))
+
+
+def kernel(S, h):
+    pivs = [next(j for j in range(h) if row[j]) for row in S]
+    ps = set(pivs)
+    out = []
+    for f in range(h):
+        if f in ps:
+            continue
+        u = [0] * h
+        u[f] = 1
+        for row, c in zip(S, pivs):
+            u[c] = (-row[f]) % P
+        out.append(u)
+    return rref(out, h)
+
+
+class Table:
+    """Interned subspaces (canonical RREF) with memoized joins; id 0 is the zero space."""
+    def __init__(self, h):
+        self.h = h
+        self.rows = [()]
+        self.index = {(): 0}
+        self.jc = {}
+        self.pc = {}
+
+    def intern(self, rows):
+        S = rref(rows, self.h)
+        i = self.index.get(S)
+        if i is None:
+            i = len(self.rows)
+            self.rows.append(S)
+            self.index[S] = i
+        return i
+
+    def dim(self, i):
+        return len(self.rows[i])
+
+    def join(self, i, j):
+        if i == j or j == 0:
+            return i
+        if i == 0:
+            return j
+        if i > j:
+            i, j = j, i
+        k = self.jc.get((i, j))
+        if k is None:
+            A, B = self.rows[i], self.rows[j]
+            k = i if len(A) == self.h else j if len(B) == self.h else self.intern(A + B)
+            self.jc[(i, j)] = k
+        return k
+
+    def join_many(self, ids):
+        k = 0
+        for i in ids:
+            k = self.join(k, i)
+        return k
+
+    def contained(self, i, j):
+        return self.join(i, j) == j
+
+    def perp(self, i):
+        k = self.pc.get(i)
+        if k is None:
+            k = self.intern(kernel(self.rows[i], self.h))
+            self.pc[i] = k
+        return k
+
+
+class Geometry:
+    """Bit geometry: source line <chi_S>; target cap annihilated by 3 chi_T - 1 (the H0 = (I-J/9)/2 cap)."""
+    def __init__(self, h, labels):
+        self.h = h
+        self.T = Table(h)
+        self.src = [self.T.intern([[1 if j in lab else 0 for j in range(h)]]) for lab in labels]
+        self.tcov = [self.T.intern([[(3 if j in lab else 0) - 1 for j in range(h)]]) for lab in labels]
+        self.coord = [self.T.intern([[1 if k == j else 0 for k in range(h)]]) for j in range(h)]
+
+    def join(self, a, b): return self.T.join(a, b)
+    def join_many(self, ids): return self.T.join_many(ids)
+    def dim(self, a): return self.T.dim(a)
+    def perp(self, a): return self.T.perp(a)
+    def contained(self, a, b): return self.T.contained(a, b)
+
+
+def gram_nondegenerate_frame(rows, h):
+    """G = I - J/9 nondegenerate on the F_P-subspace with basis rows (exact sound test: an integer determinant
+    nonzero mod P is nonzero over Q; frames here are reductions of rational frames of the same dimension)."""
+    k = len(rows)
+    if k == 0:
+        return True
+    inv9 = pow(9, P - 2, P)
+    sums = [sum(s) % P for s in rows]
+    M = [[(sum(a * b for a, b in zip(rows[i], rows[j])) - inv9 * sums[i] * sums[j]) % P for j in range(k)] for i in range(k)]
+    return len(rref(M, k)) == k
+
+
+# ----------------------------------------------------------------------------- graph
+class BitGraph:
+    def __init__(self, p):
+        self.p, self.h = p, 2 * p
+        self.cubes = list(combinations(range(p), 3))
+        self.labels = [tuple(2 * i + b for i, b in zip(I, bits)) for I in self.cubes for bits in product(range(2), repeat=3)]
+        self.a = [None] * len(self.labels)
+        self.s = [1 << i for i in range(len(self.labels))]
+        self.intern = {}
+        self.source = {(I, bits): 8 * j + k for j, I in enumerate(self.cubes) for k, bits in enumerate(product(range(2), repeat=3))}
+        self.A, self.G = {}, {}
+        self.root, self.centers, self.mix = [], [], []
+
+    def add(self, a, b):
+        if a is None:
+            return b
+        if b is None:
+            return a
+        if a > b:
+            a, b = b, a
+        if (a, b) not in self.intern:
+            require(not self.s[a] & self.s[b], 'support-disjoint addition')
+            self.intern[a, b] = len(self.a)
+            self.a.append([a, b])
+            self.s.append(self.s[a] | self.s[b])
+        return self.intern[a, b]
+
+    def sum(self, xs):
+        xs = [x for x in xs if x is not None]
+        while len(xs) > 1:
+            xs = [self.add(xs[i], xs[i + 1]) if i + 1 < len(xs) else xs[i] for i in range(0, len(xs), 2)]
+        return xs[0] if xs else None
+
+    def module(self, data, inputs):
+        image = list(inputs)
+        n = data['input_count']
+        require(len(image) == n, 'module arity')
+        for pair in data['args'][n:]:
+            image.append(self.add(image[pair[0]], image[pair[1]]))
+        return [image[x] for x in data['roots']]
+
+    def local_channels(self):
+        for I in self.cubes:
+            src = lambda bits: self.source[I, tuple(bits)]
+            edges = {}
+            for ii, jj in combinations(range(3), 2):
+                kk = 3 - ii - jj
+                for a, b in product(range(2), repeat=2):
+                    b0 = [0] * 3
+                    b0[ii], b0[jj] = a, b
+                    b1 = b0[:]
+                    b1[kk] = 1
+                    edges[ii, jj, a, b] = self.add(src(b0), src(b1))
+                self.G[I, I[ii], I[jj], 0] = self.add(edges[ii, jj, 0, 0], edges[ii, jj, 1, 1])
+                self.G[I, I[ii], I[jj], 1] = self.add(edges[ii, jj, 0, 1], edges[ii, jj, 1, 0])
+            for ii in range(3):
+                jj = next(j for j in range(3) if j != ii)
+                for a in range(2):
+                    ids = [edges[(ii, jj, a, b) if ii < jj else (jj, ii, b, a)] for b in range(2)]
+                    self.A[I, I[ii], a] = self.add(*ids)
+
+    def local_l1(self):
+        """L1 local-channel association (eumemic, Claude assistance): the G sums listed in L1_DIAGONAL add the two
+        long diagonals of their cube face, the other G sums and the A sums add two edges; same supports as
+        local_channels, with the nodes created in channel order."""
+        for I in self.cubes:
+            def at(bits):
+                b = [0] * 3
+                for q, x in bits.items():
+                    b[q] = x
+                return self.source[I, tuple(b)]
+
+            def edge(d, fixed):
+                return self.add(at({**fixed, d: 0}), at({**fixed, d: 1}))
+            for j, k in combinations(range(3), 2):
+                r = 3 - j - k
+                for mode in range(2):
+                    if (j, k, mode) in L1_DIAGONAL:
+                        node = self.add(self.add(at({j: 0, k: mode, r: 0}), at({j: 1, k: 1 - mode, r: 1})),
+                                        self.add(at({j: 0, k: mode, r: 1}), at({j: 1, k: 1 - mode, r: 0})))
+                    else:
+                        node = self.add(edge(r, {j: 0, k: mode}), edge(r, {j: 1, k: 1 - mode}))
+                    self.G[I, I[j], I[k], mode] = node
+            for i in range(3):
+                j, k = [q for q in range(3) if q != i]
+                for a in range(2):
+                    self.A[I, I[i], a] = self.add(edge(k, {i: a, j: 0}), edge(k, {i: a, j: 1}))
+
+    def local_design(self, design):
+        """Design-driven local channels (agent-helpers search): every plane channel of every cube is built by the
+        recipe tree of `design` (a list of [plane key, tree] in creation order; a plane key is ['A', i, a] for the
+        sources with selector a at cube position i, or ['G', j, k, m] for the sources with s_j ^ s_k = m; a tree is a
+        3-bit selector (leaf) or a pair of trees).  Equal supports must have equal recipes (checked)."""
+        def members(key):
+            allb = list(product(range(2), repeat=3))
+            if key[0] == 'A':
+                return {b for b in allb if b[key[1]] == key[2]}
+            return {b for b in allb if b[key[1]] ^ b[key[2]] == key[3]}
+        for I in self.cubes:
+            def build(t):
+                if isinstance(t[0], int):
+                    return self.source[I, tuple(t)], {tuple(t)}
+                (a, sa), (b, sb) = build(t[0]), build(t[1])
+                require(not sa & sb, 'design support-disjoint')
+                return self.add(a, b), sa | sb
+            for key, tree in design:
+                node, sup = build(tree)
+                require(sup == members(key), 'design plane support')
+                if key[0] == 'A':
+                    self.A[I, I[key[1]], key[2]] = node
+                else:
+                    self.G[I, I[key[1]], I[key[2]], key[3]] = node
+
+    def finish(self, pair, allbut, merge=False, l1=False, design=None):
+        p = self.p
+        if design is not None:
+            self.local_design(design)
+        else:
+            self.local_l1() if l1 else self.local_channels()
+        Pm, Qm = {}, {}
+        cen = {}
+        for i in range(p):
+            pairs = list(combinations([a for a in range(p) if a != i], 2))
+            for bit in range(2):
+                outs = self.module(pair, [self.A[tuple(sorted((i, *K))), i, bit] for K in pairs])
+                for K, node in zip(pairs, outs):
+                    Pm[tuple(sorted((i, *K))), i, bit] = node
+                if len(outs) == len(pairs) + 1:
+                    # centre-sharing pair module (agent-helpers): the extra root sums all inputs = star(2i+bit)
+                    cen[2 * i + bit] = outs[-1]
+        for i, j in combinations(range(p), 2):
+            others = [a for a in range(p) if a not in (i, j)]
+            for mode in range(2):
+                for k, node in zip(others, self.module(allbut, [self.G[tuple(sorted((i, j, k))), i, j, mode] for k in others])):
+                    Qm[tuple(sorted((i, j, k))), i, j, mode] = node
+        allb = list(product(range(2), repeat=3))
+
+        def emit(I, bl, node, channel):
+            self.root.append(dict(node=node, targets=[self.source[I, b] for b in bl], kind='side', channel=channel))
+        for I in self.cubes:
+            for a in range(2):
+                emit(I, [b for b in allb if b[0] == a], Pm[I, I[0], a], 'face0')
+            for a in range(2):
+                for m12 in range(2):
+                    emit(I, [b for b in allb if b[0] == a and (b[1] ^ b[2]) == m12], Qm[I, I[1], I[2], 1 - m12], 'edge12')
+            if merge:
+                # variant u output merge (eumemic, Claude assistance): u(b0,b1) = face1 + edge01 and
+                # w(b0,b2) = face2 + edge02, each read by two single roots, replace the four single reads
+                u = {(b0, b1): self.add(Pm[I, I[1], b1], Qm[I, I[0], I[1], 1 - (b0 ^ b1)]) for b0 in range(2) for b1 in range(2)}
+                w = {(b0, b2): self.add(Pm[I, I[2], b2], Qm[I, I[0], I[2], 1 - (b0 ^ b2)]) for b0 in range(2) for b2 in range(2)}
+            for b in allb:
+                if merge:
+                    emit(I, [b], u[b[0], b[1]], 'u01')
+                    emit(I, [b], w[b[0], b[2]], 'w02')
+                else:
+                    emit(I, [b], Pm[I, I[1], b[1]], 'face1')
+                    emit(I, [b], Qm[I, I[0], I[1], 1 - (b[0] ^ b[1])], 'edge01')
+                    emit(I, [b], Pm[I, I[2], b[2]], 'face2')
+                    emit(I, [b], Qm[I, I[0], I[2], 1 - (b[0] ^ b[2])], 'edge02')
+                emit(I, [b], self.source[I, (b[0], 1 - b[1], 1 - b[2])], 'partner')
+            # partner-pair source mixing: in each parity class the pair with selector a on cube pair 0
+            # (carrier = smaller bits, passive = its partner) is delivered to the opposite pair of the class.
+            for par in range(2):
+                for a in range(2):
+                    pair_ = sorted(b for b in allb if sum(b) % 2 == par and b[0] == a)
+                    recv = sorted(b for b in allb if sum(b) % 2 == par and b[0] == 1 - a)
+                    self.mix.append(dict(carrier=self.source[I, pair_[0]], passive=self.source[I, pair_[1]],
+                                         receivers=[self.source[I, r] for r in recv]))
+        for i in range(p):
+            for e in range(2):
+                if 2 * i + e in cen:
+                    self.centers.append(cen[2 * i + e])
+                else:
+                    self.centers.append(self.sum(self.A[I, i, e] for I in self.cubes if i in I))
+        for coordinate, node in enumerate(self.centers):
+            self.root.append(dict(node=node, targets=[t for t, lab in enumerate(self.labels) if coordinate in lab],
+                                  kind='center', coordinate=coordinate))
+        return dict(p=p, h=self.h, v=len(self.labels), labels=[list(l) for l in self.labels], args=self.a,
+                    roots=self.root, partner_mix=self.mix)
+
+
+def check_decoder(g):
+    v, args = g['v'], g['args']
+    sup = [1 << i for i in range(v)] + [0] * (len(args) - v)
+    for x in range(v, len(args)):
+        a, b = args[x]
+        require(not sup[a] & sup[b], 'disjoint supports')
+        sup[x] = sup[a] | sup[b]
+    acc = [0] * v
+    for r in g['roots']:
+        for t in r['targets']:
+            acc[t] ^= sup[r['node']]
+    for mx in g['partner_mix']:
+        for t in mx['receivers']:
+            acc[t] ^= (1 << mx['carrier']) | (1 << mx['passive'])
+    return sum(acc[t] != 1 << t for t in range(v))
+
+
+# ----------------------------------------------------------------------------- matching
+def hopcroft_karp(adj, nleft, nright):
+    INF = 1 << 30
+    mL, mR = [-1] * nleft, [-1] * nright
+    while True:
+        dist = [INF] * nleft
+        dq = deque(u for u in range(nleft) if mL[u] < 0)
+        for u in dq:
+            dist[u] = 0
+        found = False
+        while dq:
+            u = dq.popleft()
+            for w in adj[u]:
+                m = mR[w]
+                if m < 0:
+                    found = True
+                elif dist[m] == INF:
+                    dist[m] = dist[u] + 1
+                    dq.append(m)
+        if not found:
+            return mL
+        it = [0] * nleft
+        for u0 in range(nleft):
+            if mL[u0] >= 0:
+                continue
+            stack = [u0]
+            while stack:
+                u = stack[-1]
+                if it[u] < len(adj[u]):
+                    w = adj[u][it[u]]
+                    it[u] += 1
+                    m = mR[w]
+                    if m < 0:
+                        ws = w
+                        for uu in reversed(stack):
+                            prev = mL[uu]
+                            mL[uu], mR[ws] = ws, uu
+                            ws = prev
+                        break
+                    if dist[m] == dist[u] + 1:
+                        stack.append(m)
+                else:
+                    dist[u] = INF
+                    stack.pop()
+
+
+# ----------------------------------------------------------------------------- compiler
+def compile_word(g, frozen=None, plain_k=PLAIN, log=lambda *a: None):
+    h, v = g['h'], g['v']
+    geo = Geometry(h, [tuple(l) for l in g['labels']])
+    args = [None] + [None if a is None else [x + 1 for x in a] for a in g['args']]  # node 0 reserved
+    roots = [dict(r, node=r['node'] + 1) for r in g['roots']]
+    n, q = len(args), len(roots)
+    sup = [0] * n
+    for i in range(v):
+        sup[i + 1] = 1 << i
+    spans = [0] * n
+    for i in range(v):
+        spans[i + 1] = geo.src[i]
+    for x in range(v + 1, n):
+        a, b = args[x]
+        spans[x] = geo.join(spans[a], spans[b])
+        sup[x] = sup[a] | sup[b]
+    rframe, rann, ell = [], [], 0
+    Y, targetH = [0] * v, Counter()
+    for r in roots:
+        x = r['node']
+        if r['kind'] == 'center':
+            U = spans[x]; A = geo.perp(U); ell += geo.dim(U)
+        else:
+            A = geo.join_many(geo.tcov[t] for t in r['targets']); U = geo.perp(A)
+            for t in r['targets']:
+                require(geo.contained(Y[t], U), 'target retreat')
+                targetH[geo.dim(U) - geo.dim(Y[t])] += 1
+                Y[t] = U
+        require(geo.contained(spans[x], U), 'root physical compatibility')
+        rframe.append(U); rann.append(A)
+    for t in range(v):
+        require(geo.contained(Y[t], geo.perp(geo.tcov[t])), 'target cap')
+        targetH[h - 1 - geo.dim(Y[t])] += 1
+    active, todo = set(range(1, v + 1)), [r['node'] for r in roots]
+    while todo:
+        x = todo.pop()
+        if x not in active:
+            active.add(x)
+            if args[x]:
+                todo.extend(args[x])
+    succ0, cons = [[] for _ in args], [[] for _ in args]
+    for x in sorted(active):
+        if args[x]:
+            for y in args[x]:
+                succ0[y].append(x)
+    for j, r in enumerate(roots):
+        cons[r['node']].append(rann[j])
+    preann, initial = [0] * n, [0] * n
+    for x in sorted(active, reverse=True):
+        preann[x] = geo.join_many(cons[x] + [preann[y] for y in succ0[x]])
+        cover = 0
+        s = sup[x]
+        while s:
+            b = s & -s; s ^= b
+            for j in g['labels'][b.bit_length() - 1]:
+                cover |= 1 << j
+        initial[x] = geo.join_many([preann[x]] + [geo.coord[j] for j in range(h) if not cover >> j & 1])
+    order = sorted(active, key=lambda x: (h - geo.dim(initial[x]), x))
+    position = {x: i for i, x in enumerate(order)}
+    uses, usevalue, usetarget, useann, usecode = [[] for _ in args], [], [], [], []
+    for x in order:
+        if args[x]:
+            for j, y in enumerate(args[x]):
+                uses[y].append(len(usevalue)); usevalue.append(y); usetarget.append(x); useann.append(initial[x]); usecode.append(['op', x - 1, j])
+    for j, r in enumerate(roots):
+        x = r['node']
+        uses[x].append(len(usevalue)); usevalue.append(x); usetarget.append(n + j); useann.append(rann[j]); usecode.append(['root', j])
+    donors = [x for x in order if args[x]]
+    code_index = {tuple(c): u for u, c in enumerate(usecode)}
+    if frozen is not None:
+        arcs = {d + 1: code_index[tuple(c)] for d, c in frozen}
+    else:
+        dindex = {x: i for i, x in enumerate(donors)}
+        adj = [[] for _ in donors]
+        for x in donors:
+            for y in args[x]:
+                for u in uses[y]:
+                    t = usetarget[u]
+                    if t == x or (t < n and position[t] <= position[x]):
+                        continue
+                    if geo.contained(useann[u], initial[x]):
+                        adj[dindex[x]].append(u)
+        mL = hopcroft_karp(adj, len(donors), len(usevalue))
+        arcs = {donors[i]: u for i, u in enumerate(mL) if u >= 0}
+    for x, u in arcs.items():
+        t = usetarget[u]
+        require(usevalue[u] in args[x] and (t >= n or position[t] > position[x]), 'arc order')
+        require(geo.contained(useann[u], initial[x]), 'arc frame')
+    succ, direct = [[] for _ in args], [[] for _ in args]
+    for x in order:
+        if args[x]:
+            for y in args[x]:
+                succ[y].append(x)
+    for j, r in enumerate(roots):
+        direct[r['node']].append(rann[j])
+    for x, u in arcs.items():
+        t = usetarget[u]
+        (succ[x].append(t) if t < n else direct[x].append(rann[t - n]))
+    ann, rank = [0] * n, [0] * n
+    for x in reversed(order):
+        ann[x] = geo.join_many(direct[x] + [ann[y] for y in succ[x]])
+        rank[x] = h - geo.dim(ann[x])
+        require(geo.contained(ann[x], geo.perp(spans[x])), 'span inside frame')
+    # plain frames span(n): leaves and small additions, closed under operands; a linked donor must be plain and
+    # its span must lie in the plain target's span
+    cand = set(x for x in active if not args[x])
+    for x in sorted(active):
+        if args[x] and geo.dim(spans[x]) <= plain_k and all(y in cand for y in args[x]):
+            cand.add(x)
+    arcin, users = defaultdict(list), defaultdict(list)
+    for x, u in arcs.items():
+        if usetarget[u] < n:
+            arcin[usetarget[u]].append(x)
+    for x in active:
+        if args[x]:
+            for y in args[x]:
+                users[y].append(x)
+    changed = True
+    while changed:
+        changed = False
+        for t in sorted(cand):
+            if t in cand and any(x not in cand or not geo.contained(spans[x], spans[t]) for x in arcin[t]):
+                cand.discard(t); changed = True
+                st = [t]
+                while st:
+                    z = st.pop()
+                    for w in users[z]:
+                        if w in cand:
+                            cand.discard(w); st.append(w)
+    plain = sorted(cand)
+    for x in plain:
+        ann[x] = geo.perp(spans[x]); rank[x] = h - geo.dim(ann[x])
+    H = Counter()
+    for x in order:
+        r, deg = rank[x], len(uses[x])
+        require(deg > 0, 'unused node')
+        H[r] += deg - 1
+        if args[x]:
+            H[h - r] += 1
+            for y in args[x]:
+                require(geo.contained(ann[x], ann[y]), 'operand nesting')
+                H[r - rank[y]] += 1
+        else:
+            H[1] += 1; H[r - 1] += 1
+    for j, root in enumerate(roots):
+        x = root['node']; r = rank[x]; rt = geo.dim(rframe[j])
+        require(r <= rt, 'root climb')
+        if root['kind'] == 'center':
+            require(r == rt, 'centre frame')
+            H[r] += 1; H[h - r] += 1
+        else:
+            H[rt - r] += 1; H[h - rt] += 1
+    for x, u in arcs.items():
+        val, t = usevalue[u], usetarget[u]
+        rv, rd = rank[val], rank[x]
+        rt = rank[t] if t < n else geo.dim(rframe[t - n])
+        require(rt >= rd >= rv, 'arc ranks')
+        H[h - rd] -= 1; H[rv] -= 1; H[rt - rv] -= 1; H[rt - rd] += 1
+    require(min(H.values()) >= 0, 'nonnegative ledger')
+    R = len(donors) + q - len(arcs)
+    require(sum(r * c for r, c in H.items()) == h * R + ell, 'mass identity')
+    prof = dict(h=h, v=v, R=R, q=q, c=len(donors), matched=len(arcs), loss=ell, plain=len(plain))
+    wit = dict(geo=geo, args=args, roots=roots, n=n, order=order, arcs=arcs, ann=ann, rank=rank, uses=uses,
+               usevalue=usevalue, usetarget=usetarget, usecode=usecode, rframe=rframe, rann=rann, spans=spans,
+               plain=plain, H=H, targetH=targetH)
+    return prof, wit
+
+
+def nondeg_id(geo, f, cache):
+    if f not in cache:
+        cache[f] = gram_nondegenerate_frame(list(geo.T.rows[f]), geo.h)
+    return cache[f]
+
+
+def select_gauges(g, prof, wit, trial_a=0.00065):
+    """PR #144 gauges.select, exactly, plus the bit G-nondegeneracy filter on sigma."""
+    geo = wit['geo']; h, v = prof['h'], prof['v']
+    args, roots, n, order, ann, arcs = wit['args'], wit['roots'], wit['n'], wit['order'], wit['ann'], wit['arcs']
+    usevalue, usetarget = wit['usevalue'], wit['usetarget']
+    incoming = set(arcs.values())
+    uses, opuse, rootuse = [[] for _ in args], {}, {}
+    for u, (val, t) in enumerate(zip(usevalue, usetarget)):
+        uses[val].append(u)
+        if t < n:
+            opuse[t, 0 if args[t][0] == val else 1] = u
+        else:
+            rootuse[t - n] = u
+    assign, sources, ops, R = {}, {}, [], 0
+    for x in order:
+        if args[x]:
+            aa, bb = args[x]
+            dest, control = assign[opuse[x, 0]], assign[opuse[x, 1]]
+            if x in arcs:
+                u = arcs[x]
+                if usevalue[u] == aa:
+                    dest, control = control, dest
+                require(u not in assign, 'arc use assigned once')
+                assign[u] = control
+            ops.append((dest, control, x))
+        else:
+            dest = R; R += 1; sources[x] = dest
+        free = [u for u in uses[x] if u not in incoming]
+        require(free, 'free use')
+        for j, u in enumerate(free):
+            if j == 0:
+                assign[u] = dest
+            else:
+                t = R; R += 1; assign[u] = t; ops.append((t, dest, x))
+    require(R == prof['R'], 'role count')
+    rootroles = [assign[rootuse[j]] for j in range(len(roots))]
+    prev, pred, first = [-1] * R, [], [None] * R
+    for i, (a, b, x) in enumerate(ops):
+        pred.append((prev[a], prev[b])); prev[a] = prev[b] = i
+        if first[a] is None:
+            first[a] = x
+        if first[b] is None:
+            first[b] = x
+    stack = [prev[s] for r, s in zip(roots, rootroles) if r['kind'] == 'center' and prev[s] >= 0]
+    phase = set()
+    while stack:
+        i = stack.pop()
+        if i not in phase:
+            phase.add(i); stack.extend(j for j in pred[i] if j >= 0)
+    touched = set(sources.values())
+    for i in phase:
+        touched.update(ops[i][:2])
+    co = [0] * R
+    for r, s in zip(roots, rootroles):
+        co[s] |= sum(1 << t for t in r['targets'])
+    for a, b, x in reversed(ops):
+        co[b] |= co[a]
+    limit = [None] * v
+    for r in roots:
+        if r['kind'] != 'center':
+            A = geo.join_many(geo.tcov[t] for t in r['targets'])
+            for t in r['targets']:
+                if limit[t] is None:
+                    limit[t] = A
+    for t in range(v):
+        if limit[t] is None:
+            limit[t] = geo.tcov[t]
+    H = Counter(wit['H'])
+    gauges, selected, cache = Counter(), [], {}
+    cands = sorted((s for s in range(R) if s not in touched and first[s] is not None),
+                   key=lambda s: (geo.dim(ann[first[s]]), bin(co[s]).count('1'), s))
+
+    def excess(t):
+        return t * math.expm1(trial_a * math.log(3 * h / t)) if t else 0.
+    for s in cands:
+        A, targets, bits = ann[first[s]], [], co[s]
+        while bits:
+            low = bits & -bits; t = low.bit_length() - 1; bits ^= low; targets.append(t)
+            A = geo.join(A, limit[t])
+            if geo.dim(A) == h:
+                break
+        if geo.dim(A) == h:
+            continue
+        r, d = h - geo.dim(ann[first[s]]), h - geo.dim(A)
+        delta = 3 * (excess(r - d) - excess(r)) + excess(3 * d)
+        delta += 3 * math.fsum(excess(d) + excess(h - geo.dim(limit[t]) - d) - excess(h - geo.dim(limit[t])) for t in targets)
+        if delta >= -1e-12 or not nondeg_id(geo, geo.perp(A), cache):
+            continue
+        H[r] -= 1; H[r - d] += 1; gauges[d] += 1
+        require(H[r] >= 0, 'gauge ledger')
+        for t in targets:
+            limit[t] = A
+        selected.append(dict(role=s, first=first[s] - 1, targets=targets, dim=d, ann=A))
+    Yh, cur = Counter(), [0] * v
+    for z in reversed(selected):
+        U = geo.perp(z['ann'])
+        for t in z['targets']:
+            require(geo.contained(cur[t], U), 'gauge target chain')
+            Yh[geo.dim(U) - geo.dim(cur[t])] += 1; cur[t] = U
+    for r in roots:
+        if r['kind'] != 'center':
+            U = geo.perp(geo.join_many(geo.tcov[t] for t in r['targets']))
+            for t in r['targets']:
+                require(geo.contained(cur[t], U), 'side target chain')
+                Yh[geo.dim(U) - geo.dim(cur[t])] += 1; cur[t] = U
+    for t in range(v):
+        Yh[h - 1 - geo.dim(cur[t])] += 1
+    word = dict(ops=[[a, b, x - 1] for a, b, x in ops], sources={str(x - 1): s for x, s in sources.items()},
+                rootroles=rootroles, phase1=sorted(phase), gauges=[{k: z[k] for k in ('role', 'first', 'targets', 'dim')} for z in selected],
+                _gauge_ann=[z['ann'] for z in selected])
+    return gauges, H, Yh, word
+
+
+def profile(prof, gauges, H, Y):
+    h, v, R, ell = prof['h'], prof['v'], prof['R'], prof['loss']
+    m, W = 3 * h, 2 * v + R
+    source = Counter({1: v, h - 4: v // 2, 2: v // 2, h - 2: v // 2})
+    C = Counter()
+    for part in (H, source, Y):
+        for r, c in part.items():
+            if r and c:
+                C[r] += 3 * c
+    for d, c in gauges.items():
+        C[3 * d] += c
+    C[2] += 2 * v
+    mass = sum(r * c for r, c in C.items())
+    require(W * m - mass == 2 * v - 3 * ell, 'shared-core telescoping deficit')
+    srt = lambda c: {str(k): c[k] for k in sorted(c) if c[k]}
+    return dict(h=h, v=v, R=R, c=prof['c'], q=prof['q'], matched=prof['matched'], loss=ell, plain_frames=prof['plain'],
+                m=m, W_per_vertex=W, rank_per_vertex=mass, deficit_per_vertex=W * m - mass,
+                selected_roles=sum(gauges.values()), selected_rank_histogram=srt(gauges),
+                remaining_internal_histogram=srt(H), source_data_histogram=srt(source), target_data_histogram=srt(Y),
+                child_histogram=srt(C), maxchild=max(C))
+
+
+def float_root(child, W, m):
+    items = [(int(t), c) for t, c in child.items()]
+    lo, hi = 0., .1
+    for _ in range(80):
+        a = (lo + hi) / 2
+        if math.fsum(c * (t / m) ** (1 - a) for t, c in items) < W:
+            lo = a
+        else:
+            hi = a
+    return lo
+
+
+def ratrec(r):
+    """Rational reconstruction a/b of a residue mod P with |a|, b < sqrt(P/2)."""
+    r %= P
+    if r == 0:
+        return 0, 1
+    bound = math.isqrt(P // 2)
+    r0, r1, s0, s1 = P, r, 0, 1
+    while r1 > bound:
+        qq = r0 // r1
+        r0, r1 = r1, r0 - qq * r1
+        s0, s1 = s1, s0 - qq * s1
+    require(abs(s1) <= bound and s1 != 0, 'rational reconstruction')
+    a, b = (r1, s1) if s1 > 0 else (-r1, -s1)
+    require((a - r * b) % P == 0, 'reconstruction residue')
+    return a, b
+
+
+def primitive(row):
+    from fractions import Fraction
+    fr = [Fraction(*ratrec(x)) for x in row]
+    den = 1
+    for f in fr:
+        den = den * f.denominator // math.gcd(den, f.denominator)
+    ints = [int(f * den) for f in fr]
+    gg = 0
+    for x in ints:
+        gg = math.gcd(gg, abs(x))
+    ints = [x // gg for x in ints] if gg else ints
+    first = next((x for x in ints if x), 1)
+    return [-x for x in ints] if first < 0 else ints
+
+
+def frame_record(geo, ann_id):
+    """Exact integer description of the frame perp(ann): 'a' = integer annihilator rows (frame = common kernel)
+    when codim <= dim, else 'b' = integer basis rows. Both are primitive rows of the rational RREF."""
+    h = geo.h
+    A = geo.T.rows[ann_id]
+    codim = len(A)
+    if codim <= h - codim:
+        rows = [primitive(r) for r in A]
+        return dict(dim=h - codim, a=rows)
+    B = geo.T.rows[geo.perp(ann_id)]
+    return dict(dim=h - codim, b=[primitive(r) for r in B])
+
+
+def dumps(obj):
+    return json.dumps(obj, sort_keys=True, separators=(',', ':')) + '\n'
+
+
+def build(p, frozen_arcs=None, log=print):
+    mod = json.loads((HERE / 'data' / MODULES[p]).read_text())
+    abo = pinned_all_but_one(QMODULES[p], p - 2) if p in QMODULES else all_but_one(p - 2)
+    dpath = HERE / 'data' / ('local_design_p%d.json' % p)
+    design = json.loads(dpath.read_text())['design'] if dpath.exists() else None
+    g = BitGraph(p).finish(mod, abo, merge=p in MERGE, l1=p == 12, design=design)
+    require(check_decoder(g) == 0, 'mod-2 decoder identity')
+    t0 = time.time()
+    prof, wit = compile_word(g, frozen=frozen_arcs)
+    log('compiled p=%d in %.1fs: R=%d arcs=%d plain=%d' % (p, time.time() - t0, prof['R'], prof['matched'], prof['plain']))
+    gauges, H, Y, word = select_gauges(g, prof, wit)
+    prf = profile(prof, gauges, H, Y)
+    arcs = sorted([x - 1, wit['usecode'][u]] for x, u in wit['arcs'].items())
+    cache = {}
+    geo = wit['geo']
+    deg = sum(1 for x in wit['order'] if not nondeg_id(geo, geo.perp(wit['ann'][x]), cache))
+    deg += sum(1 for U in wit['rframe'] if not nondeg_id(geo, U, cache))
+    require(deg == 0, 'G-nondegenerate node and root frames')
+    out = dict(graph=dict(p=p, h=g['h'], v=g['v'], labels=g['labels'], args=g['args'], roots=g['roots'],
+                          partner_mix=g['partner_mix'], pair_module_sha256=hashlib.sha256((HERE / 'data' / MODULES[p]).read_bytes()).hexdigest()),
+               compile=dict(plain_threshold=PLAIN, order=[x - 1 for x in wit['order']], plain=[x - 1 for x in wit['plain']], arcs=arcs),
+               word={k: v for k, v in word.items() if not k.startswith('_')})
+    exp = export(p, g, prof, wit, word, prf)
+    return out, prf, arcs, exp
+
+
+def export(p, g, prof, wit, word, prf):
+    """Plain-JSON gate files: graph, word (selection.json shape), exact frames, partial-K chronology."""
+    geo, h, v = wit['geo'], g['h'], g['v']
+    n, roots = wit['n'], wit['roots']
+    ann = wit['ann']
+    frames = {}
+
+    def fid(a):
+        if a not in frames:
+            frames[a] = None
+        return a
+    node_frame = {str(x - 1): fid(ann[x]) for x in wit['order']}
+    root_frame = [fid(a) for a in wit['rann']]
+    gauges = []
+    for z, A in zip(word['gauges'], word['_gauge_ann']):
+        gauges.append(dict(z, frame=fid(A)))
+    lab = g['labels']
+    src_ann = [fid(geo.perp(geo.src[i])) for i in range(v)]
+    full = fid(0)
+    level2 = {}
+    for j, r in enumerate(g['roots']):
+        if r['kind'] == 'side' and len(r['targets']) == 2:
+            level2[tuple(sorted(r['targets']))] = j
+    kchron = []
+    for mx in g['partner_mix']:
+        c, d = mx['carrier'], mx['passive']
+        mixf = fid(geo.perp(geo.join(geo.src[c], geo.src[d])))
+        j = level2[tuple(sorted(mx['receivers']))]
+        capf = root_frame[j]
+        require(geo.contained(capf, mixf), 'mix frame inside receivers cap')
+        kchron.append(dict(carrier=c, passive=d, receivers=mx['receivers'], mix_frame=mixf, deliver_frame=capf,
+                           deliver_after_root=j, undo_frame=full,
+                           carrier_chain=[src_ann[c], mixf, capf, full], passive_chain=[src_ann[d], mixf, full],
+                           carrier_ranks=[1, h - 4, 2], passive_ranks=[1, h - 2]))
+    table = {str(a): frame_record(geo, a) for a in sorted(frames)}
+    conv = dict(target_covector='3*chi_T - 1 (target cap = {u : (3 chi_T - 1).u = 0} = H0-orthogonal complement of chi_T)',
+                gram='G = I - J/9 on Q^h (H0 = G/2, H0(chi_S,chi_T) = (|S cap T|-1)/2); nondegeneracy tested for G',
+                frame_ids='frame id = id of the canonical annihilator; record "a" lists integer annihilator rows (frame ='
+                          ' common kernel), record "b" lists integer basis rows; id 0 (empty "a") is the full space Q^h',
+                ops='[dest, control, node]: dest ^= control at the frame of node (copies: dest is the fresh role)',
+                nodes='zero-based graph nodes; nodes < v are the source leaves (port index)')
+    graph = dict(p=p, h=h, v=v, labels=g['labels'], args=g['args'],
+                 roots=[dict(r, coefficient=1) for r in g['roots']], partner_mix=g['partner_mix'],
+                 decoder='mod 2: Y_T += sum of root nodes whose targets contain T (star roots: T reads star(c) for c in T;'
+                         ' side roots; partner singles) + x_carrier + x_passive for each partner_mix entry receiving T;'
+                         ' equals x_T = sum_{c in T} star(c) + sum_{|S cap T|=1} x_S')
+    wordj = dict(ops=word['ops'], sources=word['sources'], rootroles=word['rootroles'], phase1=word['phase1'],
+                 gauges=gauges, order=[x - 1 for x in wit['order']], arcs=sorted([x - 1, wit['usecode'][u]] for x, u in wit['arcs'].items()),
+                 plain=[x - 1 for x in wit['plain']], node_frame=node_frame, root_frame=root_frame,
+                 source_frame=src_ann, full_frame=full, conventions=conv,
+                 schedule='old-value reads of non-gauged roles (frame 0); V injections at <chi_S>; ops in order (phase1 ops'
+                          ' are those listed); centre copies read at 0; gauged old-value reads at their gauge frames'
+                          ' (ascending per target); side root reads in root order; partial-K deliveries right after'
+                          ' root deliver_after_root; undo at full frame; inverse ops; V removal')
+    return dict(graph=graph, word=wordj, frames=dict(h=h, P_used_for_ranks='2^127-1', conventions=conv, frames=table),
+                kchron=dict(h=h, entries=kchron, conventions=conv))
+
+
+def nested_prefix(n):
+    """Nested-prefix all-but-one module (QMOD lane; eumemic, Claude assistance): prefix p_{k+1} = p_k + x_k, suffix
+    s_k = x_k + s_{k+1}; y_0 = s_1, y_{n-1} = p_{n-1}, y_{i+1} = p_i + (x_i + s_{i+2}). Each prefix is used twice with
+    nested supports, which gives the carrier matching more links than the balanced tree. Contract-checked. It is the
+    seed of the pinned p = 12 module data/qmod_p12.json."""
+    args = [None] * n
+
+    def add(a, b):
+        args.append([a, b])
+        return len(args) - 1
+    pre = {1: 0}
+    for k in range(1, n - 1):
+        pre[k + 1] = add(pre[k], k)
+    suf = {n - 1: n - 1}
+    for k in range(n - 2, 0, -1):
+        suf[k] = add(k, suf[k + 1])
+    roots = [None] * n
+    roots[0], roots[n - 1] = suf[1], pre[n - 1]
+    roots[1] = add(0, suf[2])
+    for i in range(1, n - 2):
+        roots[i + 1] = add(pre[i], add(i, suf[i + 2]))
+    support = []
+    for x, a in enumerate(args):
+        if a is None:
+            support.append(1 << x)
+        else:
+            require(0 <= a[0] < x and 0 <= a[1] < x and not support[a[0]] & support[a[1]], 'nested prefix disjoint')
+            support.append(support[a[0]] | support[a[1]])
+    full = (1 << n) - 1
+    require(all(support[r] == full ^ (1 << i) for i, r in enumerate(roots)), 'nested prefix all-but-one roots')
+    return dict(input_count=n, args=args, roots=roots)
+
+
+def pinned_all_but_one(name, n):
+    """Pinned all-but-one module {input_count, args, roots} in data/ (eumemic, Claude assistance). The p = 12
+    module was annealed from nested_prefix(10) by split-function moves, scored by the p = 12 bit word.
+    Contract-checked: disjoint supports, root i sums every input but i."""
+    mod = json.loads((HERE / 'data' / name).read_text())
+    args, roots = mod['args'], mod['roots']
+    require(mod['input_count'] == n == len(roots) and args[:n] == [None] * n, 'pinned all-but-one arity')
+    support = [1 << x for x in range(n)]
+    for x, a in enumerate(args[n:], n):
+        require(a and 0 <= a[0] < x and 0 <= a[1] < x and not support[a[0]] & support[a[1]], 'pinned all-but-one disjoint')
+        support.append(support[a[0]] | support[a[1]])
+    full = (1 << n) - 1
+    require(all(support[r] == full ^ (1 << i) for i, r in enumerate(roots)), 'pinned all-but-one roots')
+    return dict(input_count=n, args=args, roots=roots)
+
+
+def all_but_one(n):
+    """PR #144 modules.all_but_one (balanced binary tree upward sums and complementary downward sums)."""
+    args, support = [None] * n, [1 << i for i in range(n)]
+    by = {s: i for i, s in enumerate(support)}
+
+    def add(a, b):
+        if a is None:
+            return b
+        if b is None:
+            return a
+        s = support[a] | support[b]
+        if s not in by:
+            by[s] = len(args); args.append([a, b]); support.append(s)
+        return by[s]
+
+    def tree(lo, hi):
+        if hi - lo == 1:
+            return (lo, None, None)
+        mid = (lo + hi) // 2
+        L, Rr = tree(lo, mid), tree(mid, hi)
+        return (add(L[0], Rr[0]), L, Rr)
+    roots = [None] * n
+
+    def walk(t, outside):
+        x, L, Rr = t
+        if L is None:
+            roots[x] = outside
+            return
+        walk(L, add(outside, Rr[0])); walk(Rr, add(outside, L[0]))
+    walk(tree(0, n), None)
+    active, stack = set(range(n)), list(roots)
+    while stack:
+        x = stack.pop()
+        if x not in active:
+            active.add(x)
+            if args[x] is not None:
+                stack.extend(args[x])
+    ids = sorted(active); ren = {x: i for i, x in enumerate(ids)}
+    return dict(input_count=n, args=[None if args[x] is None else [ren[y] for y in args[x]] for x in ids], roots=[ren[x] for x in roots])
+
+
+def main():
+    require(not sys.flags.optimize, 'run without -O')
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--p', type=int, default=12)
+    ap.add_argument('--out', type=Path, default=HERE / 'out')
+    ap.add_argument('--check', action='store_true', help='regenerate from frozen arcs and compare byte-identically')
+    ap.add_argument('--solve-matching', action='store_true', help='recompute the carrier matching (Hopcroft-Karp)')
+    a = ap.parse_args()
+    a.out.mkdir(parents=True, exist_ok=True)
+    arcs_path = HERE / 'data' / ('arcs_p%d.json' % a.p)
+    frozen = None if a.solve_matching or not arcs_path.exists() else json.loads(arcs_path.read_text())
+    out, prf, arcs, exp = build(a.p, frozen)
+    root = float_root(prf['child_histogram'], prf['W_per_vertex'], prf['m'])
+    word_bytes = gzip.compress(dumps(out).encode(), mtime=0)
+    prof_bytes = dumps(prf).encode()
+    names = {'word_p%d.json.gz' % a.p: word_bytes, 'profile_p%d.json' % a.p: prof_bytes}
+    for k, obj in exp.items():
+        names['%s_p%d.json' % (k, a.p)] = dumps(obj).encode()
+    if a.check:
+        for name, data in names.items():
+            old = (a.out / name).read_bytes()
+            if name.endswith('.gz'):  # gzip bytes depend on the zlib build; compare the compressed content
+                old, data = gzip.decompress(old), gzip.decompress(data)
+            require(old == data, 'byte-identical regeneration of ' + name)
+        require(frozen is not None, 'frozen arcs present')
+        print('PASS p=%d: word and profile regenerate byte-identically (sha256 %s, %s)' % (
+            a.p, hashlib.sha256(word_bytes).hexdigest()[:16], hashlib.sha256(prof_bytes).hexdigest()[:16]))
+    else:
+        for name, data in names.items():
+            (a.out / name).write_bytes(data)
+        if frozen is None:
+            arcs_path.write_text(dumps(arcs))
+        print('wrote p=%d: R=%d R/v=%.3f loss=%d deficit=%d W=%d gauges=%d float a_b=%.7e' % (
+            a.p, prf['R'], prf['R'] / prf['v'], prf['loss'], prf['deficit_per_vertex'], prf['W_per_vertex'],
+            prf['selected_roles'], root))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/five-stage-p10-transcript-stages/bitword/producer/regenerate.py b/research/five-stage-p10-transcript-stages/bitword/producer/regenerate.py
new file mode 100644
index 0000000000..35f5b2c13e
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/producer/regenerate.py
@@ -0,0 +1,68 @@
+#!/usr/bin/env python3
+"""Rebuild bitword/selected/bit from the generator and the two physical-layer producers, and compare.
+
+    python3 -B bitword/producer/regenerate.py --work /new/scratch/dir                 (about 2 minutes)
+    python3 -B bitword/producer/regenerate.py --work /new/dir --solve-matching --emit /new/out/dir
+
+1. paired_cube_bit_word.py --p 10 (frozen arcs data/arcs_p10.json) writes the virtual word;
+2. make_physical.py --bank-parity adds the compensated reuse pairs and late recipient reads (recipients are
+   rank h - 3 = 17 gauges; trailing pairs are dropped until the 60-replica bank width is a multiple of m = 100);
+3. descent.py moves operation frames (PR200 physical-layer rules, cost r*ln(100/r)) and writes the physical word.
+The five pinned files must be reproduced exactly (gzip members compared after decompression).
+This is provenance only: verify.py admits the pinned files themselves and never runs a producer.
+
+Re-pinning (new module data): --solve-matching runs the generator on a scratch copy of this producer directory,
+first to recompute and freeze the carrier matching, then on the frozen arcs (the package is never written), and
+--emit writes the five new selected files and the new frozen arcs_p10.json to a new directory instead of
+comparing. See discovery/REPIN.md.
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+import argparse, gzip, shutil, subprocess, sys
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+BIT = HERE.parent
+P = 10
+NAMES = ['graph_p%d.json' % P, 'kchron_p%d.json' % P, 'profile_p%d.json' % P]
+GZ = ['word_p%d.json.gz' % P, 'frames_p%d.json.gz' % P]
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__); ap.add_argument('--work', type=Path, required=True)
+    ap.add_argument('--solve-matching', action='store_true', help='recompute the carrier matching on a scratch copy')
+    ap.add_argument('--emit', type=Path, help='write the new selected files and arcs here instead of comparing')
+    a = ap.parse_args(); work = a.work.resolve(); assert not work.exists(), 'work dir must be new'
+    assert a.emit is None or not a.emit.exists(), 'emit dir must be new'
+    assert a.emit is not None or not a.solve_matching, '--solve-matching is for re-pinning; use it with --emit'
+    raw, phys, pkg, final = work/'raw', work/'phys', work/'pkg', work/'final'
+    py = [sys.executable, '-B']
+    producer = HERE   # only the generator runs from a scratch copy when the matching is re-solved
+    if a.solve_matching:
+        producer = work/'producer'; shutil.copytree(HERE, producer)
+        (producer/'data'/('arcs_p%d.json' % P)).unlink(missing_ok=True)
+        # first run: solve the carrier matching and freeze it in the scratch copy's data/arcs_pP.json
+        subprocess.run(py + [str(producer/'paired_cube_bit_word.py'), '--p', str(P), '--out', str(work/'solve')], check=True)
+    # the pinned word is always the frozen-arc compile (frame ids follow the frozen arc order)
+    subprocess.run(py + [str(producer/'paired_cube_bit_word.py'), '--p', str(P), '--out', str(raw)], check=True)
+    subprocess.run(py + [str(HERE/'make_physical.py'), '--src', str(raw), '--out', str(phys), '--bank-parity'], check=True)
+    (pkg/'selected').mkdir(parents=True)
+    shutil.copytree(BIT/'bit', pkg/'bit'); shutil.copytree(BIT/'references', pkg/'references')
+    shutil.copytree(phys, pkg/'selected/bit')
+    subprocess.run(py + [str(HERE/'descent.py'), str(pkg), str(final)], check=True)
+    if a.emit is not None:
+        out = a.emit.resolve(); (out/'selected').mkdir(parents=True)
+        for name in NAMES + GZ:
+            shutil.copyfile(final/name, out/'selected'/name)
+        shutil.copyfile(producer/'data'/('arcs_p%d.json' % P), out/('arcs_p%d.json' % P))
+        print('EMITTED new p=%d bit word to %s (selected/ and arcs_p%d.json); nothing compared' % (P, out, P))
+        return
+    pinned = BIT/'selected/bit'
+    assert sorted(x.name for x in pinned.iterdir()) == sorted(NAMES + GZ), 'pinned file set'
+    for name in NAMES:
+        assert (final/name).read_bytes() == (pinned/name).read_bytes(), name
+    for name in GZ:
+        assert gzip.decompress((final/name).read_bytes()) == gzip.decompress((pinned/name).read_bytes()), name
+    print('PASS p=%d regeneration: all five pinned bit-word files reproduced exactly' % P)
+
+if __name__ == '__main__':
+    main()
diff --git a/research/five-stage-p10-transcript-stages/bitword/references/pr168-v4/SOURCE.json b/research/five-stage-p10-transcript-stages/bitword/references/pr168-v4/SOURCE.json
new file mode 100644
index 0000000000..c57edcae25
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/references/pr168-v4/SOURCE.json
@@ -0,0 +1,20 @@
+{
+  "commit": "4a3c769e5c5430e7114c4d3e099ff34664677f17",
+  "files": {
+    "certificates/paired-cube-network.json": "05b253a21dc526b6039f56d1068162a19a8a4f29291ad94eb892656b88e9142d",
+    "notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54",
+    "research/paired-cube-bit/check_paired_cube_bit.py": "4d7c86cd999a1519e0dfb6dcf33a8f26e442a353c3665a0f06881216a260fbf3",
+    "scripts/certify.py": "2348d95008276c5d5764f7e028c3918e484582cd589bd4d9b82919161745e53e",
+    "scripts/paired_cube/__init__.py": "b5fb17c79fd41a75c0648e7a5f99076f9f42a619857d5e34e71699bf00ef0c91",
+    "scripts/paired_cube/closure.py": "e4b3086f4b5663297fe06f4646e1349f10d8647997989f17eef6ec4e84aec693",
+    "scripts/paired_cube/frames.py": "7d897418dbfee47de0723ea4983098a982610ccba45e1bac9000a79626d8421c",
+    "scripts/paired_cube/gauges.py": "8a501c66e1330f054e0e11a35e9321d2deea7b51cd03ca56b6a41765e43fe061",
+    "scripts/paired_cube/graph.py": "d10478ba509c7d8abcefcaaf7c5e0b580b9cd9cbe7777b3e49b2fe24620985c8",
+    "scripts/paired_cube/modules.py": "6c134f3d24c6cd9aca03763050aaf600005c126c09b35ac0ff5f040e0e29db87",
+    "scripts/paired_cube/verify.py": "b1eb42a91381ae031d97879f7c43e6c00fc4787e132ed60eb3e124994bdb7d35",
+    "scripts/paired_cube_physical.py": "9c9ea1ea29e551ab6116d7c8ca09f4703ff9e2fa102032d5055327fde07ba319"
+  },
+  "pr": 168,
+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "scope": "Byte-identical copies of the PR168 v4 files this package executes or pins (compiler frames/closure/gauges/graph/modules, physical checkers, package bit checker, parent certificate, frame theorem note), so the package is self-contained on main."
+}
diff --git a/research/five-stage-p10-transcript-stages/bitword/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py b/research/five-stage-p10-transcript-stages/bitword/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py
new file mode 100644
index 0000000000..69d535a6c2
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py
@@ -0,0 +1,465 @@
+#!/usr/bin/env python3
+"""Standalone checker for subset-port bit words with broadcast roots (paired-cube bit word with partner-pair
+source mixing).  Standard library only; independent of the generator (own exact integer linear algebra, own
+register simulation).  Refuses to run under python -O.
+
+Inputs (plain JSON written by paired_cube_bit_word.py): graph_pP.json, word_pP.json, frames_pP.json,
+kchron_pP.json, profile_pP.json.  Checks:
+  1. exact frames: every frame record (integer annihilator rows 'a' or integer basis rows 'b') is completed to
+     the other representation by exact integer elimination; A.B^T = 0 exactly and rank A + rank B = h;
+  2. the mod-2 decoder: supports of all additions are disjoint; for every target the deliveries (star roots,
+     side roots, partner singles, partner-pair sums) XOR to {T}; stars read are exactly the c in T and the
+     side part is exactly sum_{|S cap T|=1} x_S;
+  3. geometry: source frames are the lines <chi_S>; side root frames lie in every receiver's cap
+     ker(3 chi_T - 1) and equal the common cap of the group; centre frames are the star spans; the frame of
+     every addition contains its operands' frames; every root node's frame lies in its root frame;
+  4. every role chain (start -> each op frame -> root frame -> full) is nested, including gauged starts
+     (sigma inside the first op frame, gauged roles untouched in phase one); every target chain (gauge reads
+     ascending, side root caps in root order, partner-pair delivery at the level-2 cap, final cap) is nested;
+     the partner-pair chronology: mix frame span{chi_c,chi_d} with H0-Gram I_2, contained in the receivers'
+     level-2 cap, carrier chain [<chi_c>, mix, cap, full] and passive chain [<chi_d>, mix, full] nested;
+  5. G = I - J/9 nondegenerate on every frame used (exact integer determinant test);
+  6. literal F2 replay with arbitrary dirty scratch: y = y0 + x, scratch and sources restored;
+  7. independent ledger recount from the role chains equals the saved child histogram (PR #144 bit ledger);
+  8. mutation controls (must all be REJECTED): broken partner mix, delivery outside the shared cap (full
+     frame), delivery below the level (face cap without span{chi_c,chi_d}), dropped star, non-nested role chain.
+Usage: python3 check_paired_cube_bit.py --dir out --p 12
+"""
+import argparse, json, random, sys
+from collections import Counter, defaultdict
+from math import gcd
+from operator import mul
+from pathlib import Path
+
+if sys.flags.optimize:
+    raise SystemExit('refusing to run under python -O: assertions are part of the check')
+
+
+class Fail(Exception):
+    pass
+
+
+def need(cond, msg):
+    if not cond:
+        raise Fail(msg)
+
+
+# ------------------------------------------------------------------ exact integer linear algebra
+def prim(v):
+    g = 0
+    for x in v:
+        g = gcd(g, abs(x))
+    if g > 1:
+        v = [x // g for x in v]
+    f = next((x for x in v if x), 0)
+    return tuple(-x for x in v) if f < 0 else tuple(v)
+
+
+def reduce_rows(rows, h):
+    """Integer reduced echelon form: returns (rows, pivot columns); each pivot column is zero outside its row."""
+    rows = [list(r) for r in rows]
+    out, pivs = [], []
+    for r in rows:
+        for pr, pc in zip(out, pivs):
+            if r[pc]:
+                a, b = pr[pc], r[pc]
+                r = [x * a - y * b for x, y in zip(r, pr)]
+        r = list(prim(r))
+        c = next((j for j in range(h) if r[j]), None)
+        if c is None:
+            continue
+        for i, (pr, pc) in enumerate(zip(out, pivs)):
+            if pr[c]:
+                a, b = r[c], pr[c]
+                out[i] = list(prim([x * a - y * b for x, y in zip(pr, r)]))
+        out.append(r); pivs.append(c)
+    return out, pivs
+
+
+def kernel(rows, h):
+    red, pivs = reduce_rows(rows, h)
+    ps = set(pivs)
+    basis = []
+    for f in range(h):
+        if f in ps:
+            continue
+        D = 1
+        for r, c in zip(red, pivs):
+            if r[f]:
+                D = D * abs(r[c]) // gcd(D, abs(r[c]))
+        v = [0] * h
+        v[f] = D
+        for r, c in zip(red, pivs):
+            if r[f]:
+                v[c] = -r[f] * D // r[c]
+        basis.append(prim(v))
+    return basis, len(red)
+
+
+def rank(rows, h):
+    return len(reduce_rows(rows, h)[0])
+
+
+def dot(a, b):
+    return sum(map(mul, a, b))
+
+
+# ------------------------------------------------------------------ checker
+class Checker:
+    def __init__(self, d, p, mutate=None):
+        self.mut = mutate
+        rd = lambda name: json.loads((d / ('%s_p%d.json' % (name, p))).read_text())
+        self.g, self.w, self.fr, self.k, self.prof = rd('graph'), rd('word'), rd('frames'), rd('kchron'), rd('profile')
+        self.h, self.v = self.g['h'], self.g['v']
+        if mutate == 'dropped_star':
+            j = next(i for i, r in enumerate(self.g['roots']) if r['kind'] == 'center')
+            self.g['roots'][j]['targets'] = []
+        if mutate == 'broken_mix':
+            self.k['entries'][0]['skip_mix'] = True
+        if mutate == 'outside_cap':
+            # raise the mixed carrier past the receivers' shared cap (to the full frame) and deliver there
+            e = self.k['entries'][0]
+            e['deliver_frame'] = self.w['full_frame']
+            e['carrier_chain'][2] = e['deliver_frame']
+        if mutate == 'below_level':
+            # deliver at the receivers' level-1 (face) cap, which does not contain span{chi_c, chi_d}
+            e = self.k['entries'][0]
+            face = next(j for j, r in enumerate(self.g['roots']) if r['kind'] == 'side' and set(e['receivers']) < set(r['targets']))
+            e['deliver_frame'] = self.w['root_frame'][face]
+            e['carrier_chain'][2] = e['deliver_frame']
+        if mutate == 'non_nested':
+            # move one addition's frame down to the frame of its smallest operand's source line
+            x = next(int(k) for k, f in sorted(self.w['node_frame'].items(), key=lambda kv: int(kv[0])) if int(k) >= self.v and str(int(k)) not in set(map(str, self.w['plain'])))
+            self.w['node_frame'][str(x)] = self.w['source_frame'][0]
+
+    # ---------------- frames
+    def frames(self):
+        h = self.h
+        self.A, self.B, self.dimf = {}, {}, {}
+        for key, rec in self.fr['frames'].items():
+            f = int(key)
+            if 'a' in rec:
+                A = [tuple(r) for r in rec['a']]
+                need(rank(A, h) == len(A), 'independent annihilator rows %d' % f)
+                B, _ = kernel(A, h)
+            else:
+                B = [tuple(r) for r in rec['b']]
+                need(rank(B, h) == len(B), 'independent basis rows %d' % f)
+                A, _ = kernel(B, h)
+            need(len(A) + len(B) == h and len(B) == rec['dim'], 'dimensions of frame %d' % f)
+            need(all(dot(a, b) == 0 for a in A for b in B), 'A.B = 0 for frame %d' % f)
+            self.A[f], self.B[f], self.dimf[f] = A, B, len(B)
+        self.cc = {}
+        return len(self.A)
+
+    def sub(self, f1, f2):
+        """frame f1 contained in frame f2 (exact)"""
+        if f1 == f2:
+            return True
+        key = (f1, f2)
+        r = self.cc.get(key)
+        if r is None:
+            B1, A2 = self.B[f1], self.A[f2]
+            r = len(B1) <= len(self.B[f2]) and all(dot(a, b) == 0 for a in A2 for b in B1)
+            self.cc[key] = r
+        return r
+
+    def in_frame(self, vec, f):
+        return all(dot(a, vec) == 0 for a in self.A[f])
+
+    def nondeg(self, f):
+        h = self.h
+        B, A = self.B[f], self.A[f]
+        if not B or len(B) == h:
+            return True
+        if len(B) <= len(A):
+            s = [sum(b) for b in B]
+            M = [[9 * dot(B[i], B[j]) - s[i] * s[j] for j in range(len(B))] for i in range(len(B))]
+            return rank(M, len(B)) == len(B)
+        s = [sum(a) for a in A]
+        M = [[(9 - h) * dot(A[i], A[j]) + s[i] * s[j] for j in range(len(A))] for i in range(len(A))]
+        return rank(M, len(A)) == len(A)
+
+    # ---------------- decoder
+    def decoder(self):
+        g, v = self.g, self.v
+        args = g['args']
+        lab = [frozenset(l) for l in g['labels']]
+        sup = [1 << i for i in range(v)] + [0] * (len(args) - v)
+        for x in range(v, len(args)):
+            a, b = args[x]
+            need(not sup[a] & sup[b], 'support-disjoint addition %d' % x)
+            sup[x] = sup[a] | sup[b]
+        self.sup = sup
+        acc, stars, side = [0] * v, [set() for _ in range(v)], [0] * v
+        for r in g['roots']:
+            need(r.get('coefficient', 1) == 1, 'mod-2 unit coefficients')
+            for t in r['targets']:
+                acc[t] ^= sup[r['node']]
+                if r['kind'] == 'center':
+                    stars[t].add(r['coordinate'])
+                else:
+                    side[t] ^= sup[r['node']]
+        for e in self.k['entries']:
+            for t in e['receivers']:
+                acc[t] ^= (1 << e['carrier']) | (1 << e['passive'])
+                side[t] ^= (1 << e['carrier']) | (1 << e['passive'])
+        for t in range(v):
+            need(acc[t] == 1 << t, 'decoder identity at target %d' % t)
+            need(stars[t] == set(lab[t]), 'stars read by target %d' % t)
+            orth = sum(1 << s for s in range(v) if len(lab[s] & lab[t]) == 1)
+            need(side[t] == orth, 'side part = sum over |S cap T| = 1 at target %d' % t)
+        for r in g['roots']:
+            if r['kind'] == 'center':
+                c = r['coordinate']
+                need(sup[r['node']] == sum(1 << s for s in range(v) if c in lab[s]), 'star support %d' % c)
+
+    # ---------------- geometry and chains
+    def geometry(self):
+        g, w, h, v = self.g, self.w, self.h, self.v
+        lab = g['labels']
+        chi = [tuple(1 if j in l else 0 for j in range(h)) for l in lab]
+        cov = [tuple((3 if j in l else 0) - 1 for j in range(h)) for l in lab]
+        nf = {int(k): f for k, f in w['node_frame'].items()}
+        rf = w['root_frame']
+        full = w['full_frame']
+        need(self.dimf[full] == h, 'full frame')
+        for s in range(v):
+            f = w['source_frame'][s]
+            need(self.dimf[f] == 1 and self.in_frame(chi[s], f), 'source line <chi_S>')
+        args = g['args']
+        for x, f in nf.items():
+            if x < v:
+                need(self.in_frame(chi[x], f), 'leaf label inside its frame')
+            else:
+                for y in args[x]:
+                    need(self.sub(nf[y], f), 'operand frame inside node frame (%d <- %d)' % (x, y))
+        loss = 0
+        for j, r in enumerate(g['roots']):
+            f = rf[j]
+            need(self.sub(nf[r['node']], f), 'root node frame inside root frame %d' % j)
+            if r['kind'] == 'center':
+                c = r['coordinate']
+                S = [chi[s] for s in range(v) if c in lab[s]]
+                need(all(self.in_frame(x, f) for x in S) and rank(S, h) == self.dimf[f], 'centre frame = star span')
+                loss += self.dimf[f]
+            else:
+                need(all(dot(cov[t], b) == 0 for t in r['targets'] for b in self.B[f]), 'root frame inside caps')
+                need(self.dimf[f] == h - rank([cov[t] for t in r['targets']], h), 'root frame = common cap')
+        need(loss == self.prof['loss'], 'copied-centre loss')
+        self.chi, self.cov, self.nf, self.rf = chi, cov, nf, rf
+
+    def chains(self):
+        """Role chains of the physical word and target chains; returns the recounted child histogram."""
+        g, w, h, v = self.g, self.w, self.h, self.v
+        nf, rf, full = self.nf, self.rf, w['full_frame']
+        ops, rootroles = w['ops'], w['rootroles']
+        R = 1 + max(max(a, b) for a, b, _ in ops)
+        R = max(R, 1 + max(rootroles), 1 + max(w['sources'].values()))
+        need(R == self.prof['R'], 'role count')
+        start = {}
+        for leaf, s in w['sources'].items():
+            start[s] = w['source_frame'][int(leaf)]
+        phase1 = set(w['phase1'])
+        touched_p1 = set()
+        for i in phase1:
+            touched_p1.update(ops[i][:2])
+        # phase one = closure of the centre roots' last ops under per-role precedence (recomputed)
+        prev_op, pred = {}, []
+        for i, (a, b, _) in enumerate(ops):
+            pred.append((prev_op.get(a, -1), prev_op.get(b, -1)))
+            prev_op[a] = prev_op[b] = i
+        stack = [prev_op[s] for r, s in zip(g['roots'], rootroles) if r['kind'] == 'center' and s in prev_op]
+        closure = set()
+        while stack:
+            i = stack.pop()
+            if i not in closure:
+                closure.add(i); stack.extend(j for j in pred[i] if j >= 0)
+        need(closure == phase1, 'phase one is the centre closure')
+        # conservative response support of every role (union incidence through the XOR word)
+        co = [0] * R
+        for j, (r, s) in enumerate(zip(g['roots'], rootroles)):
+            for t in r['targets']:
+                co[s] |= 1 << t
+        for a, b, _ in reversed(ops):
+            co[b] |= co[a]
+        gauge_of = {}
+        for z in w['gauges']:
+            need(sum(1 << t for t in z['targets']) == co[z['role']], 'gauge targets = response support of its role')
+            s = z['role']
+            need(s not in start, 'gauged role is not a source role')
+            need(s not in touched_p1, 'gauged role untouched in phase one')
+            need(self.dimf[z['frame']] == z['dim'] and z['dim'] > 0, 'gauge dimension')
+            need(self.nondeg(z['frame']), 'gauge frame nondegenerate')
+            start[s] = z['frame']; gauge_of[s] = z
+        seq = defaultdict(list)
+        for i, (a, b, x) in enumerate(ops):
+            f = nf[x]
+            seq[a].append(f); seq[b].append(f)
+        for j, s in enumerate(rootroles):
+            seq[s].append(rf[j])
+        H = Counter()
+        for s in range(R):
+            chain = [start.get(s)] + seq[s] + [full]
+            prev = chain[0]
+            dprev = 0 if prev is None else self.dimf[prev]
+            if prev is not None and s not in gauge_of:
+                H[1] += 1          # source role: injection frame <chi_S> (entrance child of width 1)
+            for f in chain[1:]:
+                if prev is not None:
+                    need(self.sub(prev, f), 'nested role chain (role %d)' % s)
+                d = self.dimf[f]
+                need(d >= dprev, 'ascending role chain (role %d)' % s)
+                if d > dprev:
+                    H[d - dprev] += 1
+                prev, dprev = f, d
+        for j, r in enumerate(g['roots']):
+            if r['kind'] == 'center':
+                H[self.dimf[rf[j]]] += 1   # copied-centre transform
+        # partner-pair chronology
+        src = Counter()
+        lab = [set(l) for l in g['labels']]
+        for e in self.k['entries']:
+            c, d = e['carrier'], e['passive']
+            need(len(lab[c] & lab[d]) == 1, 'carrier and passive orthogonal (H0-Gram I_2)')
+            mf, cf = e['mix_frame'], e['deliver_frame']
+            need(self.dimf[mf] == 2 and self.in_frame(self.chi[c], mf) and self.in_frame(self.chi[d], mf), 'mix frame = span{chi_c, chi_d}')
+            need(self.nondeg(mf), 'mix frame nondegenerate')
+            need(self.sub(mf, cf), 'mix frame inside the receivers shared cap')
+            need(all(dot(self.cov[t], b) == 0 for t in e['receivers'] for b in self.B[cf]), 'delivery frame inside receiver caps')
+            need(e['carrier_chain'][0] == w['source_frame'][c] and e['passive_chain'][0] == w['source_frame'][d], 'chains start at source lines')
+            need(e['carrier_chain'][1:] == [mf, cf, w['full_frame']] and e['passive_chain'][1:] == [mf, w['full_frame']], 'chain shape')
+            for ch in (e['carrier_chain'], e['passive_chain']):
+                for f1, f2 in zip(ch, ch[1:]):
+                    need(self.sub(f1, f2), 'nested source-register chain')
+                for f1, f2 in zip(ch, ch[1:]):
+                    src[self.dimf[f2] - self.dimf[f1]] += 1
+        # target chains: gauge reads (time order = reverse selection order), side caps in root order,
+        # partner-pair delivery at the level-2 cap right after its root, final cap
+        events = defaultdict(list)
+        for z in reversed(w['gauges']):
+            for t in z['targets']:
+                events[t].append(z['frame'])
+        deliveries = defaultdict(list)
+        for e in self.k['entries']:
+            deliveries[e['deliver_after_root']].append(e)
+        for j, r in enumerate(g['roots']):
+            if r['kind'] == 'center':
+                continue
+            for t in r['targets']:
+                events[t].append(rf[j])
+            for e in deliveries.get(j, []):
+                need(sorted(e['receivers']) == sorted(r['targets']), 'delivery after the receivers own level-2 root')
+                for t in e['receivers']:
+                    events[t].append(e['deliver_frame'])
+        Y = Counter()
+        cap = {}
+        for t in range(v):
+            capf = None
+            prev, dprev = None, 0
+            for f in events[t]:
+                if prev is not None:
+                    need(self.sub(prev, f), 'nested target chain (target %d)' % t)
+                need(all(dot(self.cov[t], b) == 0 for b in self.B[f]), 'target frame inside cap (target %d)' % t)
+                if self.dimf[f] > dprev:
+                    Y[self.dimf[f] - dprev] += 1
+                prev, dprev = f, self.dimf[f]
+            need(dprev <= h - 1, 'target chain below the cap')
+            Y[h - 1 - dprev] += 1 if h - 1 - dprev else 0
+        # every source register is in exactly one mixing pair
+        members = Counter()
+        for e in self.k['entries']:
+            members[e['carrier']] += 1; members[e['passive']] += 1
+        need(all(members[s] == 1 for s in range(v)), 'each source in exactly one partner pair')
+        for f in set(self.nf.values()) | set(self.rf):
+            need(self.nondeg(f), 'G-nondegenerate frame %d' % f)
+        return H, Y, src, R
+
+    # ---------------- replay
+    def replay(self, seeds=3):
+        g, w, v = self.g, self.w, self.v
+        ops, rootroles = w['ops'], w['rootroles']
+        R = self.prof['R']
+        srcmap = {int(k): s for k, s in w['sources'].items()}
+        roots = g['roots']
+        for seed in range(seeds):
+            rng = random.Random(1000 + seed)
+            x = [rng.getrandbits(1) for _ in range(v)]
+            y0 = [rng.getrandbits(1) for _ in range(v)]
+            z0 = [rng.getrandbits(1) for _ in range(R)]
+            X, Yv, z = x[:], y0[:], z0[:]
+            # y <- y - J M z (old-value response of the dirty scratch)
+            zd = z0[:]
+            for a, b, _ in ops:
+                zd[a] ^= zd[b]
+            for j, r in enumerate(roots):
+                for t in r['targets']:
+                    Yv[t] ^= zd[rootroles[j]]
+            for leaf, s in srcmap.items():      # z <- z + V x  (at the rank-one source lines)
+                z[s] ^= X[leaf]
+            for a, b, _ in ops:                  # z <- M z
+                z[a] ^= z[b]
+            for j, r in enumerate(roots):        # y <- y + J z
+                for t in r['targets']:
+                    Yv[t] ^= z[rootroles[j]]
+            for e in self.k['entries']:          # partner-pair sums on the source registers
+                if not e.get('skip_mix'):
+                    X[e['carrier']] ^= X[e['passive']]
+                for t in e['receivers']:
+                    Yv[t] ^= X[e['carrier']]
+            for e in self.k['entries']:          # undo at the full frame
+                if not e.get('skip_mix'):
+                    X[e['carrier']] ^= X[e['passive']]
+            for a, b, _ in reversed(ops):        # z <- M^-1 z
+                z[a] ^= z[b]
+            for leaf, s in srcmap.items():       # z <- z - V x
+                z[s] ^= X[leaf]
+            need(all(Yv[t] == y0[t] ^ x[t] for t in range(v)), 'replay: y = y0 + x (seed %d)' % seed)
+            need(z == z0 and X == x, 'replay: scratch and sources restored (seed %d)' % seed)
+
+    def run(self):
+        nfr = self.frames()
+        self.decoder()
+        self.geometry()
+        H, Y, src, R = self.chains()
+        self.replay()
+        h, v = self.h, self.v
+        m, W = 3 * h, 2 * v + R
+        C = Counter()
+        for part in (H, Y, src):
+            for r, c in part.items():
+                if r and c:
+                    C[r] += 3 * c
+        for z in self.w['gauges']:
+            C[3 * z['dim']] += 1
+        C[2] += 2 * v
+        saved = {int(k): c for k, c in self.prof['child_histogram'].items()}
+        need(dict(C) == saved, 'independent recount equals the saved child histogram')
+        mass = sum(r * c for r, c in C.items())
+        need(W == self.prof['W_per_vertex'] and W * m - mass == 2 * v - 3 * self.prof['loss'] == self.prof['deficit_per_vertex'],
+             'W = 2v + R and deficit 2v - 3 ell')
+        return dict(frames=nfr, roles=R, W=W, m=m, deficit=W * m - mass, children=sum(C.values()))
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--dir', type=Path, default=Path(__file__).resolve().parent / 'out')
+    ap.add_argument('--p', type=int, default=12)
+    ap.add_argument('--no-controls', action='store_true')
+    a = ap.parse_args()
+    res = Checker(a.dir, a.p).run()
+    print('PASS p=%d: %s' % (a.p, res))
+    if a.no_controls:
+        return
+    for m in ('broken_mix', 'outside_cap', 'below_level', 'dropped_star', 'non_nested'):
+        try:
+            Checker(a.dir, a.p, mutate=m).run()
+        except Fail as e:
+            print('control %-13s REJECTED: %s' % (m, e))
+            continue
+        raise SystemExit('FAIL: control %s was accepted' % m)
+    print('PASS: all 5 mutation controls rejected')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/five-stage-p10-transcript-stages/bitword/selected/bit/frames_p10.json.gz b/research/five-stage-p10-transcript-stages/bitword/selected/bit/frames_p10.json.gz
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diff --git a/research/five-stage-p10-transcript-stages/bitword/selected/bit/graph_p10.json b/research/five-stage-p10-transcript-stages/bitword/selected/bit/graph_p10.json
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+++ b/research/five-stage-p10-transcript-stages/bitword/selected/bit/graph_p10.json
@@ -0,0 +1 @@
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2: Y_T += sum of root nodes whose targets contain T (star roots: T reads star(c) for c in T; side roots; partner singles) + x_carrier + x_passive for each partner_mix entry receiving T; equals x_T = sum_{c in T} star(c) + sum_{|S cap T|=1} 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diff --git a/research/five-stage-p10-transcript-stages/bitword/selected/bit/kchron_p10.json b/research/five-stage-p10-transcript-stages/bitword/selected/bit/kchron_p10.json
new file mode 100644
index 0000000000..f1e5c67bf4
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/selected/bit/kchron_p10.json
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diff --git a/research/five-stage-p10-transcript-stages/bitword/selected/bit/profile_p10.json b/research/five-stage-p10-transcript-stages/bitword/selected/bit/profile_p10.json
new file mode 100644
index 0000000000..3e2cf5f618
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/bitword/selected/bit/profile_p10.json
@@ -0,0 +1 @@
+{"R":9120,"W_per_vertex":11040,"c":11820,"child_histogram":{"1":67920,"10":780,"11":240,"12":3300,"13":120,"14":120,"15":60,"16":2880,"17":9360,"18":2220,"2":31260,"3":17160,"4":4200,"48":1200,"5":3300,"51":960,"6":3240,"7":1740,"8":900,"9":180},"deficit_per_vertex":840,"h":20,"loss":360,"m":60,"matched":6320,"maxchild":51,"plain_frames":6420,"q":3620,"rank_per_vertex":661560,"remaining_internal_histogram":{"0":3200,"1":19280,"10":260,"11":80,"12":1100,"13":40,"14":40,"15":20,"17":2640,"18":260,"2":9300,"3":5720,"4":1400,"5":1100,"6":1080,"7":580,"8":300,"9":60},"selected_rank_histogram":{"16":1200,"17":960},"selected_roles":2160,"source_data_histogram":{"1":960,"16":480,"18":480,"2":480},"target_data_histogram":{"0":5760,"1":2400,"16":480,"17":480},"v":960}
diff --git a/research/five-stage-p10-transcript-stages/bitword/selected/bit/word_p10.json.gz b/research/five-stage-p10-transcript-stages/bitword/selected/bit/word_p10.json.gz
new file mode 100644
index 0000000000..4ff695bd68
Binary files /dev/null and b/research/five-stage-p10-transcript-stages/bitword/selected/bit/word_p10.json.gz differ
diff --git a/research/five-stage-p10-transcript-stages/code/complex_basis.py b/research/five-stage-p10-transcript-stages/code/complex_basis.py
new file mode 100644
index 0000000000..8c400798a5
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/code/complex_basis.py
@@ -0,0 +1,35 @@
+"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+Q=Fraction
+from hashlib import sha256
+from pathlib import Path
+from math import prod
+import gzip,json,sys
+
+def need(b, why):
+    if not b: raise ValueError(why)
+
+def gl_count_test():
+    # Exhaustively test a literal binary Gaussian-elimination implementation
+    # through m=4. Row swaps cost three selected-bit additions.
+    out=[]
+    for m in range(1,5):
+        good=mx=0
+        for word in range(1<<(m*m)):
+            rows=[(word>>(m*i))&((1<<m)-1) for i in range(m)]
+            ops=0
+            for k in range(m):
+                p=next((i for i in range(k,m) if rows[i]>>k&1),None)
+                if p is None: break
+                if p!=k: rows[p],rows[k]=rows[k],rows[p];ops+=3
+                for i in range(m):
+                    if i!=k and rows[i]>>k&1: rows[i]^=rows[k];ops+=1
+            else:
+                need(rows==[1<<i for i in range(m)],'basis reduction endpoint')
+                need(ops<=m*(m-1)+3*m,'row-addition count')
+                good+=1;mx=max(mx,ops)
+        need(good==prod((1<<m)-(1<<i) for i in range(m)),'GL coverage')
+        out.append(dict(m=m,invertible_matrices=good,maximum_selected_bit_additions=mx))
+    return out
diff --git a/research/five-stage-p10-transcript-stages/code/complex_gx.py b/research/five-stage-p10-transcript-stages/code/complex_gx.py
new file mode 100644
index 0000000000..0986cc810e
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/code/complex_gx.py
@@ -0,0 +1,77 @@
+"""Exact scalar-identity admission of the pinned complex gcert/1 program.
+
+The complex coarse saving is load-bearing in this package, so the complex stage now checks the complex program
+itself. It runs two of Jacob Sussman's checkers, both vendored byte-identical from jacobalansussman/
+wht-power-saving-lean at f010392c923279e3dd59ef3aa5fedad23affc5fd (Apache-2.0, Copyright 2026 Jacob Sussman) in
+inputs/complex/sources and sha-checked here:
+
+- the reference checker gx.check1(scalar=True): sizes, labels, scatter cut, shape, bracket rule, the exact
+  scalar identity (E5: every x role restored and every target receives exactly its source), block histograms,
+  N, and the exterior-gauge rule Q2;
+- the gxcore Python mirror of his two Lean checks (labels and scalars).
+
+The mirror's block histogram must equal the program's. Controls: one flipped scalar sign in a phase-A gate must
+be rejected by both checkers on the scalar identity (E5). This is a Python check. It is not a Lean run, and no
+Lean check of the program is pinned here. The run takes about 30 seconds.
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+from collections import Counter
+from hashlib import sha256
+from pathlib import Path
+import importlib.util, json, time
+
+GX = ('inputs/complex/sources/tools__gx__gx.py', '6f3dc8bb639933227a8dae181ec4a542e85c7276be9c9e330f49518e7b630b95')
+GXCORE = ('inputs/complex/sources/tools__gx__gxcore.py', 'eb972c06fe8c322db2d9a8d9a7d05596e8f40c4ca8e5f42eb6df3c7361b5d517')
+
+
+def _load(root, name, pin):
+    path = Path(root) / pin[0]
+    assert sha256(path.read_bytes()).hexdigest() == pin[1], 'vendored Sussman checker changed: ' + pin[0]
+    spec = importlib.util.spec_from_file_location('complex_' + name, path)
+    module = importlib.util.module_from_spec(spec); spec.loader.exec_module(module)
+    return module
+
+
+def _flip_one_sign(cert):
+    """Negate the first coefficient of the first phase-A add gate with a coefficient list."""
+    gate = next(g for g in cert['A'] if g[0] in ('out', 'in') and g[3])
+    t, a, b = gate[3][0]
+    gate[3][0] = [t, -a, b]
+    return cert
+
+
+def check(root, raw):
+    """raw: the uncompressed gcert/1 bytes, already bound to source-pins.json by the caller."""
+    begun = time.monotonic()
+    gx = _load(root, 'gx', GX); gxcore = _load(root, 'gxcore', GXCORE)
+    cert = json.loads(raw); stats = {}
+    assert gx.check1(cert, scalar=True, stats=stats) is True
+    blocks = Counter()
+    for w in cert['blocks'].values():
+        for r, n in w.items():
+            blocks[int(r)] += n
+    mirror = gxcore.mirror(gxcore.normal(json.loads(raw)))
+    assert mirror['hist'] == dict(blocks), 'gxcore histogram differs from the blocks'
+    controls = []
+    try:
+        gx.check1(_flip_one_sign(json.loads(raw)), scalar=True)
+    except AssertionError as error:
+        assert str(error).startswith('E5'), ('flipped sign rejected for the wrong reason', str(error))
+        controls.append(dict(name='flipped_scalar_sign', checker='gx.check1', reason=str(error)))
+    else:
+        raise AssertionError('gx.check1 accepted a flipped scalar sign')
+    try:
+        gxcore.mirror(gxcore.normal(_flip_one_sign(json.loads(raw))))
+    except gxcore.Reject as error:
+        assert str(error).startswith('E5'), ('flipped sign rejected for the wrong reason', str(error))
+        controls.append(dict(name='flipped_scalar_sign', checker='gxcore.mirror', reason=str(error)))
+    else:
+        raise AssertionError('gxcore mirror accepted a flipped scalar sign')
+    return dict(status='PASS_COMPLEX_PROGRAM_GX_CHECK1_SCALAR_AND_GXCORE_MIRROR',
+                gx_check1='ACCEPTED (labels, blocks, N, exact scalar identity E5, Q2)',
+                gxcore_mirror='ACCEPTED (label and scalar checks; histogram equals the blocks)',
+                scalar_denominators=stats['den'], scalar_max_abs=stats['maxabs'], distinct_frame_steps=stats['steps'],
+                blocks_total=sum(blocks.values()), gates_A=len(cert['A']), gates_B=len(cert['B']),
+                certificate_sha256=sha256(raw).hexdigest(), gx_sha256=GX[1], gxcore_sha256=GXCORE[1],
+                controls=controls, lean='not run here; no Lean check of this program is pinned in this package',
+                seconds=time.monotonic() - begun)
diff --git a/research/five-stage-p10-transcript-stages/code/complex_labels.py b/research/five-stage-p10-transcript-stages/code/complex_labels.py
new file mode 100644
index 0000000000..0deb6379f2
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/code/complex_labels.py
@@ -0,0 +1,176 @@
+"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+Q=Fraction
+from hashlib import sha256
+from pathlib import Path
+from math import prod
+import gzip,json,sys
+
+BASE = dict(h=22, v=1320, R=9036, cst=440, N=254672)
+EXPECTED_H = {1:29084,2:12125,3:8861,4:4656,5:1719,6:1700,7:691,8:1168,
+              9:356,10:948,11:194,12:1007,13:55,14:850,15:1309,16:114,
+              17:44,18:2640,19:709,20:22}
+class Reject(ValueError):
+    pass
+
+def need(ok, msg):
+    if not ok:
+        raise Reject(msg)
+
+def digest(obj):
+    return sha256(json.dumps(obj, separators=(",",":"), sort_keys=True).encode()).hexdigest()
+
+def hist(counter):
+    return {str(k):v for k,v in sorted(counter.items()) if v}
+
+def role(r,v):
+    return "x" if r < v else "y" if r < 2*v else "s"
+
+def reduce_binary(x, frame):
+    for b in frame:
+        if x & (1 << (b.bit_length()-1)):
+            x ^= b
+    return x
+
+def coeff(a,b, where):
+    need(type(a) is int and type(b) is int and b>0, f"{where}: coefficient shape")
+    q=Fraction(a,b)
+    odd=q.denominator
+    while odd%2==0:
+        odd//=2
+    need(odd in (1,3), f"{where}: literal coefficient outside dyadic/divisor-three grid")
+    return q
+
+def replay_label_counts(c):
+    """Full finite LABEL walk only. Never multiplies the 11,676-square scalar map."""
+    need(c.get("format")=="gcert/1", "format")
+    need(all(c.get(k)==v for k,v in BASE.items()), "baseline parameter/count mismatch")
+    h,v,R=c["h"],c["v"],c["R"]; n=2*v+R
+    need(c.get("ext")==[], "baseline has no exterior-gauged helper inputs")
+    frames=c["frames"]; dim=list(map(len,frames))
+    need(len(frames)==17861, "baseline frame-table count")
+    need(frames[0]==[] and frames[1]==[1<<i for i in range(h-1,-1,-1)], "zero/full frames")
+    need(len({tuple(f) for f in frames})==len(frames), "duplicate frames")
+    for f in frames:
+        need(all(type(b) is int and 0<b<1<<h for b in f), "frame bit range")
+        piv=[b.bit_length()-1 for b in f]
+        need(all(piv[i]>piv[i+1] for i in range(len(piv)-1)), "frame pivot order")
+        need(all(not(b>>p&1) for i,b in enumerate(f) for j,p in enumerate(piv) if i!=j),
+             "frame is not reduced echelon")
+    ports=c["ports"]
+    need(len(ports)==v==len(set(ports)), "port count/uniqueness")
+    need(all(type(p) is int and 0<p<(1<<h)-1 and p.bit_count()%2 for p in ports), "unit port/gap")
+    start=c["start"]; final=c["final"]
+    need(len(start)==len(final)==n, "live invocation role count")
+    need(all(type(f) is int and 0<=f<len(frames) for f in start+final), "endpoint frame ID")
+    for t,p in enumerate(ports):
+        need(frames[start[t]]==[p] and final[t]==1, "X endpoint")
+        need(start[v+t]==0 and dim[final[v+t]]==h-1 and
+             all((p&u).bit_count()%2==0 for u in frames[final[v+t]]), "Y endpoint")
+    need(all(f==0 for f in start[2*v:]) and all(f==1 for f in final[2*v:]), "helper endpoints")
+    need(c["ret"] and len(c["ret"])==22, "temporary-center count")
+    need([x[0] for x in c["ret"]]==list(range(22)), "center numbering")
+    need(len({x[1] for x in c["ret"]})==22, "center retained slots repeat")
+    need(c["scat"]=={"inside":[1,3],"outside":[-1,6]}, "baseline scatter rule")
+    need(len(c["A"])==17154 and len(c["B"])==34184, "phase gate count")
+    cur=start.copy(); pairs=set()
+    by_role={r:Counter() for r in "xysc"}
+    by_phase={p:Counter() for p in ("A","copy","B","final")}
+    literal=Counter(); kind=Counter(); ybracket=Counter(); ypiv=set(); ytarget=set()
+    totals={p:dict(gates=0,scalar_additions=0,register_visits=0,spectator_visits=0)
+            for p in ("A","B")}
+    transitions=0
+    def climb(reg,new,phase):
+        nonlocal transitions
+        old=cur[reg]
+        if old==new:
+            return
+        need(dim[old]<dim[new], f"{phase}: frame does not strictly climb")
+        pair=(old,new)
+        if pair not in pairs:
+            need(all(reduce_binary(b,frames[new])==0 for b in frames[old]), f"{phase}: nonnested frames")
+            pairs.add(pair)
+        rank=dim[new]-dim[old]
+        by_role[role(reg,v)][rank]+=1; by_phase[phase][rank]+=1
+        cur[reg]=new;transitions+=1
+    for phase in ("A","B"):
+        for i,g in enumerate(c[phase]):
+            where=f"{phase}[{i}]"
+            need(isinstance(g,list) and len(g)>=4 and g[0] in ("out","in"), where+": gate shape")
+            tag,f,pivot,terms=g[:4]
+            need(len(g)==(5 if tag=="out" else 4), where+": gate arity")
+            need(type(f) is int and 0<=f<len(frames), where+": frame ID")
+            need(all(isinstance(x,list) and len(x)==3 for x in terms), where+": terms")
+            spectators=g[4] if tag=="out" else []
+            regs=[pivot]+[x[0] for x in terms]+spectators
+            need(all(type(r) is int and 0<=r<n for r in regs) and len(set(regs))==len(regs),
+                 where+": duplicate/out-of-range register")
+            need(phase!="A" or all(not(v<=r<2*v) for r in regs), where+": Y role before scatter")
+            totals[phase]["gates"]+=1
+            totals[phase]["register_visits"]+=len(regs)
+            totals[phase]["spectator_visits"]+=len(spectators)
+            for reg,a,b in terms:
+                target,source=(reg,pivot) if tag=="out" else (pivot,reg)
+                sr,tr=role(source,v),role(target,v)
+                need((sr,tr) in {("x","s"),("s","s"),("s","y"),("x","y"),("x","x"),("y","y")},
+                     where+": forbidden role direction")
+                need(phase!="A" or (sr,tr) in {("x","s"),("s","s")}, where+": phase A role direction")
+                q=coeff(a,b,where)
+                need(q!=0,where+": zero scalar addition")
+                literal[str(q)]+=1;kind[f"{phase}:{sr}->{tr}"]+=1
+                totals[phase]["scalar_additions"]+=1
+                if sr==tr=="y":
+                    ybracket[(source,target)]+=q;ypiv.add(source);ytarget.add(target)
+            for r in regs:
+                climb(r,f,phase)
+        if phase=="A":
+            cut=cur.copy()
+            need(all(cur[v+t]==0 for t in range(v)), "scatter: Y role moved too early")
+            for k,r,f in c["ret"]:
+                need(type(r) is int and 2*v<=r<n, "scatter: center source is not a helper role")
+                need(type(f) is int and 0<=f<len(frames) and cur[r]==f and dim[f]==20,
+                     "scatter: center label/rank mismatch")
+                by_role["c"][20]+=1;by_phase["copy"][20]+=1
+    need(not ypiv.intersection(ytarget) and all(q==0 for q in ybracket.values()), "Y bracket cancellation")
+    before_final=cur.copy()
+    for r,f in enumerate(final):
+        climb(r,f,"final")
+    need(cur==final,"final label state")
+    measured={r:hist(cn) for r,cn in by_role.items()}
+    need(measured==c["blocks"], "role histogram/count mismatch")
+    combined=sum(by_role.values(),Counter())
+    need(dict(combined)==EXPECTED_H, "baseline invocation histogram mismatch")
+    mass=sum(r*k for r,k in combined.items())
+    need(mass==c["N"]==R*h+2*v*(h-1)+c["cst"], "rank mass")
+    need(sum(r*k for r,k in by_role["c"].items())==c["cst"],"temporary-center rank mass")
+    scatter=Counter(str(coeff(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"]),"scatter"))
+                    for p in ports for k in range(22))
+    return {
+        "frame_count":len(frames),"tested_distinct_nested_pairs":len(pairs),
+        "live_registers_per_invocation":n,"temporary_centers":22,
+        "ranked_live_transitions":transitions,
+        "phase_stats":totals,"role_histograms":measured,
+        "phase_histograms":{p:hist(x) for p,x in by_phase.items()},
+        "invocation_histogram":hist(combined),"invocation_calls":sum(combined.values()),
+        "invocation_rank_mass":mass,"retained_centers":c["ret"],
+        "phase_state_sha256":{"start":digest(start),"after_A":digest(cut),
+                              "after_B":digest(before_final),"final":digest(final)},
+        "literal_gate_coefficients":dict(sorted(literal.items())),
+        "scalar_role_directions":dict(sorted(kind.items())),
+        "scatter_coefficients":dict(sorted(scatter.items())),
+        "scatter_additions":sum(scatter.values()),"Cc_copy_additions":22,
+        "two_hosts_metadata_count":len(c.get("two_hosts",[])),
+        "two_hosts_note":"Metadata only; not an independent allocator or host-use proof.",
+        "Y_bracket_pairs":len(ybracket),
+        "literal_inverse":"Each nonself additive shear inverts by negating its coefficient; inverse phase reverses order; inverse transpose keeps chronological order and swaps source/target with negation.",
+        "limits":["No scalar all-column replay","No old-response or cleanup matrix formed",
+                  "No generated Lean data comparison or kernel build","No physical stream compiler"]
+    }
+
+def scalar_word(ops):
+    matrix=[[int(i==j) for j in range(4)] for i in range(4)]
+    for target,source,q in ops:
+        matrix[target]=[a+q*b for a,b in zip(matrix[target],matrix[source])]
+    return matrix
diff --git a/research/five-stage-p10-transcript-stages/code/complex_scalars.py b/research/five-stage-p10-transcript-stages/code/complex_scalars.py
new file mode 100644
index 0000000000..98c5574693
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/code/complex_scalars.py
@@ -0,0 +1,216 @@
+"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+Q=Fraction
+from hashlib import sha256
+from pathlib import Path
+from math import prod
+import gzip,json,sys
+
+V,R,H=1320,9036,22
+def need(x,msg):
+    if not x:raise ValueError(msg)
+
+def kind(r):return "X" if r<V else "Y" if r<2*V else "S"
+
+def live(r):return ("L",r)
+
+def tmp(r):return ("T",r-2*V)
+
+def center(k):return ("C",k)
+
+def add(t,s,q):return ("add",t,s,q.numerator,q.denominator)
+
+def clear(t):return ("clear",t)
+
+def copy(t,s):return ("copy",t,s)
+
+def flat(gs):
+    out=[]
+    for g in gs:
+        need(g[0] in ["in","out"],"literal additive gate")
+        for r,a,b in g[3]:
+            t,s=(r,g[2]) if g[0]=="out" else (g[2],r)
+            need(t!=s and kind(s)!="Y" and not(kind(s)=="S" and kind(t)=="X"),
+                 "projection requires Y never read and no helper-to-X gate")
+            out.append((t,s,Q(a,b)))
+    return out
+
+def old_positive(A,B,c):
+    """Circuit with inputs temp S and live Y; X fixed at zero.
+    tempS output is irrelevant. Y output is Y_in + K tempS_in."""
+    def part(gs):
+        for t,s,q in gs:
+            if kind(s)=="X":continue
+            need(kind(s)=="S" and kind(t) in ["S","Y"],"old-response shape")
+            yield add(tmp(t) if kind(t)=="S" else live(t),tmp(s),q)
+    yield from part(A)
+    for t,p in enumerate(c["ports"]):
+        for k,r,_ in c["ret"]:
+            q=Q(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"]))
+            yield add(live(V+t),tmp(r),q)
+    yield from part(B)
+
+def old_word(orientation,K):
+    if orientation=="forward":
+        yield from (copy(("T",q),live(2*V+q)) for q in range(R))
+        for e in K:
+            op,t,s,a,b=e
+            yield add(t,s,Q(-a if t[0]=="L" else a,b))
+    else:
+        yield from (clear(("T",q)) for q in range(R))
+        for op,t,s,a,b in reversed(K):
+            yield add(s,t,Q(a,b))
+        yield from (add(live(2*V+q),("T",q),Q(1)) for q in range(R))
+    yield from (clear(("T",q)) for q in range(R))
+
+def cleanup(orientation,AB):
+    for t,s,q in reversed(AB):
+        if kind(t)=="Y":continue
+        if orientation=="forward":yield add(live(t),live(s),-q)
+        else:yield add(live(s),live(t),q)
+
+def main_scalar(orientation,A,B,c):
+    def phase(gs):
+        for t,s,q in gs:
+            if orientation=="forward":yield add(live(t),live(s),q)
+            else:yield add(live(s),live(t),-q)
+    yield from phase(A)
+    # Every center is a complete temporary stream and one rank20 child,
+    # initialized/read/discarded before the next center uses the work stock.
+    for k,r,_ in c["ret"]:
+        yield clear(center(k))
+        if orientation=="forward":yield add(center(k),live(r),Q(1))
+        for t,p in enumerate(c["ports"]):
+            q=Q(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"]))
+            if orientation=="backward":yield add(center(k),live(V+t),q)
+        yield ("recursive_center",k,20)
+        if orientation=="forward":
+            for t,p in enumerate(c["ports"]):
+                q=Q(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"]))
+                yield add(live(V+t),center(k),q)
+        else:yield add(live(r),center(k),Q(-1))
+        yield clear(center(k))
+    yield from phase(B)
+
+def inv_schedule(orientation,A,B,c):
+    K=list(old_positive(A,B,c))
+    yield from ((p,e) for p,es in [
+       ("old_response",old_word(orientation,K)),
+       ("main",main_scalar(orientation,A,B,c)),
+       ("cleanup",cleanup(orientation,A+B))] for e in es)
+
+def coeff_steps(q):
+    """Non-destructive coefficient expansion using one complete work stream.
+    Copy source, double/halve/divide by3 as needed, add/subtract, clear.
+    Counts Gaussian operations; multiply by2 for real/imag component primitives."""
+    a,b=abs(q.numerator),q.denominator
+    need(a in (1,2) and b in (1,2,3,6),"unsupported new coefficient")
+    return 3+int(a==2)+int(b%2==0)+int(b%3==0)
+
+def bill(schedule):
+    phases={p:Counter() for p in ("old_response","main","cleanup")}
+    coeffs={p:Counter() for p in phases}
+    tape=sha256()
+    for p,e in schedule:
+        tape.update((json.dumps((p,e),separators=(",",":"))+"\n").encode())
+        phases[p]["all_macros"]+=1
+        if e[0]=="recursive_center":
+            phases[p]["recursive_centers"]+=1
+            phases[p]["recursive_rank_mass"]+=e[2]
+            continue
+        phases[p]["scalar_macros"]+=1
+        phases[p][e[0]]+=1
+        if e[0]=="add":
+            q=Q(e[3],e[4]);coeffs[p][str(q)]+=1
+            phases[p]["Gaussian_primitive_steps"]+=coeff_steps(q)
+            phases[p]["scalar_log2_magnitude_charge"]+=1+int(abs(q)==2)
+            phases[p]["halving_exposure"]+=int(q.denominator%2==0)
+            phases[p]["divisor3_exposure"]+=int(q.denominator%3==0)
+        else:phases[p]["Gaussian_primitive_steps"]+=1
+    for p in phases:phases[p]["real_component_primitive_steps"]=2*phases[p]["Gaussian_primitive_steps"]
+    total=sum((Counter({k:v for k,v in x.items() if k not in ["recursive_rank_mass"]}) for x in phases.values()),Counter())
+    return {"phases":{p:dict(x) for p,x in phases.items()},"coefficient_histograms":{p:dict(x) for p,x in coeffs.items()},
+            "totals":dict(total),"schedule_sha256":tape.hexdigest(),
+            "other_main_recursive_calls":"68230 existing live-label transitions, unchanged; not scalar macros"}
+
+def mm(A,B):return [[sum((x*y for x,y in zip(row,col)),Q(0)) for col in zip(*B)] for row in A]
+
+def lifecycle(schedule):
+    """Verify that new scalar-only work stock never survives into a child."""
+    initialized=set();dirty=set();active_centers=set();seen_main=False;children=0
+    for phase,e in schedule:
+        if phase=="main" and not seen_main:
+            need(not dirty,"old-response tableau survives into recursive main phase")
+            seen_main=True
+        need(e[0] in ("add","copy","clear","recursive_center"),"unknown or unpaid recursive operation")
+        if e[0]=="recursive_center":
+            k=e[1]
+            need(type(k) is int and 0<=k<22 and e[2]==20,"new temporary entered uncharged child")
+            need(phase=="main" and not dirty,"old-response temporary used during child")
+            need(active_centers<=set([k]),"other center was not discarded before next child")
+            children+=1
+            continue
+        target=e[1]
+        source=e[2] if e[0] in ("add","copy") else None
+        if source and source[0]=="T":need(source[1] in initialized,"uninitialized temporary read")
+        if target[0]=="T":
+            need(phase=="old_response","scalar-only tableau touched after recursive phase begins")
+            initialized.add(target[1])
+            if e[0]=="clear":dirty.discard(target[1])
+            else:dirty.add(target[1])
+        if target[0]=="C":
+            if e[0]=="clear":active_centers.discard(target[1])
+            else:active_centers.add(target[1])
+        if e[0]=="add":
+            # Coefficient expansion is deliberately local: copy into W,
+            # optionally double/halve/divide3, accumulate, and clear W.
+            expanded=["copy_work"]+["scale"]*(coeff_steps(Q(e[3],e[4]))-3)+["accumulate","clear_work"]
+            need(expanded[-1]=="clear_work","coefficient work survived scalar macro")
+    need(not dirty and not active_centers,"temporary stock not erased at invocation end")
+    need(children==22,"center child count changed")
+    return {"tableau_cleared_before_entire_main_phase":True,"tableau_absent_from_all_children":True,
+            "coefficient_work_cleared_per_add":True,"center_children":children,
+            "new_recursive_children":0,"moment_live_width":14316,
+            "new_work_stock_only":9037,"complete_stream_fraction":"1/(14316*|Orth(110,2)|)"}
+
+def ident(n):return [[Q(int(i==j)) for j in range(n)] for i in range(n)]
+
+def matrix(n,gs):
+    a=ident(n)
+    for t,s,q in gs:a[t]=[x+q*y for x,y in zip(a[t],a[s])]
+    return a
+
+def toy_checks():
+    # 2 X, 3 S, 2 Y. Explicit nontrivial X mixing is undone; helper map
+    # and K are otherwise arbitrary. Exact Fraction checks cover every column
+    # of THIS TINY TEMPLATE, not of the published 11676-register source.
+    n=7;X={0,1};S={2,3,4};Y={5,6}
+    gs=[(2,0,Q(1)),(3,2,Q(2)),(5,3,Q(-1,6)),(0,1,Q(1,2)),
+        (4,0,Q(2)),(2,4,Q(1,2)),(6,2,Q(1,3)),(0,1,Q(-1,2)),
+        (3,1,Q(-1)),(5,4,Q(1)),(6,0,Q(1))]
+    M=matrix(n,gs)
+    need(all(M[i]==ident(n)[i] for i in X),"toy source rows not restored")
+    Ugs=[e for e in gs if e[0] not in Y]
+    U=matrix(n,Ugs)
+    Uinv=matrix(n,[(t,s,-q) for t,s,q in reversed(Ugs)])
+    need(mm(Uinv,U)==ident(n),"restricted inverse identity")
+    Mi=matrix(n,[(t,s,-q) for t,s,q in reversed(gs)])
+    g8=[Mi[i] if i in S else ident(n)[i] for i in range(n)]
+    h8=[M[i] if i in S else ident(n)[i] for i in range(n)]
+    need(g8==Uinv and h8==U,"cleanup projection identities")
+    Ut=matrix(n,[(s,t,q) for t,s,q in reversed(Ugs)])
+    need(Ut==[list(x) for x in zip(*U)],"backward cleanup transpose")
+    Kgs=[e for e in gs if e[1] not in X]
+    Kmat=matrix(n,Kgs)
+    need(all(Kmat[i][j]==M[i][j] for i in Y for j in S),"zero-source old response")
+    Kt=matrix(n,[(s,t,q) for t,s,q in reversed(Kgs)])
+    need(all(Kt[i][j]==M[j][i] for i in S for j in Y),"old response adjoint")
+    bad=matrix(n,[(t,s,q) for t,s,q in reversed(Ugs)])
+    need(bad!=g8,"wrong inverse sign must fail")
+    bad_order=matrix(n,[(s,t,q) for t,s,q in Ugs])
+    need(bad_order!=Ut,"unreversed transpose must fail")
+    return {"tiny_exact_template_columns_checked":7,"checks_passed":7,
+            "wrong_inverse_sign_rejected":True,"unreversed_transpose_rejected":True,
+            "published_full_scalar_replay":False}
diff --git a/research/five-stage-p10-transcript-stages/code/complex_splice.py b/research/five-stage-p10-transcript-stages/code/complex_splice.py
new file mode 100644
index 0000000000..4644f596af
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/code/complex_splice.py
@@ -0,0 +1,277 @@
+"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+Q=Fraction
+from hashlib import sha256
+from pathlib import Path
+from math import prod
+import gzip,json,sys
+
+V,R,H,N,W=1320,9036,22,11676,14316
+PHASES=["old_response","ad0","A","centers","B","final","adF","cleanup","done"]
+def need(x,s):
+    if not x:raise ValueError(s)
+
+def blobhash(p):return sha256(p.read_bytes()).hexdigest()
+
+def digest(x):return sha256(json.dumps(x,separators=(',',':'),sort_keys=True).encode()).hexdigest()
+
+def role(r):return 'X' if r<V else 'Y' if r<2*V else 'S'
+
+def add(t,s,q):return ('add',t,s,q.numerator,q.denominator)
+
+def L(r):return ('L',r)
+
+def T(r):return ('T',r-2*V)
+
+def C(k):return ('C',k)
+
+def clear(t):return ('clear',t)
+
+def copy(t,s):return ('copy',t,s)
+
+def flat(gs):
+    for g in gs:
+        for r,a,b in g[3]:
+            t,s=(r,g[2]) if g[0]=='out' else (g[2],r)
+            need(t!=s and role(s)!='Y' and (role(s),role(t))!=('S','X'),'scalar projection shape')
+            yield t,s,Q(a,b)
+
+def scal(phase,e,frame):return ('scalar',phase,e,frame)
+
+def lower_scalar(e):
+    # The coefficient work stream is disjoint from every live and center role.
+    if e[0] in ['copy','clear']:return [e]
+    _,t,s,a,b=e;work=('W',0)
+    out=[copy(work,s)]
+    if abs(a)==2:out.append(('double',work))
+    if b%2==0:out.append(('halve',work))
+    if b%3==0:out.append(('divide3',work))
+    return out+[('accumulate',t,work,1 if a>0 else -1),clear(work)]
+
+def emit(c,ori):
+    """Construct the complete local parametric invocation, before cover routing.
+    One role stream is its full complete address rectangle. Frame labels denote
+    exact canonical representatives, never just rank or binary matrices.
+    """
+    A=list(flat(c['A']));B=list(flat(c['B']));cur=c['start'].copy()
+    K=[]
+    for part in (A,None,B):
+        if part is None:
+            for t,p in enumerate(c['ports']):
+                for k,r,f in c['ret']:
+                    K.append(add(L(V+t),T(r),Q(*(c['scat']['inside'] if p>>k&1 else c['scat']['outside']))))
+        else:
+            for t,s,q in part:
+                if role(s)=='X':continue
+                K.append(add(T(t) if role(t)=='S' else L(t),T(s),q))
+    yield ('phase','old_response')
+    if ori=='forward':
+        for q in range(R):yield scal('old_response',copy(('T',q),L(2*V+q)),'old0')
+        for _,t,s,a,b in K:yield scal('old_response',add(t,s,Q(-a if t[0]=='L' else a,b)),'old0')
+    else:
+        for q in range(R):yield scal('old_response',clear(('T',q)),'old0')
+        for _,t,s,a,b in reversed(K):yield scal('old_response',add(s,t,Q(a,b)),'old0')
+        for q in range(R):yield scal('old_response',add(L(2*V+q),('T',q),Q(1)),'old0')
+    for q in range(R):yield scal('old_response',clear(('T',q)),'old0')
+    yield ('phase','ad0')
+    for r,f in enumerate(c['start']):yield ('adapter','old_to_new',r,f)
+    for part in ['A','centers','B','final']:
+        yield ('phase',part)
+        if part in ['A','B']:
+            for g in c[part]:
+                regs=[g[2]]+[x[0] for x in g[3]]+(g[4] if g[0]=='out' else [])
+                for r in regs:
+                    if cur[r]!=g[1]:
+                        old=cur[r];cur[r]=g[1]
+                        yield ('climb',part,r,old,g[1],len(c['frames'][g[1]])-len(c['frames'][old]))
+                for t,s,q in flat([g]):
+                    e=add(L(t),L(s),q) if ori=='forward' else add(L(s),L(t),-q)
+                    yield scal('main',e,g[1])
+        elif part=='centers':
+            for k,r,f in c['ret']:
+                yield scal('main',clear(C(k)),f if ori=='forward' else 0)
+                if ori=='forward':yield scal('main',add(C(k),L(r),Q(1)),f)
+                else:
+                    for t,p in enumerate(c['ports']):
+                        yield scal('main',add(C(k),L(V+t),Q(*(c['scat']['inside'] if p>>k&1 else c['scat']['outside']))),0)
+                yield ('center',k,f if ori=='forward' else 0,0 if ori=='forward' else f,20)
+                if ori=='forward':
+                    for t,p in enumerate(c['ports']):
+                        yield scal('main',add(L(V+t),C(k),Q(*(c['scat']['inside'] if p>>k&1 else c['scat']['outside']))),0)
+                else:yield scal('main',add(L(r),C(k),Q(-1)),f)
+                yield scal('main',clear(C(k)),0 if ori=='forward' else f)
+        else:
+            for r,f in enumerate(c['final']):
+                if cur[r]!=f:
+                    old=cur[r];cur[r]=f
+                    yield ('climb','final',r,old,f,len(c['frames'][f])-len(c['frames'][old]))
+    yield ('phase','adF')
+    for r,f in enumerate(c['final']):yield ('adapter','new_to_old',r,f)
+    yield ('phase','cleanup')
+    for t,s,q in reversed(A+B):
+        if role(t)=='Y':continue
+        e=add(L(t),L(s),-q) if ori=='forward' else add(L(s),L(t),q)
+        yield scal('cleanup',e,'old1')
+    yield ('phase','done')
+
+def contains(U,V):
+    for u in U:
+        for v in V:
+            if u>>(v.bit_length()-1)&1:u^=v
+        if u:return False
+    return True
+
+def validate(events,c,ori,manifest,bill):
+    phase=None;seen=[];cur=c['start'].copy();cent={};dirty=set();initialized=set()
+    climbed=Counter();hist=Counter();projection=sha256();whole=sha256();counts=Counter();ad0=[];adF=[]
+    pairs=set();states={};all_frame_incidence=0;primitive=sha256();primitive_count=0
+    for ev in events:
+        whole.update((json.dumps(ev,separators=(',',':'))+'\n').encode())
+        tag=ev[0];counts[tag]+=1
+        if tag=='phase':
+            if phase=='A':states['after_A']=digest(cur)
+            if phase=='B':states['after_B']=digest(cur)
+            if phase=='final':states['final']=digest(cur)
+            phase=ev[1];seen.append(phase)
+            need(seen==PHASES[:len(seen)],'strict old/A/copy/B/final/adapter/cleanup chronology')
+            if phase=='ad0':need(not dirty,'old-response tableau survived before label recursion')
+            if phase=='A':need(ad0==list(enumerate(c['start'])),'missing or reordered exact entry adapter')
+            if phase=='adF':need(cur==c['final'],'final climbs omitted before cleanup')
+            if phase=='cleanup':need(adF==list(enumerate(c['final'])),'missing or reordered exact final adapter')
+            continue
+        if tag=='adapter':
+            _,which,r,f=ev
+            if which=='old_to_new':need(phase=='ad0','entry adapter position');ad0.append((r,f))
+            else:need(which=='new_to_old' and phase=='adF','final adapter position');adF.append((r,f))
+        elif tag=='climb':
+            _,p,r,old,new,d=ev
+            need(phase==p and p in ['A','B','final'],'live child outside source label walk')
+            need(not dirty and not cent,'new work stock or center active during live child')
+            need(cur[r]==old and d==len(c['frames'][new])-len(c['frames'][old]) and d>0,'wrong exact child endpoints/rank')
+            pair=(old,new)
+            if pair not in pairs:need(contains(c['frames'][old],c['frames'][new]),'nonnested child');pairs.add(pair)
+            cur[r]=new;climbed[p]+=1;hist[d]+=1
+        elif tag=='center':
+            _,k,old,new,d=ev
+            need(phase=='centers' and not dirty and set(cent)=={k},'center child ownership')
+            need(cent[k]==old and (k,c['ret'][k][1],c['ret'][k][2])==tuple(c['ret'][k]),'center input frame')
+            f=c['ret'][k][2]
+            need((old,new,d)==((f,0,20) if ori=='forward' else (0,f,20)),'center child direction/rank')
+            cent[k]=new;hist[d]+=1
+            projection.update((json.dumps(('main',('recursive_center',k,d)),separators=(',',':'))+'\n').encode())
+        elif tag=='scalar':
+            _,p,e,f=ev
+            need(p==('main' if phase in ['A','centers','B'] else phase),'scalar phase binding')
+            need(e[0] in ['add','copy','clear'],'unpaid scalar operation')
+            target=e[1];source=e[2] if e[0] in ['add','copy'] else None
+            for x in [target]+([source] if source else []):
+                bank,r=x
+                if bank=='T':need(phase=='old_response' and 0<=r<R,'tableau outside old response')
+                elif bank=='C':need(phase=='centers' and 0<=r<H,'center outside copied block')
+                elif bank=='L':
+                    need(0<=r<N,'live register range')
+                    if phase=='old_response':need(role(r) in ['S','Y'] and f=='old0','old response not at common old0')
+                    elif phase=='cleanup':need(role(r) in ['X','S'] and f=='old1' and cur[r]==1,'cleanup not at common old1')
+                    else:need(cur[r]==f,'scalar incidence uses wrong exact label');all_frame_incidence+=1
+                else:raise ValueError('unknown stream namespace')
+            if source and source[0]=='T':need(source[1] in initialized,'read before tableau initialization')
+            if source and source[0]=='C':need(cent.get(source[1])==f,'center source frame')
+            if target[0]=='T':
+                if e[0]=='add':need(target[1] in initialized,'tableau accumulation before initialization')
+                initialized.add(target[1])
+                if e[0]=='clear':dirty.discard(target[1])
+                else:dirty.add(target[1])
+            if target[0]=='C':
+                if e[0]=='clear':
+                    if target[1] in cent:del cent[target[1]]
+                else:
+                    need(not cent or set(cent)=={target[1]},'overlapping center lifetimes')
+                    need(cent.get(target[1],f)==f,'center target frame');cent[target[1]]=f
+            if e[0]=='add':need(e[4] in [1,2,3,6] and abs(e[3]) in [1,2],'unrecorded coefficient')
+            projection.update((json.dumps((p,e),separators=(',',':'))+'\n').encode())
+            lowered=lower_scalar(e)
+            if e[0]=='add':need(lowered[-1]==('clear',('W',0)),'coefficient work survives scalar macro')
+            for op in lowered:
+                primitive.update((json.dumps((p,op),separators=(',',':'))+'\n').encode())
+                primitive_count+=1
+        else:raise ValueError('unknown physical event')
+    need(seen==PHASES and not dirty and not cent,'incomplete invocation or dirty temporary')
+    need(dict(climbed)=={'A':18012,'B':41182,'final':9036},'live transition count/partition')
+    need(counts['center']==22 and counts['climb']==68230,'paid children omitted or doubled')
+    need({str(k):v for k,v in sorted(hist.items())}==manifest['checks']['invocation_histogram'],'paid source histogram changed')
+    need(states=={k:v for k,v in manifest['checks']['phase_state_sha256'].items() if k!='start'},'exact label states differ')
+    need(projection.hexdigest()==bill[ori]['schedule_sha256'],'complete scalar program differs from checked bill')
+    need(2*primitive_count==bill[ori]['totals']['real_component_primitive_steps'],'independent primitive expansion bill')
+    return dict(events=sum(counts.values()),event_counts=dict(counts),program_sha256=whole.hexdigest(),
+        scalar_projection_sha256=projection.hexdigest(),live_transition_partition=dict(climbed),
+        paid_children=counts['climb']+counts['center'],final_climbs_before_cleanup=True,
+        exact_common_label_live_incidences=all_frame_incidence,distinct_nested_pairs=len(pairs),
+        exact_label_state_sha256=states,old_response_erased_before_all_children=True,
+        entry_and_exit_old_new_adapters=2*N,Gaussian_primitives=primitive_count,
+        real_component_primitives=2*primitive_count,scalar_primitive_sha256=primitive.hexdigest())
+
+def global_contract(manifest):
+    return dict(family='baseline5stageComplex',m=110,live=14316,physical=23375,
+        stage_recipe=[dict(stage=j,window=f'G{j}',orientation=o,active_pair=p,
+            bank_owner='d' if j==0 else f'r{j}(t)^(-1)(d)',helper_owner='d' if j==0 else f's{j}(d)',
+            exterior_subset='empty' if j==0 else f'qS bs{j} l',
+            native_frame=f'(G{j} d).X.Phi(frames[f])',old_frame=f'(G{j} d).Xm.Phi(P)')
+            for j,(o,p) in enumerate([('forward',1),('backward',1),('forward',1),('backward',2),('forward',2)])],
+        chronology=manifest['chronology'],exact_frame_bindings=manifest['source_frame_equalities'],
+        scratch_namespace=dict(centers=[14316,14338],tableau=[14338,23374],coefficient=[23374,23375]),
+        recursive_volume_denominator=14316,primitive_policy='charged_fixed_tape_complete_streams',
+        label_policy='identical_exact_representative_and_paid_rank_zero_reconciliation',
+        helper_policy='arbitrary_input; inherited_dirty_lift; Z5=kernel',
+        odd_grid='2^(-P)3^(-G(D+1)); no return rounding',local_bound_exponent=48,
+        global_bound_exponent=6050,maintained_guard_changed=False,
+        primitive_recipe=dict(scalar='copy source to W; optional double/halve/divide3; signed accumulate; clear W',
+            live_child='exact target representative times inverse current representative; two rank-zero factors around one C tensor child',
+            center_forward='copy at retained frame; exact residual to frame zero; scatter; erase',
+            center_backward='zero at frame zero; accumulate transpose scatter; exact residual to retained frame; subtract into original; erase',
+            entry_exit='WinB.old_to_new and WinB.new_to_old, lowered as paid exact rank-zero Clifford operators',
+            rank_zero='binary Gaussian elimination; affine bit flips; Z4 linear phases and even cross terms; exact scalar fourth root',
+            cross_phase='i^(2xy) = i^x i^y i^(-(x xor y)); at most three parity-phase scans',
+            selected_bit='compact-control-movement proposition, complete restored borrowed fields, paid repair, no RAM lookup',
+            phase_scan='evaluate fixed Z4 quadratic descriptors per record, multiply by fourth root, record suffix pays descriptor arithmetic',
+            role_route='permutation on all complete live/work roles, at most W_physical^2 complete-stream exchanges on fixed tapes',
+            row_stock='split only live complete rows; scalar-only work creates no row coordinate or recursive branch'))
+
+def validate_global(g,m):
+    need(g==global_contract(m),'five-window exact source/tape/namespace contract changed')
+    # Injective embedding of each invocation and its disjoint temporary stock.
+    for s in g['stage_recipe']:
+        p=s['active_pair'];offset=2*V*(p-1)
+        live=[offset+r for r in range(2*V)]+[4*V+q for q in range(R)]
+        work=list(range(14316,23375))
+        need(len(set(live+work))==len(live+work),'global workstream aliases a live role')
+        need(all(0<=r<W for r in live),'global live embedding')
+    return True
+
+def controls(events,c,ori,m,b):
+    def rejected(name,fn):
+        x=list(events);fn(x)
+        try:validate(x,c,ori,m,b)
+        except ValueError as e:return dict(name=name,rejected=True,reason=str(e))
+        raise ValueError('mutation accepted: '+name)
+    out=[]
+    out.append(rejected('drop_final_climb',lambda x:x.pop(next(i for i,e in enumerate(x) if e[:2]==('climb','final')))))
+    def move_cleanup(x):
+        a=next(i for i,e in enumerate(x) if e==('phase','final'))
+        b=next(i for i,e in enumerate(x) if e==('phase','cleanup'))
+        x[a:b]=x[b:-1]+x[a:b];x[b:]=[('phase','done')]
+    out.append(rejected('cleanup_before_final_climbs',move_cleanup))
+    out.append(rejected('drop_final_frame_adapter',lambda x:x.pop(next(i for i,e in enumerate(x) if e[:2]==('adapter','new_to_old')))))
+    def wrong_frame(x):
+        i=next(i for i,e in enumerate(x) if e[0]=='scalar' and e[1]=='main' and isinstance(e[3],int))
+        e=x[i];x[i]=e[:3]+(-1,)
+    out.append(rejected('wrong_common_exact_gate_label',wrong_frame))
+    out.append(rejected('drop_center_child',lambda x:x.pop(next(i for i,e in enumerate(x) if e[0]=='center'))))
+    out.append(rejected('tableau_not_erased_before_child',lambda x:x.pop(max(i for i,e in enumerate(x) if e[0]=='scalar' and e[1]=='old_response' and e[2]==('clear',('T',0))))))
+    def wrong_sign(x):
+        i=next(i for i,e in enumerate(x) if e[0]=='scalar' and e[1]=='cleanup')
+        z=x[i];e=z[2];x[i]=z[:2]+(e[:3]+(-e[3],e[4]),z[3])
+    out.append(rejected('wrong_cleanup_sign',wrong_sign))
+    for entry in out:entry['orientation']=ori
+    return out
diff --git a/research/five-stage-p10-transcript-stages/code/geometry527.py b/research/five-stage-p10-transcript-stages/code/geometry527.py
new file mode 100644
index 0000000000..06506dd857
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/code/geometry527.py
@@ -0,0 +1,128 @@
+"""Portable exact h/m callable geometry (h = 2p, m = 5h; h20/m100 at p = 10); inherited PR234 proof and notices.
+p = 10 port (DreamingOfClouds, Anthropic Claude assistance): the h24/m120 literals are derived from the cube
+size; the idle gaps are the five-stage ranks (2h-2, h-1, 2h+2, 4); every entrance rank present is checked on
+an actual basis, the most frequent rank on two distinct actual bases.
+"""
+from array import array
+from collections import Counter
+from functools import lru_cache
+from pathlib import Path
+import hashlib,json,sys,time
+import sympy as sp
+from collections import Counter as _Counter
+sys.dont_write_bytecode=True
+if not __debug__:raise SystemExit('assertions required')
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def run(ctx,L,source_pins=None):
+ begin=time.monotonic()
+ W,C=ctx['W'],ctx['C'];v=W.v;H,M=L.H,L.M;assert W.h==H and M==5*H and W.v==L.V
+ Z=W.register([]);F=W.w['full_frame']
+ initial={i:W.w['source_frame'][i]for i in range(v)}
+ initial.update({v+t:Z for t in range(v)})
+ initial.update({2*v+j:W.gauge[r]['frame']if r in W.gauge else Z for j,r in enumerate(ctx['regs'])})
+ lower=L.Lowerer(array('i'),dict(W=W,C=C,initial_state=initial,ZERO=Z,FULL=F))
+ I=sp.eye(M);zero=sp.zeros(M)
+ S=sp.SparseMatrix
+ all_labels=[list(row)for row in W.g['labels']]
+ assert len(all_labels)==v and all(len(q)==len(set(q))==3 and all(0<=j<H for j in q)for q in all_labels)
+ ports=[0,v-1];checked=[];g1,g2,g3,g4=L.IDLE_RANKS
+ for t in ports:
+     routes=[S(lower.rho(i,t))for i in range(5)]
+     assert all(r*r==I for r in routes)
+     P=lower.frame_projector(W.w['source_frame'][t])
+     assert P*P==P and sp.trace(P)==1
+     @lru_cache(None)
+     def data(i,kind):
+         frame=F if kind=='H'else Z if kind=='0'else W.w['source_frame'][t]
+         A=S(lower.global_stage_projector(i,frame,kind=='K'))
+         return routes[i]*A*routes[i]
+     for i in range(1,5):
+         assert data(i-1,'H')==data(i,'P')
+         assert data(i-1,'K')==data(i,'0')
+     p=data(0,'P')
+     pairs=[(p,data(1,'H'),g1),(S(zero),data(1,'K'),g1),
+            (data(2,'P'),data(3,'P'),g2),(data(2,'0'),data(3,'0'),g2),
+            (data(2,'H'),S(I),g3),(data(2,'K'),S(I)-p,g3),
+            (data(4,'H'),S(I),g4),(data(4,'K'),S(I)-p,g4)]
+     original_data_boundary=lower.data_boundary
+     assert S(original_data_boundary(3,t,'P'))==data(3,'P')
+     # Feed cached exact boundary matrices through the actual idle selector.
+     # This exercises its eight emitted boundary IDs without recomputing all
+     # dense matrices once per selector call.
+     def cached_boundary(i,port,kind):
+         assert port==t
+         return data(i,kind)
+     lower.data_boundary=cached_boundary
+     for boundary,(a,b,rank) in enumerate(pairs):
+         emitted_a,emitted_b=lower.idle_projectors(boundary,t)
+         assert S(emitted_a)==a and S(emitted_b)==b
+         assert a*b==b*a==a
+         gap=b-a
+         assert gap*gap==gap and sp.trace(gap)==rank
+     lower.data_boundary=original_data_boundary
+     # D_I D_P = D_(I-P), since D_I exchanges the address head/tail blocks.
+     # Check its projector algebra before the final stream pair exchange.
+     assert p*(S(I)-p)==S(zero) and p+(S(I)-p)==S(I)
+     checked.append(dict(port=t,labels=all_labels[t],routes=5,boundaries=8,idle_ranks=[r for a,b,r in pairs]))
+ 
+ census=_Counter(rank for _,frame,rank in lower.entrances);common=max(sorted(census),key=lambda r:census[r])
+ unique={}
+ for _,frame,rank in lower.entrances:
+     if rank==common:unique.setdefault(tuple(map(tuple,C.B[frame])),frame)
+ frames=list(unique.values())[:2]
+ assert len(frames)==2
+ # Two actual bases of the most frequent entrance rank (16 at p = 10) and one actual basis of every other rank.
+ others=[next(frame for _,frame,rank in lower.entrances if rank==r)for r in sorted(census)if r!=common]
+ sigma=[S(lower.frame_projector(f))for f in frames]
+ assert sigma[0]!=sigma[1]
+ helpers=[]
+ for frame,P in zip(frames+others,sigma+[S(lower.frame_projector(f))for f in others]):
+     rank=C.dimf[frame];assert rank in census
+     assert P*P==P and sp.trace(P)==rank
+     completion=S(lower.completion_projector(frame))
+     residual=S(I)-completion
+     assert completion*completion==completion and sp.trace(completion)==5*rank
+     assert completion*residual==residual*completion==S(zero)
+     actual=[]
+     for i in range(5):
+         tau=S(lower.tau(i));local=sp.zeros(M);local[:H,:H]=sp.eye(H)-P
+         actual.append(tau*S(local)*tau)
+     assert sum(actual,S(zero))==residual
+     assert all(a*b==S(zero)for i,a in enumerate(actual)for j,b in enumerate(actual)if i!=j)
+     assert sum(actual[:4]+[actual[3]],S(zero))!=residual
+     helpers.append(dict(local_frame=frame,local_rank=rank,completion_rank=5*rank,distinct_windows=5))
+ assert lower.completion_projector(frames[0])!=lower.completion_projector(frames[1])
+ # Early restoration: one actual (sigma, E) endpoint pair; residual P_E - P_sigma and completion P_sigma + I - P_E.
+ restored=[]
+ for role,E in sorted(ctx.get('restored_endpoints',{}).items())[:1]:
+     sg=W.gauge[role]['frame'];Ps=S(lower.frame_projector(sg));Pe=S(lower.frame_projector(E));D=Pe-Ps;IH=sp.eye(H)
+     assert Ps*Pe==Ps and Pe*Ps==Ps and D*D==D and sp.trace(D)==C.dimf[E]-C.dimf[sg]
+     completion=S(lower.completion_projector(sg,end=E));residual=S(I)-completion
+     assert completion*completion==completion and sp.trace(completion)==5*(C.dimf[sg]+H-C.dimf[E])
+     actual=[]
+     for i in range(5):
+         tau=S(lower.tau(i));local=sp.zeros(M);local[:H,:H]=D;actual.append(tau*S(local)*tau)
+     assert sum(actual,S(zero))==residual and all(a*b==S(zero)for i,a in enumerate(actual)for j,b in enumerate(actual)if i!=j)
+     wrong=sp.zeros(M);wrong[:H,:H]=IH-Ps
+     assert sum([S(lower.tau(i))*S(wrong)*S(lower.tau(i))for i in range(5)],S(zero))!=residual,'old FULL residual formula must be rejected'
+     restored.append(dict(entrance_rank=C.dimf[sg],endpoint_rank=C.dimf[E],residual_rank=C.dimf[E]-C.dimf[sg],completion_rank=5*(C.dimf[sg]+H-C.dimf[E]),full_endpoint_formula_rejected=True))
+ assert len(restored)==(1 if ctx.get('restored_endpoints') else 0)
+ # Every new sparse-source injection frame is checked as an exact h-dimensional projector.
+ new_frames={r['mix_frame']for r in ctx['pair_selection']};G=sp.eye(H)-sp.ones(H)/9
+ for f in sorted(new_frames):
+  P=lower.frame_projector(f);assert P*P==P and sp.trace(P)==2 and P.T*G==G*P
+ assert len(new_frames)==0
+ 
+ 
+ assert {h['local_rank']for h in helpers}==set(census)
+ result=dict(status='PASS_EXACT_CALLABLE_LOWERING_GEOMETRY',h=H,m=M,entrance_rank_census=dict(census),
+     all_ports_coordinate_permutation_equivalent=True,ports=v,checked_actual_ports=checked,
+     checked_actual_entrances=helpers,checked_restored_endpoints=restored,checked_new_sparse_source_frames=len(new_frames),
+     distinct_entrances_noncommuting=sigma[0]*sigma[1]!=sigma[1]*sigma[0],
+     wrong_duplicate_window_rejected=True,wrong_equal_rank_correction_rejected=True,
+     terminal_exchange_frame_identity_checked=True,
+     source_pins=dict(source_pins or {}),clean_fingerprint=dict(scalar_word_sha256=hashlib.sha256(ctx['SOURCE_TEXT'].encode()).hexdigest()),
+     script_sha256=sha(Path(__file__)),seconds=time.monotonic()-begin,
+     scope='Exact rational h'+str(H)+'/m'+str(M)+' route and idle matrices for actual source ports and actual independent entrance bases. Coordinate-permutation/direct-sum arguments cover the remaining ports and independent entrances. No scalar payload replay.')
+ 
+ return result
diff --git a/research/five-stage-p10-transcript-stages/code/global_lowering.py b/research/five-stage-p10-transcript-stages/code/global_lowering.py
new file mode 100644
index 0000000000..eec2edda2c
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/code/global_lowering.py
@@ -0,0 +1,332 @@
+# Adapted from Henry Grant / hcg890's PR234; upstream code is unchanged except
+# the exact gen5 register count and fresh checked count/digest bindings.
+# p = 10 port (DreamingOfClouds, Anthropic Claude assistance): V, H, M, the idle ranks (2H-2, H-1, 2H+2, 4),
+# the copied-centre rank/count/reads (H-2, H, 3V/H) and the deficit 4V-5H(H-2) are derived from the cube size
+# (word_pins.shape); R and the entrance census are pinned in word-pins.json.
+# Prepared with substantial OpenAI Codex assistance; upstream notices retained.
+"""Source-bound callable five-stage global physical lowering, with streaming QA.
+
+The finite cover variable stays symbolic. One iteration means one cover class;
+iter_program() is the exact template to apply to every class in each phase.
+No formal F2 payload columns are replayed. The complete local tagged word is
+materialized once, then all five actual renamed/reversed instruction streams
+are checked and hashed. The local all-column theorem composes through these
+explicit namespace, frame, copy-lifetime and boundary bindings.
+"""
+from array import array
+from collections import Counter
+from contextlib import redirect_stdout
+from functools import lru_cache
+from pathlib import Path
+import hashlib, importlib.util, io, json, struct, sys, time
+from word_pins import expect, pinned, shape
+
+BASE = Path(__file__).resolve().parent
+ROOT = BASE.parent
+PHYSICAL = BASE/'five_stage_source471_physical_telescope_20261009.py'
+ACTIVE = ((0,1),(1,0),(0,1),(3,2),(2,3))
+BANKS = ('X1','Y1','X2','Y2')
+SHAPE = shape()
+V, R, H, M = SHAPE['v'], pinned('final_physical_R'), SHAPE['h'], SHAPE['m']   # after terminal sinks
+IDLE_RANKS = SHAPE['idle']   # (2H-2, H-1, 2H+2, 4); 46, 23, 50, 4 at H = 24
+CENTER, CENTERS, SCATTER, DEFICIT = SHAPE['center_rank'], SHAPE['centers'], SHAPE['scatter_reads'], SHAPE['deficit']
+assert M == 5*H
+LOCAL, LIVE, WORK = 2*V+R, 4*V+R, 4*V+R
+# Compact instruction kinds: move, add, copy, erase, idle, bridge, completion.
+MOVE, ADD, COPY, ERASE, IDLE, BRIDGE, COMPLETE, EXCHANGE = range(8)
+LOCAL_BEGIN, LOCAL_END = 2, 3
+PACK = struct.Struct('<8i')
+sha = lambda b: hashlib.sha256(b).hexdigest()
+if not __debug__:
+    raise SystemExit('refusing optimized Python: assertion checks are required')
+
+def family(stage, local):
+    assert 0 <= stage < 5 and 0 <= local <= LOCAL
+    if local == LOCAL: return WORK
+    if local < V: return ACTIVE[stage][0]*V+local
+    if local < 2*V: return ACTIVE[stage][1]*V+local-V
+    return 4*V+local-2*V
+
+def address(stage, local, cover='d'):
+    """An actual global family and an exact right-multiplication route word.
+
+    rho(stage,port) is the involution in the checked rational route template;
+    tau(stage) is the whole-block exchange. A workstream is external and is
+    reused only after ERASE. Cover-class enumeration is supplied by the compiler.
+    """
+    f = family(stage,local)
+    if local == LOCAL: return (f, ('external_work', 0))
+    if stage == 0: return (f, ('class',cover))
+    route = ('rho',stage,local%V) if local < 2*V else ('tau',stage)
+    return (f, ('right',cover,route))
+
+def check_namespace(mapper=family):
+    for stage in range(5):
+        images = [mapper(stage,i) for i in range(LOCAL+1)]
+        assert len(set(images)) == LOCAL+1, 'live/work collision'
+        assert images[-1] == WORK and WORK not in images[:-1], 'external work not preserved'
+        for i in range(LOCAL):
+            expected = (ACTIVE[stage][0]*V+i if i<V else
+                        ACTIVE[stage][1]*V+i-V if i<2*V else 4*V+i-2*V)
+            assert images[i] == expected, 'incorrect data/helper owner'
+    return True
+
+class Lowerer:
+    """Callable IR lowering; op records have exactly eight signed int fields.
+
+    Stage MOVE: (op,family,old_frame,new_frame,rank,0,stage,complement).
+    Stage ADD:  (op,dst,src,coefficient,frame,category,stage,complement).
+    COPY:       (op,temp,src,0,frame,0,stage,complement).
+    ERASE:      (op,temp,-1,0,frame,0,stage,complement).
+    IDLE:       (op,family,-1,0,rank,boundary_id,-1,0).
+    BRIDGE:     (op,dst,src,coefficient,0,boundary_id,-1,0).
+    COMPLETE:   (op,helper,-1,0,rank,entrance_frame,-1,0).
+
+    frame_projector() and global_stage_projector() supply exact rational matrix
+    meanings on demand. Data IDLE boundaries and COMPLETE are defined below.
+    """
+    def __init__(self,records,context):
+        self.records,self.ns = records,context
+        self.W,self.C = context['W'],context['C']
+        self.initial = context['initial_state']
+        self.ZERO,self.FULL = context['ZERO'],context['FULL']
+        self.entrances = [(4*V+j,self.initial[2*V+j],self.C.dimf[self.initial[2*V+j]])
+                         for j in range(R) if self.C.dimf[self.initial[2*V+j]]]
+        if 'context' in context:assert len(context['context']['regs'])==R,'register count differs from the emitted word'
+        # Early-restored helpers end at E below FULL: their completion is P_sigma + (I - P_E), rank a + H - dim E.
+        self.endpoints = dict(context.get('helper_endpoints',{}))
+        assert all(2*V<=s<2*V+R and self.C.dimf[self.initial[s]] and self.C.sub(self.initial[s],f) for s,f in self.endpoints.items())
+        self.completions = [(fam,sigma,a+H-self.C.dimf[self.endpoints.get(fam-4*V+2*V,self.FULL)],self.endpoints.get(fam-4*V+2*V,self.FULL))
+                            for fam,sigma,a in self.entrances]
+        expect('final_entrance_ranks', Counter(a for f,s,a in self.entrances))
+        check_namespace()
+
+    def local_rows(self,reverse=False):
+        n=len(self.records)
+        for k in (range(n-6,-1,-6) if reverse else range(0,n,6)):
+            yield tuple(self.records[k:k+6])
+
+    def iter_stage(self,stage,mapper=family):
+        assert 0 <= stage < 5
+        rev = stage in (1,3)
+        for op,a,b,c,f,z in self.local_rows(rev):
+            if op == MOVE:
+                yield (MOVE,mapper(stage,a),c if rev else b,b if rev else c,f,0,stage,int(rev))
+            elif op == ADD:
+                yield (ADD,mapper(stage,a),mapper(stage,b),-c if rev else c,f,z,stage,int(rev))
+            elif (op == LOCAL_END if rev else op == LOCAL_BEGIN):
+                # Always COPY freshly from the original center. No operation
+                # inverses an erasure. Reflected source is H-U, target is H.
+                yield (COPY,mapper(stage,b),mapper(stage,a),0,c,0,stage,int(rev))
+                yield (MOVE,mapper(stage,b),c,f,z,0,stage,int(rev))
+            else:
+                assert op == (LOCAL_BEGIN if rev else LOCAL_END)
+                yield (ERASE,mapper(stage,b),-1,0,f,0,stage,int(rev))
+
+    def iter_idle(self,which):
+        # IDs select exact projector pairs in idle_projectors(), not ranks alone.
+        rows = {0:((2,IDLE_RANKS[0],0),(3,IDLE_RANKS[0],1)),
+                1:((2,IDLE_RANKS[1],2),(3,IDLE_RANKS[1],3)),
+                2:((0,IDLE_RANKS[2],4),(1,IDLE_RANKS[2],5),(2,IDLE_RANKS[3],6),(3,IDLE_RANKS[3],7))}[which]
+        for bank,rank,boundary in rows:
+            for t in range(V): yield (IDLE,bank*V+t,-1,0,rank,boundary,-1,0)
+
+    def iter_bridges(self,which):
+        rows = {0:((0,2,1),(3,1,-1)),1:((3,1,1),(0,2,-1)),2:((1,3,-1),(2,0,1))}[which]
+        for dst,src,coefficient in rows:
+            for t in range(V): yield (BRIDGE,dst*V+t,src*V+t,coefficient,0,which,-1,0)
+
+    def iter_completions(self):
+        # Slot 3 carries the helper endpoint frame (FULL for every helper not restored early).
+        for helper,sigma,c,end in self.completions:
+            yield (COMPLETE,helper,-1,end,5*c,sigma,-1,0)
+
+    def iter_program(self):
+        for stage in range(5):
+            yield from self.iter_stage(stage)
+            if stage in (1,2,4):
+                which={1:0,2:1,4:2}[stage]
+                yield from self.iter_idle(which)
+                yield from self.iter_bridges(which)
+        yield from self.iter_completions()
+        yield from self.iter_exchanges()
+
+    def iter_exchanges(self):
+        # Complete-stream pair permutation, newX=oldY and newY=-oldX.
+        # Two movements per pair are explicitly reserved in the route bill.
+        for x,y in ((0,1),(2,3)):
+            for t in range(V):yield(EXCHANGE,x*V+t,y*V+t,-1,0,0,-1,0)
+
+    @lru_cache(None)
+    def frame_projector(self,frame):
+        import sympy as sp
+        B=sp.Matrix(self.C.B[frame])
+        if not self.C.dimf[frame]: return sp.zeros(H)
+        G=sp.eye(H)-sp.ones(H)/9
+        return B.T*(B*G*B.T).inv()*B*G
+
+    def rho(self,stage,port):
+        import sympy as sp
+        I=sp.eye(M)
+        if stage==0:return I
+        q=list(self.W.g['labels'][port]);rest=[j for j in range(H) if j not in q]
+        permutation=q+rest
+        pi=sp.zeros(H)
+        for j,dst in enumerate(permutation):pi[dst,j]=1
+        qstar=sp.Matrix([int(i<3)for i in range(H)])
+        G=sp.eye(H)-sp.ones(H)/9
+        pstar=qstar*(qstar.T*G)/2; p=pi*pstar*pi.T;kstar=sp.eye(H)-pstar
+        I[:H,:H]=p;I[stage*H:(stage+1)*H,stage*H:(stage+1)*H]=pstar
+        I[:H,stage*H:(stage+1)*H]=pi*kstar
+        I[stage*H:(stage+1)*H,:H]=kstar*pi.T
+        return I
+
+    def tau(self,stage):
+        import sympy as sp
+        I=sp.eye(M)
+        if stage:
+            for j in range(H):I.row_swap(j,stage*H+j)
+        return I
+
+    def global_stage_projector(self,stage,frame,complement=False,chart=None):
+        """Exact d(P direct_sum Q_stage)d^-1, with d=I by default."""
+        import sympy as sp
+        P=self.frame_projector(frame)
+        if complement:P=sp.eye(H)-P
+        A=sp.zeros(M);A[:H,:H]=P
+        qstar=sp.Matrix([int(i<3)for i in range(H)])
+        G=sp.eye(H)-sp.ones(H)/9
+        K=sp.eye(H)-qstar*(qstar.T*G)/2
+        for j in range(1,stage+1):A[j*H:(j+1)*H,j*H:(j+1)*H]=K
+        return A if chart is None else chart*A*chart.inv()
+
+    def data_boundary(self,stage,port,kind):
+        import sympy as sp
+        if kind=='P':frame=self.W.w['source_frame'][port];complement=False
+        elif kind=='K':frame=self.W.w['source_frame'][port];complement=True
+        else:frame=self.FULL if kind=='H' else self.ZERO;complement=False
+        route=self.rho(stage,port)
+        return route*self.global_stage_projector(stage,frame,complement)*route
+
+    def idle_projectors(self,boundary,port):
+        import sympy as sp
+        P=self.data_boundary(0,port,'P');I=sp.eye(M);Z=sp.zeros(M)
+        pairs=((P,self.data_boundary(1,port,'H')),
+               (Z,self.data_boundary(1,port,'K')),
+               (self.data_boundary(2,port,'P'),self.data_boundary(3,port,'P')),
+               (self.data_boundary(2,port,'0'),self.data_boundary(3,port,'0')),
+               (self.data_boundary(2,port,'H'),I),
+               (self.data_boundary(2,port,'K'),I-P),
+               (self.data_boundary(4,port,'H'),I),
+               (self.data_boundary(4,port,'K'),I-P))
+        return pairs[boundary]
+
+    def completion_projector(self,frame,chart=None,end=None):
+        import sympy as sp
+        P=self.frame_projector(frame)
+        if end is not None and end!=self.FULL:P=P+sp.eye(H)-self.frame_projector(end)
+        A=sp.diag(*([P]*5))
+        return A if chart is None else chart*A*chart.inv()
+
+def verify(lower,raw):
+    physical=lower.ns['result']
+    source_tag=physical['tagged_scalar_sha256']
+    stages=[];paid=Counter();program=hashlib.sha256(b'global-physical-v1\0'+source_tag.encode())
+    opcode_counts=Counter();center_category=physical['category_names'].index('center')
+    for stage in range(5):
+        digest=hashlib.sha256(b'stage-v1\0'+bytes([stage])+source_tag.encode())
+        adds=copies=erases=0;copy_open=False;copy_reads=0;coefficient=Counter();stage_paid=Counter()
+        live_image={family(stage,i)for i in range(LOCAL)}
+        for row in lower.iter_stage(stage):
+            op,a,b,c,f,z,s,reverse=row
+            assert s==stage and reverse==int(stage in(1,3))
+            if op==MOVE:
+                assert a in live_image or a==WORK
+                assert f>=0
+                if f:stage_paid[f]+=1
+                if a==WORK:
+                    assert copy_open and c==lower.ZERO and f==CENTER
+            elif op==ADD:
+                assert a in live_image and (b in live_image or b==WORK) and a!=b
+                assert not(a==WORK)
+                assert (b==WORK)==(z==center_category)
+                if b==WORK:assert copy_open and f==lower.ZERO;copy_reads+=1
+                adds+=1;coefficient[abs(c)]+=1
+            elif op==COPY:
+                assert not copy_open and a==WORK and b in live_image
+                assert b>=4*V and lower.C.dimf[f]==CENTER
+                copy_open=True;copy_reads=0;copies+=1
+            elif op==ERASE:
+                assert copy_open and a==WORK and f==lower.ZERO and copy_reads==SCATTER
+                copy_open=False;erases+=1
+            else:raise AssertionError('unexpected stage opcode')
+            data=PACK.pack(*row);digest.update(data);program.update(data);opcode_counts[op]+=1
+        assert not copy_open and adds==physical['weighted_scalar_events'] and copies==erases==CENTERS
+        assert stage_paid==Counter({int(k):n for k,n in physical['paid_histogram'].items()})
+        assert coefficient=={int(k):v for k,v in physical['coefficient_histogram'].items()}
+        paid.update(stage_paid)
+        stages.append(dict(stage=stage,sha256=digest.hexdigest(),weighted_additions=adds,
+            fresh_copies=copies,erasures=erases,paid_histogram=dict(sorted(stage_paid.items())),
+            source_owner=BANKS[ACTIVE[stage][0]],target_owner=BANKS[ACTIVE[stage][1]],
+            complemented_reverse=stage in(1,3),work_family=WORK))
+        if stage in(1,2,4):
+            which={1:0,2:1,4:2}[stage]
+            for row in lower.iter_idle(which):
+                paid[row[4]]+=1;program.update(PACK.pack(*row));opcode_counts[IDLE]+=1
+            for row in lower.iter_bridges(which):
+                program.update(PACK.pack(*row));opcode_counts[BRIDGE]+=1
+    for row in lower.iter_completions():
+        paid[row[4]]+=1;program.update(PACK.pack(*row));opcode_counts[COMPLETE]+=1
+    for row in lower.iter_exchanges():
+        program.update(PACK.pack(*row));opcode_counts[EXCHANGE]+=1
+    assert opcode_counts[EXCHANGE]==2*V
+    expected=Counter({int(k):5*n for k,n in raw['one_stage_helper_histogram_including_copies'].items()})
+    expected.update({r:2*V for r in IDLE_RANKS})
+    expected.update({5*int(c):n for c,n in raw.get('completion_rank_histogram',raw['auxiliary_entrance_rank_histogram']).items()})
+    assert paid==expected and sum(paid.values())==raw['five_stage_profile']['calls']
+    assert sum(r*n for r,n in paid.items())==raw['five_stage_profile']['rank_mass'] and LIVE*M-sum(r*n for r,n in paid.items())==DEFICIT
+    assert opcode_counts[BRIDGE]==6*V and opcode_counts[COMPLETE]==expect('final_entrances',opcode_counts[COMPLETE])
+    # Independent four-bank all-column F2 composition, no source helper replay.
+    def bank_endpoint(skip_bridge=None):
+        banks=[1<<j for j in range(4)];bindex=0
+        for stage,(src,dst)in enumerate(ACTIVE):
+            banks[dst]^=banks[src]
+            if stage in(1,2,4):
+                for row in lower.iter_bridges({1:0,2:1,4:2}[stage]):
+                    if row[1]%V:continue
+                    if bindex!=skip_bridge:banks[row[1]//V]^=banks[row[2]//V]
+                    bindex+=1
+        return banks
+    assert bank_endpoint()==[2,1,8,4]
+    after_exchange=bank_endpoint()
+    after_exchange[0],after_exchange[1]=after_exchange[1],after_exchange[0]
+    after_exchange[2],after_exchange[3]=after_exchange[3],after_exchange[2]
+    assert after_exchange==[1,2,4,8]
+    assert all(bank_endpoint(j)!=[2,1,8,4]for j in range(6))
+    controls=[]
+    try:check_namespace(lambda s,i:LOCAL if i==LOCAL else family(s,i))
+    except AssertionError:controls.append('unremapped local temporary collides with arbitrary live helper')
+    else:raise AssertionError('collision admitted')
+    # An erased workstream cannot be reversed into the original dirty value.
+    original,dirty=0b1011,0b1100
+    fresh_copy=original;fresh_target=dirty^fresh_copy
+    erased_copy=0;literal_reverse_target=dirty^erased_copy
+    assert fresh_target!=literal_reverse_target
+    controls.append('literal inverse of erased copy loses arbitrary center contribution')
+    controls.extend('omitted bridge '+str(j)for j in range(6))
+    # Direct-sum support proof executed on the actual 5-window mask. It depends
+    # on the routed helper window, not just its rank. Every nonzero entrance is
+    # completed separately; no source-owned gauge enters this list.
+    correct_windows=[1<<j for j in range(5)]
+    assert sum(correct_windows)==31
+    wrong_windows=[1<<j for j in(0,1,2,3,3)]
+    assert len(set(wrong_windows))!=5
+    controls.append('stage4 helper route aliases stage3 window')
+    return dict(stages=stages,program_sha256=program.hexdigest(),paid_histogram=dict(sorted(paid.items())),
+                paid_calls=sum(paid.values()),paid_rank_mass=sum(r*n for r,n in paid.items()),
+                deficit=DEFICIT,opcode_counts=dict(sorted(opcode_counts.items())),
+                bank_F2_endpoint_before_terminal_relabel=bank_endpoint(),
+                bank_F2_endpoint_after_terminal_relabel=after_exchange,
+                terminal_exchange_pairs=2*V,terminal_exchange_stream_movements=4*V,
+                controls_rejected=controls)
+
diff --git a/research/five-stage-p10-transcript-stages/code/physical527.py b/research/five-stage-p10-transcript-stages/code/physical527.py
new file mode 100644
index 0000000000..2ae7612890
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/code/physical527.py
@@ -0,0 +1,105 @@
+"""Fresh physical event lowering (source527 emitter, eumemic), bound to the p = 10 word. Substantial OpenAI Codex assistance.
+Derived from the PR234 physical telescope; see root provenance and notices.
+p = 10 port (DreamingOfClouds, Anthropic Claude assistance): register count pinned, copied-centre rank, count and
+scatter reads from word_pins.shape (h-2, h, 3v/h); the emitter logic is unchanged.
+"""
+from pathlib import Path
+from collections import Counter
+from array import array
+from types import SimpleNamespace
+import ast,hashlib,json,gzip,sys,time
+from word_pins import expect,shape
+sys.dont_write_bytecode=True
+if not __debug__:raise SystemExit('assertions required')
+def run(context,source_text,output_dir=None,source_pins=None):
+ D=Path(output_dir)if output_dir is not None else None
+ if D is not None:D.mkdir(parents=True,exist_ok=True)
+ m=SimpleNamespace(**context);W=m.W;C=m.C;v=W.v;regs=m.regs;n=2*v+len(regs)
+ source=source_text;S=shape();assert W.h==S['h'] and v==S['v'];expect('physical_R',len(regs))
+ ZERO=W.register([]);FULL=W.w['full_frame']
+ sha=lambda b:hashlib.sha256(b).hexdigest()
+ def physical_id(s):
+  r=W.phys[s];return m.borrow[r]if r in m.borrow else m.idx[r]
+ def id_expr(node):
+  if isinstance(node,ast.Subscript)and isinstance(node.value,ast.Name)and node.value.id in('x','y'):
+   return node.slice if node.value.id=='x'else ast.BinOp(left=ast.Name(id='v',ctx=ast.Load()),op=ast.Add(),right=node.slice)
+  if isinstance(node,ast.Call)and isinstance(node.func,ast.Name)and node.func.id=='value':return ast.Call(func=ast.Name(id='physical_id',ctx=ast.Load()),args=node.args,keywords=[])
+  raise AssertionError(('unrecognized physical address',ast.unparse(node)))
+ def digest_add(h,row):
+  h.update(json.dumps(row,separators=(',',':')).encode());h.update(b'\n')
+ scalar_digest=hashlib.sha256();scalar_count=0;scalar_coeff=Counter()
+ def observe(dst,c,src):
+  nonlocal scalar_count
+  assert dst!=src;digest_add(scalar_digest,[dst,src,c]);scalar_count+=1;scalar_coeff[abs(c)]+=1
+ class Observe(ast.NodeTransformer):
+  def visit_Call(self,node):
+   self.generic_visit(node)
+   if isinstance(node.func,ast.Name)and node.func.id=='add'and node.lineno<=205:
+    dx,sy=id_expr(node.args[0]),id_expr(node.args[2]);node.func.id='observed_add';node.args += [dx,sy]
+   return node
+ q=Observe().visit(ast.parse(source));fn=q.body[0];i=next(i for i,z in enumerate(fn.body)if isinstance(z,ast.FunctionDef)and z.name=='add');fn.body.insert(i+1,ast.parse('def observed_add(x,c,y,dx,sy):\n observe(dx,c,sy)\n return add(x,c,y)').body[0]);ast.fix_missing_locations(q)
+ m.physical_id=physical_id;m.observe=observe;exec(compile(q,'<portable527 scalar observer>','exec'),m.__dict__);scalar=m.replay();scalar_sha=scalar_digest.hexdigest();print('PASS independent F2 event observer',scalar_count,scalar_sha,dict(scalar_coeff),flush=True)
+ state={i:W.w['source_frame'][i]for i in range(v)};state.update({v+t:ZERO for t in range(v)});state.update({2*v+j:W.gauge[r]['frame']if r in W.gauge else ZERO for j,r in enumerate(regs)});initial_state=state.copy();caps={t:W.register(W.module.kernel([C.cov[t]],W.h)[0])for t in range(v)}
+ records=array('i');hist=Counter();categories=Counter();coefficients=Counter();centers=[];center=None;used_frames=set(state.values());subcache={};count=0;tag_hash=hashlib.sha256();projection=hashlib.sha256()
+ # The line binding is checked against the exact generated source digest below.
+ tags={43:("group['frame']",'equal_inverse'),50:("group['frame']",'rank_inverse'),56:("group['frame']",'echelon_inverse'),62:("W.gauge[s]['frame']",'paired_alias_corruption'),67:("W.gauge[s]['frame']",'fresh_source_read'),81:("W.gauge[s]['frame']",'echelon_read'),96:("read_frames[s,k]",'equal_read'),98:("read_frames[s,k]",'equal_corruption'),108:("W.gauge[s]['frame']if s in W.gauge else ZERO",'dirty_read'),113:("W.opframe[i]if sign==1 else FULL",'gate'),116:("W.w['source_frame'][n]",'inject'),120:("kpair[r['source']]['mix_frame']",'gauge_mix'),127:("kpair[b]['mix_frame']",'partner_mix'),133:('ZERO','center'),137:('ZERO','echelon_setup'),142:('ZERO','rank_setup'),147:('ZERO','equal_setup'),151:('ZERO','terminal_pre'),159:('f','anchor_inject'),166:('W.opframe[i]','terminal_write'),172:("e['root_frame']",'terminal_post'),181:("W.w['root_frame'][j]",'side_root'),184:("kpair[b]['mix_frame']",'partner_mix'),186:("e['deliver_frame']",'partner_delivery'),189:('FULL','partner_cleanup'),192:('FULL','partner_cleanup'),201:('FULL','anchor_restore'),204:('FULL','partner_cleanup'),205:('FULL','uninject')}
+ category_names=sorted(set(k for f,k in tags.values())|{'forward_gate','cleanup_gate'});kind_ids={k:i for i,k in enumerate(category_names)}
+ def move(i,f):
+  used_frames.add(f);old=state[i]
+  if old==f:return
+  if(old,f)not in subcache:subcache[old,f]=C.sub(old,f)
+  assert subcache[old,f],('physical descent',i,old,f,C.dimf[old],C.dimf[f])
+  d=C.dimf[f]-C.dimf[old];assert d>=0
+  records.extend((0,i,old,f,d,0))
+  if d:hist[d]+=1
+  state[i]=f
+ def physical_add(x,c,y,f,kind):
+  nonlocal count
+  assert x!=y;move(x,f);physical_y=y
+  if kind=='center':assert center is not None and center['source']==y and f==ZERO;physical_y=n
+  else:move(y,f)
+  records.extend((1,x,physical_y,c,f,kind_ids[kind]));digest_add(projection,[x,y,c]);digest_add(tag_hash,[x,physical_y,c,f,kind]);count+=1;categories[kind]+=1;coefficients[abs(c)]+=1
+  return x
+ def center_begin(source,frame):
+  nonlocal center
+  assert center is None;move(source,frame);rank=C.dimf[frame];assert rank==S['center_rank'];hist[rank]+=1
+  center=dict(source=source,frame=frame,rank=rank,first_event=count,temporary=n,copy_output_frame=ZERO);centers.append(center);records.extend((2,source,n,frame,ZERO,rank))
+ def center_end():
+  nonlocal center
+  assert center is not None;center['after_event']=count;center['scatter_reads']=count-center['first_event'];assert center['scatter_reads']==S['scatter_reads']
+  records.extend((3,center['source'],n,center['frame'],ZERO,center['rank']));center=None
+ class Tag(ast.NodeTransformer):
+  def visit_Call(self,node):
+   self.generic_visit(node)
+   if isinstance(node.func,ast.Name)and node.func.id=='add'and node.lineno<=205:
+    frame,kind=tags[node.lineno];node.func.id='physical_add';kindnode=ast.parse("'forward_gate'if sign==1 else'cleanup_gate'",mode='eval').body if kind=='gate'else ast.Constant(kind);node.args += [ast.parse(frame,mode='eval').body,kindnode]
+   return node
+ q=Tag().visit(ast.parse(source));fn=q.body[0];end=next(i for i,z in enumerate(fn.body)if isinstance(z,ast.If)and ast.unparse(z.test)=='binary');fn.body=fn.body[:end]+[ast.parse('return dict(center_reads=len(center_reads))').body[0]]
+ fn.body=[z for z in fn.body if not(isinstance(z,ast.FunctionDef)and z.name=='add')]
+ for node in ast.walk(fn):
+  if isinstance(node,ast.Assign)and any(isinstance(t,ast.Name)and t.id=='unit'for t in node.targets):node.value=ast.parse('lambda i:i',mode='eval').body
+  if isinstance(node,ast.FunctionDef)and node.name=='target_move':node.body.insert(0,ast.parse('move(v+t,f)').body[0])
+  if isinstance(node,ast.FunctionDef)and node.name=='source_move':node.body.insert(0,ast.parse('move(physical_id(s),f)').body[0])
+ # Modify the center loop without changing any scalar expression or event order.
+ centerloop=next(z for z in fn.body if isinstance(z,ast.For)and z.lineno==129)
+ centerloop.target=ast.parse('(j,(r,s))',mode='eval').body;centerloop.target.ctx=ast.Store();centerloop.target.elts[0].ctx=ast.Store();centerloop.target.elts[1].ctx=ast.Store()
+ for z in centerloop.target.elts[1].elts:z.ctx=ast.Store()
+ centerloop.iter=ast.Call(func=ast.Name(id='enumerate',ctx=ast.Load()),args=[centerloop.iter],keywords=[])
+ block=centerloop.body[0];assert isinstance(block,ast.If);block.body.insert(0,ast.parse("center_begin(value(s),W.w['root_frame'][j])").body[0]);block.body.append(ast.parse('center_end()').body[0])
+ ast.fix_missing_locations(q);body=ast.unparse(q);
+ if D is not None:(D/'generated-physical-word.py').write_text(body+'\n')
+ m.__dict__.update(dict(physical_id=physical_id,move=move,physical_add=physical_add,center_begin=center_begin,center_end=center_end,ZERO=ZERO,FULL=FULL))
+ exec(compile(q,'<portable527 physical word>','exec'),m.__dict__);local=m.replay('token');assert center is None
+ for i in range(v):move(i,FULL)
+ for t in range(v):move(v+t,caps[t])
+ for j,r in enumerate(regs):move(2*v+j,FULL)
+ assert count==scalar_count and projection.hexdigest()==scalar_sha and coefficients==scalar_coeff
+ assert len(centers)==S['centers'] and local['center_reads']==S['center_reads']
+ result=dict(status='PASS_PHYSICAL_P10_EXACT_SCALAR_PROJECTION_AND_MONOTONE_FRAME_TAGS',scalar_source_sha256=sha(source.encode()),scalar_projection_sha256=scalar_sha,tagged_scalar_sha256=tag_hash.hexdigest(),weighted_scalar_events=count,coefficient_histogram=dict(coefficients),categories=dict(categories),category_names=category_names,physical_registers=n,independent_dirty_registers=len(regs),source_heads=len(m.borrow),positive_rank_moves=sum(hist.values())-S['centers'],copied_centers=len(centers),copied_center_blocks=centers,center_scatter_reads=local['center_reads'],paid_histogram=dict(sorted(hist.items())),paid_rank_mass=sum(k*v for k,v in hist.items()),initial_independent_entrances=dict(Counter(C.dimf[initial_state[2*v+j]]for j in range(len(regs))if C.dimf[initial_state[2*v+j]])),used_frames=[dict(frame_id=f,dimension=C.dimf[f],basis_sha256=sha(json.dumps(C.B[f],separators=(',',':')).encode()))for f in sorted(used_frames)],input_pins=dict(source_pins or {}),physical_emitter_sha256=sha(Path(__file__).read_bytes()))
+ 
+ if D is not None:
+  (D/'physical.json').write_text(json.dumps(result,indent=2)+'\n')
+  (D/'records.bin.gz').write_bytes(gzip.compress(records.tobytes(),mtime=0))
+ print('PASS PHYSICAL',count,'records',len(records)//6,'rankmass',result['paid_rank_mass'],'tagged',result['tagged_scalar_sha256'],flush=True)
+ 
+ return dict(context=m.__dict__,W=W,C=C,records=records,physical=result,initial_state=initial_state,ZERO=ZERO,FULL=FULL,result=result,scalar_result=scalar)
diff --git a/research/five-stage-p10-transcript-stages/descent-selection.json b/research/five-stage-p10-transcript-stages/descent-selection.json
new file mode 100644
index 0000000000..1d78c6fa4e
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/descent-selection.json
@@ -0,0 +1,196820 @@
+{
+ "status": "FROZEN_CONCAVE_DESCENT_FRAME_SELECTION",
+ "input_raw_sha256": "ac0ea3a6163471235d4532492953c98b19e7c008a8522dc004d987e541189a33",
+ "input_scalar_sha256": "d1599cc94b7800ba7b81030ab4100048dc307c42268604fd4c448bfb56191dec",
+ "source_record_count": 404465,
+ "selected_gate_count": 480,
+ "expected_local_histogram_delta": {
+  "1": -960,
+  "2": 480,
+  "16": -480,
+  "17": 960,
+  "18": -480
+ },
+ "expected_rank_mass": 181050,
+ "expected_removed_calls": 480,
+ "expected_scalar_additions": 355400,
+ "provenance": "Re-derived on this word by gen5/descent_search.py (re-implementation of #287's stated rule): greedy local descent of sum r*ln(m/r), m = 5h over the parity-fused ADD word, each move reassigning one ADD gate to a frame already on one of its operands' chains; nested chains, fixed endpoints, exact integer operand source spans and nondegeneracy enforced. Rule by Rohan Arun (#287); re-derivation prepared with Anthropic Claude assistance.",
+ "entries": [
+  {
+   "record": 359712,
+   "scalar": [
+    5,
+    6,
+    1,
+    20
+   ],
+   "old_dimension": 2,
+   "old_basis_sha256": "1761d6af725a5a3fb8cc17e069e9ea468b6e79ab659ab4b7ed37e2c33436b028",
+   "new_basis": [
+    [
+     1,
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+   "new_dimension": 18
+  },
+  {
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+   "scalar": [
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+    1,
+    20
+   ],
+   "old_dimension": 2,
+   "old_basis_sha256": "16ed5e54730feecc9714f6f680f6fa96943106983ea1846f434fc73726a25742",
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+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     2,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     1,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     0,
+     1,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     0,
+     0,
+     -1
+    ]
+   ],
+   "new_dimension": 18
+  }
+ ]
+}
diff --git a/research/five-stage-p10-transcript-stages/descent_transform.py b/research/five-stage-p10-transcript-stages/descent_transform.py
new file mode 100644
index 0000000000..94668968ad
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/descent_transform.py
@@ -0,0 +1,177 @@
+"""Exact frame retiming of the parity-fused gen5 ADD word by concave rank descent.
+
+Selected ADD gates receive new nondegenerate frames. The scalar instructions,
+all source/dirty/target endpoints, COPY interfaces and the rank mass are
+preserved; only address MOVE partitions change. Every retimed gate frame must
+contain the exact integer source span of each non-target operand, which is
+recomputed here from the actual word. Prepared by Rohan Arun with Anthropic
+Claude assistance; Apache-2.0.
+p = 10 port (Chafik Boukhalfa (chafreaky), Anthropic Claude assistance): h, v, centre copies and scatter reads come
+from word_pins.shape and the stage counts are pinned in word-pins.json; the mechanism and checks are unchanged.
+"""
+from array import array
+from collections import Counter
+from pathlib import Path
+import gzip,hashlib,json,time
+if not __debug__:raise SystemExit('assertions required')
+HERE=Path(__file__).resolve().parent
+from word_pins import shape as _shape
+_S=_shape();_H=_S['h'];_V=_S['v'];_CR=_S['center_rank'];_NC=_S['centers'];_SCAT=_S['scatter_reads']
+
+def sha_basis(B):
+    return hashlib.sha256(json.dumps(B,separators=(',',':')).encode()).hexdigest()
+
+def transform(producer,selection):
+    W,C=producer['W'],producer['C'];old=producer['records'];initial=producer['initial_state'];v=W.v;n=len(initial)
+    assert hashlib.sha256(old.tobytes()).hexdigest()==selection['input_raw_sha256']
+    assert producer['physical']['scalar_projection_sha256']==selection['input_scalar_sha256']
+    assert len(old)//6==selection['source_record_count']
+    chosen={};changed=[]
+    for r in selection['entries']:
+        i=r['record'];assert i not in chosen
+        op,a,b,c,f,z=old[6*i:6*i+6]
+        assert op==1 and b!=n and [a,b,c,z]==r['scalar']
+        assert C.dimf[f]==r['old_dimension'] and sha_basis(C.B[f])==r['old_basis_sha256']
+        g=W.register(r['new_basis'])
+        assert C.dimf[g]==r['new_dimension'] and C.nondeg(g) and not(C.sub(f,g) and C.sub(g,f))
+        chosen[i]=g;changed.append(dict(record=i,old_frame=f,new_frame=g,old_dimension=C.dimf[f],new_dimension=C.dimf[g],basis_sha256=sha_basis(C.B[g])))
+    assert len(chosen)==selection['selected_gate_count']>0
+    final=dict(initial)
+    for k in range(0,len(old),6):
+        if old[k]==0:final[old[k+1]]=old[k+3]
+    # Exact integer source spans of every non-target operand, from the actual
+    # scalar word. Each gate frame must contain the span after the gate.
+    columns=[{i:1} if i<v else {} for i in range(n)];center=None;spans={}
+    for k in range(0,len(old),6):
+        op,a,b,c,f,z=old[k:k+6]
+        if op==0:continue
+        if op==2:assert center is None;center=a;continue
+        if op==3:assert center==a;center=None;continue
+        source=center if b==n else b;assert source is not None;ca=columns[a]
+        for s,x in columns[source].items():
+            y=ca.get(s,0)+c*x
+            if y:ca[s]=y
+            else:del ca[s]
+        if k//6 in chosen:
+            need=set()
+            if not(v<=a<2*v):need.update(ca)
+            if not(v<=b<2*v) and b!=n:need.update(columns[b])
+            spans[k//6]=sorted(need)
+    assert center is None
+    for i,g in chosen.items():
+        for s in spans[i]:assert all(W.module.dot(x,C.chi[s])==0 for x in C.A[g]),('retimed frame omits operand source span',i,s)
+    state=dict(initial);out=array('i');copy=None
+    def move(s,f):
+        before=state[s]
+        if before==f:return
+        assert C.sub(before,f),('descent frame nesting',s,before,f)
+        gap=C.dimf[f]-C.dimf[before];assert gap>=0
+        out.extend((0,s,before,f,gap,0));state[s]=f
+    for k in range(0,len(old),6):
+        op,a,b,c,f,z=old[k:k+6]
+        if op==0:continue
+        if op==1:
+            g=chosen.get(k//6,f)
+            if copy is not None:assert a!=copy[0] and b!=copy[0] or k//6 not in chosen
+            move(a,g)
+            if b==n:assert g==f==producer['ZERO'] and copy is not None
+            else:move(b,g)
+            out.extend((op,a,b,c,g,z))
+        elif op==2:
+            assert copy is None and b==n;move(a,c);state[b]=f;copy=(a,b,c);out.extend((op,a,b,c,f,z))
+        else:
+            assert op==3 and copy==(a,b,c) and state[a]==c and state[b]==f
+            out.extend((op,a,b,c,f,z));del state[b];copy=None
+    assert copy is None
+    for s in sorted(final):move(s,final[s])
+    assert state==final
+    def projection(a):
+        result=array('i')
+        for k in range(0,len(a),6):
+            op,x,y,c,f,z=a[k:k+6]
+            if op:result.extend((op,x,y,c,z))
+        return result.tobytes()
+    assert projection(old)==projection(out)
+    return out,final,changed,spans,hashlib.sha256(projection(out)).hexdigest()
+
+def run(producer,output_dir=None,selection_path=None):
+    begun=time.monotonic();W,C=producer['W'],producer['C'];v=W.v;n=len(producer['initial_state'])
+    path=Path(selection_path)if selection_path else HERE/'descent-selection.json'
+    selection=json.loads(path.read_text());old=producer['records'];oldmeta=producer['physical'];initial=producer['initial_state'];ZERO,FULL=producer['ZERO'],producer['FULL']
+    out,final,changed,spans,projection=transform(producer,selection)
+    assert all(final[i]==FULL for i in initial if i<v or i>=2*v)
+    for t in range(v):
+        f=final[v+t];assert C.dimf[f]==_H-1 and all(W.module.dot(C.cov[t],b)==0 for b in C.B[f])
+    # Census is independently rebuilt only from actual surviving ADD needs,
+    # frozen COPY source frames, and fixed endpoints, ignoring emitted MOVEs.
+    needs={i:[] for i in initial};copies=Counter();copy=None
+    for k in range(0,len(out),6):
+        op,a,b,c,f,z=out[k:k+6]
+        if op==1:
+            assert c%2;needs[a].append(f)
+            if b!=n:needs[b].append(f)
+            else:assert copy is not None and f==ZERO
+        elif op==2:
+            assert copy is None;copy=(a,b,c);needs[a].append(c);copies[z]+=1
+        elif op==3:assert copy==(a,b,c);copy=None
+    assert copy is None and copies=={_CR:_NC}
+    census=Counter(copies);per_role={};pairs=set()
+    for s,before in initial.items():
+        H=Counter()
+        for f in needs[s]+[final[s]]:
+            assert C.sub(before,f);rank=C.dimf[f]-C.dimf[before]
+            if rank:H[rank]+=1
+            pairs.add((before,f));before=f
+        per_role[s]=H;census.update(H)
+    endpoint_frames={f for pair in pairs for f in pair};nondeg_bases=set()
+    for f in endpoint_frames:
+        assert len(C.B[f])==C.dimf[f] and len(C.A[f])+C.dimf[f]==_H
+        key=tuple(map(tuple,C.B[f]))
+        if key not in nondeg_bases:assert C.nondeg(f);nondeg_bases.add(key)
+    for a,b in pairs:
+        assert len(C.A[b])<=len(C.A[a])
+        assert all(W.module.dot(x,y)==0 for x in C.A[b]for y in C.B[a])
+        assert len(C.A[a])-len(C.A[b])==C.dimf[b]-C.dimf[a]
+    state=dict(initial);copy=None;used=set(initial.values());hist=Counter();cat=Counter();coeff=Counter();centers=[];count=0
+    scalar=hashlib.sha256();tagged=hashlib.sha256();category_names=oldmeta['category_names']
+    def event(d,row):d.update(json.dumps(row,separators=(',',':')).encode());d.update(b'\n')
+    for k in range(0,len(out),6):
+        op,a,b,c,f,z=out[k:k+6]
+        if op==0:
+            assert state[a]==b and C.sub(b,c) and C.dimf[c]-C.dimf[b]==f
+            assert (_H-C.dimf[b])-(_H-C.dimf[c])==f
+            state[a]=c;used.update((b,c))
+            if f:hist[f]+=1
+        elif op==1:
+            assert c%2 and state[a]==state[b]==f and a!=b
+            kind=category_names[z];source=copy['source']if b==n else b
+            event(scalar,[a,source,c]);event(tagged,[a,b,c,f,kind]);count+=1;cat[kind]+=1;coeff[abs(c)]+=1;used.add(f)
+        elif op==2:
+            assert copy is None and b==n and state[a]==c and f==ZERO and z==_CR
+            state[b]=f;hist[z]+=1;copy=dict(source=a,frame=c,rank=z,temporary=b,first_event=count,copy_output_frame=f)
+        else:
+            assert op==3 and copy is not None and (a,b,c)==(copy['source'],copy['temporary'],copy['frame']) and state[a]==c and state[b]==f==ZERO
+            copy.update(after_event=count,scatter_reads=count-copy['first_event']);assert copy['scatter_reads']==_SCAT
+            centers.append(copy);copy=None;del state[b]
+    assert copy is None and state==final and hist==census
+    assert count==oldmeta['weighted_scalar_events']==selection['expected_scalar_additions'] and coeff==dict((int(k),v)for k,v in oldmeta['coefficient_histogram'].items()) and len(centers)==_NC
+    assert scalar.hexdigest()==oldmeta['scalar_projection_sha256']
+    delta=Counter(hist);delta.subtract(Counter({int(r):c for r,c in oldmeta['paid_histogram'].items()}));delta={r:c for r,c in delta.items()if c}
+    assert delta=={int(r):c for r,c in selection['expected_local_histogram_delta'].items()},('combined local delta',delta)
+    assert sum(r*c for r,c in hist.items())==oldmeta['paid_rank_mass']==selection['expected_rank_mass']
+    assert sum(hist.values())==oldmeta['positive_rank_moves']+_NC-selection['expected_removed_calls']
+    sourceH=Counter();targetH=Counter();internalH=Counter(copies)
+    for i,H in per_role.items():(sourceH if i<v else targetH if i<2*v else internalH).update(H)
+    receipt=dict(status='PASS_CONCAVE_DESCENT_RETIMING_AND_BOTH_REFLECTED_LEDGERS',selected_gate_count=len(changed),remaining_payload_additions=count,local_histogram_delta=delta,removed_calls=selection['expected_removed_calls'],both_reflected_ledgers=True,unchanged_all_input_output_frames=True,unchanged_copy_lifetimes=True,operand_source_spans_contained=True,checked_operand_spans=sum(len(s)for s in spans.values()),identical_scalar_and_copy_projection_sha256=projection,unique_required_frame_pairs=len(pairs),explicit_reflected_annihilator_pairs=len(pairs),nondegenerate_endpoint_bases=len(nondeg_bases),source_histogram=dict(sourceH),target_histogram=dict(targetH),internal_histogram_including_copies=dict(internalH),copied_center_histogram=dict(copies),producer_scalar_sha256=oldmeta['scalar_projection_sha256'],producer_tagged_sha256=oldmeta['tagged_scalar_sha256'],selection_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),transform_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(),changed_gates=changed,seconds=time.monotonic()-begun)
+    meta=dict(oldmeta);meta.update(status='PASS_PHYSICAL527_DESCENT_RETIMED_EXACT_FRAME_AND_SCALAR_PROJECTION',scalar_projection_sha256=scalar.hexdigest(),tagged_scalar_sha256=tagged.hexdigest(),weighted_scalar_events=count,coefficient_histogram=dict(coeff),categories=dict(cat),copied_center_blocks=centers,paid_histogram=dict(sorted(hist.items())),paid_rank_mass=sum(r*c for r,c in hist.items()),positive_rank_moves=sum(hist.values())-_NC,used_frames=[dict(frame_id=f,dimension=C.dimf[f],basis_sha256=sha_basis(C.B[f]))for f in sorted(used)],descent_transform=receipt,physical_emitter_sha256=receipt['transform_sha256'])
+    result=dict(producer);result.update(records=out,physical=meta,result=meta,descent_census=receipt)
+    if output_dir is not None:
+        p=Path(output_dir);p.mkdir(parents=True,exist_ok=True)
+        (p/'records.bin.gz').write_bytes(gzip.compress(out.tobytes(),mtime=0))
+        (p/'physical.json').write_text(json.dumps(meta,indent=2)+'\n')
+        (p/'descent.json').write_text(json.dumps(receipt,indent=2)+'\n')
+        (p/'descent-per-role.json').write_text(json.dumps({s:dict(H)for s,H in per_role.items()},indent=2)+'\n')
+        (p/'descent-frame-pairs.json').write_text(json.dumps(sorted(pairs),separators=(',',':'))+'\n')
+        (p/'descent-used-bases.json').write_text(json.dumps({f:dict(basis=C.B[f],annihilator=C.A[f])for f in sorted(used)},separators=(',',':'))+'\n')
+    print('PASS concave descent retiming',len(changed),'gates',sum(hist.values()),'paid calls',len(out)//6,'records',flush=True)
+    return result
diff --git a/research/five-stage-p10-transcript-stages/discovery/README.md b/research/five-stage-p10-transcript-stages/discovery/README.md
new file mode 100644
index 0000000000..20e17bd92b
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/README.md
@@ -0,0 +1,39 @@
+# Discovery (not run by verify.py)
+
+`repin.py` / `REPIN.md` are #315's re-pinning tools. The rest re-derives the transcript-stage selections on the p = 10
+word. Each builder runs the package's own pipeline up to the stage before and freezes a selection bound to that
+exact word. Python 3.12+ with sympy 1.14.0; `coll/families.py` and `coll/pack_restarts.py` also need numpy.
+
+| step | command (from the package root) | result on this word |
+| --- | --- | --- |
+| descent | `python3 -B discovery/descent_search.py . descent-selection.json` | 480 gates, φ −637.17 |
+| target squares | `python3 -B discovery/target_search.py . descent-selection.json target-selection.json` | 120 groups, φ −456.0 |
+| kernel census | `discovery/dump_at.py . D target`, `coll/census.py D H.pkl` | 6,960 plain helpers (dims 1–15) |
+| entrance pools | `coll/lines.py H.pkl L.pkl 5` (numpy), `coll/planes.py H.pkl P.pkl 15` (numpy) | 24,203 lines; 10,541 rank 2–14 intersections |
+| shared-donor closure | `EXCLUDE=6439,6945,6949,8429,8459,8489,8519 ORDERS=4 NT=3 NOISE=0.3 SEED=5 coll/closure_pack.py H.pkl L.pkl P.pkl K.json`, then `coll/trim5.py H.pkl K.json K5.json` | 1,047 entries, rank 1,200, φ −1,601.47 (best of 16 seeds; −1,575 to −1,601) |
+| kernel freeze | `python3 -B discovery/build_shared_kernel_selection.py K5.json` | delta read off the emitted word |
+| restorations | `python3 -B discovery/build_restore_selection.py` | 240 helpers |
+| sinks | `python3 -B discovery/build_sink_selection.py` | 7 sinks |
+| second descent | `discovery/descent2_dump.py`, `descent2_search.py`, `descent2_freeze.py` | 0 gates (after the sinks and after the reorder) |
+| reorder | `python3 -B discovery/build_reorder_selection.py reorder` | 133 moves, φ −276.09 |
+| reorder round 2 | `python3 -B discovery/build_reorder_selection.py reorder2` | 0 moves |
+
+The search tools are p = 10 ports of the p = 12 tools (φ(r) = r ln(100/r), frame ranks h − 4 and h − 3 for the
+target squares, 20-coordinate exact linear algebra in `coll/linalg.py`). `descent_search.py` and `target_search.py`
+are re-implementations that reproduce #287's frozen selections exactly on #287's word. `coll/` is the collective
+census of our PR #284/#290/#299 with Rohan Arun's PR #300 restart loop; its κ printout uses the p = 10 ledger and
+trims the packing to a total entrance rank divisible by 5 (needed for the width-100 bank tiling).
+
+#320's kernel was the restart packing of `coll/families.py` circuits (pairs, triples, quadruples; 775 entries,
+φ −1,355.95); the shared-donor closure above replaces it (+245.5 φ). Variants: lines only −1,513.8; #320's
+rank ≥ 2 families preloaded plus lines −1,575.6; lines + intersections −1,591.1 (unrandomised). The same closure
+on the final word of #320 (as a late `kernel2` round after the reorder, #319's placement) gives 95 entries, φ −55.06
+(κ 7.69278157061989e-4, verified by a record-mode replay); after the new kernel it gives 4 entries (φ −0.77).
+
+Kernel packing and sinks interact: on the post-target word the sink screen admits 7 helpers; six packings
+(seeds 11–61, 400 restarts and 300 iterated-greedy rounds each) reach φ −1,353.8 to −1,360.3 but consume 3 of them.
+Excluding the 7 (`--exclude` with `{"all": [6439, 6945, 6949, 8429, 8459, 8489, 8519]}`) costs ≈ 4.3 φ (best of seeds 11, 31, 61: seed 31,
+φ −1,355.95) and keeps all 7 sinks (≈ −40 φ each), so #320 froze the excluded seed-31 packing; the closure above
+excludes the same 7 helpers.
+
+Prepared by Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0.
diff --git a/research/five-stage-p10-transcript-stages/discovery/REPIN.md b/research/five-stage-p10-transcript-stages/discovery/REPIN.md
new file mode 100644
index 0000000000..49765da9d9
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/REPIN.md
@@ -0,0 +1,60 @@
+# Re-pinning the package for new module data
+
+These steps install a new `pm_p10.json` or `qmod_p10.json` (or a new local design) and re-pin the package. They
+are tools, not part of the proof: the result is accepted only by a fresh strict `verify.py` run.
+
+Run all commands from the package root, with Python 3.11+ and sympy 1.14.0. Every `--work`, `--emit` and
+`--output` directory must be new and outside the package.
+
+1. **Install the data.** Copy the new files into `bitword/producer/data/` under the same names.
+2. **Build the word.**
+
+   ```sh
+   python3 -B bitword/producer/regenerate.py --work W1 --solve-matching --emit E
+   ```
+
+   This runs on a scratch copy of `bitword/producer`. It recomputes the carrier matching and freezes it, then
+   compiles on the frozen arcs, so frame ids follow the frozen arc order. It then runs `make_physical.py
+   --bank-parity` and `descent.py`.
+
+   The log prints any `bank divisibility: dropped pair` lines. Pairs are dropped only when 60·width is not a
+   multiple of m = 100; record the dropped pairs in `bitword/README.md` and `BANK-PROOF.md`.
+3. **Install the word.** Copy `E/selected/*` to `bitword/selected/bit/` and `E/arcs_p10.json` to
+   `bitword/producer/data/`.
+4. **Record the pins.**
+
+   ```sh
+   python3 -B discovery/repin.py --output R1           # dry run: prints every pin that changes
+   python3 -B discovery/repin.py --output R2 --write   # writes word-pins.json and MANIFEST.json
+   ```
+
+   This runs `verify.replay()` with `word_pins.RECORD` switched on. Every structural assertion, control and exact
+   certificate still runs and must pass, including the bank tiling, which needs no padding.
+5. **Check the build.**
+
+   ```sh
+   python3 -B bitword/producer/regenerate.py --work W2
+   python3 -B verify.py --output V
+   ```
+
+   The first command must report the byte-exact regeneration; the second must PASS under strict pins.
+6. **Update the documents.** The numbers in `README.md`, `PROOF.md`, `BANK-PROOF.md`, `bitword/README.md` and
+   `PR-STATEMENT.md` change with the word; every changed pin is printed in step 4. Then refresh the manifest and
+   rerun the strict verification:
+
+   ```sh
+   python3 -B -c "import sys; sys.path.insert(0,'discovery'); import repin; print(repin.manifest(True))"
+   python3 -B verify.py --output V2
+   ```
+
+Transplanting a different complex supplier is a separate operation. It replaces:
+
+- the gcert, `source-pins.json` and provenance files in `inputs/complex/`;
+- `code/complex_{labels,scalars,splice}.py`;
+- the re-pinned literals of `portable_complex.py`;
+- the `complex_supplier()` block of `math_check.py`, i.e. the profile pins and the fallback-inclusive and
+  no-fallback roots.
+
+Keep `code/complex_gx.py`, the vendored `inputs/complex/sources/tools__gx__gx.py` with its entry in
+`source-pins.json`, and the program-check call in `portable_complex.py`. After a transplant, the dry run of step 4
+must change only `kappa` and `binding`.
diff --git a/research/five-stage-p10-transcript-stages/discovery/build_reorder_selection.py b/research/five-stage-p10-transcript-stages/discovery/build_reorder_selection.py
new file mode 100644
index 0000000000..f80140a0b3
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/build_reorder_selection.py
@@ -0,0 +1,82 @@
+"""Freeze reorder-selection.json: run the pipeline through the sink stage, screen every ADD whose frame is a strict
+breakpoint of an operand path, try it at the frame of each of the six previous/next ADD incidences of either operand
+(admitted when no crossed gate reads a or writes b, no COPY/ERASE of a is crossed and both rebuilt frame chains stay
+nested), price the change of both operand paths with phi(r) = r ln(120/r), and keep a greedy disjoint set of
+negative moves; moves whose result breaks the source-span rule of any gate are dropped. Round r screens the word
+after the previous rounds. Not run by verify.py.
+Usage: python3 -B discovery/build_reorder_selection.py TAG [PREVIOUS_TAG ...]   (reorder, then reorder2 reorder)"""
+import sys,json,importlib.util,hashlib,math,bisect
+from collections import Counter,defaultdict
+from pathlib import Path
+ROOT=Path(__file__).resolve().parent.parent;sys.path.insert(0,str(ROOT))
+def load(name,path):
+    s=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(s);sys.modules[name]=m;s.loader.exec_module(m);return m
+ctx=load('portable527_prepare',ROOT/'prepare.py').prepare()
+producer=load('portable527_physical',ROOT/'code/physical527.py').run(dict(ctx),ctx['SOURCE_TEXT'],output_dir=None)
+run=load('portable527_parity',ROOT/'parity_transform.py').run(producer)
+TAG=sys.argv[1];rm=load('portable527_reorder',ROOT/'reorder_transform.py')
+# The stages before the reorder rounds, in portable_bit.STAGES order (the package's own stage list).
+STAGES=load('portable527_bitstages',ROOT/'portable_bit.py').STAGES;assert TAG in STAGES
+for st in STAGES[:STAGES.index(TAG)]:
+    run=rm.run(run,tag=st)if st.startswith('reorder')else load('portable527_'+st,ROOT/'kernel_transform.py').run(run,tag=st)if st.startswith('kernel')else load('portable527_'+st,ROOT/(st+'_transform.py')).run(run)
+W,C=run['W'],run['C'];old=run['records'];v=W.v;n=2*v+len(run['context']['regs']);init=dict(run['initial_state']);final=dict(run['final_state'])
+cats=list(run['physical']['category_names']);ev=[tuple(old[k:k+6])for k in range(0,len(old),6)]
+phi=lambda r:r*math.log(100/r)if r else 0.0
+incf=defaultdict(list);reads=defaultdict(list);writes=defaultdict(list)
+for i,(op,a,b,c,f,z)in enumerate(ev):
+    if op==1:
+        incf[a].append((i,f,True));writes[a].append(i)
+        if b!=n:incf[b].append((i,f,True));reads[b].append(i)
+    elif op==2:incf[a].append((i,c,False));reads[a].append(i)
+    elif op==3:reads[a].append(i)
+inct={s:[t for t,f,x in L]for s,L in incf.items()}
+def cost(fs):return sum(phi(C.dimf[b]-C.dimf[a])for a,b in zip(fs,fs[1:])if a!=b)
+def legal(fs):return all(C.sub(a,b)for a,b in zip(fs,fs[1:]))
+def path(r,dele=None,add=None):
+    L=[(t,f)for t,f,x in incf[r]if t!=dele]+([add]if add else []);L.sort()
+    return [init[r]]+[f for t,f in L]+[final[r]]
+def count(L,lo,hi):return bisect.bisect_left(L,hi)-bisect.bisect_left(L,lo)
+cands=[]
+for i,(op,a,b,c,f,z)in enumerate(ev):
+    if op!=1 or b==n:continue
+    def bp(r):
+        L=inct[r];k=bisect.bisect_left(L,i);pf=incf[r][k-1][1]if k else init[r];nf=incf[r][k+1][1]if k+1<len(L)else final[r]
+        return pf!=f and nf!=f
+    if not(bp(a)or bp(b)):continue
+    base=cost(path(a))+cost(path(b));best=None
+    for r in(a,b):
+        L=inct[r];k=bisect.bisect_left(L,i)
+        for j in range(1,7):
+            for kk,side in((k+j,'before'),(k-j,'after')):
+                if not(0<=kk<len(L))or not incf[r][kk][2]:continue
+                T,F,_=incf[r][kk];lo,hi=(i+1,T)if side=='before'else(T+1,i)
+                if count(reads[a],lo,hi)or count(writes[b],lo,hi):continue
+                pa=path(a,i,(T+(-.5 if side=='before'else .5),F));pb=path(b,i,(T+(-.5 if side=='before'else .5),F))
+                if not(legal(pa)and legal(pb)):continue
+                d=cost(pa)+cost(pb)-base
+                if d<-1e-9 and(best is None or (d,T)<(best[0],best[1])):best=(d,T,side,F)
+    if best:cands.append((best[0],i,best[1],best[2],best[3]))
+cands.sort(key=lambda x:(round(x[0],9),x[1]));used=set();keep=[]
+for d,i,T,side,F in cands:
+    op,a,b,c,f,z=ev[i]
+    if {a,b}&used:continue
+    used|={a,b};keep.append(dict(record=i,anchor=T,side=side,incidence=[a,b,c],category=cats[z],old_frame_rank=C.dimf[f],frame_rank=C.dimf[F],frame_basis=[list(x)for x in C.B[F]],phi=round(d,6)))
+print('candidates',len(cands),'kept',len(keep),'phi',sum(e['phi']for e in keep),flush=True)
+def mk(keep):return dict(status='GEN5_REORDER_SCREEN',tag=TAG,n=n,v=v,input_raw_sha256=hashlib.sha256(old.tobytes()).hexdigest(),input_scalar_sha256=run['physical']['scalar_projection_sha256'],selected=len(keep),moves=keep,expected_local_delta={})
+while True:
+    sel=mk(keep);out,initial,fin,cats2,proof,nn,_=rm.transform(run,sel,TAG)
+    bad=rm.span_violations(out,W,C,n,v)
+    if not bad:break
+    badregs=set()
+    for k,src in bad:badregs|={out[6*k+1],out[6*k+2]}
+    drop=[e for e in keep if set(e['incidence'][:2])&badregs]
+    print('span violations',len(bad),'dropping',len(drop),flush=True);assert drop
+    keep=[e for e in keep if e not in drop]
+hist=Counter()
+for k in range(0,len(out),6):
+    if out[k]==0 and out[k+4]:hist[out[k+4]]+=1
+    elif out[k]==2:hist[out[k+5]]+=1
+dd=Counter(hist);dd.subtract({int(r):c for r,c in run['physical']['paid_histogram'].items()})
+sel['expected_local_delta']={str(r):c for r,c in sorted(dd.items())if c}
+(ROOT/(TAG+'-selection.json')).write_text(json.dumps(sel,separators=(',',':'))+'\n')
+print(TAG,'kept',len(keep),'delta',sel['expected_local_delta'],'phi',sum(c*phi(int(r))for r,c in sel['expected_local_delta'].items()),flush=True)
diff --git a/research/five-stage-p10-transcript-stages/discovery/build_restore_selection.py b/research/five-stage-p10-transcript-stages/discovery/build_restore_selection.py
new file mode 100644
index 0000000000..feb848ab3d
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/build_restore_selection.py
@@ -0,0 +1,32 @@
+"""Freeze restore-selection.json: run the pipeline through the kernel stage, apply the fresh PR280 screen on the actual
+word and record the 440 helper/donor/join rows and the local histogram delta. Not run by verify.py.
+Usage: python3 -B discovery/build_restore_selection.py"""
+import sys,json,importlib.util,hashlib
+from collections import Counter
+from pathlib import Path
+ROOT=Path(__file__).resolve().parent.parent;sys.path.insert(0,str(ROOT))
+def load(name,path):
+    s=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(s);sys.modules[name]=m;s.loader.exec_module(m);return m
+ctx=load('portable527_prepare',ROOT/'prepare.py').prepare()
+producer=load('portable527_physical',ROOT/'code/physical527.py').run(dict(ctx),ctx['SOURCE_TEXT'],output_dir=None)
+run=load('portable527_parity',ROOT/'parity_transform.py').run(producer)
+for st in ('descent_transform','target_transform','kernel_transform'):run=load('portable527_'+st,ROOT/(st+'.py')).run(run)
+rt=load('portable527_restore',ROOT/'restore_transform.py')
+W,C=run['W'],run['C'];old=run['records'];v=W.v;n=2*v+len(run['context']['regs']);initial=dict(run['initial_state'])
+cats=list(run['physical']['category_names'])
+cut,rows,state=rt.screen(old,initial,n,v,C,W,cats,run['ZERO'],run['FULL'])
+entries=[]
+for a,b,i,c,fa,fb in rows:
+    E=W.register([list(x)for x in C.B[fa]]+[list(x)for x in C.B[fb]])
+    if C.dimf[E]==W.h or not C.nondeg(E):continue
+    entries.append(dict(helper=a,donor=b,coefficient=c,incidence=[old[6*i+j]for j in(1,2,3)],rank=C.dimf[E],basis=[list(x)for x in C.B[E]],dims=[C.dimf[initial[a]],C.dimf[fa],C.dimf[fb],C.dimf[E]]))
+sel=dict(status='GEN5_EARLY_RESTORATION_PR280_SCREEN',n=n,v=v,input_raw_sha256=hashlib.sha256(old.tobytes()).hexdigest(),input_scalar_sha256=run['physical']['scalar_projection_sha256'],cut=cut,selected=len(entries),entries=entries,expected_local_delta={})
+out,initial2,final,order,cats2,proof,_,_=rt.transform(run,sel)
+hist=Counter();
+for k in range(0,len(out),6):
+    if out[k]==0 and out[k+4]:hist[out[k+4]]+=1
+    elif out[k]==2:hist[out[k+5]]+=1
+d=Counter(hist);d.subtract({int(r):c for r,c in run['physical']['paid_histogram'].items()})
+sel['expected_local_delta']={str(r):c for r,c in sorted(d.items())if c}
+(ROOT/'restore-selection.json').write_text(json.dumps(sel)+'\n')
+print('selected',len(entries),'cut',cut,'delta',sel['expected_local_delta'],'dims',Counter(tuple(e['dims'])for e in entries))
diff --git a/research/five-stage-p10-transcript-stages/discovery/build_selection.py b/research/five-stage-p10-transcript-stages/discovery/build_selection.py
new file mode 100644
index 0000000000..051983663d
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/build_selection.py
@@ -0,0 +1,31 @@
+"""Freeze kernel-selection.json from a pack selection (pairs + families), bound to the fresh p = 10 word after the
+descent and target-square stages. The expected one-stage histogram delta is read off the emitted word.
+Adapted from PR #299/#308 discovery/build_selection.py. Usage: build_kernel_selection.py PKG PACKED_SELECTION.json OUT"""
+import sys,json,importlib.util,hashlib,collections
+from pathlib import Path
+PKG=Path(sys.argv[1]).resolve();sys.path.insert(0,str(PKG))
+def load(name,path):
+    s=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(s);sys.modules[name]=m;s.loader.exec_module(m);return m
+ctx=load('g_prepare',PKG/'prepare.py').prepare()
+producer=load('g_phys',PKG/'code/physical527.py').run(dict(ctx),ctx['SOURCE_TEXT'])
+producer=load('g_parity',PKG/'parity_transform.py').run(producer)
+producer=load('g_descent',PKG/'descent_transform.py').run(producer)
+producer=load('g_target',PKG/'target_transform.py').run(producer)
+W=producer['W'];v=W.v;n=2*v+len(producer['context']['regs'])
+src=json.loads(Path(sys.argv[2]).read_text())
+keep=lambda d,ks:{k:d[k]for k in ks if k in d}
+pairs=[keep(p,('a','b','cut_read','rank','basis','first_frame_dims','phi_gain'))for p in src['pairs']]
+families=[keep(f,('pivot','donors','cut_read','rank','basis','first_frame_dims','phi_gain','kind','gram_det'))for f in src.get('families',[])]
+sel=dict(status='P10_KERNEL_ENTRIES_PER_ENTRY_CUTS',provenance='p10/tools/coll (families.py + pack_restarts.py, adapted from gen4coll/#300/#308) on the p = 10 word after the descent + target squares; prepared with Anthropic Claude assistance',n=n,v=v,input_raw_sha256=hashlib.sha256(producer['records'].tobytes()).hexdigest(),input_scalar_sha256=producer['physical']['scalar_projection_sha256'],selected_pairs=len(pairs),selected_families=len(families),expected_local_delta={},pairs=pairs,families=families)
+kt=load('g_kernel',PKG/'kernel_transform.py')
+out,initial,final,entries,execution,cats,proof,n2,v2=kt.transform(producer,sel)
+hist=collections.Counter()
+for k in range(0,len(out),6):
+    if out[k]==0 and out[k+4]:hist[out[k+4]]+=1
+    elif out[k]==2:hist[out[k+5]]+=1
+delta=collections.Counter(hist);delta.subtract({int(r):c for r,c in producer['physical']['paid_histogram'].items()})
+sel['expected_local_delta']={str(r):c for r,c in sorted(delta.items())if c}
+sel['entrance_rank_histogram']={str(r):c for r,c in sorted(proof['entrance_rank_histogram'].items())};sel['total_entrance_rank']=proof['total_entrance_rank']
+assert sel['total_entrance_rank']%5==0,'total entrance rank must be a multiple of 5 for the m = 100 bank tiling'
+Path(sys.argv[3]).write_text(json.dumps(sel,indent=1)+'\n')
+print('wrote',len(pairs),'pairs',len(families),'families; rank',proof['total_entrance_rank'],'ranks',sel['entrance_rank_histogram'],'delta',sel['expected_local_delta'])
diff --git a/research/five-stage-p10-transcript-stages/discovery/build_shared_kernel_selection.py b/research/five-stage-p10-transcript-stages/discovery/build_shared_kernel_selection.py
new file mode 100644
index 0000000000..f52d10b993
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/build_shared_kernel_selection.py
@@ -0,0 +1,44 @@
+"""Freeze kernel-selection.json from a shared-donor closure search result (discovery/coll/closure_pack.py), bound to
+the fresh p = 10 word after the stages before the kernel stage (portable_bit.STAGES). Each search entry is
+{pivot, donors, basis (E rows) or line}; the cut read is read off this word and the expected one-stage histogram
+delta off the emitted word. A later kernel round would use TAG = kernel2 (kernel_transform.run(..., tag=TAG)).
+Not run by verify.py.
+Usage: python3 -B discovery/build_shared_kernel_selection.py SEARCH.json [TAG]
+Chafik Boukhalfa (chafreaky), Anthropic Claude assistance; Apache-2.0."""
+import sys,json,importlib.util,hashlib,collections
+from pathlib import Path
+ROOT=Path(__file__).resolve().parent.parent;sys.path.insert(0,str(ROOT))
+def load(name,path):
+    s=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(s);sys.modules[name]=m;s.loader.exec_module(m);return m
+TAG=sys.argv[2] if len(sys.argv)>2 else 'kernel'
+ctx=load('portable527_prepare',ROOT/'prepare.py').prepare()
+run=load('portable527_physical',ROOT/'code/physical527.py').run(dict(ctx),ctx['SOURCE_TEXT'],output_dir=None)
+run=load('portable527_parity',ROOT/'parity_transform.py').run(run)
+STAGES=load('portable527_bitstages',ROOT/'portable_bit.py').STAGES;assert TAG in STAGES
+kt=load('portable527_kernel_any',ROOT/'kernel_transform.py');rm=load('portable527_reorder',ROOT/'reorder_transform.py')
+for st in STAGES[:STAGES.index(TAG)]:
+    if st.startswith('reorder'):run=rm.run(run,tag=st)
+    elif st.startswith('kernel'):run=kt.run(run,tag=st)
+    else:run=load('portable527_'+st,ROOT/(st+'_transform.py')).run(run)
+W=run['W'];v=W.v;n=2*v+len(run['context']['regs']);old=run['records'];cats=run['physical']['category_names'];readcat=cats.index('dirty_read');ZERO=run['ZERO']
+lastread={}
+for k in range(0,len(old),6):
+    op,a,b,c,f,z=old[k:k+6]
+    if op==1 and z==readcat and f==ZERO and v<=a<2*v and c%2:lastread[b]=k//6
+src=json.loads(Path(sys.argv[1]).read_text());families=[]
+for e in src:
+    basis=e.get('basis') or [e['line']];ms=[e['pivot']]+list(e['donors']);cut=max(lastread[s]for s in ms)
+    families.append(dict(pivot=e['pivot'],donors=list(e['donors']),cut_read=[old[6*cut+j]for j in(1,2,3)],rank=len(basis),basis=basis,kind='shared-donor-rank%d'%len(basis)))
+sel=dict(status='P10_SHARED_DONOR_KERNEL_ENTRIES',tag=TAG,provenance='discovery/coll (lines.py/planes.py + closure_pack.py: per-entrance maximum-weight closure over alternate response bases; shared donors after PR319) on the p = 10 word after '+'/'.join(STAGES[:STAGES.index(TAG)])+'; prepared with Anthropic Claude assistance',n=n,v=v,input_raw_sha256=hashlib.sha256(old.tobytes()).hexdigest(),input_scalar_sha256=run['physical']['scalar_projection_sha256'],selected_pairs=0,selected_families=len(families),expected_local_delta={},pairs=[],families=families)
+out,initial,final,entries,execution,cats2,proof,n2,v2=kt.transform(run,sel,TAG)
+hist=collections.Counter()
+for k in range(0,len(out),6):
+    if out[k]==0 and out[k+4]:hist[out[k+4]]+=1
+    elif out[k]==2:hist[out[k+5]]+=1
+delta=collections.Counter(hist);delta.subtract({int(r):c for r,c in run['physical']['paid_histogram'].items()})
+sel['expected_local_delta']={str(r):c for r,c in sorted(delta.items())if c}
+sel['entrance_rank_histogram']={str(r):c for r,c in sorted(proof['entrance_rank_histogram'].items())};sel['total_entrance_rank']=proof['total_entrance_rank'];sel['donor_sharing_histogram']=proof['donor_sharing_histogram']
+assert sel['total_entrance_rank']%5==0,'total entrance rank must be a multiple of 5 for the m = 100 bank tiling'
+import math;phi=lambda r:r*math.log(100/r)
+(ROOT/(TAG+'-selection.json')).write_text(json.dumps(sel,indent=1)+'\n')
+print('wrote',TAG,len(families),'entries; rank',proof['total_entrance_rank'],'delta',sel['expected_local_delta'],'phi %.3f'%sum(c*phi(int(r))for r,c in sel['expected_local_delta'].items()),'sharing',proof['donor_sharing_histogram'])
diff --git a/research/five-stage-p10-transcript-stages/discovery/build_sink_selection.py b/research/five-stage-p10-transcript-stages/discovery/build_sink_selection.py
new file mode 100644
index 0000000000..4884ac04e6
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/build_sink_selection.py
@@ -0,0 +1,32 @@
+"""Freeze sink-selection.json: run the pipeline through the restoration stage, apply the fresh terminal-sink screen
+(PR283 rule plus: no target of the set is ever a scalar/COPY source; pivot unwritten on the interval) and record the
+sinks and the local histogram delta. Not run by verify.py. Usage: python3 -B discovery/build_sink_selection.py"""
+import sys,json,importlib.util,hashlib
+from collections import Counter
+from pathlib import Path
+ROOT=Path(__file__).resolve().parent.parent;sys.path.insert(0,str(ROOT))
+def load(name,path):
+    s=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(s);sys.modules[name]=m;s.loader.exec_module(m);return m
+ctx=load('portable527_prepare',ROOT/'prepare.py').prepare()
+producer=load('portable527_physical',ROOT/'code/physical527.py').run(dict(ctx),ctx['SOURCE_TEXT'],output_dir=None)
+run=load('portable527_parity',ROOT/'parity_transform.py').run(producer)
+for st in ('descent_transform','target_transform','kernel_transform','restore_transform'):run=load('portable527_'+st,ROOT/(st+'.py')).run(run)
+sm=load('portable527_sink',ROOT/'sink_transform.py')
+W=run['W'];old=run['records'];v=W.v;regs=run['context']['regs'];n=2*v+len(regs)
+entry,rows=sm.screen(old,dict(run['initial_state']),dict(run['final_state']),n,v,list(run['physical']['category_names']),run['ZERO'],run['FULL'])
+used=set();keep=[]
+for r in rows:
+    if used&set(r['targets']):continue
+    used.update(r['targets']);keep.append(r)
+assert len(keep)==len(rows)
+sel=dict(status='GEN5_TERMINAL_SINKS_PR283_SCREEN',n=n,v=v,input_raw_sha256=hashlib.sha256(old.tobytes()).hexdigest(),input_scalar_sha256=run['physical']['scalar_projection_sha256'],entry=entry,selected=len(keep),
+    sinks=[dict(role=regs[r['stream']-2*v],stream=r['stream'],targets=r['targets'],pivot=r['pivot'],root_frame_basis=[list(x)for x in run['C'].B[r['root_frame']]],forward_writes=len(r['writes']),cleanups=len(r['cleanups']))for r in keep],expected_local_delta={})
+out,initial,final,ends,rows2,ctx2,cats,proof,nn,_,mp=sm.transform(run,sel)
+hist=Counter()
+for k in range(0,len(out),6):
+    if out[k]==0 and out[k+4]:hist[out[k+4]]+=1
+    elif out[k]==2:hist[out[k+5]]+=1
+d=Counter(hist);d.subtract({int(r):c for r,c in run['physical']['paid_histogram'].items()})
+sel['expected_local_delta']={str(r):c for r,c in sorted(d.items())if c}
+(ROOT/'sink-selection.json').write_text(json.dumps(sel,indent=1)+'\n')
+print('selected',len(keep),'entry',entry,'delta',sel['expected_local_delta'],'removed roles',proof['removed_roles'],'new n',nn)
diff --git a/research/five-stage-p10-transcript-stages/discovery/coll/census.py b/research/five-stage-p10-transcript-stages/discovery/coll/census.py
new file mode 100644
index 0000000000..24d761b15e
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/coll/census.py
@@ -0,0 +1,29 @@
+"""Kernel-eligible helper census on a dumped word (dump_at.py): ZERO->FULL ungauged helpers, F2 response, last initial read, first touch and first frame. Usage: census.py DUMP OUT.pkl
+Chafik Boukhalfa (chafreaky), Anthropic Claude assistance; Apache-2.0."""
+import sys,json,struct,collections,pickle,math
+D=sys.argv[1]
+meta=json.load(open(D+'/meta.json'));frames=json.load(open(D+'/frames.json'))
+init={int(k):v for k,v in json.load(open(D+'/initial.json')).items()};final={int(k):v for k,v in json.load(open(D+'/final.json')).items()}
+n,v,ZERO,FULL=meta['n'],meta['v'],meta['ZERO'],meta['FULL'];cats=meta['category_names'];readcat=cats.index('dirty_read')
+ev=list(struct.iter_unpack('<6i',open(D+'/records.bin','rb').read()))
+bad=set(int(k) for k in meta['gauge'])|set(meta['donor_streams'])|set(meta['borrow_streams'])
+cand=[s for s in range(2*v,n) if s not in bad and init[s]==ZERO and final[s]==FULL]
+C=set(cand);reads=collections.defaultdict(list);touch={};ff={}
+for i,(op,a,b,c,f,z) in enumerate(ev):
+    if op==1:
+        if b in C and z==readcat and f==ZERO and v<=a<2*v and c%2: reads[b].append((i,a));continue
+        for s in (a,b):
+            if s in C and s not in touch: touch[s]=i;ff[s]=f
+    elif op==2:
+        if a in C and a not in touch: touch[a]=i;ff[a]=c
+hel=[s for s in cand if reads[s]]
+print('eligible (ZERO->FULL, ungauged)',len(cand),'with reads',len(hel),'no reads',len(cand)-len(hel))
+resp={};lastread={}
+for s in hel:
+    cnt=collections.Counter(a for i,a in reads[s]);resp[s]=sum(1<<(a-v) for a,c in cnt.items() if c%2);lastread[s]=reads[s][-1][0]
+print('lastread<touch for all', all(lastread[s]<touch[s] for s in hel))
+print('max lastread',max(lastread.values()),'min touch',min(touch[s] for s in hel))
+print('first-frame dims', sorted(collections.Counter(frames[str(ff[s])]['dim'] for s in hel).items()))
+print('zero response', sum(1 for s in hel if resp[s]==0))
+cats_touch=collections.Counter(cats[ev[touch[s]][5]] if ev[touch[s]][0]==1 else 'copy' for s in hel);print('first touch categories',cats_touch.most_common(10))
+pickle.dump(dict(n=n,v=v,ZERO=ZERO,FULL=FULL,helpers=hel,resp=resp,lastread=lastread,touch=touch,firstframe=ff,ftab={f:frames[str(f)] for f in set(ff.values())},nreads={s:len(reads[s]) for s in hel}),open(sys.argv[2],'wb'))
diff --git a/research/five-stage-p10-transcript-stages/discovery/coll/closure_pack.py b/research/five-stage-p10-transcript-stages/discovery/coll/closure_pack.py
new file mode 100644
index 0000000000..098106cfef
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/coll/closure_pack.py
@@ -0,0 +1,128 @@
+"""Shared-donor kernel search: per entrance E, maximum-weight closure (pivot -> donors of its representation in a cost-ordered response basis; several bases and common cut points), lazy global greedy over entrances with helper exclusivity; env ORDERS, NT, SEED, NOISE, EXCLUDE (comma list), PRELOAD. Usage: closure_pack.py HELPERS.pkl POOL.pkl [POOL2.pkl ...] OUT.json
+Chafik Boukhalfa (chafreaky), Anthropic Claude assistance; Apache-2.0."""
+import pickle,sys,math,collections,json,random,heapq,os
+from collections import deque
+d=pickle.load(open(sys.argv[1],'rb'));OUT=sys.argv[-1];mem={};BAS={}
+for path in sys.argv[2:-1]:
+    P=pickle.load(open(path,'rb'))
+    for k,val in P.items():
+        if isinstance(val,tuple):basis,L=val
+        else:basis,L=[list(k)],val
+        key=tuple(map(tuple,basis));mem[key]=list(L);BAS[key]=basis
+ORDERS=int(os.environ.get('ORDERS','6'));NT=int(os.environ.get('NT','4'));SEED=int(os.environ.get('SEED','1'))
+ff=d['firstframe'];ft=d['ftab'];resp=d['resp'];lr=d['lastread'];tc=d['touch']
+phi=lambda r:0.0 if r<=0 else r*math.log(100/r);dim=lambda s:ft[ff[s]]['dim']
+PGe=lambda s,e:-(phi(dim(s)-e)-phi(dim(s)))
+DCe=lambda s,e:phi(e)+phi(dim(s)-e)-phi(dim(s))
+def rank(vs):
+    b={};r=0
+    for x in vs:
+        while x:
+            h=x.bit_length()-1
+            if h in b:x^=b[h]
+            else:b[h]=x;r+=1;break
+    return r
+def maxflow_closure(prof,req,cost):
+    # nodes: 0=S,1=T, pivots, donors
+    P=list(prof);D=sorted({m for p in P for m in req[p]})
+    idx={('p',p):i+2 for i,p in enumerate(P)};idx.update({('d',m):i+2+len(P) for i,m in enumerate(D)})
+    N=2+len(P)+len(D);g=[[] for _ in range(N)]
+    def add(a,b,c):g[a].append([b,c,len(g[b])]);g[b].append([a,0,len(g[a])-1])
+    INF=1e18
+    for p in P:
+        add(0,idx[('p',p)],prof[p])
+        for m in req[p]:add(idx[('p',p)],idx[('d',m)],INF)
+    for m in D:
+        if cost[m]>0:add(idx[('d',m)],1,cost[m])
+    flow=0
+    while True:
+        lvl=[-1]*N;lvl[0]=0;q=deque([0])
+        while q:
+            a=q.popleft()
+            for b,c,r in g[a]:
+                if c>1e-12 and lvl[b]<0:lvl[b]=lvl[a]+1;q.append(b)
+        if lvl[1]<0:break
+        it=[0]*N
+        def dfs(a,f):
+            if a==1:return f
+            while it[a]<len(g[a]):
+                e=g[a][it[a]];b,c,r=e
+                if c>1e-12 and lvl[b]==lvl[a]+1:
+                    x=dfs(b,min(f,c))
+                    if x>1e-12:e[1]-=x;g[b][r][1]+=x;return x
+                it[a]+=1
+            return 0
+        while True:
+            x=dfs(0,INF)
+            if x<=1e-12:break
+            flow+=x
+    seen=[False]*N;seen[0]=True;q=deque([0])
+    while q:
+        a=q.popleft()
+        for b,c,r in g[a]:
+            if c>1e-12 and not seen[b]:seen[b]=True;q.append(b)
+    selP=[p for p in P if seen[idx[('p',p)]]];selD=sorted({m for p in selP for m in req[p]})
+    val=sum(prof[p] for p in selP)-sum(cost[m] for m in selD)
+    return val,selP,selD
+rng=random.Random(SEED)
+EXCL={int(x) for x in os.environ.get('EXCLUDE','').split(',') if x}
+for k in mem:mem[k]=[s for s in mem[k] if s not in EXCL]
+def solve_line(u,taken,free):
+    G=[s for s in mem[u] if s not in taken]
+    if len(G)<2:return None
+    e=len(BAS[u]);cost={s:(0.0 if s in free else DCe(s,e)) for s in G}
+    ts=sorted(set(lr[s] for s in G));cands=[]
+    for t in ts:
+        S=[s for s in G if lr[s]<=t<tc[s]]
+        if len(S)>=2:cands.append((len(S)-rank([resp[s] for s in S]),t,S))
+    cands=[c for c in cands if c[0]>0]
+    if not cands:return None
+    cands.sort(key=lambda c:(-c[0],-c[1]));best=None;seenS=set()
+    for k,t,S in cands[:NT]:
+        key=tuple(S)
+        if key in seenS:continue
+        seenS.add(key)
+        for o in range(ORDERS):
+            order=sorted(S,key=lambda s:cost[s]*(1+(0.5*rng.random() if o else 0))+(1e-3*rng.random() if o else 0))
+            basis={};req={};prof={}
+            for s in order:
+                x=resp[s];combo=set()
+                while x:
+                    h=x.bit_length()-1
+                    if h in basis:bx,bc=basis[h];x^=bx;combo^=bc
+                    else:break
+                if x:basis[x.bit_length()-1]=(x,combo|{s})
+                else:req[s]=sorted(combo);prof[s]=PGe(s,e)
+            if not prof:continue
+            val,P,Dn=maxflow_closure(prof,req,cost)
+            if val>1e-9 and (best is None or val>best[0]):best=(val,t,[(p,req[p]) for p in P],Dn)
+    return best
+taken=set();free=collections.defaultdict(set);heap=[];sol={}
+PRE=json.load(open(os.environ['PRELOAD'])) if os.environ.get('PRELOAD') else []
+for e in PRE:taken.add(e['pivot']);taken.update(e['donors'])
+lines=list(mem)
+for i,u in enumerate(lines):
+    b=solve_line(u,taken,free[u])
+    if b:heap.append((-b[0]*(1+float(os.environ.get('NOISE','0'))*rng.random()),i));sol[i]=b
+heapq.heapify(heap);print('lines with positive closure',len(heap),'upper sum',-sum(h[0] for h in heap),flush=True)
+sel=[dict(pivot=e['pivot'],donors=e['donors'],basis=e['basis'],cut=max(lr[m] for m in [e['pivot']]+e['donors'])) for e in PRE];total=0.0
+while heap:
+    nv,i=heapq.heappop(heap);u=lines[i]
+    b=solve_line(u,taken,free[u])
+    if not b:continue
+    NZ=float(os.environ.get('NOISE','0'))
+    key=-b[0]*(1+NZ*rng.random())
+    if heap and key>heap[0][0]+1e-9 and nv!=key:heapq.heappush(heap,(key,i));continue
+    val,t,ents,Dn=b;total+=val
+    for p,D in ents:
+        sel.append(dict(pivot=p,donors=D,basis=BAS[u],cut=max(lr[m] for m in [p]+D)));taken.add(p)
+    for m in Dn:taken.add(m);free[u].add(m)
+    # allow the same line again (donors free)
+    mem[u]=[s for s in mem[u] if s not in taken or s in free[u]]
+    b2=solve_line(u,taken-free[u],free[u])
+    if b2:heapq.heappush(heap,(-b2[0],i))
+    print('accept rank',len(BAS[u]),'val %.3f'%val,'pivots',len(ents),'donors',len(Dn),'total %.3f'%total,flush=True)
+print('entries',len(sel),'phi gain',-total)
+print('donor-count hist',sorted(collections.Counter(len(e['donors']) for e in sel).items()))
+print('pivot dims',sorted(collections.Counter(dim(e['pivot']) for e in sel).items()))
+json.dump(sel,open(OUT,'w'))
diff --git a/research/five-stage-p10-transcript-stages/discovery/coll/fameval.py b/research/five-stage-p10-transcript-stages/discovery/coll/fameval.py
new file mode 100644
index 0000000000..784fa09300
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/coll/fameval.py
@@ -0,0 +1,30 @@
+import math, collections
+from linalg import *
+phi=lambda r: 0.0 if r<=0 else r*math.log(100/r)
+class Evaluator:
+    def __init__(self,d):
+        self.d=d; self.icache={}; self.stats=collections.Counter()
+    def evaluate(self,kind,hs):
+        d=self.d; ff=d['firstframe']; ftab=d['ftab']; lastread=d['lastread']; touch=d['touch']; stats=self.stats
+        cut=max(lastread[s] for s in hs); first=min(touch[s] for s in hs)
+        if cut>=first: stats[(kind,'no common cut')]+=1; return None
+        fr=tuple(sorted(set(ff[s] for s in hs)))
+        if fr not in self.icache:
+            E=intersect([ftab[f]['B'] for f in fr],[ftab[f]['A'] for f in fr])
+            self.icache[fr]=(E, nondeg_subspaces(E) if E else {})
+        E,subs=self.icache[fr]
+        if not E: stats[(kind,'zero intersection')]+=1; return None
+        if not subs: stats[(kind,'no nondegenerate subspace')]+=1; return None
+        dims={s:ftab[ff[s]]['dim'] for s in hs}
+        options=[]
+        for e,basis in subs.items():
+            assert rank(basis)==e and contains(E,basis), 'entrance basis outside the exact intersection'
+            for f in fr: assert all(sum(a*b for a,b in zip(arow,brow))==0 for arow in ftab[f]['A'] for brow in basis), 'entrance outside a first frame'
+            best=None
+            for p in hs:
+                g=phi(dims[p]-e)-phi(dims[p])+sum(phi(e)+phi(dims[q]-e)-phi(dims[q]) for q in hs if q!=p)
+                if best is None or g<best[0]: best=(g,p)
+            options.append(dict(e=e,pivot=best[1],gain=best[0],basis=basis,gram_det=det(gram(basis))))
+        options.sort(key=lambda o:o['gain'])
+        stats[(kind,'ok',len(E),max(subs))]+=1
+        return dict(kind=kind,members=list(hs),cut=cut,first_touch=first,dims=[dims[s] for s in hs],dim_intersection=len(E),E=E,options=options)
diff --git a/research/five-stage-p10-transcript-stages/discovery/coll/families.py b/research/five-stage-p10-transcript-stages/discovery/coll/families.py
new file mode 100644
index 0000000000..ed967c5ed5
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/coll/families.py
@@ -0,0 +1,64 @@
+"""Candidate collective-kernel families on gen4: twin pairs (any e), size-3 and size-4 F2 circuits of helper responses
+with a common nondegenerate entrance inside all members' first frames and a common per-family cut."""
+import pickle, json, math, random, itertools, collections, sys, time, os; sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+import numpy as np
+from linalg import *
+d = pickle.load(open(sys.argv[1],'rb')); OUT=sys.argv[2]
+helpers=d['helpers']; resp=d['resp']; lastread=d['lastread']; touch=d['touch']; ff=d['firstframe']; ftab=d['ftab']; v=d['v']
+phi=lambda r: 0.0 if r<=0 else r*math.log(100/r)
+random.seed(1); key=[random.getrandbits(64) for _ in range(v)]
+def h(R):
+    x=0
+    while R:
+        b=R&-R; x^=key[b.bit_length()-1]; R^=b
+    return x
+classes={}
+for s in helpers: classes.setdefault(resp[s],[]).append(s)
+R=list(classes); m=len(R); H=np.array([h(r) for r in R],dtype=np.uint64); hidx={int(x):i for i,x in enumerate(H)}
+assert len(hidx)==m
+t0=time.time()
+Hs=np.sort(H)
+tri=set()
+for a in range(m):
+    X=H[a]^H[a+1:]
+    for j in np.nonzero(np.isin(X,Hs))[0]:
+        b=a+1+int(j); c=hidx[int(X[j])]
+        if c>b: assert R[a]^R[b]==R[c]; tri.add((a,b,c))
+print('triangles (class level)', len(tri), time.time()-t0, flush=True)
+iu=np.triu_indices(m,1); P=H[iu[0]]^H[iu[1]]; order=np.argsort(P,kind='stable'); Ps=P[order]
+quad=set(); i=0
+while i<len(Ps):
+    j=i
+    while j+1<len(Ps) and Ps[j+1]==Ps[i]: j+=1
+    if j>i:
+        prs=[(int(iu[0][order[k]]),int(iu[1][order[k]])) for k in range(i,j+1)]
+        for (a,b),(c,e) in itertools.combinations(prs,2):
+            q=tuple(sorted((a,b,c,e))); assert len(set(q))==4
+            assert R[a]^R[b]^R[c]^R[e]==0; quad.add(q)
+    i=j+1
+print('quadruples (class level)', len(quad), time.time()-t0, flush=True)
+del P,order,Ps
+twins=[tuple(sorted(ss)) for ss in classes.values() if len(ss)>1]
+# expand to helper tuples
+def expand(cls_tuple):
+    for combo in itertools.product(*(classes[R[c]] for c in cls_tuple)): yield tuple(sorted(combo))
+cands=[]
+for t in twins:
+    for pr in itertools.combinations(t,2): cands.append(('pair',pr))
+for t in tri:
+    for hs in expand(t): cands.append(('tri',hs))
+for q in quad:
+    for hs in expand(q): cands.append(('quad',hs))
+print('helper-level candidates', collections.Counter(k for k,_ in cands), flush=True)
+from fameval import Evaluator
+ev=Evaluator(d); fams=[]
+for kind,hs in cands:
+    f=ev.evaluate(kind,list(hs))
+    if f: fams.append(f)
+stats=ev.stats
+print('families', len(fams), time.time()-t0)
+for k,c in sorted(stats.items(), key=lambda x:str(x)): print('  ',k,c)
+shape=collections.Counter((f['kind'],tuple(sorted(f['dims'])),f['options'][0]['e'],round(f['options'][0]['gain'],2)) for f in fams)
+print('top shapes by best gain:'); 
+for k,c in sorted(shape.items(), key=lambda x:x[0][3])[:40]: print('  ',k,c)
+json.dump(dict(families=fams, stats={str(k):c for k,c in stats.items()}), open(OUT,'w'))
diff --git a/research/five-stage-p10-transcript-stages/discovery/coll/linalg.py b/research/five-stage-p10-transcript-stages/discovery/coll/linalg.py
new file mode 100644
index 0000000000..1f43db8439
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/coll/linalg.py
@@ -0,0 +1,113 @@
+"""Exact rational helpers for 20-dim frames (p = 10) (bases B, annihilators A) and the G=I-J/9 Gram form."""
+from fractions import Fraction as Q
+from math import gcd, lcm
+import itertools, random
+
+def rref(rows):
+    M=[[Q(x) for x in r] for r in rows]; piv=[]; r=0
+    ncol=len(M[0]) if M else 0
+    for c in range(ncol):
+        p=next((i for i in range(r,len(M)) if M[i][c]),None)
+        if p is None: continue
+        M[r],M[p]=M[p],M[r]; pv=M[r][c]; M[r]=[x/pv for x in M[r]]
+        for i in range(len(M)):
+            if i!=r and M[i][c]:
+                m=M[i][c]; M[i]=[x-m*y for x,y in zip(M[i],M[r])]
+        piv.append(c); r+=1
+        if r==len(M): break
+    return M[:r],piv
+
+def rank(rows): return len(rref(rows)[0]) if rows else 0
+
+def nullspace(rows, ncol=20):
+    """integer basis of {x : rows x = 0}"""
+    if not rows: return [[int(i==j) for j in range(ncol)] for i in range(ncol)]
+    R,piv=rref(rows); free=[j for j in range(ncol) if j not in piv]; out=[]
+    for fj in free:
+        x=[Q(0)]*ncol; x[fj]=Q(1)
+        for row,pc in zip(R,piv): x[pc]=-row[fj]
+        out.append(integerize(x))
+    return out
+
+def integerize(x):
+    d=lcm(*(q.denominator for q in x)) if x else 1
+    v=[int(q*d) for q in x]; g=0
+    for a in v: g=gcd(g,abs(a))
+    if g>1: v=[a//g for a in v]
+    # sign normalisation: first nonzero positive
+    for a in v:
+        if a: 
+            if a<0: v=[-b for b in v]
+            break
+    return v
+
+def intersect(frames_B, frames_A):
+    """exact intersection of frames given by (B,A) pairs: nullspace of stacked annihilators, then confirm."""
+    A=[row for a in frames_A for row in a]
+    return nullspace(A)
+
+def contains(big_rows, small_rows):
+    """span(small) subseteq span(big)?"""
+    if not small_rows: return True
+    if not big_rows: return False
+    return rank(list(big_rows)+list(small_rows))==rank(big_rows)
+
+def gram(rows):
+    s=[sum(r) for r in rows]
+    return [[9*sum(a*b for a,b in zip(x,y))-s[i]*s[k] for k,y in enumerate(rows)] for i,x in enumerate(rows)]
+
+def det(A):
+    A=[list(r) for r in A];n=len(A)
+    if not n:return 1
+    sign=1;previous=1
+    for k in range(n-1):
+        pivot=next((i for i in range(k,n) if A[i][k]),None)
+        if pivot is None:return 0
+        if pivot!=k:A[k],A[pivot]=A[pivot],A[k];sign=-sign
+        p=A[k][k]
+        for i in range(k+1,n):
+            for j in range(k+1,n):
+                v=A[i][j]*p-A[i][k]*A[k][j]
+                assert v%previous==0
+                A[i][j]=v//previous
+            A[i][k]=0
+        previous=p
+    return sign*A[-1][-1]
+
+def nondeg(rows): return det(gram(rows))!=0
+
+def canon(rows):
+    """canonical hashable key of a subspace"""
+    R,_=rref(rows); return tuple(tuple(integerize(r)) for r in R)
+
+def nondeg_subspaces(E, max_tries=200, seed=0):
+    """for each e=1..dim E, one nondegenerate e-dim integer basis inside span(E), or None"""
+    k=len(E); out={}
+    if k==0: return out
+    rng=random.Random(seed)
+    ann=nullspace(E)   # annihilator rows of span(E)
+    simple=[]
+    for i in range(20):
+        for j in range(i+1,20):
+            if all(a[i]-a[j]==0 for a in ann):
+                u=[0]*20; u[i]=1; u[j]=-1; simple.append(u)
+    for e in range(k,0,-1):
+        found=None
+        if e==k and nondeg(E): found=[list(r) for r in E]
+        if found is None:
+            cands=[]
+            if e==1: cands=[[u] for u in simple]+[[list(r)] for r in E]
+            subs=list(itertools.combinations(range(k),e)) if e<k else [tuple(range(k))]
+            if len(subs)>max_tries: subs=rng.sample(subs,max_tries)
+            cands+= [[list(E[i]) for i in sub] for sub in subs]
+            for c in cands:
+                if nondeg(c): found=c; break
+            if found is None:
+                for _ in range(40):
+                    rows=[]
+                    for _ in range(e):
+                        coef=[rng.choice((-1,0,1,1)) for i in range(k)]
+                        rows.append([sum(coef[i]*E[i][c] for i in range(k)) for c in range(20)])
+                    if rank(rows)==e and nondeg(rows): found=[integerize([Q(x) for x in r]) for r in rows]; break
+        if found is not None: out[e]=found
+    return out
diff --git a/research/five-stage-p10-transcript-stages/discovery/coll/lines.py b/research/five-stage-p10-transcript-stages/discovery/coll/lines.py
new file mode 100644
index 0000000000..7df30566ab
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/coll/lines.py
@@ -0,0 +1,39 @@
+"""Rank-1 entrance pool: nondegenerate small-coefficient lines inside first frames of dim <= MAXD, with all helpers whose first frame contains each line. Usage: lines.py HELPERS.pkl OUT.pkl [MAXD]
+Chafik Boukhalfa (chafreaky), Anthropic Claude assistance; Apache-2.0."""
+import pickle,sys,itertools,collections,math
+from math import gcd
+import numpy as np
+d=pickle.load(open(sys.argv[1],'rb'));ff=d['firstframe'];ft=d['ftab'];MAXD=int(sys.argv[3]) if len(sys.argv)>3 else 5
+def prim(v):
+    g=0
+    for a in v:g=gcd(g,abs(a))
+    if g==0:return None
+    v=[a//g for a in v]
+    for a in v:
+        if a:
+            if a<0:v=[-x for x in v]
+            break
+    return tuple(v)
+def nondeg(u):return 9*sum(x*x for x in u)-sum(u)**2!=0
+pool=set()
+for f,F in ft.items():
+    B=F['B'];k=F['dim']
+    if k>MAXD:continue
+    rng=(-1,0,1) if k>2 else (-2,-1,0,1,2)
+    for co in itertools.product(rng,repeat=k):
+        if not any(co):continue
+        u=prim([sum(c*b[i] for c,b in zip(co,B)) for i in range(20)])
+        if u and nondeg(u):pool.add(u)
+pool=sorted(pool);print('pool lines',len(pool),flush=True)
+U=np.array(pool,dtype=np.int64).T  # 20 x L
+frames=sorted(ft);mem=collections.defaultdict(list)
+byframe=collections.defaultdict(list)
+for s in d['helpers']:byframe[ff[s]].append(s)
+for f in frames:
+    A=np.array(ft[f]['A'],dtype=np.int64)
+    if A.size==0:hit=np.ones(len(pool),bool)
+    else:hit=~np.any(A@U,axis=0)
+    for j in np.nonzero(hit)[0]:mem[pool[j]].extend(byframe[f])
+mem={u:L for u,L in mem.items() if len(L)>1}
+print('lines with >=2 helpers',len(mem),'max group',max(len(L) for L in mem.values()),flush=True)
+pickle.dump(mem,open(sys.argv[2],'wb'))
diff --git a/research/five-stage-p10-transcript-stages/discovery/coll/load.py b/research/five-stage-p10-transcript-stages/discovery/coll/load.py
new file mode 100644
index 0000000000..a6b5fc8084
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/coll/load.py
@@ -0,0 +1,30 @@
+import sys, json, struct, collections, pickle
+D = sys.argv[1]; OUT = sys.argv[2]
+meta = json.load(open(D+'/meta.json')); frames = json.load(open(D+'/frames.json')); init = {int(k):v for k,v in json.load(open(D+'/initial.json')).items()}
+n, v, ZERO, FULL = meta['n'], meta['v'], meta['ZERO'], meta['FULL']
+cats = meta['category_names']; readcat = cats.index('dirty_read')
+ev = list(struct.iter_unpack('<6i', open(D+'/records.bin','rb').read()))
+gauge = {int(k) for k in meta['gauge']}
+helpers = [s for s in range(2*v, n) if init[s]==ZERO and s not in gauge]
+H = set(helpers)
+reads = collections.defaultdict(list); touch = {}; firstframe = {}
+for i,e in enumerate(ev):
+    op,a,b,c,f,z = e
+    if op==1:
+        if z==readcat and b in H and f==ZERO and v<=a<2*v and c%2:
+            reads[b].append((i,a)); continue
+        for s in (a,b):
+            if s in H and s not in touch: touch[s]=i; firstframe[s]=f
+    elif op==2:
+        if a in H and a not in touch: touch[a]=i; firstframe[a]=c
+resp = {}; lastread = {}
+for s in helpers:
+    cnt = collections.Counter(a for i,a in reads[s])
+    resp[s] = sum(1<<(a-v) for a,c in cnt.items() if c%2)
+    lastread[s] = reads[s][-1][0]
+    assert lastread[s] < touch[s]
+ff = set(firstframe.values())
+ftab = {f: dict(B=frames[str(f)]['B'], A=frames[str(f)]['A'], dim=frames[str(f)]['dim']) for f in ff}
+print('helpers', len(helpers), 'distinct first frames', len(ff), 'dim hist of distinct first frames', sorted(collections.Counter(x['dim'] for x in ftab.values()).items()))
+print('helpers per first frame: hist', sorted(collections.Counter(collections.Counter(firstframe.values()).values()).items())[:30])
+pickle.dump(dict(n=n,v=v,ZERO=ZERO,FULL=FULL,readcat=readcat,helpers=helpers,resp=resp,lastread=lastread,touch=touch,firstframe=firstframe,ftab=ftab,nreads={s:len(reads[s]) for s in helpers}), open(OUT,'wb'))
diff --git a/research/five-stage-p10-transcript-stages/discovery/coll/pack_restarts.py b/research/five-stage-p10-transcript-stages/discovery/coll/pack_restarts.py
new file mode 100644
index 0000000000..56d6f98d6f
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/coll/pack_restarts.py
@@ -0,0 +1,207 @@
+"""Greedy packing of collective-kernel families (disjoint pivots, donors shareable along nested chronological chains),
+phi-ledger kappa projection with #276's moment.py, selection JSON in kernel-selection.json schema + receipt in kernel500.json schema."""
+import pickle, json, math, itertools, collections, sys, time, os, struct, importlib.util, argparse
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+from fractions import Fraction as Q
+from linalg import *
+ap=argparse.ArgumentParser(); ap.add_argument('--helpers'); ap.add_argument('--families',nargs='+'); ap.add_argument('--dump'); ap.add_argument('--pkg'); ap.add_argument('--out')
+ap.add_argument('--exclude',default='',help='JSON with key all: helper streams that must not appear in any accepted family'); ap.add_argument('--ledger283',default='',help='PR283 expected/PRICE.json: also price on its 120-replica ledger (cohort_candidate + 120*one-stage delta, W=510316-sum e)'); ap.add_argument('--preload',type=int,default=0,help='preload the first K census2 twin pairs (gen4_kernel.py order)'); ap.add_argument('--kinds',default='pair,tri,quad,quint'); ap.add_argument('--sweep',default='') ; ap.add_argument('--maxfam',type=int,default=10**9)
+args=ap.parse_args()
+d=pickle.load(open(args.helpers,'rb')); ff=d['firstframe']; ftab=d['ftab']; v=d['v']; lastread=d['lastread']; touch=d['touch']
+phi=lambda r: 0.0 if r<=0 else r*math.log(100/r)
+rec=open(args.dump+'/records.bin','rb').read()
+def cut_read(i):
+    op,a,b,c,f,z=struct.unpack_from('<6i',rec,24*i); assert op==1; return [a,b,c]
+fams=[]
+for p in args.families:
+    fams+= [f for f in json.load(open(p))['families'] if f['kind'] in args.kinds.split(',')]
+fams=fams[:args.maxfam]
+if args.exclude:
+    EX=set(json.load(open(args.exclude))['all']); before=len(fams); fams=[f for f in fams if not (set(f['members'])&EX)]; print('excluded families touching PR283 helpers:', before-len(fams), 'remaining', len(fams), flush=True)
+print('candidate families', collections.Counter(f['kind'] for f in fams), flush=True)
+# ---- model
+def load(name):
+    s=importlib.util.spec_from_file_location('m_'+name, args.pkg+'/'+name+'.py'); m=importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+cost=load('moment'); raw=json.load(open(args.dump+'/raw.json'))
+H5=collections.Counter({int(k):n for k,n in raw['five_stage_profile']['histogram'].items()})
+for a,n in {int(k):c for k,c in raw.get('completion_rank_histogram',raw['auxiliary_entrance_rank_histogram']).items()}.items(): H5[5*a]-=n
+H5={k:n for k,n in H5.items() if n}
+def kappa(H5p):
+    # p = 10 deficit-fixed ledger (m = 100, deficit 4v-5h(h-2) = 2040 per replica, normalized = 12 x one-invocation five-stage)
+    norm={k:12*n for k,n in H5p.items() if n}; mass=sum(k*n for k,n in norm.items()); m=100
+    Wq=Q(mass+12*2040,m); W=int(Wq) if Wq.denominator==1 else int(Wq)+1
+    root=cost.certify(norm,m,W,True); c=Q(int(Q(root['lower'])*10**18),10**18)
+    chain=[Q(384599,10**10)]
+    for _ in range(3): chain.append((1-c)*c+c*chain[-1])
+    bit=chain[-1]; eta=Q(1,10**12); q=bit*(1-2*eta); mn=(1-eta)*q/(1+q); t=mn*10**18; return Q((t.numerator-1)//t.denominator,10**18), 5*W, c
+# ---- packing state
+pivots={}            # pivot -> entry
+donors=collections.defaultdict(list)   # donor -> [(cut,e,basis,entry_idx)]
+entries=[]
+def chain_cost(dn, chain):
+    r=ftab[ff[dn]]['dim']; ch=sorted(chain,key=lambda x:(x[0],x[1]))
+    c=phi(ch[0][1]); 
+    for a,b in zip(ch,ch[1:]): c+=phi(b[1]-a[1])
+    return c+phi(r-ch[-1][1])-phi(r)
+def chain_ok(chain):
+    ch=sorted(chain,key=lambda x:(x[0],x[1]))
+    for a,b in zip(ch,ch[1:]):
+        if not contains(b[2],a[2]): return False
+    return True
+def marginal(p,ds,cut,e,basis):
+    if p in pivots or p in donors: return None
+    g=phi(ftab[ff[p]]['dim']-e)-phi(ftab[ff[p]]['dim'])
+    for dn in ds:
+        if dn in pivots: return None
+        old=donors[dn]; new=old+[(cut,e,basis,None)]
+        if not chain_ok(new): return None
+        g+=chain_cost(dn,new)-(chain_cost(dn,old) if old else 0.0)
+    return g
+def accept(p,ds,cut,e,basis,kind,gain,members_dims):
+    idx=len(entries)
+    entries.append(dict(kind=kind,pivot=p,donors=list(ds),cut=cut,cut_read=cut_read(cut),rank=e,basis=basis,first_frame_dims=dict((str(s),ftab[ff[s]]['dim']) for s in [p]+list(ds)),phi_gain=round(gain,6),gram_det=det(gram(basis))))
+    pivots[p]=idx
+    for dn in ds: donors[dn].append((cut,e,basis,idx))
+# preload census2 twin pairs in gen4_kernel.py order
+if args.preload:
+    cen=json.load(open(args.dump+'/census2.json'))['pairs']
+    g2=lambda p: phi(p['dima']-1)-phi(p['dima'])+phi(1)+phi(p['dimb']-1)-phi(p['dimb'])
+    cen.sort(key=g2)
+    for p in cen[:args.preload]:
+        if p['line'][0]=='e_i-e_j':
+            u=[0]*24; u[p['line'][1]]=1; u[p['line'][2]]=-1
+        else:
+            q=[Q(x) for x in p['line'][1]]; u=integerize(q)
+        mg=marginal(p['a'],[p['b']],p['cut'],1,[u]); assert mg is not None
+        accept(p['a'],[p['b']],p['cut'],1,[u],'pair500',mg,None)
+    print('preloaded', len(entries), 'pairs; phi', sum(e['phi_gain'] for e in entries), flush=True)
+base=len(entries)
+# greedy: families by best standalone gain; optional randomized restarts keep the order with the best total phi
+import random
+def greedy_total(order_f):
+    global pivots,donors,entries
+    sp,sd,se=pivots,donors,entries
+    pivots={};donors=collections.defaultdict(list);entries=[]
+    tot=0.0
+    for f in order_f:
+        best=None
+        for o in f['options']:
+            for pv in f['members']:
+                ds=[s for s in f['members'] if s!=pv]
+                mg=marginal(pv,ds,f['cut'],o['e'],o['basis'])
+                if mg is not None and (best is None or mg<best[0]): best=(mg,pv,ds,o)
+        if best is None or best[0]>=-1e-9: continue
+        mg,pv,ds,o=best; accept(pv,ds,f['cut'],o['e'],o['basis'],f['kind'],mg,None); tot+=mg
+    out=(tot,len(entries)); pivots,donors,entries=sp,sd,se; return out
+fams.sort(key=lambda f:f['options'][0]['gain'])
+RESTARTS=int(os.environ.get('PACK_RESTARTS','0')); best_order=list(fams)
+if RESTARTS:
+    base0=greedy_total(list(fams)); print('greedy order phi',base0,flush=True); bestphi=base0[0]
+    rng=random.Random(int(os.environ.get('PACK_SEED','1')))
+    for it in range(RESTARTS):
+        noise=float(os.environ.get('PACK_NOISE','0.3'))
+        cand=sorted(fams,key=lambda f:f['options'][0]['gain']*(1+noise*rng.random())-noise*rng.random())
+        tot,cnt=greedy_total(cand)
+        if tot<bestphi-1e-9: bestphi=tot; best_order=cand; print('restart',it,'better phi',tot,'count',cnt,flush=True)
+    print('best phi after restarts',bestphi,flush=True)
+    # iterated greedy: keep the accepted families of the best order first (minus a random ruin set pushed to the end)
+    IG=int(os.environ.get('PACK_IG','0'))
+    def accepted_of(order_f):
+        global pivots,donors,entries
+        sp,sd,se=pivots,donors,entries;pivots={};donors=collections.defaultdict(list);entries=[]
+        acc=[]
+        for f in order_f:
+            best=None
+            for o in f['options']:
+                for pv in f['members']:
+                    ds=[s for s in f['members'] if s!=pv]
+                    mg=marginal(pv,ds,f['cut'],o['e'],o['basis'])
+                    if mg is not None and (best is None or mg<best[0]): best=(mg,pv,ds,o)
+            if best is None or best[0]>=-1e-9: continue
+            mg,pv,ds,o=best; accept(pv,ds,f['cut'],o['e'],o['basis'],f['kind'],mg,None); acc.append(f)
+        pivots,donors,entries=sp,sd,se; return acc
+    cur_order=best_order; cur_acc=accepted_of(cur_order); cur_phi=bestphi
+    ids={id(f):i for i,f in enumerate(fams)}
+    for it in range(IG):
+        ruin=set(rng.sample(range(len(cur_acc)),max(1,int(float(os.environ.get('PACK_RUIN','0.12'))*len(cur_acc)))))
+        keep=[f for i,f in enumerate(cur_acc) if i not in ruin];out=[f for i,f in enumerate(cur_acc) if i in ruin]
+        keepset=set(map(id,cur_acc));rest=sorted((f for f in fams if id(f) not in keepset),key=lambda f:f['options'][0]['gain']*(1+0.2*rng.random()))
+        cand=keep+rest+out
+        tot,cnt=greedy_total(cand)
+        if tot<cur_phi-1e-9:
+            cur_phi=tot;cur_order=cand;cur_acc=accepted_of(cand);print('ig',it,'better phi',tot,'count',cnt,flush=True)
+    if cur_phi<bestphi: bestphi=cur_phi;best_order=cur_order
+    print('best phi after iterated greedy',bestphi,flush=True)
+fams=best_order
+acc=collections.Counter(); rej=collections.Counter(); order=[]
+for f in fams:
+    best=None
+    for o in f['options']:
+        p=o['pivot']; ds=[s for s in f['members'] if s!=p]
+        # also try other pivots for this e (shared-donor state can change the best pivot)
+        for pv in f['members']:
+            ds=[s for s in f['members'] if s!=pv]
+            mg=marginal(pv,ds,f['cut'],o['e'],o['basis'])
+            if mg is not None and (best is None or mg<best[0]): best=(mg,pv,ds,o)
+    if best is None: rej[f['kind']]+=1; continue
+    mg,pv,ds,o=best
+    if mg>=-1e-9: rej[(f['kind'],'nonnegative marginal')]+=1; continue
+    accept(pv,ds,f['cut'],o['e'],o['basis'],f['kind'],mg,None); acc[(f['kind'],o['e'])]+=1
+print('accepted', sorted(acc.items()), 'rejected', dict(rej), flush=True)
+print('total phi gain (new families)', sum(e['phi_gain'] for e in entries[base:]), 'count', len(entries)-base, flush=True)
+# ---- histogram delta + kappa for prefixes of the acceptance order
+def histogram(upto):
+    H=collections.Counter(H5); ch=collections.defaultdict(list)
+    for e in entries[:upto]:
+        r=ftab[ff[e['pivot']]]['dim']; H[r]-=5
+        if r-e['rank']>0: H[r-e['rank']]+=5
+        for dn in e['donors']: ch[dn].append((e['cut'],e['rank']))
+    for dn,c in ch.items():
+        r=ftab[ff[dn]]['dim']; c.sort(); H[r]-=5; H[c[0][1]]+=5
+        for a,b in zip(c,c[1:]):
+            if b[1]-a[1]>0: H[b[1]-a[1]]+=5
+        if r-c[-1][1]>0: H[r-c[-1][1]]+=5
+    assert min(H.values())>=0
+    return {k:n for k,n in H.items() if n}
+k0,W0,c0=kappa(H5); print('baseline kappa %.15e W_lit %d' % (float(k0),W0), flush=True)
+if args.ledger283:
+    PR=json.load(open(args.ledger283)); CH=collections.Counter({int(k):n for k,n in PR['cohort_candidate']['histogram'].items()}); W283=510316
+    massC=sum(r*n for r,n in CH.items()); assert 120*W283-massC==PR['cohort_candidate']['deficit']==105600, (120*W283-massC)
+    ratio=Q(PR['cohort_candidate']['kappa_decimal'])/Q(PR['cohort_candidate']['coarse_decimal'])
+    def kappa283(upto):
+        Hh=histogram(upto); d=collections.Counter({r:(n-H5.get(r,0))//5 for r,n in Hh.items()}); d.update({r:-H5[r]//5 for r in H5 if r not in Hh})
+        H=collections.Counter(CH)
+        for r,n in d.items(): H[r]+=120*n
+        H={r:n for r,n in H.items() if n}; assert min(H.values())>0
+        W=W283-sum(e['rank'] for e in entries[:upto]); assert 120*W-sum(r*n for r,n in H.items())==105600
+        root=cost.certify(H,120,W,True); c=Q(int(Q(root['lower'])*10**18),10**18)
+        chain=[Q(384599,10**10)]
+        for _ in range(3): chain.append((1-c)*c+c*chain[-1])
+        bit=chain[-1]; eta=Q(1,10**12); q=bit*(1-2*eta); mn=(1-eta)*q/(1+q); t=mn*10**18; k=Q((t.numerator-1)//t.denominator,10**18)
+        return float(c), float(k), W
+    c283,k283,_=kappa283(0); print('PR283 cohort ledger reproduced: coarse %.15e (PRICE.json %s) -> PR276-chain kappa %.15e (PRICE.json %s)' % (c283, PR['cohort_candidate']['coarse_decimal'], k283, PR['cohort_candidate']['kappa_decimal']), flush=True)
+results=[]
+sweep=[int(x) for x in args.sweep.split(',') if x] if args.sweep else []
+def even_prefix(upto):
+    # the ledger model is exact only when the total entrance rank is even (W_lit = mass/2+2200 integer and divisible by 5 keeps the 52800 deficit); trim to the longest even prefix
+    while upto>0 and sum(e['rank'] for e in entries[:upto])%5: upto-=1
+    return upto
+pts=sorted(set(even_prefix(u) for u in [base,len(entries)]+[base+s for s in sweep if base+s<=len(entries)]))
+for upto in pts:
+    Hh=histogram(upto); k,W,c=kappa(Hh); results.append((upto,float(k),W)); print('prefix %d (new %d): kappa %.15e W_lit %d' % (upto,upto-base,float(k),W), flush=True)
+    if args.ledger283: c3,k3,W3=kappa283(upto); print('   on PR283 ledger: coarse %.15e kappa_est %.15e W %d phi_sum %.3f' % (c3,k3,W3,sum(e['phi_gain'] for e in entries[:upto])), flush=True); results[-1]=(upto,float(k),W,c3,k3,W3)
+best=max(results,key=lambda x:(x[4] if args.ledger283 else x[1])); upto=best[0]
+Hh=histogram(upto); k,W,c=kappa(Hh)
+delta=collections.Counter({r:n//5 for r,n in Hh.items()}); delta.subtract({r:n//5 for r,n in H5.items()}); delta={str(r):n for r,n in sorted(delta.items()) if n}
+sel=entries[:upto]
+pairs=[dict(a=e['pivot'],b=e['donors'][0],cut=e['cut'],cut_read=e['cut_read'],rank=e['rank'],basis=e['basis'],first_frame_dims=list(e['first_frame_dims'].values()),phi_gain=e['phi_gain']) for e in sel if len(e['donors'])==1]
+families=[dict(pivot=e['pivot'],donors=e['donors'],cut=e['cut'],cut_read=e['cut_read'],rank=e['rank'],basis=e['basis'],first_frame_dims=e['first_frame_dims'],phi_gain=e['phi_gain'],kind=e['kind'],gram_det=e['gram_det']) for e in sel if len(e['donors'])>1]
+shared=collections.Counter(len([1 for e in sel if dn in e['donors']]) for dn in {dn for e in sel for dn in e['donors']})
+selection=dict(status='GEN4_COLLECTIVE_KERNEL_FAMILIES_PER_FAMILY_CUTS',provenance='gen4coll/families.py + pack.py on the gen4 dump (scratch research; not a package)',n=d['n'],v=v,
+    input_raw_sha256='60830cb24fbdd5a26942c4aa897d0ae30738ca5772ab83d6c57be666ddc95f7a',input_scalar_sha256='c0f4da07311f1998e0813b39098da9015969c180fa55d72f281e45cdd50aaba8',
+    selected_pairs=len(pairs),selected_families=len(families),expected_local_delta=delta,pairs=pairs,families=families,
+    donor_sharing_histogram={str(k):n for k,n in sorted(shared.items())},entrance_rank_histogram={str(k):n for k,n in sorted(collections.Counter(e['rank'] for e in sel).items())})
+json.dump(selection,open(args.out+'.selection.json','w'))
+receipt=dict(pairs=len(pairs),families=len(families),family_shapes={str(k):n for k,n in sorted(collections.Counter((e['kind'],len(e['donors'])+1,e['rank']) for e in sel).items())},delta=delta,W_lit=W,kappa=str(k),kappa_float=float(k),coarse=str(c),baseline_kappa_float=float(k0),phi_gain_total=sum(e['phi_gain'] for e in sel),sweep=results)
+json.dump(receipt,open(args.out+'.json','w'),indent=1)
+print('BEST prefix', upto, 'coarse %.15e (complex cap 7.47454944651775e-4)' % float(c), 'kappa %.15e' % float(k), 'W_lit', W, 'pairs', len(pairs), 'families', len(families), 'shapes', receipt['family_shapes'])
diff --git a/research/five-stage-p10-transcript-stages/discovery/coll/planes.py b/research/five-stage-p10-transcript-stages/discovery/coll/planes.py
new file mode 100644
index 0000000000..a85b2a62cb
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/coll/planes.py
@@ -0,0 +1,33 @@
+"""Rank >= 2 entrance pool: exact pairwise intersections of first frames (dims 2..MAXD), nondegenerate, with member helpers. Usage: planes.py HELPERS.pkl OUT.pkl MAXD
+Chafik Boukhalfa (chafreaky), Anthropic Claude assistance; Apache-2.0."""
+import pickle,sys,collections,itertools,time
+import numpy as np
+sys.path.insert(0,__import__('os').path.dirname(__import__('os').path.abspath(__file__)))
+from linalg import nullspace,rref,integerize,det,gram
+d=pickle.load(open(sys.argv[1],'rb'));ff=d['firstframe'];ft=d['ftab'];MAXD=int(sys.argv[3])
+byframe=collections.defaultdict(list)
+for s in d['helpers']:byframe[ff[s]].append(s)
+F=[f for f in byframe if 2<=ft[f]['dim']<=MAXD];print('frames',len(F),flush=True)
+B={f:np.array(ft[f]['B'],dtype=float) for f in F}
+t0=time.time();cand={}
+dims=np.array([ft[f]['dim'] for f in F])
+for i,f in enumerate(F):
+    for j in range(i+1,len(F)):
+        g=F[j];k=dims[i]+dims[j]-np.linalg.matrix_rank(np.vstack([B[f],B[g]]))
+        if k>=2:
+            key=tuple(sorted((f,g)))
+            A=[list(r) for r in ft[f]['A']]+[list(r) for r in ft[g]['A']]
+            E=nullspace(A);R,_=rref(E);basis=[integerize(r) for r in R]
+            kk=tuple(map(tuple,basis))
+            if kk not in cand and det(gram(basis))!=0:cand[kk]=basis
+print('candidate subspaces',len(cand),'time',time.time()-t0,flush=True)
+allF=list(byframe);out={}
+for kk,basis in cand.items():
+    U=np.array(basis,dtype=np.int64).T;mem=[]
+    for f in allF:
+        if ft[f]['dim']<len(basis):continue
+        A=np.array(ft[f]['A'],dtype=np.int64)
+        if A.size==0 or not np.any(A@U):mem.extend(byframe[f])
+    if len(mem)>1:out[kk]=(basis,mem)
+print('subspaces with >=2 helpers',len(out),collections.Counter(len(b) for b,m in out.values()),flush=True)
+pickle.dump(out,open(sys.argv[2],'wb'))
diff --git a/research/five-stage-p10-transcript-stages/discovery/coll/trim5.py b/research/five-stage-p10-transcript-stages/discovery/coll/trim5.py
new file mode 100644
index 0000000000..829d873557
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/coll/trim5.py
@@ -0,0 +1,17 @@
+"""phi of a shared-donor selection; trims to a total entrance rank divisible by 5 (width-100 bank tiling). Usage: trim5.py HELPERS.pkl SEL.json OUT.json
+Chafik Boukhalfa (chafreaky), Anthropic Claude assistance; Apache-2.0."""
+import pickle,sys,json,math
+d=pickle.load(open(sys.argv[1],'rb'));sel=json.load(open(sys.argv[2]))
+ff=d['firstframe'];ft=d['ftab'];phi=lambda r:0.0 if r<=0 else r*math.log(100/r);dim=lambda s:ft[ff[s]]['dim']
+rk=lambda e:len(e['basis']) if e.get('basis') else 1
+def total(S):
+    don={}
+    for e in S:
+        for m in e['donors']:don[m]=rk(e)
+    return sum(phi(dim(e['pivot'])-rk(e))-phi(dim(e['pivot'])) for e in S)+sum(phi(r)+phi(dim(m)-r)-phi(dim(m)) for m,r in don.items())
+S=list(sel);print('entries',len(S),'rank',sum(map(rk,S)),'phi %.3f'%total(S))
+while sum(map(rk,S))%5:
+    best=min(range(len(S)),key=lambda i:total(S[:i]+S[i+1:]))
+    S=S[:best]+S[best+1:]
+print('trimmed',len(S),'rank',sum(map(rk,S)),'phi %.3f'%total(S))
+json.dump(S,open(sys.argv[3],'w'))
diff --git a/research/five-stage-p10-transcript-stages/discovery/descent2_dump.py b/research/five-stage-p10-transcript-stages/discovery/descent2_dump.py
new file mode 100644
index 0000000000..ca0eab9d73
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/descent2_dump.py
@@ -0,0 +1,14 @@
+"""Replay the package through the terminal-sink stage and dump the post-sink word for discovery/descent2_search.py.
+Not run by verify.py. Usage: python3 -B discovery/descent2_dump.py OUT.pkl"""
+import sys,importlib.util,pickle
+from pathlib import Path
+ROOT=Path(__file__).resolve().parent.parent;sys.path.insert(0,str(ROOT))
+def load(name,path):
+    s=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(s);sys.modules[name]=m;s.loader.exec_module(m);return m
+ctx=load('portable527_prepare',ROOT/'prepare.py').prepare()
+run=load('portable527_physical',ROOT/'code/physical527.py').run(dict(ctx),ctx['SOURCE_TEXT'],output_dir=None)
+run=load('portable527_parity',ROOT/'parity_transform.py').run(run)
+for st in ('descent_transform','target_transform','kernel_transform','restore_transform','sink_transform'):run=load('portable527_'+st,ROOT/(st+'.py')).run(run)
+W,C=run['W'],run['C']
+d=dict(records=run['records'].tobytes(),initial=dict(run['initial_state']),final=dict(run['final_state']),ends=dict(run['helper_endpoints']),A=dict(C.A),B=dict(C.B),dimf=dict(C.dimf),chi=C.chi,cov=C.cov,h=C.h,v=W.v,ZERO=run['ZERO'],FULL=run['FULL'],cats=list(run['physical']['category_names']),physical={k:run['physical'][k] for k in ('paid_histogram','weighted_scalar_events','scalar_projection_sha256')},nregs=len(run['initial_state']))
+pickle.dump(d,open(sys.argv[1],'wb'));print('dumped',sys.argv[1])
diff --git a/research/five-stage-p10-transcript-stages/discovery/descent2_freeze.py b/research/five-stage-p10-transcript-stages/discovery/descent2_freeze.py
new file mode 100644
index 0000000000..8edc051139
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/descent2_freeze.py
@@ -0,0 +1,10 @@
+"""Freeze descent2-selection.json from a desc2_search output. usage: freeze.py postsink.pkl search.json OUT"""
+import sys,pickle,json,hashlib
+D=pickle.load(open(sys.argv[1],'rb'));S=json.load(open(sys.argv[2]))
+ph=D['physical'];mass=sum(int(r)*c for r,c in ph['paid_histogram'].items())
+sel=dict(status='FROZEN_POST_SINK_CONCAVE_DESCENT_FRAME_SELECTION',input_raw_sha256=hashlib.sha256(D['records']).hexdigest(),input_scalar_sha256=ph['scalar_projection_sha256'],
+ source_record_count=S['source_record_count'],selected_gate_count=S['selected_gate_count'],move_types=S['moves'],expected_local_histogram_delta=S['local_delta'],expected_rank_mass=mass,
+ expected_removed_calls=S['removed_calls'],expected_scalar_additions=ph['weighted_scalar_events'],predicted_local_phi_change=S['dL_local'],
+ provenance="Derived on the post-sink word by discovery/descent2_search.py: greedy descent of sum r*ln(100/r) (PR #287's rule, rohanarun) with single-gate moves to operand-chain frames and constructed minimal-join / maximal-meet frames (PR #291), join with the operand span, and chain-adjacent pair/triple blocks moved to one common frame (PR #270-style connected blocks). Prepared with Anthropic Claude assistance.",
+ entries=[{k:e[k] for k in ('record','scalar','category','old_dimension','old_basis_sha256','new_basis','new_dimension','constructed')} for e in S['entries']])
+open(sys.argv[3],'w').write(json.dumps(sel,indent=1)+'\n');print('frozen',sel['selected_gate_count'],sel['expected_local_histogram_delta'],sel['expected_removed_calls'])
diff --git a/research/five-stage-p10-transcript-stages/discovery/descent2_search.py b/research/five-stage-p10-transcript-stages/discovery/descent2_search.py
new file mode 100644
index 0000000000..b9dffed2b8
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/descent2_search.py
@@ -0,0 +1,209 @@
+"""Second retiming search on the post-sink word: greedy descent of sum phi(r), phi(r)=r ln(100/r), over single ADD gates
+(candidates: frames on either operand chain, constructed minimal join of the preceding frames [+ operand span], maximal
+meet of the following frames) and connected same-frame blocks. usage: python3 -B discovery/descent2_dump.py POSTSINK.pkl; python3 -B discovery/descent2_search.py POSTSINK.pkl OUT.json [passes] [--noblocks] [--runmax=K]; python3 discovery/descent2_freeze.py POSTSINK.pkl OUT.json descent2-selection.json. Prepared with Anthropic Claude assistance; Apache-2.0"""
+import sys,pickle,json,math,time,hashlib,importlib.util
+from collections import Counter,defaultdict
+from array import array
+from pathlib import Path
+t0=time.time()
+D=pickle.load(open(sys.argv[1],'rb'));outp=Path(sys.argv[2]);PASSES=int(sys.argv[3]) if len(sys.argv)>3 else 6;BLOCKS='--noblocks' not in sys.argv;RUNMAX=int(next((a.split('=')[1] for a in sys.argv if a.startswith('--runmax=')),'3'))
+spec=importlib.util.spec_from_file_location('bk',Path(__file__).resolve().parent.parent/'bitword/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py');bk=importlib.util.module_from_spec(spec);spec.loader.exec_module(bk)
+reduce_rows,kernel,rank,dot=bk.reduce_rows,bk.kernel,bk.rank,bk.dot
+old=array('i');old.frombytes(D['records']);A,B,dimf=D['A'],D['B'],D['dimf'];chi=D['chi'];h=D['h'];v=D['v'];n=D['nregs'];initial=D['initial'];final=D['final'];ZERO=D['ZERO']
+assert n==len(initial)
+def canon(rows):
+    Bc,_=reduce_rows(rows,h);return tuple(sorted(map(tuple,Bc),key=lambda r:next(i for i,x in enumerate(r) if x)))
+ids={}
+for f in sorted(B):ids.setdefault(canon(B[f]),f)
+NEW={}
+def register(rows):
+    key=canon(rows)
+    if key in ids:return ids[key]
+    f=max(B)+1;An,_=kernel(list(key),h);B[f],A[f],dimf[f]=key,An,len(key);ids[key]=f;NEW[f]=key;return f
+cc={}
+def sub(f1,f2):
+    if f1==f2:return True
+    r=cc.get((f1,f2))
+    if r is None:
+        r=dimf[f1]<=dimf[f2] and all(dot(a,b)==0 for a in A[f2] for b in B[f1]);cc[(f1,f2)]=r
+    return r
+nd={}
+def nondeg(f):
+    r=nd.get(f)
+    if r is None:
+        Bf,Af=B[f],A[f]
+        if not Bf or len(Bf)==h:r=True
+        elif len(Bf)<=len(Af):
+            s=[sum(b) for b in Bf];M=[[9*dot(Bf[i],Bf[j])-s[i]*s[j] for j in range(len(Bf))] for i in range(len(Bf))];r=rank(M,len(Bf))==len(Bf)
+        else:
+            s=[sum(a) for a in Af];M=[[(9-h)*dot(Af[i],Af[j])+s[i]*s[j] for j in range(len(Af))] for i in range(len(Af))];r=rank(M,len(Af))==len(Af)
+        nd[f]=r
+    return r
+jc={};mc={}
+def join(fs):
+    fs=tuple(sorted(set(fs)))
+    if len(fs)==1:return fs[0]
+    r=jc.get(fs)
+    if r is None:
+        top=max(fs,key=lambda f:dimf[f])
+        if all(sub(f,top) for f in fs):r=top
+        else:r=register([row for f in fs for row in B[f]])
+        jc[fs]=r
+    return r
+def meet(fs):
+    fs=tuple(sorted(set(fs)))
+    if len(fs)==1:return fs[0]
+    r=mc.get(fs)
+    if r is None:
+        bot=min(fs,key=lambda f:dimf[f])
+        if all(sub(bot,f) for f in fs):r=bot
+        else:
+            K,_=kernel([row for f in fs for row in A[f]],h);r=register(K) if K else register([])
+        mc[fs]=r
+    return r
+LN=[0.0]+[d*math.log(100/d) for d in range(1,101)]
+def cost(x,y):return LN[dimf[y]-dimf[x]]
+N=len(old)//6
+chain={i:[] for i in initial};owner={i:[] for i in initial};gate_slots={};gates=[];fixed=set();copy=None
+for k in range(N):
+    op,a,b,c,f,z=old[6*k:6*k+6]
+    if op==1:
+        sl=[(a,len(chain[a]))];chain[a].append(f);owner[a].append(k)
+        if b!=n:sl.append((b,len(chain[b])));chain[b].append(f);owner[b].append(k)
+        gate_slots[k]=sl;gates.append(k)
+        if b==n or (copy is not None and (a==copy[0] or b==copy[0])):fixed.add(k)
+    elif op==2:copy=(a,b,c);chain[a].append(c);owner[a].append(-1)
+    elif op==3:copy=None
+gate_frame={k:old[6*k+4] for k in gates}
+def prevf(r,p):return chain[r][p-1] if p>0 else initial[r]
+def nextf(r,p):return chain[r][p+1] if p+1<len(chain[r]) else final[r]
+def hist():
+    H=Counter()
+    for i in initial:
+        bef=initial[i]
+        for f in chain[i]+[final[i]]:
+            d=dimf[f]-dimf[bef];assert d>=0
+            if d:H[d]+=1
+            bef=f
+    return H
+H0=hist();L0=sum(LN[d]*c for d,c in H0.items())
+print('gates',len(gates),'fixed',len(fixed),'calls',sum(H0.values()),'mass',sum(d*c for d,c in H0.items()),'L %.3f'%L0,'%.0fs'%(time.time()-t0),flush=True)
+def spanok(g,need):
+    Ag=A[g]
+    return all(all(dot(x,chi[s])==0 for x in Ag) for s in need)
+spanframe_cache={}
+def spanframe(need):
+    key=frozenset(need)
+    r=spanframe_cache.get(key)
+    if r is None:r=register([chi[s] for s in need]) if need else register([]);spanframe_cache[key]=r
+    return r
+selected={};moves=Counter();gain_by=Counter()
+# block bookkeeping: span need of each gate is recorded during sweep (only for gates in plateau candidate blocks)
+def gate_eval(slots,g):
+    return sum(cost(prevf(r,p),g)+cost(g,nextf(r,p)) for r,p in slots)
+def setframe(k,g):
+    for r,p in gate_slots[k]:chain[r][p]=g
+    gate_frame[k]=g
+    if g==old[6*k+4]:selected.pop(k,None)
+    else:selected[k]=g
+for it in range(PASSES):
+    columns=[{i:1} if i<v else {} for i in range(n)];center=None;moved=0;gain=0.0;needs={}
+    for k in range(N):
+        op,a,b,c,f,z=old[6*k:6*k+6]
+        if op==0:continue
+        if op==2:center=a;continue
+        if op==3:center=None;continue
+        source=center if b==n else b;ca=columns[a]
+        for s,x in columns[source].items():
+            y=ca.get(s,0)+c*x
+            if y:ca[s]=y
+            else:del ca[s]
+        if k in fixed:continue
+        need=set()
+        if not(v<=a<2*v):need.update(ca)
+        if not(v<=b<2*v) and b!=n:need.update(columns[b])
+        if BLOCKS:needs[k]=frozenset(need)
+        slots=gate_slots[k];cur=gate_frame[k]
+        P=[prevf(r,p) for r,p in slots];Nx=[nextf(r,p) for r,p in slots]
+        cand=set()
+        for r,p in slots:cand.update(chain[r]);cand.add(initial[r]);cand.add(final[r])
+        J=join(P);M=meet(Nx)
+        if not sub(J,M):continue
+        cand.add(J);cand.add(M)
+        base=gate_eval(slots,cur)
+        opts=[]
+        for g in cand:
+            if g==cur:continue
+            if not(sub(J,g) and sub(g,M)):continue
+            d=gate_eval(slots,g)-base
+            if d<-1e-9:opts.append((d,g))
+        if not opts:continue
+        opts.sort()
+        done=False
+        for d,g in opts:
+            if nondeg(g) and spanok(g,need):
+                setframe(k,g);moved+=1;gain+=d;moves['chain' if g in initial.values() or any(g in chain[r] for r,p in slots) and g not in NEW else 'constructed']+=1;done=True;break
+        if not done:
+            # minimal frame containing the operand span as well
+            JS=join([J,spanframe(need)])
+            if JS!=J and sub(JS,M) and JS!=cur and nondeg(JS):
+                d=gate_eval(slots,JS)-base
+                if d<-1e-9:setframe(k,JS);moved+=1;gain+=d;moves['constructed_span']+=1
+    print('pass',it,'single moved',moved,'gain %.4f'%gain,'selected',len(selected),'new frames',len(NEW),'%.0fs'%(time.time()-t0),flush=True)
+    bm=0;bgain=0.0
+    if BLOCKS:
+        def block_try(ks,tag):
+            ks=set(ks);slots=[(r,p) for k in ks for r,p in gate_slots[k]];sset=set(slots)
+            bprev=[];bnext=[];regs=set();edges=set()
+            for r,p in slots:
+                regs.add(r);edges.add((r,p-1,p));edges.add((r,p,p+1))
+                if (r,p-1) not in sset:bprev.append(prevf(r,p))
+                if (r,p+1) not in sset:bnext.append(nextf(r,p))
+            J=join(bprev);M=meet(bnext)
+            if not sub(J,M):return 0
+            def fr(r,p,g):
+                if g is not None and (r,p) in sset:return g
+                return initial[r] if p<0 else final[r] if p>=len(chain[r]) else chain[r][p]
+            def ev(g):
+                return sum(cost(fr(r,p,g) if (r,p) in sset else fr(r,p,None),fr(r,q,g) if (r,q) in sset else fr(r,q,None)) for r,p,q in edges)
+            # current cost uses actual frames
+            base=sum(cost(fr(r,p,None),fr(r,q,None)) for r,p,q in edges)
+            cand={J,M}
+            for r in regs:cand.update(chain[r]);cand.add(initial[r]);cand.add(final[r])
+            opts=sorted((ev(g)-base,g) for g in cand if sub(J,g) and sub(g,M))
+            for d,g in opts:
+                if d>=-1e-9:break
+                if nondeg(g) and all(spanok(g,needs[k]) for k in ks):
+                    for k in ks:setframe(k,g)
+                    moves[tag]+=1;moves[tag+'_gates']+=len(ks);return d
+            return 0
+        for r in chain:
+            ow=owner[r]
+            for p in range(1,len(ow)):
+                k1,k2=ow[p-1],ow[p]
+                if k1>=0 and k2>=0 and k1!=k2 and k1 in needs and k2 in needs:
+                    d=block_try((k1,k2),'pair')
+                    if d:bm+=2;bgain+=d
+                for L in range(4,RUNMAX+1):
+                    if p>=L-1:
+                        ks=ow[p-L+1:p+1]
+                        if min(ks)>=0 and len(set(ks))==L and all(k in needs for k in ks):
+                            d=block_try(ks,'run%d'%L)
+                            if d:bm+=L;bgain+=d
+                if p>=2:
+                    k0=ow[p-2]
+                    if k0>=0 and k0 in needs and len({k0,k1,k2})==3 and k1 in needs and k2 in needs:
+                        d=block_try((k0,k1,k2),'triple')
+                        if d:bm+=3;bgain+=d
+        print('pass',it,'blocks moved gates',bm,'gain %.4f'%bgain,'%.0fs'%(time.time()-t0),flush=True)
+    if not moved and not bm:break
+H1=hist();L1=sum(LN[d]*c for d,c in H1.items())
+delta=Counter(H1);delta.subtract(H0);delta={d:c for d,c in sorted(delta.items()) if c}
+print('moves',dict(moves),'delta',delta,'removed calls',sum(H0.values())-sum(H1.values()),'L %.4f -> %.4f (dL %.4f)'%(L0,L1,L1-L0),flush=True)
+def sha_basis(Bf):return hashlib.sha256(json.dumps([list(r) for r in Bf],separators=(',',':')).encode()).hexdigest()
+entries=[]
+for k in sorted(selected):
+    op,a,b,c,f,z=old[6*k:6*k+6];g=selected[k]
+    entries.append(dict(record=k,scalar=[a,b,c,z],category=D['cats'][z],old_dimension=dimf[f],old_basis_sha256=sha_basis(B[f]),new_basis=[list(map(int,r)) for r in B[g]],new_dimension=dimf[g],constructed=g in NEW))
+outp.write_text(json.dumps(dict(source_record_count=N,selected_gate_count=len(entries),local_delta={str(d):c for d,c in delta.items()},removed_calls=sum(H0.values())-sum(H1.values()),dL_local=L1-L0,moves=dict(moves),new_frames=len({e['new_basis'].__repr__() for e in entries if e['constructed']}),entries=entries),indent=1)+'\n')
+print('wrote',outp,len(entries),'%.0fs'%(time.time()-t0))
diff --git a/research/five-stage-p10-transcript-stages/discovery/descent_search.py b/research/five-stage-p10-transcript-stages/discovery/descent_search.py
new file mode 100644
index 0000000000..007ff280c5
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/descent_search.py
@@ -0,0 +1,121 @@
+"""Re-derive a concave-descent frame selection (Rohan Arun's #287 rule, re-implemented): local descent of
+sum_r n_r r ln(m/r), m = 5h over the parity-fused ADD word; each move reassigns one ADD gate to a frame already on one of
+its operands' chains, keeping nested chains, fixed endpoints, exact integer operand source spans and nondegeneracy.
+usage: descent_search.py PKG OUT.json [--compare FROZEN.json]"""
+import sys, importlib.util, json, time, math, hashlib
+from collections import Counter, defaultdict
+from pathlib import Path
+root = Path(sys.argv[1]).resolve(); sys.path.insert(0, str(root)); outp = Path(sys.argv[2])
+def load(name, p):
+    spec = importlib.util.spec_from_file_location(name, p); m = importlib.util.module_from_spec(spec); sys.modules[name] = m; spec.loader.exec_module(m); return m
+t0 = time.time()
+context = load('portable527_prepare', root / 'prepare.py').prepare()
+phys = load('portable527_physical', root / 'code/physical527.py')
+producer = phys.run(dict(context), context['SOURCE_TEXT'], output_dir=None)
+pr = load('portable527_parity', root / 'parity_transform.py').run(producer, output_dir=None)
+print('parity done %.0fs' % (time.time() - t0), flush=True)
+W, C = pr['W'], pr['C']; v = W.v; old = pr['records']; initial = pr['initial_state']; n = len(initial); ZERO, FULL = pr['ZERO'], pr['FULL']
+final = {i: FULL for i in initial}
+for t in range(v): final[v + t] = W.register(W.module.kernel([C.cov[t]], W.h)[0])
+M = 5 * W.h; LN = [0.0] + [d * math.log(M / d) for d in range(1, M + 1)]
+def cost(x, y): return LN[C.dimf[y] - C.dimf[x]]
+# chains: per register list of frames (needs); gate -> [(reg, pos)]
+chain = {i: [] for i in initial}; gate_slots = {}; gates = []
+copy = None; in_copy = set()
+N = len(old) // 6
+for k in range(N):
+    op, a, b, c, f, z = old[6*k:6*k+6]
+    if op == 1:
+        slots = [(a, len(chain[a]))]; chain[a].append(f)
+        if b != n: slots.append((b, len(chain[b]))); chain[b].append(f)
+        gate_slots[k] = slots; gates.append(k)
+        if copy is not None and (a == copy[0] or b == copy[0]): in_copy.add(k)
+        if b == n: in_copy.add(k)
+    elif op == 2: copy = (a, b, c); chain[a].append(c)
+    elif op == 3: copy = None
+gate_frame = {k: old[6*k+4] for k in gates}
+def prevf(reg, pos): return chain[reg][pos-1] if pos > 0 else initial[reg]
+def nextf(reg, pos): return chain[reg][pos+1] if pos + 1 < len(chain[reg]) else final[reg]
+def total():
+    H = Counter()
+    for i in initial:
+        bef = initial[i]
+        for f in chain[i] + [final[i]]:
+            d = C.dimf[f] - C.dimf[bef]
+            if d: H[d] += 1
+            bef = f
+    return H
+H0 = total(); L0 = sum(LN[d] * c for d, c in H0.items())
+print('base chain histogram mass', sum(d*c for d, c in H0.items()), 'calls', sum(H0.values()), 'L %.1f' % L0, flush=True)
+nd_cache = {}
+def nondeg(g):
+    if g not in nd_cache: nd_cache[g] = C.nondeg(g)
+    return nd_cache[g]
+chi = C.chi
+def contains_span(g, srcs):
+    A = C.A[g]
+    return all(all(W.module.dot(x, chi[s]) == 0 for x in A) for s in srcs)
+selected = {}
+for it in range(4):
+    columns = [{i: 1} if i < v else {} for i in range(n)]; center = None; moved = 0; gain = 0.0
+    for k in range(N):
+        op, a, b, c, f, z = old[6*k:6*k+6]
+        if op == 0: continue
+        if op == 2: center = a; continue
+        if op == 3: center = None; continue
+        source = center if b == n else b; ca = columns[a]
+        for s, x in columns[source].items():
+            y = ca.get(s, 0) + c * x
+            if y: ca[s] = y
+            else: del ca[s]
+        if k in in_copy: continue
+        slots = gate_slots[k]; cur = gate_frame[k]
+        cand = set()
+        for reg, pos in slots:
+            cand.update(chain[reg]); cand.add(initial[reg]); cand.add(final[reg])
+        cand.discard(cur)
+        base = sum(cost(prevf(r, p), cur) + cost(cur, nextf(r, p)) for r, p in slots)
+        best = None
+        for g in cand:
+            if not all(C.sub(prevf(r, p), g) and C.sub(g, nextf(r, p)) for r, p in slots): continue
+            d = sum(cost(prevf(r, p), g) + cost(g, nextf(r, p)) for r, p in slots) - base
+            if d < -1e-9 and (best is None or d < best[0]): best = (d, g)
+        if best is None: continue
+        # verify span + nondegeneracy for candidates in improving order
+        opts = sorted(((sum(cost(prevf(r, p), g) + cost(g, nextf(r, p)) for r, p in slots) - base, g) for g in cand
+                       if all(C.sub(prevf(r, p), g) and C.sub(g, nextf(r, p)) for r, p in slots)), key=lambda t: (t[0], t[1]))
+        need = set()
+        if not (v <= a < 2*v): need.update(ca)
+        if not (v <= b < 2*v) and b != n: need.update(columns[b])
+        for d, g in opts:
+            if d >= -1e-9: break
+            if nondeg(g) and contains_span(g, need):
+                for r, p in slots: chain[r][p] = g
+                gate_frame[k] = g; moved += 1; gain += d
+                if g == old[6*k+4]: selected.pop(k, None)
+                else: selected[k] = g
+                break
+    print('pass', it, 'moved', moved, 'gain %.2f' % gain, 'selected', len(selected), '%.0fs' % (time.time() - t0), flush=True)
+    if not moved: break
+H1 = total(); L1 = sum(LN[d] * c for d, c in H1.items())
+delta = Counter(H1); delta.subtract(H0); delta = {d: c for d, c in sorted(delta.items()) if c}
+print('delta', delta, 'removed calls', sum(H0.values()) - sum(H1.values()), 'L %.1f -> %.1f' % (L0, L1), flush=True)
+def sha_basis(B): return hashlib.sha256(json.dumps(B, separators=(',', ':')).encode()).hexdigest()
+entries = []
+for k in sorted(selected):
+    op, a, b, c, f, z = old[6*k:6*k+6]; g = selected[k]
+    entries.append(dict(record=k, scalar=[a, b, c, z], old_dimension=C.dimf[f], old_basis_sha256=sha_basis(C.B[f]),
+                        new_basis=[list(map(int, row)) for row in C.B[g]], new_dimension=C.dimf[g]))
+copies = Counter({W.h - 2: W.h})
+sel = dict(status='FROZEN_CONCAVE_DESCENT_FRAME_SELECTION', input_raw_sha256=hashlib.sha256(old.tobytes()).hexdigest(),
+           input_scalar_sha256=pr['physical']['scalar_projection_sha256'], source_record_count=N, selected_gate_count=len(entries),
+           expected_local_histogram_delta={str(d): c for d, c in delta.items()}, expected_rank_mass=sum(d*c for d, c in (H1 + copies).items()),
+           expected_removed_calls=sum(H0.values()) - sum(H1.values()), expected_scalar_additions=pr['physical']['weighted_scalar_events'],
+           provenance="Re-derived on this word by gen5/descent_search.py (re-implementation of #287's stated rule): greedy local descent of sum r*ln(m/r), m = 5h over the parity-fused ADD word, each move reassigning one ADD gate to a frame already on one of its operands' chains; nested chains, fixed endpoints, exact integer operand source spans and nondegeneracy enforced. Rule by Rohan Arun (#287); re-derivation prepared with Anthropic Claude assistance.",
+           entries=entries)
+outp.write_text(json.dumps(sel, indent=1) + '\n')
+if len(sys.argv) > 4 and sys.argv[3] == '--compare':
+    fz = json.loads(Path(sys.argv[4]).read_text()); fr = {e['record']: e for e in fz['entries']}
+    mine = {e['record']: e for e in entries}
+    print('frozen', len(fr), 'mine', len(mine), 'common records', len(set(fr) & set(mine)), 'same new basis', sum(fr[r]['new_basis'] == mine[r]['new_basis'] for r in set(fr) & set(mine)))
+    print('frozen delta', fz['expected_local_histogram_delta'], 'removed', fz['expected_removed_calls'])
diff --git a/research/five-stage-p10-transcript-stages/discovery/dump_at.py b/research/five-stage-p10-transcript-stages/discovery/dump_at.py
new file mode 100644
index 0000000000..b9b4629837
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/dump_at.py
@@ -0,0 +1,47 @@
+"""Run the package pipeline through a stage of portable_bit.STAGES and dump records/frames/meta. Usage: dump_at.py PKG OUT STAGE
+Chafik Boukhalfa (chafreaky), Anthropic Claude assistance; Apache-2.0."""
+import sys, json, importlib.util, time
+from pathlib import Path
+PKG = Path(sys.argv[1]).resolve(); OUT = Path(sys.argv[2]).resolve(); OUT.mkdir(parents=True, exist_ok=True); sys.path.insert(0, str(PKG))
+UPTO = sys.argv[3]  # last stage to run (inclusive), or 'none'
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); sys.modules[name] = m; s.loader.exec_module(m); return m
+t0 = time.time()
+ctx = load('portable527_prepare', PKG/'prepare.py').prepare()
+raw = load('portable527_raw_ledger', PKG/'raw_ledger.py').run(ctx)
+producer = load('portable527_physical', PKG/'code/physical527.py').run(dict(ctx), ctx['SOURCE_TEXT'], output_dir=None)
+run = load('portable527_parity', PKG/'parity_transform.py').run(producer)
+STAGES = load('portable527_bitstages', PKG/'portable_bit.py').STAGES
+todo = [] if UPTO == 'none' else list(STAGES[:STAGES.index(UPTO)+1])
+for st in todo:
+    if st.startswith('reorder'):
+        run = load('portable527_reorder', PKG/'reorder_transform.py').run(run, tag=st)
+    else:
+        run = load('portable527_'+st, PKG/(st.rstrip('0123456789')+'_transform.py') if not (PKG/(st+'_transform.py')).exists() else PKG/(st+'_transform.py')).run(run)
+    print(st, time.time()-t0, flush=True)
+W, C = run['W'], run['C']
+rec = run['records']; (OUT/'records.bin').write_bytes(rec.tobytes())
+init = run['initial_state']; regs = run['context']['regs']; v = W.v; n = 2*v+len(regs)
+final = dict(run.get('final_state') or init)
+if not run.get('final_state'):
+    for k in range(0, len(rec), 6):
+        if rec[k] == 0: final[rec[k+1]] = rec[k+3]
+used = set(init.values()) | set(final.values())
+for k in range(0, len(rec), 6):
+    op,a,b,c,f,z = rec[k:k+6]
+    if op==0: used.update((b,c))
+    elif op==1: used.add(f)
+    elif op==2: used.update((c,f))
+for s,z in W.gauge.items(): used.add(z['frame'])
+frames = {str(f): dict(B=C.B[f], A=C.A[f], dim=C.dimf[f]) for f in used}
+meta = dict(n=n, v=v, R=len(regs), ZERO=run['ZERO'], FULL=run['FULL'], category_names=run['physical']['category_names'], stages=todo,
+            regs=regs, gauge={str(2*v+j): dict(frame=W.gauge[r]['frame'], dim=W.gauge[r]['dim']) for j,r in enumerate(regs) if r in W.gauge},
+            donor_streams=sorted(2*v+j for j,r in enumerate(regs) if r in W.donor), borrow_streams=sorted(2*v+j for j,r in enumerate(regs) if r in run['context']['borrow']),
+            paid_histogram=run['physical']['paid_histogram'], paid_rank_mass=run['physical']['paid_rank_mass'],
+            scalar_projection_sha256=run['physical']['scalar_projection_sha256'], raw_sha256=__import__('hashlib').sha256(rec.tobytes()).hexdigest())
+(OUT/'initial.json').write_text(json.dumps({str(k):v for k,v in init.items()}))
+(OUT/'final.json').write_text(json.dumps({str(k):v for k,v in final.items()}))
+(OUT/'frames.json').write_text(json.dumps(frames))
+(OUT/'meta.json').write_text(json.dumps(meta))
+(OUT/'raw.json').write_text(json.dumps(raw, default=str))
+print('dumped', len(rec)//6, 'records; n', n, 'v', v, 'frames', len(frames), time.time()-t0, flush=True)
diff --git a/research/five-stage-p10-transcript-stages/discovery/repin.py b/research/five-stage-p10-transcript-stages/discovery/repin.py
new file mode 100644
index 0000000000..291745c26f
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/repin.py
@@ -0,0 +1,61 @@
+#!/usr/bin/env python3
+"""Mechanical re-pinning after a new bit word (new module data) is installed. Not part of the proof.
+
+    python3 -B discovery/repin.py --output /new/scratch/dir            (dry run: prints the changed pins)
+    python3 -B discovery/repin.py --output /new/scratch/dir --write    (writes word-pins.json and MANIFEST.json)
+
+It runs verify.replay(), the exact stage sequence of verify.py, in this process with word_pins.RECORD switched on,
+so every expect(name, value) records the value of the installed word instead of asserting it. Every structural
+assertion, control and exact certificate still runs and must pass. verify.py itself always runs with
+RECORD = None (it asserts so), so after --write the new pins are checked by a fresh, strict `verify.py` run.
+See discovery/REPIN.md for the whole procedure. Prepared by DreamingOfClouds with Anthropic Claude assistance;
+Apache-2.0.
+"""
+import argparse, hashlib, importlib.util, json, sys, time
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+sys.path.insert(0, str(ROOT))
+sys.dont_write_bytecode = True
+
+
+def manifest(write):
+    p = ROOT / 'MANIFEST.json'; old = json.loads(p.read_text()); files = {}
+    for q in ROOT.rglob('*'):
+        assert not q.is_symlink(), q
+        if q.is_file() and q != p:
+            assert '__pycache__' not in q.parts and q.suffix != '.pyc' and q.name != '.DS_Store', q
+            files[q.relative_to(ROOT).as_posix()] = hashlib.sha256(q.read_bytes()).hexdigest()
+    changed = sorted(k for k in set(files) | set(old['files']) if files.get(k) != old['files'].get(k))
+    if write:
+        p.write_text(json.dumps(dict(files=dict(sorted(files.items())), schema=old['schema']), indent=1, sort_keys=True) + '\n')
+    return changed
+
+
+def main():
+    if not __debug__: raise SystemExit('assertions required')
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--output', type=Path, required=True); ap.add_argument('--write', action='store_true')
+    a = ap.parse_args(); out = a.output.resolve(); assert not out.exists() and not out.is_relative_to(ROOT); out.mkdir(parents=True)
+    import word_pins
+    assert Path(word_pins.__file__).resolve() == ROOT / 'word_pins.py'
+    old = dict(word_pins.PINS); word_pins.RECORD = {}
+    spec = importlib.util.spec_from_file_location('repin_verify', ROOT / 'verify.py'); verify = importlib.util.module_from_spec(spec); spec.loader.exec_module(verify)
+    results, timings = {}, {}
+    def save(name, value): (out / name).write_text(json.dumps(verify.serial(value), sort_keys=True, indent=2) + '\n')
+    t = time.monotonic(); verify.replay(out, results, timings, save)
+    new = dict(sorted(word_pins.RECORD.items()))
+    for k in sorted(set(old) | set(new)):
+        if old.get(k) != new.get(k):
+            print('PIN', k, ':', json.dumps(old.get(k))[:160], '->', json.dumps(new.get(k))[:160])
+    (out / 'word-pins.json').write_text(json.dumps(new, indent=1, sort_keys=True) + '\n')
+    if a.write:
+        (ROOT / 'word-pins.json').write_text(json.dumps(new, indent=1, sort_keys=True) + '\n')
+        print('wrote word-pins.json; MANIFEST changes:', manifest(True))
+    else:
+        print('dry run; MANIFEST would change:', manifest(False))
+    print('recorded %d pins in %.0fs; now run verify.py (strict) on a new output directory' % (len(new), time.monotonic() - t))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/five-stage-p10-transcript-stages/discovery/target_search.py b/research/five-stage-p10-transcript-stages/discovery/target_search.py
new file mode 100644
index 0000000000..f88b1aa8aa
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/discovery/target_search.py
@@ -0,0 +1,128 @@
+"""Re-derive target-prefix square groups (eumemic #268 / #287 transform) on a word.
+usage: target_search.py PKG DESCENT_SELECTION OUT.json [--compare FROZEN]"""
+import sys, importlib.util, json, time, math, hashlib
+from itertools import combinations
+from collections import Counter, defaultdict
+from pathlib import Path
+root = Path(sys.argv[1]).resolve(); sys.path.insert(0, str(root)); dsel = sys.argv[2]; outp = Path(sys.argv[3])
+def load(name, p):
+    spec = importlib.util.spec_from_file_location(name, p); m = importlib.util.module_from_spec(spec); sys.modules[name] = m; spec.loader.exec_module(m); return m
+t0 = time.time()
+context = load('portable527_prepare', root / 'prepare.py').prepare()
+producer = load('portable527_physical', root / 'code/physical527.py').run(dict(context), context['SOURCE_TEXT'], output_dir=None)
+pr = load('portable527_parity', root / 'parity_transform.py').run(producer, output_dir=None)
+dr = load('portable527_descent', root / 'descent_transform.py').run(pr, output_dir=None, selection_path=dsel)
+print('descent done %.0fs' % (time.time() - t0), flush=True)
+W, C = dr['W'], dr['C']; v = W.v; rec = dr['records']; initial = dr['initial_state']; n = len(initial); ZERO, FULL = dr['ZERO'], dr['FULL']
+N = len(rec) // 6
+final = {i: FULL for i in initial}
+for t in range(v): final[v + t] = W.register(W.module.kernel([C.cov[t]], W.h)[0])
+cut = None
+for i in range(N):
+    if rec[6*i] == 0 and v <= rec[6*i+1] < 2*v: cut = i; break
+print('cut', cut, flush=True)
+# pass: columns as int bitsets; per-target add list (i, dim, frame, src) and response snapshots after cut; first move per target
+columns = [1 << i for i in range(n)]; center = None
+adds = defaultdict(list); snaps = defaultdict(list); resp = defaultdict(int); firstmove = {}; src_use = defaultdict(list)
+needs = {s: [] for s in initial}   # (record, frame) for census simulation
+for i in range(N):
+    op, a, b, c, f, z = rec[6*i:6*i+6]
+    if op == 0:
+        if v <= a < 2*v and a - v not in firstmove: firstmove[a - v] = i
+        continue
+    if op == 2: center = a; needs[a].append((i, c)); continue
+    if op == 3: center = None; continue
+    actual = center if b == n else b
+    needs[a].append((i, f))
+    if b != n: needs[b].append((i, f))
+    if v <= actual < 2*v: src_use[actual - v].append(i)
+    if v <= a < 2*v:
+        t = a - v; adds[t].append((i, C.dimf[f], f, actual))
+        if i > cut and not (v <= actual < 2*v):
+            resp[t] ^= columns[actual]; snaps[t].append((i, resp[t]))
+    columns[a] ^= columns[actual]
+assert center is None
+print('scan done %.0fs' % (time.time() - t0), flush=True)
+def resp_upto(t, close):
+    r = 0
+    for i, x in snaps[t]:
+        if i <= close: r = x
+        else: break
+    return r
+M = 5 * W.h; LN = [0.0] + [d * math.log(M / d) for d in range(1, M + 1)]
+def chain_hist(s, seq):
+    H = Counter(); bef = initial[s]
+    for f in seq + [final[s]]:
+        assert C.sub(bef, f), ('nest', s); d = C.dimf[f] - C.dimf[bef]
+        if d: H[d] += 1
+        bef = f
+    return H
+def try_group(T, dep):
+    if any(C.dimf[f] != 0 or f != ZERO for t in T for (i, f) in needs[v + t] if i <= cut): return None
+    if any(initial[v + t] != ZERO for t in T): return None
+    l20 = [i for t in T for (i, d, f, s) in adds[t] if i > cut and d == W.h - 4]
+    if not l20: return None
+    close = max(l20)
+    if any(i <= close for t in T for i in src_use[t]): return None
+    ret = [t for t in T if t != dep]
+    if resp_upto(dep, close) ^ resp_upto(ret[0], close) ^ resp_upto(ret[1], close) ^ resp_upto(ret[2], close): return None
+    # dependent's deleted adds must have non-target sources (they do by construction of snaps); every add of dep in (cut,close] deleted
+    # close frame: the common first need after close of all four targets (the frozen #287 groups all have this form)
+    nxts = []
+    for t in T:
+        nx = [f for (i, f) in needs[v + t] if i > close]
+        nxts.append(nx[0] if nx else final[v + t])
+    F = nxts[0]
+    if not all(C.sub(F, g) and C.sub(g, F) for g in nxts): return None
+    if C.dimf[F] != W.h - 3 or not C.nondeg(F): return None
+    if not all(all(W.module.dot(C.cov[t], b) == 0 for b in C.B[F]) for t in T): return None
+    # census simulation for the 4 targets
+    delta = Counter(); ok = True
+    for t in T:
+        s = v + t; seq_old = [f for (i, f) in needs[s]]
+        new = []; inserted_cut = False; inserted_close = False
+        for (i, f) in needs[s]:
+            if i > cut and not inserted_cut:
+                new.extend([ZERO] * (3 if t == dep else 1)); inserted_cut = True
+            if i > close and not inserted_close:
+                new.extend([F] * (3 if t == dep else 1)); inserted_close = True
+            if t == dep and cut < i <= close: continue
+            new.append(f)
+        if not inserted_cut: new.extend([ZERO] * (3 if t == dep else 1))
+        if not inserted_close: new.extend([F] * (3 if t == dep else 1))
+        try:
+            H0 = chain_hist(s, seq_old); H1 = chain_hist(s, new)
+        except AssertionError:
+            return None
+        delta.update(H1); delta.subtract(H0)
+    delta = {d: c for d, c in delta.items() if c}
+    gain = sum(LN[d] * c for d, c in delta.items())
+    return dict(targets=sorted(T), cut_record=cut, close_after_record=close, dependent={str(dep): ret}, retained=ret, close_rank=W.h - 3,
+                close_basis=[list(map(int, r)) for r in C.B[F]], local_histogram_delta={str(d): c for d, c in sorted(delta.items())},
+                score=round(-gain, 2), extra_setup_restore_additions=6)
+groups = []; used = set()
+cubes = v // 8
+for cube in range(cubes):
+    ports = list(range(8 * cube, 8 * cube + 8))
+    cands = []
+    for T in combinations(ports, 4):
+        for dep in T:
+            g = try_group(T, dep)
+            if g and g['score'] > 0: cands.append(g)
+    cands.sort(key=lambda g: -g['score'])
+    for g in cands:
+        if not set(g['targets']) & used:
+            groups.append(g); used.update(g['targets'])
+print('groups', len(groups), 'score sum %.2f' % sum(g['score'] for g in groups), Counter(json.dumps(g['local_histogram_delta']) for g in groups).most_common(5), '%.0fs' % (time.time() - t0), flush=True)
+tot = Counter()
+for g in groups: tot.update({int(k): v_ for k, v_ in g['local_histogram_delta'].items()})
+sel = dict(input_raw_sha256=hashlib.sha256(rec.tobytes()).hexdigest(), input_scalar_sha256=dr['physical']['scalar_projection_sha256'], cut_record=cut,
+           rebase_parent='gen5 parity-fused word after the concave-descent retiming (groups re-derived by gen5/target_search.py)',
+           expected_total_delta={str(k): c for k, c in sorted(tot.items()) if c}, groups=groups)
+outp.write_text(json.dumps(sel, indent=1) + '\n')
+if len(sys.argv) > 5 and sys.argv[4] == '--compare':
+    fz = json.loads(Path(sys.argv[5]).read_text())
+    A = {tuple(g['targets']): g for g in fz['groups']}; B = {tuple(g['targets']): g for g in groups}
+    print('frozen', len(A), 'mine', len(B), 'same targets', len(set(A) & set(B)), 'identical rows', sum(json.dumps(A[k], sort_keys=True) == json.dumps(B[k], sort_keys=True) for k in set(A) & set(B)), 'frozen total', fz['expected_total_delta'], 'mine', sel['expected_total_delta'])
+    k = next(iter(set(A) & set(B)), None)
+    if k: print('frozen', {x: A[k][x] for x in A[k] if x != 'close_basis'}); print('mine  ', {x: B[k][x] for x in B[k] if x != 'close_basis'}, A[k]['close_basis'] == B[k]['close_basis'])
diff --git a/research/five-stage-p10-transcript-stages/finite_check.py b/research/five-stage-p10-transcript-stages/finite_check.py
new file mode 100644
index 0000000000..9de117280e
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/finite_check.py
@@ -0,0 +1,144 @@
+"""Finite bill for the literal 60-replica banked five-stage p = 10 word (source527 finite bill, rebound).
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+Retains PR234exact-tape/prime/ordinary-leaf hypotheses, and pays bankroutes.
+p = 10 port (DreamingOfClouds, Anthropic Claude assistance): m = 5h, d = m^2, N = 2m, the 2h-dimensional rational
+route (its factor counts pinned), h copied-centre temporaries and 5h copy/erase episodes per replica; the data
+route families stay 20v + 4v (five stages of 4v data families plus the final exchange); word counts pinned.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from hashlib import sha256
+from pathlib import Path
+import importlib.util,json
+from word_pins import expect,shape
+HERE=Path(__file__).resolve().parent
+THEOREM_PINS={
+ 'proof/three-stage-cover-bit.tex':'47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511',
+ 'proof/three-stage-cover-rows.tex':'6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8',
+ 'proof/copied-centers-lemma.tex':'d0ce6d3d504996aadb098227885224e48df46101daec8893523a0a8b7364d8fe'}
+def ceilq(x):return -((-x.numerator)//x.denominator)
+
+def cutoff_log2(delta,C):
+    assert 0<delta<=1 and isinstance(C,int) and C>=1
+    return max(1,ceilq(36/delta**2),ceilq(2*(4+(C-1).bit_length())/delta))
+
+def hist(x):return Counter({int(k):v for k,v in x.items()if v})
+
+def route_template(h):
+    """Recompute the actual 2h-dimensional rational route (48 at h = 24, 40 at h = 20), not its receipt."""
+    I=lambda n:[[Q(i==j)for j in range(n)]for i in range(n)]
+    q=[int(i<3)for i in range(h)]
+    P=[[Q(q[i])*(Q(q[j])-Q(1,3))/2 for j in range(h)]for i in range(h)]
+    K=[[Q(i==j)-P[i][j]for j in range(h)]for i in range(h)]
+    rho=[P[i]+K[i]for i in range(h)]+[K[i]+P[i]for i in range(h)]
+    a=[r[:]for r in rho];factors=[]
+    for j in range(2*h):
+        p=next(i for i in range(j,2*h)if a[i][j])
+        if p!=j:a[j],a[p]=a[p],a[j];factors.append(('swap',j,p,None))
+        if a[j][j]!=1:
+            c=1/a[j][j];a[j]=[c*x for x in a[j]];factors.append(('scale',j,None,c))
+        for i in range(2*h):
+            if i!=j and a[i][j]:
+                c=-a[i][j];a[i]=[x+c*y for x,y in zip(a[i],a[j])];factors.append(('add',i,j,c))
+    assert a==I(2*h)
+    def replay(omit=None):
+        a=I(2*h)
+        for z in reversed(range(len(factors))):
+            if z==omit:continue
+            kind,i,j,c=factors[z]
+            if kind=='swap':a[i],a[j]=a[j],a[i]
+            elif kind=='scale':a[i]=[x/c for x in a[i]]
+            else:a[i]=[x-c*y for x,y in zip(a[i],a[j])]
+        return a
+    assert replay()==rho
+    assert replay(next(i for i,f in enumerate(factors)if f[0]=='add'))!=rho
+    counts=dict(Counter(f[0]for f in factors));denoms=sorted({c.denominator for kind,i,j,c in factors if c is not None})
+    expect('route_factor_counts',counts);assert denoms==[1,2,3,6]
+    serialization=[[kind,i,j,None if c is None else str(c)]for kind,i,j,c in factors]
+    return dict(factors=len(factors),factor_counts=counts,denominators=denoms,
+        factor_program_sha256=sha256(json.dumps(serialization,separators=(',',':')).encode()).hexdigest(),
+        exact_inverse_reconstruction=True,missing_addition_rejected=True)
+
+def run(raw,physical,scalar,prime_result,math_result,banks,banked_result,global_result):
+ for name,h in THEOREM_PINS.items():assert sha256((HERE/name).read_bytes()).hexdigest()==h,('changed theorem',name)
+ bit=(HERE/'proof/three-stage-cover-bit.tex').read_text();rows=(HERE/'proof/three-stage-cover-rows.tex').read_text();copied=(HERE/'proof/copied-centers-lemma.tex').read_text()
+ for s in ('constants are independent of $w,n$ and ancestor values','absorbed by the complete $q^w$ target fiber','spectator counters','32m^2','only units are inverted'):assert s in bit
+ for s in ('W(w)^{D(n)}','padding factor is less than two','below $q^2$'):assert s in rows
+ assert 'Copying, pointwise reads and erasure are linear'in copied and'fixed work stream'in copied
+ S=shape();h=S['h']
+ assert raw['physical_R']==expect('final_physical_R',raw['physical_R']) and raw['v']==S['v'] and raw['h']==h and raw['source_aliases']==0
+ assert scalar['forward']['event_sha256']==physical['scalar_projection_sha256']==global_result['scalar_projection_sha256']
+ assert physical['tagged_scalar_sha256']==global_result['local_tagged_sha256']
+ f,b=scalar['forward'],scalar['inverse'];n=2*raw['v']+raw['physical_R']
+ for row in(f,b):
+  assert row['all_source_and_dirty_restored']and row['arbitrary_target_contents_preserved']and row['all_formal_columns']==n
+  assert row['weighted_additions']==physical['weighted_scalar_events']==expect('weighted_scalar_events',row['weighted_additions'])
+  assert hist(row['coefficient_counts'])==hist(physical['coefficient_histogram'])
+  assert row['literal_unit_additions']==sum(c*v for c,v in hist(row['coefficient_counts']).items())==expect('literal_unit_additions',row['literal_unit_additions'])
+ assert f['max_intermediate_row_l1']==expect('forward_max_row_l1',f['max_intermediate_row_l1']) and b['max_intermediate_row_l1']==expect('inverse_max_row_l1',b['max_intermediate_row_l1'])
+ assert raw['parity_transform']['both_reflected_ledgers'] and raw['parity_transform']['remaining_payload_additions']==expect('surviving_additions',raw['parity_transform']['remaining_payload_additions'])
+ assert raw['parity_transform']['removed_even_add_count']==expect('removed_even_adds',raw['parity_transform']['removed_even_add_count'])
+ # Every transcript stage receipt: both reflected ledgers, the selected counts pinned, and its rejected controls.
+ checks=dict(
+  descent=lambda r:r['both_reflected_ledgers'] and r['operand_source_spans_contained'] and r['selected_gate_count']==expect('descent_selected_gates',r['selected_gate_count']),
+  target=lambda r:r['both_reflected_ledgers'] and r['negative_control']=='omitted target-prefix setup rejected' and r['selected_groups']==expect('target_groups',r['selected_groups']),
+  kernel=lambda r:r['both_reflected_ledgers'] and r['selected_entries']==expect('kernel_entries',r['selected_entries']) and all(c['wrong_rows']>0 for c in r['scalar']['controls']),
+  restore=lambda r:r['both_reflected_ledgers'] and r['selected']==expect('restore_helpers',r['selected']) and r['scalar']['controls'][0]['wrong_rows']>0 and not r['scalar']['forward']['wrong_rows'],
+  sink=lambda r:r['both_reflected_ledgers'] and r['selected']==expect('sink_count',r['selected']) and all(c['wrong_rows']>0 for c in r['scalar']['controls']),
+  reorder=lambda r:r['both_reflected_ledgers'] and r['integer_replay']['identical'] and r['all_gate_frames_contain_operand_source_spans'] and r['selected']==expect('reorder_count',r['selected']) and all(c['wrong_rows']>0 for c in r['scalar']['controls']),
+  reorder2=lambda r:r['both_reflected_ledgers'] and r['integer_replay']['identical'] and r['all_gate_frames_contain_operand_source_spans'] and r['selected']==expect('reorder2_count',r['selected']) and all(c['wrong_rows']>0 for c in r['scalar']['controls']))
+ stages=raw['transcript_stages'];assert set(stages)<=set(checks) and len(set(stages))==len(stages)
+ assert {k[:-len('_transform')]for k in raw if k.endswith('_transform')}=={'parity'}|set(stages),'every executed stage leaves exactly one receipt'
+ for name in stages:assert checks[name](raw[name+'_transform']),('stage receipt',name)
+ assert physical['copied_centers']==S['centers'] and len(physical['copied_center_blocks'])==S['centers']
+ assert all(z['rank']==S['center_rank'] and z['scatter_reads']==S['scatter_reads'] for z in physical['copied_center_blocks'])
+ assert hist(physical['paid_histogram'])==hist(raw['one_stage_helper_histogram_including_copies'])
+ assert prime_result['all_remaining_factors_below_2_power_80']and prime_result['physical_inventory_bound']
+ assert prime_result['independent_entrances']==expect('final_entrances',prime_result['independent_entrances']) and prime_result['bundled_unique_bases']==expect('final_entrance_bases',prime_result['bundled_unique_bases'])
+ assert hist(prime_result['entrance_rank_counts'])==hist(raw['auxiliary_entrance_rank_histogram'])
+ assert banks['conservative_extra_selector_calls']==expect('extra_selector_calls',banks['conservative_extra_selector_calls']) and banks['normalizer_factor_bound']==expect('normalizer_factor_bound',banks['normalizer_factor_bound'])
+ assert banks['physical_replicas']==S['replicas'] and banks['literal_stock']==expect('literal_stock',banks['literal_stock']) and banks['assignments']==5*S['replicas']*raw['physical_R']
+ assert banked_result['all_assignments_match']and banked_result['all_logical_helpers_bound']and banked_result['independent_completions_removed']==expect('final_entrances',banked_result['independent_completions_removed'])
+ m=S['m'];v=raw['v'];R=raw['physical_R'];T=banks['physical_replicas'];stock=banks['literal_stock'];d=m*m;N=2*m
+ H=hist(raw['five_stage_profile']['histogram']);assert H==hist(global_result['paid_histogram'])
+ for a,cnt in hist(raw.get('completion_rank_histogram',raw['auxiliary_entrance_rank_histogram'])).items():
+  assert H[5*a]>=cnt;H[5*a]-=cnt
+  if not H[5*a]:del H[5*a]
+ literal=Counter({r:T*cnt for r,cnt in H.items()});E=sum(literal.values());mass=sum(r*cnt for r,cnt in literal.items())
+ assert m*stock-mass==T*S['deficit'] and max(literal)==S['idle'][2] and Q(max(literal),m)<Q(1,2)
+ assert hist(banked_result['literal_paid_histogram'])==literal and banked_result['literal_stock']==stock
+ mathematics=math_result['mathematics'];bp=mathematics['bit_profile'];assert bp['literal_stock']==stock and bp['literal_children']==E and bp['literal_rank_mass']==mass
+ weighted=T*(5*f['weighted_additions']+6*v);unit=T*(5*f['literal_unit_additions']+6*v)
+ assert weighted==T*global_result['total_weighted_additions']
+ # Preserve alloriginalroutes/bridges, paidcopies and finiteprimitiveovercharges.
+ # The actual physicalstock and60replicas enter this bill; normalizedmomentW doesnot.
+ J=T*(20*v+4*v+10*R);good=8*m*m+8;high=16*(d+1)**2;K=banks['conservative_extra_selector_calls']
+ payload=64*f['max_intermediate_row_l1']**3*b['max_intermediate_row_l1']**2;payloadbits=payload.bit_length();assert payload<2**104
+ fallback=6*N*(N-1)+3*N+6*(N-1);assert fallback<32*m*m
+ # h copied-centre temporary roles per invocation (24 at p = 12); 5h copy/erase episodes per replica (120 at p = 12)
+ coefficient=unit+J*high+J*(stock+h)+E*good+E*(128*N**3)+16*m**3+5*h*T+E+K+1
+ assert coefficient<2**80 and 2*m**3*10**16<2**80 and 0<K<2**40
+ # Internal borrowed rows are restored; the external complex row reserve is
+ # independently regenerated in portable_complex and bound by verify.py.
+ assert stock+h < 2**80
+ row_reserve=dict(internal_coefficient=d+1,halving_degree=1,
+     bound=str(d+1)+'*w*ceil(log2(n)) + inherited ordinary-leaf reserve',
+     restored=True,physical_stock_less_than_prime=True,external_complex_coefficient=20161)
+ assert row_reserve['internal_coefficient']==m*m+1
+ route=route_template(h);spec=importlib.util.spec_from_file_location('bankedfinite_moment',HERE/'moment.py');mod=importlib.util.module_from_spec(spec);spec.loader.exec_module(mod)
+ c=Q(mathematics['bit_coarse']);lo,hi=mod.moment(dict(literal),m,stock,c,True)
+ assert list(map(Q,mathematics['bit_moment_interval']))==[lo,hi]
+ delta_tau=1-hi;delta1=1-Q(mass,m*stock)-Q(1,10**16)*32*m*E/stock;assert delta_tau>0 and delta1>0
+ chain=[Q(384599,10**10)];gaps=[]
+ for j in range(3):
+  old=chain[-1];a=(1-c)*c+c*old;ds=dict(atom=c-a,borrowing=1-a-c,remainder=1-a-c*(1-old),stock=1-c);assert old<a<c<1-a and min(ds.values())>0
+  delta=min(ds.values());L=cutoff_log2(delta,coefficient);assert Q(L)*delta**2>=36 and Q(L)*delta>=2*(4+(coefficient-1).bit_length())
+  gaps.append(dict(stage=j+1,gaps={k:str(x)for k,x in ds.items()},minimum_gap=str(delta),cutoff_log2_at_charged_coefficient=str(L),full_cutoff_rule='Apply cutoff_log2(delta, C_full), where C_full bounds the displayed coefficient times every inherited primitive, wrapper and preceding ordinary-level constant.'));chain.append(a)
+ assert list(map(Q,mathematics['ordinary_bootstrap_chain']))==chain
+ controls=[]
+ for name,test in [('zero cutoff gap',lambda:cutoff_log2(Q(0),coefficient)),('negative constant',lambda:cutoff_log2(Q(1,2),0))]:
+  try:test()
+  except AssertionError:controls.append(name)
+  else:raise AssertionError('bad finitecutoff accepted')
+ expect('finite_coefficient',coefficient)
+ return dict(status='PASS_LITERAL_PARITY_FUSED_BANKED_FIVE_STAGE_P10_FINITE_BILL',theorem_pins=THEOREM_PINS,source_binding=dict(event=physical['scalar_projection_sha256'],tagged=physical['tagged_scalar_sha256'],global_program=global_result['program_sha256']),paid_inventory=dict(m=m,literal_stock=stock,physical_replicas=T,positive_rank_children=E,rank_mass=mass,weighted_additions=weighted,unit_expanded_additions=unit,bridge_additions=T*6*v,route_families=J,terminal_exchange_stream_movements=T*4*v,high_affine_factors=J*high,low_transposition_coefficient=J*(stock+h),generic_wrappers=E*good,matrix_preparation=E*128*N**3,copy_erase_episodes=5*h*T,fallback_per_child=32*m*m,extra_bank_selector_calls=K,normalizer_factor_bound=banks['normalizer_factor_bound'],simultaneous_extra_work_streams=1,payload_prefix_upper=payload,payload_prefix_bits=payloadbits),q_power_bound=dict(coefficient=coefficient,low_matrix_power=d,strict_upper='q^'+str(d+1)),rational_route=route,row_reserve=row_reserve,moment=dict(coarse=str(c),tau=str(1-c),delta_tau_lower=str(delta_tau),delta_linear=str(delta1),fallback_added_in_full=True),recurrence=dict(bound='A*(n+n^(1-c)*w^(1-a_j))',A='C*(1+1/delta_linear+1/delta_tau)',halving_degree=1,one_level_histogram=True),bootstrap=dict(chain=list(map(str,chain)),ordinary=str(chain[-1]),gaps=gaps),rejected_controls=controls,scope='Actual60replicas/literalbankstock andallfixedbanknormalizerschargedbefore finiteordinaryleaf absorption. Inheritedweightedcompiler,commonancestorchart,restoredrow,routing,prime,recoveryandanalyticinterfacesremainconditional.')
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/LICENSE b/research/five-stage-p10-transcript-stages/inputs/complex/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache 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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+      other commercial damages or losses), even if such Contributor
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+      To apply the Apache License to your work, attach the following
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+   Copyright [yyyy] [name of copyright owner]
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+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
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+
+   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
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diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/NOTICE b/research/five-stage-p10-transcript-stages/inputs/complex/NOTICE
new file mode 100644
index 0000000000..63aa295646
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/NOTICE
@@ -0,0 +1,290 @@
+Walsh-Hadamard power saving (wht-power-saving-lean)
+Copyright 2026 Jacob Sussman
+
+Repository: https://github.com/jacobalansussman/wht-power-saving-lean
+
+This repository is not a project of OpenAI. OpenAI did not write, review or
+endorse it. The package name "OAI" and the namespace "OAI.PowerSaving" are
+those of openai/math and are kept only because the new files extend that
+development.
+
+This repository is not a project of CrocSwap/integer-mult-bounds either. Its
+authors did not write, review or endorse it. Section 6 says what is taken
+from their repository.
+
+This repository contains files from, and files derived from, the repository
+"openai/math" (https://github.com/openai/math), family 130, "Exact Fourier
+transforms below n log n", at commit fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.
+That repository is published under the Apache License, Version 2.0. A copy of
+the licence is in the file LICENSE. The upstream repository has no NOTICE file
+and its licence text names no copyright holder; the files are attributed here
+to the authors of openai/math (OpenAI).
+
+1. Unmodified upstream files.
+   The 89 files under OAI/Computability/ are byte-for-byte copies of the files
+   with the same paths under lean/ in openai/math at the commit above. They
+   have not been changed. Modified copies of some of them are under
+   Work/Fourier/ and are listed in section 7.
+   One more file of openai/math is here unchanged, outside the Lean build:
+   third-party/openai-math/lean/ComparatorChallenges/UniformFourier.lean is a
+   byte-for-byte copy of lean/ComparatorChallenges/UniformFourier.lean at the
+   commit above (the statement of OpenAI's Fourier challenge). It is included
+   so that the modified copy named in section 2 can be compared with it.
+
+2. Files that contain upstream text.
+   - Work/CarrierCheck/ChallengeB2Ke16x.lean,
+     Work/CarrierCheck/ChallengeB2Ke16xR.lean,
+     Work/GCert/Data/ChallengeB2Gp193x.lean and the text template
+     tools/gen/templates/ChallengeB2L16x.lean.txt each contain, as their
+     lines 22-270, lines 9-257 of
+     lean/ComparatorChallenges/UniformFourier.lean of openai/math (the RAM cost
+     model), unchanged. Everything else in these files was written for this
+     repository.
+   - Work/Fourier/UniformFourierChallenge.lean is a modified copy of
+     lean/ComparatorChallenges/UniformFourier.lean of openai/math (the
+     statement of OpenAI's Fourier challenge, 336 lines). Changes: a comment
+     was added at the top; the exponent 1 - 1/(10^(13:ℕ)) was replaced by
+     1 - 7474546/(10^(10:ℕ)); seven names received the suffix "Z"
+     (decimalExponent, decimalTime, TimeBounds, DFTGoal, ConvGoal,
+     transform_main, convolution_main). Everything else in the file is the
+     upstream text, unchanged. See section 7.
+   - Work/Scratch/Engine.lean and Work/Block/Engine.lean contain copies of
+     proofs of openai/math, changed for this repository: sections 1, 2 and 5
+     of Work/Scratch/Engine.lean are upstream proofs with the batch layout
+     renamed, and both files contain a copy of the private upstream theorem
+     "hills_project" (lean/OAI/Computability/FourierTransform/
+     TensorProgram.lean) with its envelope generalised. The comments in the
+     two files mark these places.
+   - lakefile.lean is adapted from lean/lakefile.lean of openai/math: the same
+     package name, toolchain, package option and Mathlib pin; every other
+     dependency was removed and the libraries of this repository were added.
+     lean-toolchain is a byte-for-byte copy of lean/lean-toolchain.
+     lake-manifest.json lists Mathlib and its dependencies at the revisions of
+     lean/lake-manifest.json.
+   - RELATED-WORK.md reproduces the BibTeX entries of two manuscripts of
+     openai/math.
+
+3. New files that build on upstream proofs.
+   The other files under WHTCheck/ and Work/ were written for this
+   repository. They import the upstream files, and several of them generalise
+   or adapt proofs of upstream files (for example Work/Block/Recursion.lean,
+   which says so in its header). They are changes and additions made for this
+   repository and are not part of openai/math.
+
+4. How the new files were made.
+   Jacob Sussman made the new files on 2026-10-08 and 2026-10-09 by directing
+   a team of AI agents (Claude). The agents wrote the new Lean files, the
+   certificate data and the generator scripts. See README.md, section 4.
+
+5. Ideas taken from other public work.
+   The network of the first result uses ideas published by others, among them
+   the helper circuit "NStar3" (Swapnil-jain/integer-mult-kappa, which credits
+   CrocSwap pull request #36 and Paureel for parts of it), its transfer to
+   family 130 (shea256/fourier-transform-below-nlogn), and "carrier links" and
+   "whole-residual batching" (pull requests to CrocSwap/integer-mult-bounds).
+   No file of Swapnil-jain/integer-mult-kappa or of
+   shea256/fourier-transform-below-nlogn is included here. One comment in
+   Work/Scratch/Engine.lean quotes three counts reported in
+   Swapnil-jain/integer-mult-kappa and names that source. The general frame
+   lemma that Work/GFrame proves is stated in
+   notes/general-clifford-frames.tex of CrocSwap/integer-mult-bounds; its Lean
+   proof was written for this repository. The credits, with links, are in
+   RELATED-WORK.md.
+
+6. Data derived from CrocSwap/integer-mult-bounds (second result).
+   The helper circuit of the second result is the paired-cube circuit of the
+   repository "CrocSwap/integer-mult-bounds"
+   (https://github.com/CrocSwap/integer-mult-bounds), in the state of its pull
+   request #193. It is the design of that community: icekylinx (pull requests
+   #144 and #184), eumemic (#168, and #117 behind its modules), ikeboy /
+   Avi Eisenberg (#191 and #193), with an664 (#128) credited there for the
+   workspace-sharing principle. That repository is published under the Apache
+   License, Version 2.0 (the same licence text as the file LICENSE). Its
+   NOTICE file begins "A sharper exponent for integer multiplication /
+   Copyright 2026 Douglas Colkitt" and says that the community release "is
+   not solely Douglas Colkitt's work". A complete copy of that NOTICE file, as
+   it is at the head of pull request #193, is in
+   third-party/CrocSwap-integer-mult-bounds/NOTICE.
+
+   The data were taken from these files of that repository. They were loaded
+   as data by programs written for this repository; no program of that
+   repository was run, and none is included here.
+   - at the head of pull request #168 (eumemic),
+     4a3c769e5c5430e7114c4d3e099ff34664677f17:
+       references/paired-cube/sources/local_L1.json
+       references/paired-cube/sources/tmod_TE_TD_TB3_1_1_4_full_6.0617964e-4.json
+       references/paired-cube/sources/pmod_J0_full_6.0666810e-4.json
+       references/paired-cube/sources/qmod_climb3u_best.json
+       references/paired-cube/selected-module/matching-arcs.json
+       references/paired-cube/physical/frames.json
+   - at the head of pull request #193 (ikeboy),
+     187e1010ac8b259af8e9b5166f68b64bc27b4b47:
+       research/source-assisted-v4/data/physical-pairs.json
+
+   Files of this repository that contain data derived from them:
+   tools/certificate/gcert1-p11-pr193.json.gz and the Lean data modules
+   generated from it, Work/GCert/Data/Gen/P193*.lean and the files they import
+   from Work/GCert/Data/Gen/P193/; its block counts are also in the generated
+   modules Work/GCert/Data/P193Price.lean, RateB2Gp193.lean, RateB2Gp193x.lean
+   and InstB2Gp193.lean.
+   Changes made: the circuit was rebuilt from those data as one explicit,
+   renumbered list of additions with a table of frames, in the certificate
+   format "gcert/1" of this repository; its 1,980 in-place steps were written
+   as pairs of additions with rescaled coefficients; the Lean data modules
+   were generated from that list. No file of that repository is included
+   unchanged, except the copy of its NOTICE file named above.
+
+   Notices of that NOTICE file that pertain to these data, quoted:
+
+     Paired-cube and shared-core extension, 9 October 2026
+     Copyright 2026 icekylinx
+
+     Source-assisted common-frame extension (2026-10-09)
+     Copyright 2026 icekylinx. Apache-2.0.
+     Substantial dependency: eumemic PR168,
+     fd25adb7fbaa12ee761d02c733c54d1d2a7687ee
+
+   The full text of both notices, and the notices of the work they build on,
+   are in the copy named above. The credits, with links and with the words of
+   pull request #193 about its own sources, are in README.md ("Whose circuit
+   this is") and in RELATED-WORK.md, section 1.
+
+7. Modified copies of upstream files (third result).
+   The files listed below are copies of files of openai/math at the commit
+   above, changed for this repository. Each begins with a comment that names
+   the upstream file it is derived from and states what was changed. The
+   upstream originals under lean/OAI/Computability/ are in this repository
+   as well, unchanged (section 1), and the copies import them. The upstream
+   challenge file lean/ComparatorChallenges/UniformFourier.lean is in this
+   repository in both forms: unchanged under third-party/openai-math/
+   (section 1) and modified (section 2).
+
+   - Work/Fourier/ArbitraryLength.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/ArbitraryLength.lean (224
+     lines; 159 of them unchanged in the copy). Changes: identifiers renamed
+     on 64 lines (18 names: 15 with the suffix Z, 3 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/Asymptotics.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/Asymptotics.lean (187 lines;
+     112 of them unchanged in the copy). Changes: identifiers renamed on 74
+     lines (32 names: 26 with the suffix Z, 6 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+   - Work/Fourier/Axioms.lean: written for this repository (not a copy of an
+     upstream file).
+   - Work/Fourier/ConvolutionProgram.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/ConvolutionProgram.lean (100
+     lines; 77 of them unchanged in the copy). Changes: identifiers renamed
+     on 22 lines (10 names: 9 with the suffix Z, 1 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/Goal.lean: written for this repository; contains lines of
+     upstream files: of its 7 code lines, 6 are lines of
+     lean/OAI/Computability/FourierTransform/Goal.lean (original lines 35,
+     75-77, 79, 81): unchanged: its lines 25; with identifiers renamed: its
+     lines 21, 24, 26, 28, 30.
+   - Work/Fourier/Main.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/Main.lean (151 lines; 90 of
+     them unchanged in the copy). Changes: identifiers renamed on 59 lines
+     (40 names: 35 with the suffix Z, 5 with Z inserted); 1 import line
+     replaced by 2; 24 comment lines added; other code lines changed: 1 of
+     the original, 1 of the copy (copy line 59).
+   - Work/Fourier/Seam.lean: written for this repository; contains lines of
+     upstream files: of its 122 code lines, 15 are lines of
+     lean/OAI/Computability/FourierTransform/TensorProgram.lean (original
+     lines 36-37, 95-96): unchanged: its lines 93-94, 113-114, 141-142,
+     163-164, 185-187, 194-196; with identifiers renamed: its lines 184; 3
+     are lines of lean/OAI/Computability/FourierTransform/TensorSaving.lean
+     (original lines 83-84, 114): with identifiers renamed: its lines 45-46,
+     59; 1 is a line of lean/OAI/Computability/FourierTransform/Main.lean
+     (original line 60): with identifiers renamed: its lines 213.
+   - Work/Fourier/SectorAlgorithm.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/SectorAlgorithm.lean (224
+     lines; 162 of them unchanged in the copy). Changes: identifiers renamed
+     on 61 lines (17 names: 13 with the suffix Z, 4 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/SynchronizedAlgorithm.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/SynchronizedAlgorithm.lean (126
+     lines; 94 of them unchanged in the copy). Changes: identifiers renamed
+     on 31 lines (12 names: 10 with the suffix Z, 1 with Z inserted, 1
+     other), the other being "canopy" to "Grove.canopy" (5 lines); 1 import
+     line replaced by 1; 16 comment lines added; no other change to the
+     code.
+   - Work/Fourier/TransformProgram.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/TransformProgram.lean (146
+     lines; 94 of them unchanged in the copy). Changes: identifiers renamed
+     on 51 lines (21 names: 19 with the suffix Z, 2 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/UniformBounds.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/UniformBounds.lean (183 lines;
+     115 of them unchanged in the copy). Changes: identifiers renamed on 67
+     lines (29 names: 25 with the suffix Z, 4 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+   - Work/Fourier/UniformFourierChallenge.lean: modified copy of
+     lean/ComparatorChallenges/UniformFourier.lean (336 lines; 328 of them
+     unchanged in the copy). Changes: identifiers renamed on 7 lines (7
+     names: 7 with the suffix Z); 12 comment lines added; other code lines
+     changed: 1 of the original, 1 of the copy (copy line 281).
+   - Work/Fourier/WorkingCompiler.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingCompiler.lean (153
+     lines; 104 of them unchanged in the copy). Changes: identifiers renamed
+     on 48 lines (14 names: 14 with the suffix Z); 1 import line replaced by
+     1; 15 comment lines added; no other change to the code.
+   - Work/Fourier/WorkingPreparation.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingPreparation.lean (212
+     lines; 156 of them unchanged in the copy). Changes: identifiers renamed
+     on 55 lines (30 names: 28 with the suffix Z, 2 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/WorkingTransform.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingTransform.lean (119
+     lines; 91 of them unchanged in the copy). Changes: identifiers renamed
+     on 27 lines (9 names: 8 with the suffix Z, 1 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+
+   Changes made to the eleven copied proof files: every declaration received
+   the letter "Z" in its name (as a suffix of its own name, or of the name
+   of the declaration it belongs to), so that it does not collide with the
+   upstream declaration of the same name; the upstream exponent "alpha"
+   (1 - 2/10^11) and the bound "hills" defined from it were replaced by
+   "alphaZ" (1 - 7474547/10^10) and "hillsZ", which are defined in
+   Work/Fourier/Seam.lean, and the single use of the upstream theorem
+   "hills_program" by "hillsZ_program"; the five definitions of the upstream
+   statement that contain its exponent (decimalExponent, decimalTime,
+   TimeBounds, DFTGoal, ConvGoal) were replaced by the versions of
+   Work/Fourier/Goal.lean, whose exponent is 1 - 7474546/(10^(10:ℕ));
+   the import lines point to the copies; a header comment was added.
+      Two further changes: in the copy of Main.lean the same constant stands
+   once as the literal 2/10^11 and was replaced there too, and the two
+   final theorems of that copy received a documentation comment; in the
+   copy of SynchronizedAlgorithm.lean the name "canopy" was written out as
+   "Grove.canopy" in 5 places, because the short name is shadowed in the
+   larger environment of the copy. The script also renamed three names
+   inside upstream comments; the comments are otherwise the upstream ones
+   and describe the upstream network.
+   The proofs are those of openai/math. The copies were made by the script
+   tools/fourier/mkchain.py of this repository.
+
+   Work/Fourier/Goal.lean contains copies of those five definitions of
+   lean/OAI/Computability/FourierTransform/Goal.lean, with the exponent
+   replaced and the suffix "Z" on the five names.
+
+   Work/Fourier/Seam.lean was written for this repository. It repeats the
+   statement of the upstream theorem "hills_program" (TensorProgram.lean) and
+   the definition of "hills" (TensorSaving.lean) with the two names replaced;
+   its header says so.
+
+   The work of others that the third result follows (danadran01, shea256,
+   eumemic) is credited in README.md ("Whose reduction this is") and in
+   RELATED-WORK.md, section 1. No file of their repositories is included
+   here.
+
+Not included in this repository and fetched by the build: Mathlib
+(https://github.com/leanprover-community/mathlib4, Apache License 2.0) and its
+dependencies. The comparator (https://github.com/leanprover/comparator) is a
+separate tool and is not included.
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/NOTICE-PR304 b/research/five-stage-p10-transcript-stages/inputs/complex/NOTICE-PR304
new file mode 100644
index 0000000000..a770422c6f
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/NOTICE-PR304
@@ -0,0 +1,61 @@
+Prepared by DreamingOfClouds with Anthropic Claude assistance. Apache-2.0.
+Inherited files retain their original notices and assistance disclosures.
+This package claims no exclusive priority over concurrent work and reports
+no new kappa.
+
+What this package contributes: the three re-annealed query modules of the
+source-assisted complex word (modules/: pair module n = 10, all-but-one
+module n = 9, disjoint-triple module p = 11, found by simulated annealing
+from PR168 v4's modules against the exact compile ledger of the aligned
+word), one frozen compilation recipe applied to them and, as the control, to
+PR168 v4's own modules (layers/), aligned_word.py (PR194's source-aligned
+word with the module files and a frozen physical layer as inputs),
+paircheck.py (an independent re-check of the reuse pairs with five mutation
+controls), normalize_scatter.py (the star scatter by re-signing the
+registers of retained totals with unit -1), the discovery driver
+discovery/make_layer.py, and the four resulting programs with their checks.
+Everything else is retained and credited:
+
+- icekylinx (OpenAI GPT-6 Astra and Codex assistance): PR144 paired cubes
+  and signed decoder (the K blocks and the star scatter of every program),
+  PR184 source-assisted construction: source-parity local factorization,
+  frame flow, exact lifts, contract (complex_frame_flow.py,
+  exact_complex_flow_lift.py, and source_aligned_local.py, from which
+  aligned_word.py derives through PR194).
+- Avi Eisenberg (ikeboy): PR191/193/194, the rebuild of PR184's
+  construction on the PR168 v4 modules (source_aligned_local_v4.py, whose
+  code aligned_word.py keeps, contract_v4.py run here), the
+  parity-erasure-avoiding pairing of PR193 (the "parity" pair recipe) and
+  PR194's frozen pairs of the anchor.
+- chafreaky / Chafik Boukhalfa (Anthropic Claude and OpenAI Codex
+  assistance): PR200 operation-frame descent (the frames of every layer),
+  maximum-weight late compensated reuse pairing (the "mw" pair recipe) and
+  the complete complex checker complex/physical.py (run here to admit every
+  layer); PR233 layer and package (vendored in references/pr233-layer/, its
+  discovery harness vendored in discovery/pr233/); PR256 gcert emitter
+  (gcert_emit.py, vendored unchanged) and the package whose structure and
+  checks this one mirrors; PR225 exact moment bounds (scripts/moment.py).
+- Jacob Sussman (Anthropic Claude assistance): the certificate format
+  gcert/1, the reference checker gx.py and the Python mirror of the two
+  Lean checks gxcore.py (both vendored unchanged in gx/, Apache-2.0,
+  Copyright 2026 Jacob Sussman, jacobalansussman/wht-power-saving-lean at
+  f010392c), the bridged five-stage layout (Lean-checked in his repository)
+  in which the programs are priced, the unit convention of gxconv.py reused
+  by gcert_emit.py for scalings (and by normalize_scatter.py), and the
+  published certificate of #193 whose histogram anchors the chain
+  (references/sussman/).
+- eumemic (Anthropic Claude and OpenAI Codex assistance): PR168 annealed
+  modules (the control's modules and the starting points of the annealing),
+  schedules and physical frames; PR117/155/157/161 module infrastructure,
+  physical frames and reuse; the exact-DFT arena (scripts/moment.py adapts
+  eumemic/exact-dft-bounds, Apache-2.0).
+- DaysSky: PR162 extended carrier closure (compile_closure, and the greedy
+  extension in discovery/extend_floor.py).
+- hcg890 (PR234), SovereignSteak (PR250: the five-stage ledger statement
+  used for the price), rohanarun (PR209/237).
+- PR202 baseline lineage as credited in references/pr233-layer/NOTICE:
+  jamesyc / James Chang, DaysSky, GamingPuzzled, gupt1156, Abhinav
+  Ramachandran/geckods, jacklightChen / Zhihao Chen, Rohan Arun, an664,
+  Swapnil Jain, hpst3r, Aurel Prosz, dleen, Douglas Colkitt.
+- OpenAI: the original complex phase network of "Integer multiplication
+  below n log n".
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/NOTICE b/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/NOTICE
new file mode 100644
index 0000000000..af71ab694b
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/NOTICE
@@ -0,0 +1,40 @@
+Provenance of inputs/complex/gcert1-p11-cmod-centre-mw-flow.json.gz (local research, not published)
+
+Prepared by DreamingOfClouds with Anthropic Claude assistance. Apache-2.0. No exclusive priority is claimed.
+
+The program is the source-assisted complex word of PR #184/#194, built with PR #304's recipe on three query
+modules, all shipped here:
+
+  pmod46_ptc1_final.json   centre-sharing pair module (new): besides its 45 pair outputs it returns one extra
+                           root, the sum of all its inputs, which is the star centre S(2i+bit)
+  tmod_final.json          disjoint-triple module (p = 11): an earlier re-annealed version (v1, 2,069 additions),
+                           NOT PR #304's modules/tmod_cmod_v2.json (2,067 additions)
+  qmod_q1_snap1.json       all-but-one module: the same args and roots as PR #304's modules/qmod_cmod.json
+
+How it was built. PR #304's aligned_word.py cannot build this graph unchanged: its pair-module loader expects 45
+roots, and PR #144's Graph.finish sums every centre separately. The program was built by a local loader
+(agent-cmod's cmgraph.build46 / exact_chain.py, not shipped). It loads the 46-root pair module and runs PR #144's
+scripts/paired_cube/graph.py with the 10-line Graph.finish patch centre46_graph.diff (icekylinx, Apache-2.0;
+graph.py itself is not vendored here). When a pair module returns more roots than pairs, the patched graph uses
+the extra root as the centre instead of summing it separately; with any other module it is unchanged. The rest
+of the recipe is PR #304's:
+
+- the merge f8:00111100 and coordinate frames;
+- PR #233's maximum-weight late compensated reuse pairing;
+- PR #184's frame flow and exact lift;
+- PR #256's gcert_emit.py (credits in ../NOTICE-PR304).
+
+A separate local audit rebuilt the graph from this patch and these modules and reproduced the program's graph
+exactly.
+
+exact_result.json is the exact chain's record: flow R = 9,036 and W = 4v + R = 14,316 at m = 110, gx.check1
+ACCEPTED, and the five-stage saving 7727/10^7 certified with 7728/10^7 rejected (priced without the 10^-16
+fallback). The emitter wrote the scatter as the star rule directly (every retained-total unit is +1), so no
+normalize_scatter.py step was needed. The gzip file is gzip.compress(gcert1.json, compresslevel=9, mtime=0) of
+the emitted bytes. Its JSON keys are not in canonical (sorted) order, and it records derived_from
+'agent-cmod candidate'. The bytes are kept as emitted, because a separate Lean run checks exactly these bytes.
+
+verify.py consumes only the gcert/1 program. Every run checks it fresh with Jacob Sussman's gx.check1 (exact
+scalar identity) and gxcore mirror (code/complex_gx.py), and prices it with the 10^-16 fallback included
+(772714351296671/10^18; without the fallback, 772714354722691/10^18). The files in this directory are not read
+by any check. No Lean check of this program is pinned in this package.
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/centre46_graph.diff b/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/centre46_graph.diff
new file mode 100644
index 0000000000..76437ab856
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/centre46_graph.diff
@@ -0,0 +1,33 @@
+--- graph_orig.py	2026-10-10 03:55:31
++++ graph.py	2026-10-10 03:55:31
+@@ -190,14 +190,18 @@
+         self.local_channels()
+         base_nodes = len(self.a)
+         D = dict(zip(self.cubes, self.module(triple, [self.F[I] for I in self.cubes])))
+-        P, Q = {}, {}
++        P, Q, star = {}, {}, {}
+         for i in range(self.p):
+             others = [a for a in range(self.p) if a != i]
+             pairs = list(combinations(others, 2))
+             for bit in range(2):
+                 inputs = [self.A[tuple(sorted((i, *K))), i, bit] for K in pairs]
+-                for K, node in zip(pairs, self.module(pair, inputs)):
++                outs = self.module(pair, inputs)
++                for K, node in zip(pairs, outs[:len(pairs)]):
+                     P[tuple(sorted((i, *K))), i, bit] = node
++                if len(outs) > len(pairs):
++                    # centre-sharing pair module: its extra root is the sum of all inputs = star(2i+bit)
++                    star[i, bit] = outs[len(pairs)]
+         for i, j in combinations(range(self.p), 2):
+             others = [a for a in range(self.p) if a not in (i, j)]
+             for mode in range(2):
+@@ -231,7 +235,8 @@
+             # Their scatter is 1/2 sum_(i in T) S_i - 1/6 sum_i S_i.
+             for i in range(self.p):
+                 for e in range(2):
+-                    self.centers.append(self.sum(self.A[I, i, e] for I in self.cubes if i in I))
++                    self.centers.append(star[i, e] if (i, e) in star else
++                                        self.sum(self.A[I, i, e] for I in self.cubes if i in I))
+             incidences = 0
+             center_scatter = '1/2 sum_(i in T) S_i - 1/6 sum_i S_i'
+         else:
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/exact_result.json b/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/exact_result.json
new file mode 100644
index 0000000000..0380737113
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/exact_result.json
@@ -0,0 +1,21 @@
+{
+ "R": 9036,
+ "N": 254672,
+ "W5": 14316,
+ "m5": 110,
+ "gx_check1": "ACCEPTED",
+ "scalar_denominators": {
+  "x": 2,
+  "y": 6,
+  "s": 2
+ },
+ "blocks_total": 68252,
+ "float_root5": 0.0007727143547226677,
+ "flow_root3": 0.0007272300987099986,
+ "lift_status": "Exact rational local lifts and inverse gate programs verified; monotone flow and zero-fresh kernel reuse DAG verified.",
+ "seconds": 206.82464708399493,
+ "margin_at_7727": 0.0005207623638446622,
+ "margin_at_7728": -0.0031071001379776387,
+ "certified_a": "7727/10^7",
+ "next_rejected": true
+}
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/pmod46_ptc1_final.json b/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/pmod46_ptc1_final.json
new file mode 100644
index 0000000000..ca39e45e46
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/pmod46_ptc1_final.json
@@ -0,0 +1 @@
+{"input_count": 45, "args": [null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, [33, 34], [18, 45], [24, 46], [24, 32], [4, 12], [2, 10], [28, 50], [24, 51], [25, 52], [33, 37], [34, 38], [54, 55], [8, 16], [15, 57], [7, 58], [56, 59], [0, 49], [60, 61], [53, 62], [27, 29], [44, 64], [63, 65], [6, 14], [32, 36], [42, 68], [67, 69], [3, 30], [11, 71], [70, 72], [43, 73], [66, 74], [5, 13], [31, 76], [26, 77], [29, 35], [78, 79], [61, 71], [60, 81], [44, 82], [40, 41], [11, 84], [83, 85], [80, 86], [22, 28], [7, 15], [88, 89], [7, 8], [1, 91], [2, 92], [26, 39], [20, 21], [17, 22], [23, 96], [28, 29], [27, 98], [44, 99], [97, 100], [95, 101], [94, 102], [5, 6], [42, 43], [84, 105], [104, 106], [103, 107], [93, 108], [30, 68], [35, 110], [12, 13], [31, 35], [44, 98], [23, 114], [13, 14], [15, 116], [39, 104], [31, 118], [116, 119], [3, 11], [61, 121], [120, 122], [111, 123], [33, 42], [40, 125], [89, 126], [124, 127], [1, 9], [18, 20], [19, 130], [21, 131], [129, 132], [22, 37], [133, 134], [128, 135], [31, 48], [24, 25], [39, 111], [31, 139], [131, 140], [17, 27], [21, 142], [141, 143], [138, 144], [26, 28], [126, 134], [146, 147], [145, 148], [10, 12], [11, 150], [149, 151], [23, 29], [41, 153], [43, 55], [26, 145], [155, 156], [154, 157], [9, 117], [152, 159], [55, 130], [8, 154], [161, 162], [38, 54], [44, 106], [34, 165], [164, 166], [22, 115], [54, 90], [70, 169], [18, 19], [30, 122], [24, 172], [25, 173], [9, 10], [17, 175], [1, 176], [2, 177], [174, 178], [171, 179], [43, 57], [41, 181], [7, 50], [25, 37], [38, 184], [12, 185], [4, 186], [183, 187], [0, 2], [1, 189], [176, 190], [89, 191], [168, 192], [26, 27], [138, 194], [47, 121], [20, 40], [26, 197], [115, 198], [41, 198], [14, 15], [41, 199], [19, 190], [124, 132], [95, 203], [6, 93], [30, 138], [171, 207], [54, 208], [55, 209], [21, 101], [105, 211], [210, 212], [68, 213], [3, 4], [214, 215], [206, 216], [175, 205], [14, 118], [13, 219], [95, 220], [191, 194], [221, 222], [154, 181], [223, 224], [21, 27], [180, 226], [170, 227], [194, 221], [90, 191], [229, 230], [91, 104], [31, 195], [139, 167], [98, 234], [233, 235], [215, 218], [236, 237], [18, 238], [232, 239], [22, 23], [1, 241], [132, 140], [167, 243], [242, 244], [153, 155], [36, 246], [180, 247], [95, 219], [0, 44], [129, 241], [19, 251], [130, 252], [57, 193], [19, 187], [254, 255], [113, 202], [53, 87], [15, 16], [116, 259], [105, 260], [193, 196], [41, 103], [96, 210], [257, 264], [16, 19], [94, 99], [35, 77], [86, 268], [67, 226], [57, 270], [32, 248], [271, 272], [107, 267], [58, 250], [116, 275], [274, 276], [45, 275], [9, 151], [16, 279], [36, 280], [32, 281], [178, 194], [138, 283], [55, 182], [204, 284], [2, 215], [5, 287], [265, 288], [13, 259], [215, 232], [92, 289], [11, 260], [12, 293], [97, 294], [50, 116], [24, 296], [32, 121], [31, 298], [297, 299], [54, 180], [168, 301], [55, 302], [167, 241], [156, 304], [35, 36], [19, 306], [4, 307], [38, 308], [98, 305], [59, 303], [2, 3], [236, 293], [40, 261], [306, 314], [188, 306], [200, 254], [76, 317], [240, 295], [6, 7], [1, 288], [320, 321], [175, 263], [265, 290], [149, 322], [59, 250], [251, 326], [105, 270], [32, 271], [277, 316], [6, 321], [278, 300], [7, 332], [274, 333], [35, 78], [179, 335], [120, 298], [95, 337], [25, 49], [307, 339], [37, 340], [40, 231], [42, 342], [232, 236], [287, 344], [341, 343], [46, 137], [108, 347], [50, 195], [110, 349], [123, 285], [79, 351], [350, 352], [92, 312], [348, 354], [106, 327], [106, 229], [255, 318], [124, 133], [285, 359], [163, 336], [109, 184], [254, 357], [266, 361], [309, 362], [23, 360], [150, 313], [35, 358], [241, 244], [294, 369], [9, 370], [18, 338], [45, 356], [372, 373], [18, 299], [40, 347], [249, 356], [44, 62], [74, 378], [18, 252], [379, 380], [213, 282], [21, 381], [201, 382], [24, 375], [112, 377], [51, 195], [37, 309], [37, 128], [387, 389], [386, 388], [169, 180], [223, 340], [224, 393], [116, 280], [162, 331], [157, 396], [197, 335], [196, 317], [256, 328], [38, 394], [158, 395], [12, 315], [392, 398], [77, 399], [36, 400], [261, 323], [11, 407], [60, 165], [124, 409], [376, 408], [24, 34], [225, 412], [279, 324], [375, 413], [253, 269], [245, 291], [262, 329], [105, 418], [231, 385], [126, 420], [19, 403], [185, 422], [323, 423]], "roots": [310, 367, 371, 424, 411, 384, 414, 402, 160, 345, 417, 365, 355, 217, 292, 397, 325, 410, 330, 334, 75, 258, 353, 390, 391, 374, 383, 416, 366, 136, 363, 406, 368, 401, 346, 419, 405, 415, 421, 311, 273, 228, 364, 404, 286, 319]}
\ No newline at end of file
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/qmod_q1_snap1.json b/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/qmod_q1_snap1.json
new file mode 100644
index 0000000000..78965fba83
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/qmod_q1_snap1.json
@@ -0,0 +1 @@
+{"input_count": 9, "args": [null, null, null, null, null, null, null, null, null, [0, 3], [6, 9], [5, 7], [8, 11], [2, 4], [12, 13], [6, 14], [6, 8], [3, 16], [7, 17], [0, 1], [2, 19], [18, 20], [3, 20], [4, 22], [5, 23], [6, 24], [7, 25], [16, 24], [12, 23], [4, 21], [11, 17], [20, 30], [15, 19], [1, 30], [4, 33], [0, 34], [10, 14], [13, 33]], "roots": [37, 36, 35, 32, 31, 29, 28, 27, 26]}
\ No newline at end of file
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/tmod_final.json b/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/tmod_final.json
new file mode 100644
index 0000000000..3d4f3ccb44
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/centre-mw/tmod_final.json
@@ -0,0 +1 @@
+{"kind": "disjoint_triples", "p": 11, "input_labels": [[0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 1, 5], [0, 1, 6], [0, 1, 7], [0, 1, 8], [0, 1, 9], [0, 1, 10], [0, 2, 3], [0, 2, 4], [0, 2, 5], [0, 2, 6], [0, 2, 7], [0, 2, 8], [0, 2, 9], [0, 2, 10], [0, 3, 4], [0, 3, 5], [0, 3, 6], [0, 3, 7], [0, 3, 8], [0, 3, 9], [0, 3, 10], [0, 4, 5], [0, 4, 6], [0, 4, 7], [0, 4, 8], [0, 4, 9], [0, 4, 10], [0, 5, 6], [0, 5, 7], [0, 5, 8], [0, 5, 9], [0, 5, 10], [0, 6, 7], [0, 6, 8], [0, 6, 9], [0, 6, 10], [0, 7, 8], [0, 7, 9], [0, 7, 10], [0, 8, 9], [0, 8, 10], [0, 9, 10], [1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 7], [1, 2, 8], [1, 2, 9], [1, 2, 10], [1, 3, 4], [1, 3, 5], [1, 3, 6], [1, 3, 7], [1, 3, 8], [1, 3, 9], [1, 3, 10], [1, 4, 5], [1, 4, 6], [1, 4, 7], [1, 4, 8], [1, 4, 9], [1, 4, 10], [1, 5, 6], [1, 5, 7], [1, 5, 8], [1, 5, 9], [1, 5, 10], [1, 6, 7], [1, 6, 8], [1, 6, 9], [1, 6, 10], [1, 7, 8], [1, 7, 9], [1, 7, 10], [1, 8, 9], [1, 8, 10], [1, 9, 10], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 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[1312, 1416], [387, 1010], [752, 1418], [1417, 1419], [1411, 1420], [538, 1351], [338, 408], [33, 147], [118, 1424], [31, 1304], [1425, 1426], [97, 1427], [787, 1428], [157, 377], [1115, 1289], [130, 989], [1431, 1432], [45, 81], [836, 1239], [1434, 1435], [1433, 1436], [237, 1437], [223, 226], [734, 1327], [1439, 1440], [428, 1441], [124, 578], [613, 862], [49, 941], [301, 1116], [1126, 1446], [1445, 1447], [73, 156], [208, 1449], [436, 1450], [222, 1442], [729, 903], [176, 1310], [735, 1454], [1453, 1455], [56, 754], [1040, 1457], [169, 1458], [908, 1247], [563, 912], [1245, 1336], [126, 336], [810, 1156], [1463, 1464], [191, 1465], [564, 1466], [1024, 1047], [44, 1468], [1223, 1456], [870, 1444], [138, 141], [11, 905], [114, 145], [93, 1474], [849, 943], [1110, 1476], [542, 1477], [84, 1478], [49, 1479], [1095, 1480], [73, 1312], [397, 399], [7, 1483], [933, 1484], [37, 1485], [1482, 1486], [637, 1441], [317, 1488], [914, 1489], [1472, 1490], [1423, 1459], [98, 119], [155, 1493], [1306, 1494], [1194, 1495], [146, 1219], [87, 1384], [1323, 1467], [109, 990], [1446, 1500], [187, 1501], [1491, 1502], [55, 68], [164, 657], [461, 1505], [527, 1506], [175, 1225], [113, 1508], [28, 1310], [1509, 1510], [1042, 1047], [44, 896], [825, 841], [165, 1514], [1513, 1515], [1512, 1516], [144, 237], [1517, 1518], [1511, 1519], [1300, 1520], [1393, 1394], [438, 1522], [18, 999], [19, 1524], [1523, 1525], [830, 1526], [1380, 1527], [836, 1528], [241, 1529], [112, 225], [58, 1040], [129, 1236], [1229, 1256], [1231, 1534], [96, 1037], [1254, 1536], [12, 1537], [131, 712], [10, 86], [206, 869], [29, 1472], [114, 1542], [55, 726], [1017, 1544], [579, 1065], [717, 1539], [1134, 1547], [553, 1548], [869, 1549], [55, 694], [441, 1130], [682, 1064], [1184, 1553], [379, 1349], [910, 1545], [592, 1124], [54, 634], [62, 1558], [1389, 1487], [493, 1471], [454, 1561], [81, 1355], [466, 1563], [1102, 1560], [500, 1562], [599, 752], [441, 1567], [75, 1169], [80, 1569], [1565, 1570], [78, 1088], [1564, 1572], [289, 935], [704, 1574], [343, 844], [364, 1576], [8, 1577], [31, 1056], [148, 949], [1579, 1580], [1359, 1361], [1566, 1582], [410, 1569], [649, 1418], [586, 1584], [79, 281], [206, 422], [73, 788], [1588, 1589], [276, 1590], [1587, 1591], [341, 1592], [1568, 1585], [767, 1427], [8, 1108], [1295, 1532], [7, 933], [22, 1598], [974, 1599], [1597, 1600], [44, 1601], [528, 563], [580, 895], [1603, 1604], [1602, 1605], [194, 1188], [240, 1607], [729, 736], [1543, 1609], [143, 1610], [1191, 1611], [223, 777], [718, 1539], [988, 1614], [215, 1615], [146, 147], [90, 455], [95, 1618], [1132, 1619], [477, 945], [1374, 1451], [1242, 1382], [157, 1596], [8, 1113], [1401, 1625], [481, 1626], [640, 1627], [776, 1628], [989, 1177], [898, 1630], [28, 137], [858, 1632], [113, 216], [1633, 1634], [62, 634], [3, 1636], [54, 1637], [1635, 1638], [64, 1639], [1588, 1640], [803, 1641], [825, 1631], [633, 1627], [494, 1398], [139, 1612], [1608, 1646], [711, 1219], [150, 891], [1617, 1649], [1648, 1650], [215, 1651], [908, 1535], [1228, 1653], [1302, 1654], [115, 1655], [532, 618], [1101, 1487], [38, 684], [1141, 1261], [200, 915], [355, 1661], [366, 1662], [1660, 1663], [865, 1210], [848, 1665], [625, 759], [1036, 1262], [576, 1668], [1667, 1669], [38, 844], [105, 157], [41, 354], [1672, 1673], [688, 1674], [1671, 1675], [1496, 1676], [33, 1221], [1309, 1634], [980, 1679], [1268, 1680], [1297, 1681], [1182, 1682], [221, 225], [551, 1684], [27, 731], [494, 1686], [1685, 1687], [398, 1012], [450, 556], [1689, 1690], [316, 1645], [495, 1692], [1081, 1693], [726, 1152], [1694, 1695], [845, 1278], [34, 1691], [43, 1698], [535, 1699], [1388, 1700], [881, 1052], [920, 1697], [328, 1696], [331, 1658], [1022, 1081], [1692, 1706], [28, 438], [1703, 1708], [574, 1558], [1688, 1710], [1116, 1177], [1702, 1712], [154, 804], [87, 542], [55, 1153], [1429, 1716], [1714, 1717], [15, 1485], [44, 1719], [206, 801], [1009, 1657], [701, 1260], [500, 1105], [195, 818], [26, 1224], [81, 1162], [991, 1706], [1727, 1728], [75, 1729], [419, 1722], [271, 281], [190, 1504], [1153, 1308], [1733, 1734], [1724, 1735], [545, 876], [873, 899], [1556, 1738], [18, 727], [171, 1223], [1740, 1741], [1328, 1742], [1431, 1743], [862, 1737], [1028, 1745], [616, 1731], [842, 1557], [292, 1748], [909, 1749], [1526, 1750], [178, 1473], [1286, 1619], [1391, 1753], [1013, 1754], [426, 496], [433, 873], [1081, 1756], [493, 496], [1488, 1694], [809, 1097], [815, 1761], [84, 1762], [107, 848], [51, 1764], [86, 1765], [1478, 1766], [956, 1767], [519, 1219], [69, 150], [1769, 1770], [1272, 1771], [648, 1772], [50, 1768], [85, 1715], [86, 1775], [1763, 1776], [1636, 1760], [731, 1778], [510, 1581], [52, 1448], [1706, 1781], [98, 1782], [146, 1214], [1783, 1784], [519, 1497], [138, 143], [330, 1158], [112, 1205], [1475, 1789], [1676, 1790], [280, 885], [1109, 1792], [281, 591], [1362, 1794], [279, 1795], [407, 1796], [747, 1797], [985, 1746], [592, 1799], [655, 1800], [1076, 1786], [1744, 1752], [92, 1803], [1121, 1804], [1430, 1802], [67, 711], [1806, 1807], [54, 974], [6, 439], [21, 1810], [1809, 1811], [1080, 1812], [528, 1506], [1461, 1814], [42, 1815], [1813, 1816], [22, 122], [128, 1818], [1788, 1819], [719, 746], [1262, 1664], [1040, 1156], [1024, 1823], [756, 903], [1082, 1825], [669, 1826], [517, 785], [277, 1828], [1592, 1829], [664, 1616], [844, 1659], [128, 341], [1832, 1833], [281, 1834], [767, 1835], [90, 92], [994, 1830], [1365, 1549], [279, 1264], [1732, 1840], [71, 1841], [1447, 1498], [86, 1843], [1192, 1844], [521, 1058], [1147, 1839], [1296, 1842], [1374, 1847], [34, 153], [261, 1850], [148, 1851], [137, 983], [79, 645], [801, 1541], [159, 1855], [373, 1856], [1854, 1857], [1853, 1858], [371, 627], [1337, 1860], [1288, 1861], [639, 1862], [391, 962], [1552, 1864], [1077, 1865], [277, 1852], [1332, 1341], [27, 1685], [1458, 1866], [578, 1870], [1603, 1871], [1240, 1872], [1506, 1873], [532, 1824], [5, 1350], [1875, 1876], [911, 1877], [1240, 1603], [1123, 1879], [1878, 1880], [41, 1822], [1298, 1882], [112, 224], [170, 1884], [979, 1885], [27, 1886], [1883, 1887], [455, 1881], [55, 725], [340, 1355], [866, 1891], [177, 1437], [1290, 1893], [1, 1369], [1892, 1895], [21, 22], [1198, 1246], [1894, 1898], [153, 1197], [95, 1900], [1757, 1758], [681, 1090], [238, 641], [1438, 1904], [113, 1633], [1743, 1905], [179, 1837], [82, 1908], [542, 1540], [84, 1910], [848, 1911], [1215, 1846], [904, 1299], [1223, 1284], [837, 1915], [1909, 1916], [1868, 1917], [62, 739], [1376, 1919], [159, 185], [1914, 1920], [868, 1384], [1466, 1715], [32, 1882], [1923, 1924], [92, 1377], [247, 251], [581, 1533], [1705, 1824], [1507, 1929], [1073, 1931], [1535, 1913], [1538, 1933], [1046, 1930], [912, 1606], [1029, 1932], [661, 1364], [871, 1938], [1578, 1587], [1833, 1940], [805, 1941], [308, 480], [371, 1943], [441, 1864], [1159, 1619], [591, 1946], [967, 1947], [1945, 1948], [1944, 1949], [295, 415], [1555, 1921], [104, 1073], [618, 1951], [1542, 1791], [1774, 1953], [15, 879], [889, 1468], [1957, 1958], [1137, 1954], [848, 1959], [893, 1877], [1532, 1767], [1295, 1963], [1322, 1964], [862, 1480], [1962, 1966], [1360, 1700], [541, 1967], [371, 1947], [1745, 1961], [1700, 1820], [1835, 1867], [1128, 1910], [3, 1328], [596, 1662], [1006, 1078], [1318, 1597], [1976, 1977], [151, 1494], [1313, 1483], [1299, 1518], [41, 429], [1624, 1983], [481, 495], [1707, 1985], [370, 984], [64, 1559], [1622, 1988], [63, 1989], [623, 1986], [1383, 1974], [673, 1992], [480, 1991], [797, 1578], [982, 1726], [1995, 1996], [1613, 1997], [48, 49], [1577, 1984], [229, 1990], [23, 1897], [617, 2002], [813, 2003], [1375, 1575], [2004, 2005], [32, 1551], [726, 2007], [565, 2006], [1063, 2009], [440, 1987], [576, 1678], [1885, 2011], [1611, 1927], [1845, 2014], [764, 933], [1209, 1637], [1286, 1861], [1333, 2018], [322, 2019], [501, 1725], [330, 885], [279, 2022], [479, 508], [2020, 2024], [12, 241], [784, 2026], [1620, 2027], [11, 2028], [2021, 2029], [965, 2030], [998, 1748], [141, 1475], [143, 2033], [153, 1980], [29, 2034], [148, 1952], [2035, 2037], [847, 2036], [1869, 2039], [1652, 2038], [1575, 2004], [1041, 2003], [380, 1721], [1550, 2044], [119, 1595], [2023, 2045], [743, 1510], [1509, 2048], [1546, 1701], [1787, 2033], [130, 2050], [946, 2049], [230, 2051], [1055, 2053], [1952, 2054], [1820, 2052], [152, 1198], [16, 541], [82, 2059], [816, 1443], [149, 2058], [1167, 2062], [1730, 2063], [1246, 2064], [566, 2061], [585, 2066], [14, 83], [1813, 2068], [50, 956], [1477, 2070], [2069, 2071], [358, 1139], [405, 1422], [2060, 2072], [1081, 2074], [238, 1730], [1301, 1455], [87, 1912], [950, 1346], [2077, 2078], [1665, 2079], [1972, 2082], [1658, 1666], [896, 1469], [889, 2085], [579, 2086], [108, 1588], [1561, 2088], [51, 2084], [52, 1895], [2090, 2091], [1968, 2089], [1033, 2087], [187, 481], [855, 1555], [2095, 2096], [23, 2097], [1399, 1575], [936, 2099], [1363, 2100], [1160, 2101], [548, 781], [224, 2103], [170, 1680], [1531, 2105], [371, 1994], [646, 1622], [1840, 2022], [2073, 2109], [1793, 2029], [648, 2106], [1590, 2111], [1193, 1502], [745, 884], [905, 2115], [534, 2110], [552, 558], [1181, 2117], [1273, 1854], [147, 2120], [847, 1222], [1980, 2122], [620, 1409], [1851, 2114], [1850, 2123], [329, 2125], [139, 1879], [1166, 1785], [35, 177], [1460, 2130], [2, 1217], [2016, 2124], [1152, 1374], [1651, 2134], [1211, 1212], [1933, 2131], [2008, 2012], [2043, 2132], [1604, 1978], [2128, 2140], [1890, 2135], [589, 2141], [1451, 2142], [300, 1720], [1679, 1859], [206, 282], [1970, 2147], [479, 511], [1928, 2149], [1482, 1981], [2148, 2151], [148, 1807], [1644, 2150], [195, 235], [987, 2155], [567, 2156], [1135, 2157], [179, 742], [1781, 2159], [193, 539], [1455, 1706], [2160, 2162], [1337, 1349], [704, 2161], [1325, 1556], [1780, 1995], [714, 797], [855, 1648], [892, 2169], [114, 1906], [553, 1135], [2168, 2172], [2108, 2164], [322, 2167], [699, 1062], [1471, 1759], [331, 2165], [1176, 1470], [1465, 2178], [591, 1101], [190, 1875], [2136, 2176], [18, 1452], [2177, 2181], [155, 1769], [1836, 2171], [2118, 2173], [938, 1775], [180, 2184], [320, 2170], [167, 390], [216, 1348], [12, 951], [1901, 2194], [393, 954], [2187, 2193], [1354, 2182], [1097, 2196], [2042, 2189], [1925, 2186], [1723, 2201], [1844, 2195], [1011, 2192], [1540, 2200], [1340, 1916], [142, 1462], [2206, 2207], [1077, 2198], [1999, 2199], [1629, 1975], [1006, 1960], [932, 2032], [775, 2213], [15, 1600], [1964, 2215], [786, 1510], [2059, 2216], [1593, 2217], [1973, 2046], [216, 2219], [1857, 2153], [2121, 2222], [1481, 2070], [1061, 1512], [1248, 2225], [882, 1214], [1982, 2208], [100, 2224], [1870, 2229], [1739, 2227], [1198, 2226], [1516, 2232], [83, 2231]], "roots": [2067, 1939, 2041, 2056, 1415, 1421, 1594, 1831, 1777, 1586, 1366, 2228, 1937, 2143, 1874, 1623, 1492, 2025, 1863, 1798, 2152, 1950, 1755, 2210, 2174, 1773, 2223, 1808, 2144, 2080, 2112, 2146, 2013, 2001, 1918, 1848, 1979, 2158, 1956, 2204, 2047, 1965, 1849, 2230, 2214, 708, 1203, 1647, 2010, 2057, 1499, 1554, 2180, 2127, 1503, 2102, 2093, 1583, 1075, 1155, 2098, 2126, 2220, 1677, 2191, 2203, 2040, 2197, 1955, 2190, 2015, 2133, 644, 1709, 2205, 1747, 807, 2083, 1821, 1926, 1993, 2065, 2081, 1218, 1571, 1573, 1903, 2076, 1643, 1899, 2233, 2137, 2166, 1216, 1907, 1521, 1656, 1922, 2179, 1936, 1817, 1530, 2139, 1889, 2094, 1935, 1035, 2209, 1827, 2107, 2154, 1838, 523, 1704, 2129, 2211, 2221, 2104, 1779, 2163, 2145, 975, 1406, 1621, 2185, 2113, 2092, 2031, 1896, 1373, 1670, 1942, 2000, 1902, 1713, 1275, 2202, 2138, 1292, 2175, 1718, 2183, 1736, 1934, 2234, 1683, 1888, 1711, 1805, 1998, 1642, 2055, 2017, 1276, 2116, 2212, 2119, 2218, 1149, 2075, 1751, 2188, 1969, 1971, 1801], "contract": "Root indexed by J sums input I exactly when I and J are disjoint.", "source": "agent-cmod ctsa annealing of the complex compile ledger"}
\ No newline at end of file
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diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/retained/FINITE_BRIDGE.txt b/research/five-stage-p10-transcript-stages/inputs/complex/retained/FINITE_BRIDGE.txt
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+FINITE ROUTER, ROW-STOCK, AND SEMANTIC BRIDGE FOR ROUND 13
+
+Prepared for icekylinx by GPT-6 Astra, 9 October 2026. Apache-2.0.
+
+This bridge applies to a completed, physically proved round-13 profile.
+It cannot make a numerically attractive but unconstructed profile valid.
+The local source/target flags, controlled injections, old-response
+subtraction, inverse cleanup, and retained alias boundaries are separate
+construction obligations. assemble_profiles.py records their role as
+proof dependencies and independently checks the exact arithmetic.
+
+1. The inherited uniform interfaces
+
+Retain the three completed-core cover of PR144/PR168 and all of its
+analytic and fixed-tape assumptions. The complex cover is O(m,2), m<=72,
+with order V<2^(m*m)<=2^5184. No new independent cover coordinates are
+introduced by common-frame scalar lifts or source-controlled local
+rewrites. Every stage still uses one completed invocation at each vertex.
+
+For a supplied profile with W0<10^7 roles per cover vertex, the full
+physical stock W=V W0 is less than2^5208. Its total rank s is less
+than mW<2^5215. The profile's actual proper-child maximum is retained;
+the selected complex maximum must be less than m/2. The script checks
+these inequalities rather than assuming that fewer auxiliary rows imply
+a better contraction or a shorter recursion.
+
+The bit word uses the same weighted q-adic frame interface and the same
+internally borrowed selectors as its pinned parent. New source controls
+must use existing nondegenerate source-meeting planes or separately
+certified new frames. All zero-rank adapters remain charged scalar work.
+The group-size factor is not omitted and is not inserted into an external
+polynomial row reserve. The inherited ordinary leaf saving is exactly
+384599/10^10. The bad-row allowance is1/10^16; the charged fallback per
+edge is32m^2. Its inequality2m^3/2^80<1/10^16 is checked explicitly.
+
+2. A deliberately loose finite scalar bound
+
+The pinned words and round-13 modifications are finite straight-line
+programs with fewer than2^40 stored nodes, roles, coefficients, and
+boundary entries. Scalar sum/difference lifts use actual invertible
+matrices and are executed pointwise at common frame representatives.
+For the selected dyadic rewrite, new elementary coefficients are
+dyadic; the inherited center scatters retain their fixed odd divisor3.
+No unrecorded new odd denominator may be included under this bridge.
+
+Fixed integer multipliers can be expanded into scalar doublings and
+additions; dyadic divisions can be expanded into halvings. The explicit
+low words and full-frame inverses are much smaller than2^4096 primitive
+scalar/movement groups per invocation. Even constructing their fixed
+old-response matrices by exact elimination is dominated by this bound:
+matrix order is below2^40, original finite-word coefficient bit lengths
+are below2^80, and the elementary elimination and coefficient expansion
+bounds are below2^1024. No input-size-dependent dense elimination is
+being performed. These are constants of the chosen finite construction.
+
+Consequently all3V invocation words, endpoint adapters, and finite role
+bookkeeping fit within K<2^9300 logical groups. The retained universal
+router is overcharged by a full W-role permutation for every group:
+
+    64 (m+1)^3 (K+1) (W+1)^2 < 2^20000.
+
+Choose the exact dominating scalar/router budget G=2^30000. This also
+dominates the primitive arithmetic required to realize the fixed scalar
+coefficients and source-controlled inverse cleanup. The router still
+uses a fixed number of tapes, with sequential reuse of row stock.
+
+3. Explicit semantic constants
+
+Choose the exact integer E=2^100000 and put B=s+E. Then
+
+    2 G W^2 + 8s + 4W + 4 + 32m < 2^40500 < E,
+    E <= B < 2^100001.
+
+For the actual maximum child r<m, the induction gap obeys
+
+    2B(m-r)-s-E >= s+E >= 1.
+
+Choose C0=2^210000 and C1=1. These dominate both the retained semantic
+requirement32m B^2 and2B+18. The reported strict_literal_gap=1 and
+induction_gap_lower=1 are proved lower bounds on the positive actual
+integer gaps; they are not claims that those gaps equal one.
+
+Use the inherited common dyadic grid with fixed3^(-K') exposure and
+retain its precision/rounding contract. No child receives an independent
+rounding allowance and no source-controlled injection is treated as an
+unpaid numerical operation.
+
+4. External rows and stopping
+
+The complex child maximum below m/2 gives halving degree1, while
+log2 W<5208<10000. Keep the deliberately conservative inherited bit
+coarse reserve9909 and ordinary-leaf reserve252. Thus the external
+row coefficient is bounded by
+
+    A=10000+9909+252=20161.
+
+Choose degree D=1000000 and suffix slope4D. The exact row gap is
+
+    D - (51/25)A > 0.
+
+The q-adic selector fields and source-control labels remain internally
+borrowed and restored. Increasing these finite overcharges changes
+constants and the all-size bridge, not the selected exponent saving.
+
+5. Exact supplier moments and balanced assembly
+
+For each actual histogram, assemble_profiles.py proves
+
+    sum_r n_r r exp(a log(m/r))/(mW0) + bad_allowance < 1
+
+using rational upper bounds, with upward rounding on the2^120 grid.
+The bit atom stop is the first10^(-12) grid point above
+a/(1+a-old), which implies both required strict toll inequalities.
+Its effective saving is(1-beta)a+beta*old. This stopping rule is the
+already reviewed PR158 edge rule, not a new local-word contribution.
+
+The final assembly uses the substantial PR168 balanced-prefix adapter,
+with eta=10^(-8) and phase stop10^(-9), retaining all47 strict
+constraints and all7 margins. The selected final kappa is rounded
+down on the10^(-10) grid below the minimum complete margin. The
+script checks every constraint exactly and reports whether the fixed
+target0.0009218338 is reached.
+
+This is a conditional bound of the retained theorem form
+
+    T(n)=O(n (log n)^(1-kappa)).
+
+The improvement ratio refers to kappa, the logarithmic exponent saving.
+It is not a measurement of practical multiplication throughput.
+
+Credits
+
+The base supplier, scalar/frame verification, and actual profiles are
+pinned to PR168 fd25adb7fbaa12ee761d02c733c54d1d2a7687ee, eumemic
+(Anthropic Claude assistance), building on icekylinx's PR144. The
+balanced prefix is RaD/hipotures; the semantic constraints are retained
+from the reviewed PR23 line; completed-core sharing is credited to
+an664 PR128; the atom-edge stop is credited to geckods PR158. Existing
+source notices retain their more detailed upstream attributions.
+The new source-controlled boundary construction, this conservative
+bridge, and its integration are GPT-6 Astra's round-13 work.
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/retained/compact-control-layout.tex b/research/five-stage-p10-transcript-stages/inputs/complex/retained/compact-control-layout.tex
new file mode 100644
index 0000000000..16f4d23347
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/retained/compact-control-layout.tex
@@ -0,0 +1,118 @@
+\paragraph{Rows and complete compact fields.}
+Let $m,W,s$ denote the complex network constants and keep the layer's global
+$p,d,K$ at every node. Put
+\[
+ G=4\lceil\log_2p\rceil+6,\quad H=dG,\quad
+ q_F=\left\lceil\frac{2H}{K}\right\rceil,\quad
+ q_B=\left\lceil\frac{H}{K}\right\rceil,
+\]
+\[
+ q_0=\lceil\log_2W\rceil\lceil\log_m(2d)\rceil,
+ \quad k_0=\lceil\log_m d\rceil,\quad Q_0=q_0+q_F+q_B.
+\]
+If $D\le Q_0$, apply all $D$ selected kernels individually. Otherwise,
+process individually the first $q_0+q_F$ and last $q_B$ selected axes.
+This uses existing coordinates only. The remaining active axes are a
+consecutive middle block of length $D-Q_0$.
+
+Regard the first $q_0$ chunks as the row index. Immediately after it, the
+next $q_F$ chunks have at least $2H$ bits. Reinterpret these consecutive
+bits as two $H$-bit front fields and a spectator remainder; a remainder
+of length zero is omitted. The last $q_B$ chunks similarly supply one
+$H$-bit back field and a spectator remainder. These reinterpretations move
+no records and preserve the total address space. For a call with $f$ axes
+per slot, carve $nG=(f-1)G\le H$ consecutive bits from each of these
+fields; collapse their unused bits into spectators. The resulting field
+list has a fixed number of entries. Both front fields precede all active
+slots and the back field follows them, so the compact-control proposition
+applies to every ordered pair of slots. For $f=1$ no compact fields are used.
+
+The original row range has length $R_{\rm row}=2^{q_0K}\ge W^{k_0}$.
+For each original prefix, pad this row range to the next multiple of
+$W^{k_0}$ by adding zero rows. A row includes the entire complete front
+fields, active middle block, back field, all spectator coordinates and
+polynomial record suffix. Padding adds whole such rows, so increases total
+volume by at most two and does not change any within-row range.
+
+At a node write the row index as $u=Wg+w$, $0\le w<W$, and send the entire
+row to role $w$. The index $u$ consists solely of the first row region:
+\emph{no compact-field bit is included in it}. Each role therefore has
+the same complete within-row address set and exactly $1/W$ of the parent
+volume. At depth $j$ the remaining row count is divisible by $W^{k_0-j}$.
+This invariant survives further splits, padding, and reassembly. Pointwise
+gates on different roles have aligned $g$ and every remaining coordinate.
+All compact operations restore the temporary fields before a scalar gate,
+recursive child, or returned result uses that layout.
+
+The fixed-tape scheduler is unchanged: park only the other role streams at
+the active stack top, execute the child on a complete role stream, and restore
+the parked streams on return. Every child has its own current logical volume;
+copying, parking, rewinds and clearing cost a fixed multiple of that volume.
+The constant number of compact operations per edge use fixed work areas.
+Descriptors include the global $p,d,K,G,H$ and the carved field lengths;
+all have $O(p)$ bits and there are a fixed number of fields. The existing
+record suffix absorbs polynomial setup at every node and per record.
+
+Each completed invocation acts as the desired $C$ tensor on its active axes
+and as identity on the reserved and spectator coordinates. It therefore
+commutes with the earlier individual kernels, including those on bits now
+interpreted as compact fields. Restoring the row permutation returns the
+result to each original row separately. A padded zero row is consequently
+zero at completion and can be deleted exactly as before. Neither temporary
+field contents nor intermediate scratch payloads were assumed to be zero.
+
+The number of individually processed axes is at most $Q_0$, including the
+fallback $D\le Q_0$. For large $p$, $K\ge d^c/2$ and
+\[
+ q_F+q_B\le\frac{3dG}{K}+2\le6d^{1-c}G+2.
+\]
+Thus preprocessing, padding and reservation cost
+\[
+ O\bigl(V(\log(2d)+d^{\max\{1-c,0\}}\log p+1)\bigr).
+\]
+All reserved axes lie within the original $D$ axes; in particular their
+total number never exceeds $d$. This fact also bounds their coefficient
+dependency depth by the same $8d$ allowance used in the guard proof.
+
+\paragraph{Unrolling the compact-control recurrence.}
+Fix rational $0<\beta<1$. Choose $0<\tau<1$ and
+$\max\{0,\log_m(s/W)\}<\sigma<1$. Stop when $e<d^\beta$ and apply
+the remaining kernels individually. With $F(e)$ denoting time per current
+logical volume, the exact row split gives
+\[
+ F(e)\le(s/W)F(e/m)+O(G^\tau e^\tau+1),\qquad
+ F(e)=O(e)\quad(e<d^\beta).
+\]
+Here $G$ and the compact reservations are global parameters, not rebuilt
+at each node. This is why no factor $K^\tau$ appears in the overhead.
+Repair costs are already included in the node overhead.
+
+Write $b=s/W$. At level $j$ the internal contribution is bounded by
+$O(G^\tau e^\tau(b/m^\tau)^j)$. Summing through the stopping depth gives
+\[
+ O(G^\tau\log(2d)d^\chi),\qquad
+ \chi=\tau+(1-\beta)\max\{\sigma-\tau,0\}.
+\]
+Indeed if $\sigma\le\tau$ the root bounds every summand; otherwise the
+last internal level costs at most the root bound times a fixed constant
+and $d^{(1-\beta)(\sigma-\tau)}$. The additive $1$ is absorbed by
+$G^\tau e^\tau$ at internal nodes. The leaf contribution is at most
+$O(d^{\sigma+\beta(1-\sigma)})$, by the original volume-weighted argument.
+
+Partition $D-Q_0$ into consecutive powers of $m$, using its base-$m$
+expansion. There are $O(\log(2d))$ pieces. Include their costs and the
+reservation cost to obtain, per original volume,
+\[
+ O\!\left((\log p)^3
+ [d^\chi+d^{\sigma+\beta(1-\sigma)}+d^{\max\{1-c,0\}}+1]\right).
+\]
+We used $\log d=\Theta(\log p)$ and $G=O(\log p)$ for each fixed
+$d=\Theta(p^\epsilon)$ family. Any fixed rational exponents satisfying
+\[
+ \max\{\tau,\sigma,\chi\}<\lambda<\lambda'<1,\qquad
+ \max\{\sigma+\beta(1-\sigma),1-c,0\}<\lambda'
+\]
+therefore give the complete $O(Vd^{\lambda'})$ layer bound. The strict gaps
+absorb the logarithms. The small-$D$ fallback obeys the same bound.
+For fixed rational $\beta=u/v$, implement stopping by the integer test
+$e^v<d^u$; its polynomial descriptor cost is already included.
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/retained/compact-control-movement.tex b/research/five-stage-p10-transcript-stages/inputs/complex/retained/compact-control-movement.tex
new file mode 100644
index 0000000000..06b6a9ef24
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/retained/compact-control-movement.tex
@@ -0,0 +1,167 @@
+\subsection{Compact dirty controls for selected-bit additions}
+\label{sec:compact-control-movement}
+The following replacement for the wide-slot packed operation moves only
+compact control fields. Temporary address fields have arbitrary contents;
+they are complete ranges of existing address bits, not newly allocated
+independent coordinates. Their availability in every recursive call is
+proved separately below.
+
+\begin{lemma}[Controlled rotations with record-paid offset work]
+\label{lem:record-paid-rotation}
+Consider $M$ records of $R$ bits on a complete rectangular address set, of
+volume $V=MR$. Its fixed number of field lengths and controls have at most
+$A=\lceil\log_2(2V)\rceil$ bits each. A binary target field follows all its
+controls. Suppose its rotation offset, independent of that target, is
+computable from the controls and descriptors in $O(A^C)$ tape steps for
+some fixed $C$. Then the rotation can be performed on fixed tapes in
+$O(V+MA^{C'})$ time for a fixed $C'$. In particular, this is $O(V)$ when
+$A=O(p)$ and $R$ exceeds every fixed power of $p$.
+\end{lemma}
+\begin{proof}
+Fix the prefix before the target. If its range is $Q$ and each target block
+has $B$ suffix bits, rotate by $a$ through the two-piece split at $Q-a$ and
+merge in the opposite piece order. This is the controlled-rotation
+construction from the ordered-affine streaming lemma. Each data bit is
+copied a bounded number of times. There are at most $M$ prefix fibers, since
+every fiber contains at least one complete record. At each fiber, compute
+the offset, initialize its two piece lengths, and reset the finite collection
+of counters; recompute the offset at the merge. Ordinary binary arithmetic
+and descriptor copies cost a fixed polynomial in $A$ per fiber. The controls
+can be wider than the target: their lengths are bounded by $A$, not by the
+target width. Local suffix-length copies and ripple counters are charged as
+in the original streaming proof, so no growing descriptor is scanned per
+payload bit. Two piece tapes, output and fixed arithmetic work tapes suffice;
+rewinds and clearing are over the regions just written. This gives the stated
+bound. Finally $MA^{C'}/V=A^{C'}/R=o(1)$ in the specified record regime.
+\end{proof}
+
+Let $x,y$ be disjoint slots of $fK$ bits, with corresponding selected
+positions $j_i=\rho+iK$, $0\le i<f$, $0\le\rho<K$. Put $n=f-1$.
+For $f=1$ use the elementary two-bit XOR. Otherwise fix a positive integer
+$G$, put $B=2^G$, and assume two disjoint complete $nG$-bit fields $u,t$
+precede both slots and a third such field $b$ follows both slots. Arbitrary
+spectator fields may intervene. Each compact field has $n$ radix-$B$ digits.
+The selected-bit operation will preserve these three entire fields.
+
+\paragraph{Earlier source.}
+Suppose $x$ precedes $y$. The unused field $u$ is a spectator. For an integer
+target segment $v$, a bit $z$, and an arbitrary integer temporary $w$, perform
+\[
+ v\gets v+2zw,\qquad w\gets w+(v\bmod2),\qquad
+ v\gets v+z(1-2w),\qquad w\gets w-((v\bmod2)\mathbin\oplus z).
+\]
+Writing the original parity as $a$, the first update leaves it unchanged.
+The final values are $v+z(1-2a)$ and the original $w$. Thus this toggles
+only the parity of $v$ when $z=1$, and restores the dirty temporary.
+
+Apply these four updates simultaneously, with $z_i=x_{j_i}$, to the low
+$n$ selected segments of $y$ and the digits $t_i$ of $t$. A target-slot
+update is one modular rotation of $y$, whose offsets are respectively
+\[
+ \sum_{i<n}2x_{j_i}t_i2^{j_i},\qquad
+ \sum_{i<n}x_{j_i}(1-2t_i)2^{j_i} \pmod{2^{fK}}.
+\]
+Both control fields precede $y$. For a temporary update, swap $t$ with $b$,
+rotate the back field by the packed selected bits of the current $y$, and
+swap back. For unloading, use minus the packed bits
+$y_{j_i}\mathbin\oplus x_{j_i}$. These controls precede the back field.
+There are four width-$nG$ swaps and four rotations. The arbitrary original
+contents of $b$ return after each pair of swaps.
+
+\paragraph{Later source.}
+If $x$ follows $y$, first execute the earlier-source construction with control
+bits $u_i\bmod2$. Load the selected bits of $x$ into $u$ by swapping $u,b$,
+rotating the back field by their packed radix-$B$ representation, and swapping
+back. Repeat the earlier-source construction with the new parities of $u$,
+then unload the selected bits of $x$ from $u$ by the inverse load.
+When the digit loads do not overflow, the two control parities differ by
+exactly $x_{j_i}$. The resulting target update is the required XOR, with
+$u,t,b$ restored. This version uses twelve compact swaps and ten rotations.
+Every offset depends on a fixed number of fields preceding its target.
+
+\paragraph{Guards and deterministic repair.}
+Temporarily omit the highest selected position. The low $n$ segments
+$[j_i,j_i+K)$ are disjoint and fit inside $y$, including when $\rho=K-1$.
+Write each initial segment as $2g_i+a_i$, $a_i\in\{0,1\}$.
+Declare an address bad if a $t$ digit is $B-1$, or a target guard fails
+\[
+ 2B\le g_i<2^{K-1}-2B.
+\]
+For a later source also declare it bad if any $u$ digit is $B-1$.
+On a good address each temporary load stays within its digit, and the target
+displacement is at most $2B$ in either execution of the four-step identity.
+The conservative guard interval therefore prevents every carry or borrow
+between the wide segments. After each completed identity the guard is
+unchanged. Induction through the later-source sequence proves the desired
+map on the good set, including restoration of every temporary and every
+unselected address bit.
+
+Uniform complete ranges give the common bound
+\[
+ \delta=\min\{1,n(2\cdot2^{-G}+8\cdot2^{G-K})\}
+\]
+on the bad fraction; for an earlier source the first factor 2 can be omitted.
+The ideal map $T$ changes only the selected target parities, so it preserves
+the bad set. The actual sequence $S$ is a bijection on the entire rectangle:
+each rotation is independent of its target and all swaps are bijections.
+Since $S=T$ off the bad set, $S$ preserves that set too. Thus $TS^{-1}$ is
+supported there, exactly as in the original exceptional-stream repair.
+
+Extract the bad records, retaining marked holes in the full stream. For each
+extracted address $q$, reverse the swaps and modular rotations to compute
+$S^{-1}q$, then compute $T(S^{-1}q)$. All fields and descriptors have $O(A)$
+bits. A constant number of offset calculations each scan at most $n\le A$
+digits and combine shifted integers of $O(A)$ bits. Integer arithmetic,
+mixed-radix decoding, inverse offsets and the destination key can consequently
+be computed in $O(A^3)$ per record. Sort only the extracted records by their
+$O(A)$-bit destination keys, using stable binary radix passes, then reinsert
+them in their marked holes. Keys are distinct and fill precisely those holes
+because $TS^{-1}$ permutes the bad set. This uses fixed tapes and costs
+\[
+ O(V+MA^3+\delta MA(R+A)).
+\]
+Every inverse offset is evaluated on the current inverse controls; modular
+overflow on bad addresses is handled exactly, rather than treated as an
+integer identity. Finally, supply the omitted highest selected position
+through the elementary two-bit XOR in $O(V)$ time.
+
+\begin{proposition}[Compact-control selected-bit addition]
+\label{prop:compact-selected-addition}
+Under the stated complete-field hypotheses, take
+\[
+ G=4\lceil\log_2 p\rceil+6,\quad f\le p,\quad A=O(p),
+ \quad K/\log p\longrightarrow\infty,
+\]
+and let $R$ exceed every fixed power of $p$. The exact selected-bit row
+addition, with all temporary fields restored, costs
+\[
+ O\bigl(V((f\log p)^\tau+1)\bigr)
+\]
+on a fixed number of tapes, for either order of the two slots. Constants and
+cutoffs are uniform within each fixed parameter family of the layer theorem.
+\end{proposition}
+\begin{proof}
+Use the retained arbitrary-width chunk-swap primitive for the at most twelve
+swaps, each of width $nG$. Its padding, cleanup and all spectator intervals
+are covered by that interface. For every rotation, apply
+Lemma~\ref{lem:record-paid-rotation}; its offset arithmetic is polynomial
+in $A$. No new record volume is introduced by describing the compact fields.
+For $\ell_p=\lceil\log_2 p\rceil$, eventually
+$K\ge G+4\ell_p+10$. Then
+\[
+ \delta\le \frac{5}{128p^3},\qquad
+ \frac{A^3}{R}=o(1),\qquad
+ \delta A(1+A/R)=O(p^{-2}).
+\]
+The repair is therefore $O(V)$ per call, including predicate scans and key
+arithmetic. The elementary highest-bit operation costs $O(V)$. All calls
+reuse their fixed work tapes and finish in the declared physical field order.
+\end{proof}
+
+\paragraph{Application to a fixed binary change of basis.}
+The original phase-frame construction expresses each binary basis change
+as a fixed number of row additions on $m$ slots of $f=e/m$ axes. Use the
+two slots of each addition as $x,y$ and the reserved front/back compact
+fields as controls. The complete basis change and its inverse cost
+$O(V((e\log p)^\tau+1))$. The reservations below guarantee their complete
+ranges, independently of which slots are involved, at every recursive node.
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/retained/copied-centers-assembly.tex b/research/five-stage-p10-transcript-stages/inputs/complex/retained/copied-centers-assembly.tex
new file mode 100644
index 0000000000..b0c69166c3
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/retained/copied-centers-assembly.tex
@@ -0,0 +1,118 @@
+\subsection{Selected semantic guard and product rows}
+For each local producer retain
+\[
+ g_h=4(c_h+v_h)+10v_h+4hv_h+4h^2+8h+8.
+\]
+The two-stage literal scalar count includes two additional groups per
+copied center and one endpoint-addition group per data pair:
+\[
+ G=N_c+2v(g_{28}+2\cdot28)=4793351472.
+\]
+These are local scalar charges; the recursive copied transformations
+are already included in $s_c$. Set
+\[
+\begin{aligned}
+ E&=64(W_c+m_c+G+1)^3=9696565176891520488192506033216,\\
+ \mathcal E&=2GW_c^2+8s_c+4W_c+4+32m_c\\
+           &=2771683137698171397039558468<E,\\
+ B_{
m guard}&=s_c+E,\qquad C_0=32m_cB_{
m guard}^2.
+\end{aligned}
+\]
+A completed $u$-axis child has coefficients in $2^{-u}\mathbb Z[i]$
+and absolute row sum at most $2^u$. Its internal excess stays local;
+other streams, including originals of active copies, are parked.
+No return rounding or encoding change is performed. A copied input
+has the same incoming magnitude/grid bound as its original, and its
+completed output obeys the same semantic bound. Consequently, with
+$f=\lfloor e/m_c\rfloor$,
+\[
+ A(e)\le A(756f)+s_cf+E\le2B_{
m guard}e,
+\]
+using $2B_{
m guard}(m_c-756)\ge s_c+E$ and the direct-leaf bound
+$A(e)\le8e$. Prefix kernels, phases and normalization add the retained
+$18e$, which is less than $C_0e-2B_{
m guard}e$. Thus $C_1=1$,
+with the fixed fine-grid precision proof of RaD/PR23 unchanged.
+
+The actual least halving degrees and wire bitlengths are
+\[
+ (t_b,w_b)=(9,28),\qquad(t_c,w_c)=(20,30),
+\]
+where $m_j^{t_j}>2r_j^{t_j}$ for largest children $r_b=529,r_c=756$.
+At width $e$ reserve the product
+$Q=W_c^{D_c(e)}W_b^{D_b(e)}$, with
+$D_j(e)=t_j\lceil\log_2e\rceil$. Its coefficient is
+$9\cdot28+20\cdot30=852$, and
+\[
+ 2000>\frac{51}{25}\,852.
+\]
+The sufficient stock is therefore $p^{2000}$, supplied by the retained
+physically preceding transformed prefix and a single complete-row
+padding. Nested bit stock is restored before another complex child.
+Sequential copies introduce no independent row field. The supplementary
+suffix condition $b_{\rm in}^{1-\epsilon}>8000(\log_2b_{\rm in}+8)$
+is eventual for fixed $\epsilon<1$.
+
+\subsection{Exact conditional assembly}
+Use the analytic proof map in
+\path{notes/structured-bulk-assembly.tex}: arbitrary-source routing
+with active masking and paid repair scans; one rounded phase-cell
+matrix with preserved period cuts and downward-weight error bounds;
+persistent target halos, sequential overlap tapes and factor pages;
+Baker--Harman--Pintz prime packing; and the retained exact-recovery
+interface. Their full costs are unchanged. In particular the bulk
+bound retains the terms
+\[
+ O\!\left(Tp\left[p^\tau\operatorname{polylog}p+
+ d\operatorname{polylog}p+dp^\delta+w^2p^\delta+
+ dw^2p^\delta/L\right]\right)+n^{o(1)},
+\]
+with $L=2^{\lceil8\log_2p\rceil}$,
+$w^2=O(p^{1-r})$, and normalization exponent requiring
+$\epsilon+r<1$. These arguments, not a change of arithmetic model,
+justify the seven margins below.
+
+\begin{theorem}[Conditional fixed-tape multiplication bound]
+Under the retained analytic and fixed-tape interfaces of PR23/PR29
+and the preceding proof map, the selected copied-center networks give
+\[
+ T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad
+ \boxed{\kappa=\frac{384569}{10000000000}=3.84569\times10^{-5}}.
+\]
+\end{theorem}
+\begin{proof}
+Take the strict finite savings $a=a_b=384599/10^{10}$ and
+$b=a_c=717/10^7$, with $\tau=1-a$, $\sigma=1-b$, and put
+\[
+\begin{gathered}
+ \eta=10^{-8},\quad\beta=\tfrac14,\quad q=a(1-2\eta),\quad
+ c=q(1+\eta),\quad\epsilon=\frac{1-\eta}{1+c+q},\\
+ \lambda'=1-q,\quad\lambda=(\tau+\lambda')/2,\quad
+ g=\epsilon q,\quad r=(g+1-\epsilon)/2,\quad\delta=\eta/8.
+\end{gathered}
+\]
+The stopped complex leaf saving $(1-\beta)b=53.775\times10^{-6}$
+is strictly above $a$, so paid internal adapters use exponent $\tau$
+and both layer exponents lie below $\lambda'$. The exact certificate
+checks all 47 strict constraints of the retained semantic/bulk
+composition, using the new literal scalar charge and product-row gap.
+These include compact reservations, geometry, the linear guard,
+$\epsilon+r<1$, phase-cell/band separation, prime packing, short-record
+fallback and artificial-boundary allowances.
+
+The seven final savings are
+\[
+ 1-\epsilon(1+c),\quad a,\quad g,\quad a,\quad
+ \min(1-\epsilon-\delta,r-\delta),\quad
+ 1-\epsilon-\delta,\quad\epsilon.
+\]
+Their minimum is exactly $g$ and the prefix margin equals $g+\eta$.
+Exact rational comparison gives
+\[
+ g-\frac{384569}{10^{10}}>4.0746056580\times10^{-11}>0.
+\]
+These positive gaps absorb fixed logarithms. The all-size conclusion
+retains constructive finite setup, descriptor and catalogue domination,
+prime existence and analytic recovery as eventual thresholds. The
+strict bit and complex moments, copied-stream recurrence contracts and
+these assembly inequalities prove the claimed conditional bound.
+\end{proof}
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/retained/copied-centers-lemma.tex b/research/five-stage-p10-transcript-stages/inputs/complex/retained/copied-centers-lemma.tex
new file mode 100644
index 0000000000..8933aaf508
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/retained/copied-centers-lemma.tex
@@ -0,0 +1,103 @@
+\subsection{Scalar, frame and temporary-stream contracts}
+The retained source-copy, reversible mixer and scatter maps satisfy
+$JLV=I$. Over $\mathbb F_2$ the chronological word
+\[
+ L,\ J,\ L^{-1},\ V,\ L,\ J,\ L^{-1},\ V
+\]
+adds the input to the target and restores every arbitrary auxiliary.
+Over Gaussian dyadics use its corresponding old-value subtraction and
+new-value addition. A designated retained output has a distinct terminal
+output-use carrier: a matching may feed that carrier, but cannot merge
+two designated terminals or append a later middle-producer consumer.
+Its remaining uses before cleanup are its scatter reads, all of which
+leave its scalar value unchanged.
+
+Within one tensor invocation suppress the fixed future line and put
+\[
+ D_0=B\otimes F_h,\quad D_1=A\otimes F_h,\quad
+ A=B\mathbin{\perp}P,\quad D_U=D_0\mathbin{\perp}(P\otimes U),
+\]
+where $P$ and the suppressed future factor are one-dimensional and
+$U$ is a nondegenerate retained-center space of dimension $r$.
+Thus a local change of rank $d$ has ambient rank $d$.
+Write $\mathcal F_Q$ for the address frame: it is the rational partial
+swap $D_Q$ in the bit construction, and the binary phase $C_Q$ in the
+complex construction. Changing a copy from frame $Q_1$ to $Q_2$ means
+applying $\mathcal F_{Q_2}\mathcal F_{Q_1}^{-1}$ to its physical stream.
+Orthogonal backgrounds cancel in this quotient.
+
+Copies use Paureel's retained copy/transform/read/discard interface
+\cite{paureel,pr29}. A copy has precisely the original complete role
+stream, including all control and spectator ranges, and volume $V/W$.
+It is processed while inactive original streams are parked on the fixed
+depth-first stack tapes. Copying, pointwise reads and erasure are linear
+in that stream's volume. Sequential processing needs one additional
+fixed work stream, not an independently varying row coordinate.
+
+\begin{lemma}[Copied retained-center schedule]
+In either invocation orientation a designated retained center's
+physical rank profile can be changed from $z^r+z^h$ to
+$z^r+z^{h-r}$, with the same scalar action, original role endpoints,
+and arbitrary-scratch restoration. The rank-$r$ transform on the copy
+is included in the recursive call list.
+\end{lemma}
+\begin{proof}
+In the forward orientation the original center has scalar value $w$
+at frame $D_U$ after the middle mixer. Its old sequence was
+$D_U\to D_0\to D_1$: scatter at $D_0$, then cleanup at $D_1$,
+with ranks $r,h$.
+Keep the original at $D_U$, copy its physical stream, and transform
+only the copy to $D_0$, paying rank $r$. Supply every scatter read
+from that transformed copy while its data targets remain at their
+unchanged common frame $D_0$, then erase the temporary. The reads
+are exactly those of $w$ in the old schedule. Since they do not change
+$w$, move the original directly from $D_U$ to $D_1$ before its first
+cleanup incidence; this costs $h-r$. Every subsequent original gate
+therefore receives the same scalar value at its required frame.
+
+In the reverse complementary orientation the old sequence was
+$D_0\to D_1\to D_{U^\perp}$, with ranks $h,r$ and scatter at $D_1$.
+After the preceding all-$D_0$ operations, advance the original directly
+to $D_{U^\perp}=D_0\mathbin{\perp}(P\otimes U^\perp)$, paying
+$h-r$. Copy it and transform the copy to $D_1$, paying $r$.
+Use that copy for all early scatter reads, then erase it. The original
+already has the exact frame and unchanged scalar value required by the
+following inverse mixer. Terminal output-use separation ensures no
+intervening producer consumer has been bypassed.
+
+For partial swaps either direction of the rank-$r$ change is the same
+involution. For complex phases the forward copy uses $C_U^{-1}$,
+the direct original growth uses $C_{U^\perp}$, and the reverse copy
+uses $C_FC_{U^\perp}^{-1}=C_U$. These are the same charged ranks,
+implemented by the retained forward/inverse residual interface.
+All tensor backgrounds cancel as stated. Every original scalar
+incidence, final source-copy cancellation and auxiliary source/sink
+operator is unchanged. Thus the scalar identity and all endpoints
+remain exact on arbitrary initial auxiliary values.
+\end{proof}
+
+For the selected centers $r=h-1$, and there are $h$ distinct retained
+output uses per invocation. Their old histogram has rank mass
+$hR_h+2\ell_h$, where $\ell_h=h(h-1)$. The new histogram is exactly
+\[
+ H'_{h,1}=H_{h,1}+h,\qquad H'_{h,h}=H_{h,h}-h,
+ \qquad H'_{h,r}=H_{h,r}\quad(r\ne1,h),
+\]
+and hence $\sum_r rH'_{h,r}=hR_h+\ell_h$.
+Every old rank-$(h-1)$ residual remains as a paid transform of a copy;
+its projector and ordinary bit pivot profile are unchanged. Only the
+full-rank original transition becomes the rank-one complement.
+The physical role count $R_h$ is unchanged.
+
+For two factors, put $N=v_av_b$, $B_a=v_bR_a$, $B_b=v_aR_b$,
+$W=2N+B_a+B_b$ and $L=v_b\ell_a+v_a\ell_b$.
+All exterior, data-front and endpoint-correction calls remain in place.
+The resulting complete rank mass is
+\[
+ s=Wm-N+L,\qquad Wm-s=N-L.
+\]
+This follows by subtracting exactly $L$ from the retained two-stage
+physical mass $Wm-N+2L$. The $N$ rank-one endpoint-copy calls are
+separate and remain fully charged. Because center copies retain the
+same complete role-volume fraction $1/W$, the existing complete-row,
+integer-width remainder and fixed-tape recurrence proofs apply.
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/retained/endpoint-gauge-complex.tex b/research/five-stage-p10-transcript-stages/inputs/complex/retained/endpoint-gauge-complex.tex
new file mode 100644
index 0000000000..907a0ceda8
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/retained/endpoint-gauge-complex.tex
@@ -0,0 +1,225 @@
+\subsection{A normal form for every nondegenerate binary residual}
+Let $E$ have binary basis matrix $V$ and nonsingular Gram matrix
+$G=V^tV$. In dual Fourier coordinates put
+$q(z)=\operatorname{wt}(VG^{-1}z)\pmod4$.
+Its polarization is $2z^tG^{-1}w$. The same argument applies to mixed
+signs on orthogonal summands, since reversing a sign preserves this
+polarization. Write $S_q=\sum_z i^{q(z)}$. Completing the square gives
+\[
+\begin{aligned}
+K(x,y)&=2^{-r}\sum_z i^{q(z)}(-1)^{z^t(x+y)}\\
+ &=2^{-r}S_q\,i^{-q(Gx)}(-1)^{x^tGy}i^{-q(Gy)}.
+\end{aligned}
+\]
+The scaled Walsh kernel in the middle is a binary permutation of
+$H_0^{\otimes r}$, where
+\[
+ H_0=\tfrac12\begin{pmatrix}1&1\\1&-1\end{pmatrix}
+     =bSCS,\qquad b=(1-i)/2,\quad S=\operatorname{diag}(1,i).
+\]
+The remaining scalar $S_qb^r$ is a fourth root of unity. To verify
+this, decompose the nondegenerate quadratic module into odd
+one-dimensional and alternating two-dimensional blocks. Their Gauss
+sums are $1\pm i$ and $\pm2$, respectively; multiplying by $b$ and
+$b^2$ gives a fourth root in each case. This is a proof device, not
+an orthonormal-basis assumption on $E$.
+
+Consequently one rank-$r$ child suffices, with binary address changes,
+diagonal fourth-root phases, and one scalar fourth-root phase.
+On $f$ parallel columns it is one $C^{\otimes rf}$ child, the scalar
+raised to power $f$, and columnwise quadratic phases modulo four.
+The retained packed address operations evaluate these fixed formulas.
+These wrappers have modulus one and introduce no denominator loss.
+
+\subsection{The selected Gaussian-dyadic producer}
+Use paired triple exclusion with base threshold two, complete unsplit
+disjoint and pair-star sums, and sharing by actual ordinary support.
+For an ordinary support with at least two common points use the span
+of its triple indicators; these form an orthonormal common-pair star.
+Otherwise use the coordinate space of its union. Support inclusion
+preserves these labels: losing the common pair enters a containing
+coordinate space. Source lines use ordinary triple containment.
+
+Retain every full pair-star $P_{uv}=\sum_{w\ne u,v}X_{uvw}$ and form
+$B_u=\sum_{v\ne u}P_{uv}=2\sum_{T\ni u}X_T$.
+For even $h$ label these central additions by the nondegenerate
+hyperplane $E_u=\{x:\sum_{j\ne u}x_j=0\}$; every contributing star
+lies in it. Retain the global total $T$ with full-space label.
+The central correction at target $S$ is
+\[
+ \frac14\sum_{u\in S}B_u-\frac12T
+       =\sum_U\frac{|S\cap U|-1}{2}X_U.
+\]
+Adding half the disjoint sum and subtracting half the intersection-two
+sum gives exactly $X_S$. All coefficients are Gaussian dyadic.
+The transparent retained-output wrapper and oriented carrier compiler
+apply to these nested nondegenerate labels. The $h$ hyperplane centers
+lose $h(h-1)$ and the global center loses $h$, so loss is $h^2$.
+The selected counts, including all point centers, are
+\[
+\begin{array}{c|rrrrrr}
+h&v_h&c_h&q_h&|\mathcal M_h|&R_h&\text{loss}\\\hline
+32&4960&122512&19873&19241&123144&1024\\
+30&4060&99153&16271&15873&99551&900\\
+40&9880&252023&39561&37642&253942&1600
+\end{array}
+\]
+Their internal histograms satisfy $\sum_r rH_{h,r}=hR_h+2h^2$.
+They are distinct from the bit histograms.
+
+\subsection{Endpoint normalization and the complex characteristic}
+For nondegenerate $U$, Fourier phases give
+\[
+ C_U^2=X_{P_U\mathbf1},\qquad
+ C_{U^\perp}C_U^{-1}=C_FX_{P_U\mathbf1}.
+\]
+Put $v=P_U\mathbf1$. On coordinates in $v$, this endpoint has
+$C^{-1}$ instead of $C$. The identity $C^{-1}=-iZCZ$ shows that
+conjugating by $Z_v$ and multiplying by $i^{\operatorname{wt}(v)}$
+normalizes it to $C_F$; for $f$ columns the exponent is
+$f\operatorname{wt}(v)$. These are diagonal wrappers without a child.
+
+Choose stage-two source $C_{D_0}$ and sink $C_{D_0^\perp}$, where
+$D_1=D_0\mathbin{\perp} A$ and $\dim A=b$. The same refined copy
+schedule removes the entrance on every auxiliary role. With
+$R=D_1^\perp$, the exit is $C_RC_{D_0}^{-1}$ on
+$E=R\mathbin{\perp}D_0=A^\perp$. Its rank is $m-b$ and its
+nondegenerate polar form is unchanged by the mixed signs. The normal
+form above executes it as one child. Arbitrary auxiliary restoration
+justifies the endpoint normalization on the entire $B_2$ bank.
+
+Use the complex counts to define $B_i=NR_{h_i}/v_{h_i}$, and now
+\[
+\begin{aligned}
+W&=2N+B_2+B_3=10390178240000,\\
+L&=\sum_i(N/v_{h_i})h_i^2=117399987200,\\
+s&=Wm-2N+2L=398982681296998400.
+\end{aligned}
+\]
+The whole-residual macro list is
+\[
+\begin{array}{c|rrrrr}
+t&38328&38360&38370&37401&899\\\hline
+n_t&B_1&B_3-B_1&B_2&2N&2N.
+\end{array}
+\]
+Add $(N/v_h)H_{h,r}$ rank-$r$ children for each positive internal rank.
+Leave the remaining physical-data rank, 39393978624000, as singleton
+calls. The resulting list has weighted rank exactly $s$.
+For $a_c=3/125000$ and $\sigma=1-a_c$, the rational logarithm bounds
+above and $e^u\le(1-u)^{-1}$, $0\le u<1$, give
+\[
+ \Psi_c(\sigma)\le\sum_t\frac{n_tt}{Wm(1-a_c\ell_t)}
+ <1-\frac{792981575160764}{10^{23}}.
+\]
+
+\subsection{The dependency-path guard}
+Before gauging, nested producer labels telescope along every arithmetic
+path, including wire switches at common-frame scalar gates. Retained
+center drops occur on one return frontier per stage, crossed at most
+once by a path, and each costs at most that axis dimension. Carrier
+reuse adds only increasing continuations. This gives
+$q_0=m+2(a+b+k)$. Gauging removes an early edge and adds $ab-b$ at
+a late stage-two edge. A path meets at most one such edge, since it
+terminates that stage-two role, which is not shared across stages.
+Thus the conservative total rank budget is
+\[
+ q=m+2(a+b+k)+ab=39564.
+\]
+Every child except the four large macros is at most 899; two large
+macros cannot fit within $q$. Set $\rho=19/10$, $\gamma=9997/10000$.
+The integer comparisons $m^{19}>500000000^{10}$ and
+$899^9<460^{10}$ give $m^\rho>500000000$ and
+$899^{\rho-1}<460$.
+If a path has one large child $t$, its moment is at most
+\[
+ (t/m)^\rho+(q-t)899^{\rho-1}/m^\rho.
+\]
+This expression increases over the large-child range, since its
+numerator derivative is $\rho t^{\rho-1}-899^{\rho-1}>0$.
+Use $t=m-b$ and the concavity bound
+$(1-x)^{19/10}\le1-19x/10+9x^2/10$ to obtain
+\[
+ \sum_{\rm path}(r/m)^\rho
+ <1-\frac{19}{12800}+\frac9{10\cdot1280^2}
+       +\frac{1194\cdot460}{500000000}
+ =\frac{51180270301}{51200000000}<\gamma.
+\]
+Without a large macro the bound is $227493/6250000<\gamma$.
+
+For coefficient-depth accounting take $E_0=128(W+m+1)^3$.
+There are at most $s$ positive-rank residual calls and $W$ endpoint
+normalizations. Combining the quadratic phases with the $S$ factors,
+each uses at most two diagonal phase passes and one scalar phase.
+The inherited gate and remainder count is therefore bounded conservatively by
+\[
+ 36W^3+16s+16W+8m+4<E_0.
+\]
+Binary address changes only permute coefficients; descriptor evaluation
+is paid by the retained packed record work and does not increase
+coefficient depth.
+Stop below width $d^\beta$, where $\beta=1/1000$.
+For $e=mf+r$, $0\le r<m$, recurse on $tf$ and treat the remainder
+individually. For sufficiently large $d$, a leaf descending from an
+internal node has width at least $d^\beta/(2m)$. Choose
+$C_{\rm dep}\ge16m$ and
+$(1-\gamma)C_{\rm dep}\ge E_0+16m+1$.
+The retained elementary-kernel bound $A(e)\le8e$ and strong induction
+using the path moment imply
+\[
+ A(e)\le C_{\rm dep}d^{-\beta(\rho-1)}e^\rho.
+\]
+At a leaf the lower width bound proves this inequality, while at an
+internal node the unused $1-\gamma$ fraction covers local work.
+Small roots are handled directly. With $\zeta=1/10000$ take
+\[
+ C_1=\rho-(\rho-1)\beta+\zeta=\frac{1187}{625},\quad
+ C_0=\left\lceil128m(1+1/\zeta)C_{\rm dep}\right\rceil,
+ \quad\Delta=\lceil C_0d^{C_1}\rceil.
+\]
+The retained exact denominator/magnitude-depth induction gives
+$p+\Delta$ fractional bits and $\Delta+3$ integer/sign bits.
+All selected scalar coefficients are Gaussian dyadic and the new
+wrappers have modulus one, so that induction still applies.
+For $\epsilon C_1<1$ their total width is $O(p)$.
+\subsection{Rows, stopping, and transfer to the layer interface}
+Let $t_*<m$ be the largest child and compute
+$D(e)=0$ for $e<m$ and $D(e)=1+D(t_*\lfloor e/m\rfloor)$ otherwise.
+It is $O(\log e)$ and bounds every descendant depth.
+With the retained compact-control parameters, reserve
+\[
+ q_0=\lceil\log_2W\rceil D(d),\qquad Q_0=q_0+q_F+q_B.
+\]
+Process the first $q_0+q_F$ and last $q_B$ selected axes individually;
+if at most $Q_0$ axes exist, process them all individually. Otherwise
+the middle active interval is consecutive. Only the $q_0$ row chunks
+supply row indices, separate from the two compact fields. Pad their
+count once to a multiple of $W^{D(d)}$, by a factor below two.
+Every child retains complete compact and spectator ranges and has
+exactly $1/W$ of its parent's volume. No internal padding is needed.
+The reserved-axis bound remains
+\[
+ Q_0=O(\log(2d)+d^{\max\{1-c,0\}}\log p+1).
+\]
+Remainders commute with the completed tensor map and cost $O(V)$ per
+node. The fixed-tape depth-first scheduler and complete-row argument
+of the bit construction apply with the retained compact descriptors.
+
+Since $\Psi_c(\sigma)<1$, the total leaf $\sigma$-weighted width,
+including the volume factor $W^{-j}$ at depth $j$, is at most
+$d^\sigma$. Thus leaf work is
+$O(d^{\sigma+\beta(1-\sigma)})$. Internal compact operations cost
+$O(G^\tau e^\tau+1)$ per current volume. Summing the strict moments
+gives the retained complete normalized layer bound
+\[
+ O\!\left((\log p)^3\left[
+ d^\chi+d^{\sigma+\beta(1-\sigma)}+d^{\max\{1-c,0\}}+1
+ \right]\right),\qquad
+ \chi=\tau+(1-\beta)\max\{\sigma-\tau,0\}.
+\]
+For $\sigma\le\tau$, use $\Psi_c(\tau)\le\Psi_c(\sigma)$;
+otherwise use $e^\tau\le d^{\beta(\tau-\sigma)}e^\sigma$ at each
+internal node. These arguments do not assume equal leaf depth.
+The usual strict conditions on $\lambda,\lambda'$ therefore give
+the retained $O(Vd^{\lambda'})$ layer interface, now with the new
+moment and the new $C_{\rm dep}$.
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/retained/general-clifford-frames.tex b/research/five-stage-p10-transcript-stages/inputs/complex/retained/general-clifford-frames.tex
new file mode 100644
index 0000000000..0367eeb005
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/retained/general-clifford-frames.tex
@@ -0,0 +1,102 @@
+\subsection{Preimage frames for arbitrary binary subspaces}
+This frame construction is due to icekylinx with OpenAI GPT-6 Astra assistance;
+the present exposition and integration use Codex.
+Let $H=\mathbb F_2^h$ with the standard dot product. In the binary
+symplectic space $H\oplus H$ put
+\[
+ L_0=\{(0,z)\},\qquad
+ F=\begin{pmatrix}I&I\\0&I\end{pmatrix},\qquad
+ L_F=FL_0=\{(z,z)\}.
+\]
+We also write $F$ for the exact Gaussian-dyadic operator $C^{\otimes h}$.
+Its exact square is a Pauli translation; only its binary symplectic square
+is the identity. For an exact Clifford operator $T$ the frame label is
+$L(T)=T^{-1}L_0$. The physical transition from $T$ to $S$ is $ST^{-1}$,
+and its Fourier rank is
+$d(L(S),L(T))$, where $d(L,L')=h-\dim(L\cap L')$.
+This follows by transporting the intersection by $S$: the intersection
+with $L_0$ computes the kernel dimension of the $B$ block of $ST^{-1}$.
+
+\begin{lemma}
+For every subspace $U\subseteq H$, including degenerate subspaces,
+\[
+ L_U=\{(u,u+v):u\in U,\ v\in U^\perp\}
+\]
+is Lagrangian, and
+\[
+ d(L_U,L_V)=\dim U+\dim V-2\dim(U\cap V),\qquad
+ FL_U=L_{U^\perp}.
+\]
+\end{lemma}
+\begin{proof}
+The displayed parametrization is injective and has dimension $h$.
+Its symplectic pairing is $u\cdot v'+v\cdot u'=0$.
+In an intersection, $u$ belongs to $U\cap V$ and $v$ to
+$(U+V)^\perp$, giving the asserted dimension and distance.
+Finally $F(u,u+v)=(v,u+v)$ proves the complement identity.
+\end{proof}
+
+\subsection{Exact representatives and nested children}
+Choose a deterministic invertible binary matrix $G$ carrying the first
+$r=\dim U$ coordinate space $E_r$ to $U$, and set
+\[
+ K_G=\begin{pmatrix}G&0\\G+G^{-T}&G^{-T}\end{pmatrix},\qquad
+ T_U=K_G T_{E_r}K_G^{-1}.
+\]
+Here $T_{E_r}$ is the exact coordinate $C$ operator, and the $K_G$ are
+exact Gaussian-dyadic Clifford lifts. The matrix $K_G$ is symplectic
+because $G^TG+I$ is symmetric. It fixes both $L_0,L_F$ and maps $L_V$
+to $L_{GV}$. Thus both $K_G$ and $FK_GF^{-1}$ have Fourier rank zero;
+their lifts are fixed binary address permutations with unit quadratic
+phases. In particular,
+\[
+ L(T_U)=L_U,\quad \operatorname{rank}B(T_U)=r,\quad
+ \operatorname{rank}B(FT_UF^{-1})=r,\quad T_U^2\text{ is Pauli}.
+\]
+Set $V_U=GE_r^\perp$, a direct complement of $U$. The binary action gives
+$T_U^{-1}L_F=L_{V_U}$ and hence
+$\operatorname{rank}B(FT_U^{-1})=h-r$.
+No assertion $V_U=U^\perp$ is needed.
+For the norm-one source lines and their orthogonal target hyperplanes,
+retain the inherited exact representatives; set $T_0=I,T_H=F$.
+At every common scalar gate use one identical exact representative on all
+incident registers. If separately transported representatives have the
+same preimage, their physical ratio has rank zero and is implemented as
+an actual left adapter before the gate.
+
+For $U\subseteq V$, the exact transition $T_VT_U^{-1}$ has rank
+$\dim V-\dim U$. Clifford elimination expresses it as two rank-zero
+adapters surrounding that many coordinate Fourier factors. These factors
+are a single $C^{\otimes r}$ child: the scaled Hadamard satisfies
+\[
+ \frac{1+i}{2}\begin{pmatrix}1&1\\1&-1\end{pmatrix}
+   =SCS,\qquad S=\operatorname{diag}(1,i).
+\]
+Thus no new irrational field is introduced. All adapters are charged
+finite movement and scalar operations. Exact transitions telescope;
+commutativity between distinct $T_U$ is unnecessary.
+
+\subsection{Dirty tails and reverse/complement words}
+A dirty role entering with gauge $T_\sigma$ and whose last active frame
+is $T_U$, with $\sigma\subseteq U$, is assigned terminal gauge
+$FT_\sigma$. Its logical value is restored by the complete transparent
+scalar word, so its physical action is exactly $F$. The tail is
+$FT_\sigma T_U^{-1}$. Its rank is
+\[
+ d(L_U,L_{V_\sigma})=h-\dim U+\dim\sigma.
+\]
+Indeed $H=\sigma\oplus V_\sigma$ and $U\supseteq\sigma$ imply
+$\dim(U\cap V_\sigma)=\dim U-\dim\sigma$.
+An inactive exterior adds $m-h$, giving $m-\dim U+\dim\sigma$.
+
+For the complete time-reversed word use
+\[
+ D_U=T_UF^{-1},\qquad L(D_U)=L_{U^\perp},\qquad
+ D_UD_V^{-1}=T_UT_V^{-1}.
+\]
+The last equality is exact, so reversal preserves every inverse transition
+rank. Reverse the scalar signs and the whole transparent word, including
+old-value corrections and final cleanup. The endpoints $D_0=F^{-1}$
+and $F$ differ by a Pauli, and the inherited norm-one endpoints are
+reconciled by actual rank-zero adapters. Neither equality of binary
+matrices nor equality of frame cosets substitutes for these operators.
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/retained/stopped-product-complex.tex b/research/five-stage-p10-transcript-stages/inputs/complex/retained/stopped-product-complex.tex
new file mode 100644
index 0000000000..4a9037137c
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/retained/stopped-product-complex.tex
@@ -0,0 +1,137 @@
+\subsection{All-disjoint retained centers}
+Use two factors $h=24$. For triple inputs write $G=\sum_TX_T$,
+$T_i=\sum_{T\ni i}X_T$, and retain all $A_i=G-T_i$.
+Each input triple avoids exactly 21 points, so
+\[
+ \sum_{i=1}^{24}A_i=21G,\qquad G=\frac1{21}\sum_i A_i.
+\]
+For a target triple $S$ the central correction is
+\[
+ G-\frac12\sum_{i\in S}A_i
+       =\frac{\sum_{i\in S}T_i-G}{2}.
+\]
+An input triple meeting $S$ in $j$ points has central coefficient
+$(j-1)/2$. Adding half the disjoint sum and subtracting half the
+intersection-two sum leaves coefficient one exactly when $j=3$.
+The scalar source-to-scatter transfer is therefore the identity.
+The transparent old-value subtraction and new-value addition use this
+identity only on fresh contributions and restore arbitrary old values.
+
+The base-two paired exclusion and aligned pair-star producer retains
+nested binary labels: common-pair supports have their orthonormal triple
+span, other ordinary sums have their coordinate cover. Each retained
+$A_i$ has the nondegenerate coordinate hyperplane excluding $i$,
+of dimension 23. Hence all copied-center arguments and general
+nondegenerate binary residuals of the preceding proof apply. The
+selected local counts are
+\[
+ v=2024,\quad c_h=45764,\quad q_h=8120,\quad
+ |\mathcal M|=8966,\quad R=44918,\quad\ell=552.
+\]
+The old internal histogram, starting at rank zero, is
+\begin{small}\begin{align*}
+[&8930,49042,30844,15972,11883,8272,6399,4356,6682,2263,\\
+ &5109,1808,5317,1733,5391,1757,4908,3290,6233,4363,\\
+ &4056,264,564,24,24].
+\end{align*}\end{small}
+It has rank mass $24R+2\ell$. Replace 24 rank-24 original transitions
+by 24 rank-one transitions; all rank-23 copied transforms remain.
+The new mass is $24R+\ell$.
+
+\subsection{Physical endpoints and strict complex moment}
+The copied-center two-stage complex contract in
+\path{notes/copied-centers-complex.tex} is unchanged by the scalar
+center decoding. For the tensor triple line $U$, let
+$T=C_U$, $F=C_I$, $E=C_{U^\perp}=FT^{-1}$.
+The two data outputs are $A=-Fy$ and $B=FT^{-2}x+Ey$.
+Add $T^{-1}$ applied to a copy of $A$ into $B$, paying one rank-one
+child per data pair. The inherited input/output $Z$ phases and
+$i^{9f}$ scalar normalize $FT^{-2}$ to $F$; sign and bank corrections
+complete the exact tensor $C$. Auxiliary source/sink operators remain
+$C_{D_0}$ and $FC_{D_0}$ in the second stage. Every original role
+therefore returns the exact selected-axis tensor operation on arbitrary
+inputs. This algebraic statement holds over $\mathbb Q(i)$ as well as
+over Gaussian dyadics.
+
+With $m_c=576$, $N_c=v^2=4096576$, $B_c=vR=90914032$, put
+\[
+ W_c=2N_c+2B_c=190021216,\quad L_c=2v\ell=2234496,
+\]
+\[
+ s_c=W_cm_c-N_c+L_c=109450358336,\qquad N_c-L_c=1862080.
+\]
+The complete list is $2B_c$ width-552 auxiliary exteriors,
+$2N_c$ width-529 data macros, $2vH'_r$ width-$r$ internal children,
+$4N_c$ width-23 data fronts, and $N_c$ width-one endpoint copies.
+These disjoint classes include both kinds of paid copies and sum to
+$s_c$. All binary residuals, including alternating forms, use the retained
+one-child Gauss normal form with paid bit adapters and unit phases.
+At $a_c=1949/25000000$ the exact rational enclosure gives
+\[
+ \sum_r\frac{n_r}{W_c}(r/m_c)^{1-a_c}
+ <1-1.3338373969\times10^{-10}.
+\]
+
+\subsection{One exact odd-denominator grid}
+The only new odd divisor is 21. Let $d$ bound the root axis count,
+$D$ bound its maximum complex recursion depth, and $G_0$ bound the
+number of grouped scalar operations per node. Choose
+\[
+ K=G_0(D+1),\qquad \text{common grid }2^{-P}21^{-K}.
+\]
+Root inputs and arbitrary dirty auxiliaries start Gaussian dyadic.
+Multiply their integer numerators by $21^K$ once at the outer boundary.
+Every local coefficient contains at most one factor 21 in its denominator,
+so a local finite program adds at most $G_0$ to the odd-denominator
+exponent. A completed $u$-axis child has Gaussian-dyadic coefficients
+and therefore preserves its input's existing odd-denominator exponent;
+it adds no new odd factor. Only the active chain of unfinished calls
+can accumulate new factors. Its length is at most $D+1$, proving that
+all intermediates lie on the common grid and every local division by
+21 is an exact integer division of its encoded numerator.
+
+This divisibility claim uses the root dyadic-input invariant, not an
+assumption about arbitrary numerators on the finest grid. Internal values
+may have odd denominators. They are neither rounded nor re-encoded when
+a child returns. At the completed outer return the operator is the exact
+Gaussian-dyadic tensor on root dyadic inputs, so the final numerators
+are divisible by $21^K$; exact unscaling restores dyadic encoding.
+
+Since the largest child is $552<576$, $D=O(\log d)$ and
+$K=O(\log d)$ with fixed constants. Constant-divisor long division
+is linear in numerator length. Initial and final scaling by $K$
+successive constant multiplications/divisions cost $O(V\log d)$ and
+occur only at the outer boundary. The extra numerator length is
+$O(\log d)$, preserving the retained $O(p)$ word bound. This overhead
+is subordinate to the positive-power complex layer bound.
+
+For explicit semantic constants use
+\[
+ g_h=4(c_h+v)+10v+4hv+4h^2+8h+8=408200,
+\]
+\[
+ G_0=N_c+2v(g_h+2h)=1656684480,
+\]
+where endpoint additions and copied-center scalar work are included.
+The complete child contributes at most $u$ binary denominator bits
+and row-norm factor $2^u$, with no additional odd exponent. A local
+21-division contributes fewer than five denominator-height bits,
+covered by the fixed scalar charge. Set
+\[
+\begin{aligned}
+ E_0&=64(W_c+m_c+G_0+1)^3=403063477262941121443761178688,\\
+ \mathcal E&=2G_0W_c^2+8s_c+4W_c+4+32m_c\\
+           &=119639333593035096270287748<E_0,\\
+ B_0&=s_c+E_0,\qquad C_0=32m_cB_0^2.
+\end{aligned}
+\]
+With $f=\lfloor e/m_c\rfloor$, the completed-child induction is
+\[
+ A(e)\le A(552f)+s_cf+E_0\le2B_0e,
+\]
+since $2B_0(m_c-552)\ge s_c+E_0$. It counts total denominator height
+and magnitude, including the local odd factor. The retained prefix and
+normalization allowance $18e$ fits inside $C_0e$. Together with the
+$O(\log d)$ common-grid encoding overhead this gives $C_1=1$ and
+$O(p)$ records for $d=\lfloor b_{\rm in}^{\epsilon}\rfloor$,
+$p=6b_{\rm in}$, fixed $\epsilon<1$.
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/source-pins.json b/research/five-stage-p10-transcript-stages/inputs/complex/source-pins.json
new file mode 100644
index 0000000000..f6eada0a6d
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/source-pins.json
@@ -0,0 +1,221 @@
+{
+  "schema": "primary-complex-input-pins/1",
+  "certificate": {
+    "compressed_sha256": "bb0499ab342aee3594904fc1cd72b9ff496cdb315d0840f4cdd5ba64ef794d34",
+    "uncompressed_sha256": "91c349b9680b023449d3bc4fb58f00a22c9d9f38b776ae3a3597259431de78eb",
+    "path": "inputs/complex/gcert1-p11-cmod-centre-mw-flow.json.gz"
+  },
+  "files": {
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+      "upstream": "Work/Bridge/Cert.lean",
+      "source_pin": "f010392c923279e3dd59ef3aa5fedad23affc5fd",
+      "url": "https://github.com/jacobalansussman/wht-power-saving-lean/blob/f010392c923279e3dd59ef3aa5fedad23affc5fd/Work/Bridge/Cert.lean"
+    },
+    "inputs/complex/sources/Work__Bridge__Net.lean": {
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+    },
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+      "sha256": "6f3dc8bb639933227a8dae181ec4a542e85c7276be9c9e330f49518e7b630b95",
+      "upstream": "tools/gx/gx.py",
+      "source_pin": "f010392c923279e3dd59ef3aa5fedad23affc5fd",
+      "url": "https://github.com/jacobalansussman/wht-power-saving-lean/blob/f010392c923279e3dd59ef3aa5fedad23affc5fd/tools/gx/gx.py"
+    }
+  }
+}
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Bridge__Cert.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Bridge__Cert.lean
new file mode 100644
index 0000000000..f7bdc3d903
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Bridge__Cert.lean
@@ -0,0 +1,241 @@
+import Work.Bridge.Net
+
+/-!
+# (key: bridge-net) The certificate of the BRIDGED five-stage network B_2
+
+The three layers of free gates between twins, the signed exchange, and
+
+    theorem bridge2_certificate (N : Bridge2 H T Sl C α Γ) :
+        BCert α (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C) (fun φ => card Γ * N.unit φ)
+
+Scalar chain of one class (`x1 y1 x2 y2` on `X1 Y1 X2 Y2`), as in `bridged-word.md`:
+
+    stage 0  F on pair 1     Y1 = y1 + x1
+    stage 1  B on pair 1     X1 = -y1
+    gates A  X1 += X2,  Y2 -= Y1
+    stage 2  F on pair 1     Y1 = x1 + x2
+    gates B  Y2 += Y1,  X1 -= X2          (X1 = -y1, Y2 = y2 - y1 + x2)
+    stage 3  B on pair 2     X2 = y1 - y2
+    stage 4  F on pair 2     Y2 = x2
+    gates C  Y1 -= Y2,  X2 += X1          (X1 = -y1, X2 = -y2, Y1 = x1, Y2 = x2)
+    exchange X_i := Y_i, Y_i := -X_i
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace BR
+open Binary Matrix Finset RAM SS CB RF
+noncomputable section
+
+section Gates
+variable {Γ T Sl C : Type}
+
+/-- source of the gates of the layers A and B: `X1 ← X2`, `Y2 ← Y1`. -/
+def pAB : BRole Γ T Sl C → BRole Γ T Sl C :=
+  mkB (fun g t => kX2 (g,t)) (fun g t => kY1 (g,t)) (fun g t => kX2 (g,t))
+    (fun g t => kY1 (g,t)) (fun g q => kS (g,q)) (fun g c => kC (g,c))
+
+/-- layer A: `X1 += X2`, `Y2 -= Y1`. -/
+def kA : BRole Γ T Sl C → ℚ :=
+  mkB (fun _ _ => 1) (fun _ _ => 0) (fun _ _ => 0) (fun _ _ => -1) (fun _ _ => 0) (fun _ _ => 0)
+
+/-- layer B: `X1 -= X2`, `Y2 += Y1`. -/
+def kB : BRole Γ T Sl C → ℚ :=
+  mkB (fun _ _ => -1) (fun _ _ => 0) (fun _ _ => 0) (fun _ _ => 1) (fun _ _ => 0) (fun _ _ => 0)
+
+/-- source of the gates of the layer C: `Y1 ← Y2`, `X2 ← X1`. -/
+def pC : BRole Γ T Sl C → BRole Γ T Sl C :=
+  mkB (fun g t => kX1 (g,t)) (fun g t => kY2 (g,t)) (fun g t => kX1 (g,t))
+    (fun g t => kY2 (g,t)) (fun g q => kS (g,q)) (fun g c => kC (g,c))
+
+/-- layer C: `Y1 -= Y2`, `X2 += X1`. -/
+def kCc : BRole Γ T Sl C → ℚ :=
+  mkB (fun _ _ => 0) (fun _ _ => -1) (fun _ _ => 1) (fun _ _ => 0) (fun _ _ => 0) (fun _ _ => 0)
+
+/-- scalar map of a gate layer. -/
+def gsc (p : BRole Γ T Sl C → BRole Γ T Sl C) (k : BRole Γ T Sl C → ℚ)
+    (x : BRole Γ T Sl C → ℂ) : BRole Γ T Sl C → ℂ := fun i => x i + (k i : ℂ) * x (p i)
+
+/-- the signed exchange `X_i := Y_i`, `Y_i := -X_i` on both pairs. -/
+def bpull : BRole Γ T Sl C → BRole Γ T Sl C :=
+  mkB (fun g t => kY1 (g,t)) (fun g t => kX1 (g,t)) (fun g t => kY2 (g,t))
+    (fun g t => kX2 (g,t)) (fun g q => kS (g,q)) (fun g c => kC (g,c))
+
+def bsgn : BRole Γ T Sl C → ℚ :=
+  mkB (fun _ _ => 1) (fun _ _ => -1) (fun _ _ => 1) (fun _ _ => -1) (fun _ _ => 1) (fun _ _ => 1)
+
+variable [Fintype Γ] [DecidableEq Γ] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+
+def brecM : Matrix (BRole Γ T Sl C) (BRole Γ T Sl C) ℚ :=
+  fun i j => if j = bpull i then bsgn i else 0
+
+lemma actPoint_brecM (x : BRole Γ T Sl C → ℂ) (i : BRole Γ T Sl C) :
+    actPoint brecM x i = (bsgn i : ℂ) * x (bpull i) := by
+  unfold actPoint
+  rw [sum_eq_single (bpull i)]
+  · simp [brecM]
+  · intro j _ hj; simp [brecM, hj]
+  · simp
+
+/-- the scalar map of the whole network before the exchange, on one class. -/
+def chain (x : BRole Γ T Sl C → ℂ) : BRole Γ T Sl C → ℂ :=
+  gsc pC kCc (lift2 GF (lift2 GB (gsc pAB kB (lift1 GF (gsc pAB kA (lift1 GB (lift1 GF x)))))))
+
+/-- **The scalar identity of the bridged chain**: `X_i = -y_i`, `Y_i = x_i` on both pairs,
+helper slots unchanged. -/
+lemma chain_eq (x : BRole Γ T Sl C → ℂ) (l : BLive Γ T Sl) :
+    chain x (Sum.inl l) = mkB (fun g t => -x (kY1 (g,t))) (fun g t => x (kX1 (g,t)))
+      (fun g t => -x (kY2 (g,t))) (fun g t => x (kX2 (g,t)))
+      (fun g q => x (kS (g,q))) (fun g c => x (kC (g,c))) (Sum.inl l) := by
+  rcases l with (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+  all_goals
+    simp only [chain, gsc, lift1, lift2, GF, GB, mkB, mkS, pAB, pC, kA, kB, kCc, pos1, pos2,
+      kX1, kY1, kX2, kY2, kS, kC, jX, jY, jS, jC, Function.comp_apply]
+    first
+      | (push_cast; ring)
+      | (push_cast; done)
+      | ring
+
+end Gates
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : Bridge2 H T Sl C α Γ)
+
+/-- gate layer A, after stage 1 and the first idle climb of pair 2: twins have equal frames. -/
+lemma Bridge2.gateA : XRoute N.S3 N.S3 (gsc pAB kA) (fun _ => 0) := by
+  refine gateP pAB kA N.S3 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- gate layer B, after stage 2 and the second idle climb of pair 2. -/
+lemma Bridge2.gateB : XRoute N.S5 N.S5 (gsc pAB kB) (fun _ => 0) := by
+  refine gateP pAB kB N.S5 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · exact N.x23 g t
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · exact (N.y23 g t).symm
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- gate layer C, after the final climbs. -/
+lemma Bridge2.gateC : XRoute N.S8 N.S8 (gsc pC kCc) (fun _ => 0) := by
+  refine gateP pC kCc N.S8 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · exact (hk rfl).elim
+  · rfl
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- the free shifts at the end. -/
+def Bridge2.corr : BRole Γ T Sl C → Space α :=
+  mkB (fun _ _ => 0) (fun g t => N.u g t) (fun _ _ => 0) (fun g t => N.u g t)
+    (fun _ _ => 0) (fun _ _ => 0)
+
+def Bridge2.S9 : BRole Γ T Sl C → CMat α := fun r => shift (N.corr r) * N.S8 r
+
+/-- the whole word before the exchange: five stages, three idle-climb layers, three gate
+layers. -/
+lemma Bridge2.route :
+    XRoute N.S0 N.S8 chain (fun φ => (Fintype.card Γ : ℝ) * N.unit φ) := by
+  have R := ((((((((((N.stage0.trans N.stage1).trans N.climbA).trans N.gateA).trans
+    N.stage2).trans N.climbB).trans N.gateB).trans N.stage3).trans N.stage4).trans
+    N.fin).trans N.gateC)
+  refine (R.castg ?_).cast (fun φ => ?_)
+  · rfl
+  · simp only [Bridge2.unit]
+    ring
+
+/-- **The scratch certificate of the bridged five-stage network with shared helper sets**,
+in whole blocks, with its exact price for every price list. -/
+theorem bridge2_certificate :
+    BCert α (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C)
+      (fun φ => (Fintype.card Γ : ℝ) * N.unit φ) := by
+  have R2 : XRoute N.S8 N.S9 id (fun _ => 0) := XRoute.shifts N.hm N.S8 N.corr
+  have R3 : XRoute N.S9 (fun r => N.S9 (bpull r)) (actPoint brecM) (fun _ => 0) :=
+    XRoute.gate brecM N.S9 _ (fun i j h => by
+      have hj : j = bpull i := by
+        by_contra hne
+        exact h (by simp [brecM, hne])
+      rw [hj])
+  have Rt := ((N.route.trans R2).trans R3).cast (c' := fun φ => (Fintype.card Γ : ℝ) * N.unit φ)
+    (fun φ => by first | ring | simp)
+  have hSinv : ∀ r, ∃ M, N.S0 r * M = 1 := by
+    rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.inv0 g t
+    · refine ⟨1, ?_⟩
+      show (N.M0 g).Φ 0 * 1 = 1
+      rw [N.z0, Matrix.mul_one]
+    · exact N.inv0 g t
+    · refine ⟨1, ?_⟩
+      show (N.M0 g).Φ 0 * 1 = 1
+      rw [N.z0, Matrix.mul_one]
+    · exact ⟨1, Matrix.mul_one _⟩
+    · exact ⟨1, Matrix.mul_one _⟩
+  choose S' hS' using hSinv
+  have hT : ∀ l : BLive Γ T Sl, N.S9 (bpull (Sum.inl l)) = kernel α * N.S0 (Sum.inl l) := by
+    rintro (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+    · show shift (N.u g t) * N.YF g t = kernel α * (N.M0 g).Φ (tt (N.I.tv t))
+      exact (N.term g t).symm
+    · show shift (0 : Space α) * kernel α = kernel α * (N.M0 g).Φ 0
+      rw [shift_zero, Matrix.one_mul, N.z0, Matrix.mul_one]
+    · show shift (N.u g t) * N.YF g t = kernel α * (N.M0 g).Φ (tt (N.I.tv t))
+      exact (N.term g t).symm
+    · show shift (0 : Space α) * kernel α = kernel α * (N.M0 g).Φ 0
+      rw [shift_zero, Matrix.one_mul, N.z0, Matrix.mul_one]
+    · show shift (0 : Space α) * kernel α = kernel α * 1
+      rw [shift_zero, Matrix.one_mul, Matrix.mul_one]
+  have hg : ∀ x : BRole Γ T Sl C → ℂ,
+      (∀ s, (∀ l : BLive Γ T Sl, (Sum.inl l : BRole Γ T Sl C) ≠ s) → x s = 0) →
+      ∀ l : BLive Γ T Sl,
+        (actPoint brecM ∘ (id ∘ chain)) x (Sum.inl l) = x (Sum.inl l) := by
+    intro x _ l
+    change actPoint brecM (chain x) (Sum.inl l) = _
+    rw [actPoint_brecM]
+    rcases l with (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inl (Sum.inr (g,t))))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kX1 (g,t)) = x (kX1 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((-1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inl (Sum.inl (g,t))))) = _
+      rw [chain_eq]
+      show ((-1:ℚ):ℂ) * (-x (kY1 (g,t))) = x (kY1 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inr (Sum.inr (g,t))))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kX2 (g,t)) = x (kX2 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((-1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inr (Sum.inl (g,t))))) = _
+      rw [chain_eq]
+      show ((-1:ℚ):ℂ) * (-x (kY2 (g,t))) = x (kY2 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inr (g,q))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kS (g,q)) = x (kS (g,q))
+      first | (push_cast; ring) | simp
+  exact XRoute.liveKernel (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C) N.S0 S'
+    (fun r => N.S9 (bpull r)) hS' _ _ Rt hg hT
+
+end Net
+end
+end BR
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.BR.chain_eq
+#print axioms OAI.PowerSaving.BR.Bridge2.route
+#print axioms OAI.PowerSaving.BR.bridge2_certificate
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Bridge__Net.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Bridge__Net.lean
new file mode 100644
index 0000000000..204f6d9cf9
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Bridge__Net.lean
@@ -0,0 +1,345 @@
+import Work.Bridge.Inv
+
+/-!
+# (key: bridge-net) The BRIDGED five-stage network B_2 with shared helper sets, abstract form
+
+Generalises `RF.Fold3S` / `RF.fold3s_certificate` (`Work.Reframe.SCert`) to the bridged word
+of PLAN2.md B1: every class `(g,t)` has TWO bank pairs `(X1,Y1)`, `(X2,Y2)` with the same
+line; five stages of invocations
+
+    stage 0  forward   on pair 1      invocation of the class (g,t):  g
+    stage 1  backward  on pair 1                                      r1 t g
+    stage 2  forward   on pair 1                                      r2 t g
+    stage 3  backward  on pair 2                                      r3 t g
+    stage 4  forward   on pair 2                                      r4 t g
+
+and three layers of FREE gates between twins at equal frames:
+
+    after stage 1 (pair 2 has climbed to the frames of pair 1):   X1 += X2,  Y2 -= Y1
+    after stage 2 (pair 2 has climbed one more window):           Y2 += Y1,  X1 -= X2
+    after the final climbs (all four roles at their end frames):  Y1 -= Y2,  X2 += X1
+
+Result on both pairs: `X_i = -y_i`, `Y_i = x_i`; then the usual signed exchange.
+
+The idle pair does not move during a stage.  Its climbs are ONE block per role:
+`aX2`, `aY2` (pair 2 before the first gate layer, prices `caX`, `caY`; in B_2 ONE block of
+rank `2h-2` each),
+the window of stage 2 (pair 2 before the second gate layer, rank `card H - 1`, from the
+package: `Inv.climbX`, `Inv.climbY`), `fX1`, `fY1` (pair 1 at the end, prices `cX1`, `cY1`;
+in B_2 ONE block of rank `2h+2` each), `fX2`, `fY2` (pair 2 at the end, prices `cX2`, `cY2`;
+in B_2 one block of rank `4` each).  The prices are arbitrary functions of the price list, so
+a geometry that makes an idle climb in several blocks can be plugged in as well.
+
+`Bridge2 H T Sl C α Γ` is everything the wiring needs to know about the geometry;
+`bridge2_certificate`: a `BCert` on the live roles `BLive Γ T Sl`
+(`card Γ * (4 card T + card Sl)` of them, `BR.card_BLive`) whose price, for EVERY price
+list, is `card Γ * N.unit φ`,
+
+    N.unit φ = 5 * N.I.cost φ + card T * ((caX φ + caY φ) + 2 * bcost φ (card H - 1)
+                 + (cX1 φ + cY1 φ) + (cX2 φ + cY2 φ)).
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace BR
+open Binary Matrix Finset RAM SS CB RF
+noncomputable section
+
+/-- See the file header.  Fields in the style of `RF.Fold3S`; stages are numbered 0 to 4. -/
+structure Bridge2 (H T Sl C α Γ : Type) [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α] where
+  /-- the invocation (for a block circuit `X`: `X.inv`). -/
+  I : Inv H T Sl C
+  /-- frame maps of the invocations of the five stages. -/
+  M0 : Γ → XMap H α
+  M1 : Γ → XMap H α
+  M2 : Γ → XMap H α
+  M3 : Γ → XMap H α
+  M4 : Γ → XMap H α
+  /-- the class `(g,t)` is served by the invocation `g` in stage 0 and `r_l t g` in stage `l`. -/
+  r1 : T → Γ ≃ Γ
+  r2 : T → Γ ≃ Γ
+  r3 : T → Γ ≃ Γ
+  r4 : T → Γ ≃ Γ
+  /-- the invocation `d` of stage `l` uses the helper set (and the copies) `s_l d`. -/
+  s1 : Γ ≃ Γ
+  s2 : Γ ≃ Γ
+  s3 : Γ ≃ Γ
+  s4 : Γ ≃ Γ
+  /-- inverse of the frame of the base, and frame of the window, of every invocation. -/
+  N1 : Γ → CMat α
+  W1 : Γ → CMat α
+  N2 : Γ → CMat α
+  W2 : Γ → CMat α
+  N3 : Γ → CMat α
+  W3 : Γ → CMat α
+  N4 : Γ → CMat α
+  W4 : Γ → CMat α
+  u : Γ → T → Space α
+  YF : Γ → T → CMat α
+  hm : 2 ≤ Fintype.card α
+  /-- prices of the idle climbs, for every price list.  B_2 with merged climbs:
+  `caX = caY = fun φ => bcost φ (2h-2)`, `cX1 = cY1 = fun φ => bcost φ (2h+2)`,
+  `cX2 = cY2 = fun φ => bcost φ 4`. -/
+  caX : (ℕ → ℝ) → ℝ
+  caY : (ℕ → ℝ) → ℝ
+  cX1 : (ℕ → ℝ) → ℝ
+  cY1 : (ℕ → ℝ) → ℝ
+  cX2 : (ℕ → ℝ) → ℝ
+  cY2 : (ℕ → ℝ) → ℝ
+  inv0 : ∀ g t, ∃ N : CMat α, (M0 g).Φ (tt (I.tv t)) * N = 1
+  z0 : ∀ g, (M0 g).Φ 0 = 1
+  hN1 : ∀ d, (M1 d).Φ 0 * N1 d = 1
+  hW1 : ∀ d, (M1 d).Φ 1 = W1 d * (M1 d).Φ 0
+  hN2 : ∀ d, (M2 d).Φ 0 * N2 d = 1
+  hW2 : ∀ d, (M2 d).Φ 1 = W2 d * (M2 d).Φ 0
+  hN3 : ∀ d, (M3 d).Φ 0 * N3 d = 1
+  hW3 : ∀ d, (M3 d).Φ 1 = W3 d * (M3 d).Φ 0
+  hN4 : ∀ d, (M4 d).Φ 0 * N4 d = 1
+  hW4 : ∀ d, (M4 d).Φ 1 = W4 d * (M4 d).Φ 0
+  /-- the bank frames a stage leaves are the bank frames the next stage starts from. -/
+  x01 : ∀ g t, (M0 g).Φ 1 = (M1 (r1 t g)).Φ (tt (I.tv t))
+  y01 : ∀ g t, (M0 g).Φ (1 + tt (I.tv t)) = (M1 (r1 t g)).Φ 0
+  x12 : ∀ g t, (M1 (r1 t g)).Φ 1 = (M2 (r2 t g)).Φ (tt (I.tv t))
+  y12 : ∀ g t, (M1 (r1 t g)).Φ (1 + tt (I.tv t)) = (M2 (r2 t g)).Φ 0
+  x23 : ∀ g t, (M2 (r2 t g)).Φ 1 = (M3 (r3 t g)).Φ (tt (I.tv t))
+  y23 : ∀ g t, (M2 (r2 t g)).Φ (1 + tt (I.tv t)) = (M3 (r3 t g)).Φ 0
+  x34 : ∀ g t, (M3 (r3 t g)).Φ 1 = (M4 (r4 t g)).Φ (tt (I.tv t))
+  y34 : ∀ g t, (M3 (r3 t g)).Φ (1 + tt (I.tv t)) = (M4 (r4 t g)).Φ 0
+  /-- the five windows of a helper set make up the kernel. -/
+  sfin : ∀ g, W4 (s4.symm g) * (W3 (s3.symm g) * (W2 (s2.symm g) *
+    (W1 (s1.symm g) * (M0 g).Φ 1))) = kernel α
+  /-- pair 2, idle in stages 0 and 1: ONE block from its start frame to the frame of its
+  twin after stage 1. -/
+  aX2 : ∀ g t, XReach ((M0 g).Φ (tt (I.tv t))) ((M1 (r1 t g)).Φ 1) caX
+  aY2 : ∀ g t, XReach ((M0 g).Φ 0) ((M1 (r1 t g)).Φ (1 + tt (I.tv t))) caY
+  /-- pair 1, idle in stages 3 and 4: ONE block from its frame after stage 2 to the end. -/
+  fX1 : ∀ g t, XReach ((M2 (r2 t g)).Φ 1) (kernel α) cX1
+  fY1 : ∀ g t, XReach ((M2 (r2 t g)).Φ (1 + tt (I.tv t))) (YF g t) cY1
+  /-- pair 2 after stage 4: ONE final block. -/
+  fX2 : ∀ g t, XReach ((M4 (r4 t g)).Φ 1) (kernel α) cX2
+  fY2 : ∀ g t, XReach ((M4 (r4 t g)).Φ (1 + tt (I.tv t))) (YF g t) cY2
+  term : ∀ g t, kernel α * (M0 g).Φ (tt (I.tv t)) = shift (u g t) * YF g t
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : Bridge2 H T Sl C α Γ)
+
+/-- price of the blocks of one unit (one element of `Γ`): five invocations and the idle
+climbs of the four bank roles of every class. -/
+def Bridge2.unit (φ : ℕ → ℝ) : ℝ :=
+  5 * N.I.cost φ + (Fintype.card T : ℝ) * ((N.caX φ + N.caY φ)
+    + 2 * bcost φ (Fintype.card H - 1)
+    + (N.cX1 φ + N.cY1 φ) + (N.cX2 φ + N.cY2 φ))
+
+/-- scratch copies always enter and leave with the matrix `1` (also: the helper slots at the
+start, with `C := Sl`). -/
+def cOne (Γ C α : Type) [Fintype α] [DecidableEq α] : Γ → C → CMat α := fun _ _ => 1
+
+/-- the bank index of stage 0: the class `(g,t)` belongs to the invocation `g`. -/
+abbrev bid (Γ T : Type) : T → Γ ≃ Γ := fun _ => Equiv.refl Γ
+
+/-! bank frames of the class `(g,t)`: `xi l`, `yi l` at the START of stage `l`; `xo l`,
+`yo l` at the END of stage `l` (only where no next stage follows on that pair). -/
+def Bridge2.xi0 (g : Γ) (t : T) : CMat α := (N.M0 g).Φ (tt (N.I.tv t))
+def Bridge2.yi0 (g : Γ) (t : T) : CMat α := (N.M0 g).Φ 0
+def Bridge2.xi1 (g : Γ) (t : T) : CMat α := (N.M1 (N.r1 t g)).Φ (tt (N.I.tv t))
+def Bridge2.yi1 (g : Γ) (t : T) : CMat α := (N.M1 (N.r1 t g)).Φ 0
+def Bridge2.xi2 (g : Γ) (t : T) : CMat α := (N.M2 (N.r2 t g)).Φ (tt (N.I.tv t))
+def Bridge2.yi2 (g : Γ) (t : T) : CMat α := (N.M2 (N.r2 t g)).Φ 0
+def Bridge2.xo2 (g : Γ) (t : T) : CMat α := (N.M2 (N.r2 t g)).Φ 1
+def Bridge2.yo2 (g : Γ) (t : T) : CMat α := (N.M2 (N.r2 t g)).Φ (1 + tt (N.I.tv t))
+def Bridge2.xi3 (g : Γ) (t : T) : CMat α := (N.M3 (N.r3 t g)).Φ (tt (N.I.tv t))
+def Bridge2.yi3 (g : Γ) (t : T) : CMat α := (N.M3 (N.r3 t g)).Φ 0
+def Bridge2.xi4 (g : Γ) (t : T) : CMat α := (N.M4 (N.r4 t g)).Φ (tt (N.I.tv t))
+def Bridge2.yi4 (g : Γ) (t : T) : CMat α := (N.M4 (N.r4 t g)).Φ 0
+def Bridge2.xo4 (g : Γ) (t : T) : CMat α := (N.M4 (N.r4 t g)).Φ 1
+def Bridge2.yo4 (g : Γ) (t : T) : CMat α := (N.M4 (N.r4 t g)).Φ (1 + tt (N.I.tv t))
+
+/-- helper slots after the stages 0, 1, 2, 3, 4 (at the start: `cOne Γ Sl α`). -/
+def Bridge2.Z1 : Γ → Sl → CMat α := fun g _ => (N.M0 g).Φ 1
+def Bridge2.Z2 : Γ → Sl → CMat α := fun g q => N.W1 (N.s1.symm g) * N.Z1 g q
+def Bridge2.Z3 : Γ → Sl → CMat α := fun g q => N.W2 (N.s2.symm g) * N.Z2 g q
+def Bridge2.Z4 : Γ → Sl → CMat α := fun g q => N.W3 (N.s3.symm g) * N.Z3 g q
+def Bridge2.Z5 : Γ → Sl → CMat α := fun g q => N.W4 (N.s4.symm g) * N.Z4 g q
+
+/-- frames: at the start; after stage 0; after stage 1; after the first idle climb of pair 2
+(first gate layer here); after stage 2; after the second idle climb of pair 2 (second gate
+layer here); after stage 3; after stage 4; after the final climbs (third gate layer here). -/
+def Bridge2.S0 : BRole Γ T Sl C → CMat α := mkB N.xi0 N.yi0 N.xi0 N.yi0 (cOne Γ Sl α) (cOne Γ C α)
+def Bridge2.S1 : BRole Γ T Sl C → CMat α := mkB N.xi1 N.yi1 N.xi0 N.yi0 N.Z1 (cOne Γ C α)
+def Bridge2.S2 : BRole Γ T Sl C → CMat α := mkB N.xi2 N.yi2 N.xi0 N.yi0 N.Z2 (cOne Γ C α)
+def Bridge2.S3 : BRole Γ T Sl C → CMat α := mkB N.xi2 N.yi2 N.xi2 N.yi2 N.Z2 (cOne Γ C α)
+def Bridge2.S4 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi2 N.yi2 N.Z3 (cOne Γ C α)
+def Bridge2.S5 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi3 N.yi3 N.Z3 (cOne Γ C α)
+def Bridge2.S6 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi4 N.yi4 N.Z4 (cOne Γ C α)
+def Bridge2.S7 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xo4 N.yo4 N.Z5 (cOne Γ C α)
+def Bridge2.S8 : BRole Γ T Sl C → CMat α :=
+  mkB (fun _ _ => kernel α) N.YF (fun _ _ => kernel α) N.YF (fun _ _ => kernel α) (cOne Γ C α)
+
+/-- stage 0: forward on pair 1, every helper set starts at the matrix `1`. -/
+lemma Bridge2.stage0 :
+    XRoute N.S0 N.S1 (lift1 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := istage_fwd N.I (bid Γ T) (Equiv.refl Γ) N.M0 (fun _ => 1) (fun g => (N.M0 g).Φ 1)
+    (fun d => by rw [N.z0, Matrix.mul_one]) (fun d => by rw [N.z0, Matrix.mul_one])
+    (cOne Γ Sl α) (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv (bid Γ T) N.M0
+      (fun g (q : Sl) => (N.M0 ((Equiv.refl Γ).symm g)).Φ 1 * cOne Γ Sl α g q) (cOne Γ C α)
+      = mkS N.xi1 N.yi1 N.Z1 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x01 g t
+    · exact N.y01 g t
+    · show (N.M0 g).Φ 1 * 1 = (N.M0 g).Φ 1
+      rw [Matrix.mul_one]
+    · rfl
+  have h' : XRoute (bIn N.I.tv (bid Γ T) N.M0 (cOne Γ Sl α) (cOne Γ C α))
+      (mkS N.xi1 N.yi1 N.Z1 (cOne Γ C α)) GF (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact blift1 N.xi0 N.yi0 h'
+
+/-- stage 1: backward on pair 1; the helper set `g` serves the invocation `s1⁻¹ g`. -/
+lemma Bridge2.stage1 :
+    XRoute N.S1 N.S2 (lift1 GB) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := istage_bwd N.I N.r1 N.s1 N.M1 N.N1 N.W1 N.hN1 N.hW1 N.Z1 (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv N.r1 N.M1 (fun g q => N.W1 (N.s1.symm g) * N.Z1 g q) (cOne Γ C α)
+      = mkS N.xi2 N.yi2 N.Z2 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x12 g t
+    · exact N.y12 g t
+    · rfl
+    · rfl
+  have h' : XRoute (bIn N.I.tv N.r1 N.M1 N.Z1 (cOne Γ C α))
+      (mkS N.xi2 N.yi2 N.Z2 (cOne Γ C α)) GB (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact blift1 N.xi0 N.yi0 h'
+
+/-- stage 2: forward on pair 1. -/
+lemma Bridge2.stage2 :
+    XRoute N.S3 N.S4 (lift1 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) :=
+  blift1 N.xi2 N.yi2
+    (istage_fwd N.I N.r2 N.s2 N.M2 N.N2 N.W2 N.hN2 N.hW2 N.Z2 (cOne Γ C α) (cOne Γ C α))
+
+/-- stage 3: backward on pair 2. -/
+lemma Bridge2.stage3 :
+    XRoute N.S5 N.S6 (lift2 GB) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := istage_bwd N.I N.r3 N.s3 N.M3 N.N3 N.W3 N.hN3 N.hW3 N.Z3 (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv N.r3 N.M3 (fun g q => N.W3 (N.s3.symm g) * N.Z3 g q) (cOne Γ C α)
+      = mkS N.xi4 N.yi4 N.Z4 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x34 g t
+    · exact N.y34 g t
+    · rfl
+    · rfl
+  have h' : XRoute (bIn N.I.tv N.r3 N.M3 N.Z3 (cOne Γ C α))
+      (mkS N.xi4 N.yi4 N.Z4 (cOne Γ C α)) GB (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact blift2 N.xo2 N.yo2 h'
+
+/-- stage 4: forward on pair 2. -/
+lemma Bridge2.stage4 :
+    XRoute N.S6 N.S7 (lift2 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) :=
+  blift2 N.xo2 N.yo2
+    (istage_fwd N.I N.r4 N.s4 N.M4 N.N4 N.W4 N.hN4 N.hW4 N.Z4 (cOne Γ C α) (cOne Γ C α))
+
+/-- first idle climb of pair 2 (stages 0 and 1 in ONE block per role), to the frames of
+pair 1 after stage 1. -/
+lemma Bridge2.climbA :
+    XRoute N.S2 N.S3 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * (N.caX φ + N.caY φ))) := by
+  have H1 := XRoute.reach_all N.S2 N.S3
+    (mkB (fun _ _ _ => 0) (fun _ _ _ => 0) (fun _ _ => N.caX)
+      (fun _ _ => N.caY) (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact XReach.refl _
+      · exact XReach.refl _
+      · show XReach ((N.M0 g).Φ (tt (N.I.tv t))) ((N.M2 (N.r2 t g)).Φ (tt (N.I.tv t))) N.caX
+        rw [← N.x12 g t]
+        exact N.aX2 g t
+      · show XReach ((N.M0 g).Φ 0) ((N.M2 (N.r2 t g)).Φ 0) N.caY
+        rw [← N.y12 g t]
+        exact N.aY2 g t
+      · exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+/-- second idle climb of pair 2: the window of stage 2, ONE block of rank `card H - 1` per
+role, to the frames of pair 1 after stage 2. -/
+lemma Bridge2.climbB :
+    XRoute N.S4 N.S5 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * (2 * bcost φ (Fintype.card H - 1)))) := by
+  have H1 := XRoute.reach_all N.S4 N.S5
+    (mkB (fun _ _ _ => 0) (fun _ _ _ => 0) (fun _ _ φ => bcost φ (Fintype.card H - 1))
+      (fun _ _ φ => bcost φ (Fintype.card H - 1)) (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact XReach.refl _
+      · exact XReach.refl _
+      · show XReach ((N.M2 (N.r2 t g)).Φ (tt (N.I.tv t))) ((N.M3 (N.r3 t g)).Φ (tt (N.I.tv t)))
+          (fun φ => bcost φ (Fintype.card H - 1))
+        rw [← N.x23 g t]
+        exact N.I.climbX (N.M2 (N.r2 t g)) t
+      · show XReach ((N.M2 (N.r2 t g)).Φ 0) ((N.M3 (N.r3 t g)).Φ 0)
+          (fun φ => bcost φ (Fintype.card H - 1))
+        rw [← N.y23 g t]
+        exact N.I.climbY (N.M2 (N.r2 t g)) t
+      · exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+/-- the final climbs: pair 1 from its frames after stage 2 (ONE block per role for the
+stages 3, 4 and the rest), pair 2 from its frames after stage 4; the helper slots are
+already at the kernel. -/
+lemma Bridge2.fin :
+    XRoute N.S7 N.S8 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * ((N.cX1 φ + N.cY1 φ) + (N.cX2 φ + N.cY2 φ)))) := by
+  have H1 := XRoute.reach_all N.S7 N.S8
+    (mkB (fun _ _ => N.cX1) (fun _ _ => N.cY1) (fun _ _ => N.cX2) (fun _ _ => N.cY2)
+      (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact N.fX1 g t
+      · exact N.fY1 g t
+      · exact N.fX2 g t
+      · exact N.fY2 g t
+      · show XReach (N.W4 (N.s4.symm g) * (N.W3 (N.s3.symm g) * (N.W2 (N.s2.symm g) *
+          (N.W1 (N.s1.symm g) * (N.M0 g).Φ 1)))) (kernel α) (fun _ => 0)
+        rw [N.sfin g]
+        exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+end Net
+end
+end BR
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.BR.Bridge2.stage0
+#print axioms OAI.PowerSaving.BR.Bridge2.stage1
+#print axioms OAI.PowerSaving.BR.Bridge2.stage2
+#print axioms OAI.PowerSaving.BR.Bridge2.stage3
+#print axioms OAI.PowerSaving.BR.Bridge2.stage4
+#print axioms OAI.PowerSaving.BR.Bridge2.climbA
+#print axioms OAI.PowerSaving.BR.Bridge2.climbB
+#print axioms OAI.PowerSaving.BR.Bridge2.fin
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Carrier__Live.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Carrier__Live.lean
new file mode 100644
index 0000000000..b8306527d6
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Carrier__Live.lean
@@ -0,0 +1,232 @@
+import Work.Carrier.Pack
+import Work.Carrier.Ring
+
+/-!
+# (key: carrier-thm) The live roles of an invocation, and the four dirt gates as matrices
+
+`L3 T Sl = (T ⊕ T) ⊕ Sl`: the bank roles `x` (`lX`), `y` (`lY`) and the helper slots (`lS`), all
+on the same footing (no scratch copies).  `PX`, `PY`: the coordinate projectors.
+
+For the matrix `M` of all gates of the main phase and its inverse `Mi`:
+
+    g1 M  = 1 - PY * M * PS      `y -= K s`            g1i M = 1 + PY * M * PS   (its inverse)
+    g8 Mi = PX + PY + PS * Mi    slot rows of `M⁻¹`    h8 M  = PX + PY + PS * M  (its inverse)
+
+(`PS = 1 - PX - PY`).  This file: unit rows / columns of these gates (hence between which roles
+their entries can be nonzero), the scatter with the copies eliminated (`scatM`), and the scalar
+maps of `1 + PY * M * PX` and of the transpose of `1 - PY * M * PX`.
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace CR
+open Binary Matrix Finset RAM SS CB BR
+noncomputable section
+
+section Diag
+variable {ρ : Type*} [Fintype ρ] [DecidableEq ρ]
+
+lemma col_zero_of {d : ρ → ℚ} {G : Matrix ρ ρ ℚ}
+    (h : G * Matrix.diagonal d = Matrix.diagonal d) {i j : ρ} (hj : d j = 1) (hij : i ≠ j) :
+    G i j = 0 := by
+  have e := congrFun (congrFun h i) j
+  rw [Matrix.mul_diagonal, Matrix.diagonal_apply_ne _ hij, hj, mul_one] at e
+  exact e
+
+lemma row_zero_of {d : ρ → ℚ} {G : Matrix ρ ρ ℚ}
+    (h : Matrix.diagonal d * G = Matrix.diagonal d) {i j : ρ} (hi : d i = 1) (hij : i ≠ j) :
+    G i j = 0 := by
+  have e := congrFun (congrFun h i) j
+  rw [Matrix.diagonal_mul, Matrix.diagonal_apply_ne _ hij, hi, one_mul] at e
+  exact e
+
+lemma diag_mul_of_rows {d : ρ → ℚ} {G : Matrix ρ ρ ℚ}
+    (h : ∀ i j, d i ≠ 0 → G i j = if i = j then 1 else 0) :
+    Matrix.diagonal d * G = Matrix.diagonal d := by
+  ext i j
+  rw [Matrix.diagonal_mul]
+  by_cases hd : d i = 0
+  · rw [hd, zero_mul]
+    by_cases hij : i = j
+    · subst hij; rw [Matrix.diagonal_apply_eq, hd]
+    · rw [Matrix.diagonal_apply_ne _ hij]
+  · rw [h i j hd]
+    by_cases hij : i = j
+    · subst hij; rw [if_pos rfl, mul_one, Matrix.diagonal_apply_eq]
+    · rw [if_neg hij, mul_zero, Matrix.diagonal_apply_ne _ hij]
+
+lemma mul_diag_of_cols {d : ρ → ℚ} {G : Matrix ρ ρ ℚ}
+    (h : ∀ i j, d j ≠ 0 → G i j = if i = j then 1 else 0) :
+    G * Matrix.diagonal d = Matrix.diagonal d := by
+  ext i j
+  rw [Matrix.mul_diagonal]
+  by_cases hd : d j = 0
+  · rw [hd, mul_zero]
+    by_cases hij : i = j
+    · subst hij; rw [Matrix.diagonal_apply_eq, hd]
+    · rw [Matrix.diagonal_apply_ne _ hij]
+  · rw [h i j hd]
+    by_cases hij : i = j
+    · subst hij; rw [if_pos rfl, one_mul, Matrix.diagonal_apply_eq]
+    · rw [if_neg hij, zero_mul, Matrix.diagonal_apply_ne _ hij]
+
+/-- scalar map of a diagonal gate matrix. -/
+lemma act_diag (d : ρ → ℚ) (u : ρ → ℂ) :
+    actPoint (Matrix.diagonal d) u = fun i => ((d i : ℚ) : ℂ) * u i := by
+  funext i
+  show ∑ j, ((Matrix.diagonal d i j : ℚ) : ℂ) * u j = ((d i : ℚ) : ℂ) * u i
+  rw [Finset.sum_eq_single i]
+  · rw [Matrix.diagonal_apply_eq]
+  · intro j _ hj
+    rw [Matrix.diagonal_apply_ne _ (Ne.symm hj), Rat.cast_zero, zero_mul]
+  · intro h
+    exact absurd (Finset.mem_univ i) h
+
+lemma actPoint_mul (A B : Matrix ρ ρ ℚ) (u : ρ → ℂ) :
+    actPoint (A * B) u = actPoint A (actPoint B u) :=
+  ap_mul A B u
+
+end Diag
+
+section Live
+variable {T Sl : Type} [Fintype T] [DecidableEq T] [Fintype Sl] [DecidableEq Sl]
+
+/-- live roles of one invocation: `x`, `y`, helper slots. -/
+abbrev L3 (T Sl : Type) := (T ⊕ T) ⊕ Sl
+abbrev lX (t : T) : L3 T Sl := Sum.inl (Sum.inl t)
+abbrev lY (t : T) : L3 T Sl := Sum.inl (Sum.inr t)
+abbrev lS (q : Sl) : L3 T Sl := Sum.inr q
+
+/-- indicator of the x roles. -/
+def iX : L3 T Sl → ℚ := Sum.elim (Sum.elim (fun _ => 1) (fun _ => 0)) (fun _ => 0)
+/-- indicator of the y roles. -/
+def iY : L3 T Sl → ℚ := Sum.elim (Sum.elim (fun _ => 0) (fun _ => 1)) (fun _ => 0)
+
+def PX : Matrix (L3 T Sl) (L3 T Sl) ℚ := Matrix.diagonal iX
+def PY : Matrix (L3 T Sl) (L3 T Sl) ℚ := Matrix.diagonal iY
+
+lemma iX_cases (i : L3 T Sl) : iX i = 0 ∨ iX i = 1 := by
+  rcases i with ((t|t)|q)
+  · exact Or.inr rfl
+  · exact Or.inl rfl
+  · exact Or.inl rfl
+
+lemma iY_cases (i : L3 T Sl) : iY i = 0 ∨ iY i = 1 := by
+  rcases i with ((t|t)|q)
+  · exact Or.inl rfl
+  · exact Or.inr rfl
+  · exact Or.inl rfl
+
+lemma PX_sq : (PX : Matrix (L3 T Sl) (L3 T Sl) ℚ) * PX = PX := by
+  unfold PX
+  have e : (fun i : L3 T Sl => iX i * iX i) = iX := by
+    funext i
+    rcases i with ((t|t)|q) <;> simp [iX]
+  rw [Matrix.diagonal_mul_diagonal, e]
+
+lemma PY_sq : (PY : Matrix (L3 T Sl) (L3 T Sl) ℚ) * PY = PY := by
+  unfold PY
+  have e : (fun i : L3 T Sl => iY i * iY i) = iY := by
+    funext i
+    rcases i with ((t|t)|q) <;> simp [iY]
+  rw [Matrix.diagonal_mul_diagonal, e]
+
+lemma PX_PY : (PX : Matrix (L3 T Sl) (L3 T Sl) ℚ) * PY = 0 := by
+  unfold PX PY
+  rw [Matrix.diagonal_mul_diagonal]
+  have e : (fun i : L3 T Sl => iX i * iY i) = fun _ => 0 := by
+    funext i
+    rcases i with ((t|t)|q) <;> simp [iX, iY]
+  rw [e]
+  exact Matrix.diagonal_zero
+
+lemma PY_PX : (PY : Matrix (L3 T Sl) (L3 T Sl) ℚ) * PX = 0 := by
+  unfold PX PY
+  rw [Matrix.diagonal_mul_diagonal]
+  have e : (fun i : L3 T Sl => iY i * iX i) = fun _ => 0 := by
+    funext i
+    rcases i with ((t|t)|q) <;> simp [iX, iY]
+  rw [e]
+  exact Matrix.diagonal_zero
+
+lemma PX_T : (PX : Matrix (L3 T Sl) (L3 T Sl) ℚ)ᵀ = PX := Matrix.diagonal_transpose _
+lemma PY_T : (PY : Matrix (L3 T Sl) (L3 T Sl) ℚ)ᵀ = PY := Matrix.diagonal_transpose _
+
+/-- "no gate into an x role": the x rows are unit rows. -/
+lemma PX_mul_of {M : Matrix (L3 T Sl) (L3 T Sl) ℚ}
+    (hx : ∀ t j, M (lX t) j = if lX t = j then 1 else 0) : PX * M = PX := by
+  unfold PX
+  apply diag_mul_of_rows
+  intro i j hi
+  rcases i with ((t|t)|q)
+  · exact hx t j
+  · exact absurd rfl hi
+  · exact absurd rfl hi
+
+/-- "no gate reads a y role": the y columns are unit columns. -/
+lemma mul_PY_of {M : Matrix (L3 T Sl) (L3 T Sl) ℚ}
+    (hy : ∀ i t, M i (lY t) = if i = lY t then 1 else 0) : M * PY = PY := by
+  unfold PY
+  apply mul_diag_of_cols
+  intro i j hj
+  rcases j with ((t|t)|q)
+  · exact absurd rfl hj
+  · exact hy i t
+  · exact absurd rfl hj
+
+/-! ### the four dirt gates -/
+
+def g1 (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : Matrix (L3 T Sl) (L3 T Sl) ℚ :=
+  1 - PY * M * (1 - PX - PY)
+def g1i (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : Matrix (L3 T Sl) (L3 T Sl) ℚ :=
+  1 + PY * M * (1 - PX - PY)
+def g8 (Mi : Matrix (L3 T Sl) (L3 T Sl) ℚ) : Matrix (L3 T Sl) (L3 T Sl) ℚ :=
+  PX + PY + (1 - PX - PY) * Mi
+def h8 (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : Matrix (L3 T Sl) (L3 T Sl) ℚ :=
+  PX + PY + (1 - PX - PY) * M
+
+/-- a gate with unit x rows and unit x columns joins two different roles only if neither is an
+x role. -/
+lemma offdiag_x {G : Matrix (L3 T Sl) (L3 T Sl) ℚ} (h1 : G * PX = PX) (h2 : PX * G = PX)
+    {i j : L3 T Sl} (hij : G i j ≠ 0) (e : i ≠ j) : iX i = 0 ∧ iX j = 0 := by
+  constructor
+  · by_contra h
+    exact hij (row_zero_of h2 ((iX_cases i).resolve_left h) e)
+  · by_contra h
+    exact hij (col_zero_of h1 ((iX_cases j).resolve_left h) e)
+
+/-- a gate with unit x rows, unit y rows and unit y columns: a nonzero entry off the diagonal
+is in a slot row and not in a y column. -/
+lemma offdiag_s {G : Matrix (L3 T Sl) (L3 T Sl) ℚ} (hx : PX * G = PX) (hy : PY * G = PY)
+    (hyc : G * PY = PY) {i j : L3 T Sl} (hij : G i j ≠ 0) (e : i ≠ j) :
+    iX i = 0 ∧ iY i = 0 ∧ iY j = 0 := by
+  refine ⟨?_, ?_, ?_⟩
+  · by_contra h
+    exact hij (row_zero_of hx ((iX_cases i).resolve_left h) e)
+  · by_contra h
+    exact hij (row_zero_of hy ((iY_cases i).resolve_left h) e)
+  · by_contra h
+    exact hij (col_zero_of hyc ((iY_cases j).resolve_left h) e)
+
+lemma g1_x (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : g1 M * PX = PX ∧ PX * g1 M = PX := by
+  unfold g1
+  constructor
+  · rw [sub_mul, one_mul, side_n_right (PX_sq (T := T) (Sl := Sl)) PY_PX, sub_zero]
+  · rw [mul_sub, mul_one, side_n_left (PX_PY (T := T) (Sl := Sl)), sub_zero]
+
+lemma g1i_x (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : g1i M * PX = PX ∧ PX * g1i M = PX := by
+  unfold g1i
+  constructor
+  · rw [add_mul, one_mul, side_n_right (PX_sq (T := T) (Sl := Sl)) PY_PX, add_zero]
+  · rw [mul_add, mul_one, side_n_left (PX_PY (T := T) (Sl := Sl)), add_zero]
+
+end Live
+end
+end CR
+end PowerSaving
+end OAI
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Carrier__Phases.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Carrier__Phases.lean
new file mode 100644
index 0000000000..305da15b5d
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Carrier__Phases.lean
@@ -0,0 +1,192 @@
+import Work.Carrier.Glue
+
+/-!
+# (key: carrier-thm) A carrier circuit given by its phases: hypotheses and scalar identities
+
+`Phased H T Sl C` is the hypothesis structure of the carrier invocation theorem in the general
+scope (any ordered mix of gates `(x, slot)`, `(slot, slot)`, `(x, y)`, `(slot, y)`):
+
+* phase A (before the scatter), phase B (after it) and the final climbs F are exact block routes
+  on the LIVE roles `L3 T Sl` (`x`, `y`, slots: all on the same footing), for every block frame
+  map, with the gate products `MA`, `MB` (and the transposed inverses for the backward word);
+* the scatter goes through the scratch copies: `c += Cc s` at the labels `cen`, the copies come
+  down, `y += Jr c` at 0;
+* `hx`: no gate INTO an x role, `hy`: no gate READS a y role, `hid`: the y roles receive exactly
+  the x roles — three facts about the ONE matrix `Mt = MB * scatM (Jr * Cc) * MA`.
+
+This file: `Mt`, its inverse `Mti`, and the scalar identities of the forward and of the backward
+word (`fwd_scalar`, `bwd_scalar`): with the two dirt gates `g1`, `g8` (resp. the transposes of
+`g1i`, `h8`) the word does `y += x` (resp. `x -= y`) for ARBITRARY slot contents.
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace CR
+open Binary Matrix Finset RAM SS CB BR
+noncomputable section
+
+/-- labels of the live roles at the START of an invocation. -/
+def lab3 {H T Sl : Type} (tv : T → Space H) : L3 T Sl → Lbl H :=
+  Sum.elim (Sum.elim (fun t => lineL (tv t)) (fun _ => zeroL)) (fun _ => zeroL)
+
+/-- **The hypotheses of the carrier invocation theorem, by phases.**  See the file header. -/
+structure Phased (H T Sl C : Type) [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] where
+  tv : T → Space H
+  kx : ∀ t, Climb (lineL (tv t)) fullL
+  ky : ∀ t, Climb zeroL (perpL (tv t))
+  cen : C → Lbl H
+  kc : ∀ k, Climb zeroL (cen k)
+  Cc : Matrix C Sl ℚ
+  Jr : Matrix T C ℚ
+  labA : L3 T Sl → Lbl H
+  labB : L3 T Sl → Lbl H
+  labF : L3 T Sl → Lbl H
+  hAy : ∀ t, (labA (lY t)).P = 0
+  hAc : ∀ k q, Cc k q ≠ 0 → (cen k).P = (labA (lS q)).P
+  hFx : ∀ t, (labF (lX t)).P = 1
+  hFy : ∀ t, (labF (lY t)).P = 1 + tt (tv t)
+  hFs : ∀ q, (labF (lS q)).P = 1
+  MA : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MAi : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MB : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MBi : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  hAi : MAi * MA = 1
+  hBi : MBi * MB = 1
+  hx : ∀ t j, (MB * scatM (Jr * Cc) * MA) (lX t) j = if lX t = j then 1 else 0
+  hy : ∀ i t, (MB * scatM (Jr * Cc) * MA) i (lY t) = if i = lY t then 1 else 0
+  hid : ∀ S t, (MB * scatM (Jr * Cc) * MA) (lY S) (lX t) = if S = t then 1 else 0
+  rA : List ℕ
+  rB : List ℕ
+  rF : List ℕ
+  pA : ∀ {α : Type} [Fintype α] [DecidableEq α] (Xm : XMap H α),
+    XRoute (fun r => Xm.Φ (lab3 tv r).P) (fun r => Xm.Φ (labA r).P) (actPoint MA)
+        (fun φ => rcost φ rA) ∧
+    XRoute (fun r => Xm.Φ (lab3 tv r).P) (fun r => Xm.Φ (labA r).P) (actPoint MAiᵀ)
+        (fun φ => rcost φ rA)
+  pB : ∀ {α : Type} [Fintype α] [DecidableEq α] (Xm : XMap H α),
+    XRoute (fun r => Xm.Φ (labA r).P) (fun r => Xm.Φ (labB r).P) (actPoint MB)
+        (fun φ => rcost φ rB) ∧
+    XRoute (fun r => Xm.Φ (labA r).P) (fun r => Xm.Φ (labB r).P) (actPoint MBiᵀ)
+        (fun φ => rcost φ rB)
+  pF : ∀ {α : Type} [Fintype α] [DecidableEq α] (Xm : XMap H α),
+    XRoute (fun r => Xm.Φ (labB r).P) (fun r => Xm.Φ (labF r).P) id (fun φ => rcost φ rF)
+
+section Alg
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+
+namespace Phased
+variable (K : Phased H T Sl C)
+
+/-- the product of ALL gates of the main phase (scatter with the copies eliminated). -/
+def Mt : Matrix (L3 T Sl) (L3 T Sl) ℚ := K.MB * scatM (K.Jr * K.Cc) * K.MA
+/-- its inverse. -/
+def Mti : Matrix (L3 T Sl) (L3 T Sl) ℚ := K.MAi * scatMi (K.Jr * K.Cc) * K.MBi
+
+/-- price of one invocation: the blocks of the three phases and one block per copy. -/
+def cost (φ : ℕ → ℝ) : ℝ :=
+  rcost φ K.rA + (∑ k, bcost φ (K.cen k).d) + rcost φ K.rB + rcost φ K.rF
+
+lemma im : K.Mti * K.Mt = 1 := by
+  unfold Mti Mt
+  have hB : ∀ X : Matrix (L3 T Sl) (L3 T Sl) ℚ, K.MBi * (K.MB * X) = X := fun X => by
+    rw [← Matrix.mul_assoc, K.hBi, Matrix.one_mul]
+  have hS : ∀ X : Matrix (L3 T Sl) (L3 T Sl) ℚ,
+      scatMi (K.Jr * K.Cc) * (scatM (K.Jr * K.Cc) * X) = X := fun X => by
+    rw [← Matrix.mul_assoc, scat_inv, Matrix.one_mul]
+  rw [Matrix.mul_assoc, Matrix.mul_assoc, Matrix.mul_assoc, hB, hS, K.hAi]
+
+lemma mi : K.Mt * K.Mti = 1 := mul_eq_one_comm.mp K.im
+
+lemma hxm : PX * K.Mt = PX := PX_mul_of (M := K.Mt) K.hx
+lemma hmy : K.Mt * PY = PY := mul_PY_of (M := K.Mt) K.hy
+lemma hiy : K.Mti * PY = PY := dirt_iy K.hmy K.im
+
+/-- **the dirt rule, forward**, for the matrices of the circuit. -/
+lemma hF : g8 K.Mti * K.Mt * g1 K.Mt = 1 + PY * K.Mt * PX := by
+  unfold g8 g1
+  exact dirt_fwd PX_sq PY_sq PX_PY PY_PX K.hxm K.hmy K.im K.mi
+
+/-- **the dirt rule, backward.** -/
+lemma hB : g1i K.Mt * K.Mti * h8 K.Mt = 1 - PY * K.Mt * PX := by
+  unfold g1i h8
+  exact dirt_bwd PX_sq PY_sq PX_PY PY_PX K.hxm K.hmy K.im K.mi
+
+/-- live part of the forward word before the scatter: `y -= K s`, then phase A. -/
+def f1 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint K.MA (actPoint (g1 K.Mt) u)
+/-- after the scatter: phase B, then the slot rows of the inverse. -/
+def f2 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint (g8 K.Mti) (actPoint K.MB u)
+/-- the same for the backward word (transposed inverses). -/
+def b1 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint K.MAiᵀ (actPoint (g1i K.Mt)ᵀ u)
+def b2 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint (h8 K.Mt)ᵀ (actPoint K.MBiᵀ u)
+
+lemma fwd_live (u : L3 T Sl → ℂ) :
+    K.f2 (actPoint (scatM (K.Jr * K.Cc)) (K.f1 u)) = actPoint (1 + PY * K.Mt * PX) u := by
+  rw [← K.hF]
+  show actPoint (g8 K.Mti) (actPoint K.MB (actPoint (scatM (K.Jr * K.Cc))
+      (actPoint K.MA (actPoint (g1 K.Mt) u))))
+    = actPoint (g8 K.Mti * (K.MB * scatM (K.Jr * K.Cc) * K.MA) * g1 K.Mt) u
+  rw [actPoint_mul, actPoint_mul, actPoint_mul, actPoint_mul]
+
+lemma bwd_live (u : L3 T Sl → ℂ) :
+    K.b2 (actPoint ((scatMi (K.Jr * K.Cc))ᵀ) (K.b1 u))
+      = actPoint ((1 - PY * K.Mt * PX)ᵀ) u := by
+  rw [← K.hB]
+  show actPoint (h8 K.Mt)ᵀ (actPoint K.MBiᵀ (actPoint (scatMi (K.Jr * K.Cc))ᵀ
+      (actPoint K.MAiᵀ (actPoint (g1i K.Mt)ᵀ u))))
+    = actPoint ((g1i K.Mt * (K.MAi * scatMi (K.Jr * K.Cc) * K.MBi) * h8 K.Mt)ᵀ) u
+  rw [Matrix.transpose_mul, Matrix.transpose_mul, Matrix.transpose_mul, Matrix.transpose_mul,
+    actPoint_mul, actPoint_mul, actPoint_mul, actPoint_mul]
+
+lemma liveAct_glue (φ : (L3 T Sl → ℂ) → (L3 T Sl → ℂ)) (u : L3 T Sl → ℂ) (c : C → ℂ) :
+    liveAct φ (glue u c) = glue (φ u) c :=
+  congrArg (fun v => glue (φ v) c) (glue_up u c)
+
+/-- **Scalar identity of the forward word**: `y += x`, slots restored, for ARBITRARY slot
+contents (the copies are erased before and after). -/
+theorem fwd_scalar (z : Box T Sl C → ℂ) :
+    eraseC (liveAct K.f2 (gateS bY bC K.Jr (gateS bC bS K.Cc (liveAct K.f1 (eraseC z)))))
+      = shearF z := by
+  have h1 : liveAct K.f1 (eraseC z) = glue (K.f1 (z ∘ upE)) (fun _ => 0) := by
+    rw [erase_glue z, liveAct_glue]
+  have hs : gateS bY bC K.Jr (gateS bC bS K.Cc (glue (K.f1 (z ∘ upE)) (fun _ => 0))) ∘ upE
+      = actPoint (scatM (K.Jr * K.Cc)) (K.f1 (z ∘ upE)) := by
+    have h := scat_glue K.Jr K.Cc (glue (K.f1 (z ∘ upE)) (fun _ => 0)) rfl
+    rw [glue_up] at h
+    exact h
+  rw [h1]
+  unfold liveAct
+  rw [erase_of_glue, hs, K.fwd_live, act_shear K.Mt K.hid]
+  exact glue_shearF z
+
+/-- **Scalar identity of the backward word**: `x -= y`, slots restored. -/
+theorem bwd_scalar (z : Box T Sl C → ℂ) :
+    eraseC (liveAct K.b2 (gateS bS bC (-K.Ccᵀ) (gateS bC bY K.Jrᵀ (liveAct K.b1 (eraseC z)))))
+      = shearB z := by
+  have h1 : liveAct K.b1 (eraseC z) = glue (K.b1 (z ∘ upE)) (fun _ => 0) := by
+    rw [erase_glue z, liveAct_glue]
+  have hs : gateS bS bC (-K.Ccᵀ) (gateS bC bY K.Jrᵀ (glue (K.b1 (z ∘ upE)) (fun _ => 0))) ∘ upE
+      = actPoint ((scatMi (K.Jr * K.Cc))ᵀ) (K.b1 (z ∘ upE)) := by
+    have h := scat_glueT K.Jr K.Cc (glue (K.b1 (z ∘ upE)) (fun _ => 0)) rfl
+    rw [glue_up] at h
+    exact h
+  rw [h1]
+  unfold liveAct
+  rw [erase_of_glue, hs, K.bwd_live, act_shearT K.Mt K.hid]
+  exact glue_shearB z
+
+end Phased
+end Alg
+end
+end CR
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.CR.Phased.fwd_scalar
+#print axioms OAI.PowerSaving.CR.Phased.bwd_scalar
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Fourier__Main.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Fourier__Main.lean
new file mode 100644
index 0000000000..9aa06b5bf2
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__Fourier__Main.lean
@@ -0,0 +1,176 @@
+import Work.Fourier.Asymptotics
+import OAI.Computability.FourierTransform.RegisterBounds
+import Work.Fourier.Goal
+
+/-
+Modified copy of lean/OAI/Computability/FourierTransform/Main.lean of github.com/openai/math
+(commit fd4aeeb, Apache-2.0), generated by `tools/fourier/mkchain.py`. OpenAI's file itself is
+unmodified in this repository and still imported. Changed for this repository, all mechanically:
+  * every declaration of this file (and of the other 10 copied files) has the suffix `Z`
+    on its name, so that it does not collide with OpenAI's original;
+  * OpenAI's exponent `alpha = 1 - 2/10^11` and envelope `hills` are replaced by
+    `alphaZ = 1 - 7474547/10^10` and `hillsZ` (Work/Fourier/Seam.lean), and the single use of
+    OpenAI's `hills_program` by `hillsZ_program`;
+  * `decimalExponent`, `decimalTime`, `TimeBounds`, `DFTGoal`, `ConvGoal` are replaced by their
+    `Z` versions from Work/Fourier/Goal.lean (exponent `1 - 7474546/10^10`);
+  * imports point to the copies.
+  * literal `let d : ℝ := 2/(10:ℝ)^11` -> `let d : ℝ := 7474547/(10:ℝ)^10` (alpha_thetaZ: the local constant d must equal 1 - alphaZ)
+  * `theorem transform_mainZ : DFTGoalZ :=`: docstring added
+  * `theorem convolution_mainZ : ConvGoalZ :=`: docstring added
+Comments and docstrings below are OpenAI's and describe OpenAI's network, not ours.
+-/
+
+namespace OAI
+
+/-!
+Exact uniform Fourier transforms and convolution.
+
+The construction formalizes the exact arithmetic algorithms of
+*An explicit power saving for the exact discrete Fourier transform* (OpenAI).
+The finite phase network originates in the complex construction of
+*Integer multiplication below n log n*.
+
+`transform_mainZ` and `convolution_mainZ` give fixed finite RAM programs, including
+preparation and index work, polynomial storage bounds, and a canonical root whose
+order is computed from the input length. Each includes the paper exponent, decimal
+power saving, and little-o bound. The `_order` variants also specify the root order.
+
+The implementation uses a smaller concrete tensor network (32 binary coordinates
+per factor, 4060 triples, and a `2^50` role envelope) with a stronger saving that
+implies the stated paper constants. The general rational-algebra extraction,
+symbolic certificate search, circuit printer, and bounded-printer uniformization
+from the synthesis appendix are outside this formalization.
+-/
+namespace PowerSaving
+open RAM Bench Selection Filter Asymptotics Real
+noncomputable section
+namespace Skies
+
+lemma multiplier_rangeZ : 1 < paperMultiplier ∧ paperMultiplier < paperM := by
+  norm_num [paperMultiplier,paperM,paperDelta,paperW]
+
+lemma theta_ltZ : theta < 1 := by
+  have h := multiplier_rangeZ
+  have hg : 0<log paperM := Real.log_pos (lt_trans h.1 h.2)
+  rw [theta,div_lt_iff₀ hg,one_mul]
+  exact Real.log_lt_log (by linarith) h.2
+
+lemma alpha_thetaZ : alphaZ < theta := by
+  let d : ℝ := 7474547/(10:ℝ)^10
+  have hp : 0<d := by dsimp [d]; norm_num
+  have hm : 2 ≤ paperM := by norm_num [paperM]
+  have hx : 0<paperMultiplier := lt_trans zero_lt_one multiplier_rangeZ.1
+  have hu : 0<paperM := by linarith
+  have h2 := (Real.log_le_log (by norm_num : 0 < (2:ℝ)) hm)
+  have he := log2_minZ
+  have hh : 0<log paperM := by linarith
+  have hk := Real.log_le_sub_one_of_pos (show 0<paperM/paperMultiplier by positivity)
+  rw [log_div hu.ne' hx.ne'] at hk
+  have H : paperM/paperMultiplier-1 < d*(2/3) := by
+    norm_num [d,paperM,paperMultiplier,paperW,paperDelta]
+  rw [theta,lt_div_iff₀ hh]
+  change (1-d)*log paperM < log paperMultiplier
+  have H' := mul_le_mul_of_nonneg_left (he.trans h2) hp.le
+  have hy := hk.trans_lt (lt_of_lt_of_le H H')
+  rw [sub_mul,one_mul]
+  linarith only [hy]
+
+lemma decimal_rangeZ : alphaZ < decimalExponentZ ∧ decimalExponentZ < 1 := by
+  norm_num [decimalExponentZ,alphaZ]
+
+def speedZ (v : ℝ) (n : ℕ) := (n:ℝ)*(TmZ n)^v
+
+lemma flight_littleZ {v : ℝ} (h : alphaZ < v) :
+    flightZ =o[atTop] speedZ v := by
+  rw [isLittleO_iff]
+  intro c hc
+  filter_upwards [TtopZ.eventually_ge_atTop 1,dwarfZ TtopZ 2
+    (p:=v-alphaZ) (sub_pos.mpr h) hc] with n hn hh
+  have he : 0<TmZ n := by linarith
+  change ‖(n:ℝ)*TmZ n^alphaZ*QmZ n^2‖ ≤ c*‖(n:ℝ)*TmZ n^v‖
+  rw [Real.norm_of_nonneg (by positivity),Real.norm_of_nonneg (by positivity)]
+  calc
+    _ ≤ ((n:ℝ)*TmZ n^alphaZ)*(c*TmZ n^(v-alphaZ)) :=
+      mul_le_mul_of_nonneg_left hh (by positivity)
+    _ = c*((n:ℝ)*(TmZ n^alphaZ*TmZ n^(v-alphaZ))) := by ring
+    _ = _ := by rw [← rpow_add he, show alphaZ + (v-alphaZ)=v by ring] -- a+(v-a)
+
+lemma speed_littleZ {u v : ℝ} (h : u < v) :
+    speedZ u =o[atTop] speedZ v := by
+  rw [isLittleO_iff]
+  intro c hc
+  filter_upwards [TtopZ.eventually_ge_atTop 1,dwarfZ TtopZ 0
+    (p:=v-u) (sub_pos.mpr h) hc] with n hn hh
+  have he : 0<TmZ n := by linarith
+  change ‖(n:ℝ)*TmZ n^u‖ ≤ c*‖(n:ℝ)*TmZ n^v‖
+  rw [Real.norm_of_nonneg (by positivity),Real.norm_of_nonneg (by positivity)]
+  have hh' : 1 ≤ c * TmZ n^(v-u) := by simpa only [pow_zero] using hh
+  calc
+    _ = ((n:ℝ)*TmZ n^u)*1 := by ring
+    _ ≤ ((n:ℝ)*TmZ n^u)*(c*TmZ n^(v-u)) := mul_le_mul_of_nonneg_left hh' (by positivity)
+    _ = c*((n:ℝ)*(TmZ n^u*TmZ n^(v-u))) := by ring
+    _ = _ := by rw [← rpow_add he, show u+(v-u)=v by ring]
+
+theorem decimal_littleZ : decimalTimeZ =o[atTop] nlogn := by
+  have H := speed_littleZ decimal_rangeZ.2
+  have h : speedZ 1 = nlogn := funext fun n => by rw [speedZ,Real.rpow_one]; rfl
+  rw [h] at H; exact H
+
+lemma speed_paperZ : speedZ theta =O[atTop] paperTime := by
+  rw [isBigO_iff]
+  refine ⟨1,?_⟩
+  filter_upwards [TtopZ.eventually_ge_atTop 1,QtopZ.eventually_ge_atTop 1] with n hn hh
+  have he : 0<TmZ n := by linarith
+  have he' : 0<QmZ n := by linarith
+  change ‖(n:ℝ)*TmZ n^theta‖ ≤ 1*‖(n:ℝ)*TmZ n^theta*QmZ n^(4-theta)‖
+  rw [Real.norm_of_nonneg (by positivity),Real.norm_of_nonneg (by positivity),one_mul]
+  have hb := Real.one_le_rpow hh (show 0 ≤ 4-theta by linarith [theta_ltZ])
+  exact le_mul_of_one_le_right (by positivity) hb
+
+lemma time_boundZ {N} (h : ∀ n:ℕ,n ≤ N n ∧ N n ≤ 2*n) (a b : RationZ) :
+    TimeBoundsZ (lunchZ a b N) := by
+  have H := lunch_bigZ a b h
+  have hp := H.trans_isLittleO (flight_littleZ alpha_thetaZ)
+  have hd := H.trans_isLittleO (flight_littleZ decimal_rangeZ.1)
+  have ht : (fun n => (lunchZ a b N n:ℝ)) =O[atTop] decimalTimeZ := hd.isBigO
+  exact ⟨hp.isBigO.trans speed_paperZ,ht,ht.trans_isLittleO decimal_littleZ⟩
+
+end Skies
+
+/-! Main results. Provide formula for the order besides the existential specification. -/
+theorem transform_main_orderZ : ∃ order solve W,
+    DFTProgram order solve W ∧ TimeBoundsZ W ∧
+    ∀ n, 0<n → (run order n).val = receipt n ∧ (run order n).val < 8*n^3 := by
+  obtain ⟨o,s,a,b,hp,ho⟩ := flagshipOneZ
+  exact ⟨o,s,lunchZ a b id,hp,Skies.time_boundZ (N:=id) (fun n => ⟨le_rfl,by dsimp; omega⟩)
+    a b,fun n hn => ⟨ho n hn,(ho n hn).symm ▸ (receipt_bound n hn).2⟩⟩
+
+theorem convolution_main_orderZ : ∃ order solve W,
+    ConvProgram order solve W ∧ TimeBoundsZ W ∧
+    ∀ n, 0<n → (run order n).val = receipt (2*n-1) ∧ (run order n).val < 8*(2*n-1)^3 := by
+  obtain ⟨o,s,a,b,hp,ho⟩ := flagshipBothZ
+  have h (n : ℕ) : n ≤ stretchZ n ∧ stretchZ n ≤ 2*n := by unfold stretchZ; omega
+  exact ⟨o,s,lunchZ a b stretchZ,hp,Skies.time_boundZ h a b,fun n hn =>
+    ⟨ho n hn,(ho n hn).symm ▸ (receipt_bound _ (stretch_posZ hn)).2⟩⟩
+
+/-- **The discrete Fourier transform of every length in `O(n (log n)^(1 - 7474546/10^10))`.**
+OpenAI's `transform_main` (one fixed program, OpenAI's own `DFTProgram`, `paperTime` and `nlogn`)
+with the decimal exponent `1 - 1/10^13` replaced by `decimalExponentZ = 1 - 7474546/10^10`
+(Work/Fourier/Goal.lean). Sibling of the Walsh-Hadamard theorem `wht_main_block_B2Gp193x`: both
+follow from one kernel program, `RAM.hillsZ_program` (Work/Fourier/Seam.lean). -/
+theorem transform_mainZ : DFTGoalZ :=
+  let ⟨o,s,W,h,g,_⟩ := transform_main_orderZ
+  ⟨o,s,W,h,g⟩
+
+/-- **Convolution of every length with the same bounds** (OpenAI's `convolution_main`, same change). -/
+theorem convolution_mainZ : ConvGoalZ :=
+  let ⟨o,s,W,h,g,_⟩ := convolution_main_orderZ
+  ⟨o,s,W,h,g⟩
+
+lemma matrix_definitionZ (n : ℕ) (x : Vec n) : dft n x = Matrix.mulVec (dftMatrix n) x :=
+  rfl
+
+end
+end PowerSaving
+
+end OAI
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__Geom.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__Geom.lean
new file mode 100644
index 0000000000..eb4490af8b
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__Geom.lean
@@ -0,0 +1,210 @@
+import Work.GCert.Chain.NetCert
+import Work.GCert.Chain.WinB
+import Work.BridgeGeom.B2
+
+/-!
+# (key: gx-chain) THE NETWORK LEMMA (spec statement 6): the bridged word B_2 delivers a `GCert`
+
+GENERATED by checks/wht26/gx-chain/py/netgen.py from Work/BridgeGeom/Net.lean (section Net):
+the geometry of `BG.geomBridge2`, word for word, with the windows `gwinB` (`.Xm = BG.fmapB`).
+
+`bridge2_gcert I hH`: for every generalised invocation package, a `GCert` on
+`card Γ * (4 card T + card Sl)` live roles, label dimension `5h`, unit price
+`5 * I.cost φ + card T * BG.bankPrice h φ` (unchanged).  No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR GF BG
+noncomputable section
+
+section Net
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+variable (I : GInv H T Sl C) (base : T → OBase H) (l : H)
+  (hbase : ∀ t, I.tv t = (base t).v l) (hH : 1 ≤ Fintype.card H)
+include hbase
+
+lemma ggeom_x01 (g : Orth (L5 H)) (t : T) :
+    PhiB g ∅ 1 = PhiB (RrB (base t) l (0 : Fin 4) g) (qS bs1 l) (tt (I.tv t)) := by
+  rw [hbase t]
+  exact bankT_x0 (base t) l (0 : Fin 4) g
+
+lemma ggeom_y01 (g : Orth (L5 H)) (t : T) :
+    PhiB g ∅ (1 + tt (I.tv t)) = PhiB (RrB (base t) l (0 : Fin 4) g) (qS bs1 l) 0 := by
+  rw [hbase t]
+  exact bankT_y0 (base t) l (0 : Fin 4) g
+
+/-- consecutive stages `c ∈ bs`, `c' ∉ bs`: `X` leaves where it enters. -/
+lemma ggeom_xx (bs : Finset (Fin 4)) (c c' : Fin 4) (hc : c ∈ bs) (hc' : c' ∉ bs)
+    (g : Orth (L5 H)) (t : T) :
+    PhiB (RrB (base t) l c g) (qS bs l) 1
+      = PhiB (RrB (base t) l c' g) (qS (insert c' bs) l) (tt (I.tv t)) := by
+  rw [hbase t]
+  exact bankT_xx (base t) l bs c c' hc hc' g
+
+/-- consecutive stages: `Y` leaves where it enters. -/
+lemma ggeom_yy (bs : Finset (Fin 4)) (c c' : Fin 4) (hc : c ∈ bs) (hc' : c' ∉ bs)
+    (g : Orth (L5 H)) (t : T) :
+    PhiB (RrB (base t) l c g) (qS bs l) (1 + tt (I.tv t))
+      = PhiB (RrB (base t) l c' g) (qS (insert c' bs) l) 0 := by
+  rw [hbase t]
+  exact bankT_yy (base t) l bs c c' hc hc' g
+
+/-- terminal identity of the bank pairs of the class `(g,t)`. -/
+lemma ggeom_term5 (g : Orth (L5 H)) (t : T) :
+    kernel (L5 H) * PhiB g ∅ (tt (I.tv t))
+      = shift ((BBB (base t) g).v (Sum.inl l))
+          * frame (BBB (base t) g) (univ \ {Sum.inl l}) := by
+  rw [hbase t]
+  exact class_term (base t) l g
+
+include hH
+
+/-- pair 2 before the first gate layer, `X`: ONE block of rank `2h-2`. -/
+lemma ggeom_aX2 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB g ∅ (tt (I.tv t))) (PhiB (RrB (base t) l (0 : Fin 4) g) (qS bs1 l) 1)
+      (fun φ => bcost φ (2 * Fintype.card H - 2)) := by
+  rw [hbase t]
+  exact idle_X0 (base t) l hB4 hH (0 : Fin 4) g _ (by omega)
+
+/-- pair 2 before the first gate layer, `Y`: ONE block of rank `2h-2`. -/
+lemma ggeom_aY2 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB g ∅ 0) (PhiB (RrB (base t) l (0 : Fin 4) g) (qS bs1 l) (1 + tt (I.tv t)))
+      (fun φ => bcost φ (2 * Fintype.card H - 2)) := by
+  rw [hbase t]
+  exact idle_Y0 (base t) l hB4 hH (0 : Fin 4) g _ (by omega)
+
+/-- pair 1 at the end (idle in stages 3, 4, then the last four moves), `X`: ONE block `2h+2`. -/
+lemma ggeom_fX1 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB (RrB (base t) l (1 : Fin 4) g) (qS bs2 l) 1) (kernel (L5 H))
+      (fun φ => bcost φ (2 * Fintype.card H + 2)) :=
+  idle_Xend (base t) l hB4 hH bs2 (1 : Fin 4) (Finset.mem_insert_self _ _) g _
+    (by rw [card_bs2, Fintype.card_fin]; omega)
+
+/-- pair 1 at the end, `Y`: ONE block of rank `2h+2`. -/
+lemma ggeom_fY1 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB (RrB (base t) l (1 : Fin 4) g) (qS bs2 l) (1 + tt (I.tv t)))
+      (frame (BBB (base t) g) (univ \ {Sum.inl l}))
+      (fun φ => bcost φ (2 * Fintype.card H + 2)) := by
+  rw [hbase t]
+  exact idle_Yend (base t) l hB4 hH bs2 (1 : Fin 4) (Finset.mem_insert_self _ _) g _
+    (by rw [card_bs2, Fintype.card_fin]; omega)
+
+/-- pair 2 after stage 4, `X`: ONE block of rank `4`. -/
+lemma ggeom_fX2 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB (RrB (base t) l (3 : Fin 4) g) (qS bs4 l) 1) (kernel (L5 H))
+      (fun φ => bcost φ 4) :=
+  idle_Xend (base t) l hB4 hH bs4 (3 : Fin 4) (Finset.mem_insert_self _ _) g _
+    (by rw [card_bs4, Fintype.card_fin]; omega)
+
+/-- pair 2 after stage 4, `Y`: ONE block of rank `4`. -/
+lemma ggeom_fY2 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB (RrB (base t) l (3 : Fin 4) g) (qS bs4 l) (1 + tt (I.tv t)))
+      (frame (BBB (base t) g) (univ \ {Sum.inl l})) (fun φ => bcost φ 4) := by
+  rw [hbase t]
+  exact idle_Yend (base t) l hB4 hH bs4 (3 : Fin 4) (Finset.mem_insert_self _ _) g _
+    (by rw [card_bs4, Fintype.card_fin]; omega)
+
+/-- **The bridged word B_2 as a term of `BR.Bridge2`**: five stages on the label space
+`H ⊕ (Fin 4 × H)`, for any invocation package whose lines are the vectors of index `l` of
+orthonormal bases. -/
+def ggeomBridge2 : GBridge2 H T Sl C (L5 H) (Orth (L5 H)) where
+  I := I
+  G0 := fun g => gwinB hB4 hH g ∅
+  G1 := fun d => gwinB hB4 hH d (qS bs1 l)
+  G2 := fun d => gwinB hB4 hH d (qS bs2 l)
+  G3 := fun d => gwinB hB4 hH d (qS bs3 l)
+  G4 := fun d => gwinB hB4 hH d (qS bs4 l)
+  r1 := fun t => RrB (base t) l (0 : Fin 4)
+  r2 := fun t => RrB (base t) l (1 : Fin 4)
+  r3 := fun t => RrB (base t) l (2 : Fin 4)
+  r4 := fun t => RrB (base t) l (3 : Fin 4)
+  s1 := (Orth.colPerm (tauB (0 : Fin 4))).symm
+  s2 := (Orth.colPerm (tauB (1 : Fin 4))).symm
+  s3 := (Orth.colPerm (tauB (2 : Fin 4))).symm
+  s4 := (Orth.colPerm (tauB (3 : Fin 4))).symm
+  N1 := fun d => unframeM (d.1 * Matrix.fromBlocks 0 0 0 (diagI (qS bs1 l)) * d.1ᵀ)
+  W1 := fun d => frameM (d.1 * diagI (JB univ ∅) * d.1ᵀ)
+  N2 := fun d => unframeM (d.1 * Matrix.fromBlocks 0 0 0 (diagI (qS bs2 l)) * d.1ᵀ)
+  W2 := fun d => frameM (d.1 * diagI (JB univ ∅) * d.1ᵀ)
+  N3 := fun d => unframeM (d.1 * Matrix.fromBlocks 0 0 0 (diagI (qS bs3 l)) * d.1ᵀ)
+  W3 := fun d => frameM (d.1 * diagI (JB univ ∅) * d.1ᵀ)
+  N4 := fun d => unframeM (d.1 * Matrix.fromBlocks 0 0 0 (diagI (qS bs4 l)) * d.1ᵀ)
+  W4 := fun d => frameM (d.1 * diagI (JB univ ∅) * d.1ᵀ)
+  u := fun g t => (BBB (base t) g).v (Sum.inl l)
+  YF := fun g t => frame (BBB (base t) g) (univ \ {Sum.inl l})
+  hm := two_le_card_LB hB4 hH
+  caX := fun φ => bcost φ (2 * Fintype.card H - 2)
+  caY := fun φ => bcost φ (2 * Fintype.card H - 2)
+  cX1 := fun φ => bcost φ (2 * Fintype.card H + 2)
+  cY1 := fun φ => bcost φ (2 * Fintype.card H + 2)
+  cX2 := fun φ => bcost φ 4
+  cY2 := fun φ => bcost φ 4
+  inv0 := fun g t => ⟨unframeM (g.1 * Matrix.fromBlocks (tt (I.tv t)) 0 0 (diagI ∅) * g.1ᵀ),
+    frameM_unframeM _⟩
+  z0 := fun g => PhiB_zero_empty g
+  hN1 := fun d => frameM_unframeM _
+  hW1 := fun d => PhiB_one d (qS bs1 l)
+  hN2 := fun d => frameM_unframeM _
+  hW2 := fun d => PhiB_one d (qS bs2 l)
+  hN3 := fun d => frameM_unframeM _
+  hW3 := fun d => PhiB_one d (qS bs3 l)
+  hN4 := fun d => frameM_unframeM _
+  hW4 := fun d => PhiB_one d (qS bs4 l)
+  x01 := fun g t => ggeom_x01 I base l hbase g t
+  y01 := fun g t => ggeom_y01 I base l hbase g t
+  x12 := fun g t => ggeom_xx I base l hbase bs1 0 1 (Finset.mem_singleton_self _) mem1 g t
+  y12 := fun g t => ggeom_yy I base l hbase bs1 0 1 (Finset.mem_singleton_self _) mem1 g t
+  x23 := fun g t => ggeom_xx I base l hbase bs2 1 2 (Finset.mem_insert_self _ _) mem2 g t
+  y23 := fun g t => ggeom_yy I base l hbase bs2 1 2 (Finset.mem_insert_self _ _) mem2 g t
+  x34 := fun g t => ggeom_xx I base l hbase bs3 2 3 (Finset.mem_insert_self _ _) mem3 g t
+  y34 := fun g t => ggeom_yy I base l hbase bs3 2 3 (Finset.mem_insert_self _ _) mem3 g t
+  sfin := fun g => helper_fin5 g
+  aX2 := fun g t => ggeom_aX2 I base l hbase hH g t
+  aY2 := fun g t => ggeom_aY2 I base l hbase hH g t
+  fX1 := fun g t => ggeom_fX1 I base l hbase hH g t
+  fY1 := fun g t => ggeom_fY1 I base l hbase hH g t
+  fX2 := fun g t => ggeom_fX2 I base l hbase hH g t
+  fY2 := fun g t => ggeom_fY2 I base l hbase hH g t
+  term := fun g t => ggeom_term5 I base l hbase g t
+
+end Net
+
+section End
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+
+/-- an orthonormal basis through a unit vector with a zero coordinate, at any index. -/
+theorem base_ex (z : Space H) (hz : dot z z = 1) (hg : ∃ p, z p = 0) (l : H) :
+    ∃ A : OBase H, z = A.v l := by
+  obtain ⟨p, hp⟩ := hg
+  obtain ⟨A, k, hA⟩ := exists_base_one z hz p hp
+  refine ⟨reindex A (Equiv.swap k l), ?_⟩
+  rw [← hA]
+  show A.v k = A.v (Equiv.swap k l l)
+  rw [Equiv.swap_apply_right]
+
+/-- **Generalised certificate of the bridged word B_2** for a generalised invocation package. -/
+theorem bridge2_gcert (I : GInv H T Sl C) (hH : 1 ≤ Fintype.card H) :
+    GCert (L5 H) (Sum.inl : BLive (Orth (L5 H)) T Sl → BRole (Orth (L5 H)) T Sl C)
+      (fun φ => (Fintype.card (Orth (L5 H)) : ℝ)
+        * (5 * I.cost φ + (Fintype.card T : ℝ) * bankPrice (Fintype.card H) φ)) := by
+  obtain ⟨l⟩ : Nonempty H := Fintype.card_pos_iff.mp (by omega)
+  have hb : ∀ t, ∃ A : OBase H, I.tv t = A.v l :=
+    fun t => base_ex (I.tv t) (I.hunit t) (I.hgap t) l
+  choose base hbase using hb
+  exact gbridge2_certificate (ggeomBridge2 I base l hbase hH)
+
+end End
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.ggeomBridge2
+#print axioms OAI.PowerSaving.GX.bridge2_gcert
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__InvThm.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__InvThm.lean
new file mode 100644
index 0000000000..d69fcb4992
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__InvThm.lean
@@ -0,0 +1,164 @@
+import Work.GCert.Chain.Inv
+
+/-!
+# (key: gx-chain) THE CARRIER INVOCATION THEOREM on the generalised engine: `Lab.inv`
+
+`CR.Phased.inv` (`Work/Carrier/PhasedInv.lean`) with subspace labels and `GRoute`.  Forward word:
+
+    erase | y -= K s (old frame 0) | free adapters to the labels of the certificate | phase A |
+    c += Cc s | copies down | y += Jr c | phase B | final climbs | free adapters to the old
+    frames | slots := slot rows of the inverse (old frame 1) | erase
+
+The backward word is the transposed inverse, gate by gate, on the same labels.  The scalar
+identities are `Scal.fwd_scalar` / `Scal.bwd_scalar` (those of `CR.Phased`).
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB BR CR GF RF
+noncomputable section
+
+section Thm
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+variable {α : Type} [Fintype α] [DecidableEq α]
+variable {S : Scal T Sl C} (L : Lab H S) (W : GWin H α)
+
+/-- **Forward word on clean frames.** -/
+theorem Lab.fwd_erased (c0 c1 : C → CMat α) :
+    GRoute (iin W.Xm L.tv (fun _ : Sl => W.Xm.Φ 0) c0)
+      (iout W.Xm L.tv (fun _ : Sl => W.Xm.Φ 1) c1) shearF L.cost := by
+  have a1 : GRoute (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P)
+      (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P)
+      (actPoint (g1 S.Mt)) (fun _ => 0) :=
+    GRoute.gate (g1 S.Mt) _ _ (fun i j hij => by
+      by_cases e : i = j
+      · subst e; rfl
+      · obtain ⟨h1, h2⟩ := offdiag_x (g1_x S.Mt).1 (g1_x S.Mt).2 hij e
+        exact start_frames W.Xm L.tv i j h1 h2)
+  have b3 : GRoute (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      (actPoint (g8 S.Mti)) (fun _ => 0) :=
+    GRoute.gate (g8 S.Mti) _ _ (fun i j hij => by
+      by_cases e : i = j
+      · subst e; rfl
+      · have f := g8_facts S.hiy
+        obtain ⟨h1, h2, h3⟩ := offdiag_s f.1 f.2.1 f.2.2 hij e
+        exact end_old W.Xm L.tv i j h1 h2 h3)
+  have seg1 : GRoute (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P) (fun r => W.X.Φ (L.labA r))
+      S.f1 (fun φ => rcost φ L.rA) :=
+    ((a1.trans (L.ad0 W)).trans (L.pA W.X W.big).1).cast (fun φ => by simp)
+  have seg2 : GRoute (fun r => W.X.Φ (L.labA r)) (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      S.f2 (fun φ => rcost φ L.rB + rcost φ L.rF) :=
+    ((((L.pB W.X W.big).1.trans (L.pF W.X W.big)).trans (L.adF W)).trans b3).cast
+      (fun φ => by simp)
+  have e0 : GRoute (iin W.Xm L.tv (fun _ : Sl => W.Xm.Φ 0) c0)
+      (glue (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P) (fun k => W.X.Φ (L.cen k)))
+      eraseC (fun _ => 0) :=
+    GRoute.ofX (xerase (fun t => rfl) (fun t => rfl) (fun q => rfl))
+  have L1 := glift_live (fun k => W.X.Φ (L.cen k)) seg1
+  have m1 : GRoute (glue (fun r => W.X.Φ (L.labA r)) (fun k => W.X.Φ (L.cen k)))
+      (glue (fun r => W.X.Φ (L.labA r)) (fun k => W.X.Φ (L.cen k)))
+      (fun z => addBlk bC (ap S.Cc (z ∘ bS)) z) (fun _ => 0) :=
+    GRoute.ofX (xgate_shear bC bS bS_inj S.Cc (fun k q h => congrArg W.X.Φ (L.hAc k q h)))
+  have m2 := L.cdown W (fun r => W.X.Φ (L.labA r))
+  have m3 : GRoute (glue (fun r => W.X.Φ (L.labA r)) (fun _ : C => W.X.Φ L.z0))
+      (glue (fun r => W.X.Φ (L.labA r)) (fun _ : C => W.X.Φ L.z0))
+      (fun z => addBlk bY (ap S.Jr (z ∘ bC)) z) (fun _ => 0) :=
+    GRoute.ofX (xgate_shear bY bC bC_inj S.Jr (fun t k _ => congrArg W.X.Φ (L.hAy t)))
+  have L2 := glift_live (fun _ : C => W.X.Φ L.z0) seg2
+  have e1 : GRoute (glue (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r)) (fun _ : C => W.X.Φ L.z0))
+      (iout W.Xm L.tv (fun _ : Sl => W.Xm.Φ 1) c1) eraseC (fun _ => 0) :=
+    GRoute.ofX (xerase (fun t => rfl) (fun t => rfl) (fun q => rfl))
+  have tot := (((((e0.trans L1).trans m1).trans m2).trans m3).trans L2).trans e1
+  refine (tot.castg (g' := shearF) (funext fun z => S.fwd_scalar z)).cast (fun φ => ?_)
+  simp only [Lab.cost, zero_add, add_zero]
+  ring
+
+/-- **Backward word on clean frames**: the transposed inverse gates, same labels; the copies
+start at the zero frame and climb. -/
+theorem Lab.bwd_erased (c0 c1 : C → CMat α) :
+    GRoute (iin W.Xm L.tv (fun _ : Sl => W.Xm.Φ 0) c0)
+      (iout W.Xm L.tv (fun _ : Sl => W.Xm.Φ 1) c1) shearB L.cost := by
+  have a1 : GRoute (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P)
+      (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P)
+      (actPoint (g1i S.Mt)ᵀ) (fun _ => 0) :=
+    GRoute.gate (g1i S.Mt)ᵀ _ _ (fun i j hij => by
+      by_cases e : i = j
+      · subst e; rfl
+      · have hij' : g1i S.Mt j i ≠ 0 := hij
+        obtain ⟨h1, h2⟩ := offdiag_x (g1i_x S.Mt).1 (g1i_x S.Mt).2 hij' (Ne.symm e)
+        exact start_frames W.Xm L.tv i j h2 h1)
+  have b3 : GRoute (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      (actPoint (h8 S.Mt)ᵀ) (fun _ => 0) :=
+    GRoute.gate (h8 S.Mt)ᵀ _ _ (fun i j hij => by
+      by_cases e : i = j
+      · subst e; rfl
+      · have hij' : h8 S.Mt j i ≠ 0 := hij
+        have f := h8_facts S.hmy
+        obtain ⟨h1, h2, h3⟩ := offdiag_s f.1 f.2.1 f.2.2 hij' (Ne.symm e)
+        exact (end_old W.Xm L.tv j i h1 h2 h3).symm)
+  have seg1 : GRoute (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P) (fun r => W.X.Φ (L.labA r))
+      S.b1 (fun φ => rcost φ L.rA) :=
+    ((a1.trans (L.ad0 W)).trans (L.pA W.X W.big).2).cast (fun φ => by simp)
+  have seg2 : GRoute (fun r => W.X.Φ (L.labA r)) (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      S.b2 (fun φ => rcost φ L.rB + rcost φ L.rF) :=
+    ((((L.pB W.X W.big).2.trans (L.pF W.X W.big)).trans (L.adF W)).trans b3).cast
+      (fun φ => by simp)
+  have e0 : GRoute (iin W.Xm L.tv (fun _ : Sl => W.Xm.Φ 0) c0)
+      (glue (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P) (fun _ : C => W.X.Φ L.z0))
+      eraseC (fun _ => 0) :=
+    GRoute.ofX (xerase (fun t => rfl) (fun t => rfl) (fun q => rfl))
+  have L1 := glift_live (fun _ : C => W.X.Φ L.z0) seg1
+  have m1 : GRoute (glue (fun r => W.X.Φ (L.labA r)) (fun _ : C => W.X.Φ L.z0))
+      (glue (fun r => W.X.Φ (L.labA r)) (fun _ : C => W.X.Φ L.z0))
+      (fun z => addBlk bC (ap S.Jrᵀ (z ∘ bY)) z) (fun _ => 0) :=
+    GRoute.ofX (xgate_shear bC bY bY_inj S.Jrᵀ (fun k t _ => (congrArg W.X.Φ (L.hAy t)).symm))
+  have m2 := L.cup W (fun r => W.X.Φ (L.labA r))
+  have m3 : GRoute (glue (fun r => W.X.Φ (L.labA r)) (fun k => W.X.Φ (L.cen k)))
+      (glue (fun r => W.X.Φ (L.labA r)) (fun k => W.X.Φ (L.cen k)))
+      (fun z => addBlk bS (ap (-S.Ccᵀ) (z ∘ bC)) z) (fun _ => 0) :=
+    GRoute.ofX (xgate_shear bS bC bC_inj (-S.Ccᵀ)
+      (fun q k h => (congrArg W.X.Φ (L.hAc k q (ne_of_negT S.Cc h))).symm))
+  have L2 := glift_live (fun k => W.X.Φ (L.cen k)) seg2
+  have e1 : GRoute (glue (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r)) (fun k => W.X.Φ (L.cen k)))
+      (iout W.Xm L.tv (fun _ : Sl => W.Xm.Φ 1) c1) eraseC (fun _ => 0) :=
+    GRoute.ofX (xerase (fun t => rfl) (fun t => rfl) (fun q => rfl))
+  have tot := (((((e0.trans L1).trans m1).trans m2).trans m3).trans L2).trans e1
+  refine (tot.castg (g' := shearB) (funext fun z => S.bwd_scalar z)).cast (fun φ => ?_)
+  simp only [Lab.cost, zero_add, add_zero]
+  ring
+
+/-- **THE CARRIER INVOCATION THEOREM on the generalised engine.**  The two halves of a
+certificate are an invocation package for the bridged network, with the price `L.cost`. -/
+def Lab.inv : GInv H T Sl C where
+  tv := L.tv
+  hunit := L.hunit
+  hgap := L.hgap
+  cost := L.cost
+  fwd := fun W N0 Wn hN hW Z c0 c1 =>
+    gdirty_of_erased W.Xm L.tv N0 Wn hN hW Z c0 c1 (L.fwd_erased W c0 c1)
+      (shearF_comm (fun _ => 1) (fun q => N0 * Z q) (fun _ => 1))
+  bwd := fun W N0 Wn hN hW Z c0 c1 =>
+    gdirty_of_erased W.Xm L.tv N0 Wn hN hW Z c0 c1 (L.bwd_erased W c0 c1)
+      (shearB_comm (fun _ => 1) (fun q => N0 * Z q) (fun _ => 1))
+
+@[simp] lemma Lab.inv_cost (φ : ℕ → ℝ) : L.inv.cost φ = L.cost φ := rfl
+@[simp] lemma Lab.inv_tv : L.inv.tv = L.tv := rfl
+
+end Thm
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.Lab.fwd_erased
+#print axioms OAI.PowerSaving.GX.Lab.bwd_erased
+#print axioms OAI.PowerSaving.GX.Lab.inv
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__NetCert.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__NetCert.lean
new file mode 100644
index 0000000000..6336ba0766
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__NetCert.lean
@@ -0,0 +1,157 @@
+import Work.GCert.Chain.NetStage
+import Work.GFrame.Top.Assemble
+
+/-!
+# (key: gx-chain) The bridged word B_2 on the generalised engine: the certificate `GCert`
+
+GENERATED by checks/wht26/gx-chain/py/netgen.py from Work/Bridge/Cert.lean (section Net).
+`gbridge2_certificate`: a `GCert` on the live roles `BLive Γ T Sl` with price `card Γ * N.unit φ`.
+The gate layers, the idle climbs and the exchange are the old routes (`GRoute.ofX`).  No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR GF
+noncomputable section
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : GBridge2 H T Sl C α Γ)
+
+/-- gate layer A, after stage 1 and the first idle climb of pair 2: twins have equal frames. -/
+lemma GBridge2.gateA : XRoute N.S3 N.S3 (gsc pAB kA) (fun _ => 0) := by
+  refine gateP pAB kA N.S3 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- gate layer B, after stage 2 and the second idle climb of pair 2. -/
+lemma GBridge2.gateB : XRoute N.S5 N.S5 (gsc pAB kB) (fun _ => 0) := by
+  refine gateP pAB kB N.S5 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · exact N.x23 g t
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · exact (N.y23 g t).symm
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- gate layer C, after the final climbs. -/
+lemma GBridge2.gateC : XRoute N.S8 N.S8 (gsc pC kCc) (fun _ => 0) := by
+  refine gateP pC kCc N.S8 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · exact (hk rfl).elim
+  · rfl
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- the free shifts at the end. -/
+def GBridge2.corr : BRole Γ T Sl C → Space α :=
+  mkB (fun _ _ => 0) (fun g t => N.u g t) (fun _ _ => 0) (fun g t => N.u g t)
+    (fun _ _ => 0) (fun _ _ => 0)
+
+def GBridge2.S9 : BRole Γ T Sl C → CMat α := fun r => shift (N.corr r) * N.S8 r
+
+/-- the whole word before the exchange: five stages, three idle-climb layers, three gate
+layers. -/
+lemma GBridge2.route :
+    GRoute N.S0 N.S8 chain (fun φ => (Fintype.card Γ : ℝ) * N.unit φ) := by
+  have R := ((((((((((N.stage0.trans N.stage1).trans (GRoute.ofX N.climbA)).trans
+    (GRoute.ofX N.gateA)).trans N.stage2).trans (GRoute.ofX N.climbB)).trans
+    (GRoute.ofX N.gateB)).trans N.stage3).trans N.stage4).trans
+    (GRoute.ofX N.fin)).trans (GRoute.ofX N.gateC))
+  refine (R.castg ?_).cast (fun φ => ?_)
+  · rfl
+  · simp only [GBridge2.unit]
+    ring
+
+/-- **The scratch certificate of the bridged five-stage network with shared helper sets**,
+in whole blocks, with its exact price for every price list. -/
+theorem gbridge2_certificate :
+    GCert α (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C)
+      (fun φ => (Fintype.card Γ : ℝ) * N.unit φ) := by
+  have R2 : GRoute N.S8 N.S9 id (fun _ => 0) := GRoute.shifts N.hm N.S8 N.corr
+  have R3 : GRoute N.S9 (fun r => N.S9 (bpull r)) (actPoint brecM) (fun _ => 0) :=
+    GRoute.gate brecM N.S9 _ (fun i j h => by
+      have hj : j = bpull i := by
+        by_contra hne
+        exact h (by simp [brecM, hne])
+      rw [hj])
+  have Rt := ((N.route.trans R2).trans R3).cast (c' := fun φ => (Fintype.card Γ : ℝ) * N.unit φ)
+    (fun φ => by first | ring | simp)
+  have hSinv : ∀ r, ∃ M, N.S0 r * M = 1 := by
+    rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.inv0 g t
+    · refine ⟨1, ?_⟩
+      show (N.G0 g).Xm.Φ 0 * 1 = 1
+      rw [N.z0, Matrix.mul_one]
+    · exact N.inv0 g t
+    · refine ⟨1, ?_⟩
+      show (N.G0 g).Xm.Φ 0 * 1 = 1
+      rw [N.z0, Matrix.mul_one]
+    · exact ⟨1, Matrix.mul_one _⟩
+    · exact ⟨1, Matrix.mul_one _⟩
+  have hT : ∀ l : BLive Γ T Sl, N.S9 (bpull (Sum.inl l)) = kernel α * N.S0 (Sum.inl l) := by
+    rintro (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+    · show shift (N.u g t) * N.YF g t = kernel α * (N.G0 g).Xm.Φ (tt (N.I.tv t))
+      exact (N.term g t).symm
+    · show shift (0 : Space α) * kernel α = kernel α * (N.G0 g).Xm.Φ 0
+      rw [shift_zero, Matrix.one_mul, N.z0, Matrix.mul_one]
+    · show shift (N.u g t) * N.YF g t = kernel α * (N.G0 g).Xm.Φ (tt (N.I.tv t))
+      exact (N.term g t).symm
+    · show shift (0 : Space α) * kernel α = kernel α * (N.G0 g).Xm.Φ 0
+      rw [shift_zero, Matrix.one_mul, N.z0, Matrix.mul_one]
+    · show shift (0 : Space α) * kernel α = kernel α * 1
+      rw [shift_zero, Matrix.one_mul, Matrix.mul_one]
+  have hg : ∀ x : BRole Γ T Sl C → ℂ,
+      (∀ s, (∀ l : BLive Γ T Sl, (Sum.inl l : BRole Γ T Sl C) ≠ s) → x s = 0) →
+      ∀ l : BLive Γ T Sl,
+        (actPoint brecM ∘ (id ∘ chain)) x (Sum.inl l) = x (Sum.inl l) := by
+    intro x _ l
+    change actPoint brecM (chain x) (Sum.inl l) = _
+    rw [actPoint_brecM]
+    rcases l with (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inl (Sum.inr (g,t))))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kX1 (g,t)) = x (kX1 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((-1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inl (Sum.inl (g,t))))) = _
+      rw [chain_eq]
+      show ((-1:ℚ):ℂ) * (-x (kY1 (g,t))) = x (kY1 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inr (Sum.inr (g,t))))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kX2 (g,t)) = x (kX2 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((-1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inr (Sum.inl (g,t))))) = _
+      rw [chain_eq]
+      show ((-1:ℚ):ℂ) * (-x (kY2 (g,t))) = x (kY2 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inr (g,q))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kS (g,q)) = x (kS (g,q))
+      first | (push_cast; ring) | simp
+  exact gcert_of_groute (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C) N.S0
+    (fun r => N.S9 (bpull r)) _ _ Rt hSinv hg hT
+
+end Net
+
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.GBridge2.route
+#print axioms OAI.PowerSaving.GX.gbridge2_certificate
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__NetDef.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__NetDef.lean
new file mode 100644
index 0000000000..c13042eb43
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__NetDef.lean
@@ -0,0 +1,157 @@
+import Work.GCert.Chain.Stage
+
+/-!
+# (key: gx-chain) The bridged five-stage word B_2 on the generalised engine: data and frames
+
+GENERATED by checks/wht26/gx-chain/py/netgen.py from Work/Bridge/Net.lean (`BR.Bridge2`): the
+invocation is a `GInv`, the frame maps of the stages are windows `GWin` (`G0 .. G4`; the old
+frame map of a window is `.Xm`).  Everything else word for word.  No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR GF
+noncomputable section
+
+/-- See the file header.  Fields in the style of `RF.Fold3S`; stages are numbered 0 to 4. -/
+structure GBridge2 (H T Sl C α Γ : Type) [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α] where
+  /-- the invocation (for a block circuit `X`: `X.inv`). -/
+  I : GInv H T Sl C
+  /-- frame maps of the invocations of the five stages. -/
+  G0 : Γ → GWin H α
+  G1 : Γ → GWin H α
+  G2 : Γ → GWin H α
+  G3 : Γ → GWin H α
+  G4 : Γ → GWin H α
+  /-- the class `(g,t)` is served by the invocation `g` in stage 0 and `r_l t g` in stage `l`. -/
+  r1 : T → Γ ≃ Γ
+  r2 : T → Γ ≃ Γ
+  r3 : T → Γ ≃ Γ
+  r4 : T → Γ ≃ Γ
+  /-- the invocation `d` of stage `l` uses the helper set (and the copies) `s_l d`. -/
+  s1 : Γ ≃ Γ
+  s2 : Γ ≃ Γ
+  s3 : Γ ≃ Γ
+  s4 : Γ ≃ Γ
+  /-- inverse of the frame of the base, and frame of the window, of every invocation. -/
+  N1 : Γ → CMat α
+  W1 : Γ → CMat α
+  N2 : Γ → CMat α
+  W2 : Γ → CMat α
+  N3 : Γ → CMat α
+  W3 : Γ → CMat α
+  N4 : Γ → CMat α
+  W4 : Γ → CMat α
+  u : Γ → T → Space α
+  YF : Γ → T → CMat α
+  hm : 2 ≤ Fintype.card α
+  /-- prices of the idle climbs, for every price list.  B_2 with merged climbs:
+  `caX = caY = fun φ => bcost φ (2h-2)`, `cX1 = cY1 = fun φ => bcost φ (2h+2)`,
+  `cX2 = cY2 = fun φ => bcost φ 4`. -/
+  caX : (ℕ → ℝ) → ℝ
+  caY : (ℕ → ℝ) → ℝ
+  cX1 : (ℕ → ℝ) → ℝ
+  cY1 : (ℕ → ℝ) → ℝ
+  cX2 : (ℕ → ℝ) → ℝ
+  cY2 : (ℕ → ℝ) → ℝ
+  inv0 : ∀ g t, ∃ N : CMat α, (G0 g).Xm.Φ (tt (I.tv t)) * N = 1
+  z0 : ∀ g, (G0 g).Xm.Φ 0 = 1
+  hN1 : ∀ d, (G1 d).Xm.Φ 0 * N1 d = 1
+  hW1 : ∀ d, (G1 d).Xm.Φ 1 = W1 d * (G1 d).Xm.Φ 0
+  hN2 : ∀ d, (G2 d).Xm.Φ 0 * N2 d = 1
+  hW2 : ∀ d, (G2 d).Xm.Φ 1 = W2 d * (G2 d).Xm.Φ 0
+  hN3 : ∀ d, (G3 d).Xm.Φ 0 * N3 d = 1
+  hW3 : ∀ d, (G3 d).Xm.Φ 1 = W3 d * (G3 d).Xm.Φ 0
+  hN4 : ∀ d, (G4 d).Xm.Φ 0 * N4 d = 1
+  hW4 : ∀ d, (G4 d).Xm.Φ 1 = W4 d * (G4 d).Xm.Φ 0
+  /-- the bank frames a stage leaves are the bank frames the next stage starts from. -/
+  x01 : ∀ g t, (G0 g).Xm.Φ 1 = (G1 (r1 t g)).Xm.Φ (tt (I.tv t))
+  y01 : ∀ g t, (G0 g).Xm.Φ (1 + tt (I.tv t)) = (G1 (r1 t g)).Xm.Φ 0
+  x12 : ∀ g t, (G1 (r1 t g)).Xm.Φ 1 = (G2 (r2 t g)).Xm.Φ (tt (I.tv t))
+  y12 : ∀ g t, (G1 (r1 t g)).Xm.Φ (1 + tt (I.tv t)) = (G2 (r2 t g)).Xm.Φ 0
+  x23 : ∀ g t, (G2 (r2 t g)).Xm.Φ 1 = (G3 (r3 t g)).Xm.Φ (tt (I.tv t))
+  y23 : ∀ g t, (G2 (r2 t g)).Xm.Φ (1 + tt (I.tv t)) = (G3 (r3 t g)).Xm.Φ 0
+  x34 : ∀ g t, (G3 (r3 t g)).Xm.Φ 1 = (G4 (r4 t g)).Xm.Φ (tt (I.tv t))
+  y34 : ∀ g t, (G3 (r3 t g)).Xm.Φ (1 + tt (I.tv t)) = (G4 (r4 t g)).Xm.Φ 0
+  /-- the five windows of a helper set make up the kernel. -/
+  sfin : ∀ g, W4 (s4.symm g) * (W3 (s3.symm g) * (W2 (s2.symm g) *
+    (W1 (s1.symm g) * (G0 g).Xm.Φ 1))) = kernel α
+  /-- pair 2, idle in stages 0 and 1: ONE block from its start frame to the frame of its
+  twin after stage 1. -/
+  aX2 : ∀ g t, XReach ((G0 g).Xm.Φ (tt (I.tv t))) ((G1 (r1 t g)).Xm.Φ 1) caX
+  aY2 : ∀ g t, XReach ((G0 g).Xm.Φ 0) ((G1 (r1 t g)).Xm.Φ (1 + tt (I.tv t))) caY
+  /-- pair 1, idle in stages 3 and 4: ONE block from its frame after stage 2 to the end. -/
+  fX1 : ∀ g t, XReach ((G2 (r2 t g)).Xm.Φ 1) (kernel α) cX1
+  fY1 : ∀ g t, XReach ((G2 (r2 t g)).Xm.Φ (1 + tt (I.tv t))) (YF g t) cY1
+  /-- pair 2 after stage 4: ONE final block. -/
+  fX2 : ∀ g t, XReach ((G4 (r4 t g)).Xm.Φ 1) (kernel α) cX2
+  fY2 : ∀ g t, XReach ((G4 (r4 t g)).Xm.Φ (1 + tt (I.tv t))) (YF g t) cY2
+  term : ∀ g t, kernel α * (G0 g).Xm.Φ (tt (I.tv t)) = shift (u g t) * YF g t
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : GBridge2 H T Sl C α Γ)
+
+/-- price of the blocks of one unit (one element of `Γ`): five invocations and the idle
+climbs of the four bank roles of every class. -/
+def GBridge2.unit (φ : ℕ → ℝ) : ℝ :=
+  5 * N.I.cost φ + (Fintype.card T : ℝ) * ((N.caX φ + N.caY φ)
+    + 2 * bcost φ (Fintype.card H - 1)
+    + (N.cX1 φ + N.cY1 φ) + (N.cX2 φ + N.cY2 φ))
+
+/-- the bank index of stage 0: the class `(g,t)` belongs to the invocation `g`. -/
+abbrev bid (Γ T : Type) : T → Γ ≃ Γ := fun _ => Equiv.refl Γ
+
+/-! bank frames of the class `(g,t)`: `xi l`, `yi l` at the START of stage `l`; `xo l`,
+`yo l` at the END of stage `l` (only where no next stage follows on that pair). -/
+def GBridge2.xi0 (g : Γ) (t : T) : CMat α := (N.G0 g).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi0 (g : Γ) (t : T) : CMat α := (N.G0 g).Xm.Φ 0
+def GBridge2.xi1 (g : Γ) (t : T) : CMat α := (N.G1 (N.r1 t g)).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi1 (g : Γ) (t : T) : CMat α := (N.G1 (N.r1 t g)).Xm.Φ 0
+def GBridge2.xi2 (g : Γ) (t : T) : CMat α := (N.G2 (N.r2 t g)).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi2 (g : Γ) (t : T) : CMat α := (N.G2 (N.r2 t g)).Xm.Φ 0
+def GBridge2.xo2 (g : Γ) (t : T) : CMat α := (N.G2 (N.r2 t g)).Xm.Φ 1
+def GBridge2.yo2 (g : Γ) (t : T) : CMat α := (N.G2 (N.r2 t g)).Xm.Φ (1 + tt (N.I.tv t))
+def GBridge2.xi3 (g : Γ) (t : T) : CMat α := (N.G3 (N.r3 t g)).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi3 (g : Γ) (t : T) : CMat α := (N.G3 (N.r3 t g)).Xm.Φ 0
+def GBridge2.xi4 (g : Γ) (t : T) : CMat α := (N.G4 (N.r4 t g)).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi4 (g : Γ) (t : T) : CMat α := (N.G4 (N.r4 t g)).Xm.Φ 0
+def GBridge2.xo4 (g : Γ) (t : T) : CMat α := (N.G4 (N.r4 t g)).Xm.Φ 1
+def GBridge2.yo4 (g : Γ) (t : T) : CMat α := (N.G4 (N.r4 t g)).Xm.Φ (1 + tt (N.I.tv t))
+
+/-- helper slots after the stages 0, 1, 2, 3, 4 (at the start: `cOne Γ Sl α`). -/
+def GBridge2.Z1 : Γ → Sl → CMat α := fun g _ => (N.G0 g).Xm.Φ 1
+def GBridge2.Z2 : Γ → Sl → CMat α := fun g q => N.W1 (N.s1.symm g) * N.Z1 g q
+def GBridge2.Z3 : Γ → Sl → CMat α := fun g q => N.W2 (N.s2.symm g) * N.Z2 g q
+def GBridge2.Z4 : Γ → Sl → CMat α := fun g q => N.W3 (N.s3.symm g) * N.Z3 g q
+def GBridge2.Z5 : Γ → Sl → CMat α := fun g q => N.W4 (N.s4.symm g) * N.Z4 g q
+
+/-- frames: at the start; after stage 0; after stage 1; after the first idle climb of pair 2
+(first gate layer here); after stage 2; after the second idle climb of pair 2 (second gate
+layer here); after stage 3; after stage 4; after the final climbs (third gate layer here). -/
+def GBridge2.S0 : BRole Γ T Sl C → CMat α := mkB N.xi0 N.yi0 N.xi0 N.yi0 (cOne Γ Sl α) (cOne Γ C α)
+def GBridge2.S1 : BRole Γ T Sl C → CMat α := mkB N.xi1 N.yi1 N.xi0 N.yi0 N.Z1 (cOne Γ C α)
+def GBridge2.S2 : BRole Γ T Sl C → CMat α := mkB N.xi2 N.yi2 N.xi0 N.yi0 N.Z2 (cOne Γ C α)
+def GBridge2.S3 : BRole Γ T Sl C → CMat α := mkB N.xi2 N.yi2 N.xi2 N.yi2 N.Z2 (cOne Γ C α)
+def GBridge2.S4 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi2 N.yi2 N.Z3 (cOne Γ C α)
+def GBridge2.S5 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi3 N.yi3 N.Z3 (cOne Γ C α)
+def GBridge2.S6 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi4 N.yi4 N.Z4 (cOne Γ C α)
+def GBridge2.S7 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xo4 N.yo4 N.Z5 (cOne Γ C α)
+def GBridge2.S8 : BRole Γ T Sl C → CMat α :=
+  mkB (fun _ _ => kernel α) N.YF (fun _ _ => kernel α) N.YF (fun _ _ => kernel α) (cOne Γ C α)
+
+
+end Net
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.GBridge2.unit
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__NetStage.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__NetStage.lean
new file mode 100644
index 0000000000..670f4c6a84
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__NetStage.lean
@@ -0,0 +1,186 @@
+import Work.GCert.Chain.NetDef
+
+/-!
+# (key: gx-chain) The bridged word B_2 on the generalised engine: the five stages and the idle climbs
+
+GENERATED by checks/wht26/gx-chain/py/netgen.py from Work/Bridge/Net.lean.  The stages are
+`GRoute`s (`gistage_fwd` / `gistage_bwd`, `gblift1` / `gblift2`); the idle climbs of the bank
+roles are the OLD block routes, unchanged.  No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR GF
+noncomputable section
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : GBridge2 H T Sl C α Γ)
+
+/-- stage 0: forward on pair 1, every helper set starts at the matrix `1`. -/
+lemma GBridge2.stage0 :
+    GRoute N.S0 N.S1 (lift1 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := gistage_fwd N.I (bid Γ T) (Equiv.refl Γ) N.G0 (fun _ => 1) (fun g => (N.G0 g).Xm.Φ 1)
+    (fun d => by rw [N.z0, Matrix.mul_one]) (fun d => by rw [N.z0, Matrix.mul_one])
+    (cOne Γ Sl α) (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv (bid Γ T) (fun d => (N.G0 d).Xm)
+      (fun g (q : Sl) => (N.G0 ((Equiv.refl Γ).symm g)).Xm.Φ 1 * cOne Γ Sl α g q) (cOne Γ C α)
+      = mkS N.xi1 N.yi1 N.Z1 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x01 g t
+    · exact N.y01 g t
+    · show (N.G0 g).Xm.Φ 1 * 1 = (N.G0 g).Xm.Φ 1
+      rw [Matrix.mul_one]
+    · rfl
+  have h' : GRoute (bIn N.I.tv (bid Γ T) (fun d => (N.G0 d).Xm) (cOne Γ Sl α) (cOne Γ C α))
+      (mkS N.xi1 N.yi1 N.Z1 (cOne Γ C α)) GF (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact gblift1 N.xi0 N.yi0 h'
+
+/-- stage 1: backward on pair 1; the helper set `g` serves the invocation `s1⁻¹ g`. -/
+lemma GBridge2.stage1 :
+    GRoute N.S1 N.S2 (lift1 GB) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := gistage_bwd N.I N.r1 N.s1 N.G1 N.N1 N.W1 N.hN1 N.hW1 N.Z1 (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv N.r1 (fun d => (N.G1 d).Xm) (fun g q => N.W1 (N.s1.symm g) * N.Z1 g q) (cOne Γ C α)
+      = mkS N.xi2 N.yi2 N.Z2 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x12 g t
+    · exact N.y12 g t
+    · rfl
+    · rfl
+  have h' : GRoute (bIn N.I.tv N.r1 (fun d => (N.G1 d).Xm) N.Z1 (cOne Γ C α))
+      (mkS N.xi2 N.yi2 N.Z2 (cOne Γ C α)) GB (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact gblift1 N.xi0 N.yi0 h'
+
+/-- stage 2: forward on pair 1. -/
+lemma GBridge2.stage2 :
+    GRoute N.S3 N.S4 (lift1 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) :=
+  gblift1 N.xi2 N.yi2
+    (gistage_fwd N.I N.r2 N.s2 N.G2 N.N2 N.W2 N.hN2 N.hW2 N.Z2 (cOne Γ C α) (cOne Γ C α))
+
+/-- stage 3: backward on pair 2. -/
+lemma GBridge2.stage3 :
+    GRoute N.S5 N.S6 (lift2 GB) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := gistage_bwd N.I N.r3 N.s3 N.G3 N.N3 N.W3 N.hN3 N.hW3 N.Z3 (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv N.r3 (fun d => (N.G3 d).Xm) (fun g q => N.W3 (N.s3.symm g) * N.Z3 g q) (cOne Γ C α)
+      = mkS N.xi4 N.yi4 N.Z4 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x34 g t
+    · exact N.y34 g t
+    · rfl
+    · rfl
+  have h' : GRoute (bIn N.I.tv N.r3 (fun d => (N.G3 d).Xm) N.Z3 (cOne Γ C α))
+      (mkS N.xi4 N.yi4 N.Z4 (cOne Γ C α)) GB (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact gblift2 N.xo2 N.yo2 h'
+
+/-- stage 4: forward on pair 2. -/
+lemma GBridge2.stage4 :
+    GRoute N.S6 N.S7 (lift2 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) :=
+  gblift2 N.xo2 N.yo2
+    (gistage_fwd N.I N.r4 N.s4 N.G4 N.N4 N.W4 N.hN4 N.hW4 N.Z4 (cOne Γ C α) (cOne Γ C α))
+
+/-- first idle climb of pair 2 (stages 0 and 1 in ONE block per role), to the frames of
+pair 1 after stage 1. -/
+lemma GBridge2.climbA :
+    XRoute N.S2 N.S3 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * (N.caX φ + N.caY φ))) := by
+  have H1 := XRoute.reach_all N.S2 N.S3
+    (mkB (fun _ _ _ => 0) (fun _ _ _ => 0) (fun _ _ => N.caX)
+      (fun _ _ => N.caY) (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact XReach.refl _
+      · exact XReach.refl _
+      · show XReach ((N.G0 g).Xm.Φ (tt (N.I.tv t))) ((N.G2 (N.r2 t g)).Xm.Φ (tt (N.I.tv t))) N.caX
+        rw [← N.x12 g t]
+        exact N.aX2 g t
+      · show XReach ((N.G0 g).Xm.Φ 0) ((N.G2 (N.r2 t g)).Xm.Φ 0) N.caY
+        rw [← N.y12 g t]
+        exact N.aY2 g t
+      · exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+/-- second idle climb of pair 2: the window of stage 2, ONE block of rank `card H - 1` per
+role, to the frames of pair 1 after stage 2. -/
+lemma GBridge2.climbB :
+    XRoute N.S4 N.S5 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * (2 * bcost φ (Fintype.card H - 1)))) := by
+  have H1 := XRoute.reach_all N.S4 N.S5
+    (mkB (fun _ _ _ => 0) (fun _ _ _ => 0) (fun _ _ φ => bcost φ (Fintype.card H - 1))
+      (fun _ _ φ => bcost φ (Fintype.card H - 1)) (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact XReach.refl _
+      · exact XReach.refl _
+      · show XReach ((N.G2 (N.r2 t g)).Xm.Φ (tt (N.I.tv t))) ((N.G3 (N.r3 t g)).Xm.Φ (tt (N.I.tv t)))
+          (fun φ => bcost φ (Fintype.card H - 1))
+        rw [← N.x23 g t]
+        exact N.I.climbX (N.G2 (N.r2 t g)).Xm t
+      · show XReach ((N.G2 (N.r2 t g)).Xm.Φ 0) ((N.G3 (N.r3 t g)).Xm.Φ 0)
+          (fun φ => bcost φ (Fintype.card H - 1))
+        rw [← N.y23 g t]
+        exact N.I.climbY (N.G2 (N.r2 t g)).Xm t
+      · exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+/-- the final climbs: pair 1 from its frames after stage 2 (ONE block per role for the
+stages 3, 4 and the rest), pair 2 from its frames after stage 4; the helper slots are
+already at the kernel. -/
+lemma GBridge2.fin :
+    XRoute N.S7 N.S8 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * ((N.cX1 φ + N.cY1 φ) + (N.cX2 φ + N.cY2 φ)))) := by
+  have H1 := XRoute.reach_all N.S7 N.S8
+    (mkB (fun _ _ => N.cX1) (fun _ _ => N.cY1) (fun _ _ => N.cX2) (fun _ _ => N.cY2)
+      (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact N.fX1 g t
+      · exact N.fY1 g t
+      · exact N.fX2 g t
+      · exact N.fY2 g t
+      · show XReach (N.W4 (N.s4.symm g) * (N.W3 (N.s3.symm g) * (N.W2 (N.s2.symm g) *
+          (N.W1 (N.s1.symm g) * (N.G0 g).Xm.Φ 1)))) (kernel α) (fun _ => 0)
+        rw [N.sfin g]
+        exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+end Net
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.GBridge2.stage0
+#print axioms OAI.PowerSaving.GX.GBridge2.stage1
+#print axioms OAI.PowerSaving.GX.GBridge2.stage2
+#print axioms OAI.PowerSaving.GX.GBridge2.stage3
+#print axioms OAI.PowerSaving.GX.GBridge2.stage4
+#print axioms OAI.PowerSaving.GX.GBridge2.climbA
+#print axioms OAI.PowerSaving.GX.GBridge2.climbB
+#print axioms OAI.PowerSaving.GX.GBridge2.fin
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__Phased.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__Phased.lean
new file mode 100644
index 0000000000..e68c42377f
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__Phased.lean
@@ -0,0 +1,199 @@
+import Work.Carrier.Phases
+import Work.GFrame.Labels.All
+
+/-!
+# (key: gx-chain) The certificate as two halves: `Scal` (scalar half) and `Lab` (label half)
+
+`Scal T Sl C`: the scalar fields of `CR.Phased` (three facts about ONE matrix
+`Mt = MB * scatM (Jr * Cc) * MA`).  The scalar identities of the forward and of the backward
+word (`fwd_scalar`, `bwd_scalar`) are those of `Work/Carrier/Phases.lean`, word for word.
+
+`Lab H S`: subspace labels (`GF.SLbl H`), routes of the three phases on the generalised engine
+(`GF.GRoute`) through every stage-B frame map (`GF.BXMap H α`), and facts about dimensions at
+the two ends.  No projector, no `Climb`.
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB BR CR GF
+noncomputable section
+
+/-- **The scalar half.** -/
+structure Scal (T Sl C : Type) [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] where
+  Cc : Matrix C Sl ℚ
+  Jr : Matrix T C ℚ
+  MA : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MAi : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MB : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MBi : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  hAi : MAi * MA = 1
+  hBi : MBi * MB = 1
+  hx : ∀ t j, (MB * scatM (Jr * Cc) * MA) (lX t) j = if lX t = j then 1 else 0
+  hy : ∀ i t, (MB * scatM (Jr * Cc) * MA) i (lY t) = if i = lY t then 1 else 0
+  hid : ∀ S t, (MB * scatM (Jr * Cc) * MA) (lY S) (lX t) = if S = t then 1 else 0
+
+/-- **The label half.**  See `checks/wht26/shared/gcert-interface.md`, section CHAIN. -/
+structure Lab (H : Type) [Fintype H] [DecidableEq H] {T Sl C : Type} [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] (S : Scal T Sl C) where
+  tv : T → Space H
+  hunit : ∀ t, dot (tv t) (tv t) = 1
+  hgap : ∀ t, ∃ p, tv t p = 0
+  lab0 : L3 T Sl → SLbl H
+  labA : L3 T Sl → SLbl H
+  labB : L3 T Sl → SLbl H
+  labF : L3 T Sl → SLbl H
+  cen : C → SLbl H
+  z0 : SLbl H
+  hz0 : z0.dim = 0
+  h0x : ∀ t, (lab0 (lX t)).dim = 1 ∧ (lab0 (lX t)).Mem (tv t)
+  h0y : ∀ t, (lab0 (lY t)).dim = 0
+  h0s : ∀ q, (lab0 (lS q)).dim = 0
+  hAy : ∀ t, labA (lY t) = z0
+  hAc : ∀ k q, S.Cc k q ≠ 0 → cen k = labA (lS q)
+  hcen : ∀ k, 0 < (cen k).dim
+  hFx : ∀ t, (labF (lX t)).dim = Fintype.card H
+  hFs : ∀ q, (labF (lS q)).dim = Fintype.card H
+  hFy : ∀ t, (labF (lY t)).dim + 1 = Fintype.card H ∧
+    ∀ x, (labF (lY t)).Mem x → dot (tv t) x = 0
+  rA : List ℕ
+  rB : List ℕ
+  rF : List ℕ
+  pA : ∀ {α : Type} [Fintype α] [DecidableEq α] (X : BXMap H α),
+    Fintype.card H < Fintype.card α →
+    GRoute (fun r => X.Φ (lab0 r)) (fun r => X.Φ (labA r)) (actPoint S.MA)
+        (fun φ => rcost φ rA) ∧
+    GRoute (fun r => X.Φ (lab0 r)) (fun r => X.Φ (labA r)) (actPoint S.MAiᵀ)
+        (fun φ => rcost φ rA)
+  pB : ∀ {α : Type} [Fintype α] [DecidableEq α] (X : BXMap H α),
+    Fintype.card H < Fintype.card α →
+    GRoute (fun r => X.Φ (labA r)) (fun r => X.Φ (labB r)) (actPoint S.MB)
+        (fun φ => rcost φ rB) ∧
+    GRoute (fun r => X.Φ (labA r)) (fun r => X.Φ (labB r)) (actPoint S.MBiᵀ)
+        (fun φ => rcost φ rB)
+  pF : ∀ {α : Type} [Fintype α] [DecidableEq α] (X : BXMap H α),
+    Fintype.card H < Fintype.card α →
+    GRoute (fun r => X.Φ (labB r)) (fun r => X.Φ (labF r)) id (fun φ => rcost φ rF)
+
+/-- price of one invocation: the blocks of the three phases and one block per copy. -/
+def Lab.cost {H : Type} [Fintype H] [DecidableEq H] {T Sl C : Type} [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] {S : Scal T Sl C} (L : Lab H S)
+    (φ : ℕ → ℝ) : ℝ :=
+  rcost φ L.rA + (∑ k, bcost φ (L.cen k).dim) + rcost φ L.rB + rcost φ L.rF
+
+section Alg
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+
+namespace Scal
+variable (K : Scal T Sl C)
+
+/-- the product of ALL gates of the main phase (scatter with the copies eliminated). -/
+def Mt : Matrix (L3 T Sl) (L3 T Sl) ℚ := K.MB * scatM (K.Jr * K.Cc) * K.MA
+/-- its inverse. -/
+def Mti : Matrix (L3 T Sl) (L3 T Sl) ℚ := K.MAi * scatMi (K.Jr * K.Cc) * K.MBi
+
+
+lemma im : K.Mti * K.Mt = 1 := by
+  unfold Mti Mt
+  have hB : ∀ X : Matrix (L3 T Sl) (L3 T Sl) ℚ, K.MBi * (K.MB * X) = X := fun X => by
+    rw [← Matrix.mul_assoc, K.hBi, Matrix.one_mul]
+  have hS : ∀ X : Matrix (L3 T Sl) (L3 T Sl) ℚ,
+      scatMi (K.Jr * K.Cc) * (scatM (K.Jr * K.Cc) * X) = X := fun X => by
+    rw [← Matrix.mul_assoc, scat_inv, Matrix.one_mul]
+  rw [Matrix.mul_assoc, Matrix.mul_assoc, Matrix.mul_assoc, hB, hS, K.hAi]
+
+lemma mi : K.Mt * K.Mti = 1 := mul_eq_one_comm.mp K.im
+
+lemma hxm : PX * K.Mt = PX := PX_mul_of (M := K.Mt) K.hx
+lemma hmy : K.Mt * PY = PY := mul_PY_of (M := K.Mt) K.hy
+lemma hiy : K.Mti * PY = PY := dirt_iy K.hmy K.im
+
+/-- **the dirt rule, forward**, for the matrices of the circuit. -/
+lemma hF : g8 K.Mti * K.Mt * g1 K.Mt = 1 + PY * K.Mt * PX := by
+  unfold g8 g1
+  exact dirt_fwd PX_sq PY_sq PX_PY PY_PX K.hxm K.hmy K.im K.mi
+
+/-- **the dirt rule, backward.** -/
+lemma hB : g1i K.Mt * K.Mti * h8 K.Mt = 1 - PY * K.Mt * PX := by
+  unfold g1i h8
+  exact dirt_bwd PX_sq PY_sq PX_PY PY_PX K.hxm K.hmy K.im K.mi
+
+/-- live part of the forward word before the scatter: `y -= K s`, then phase A. -/
+def f1 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint K.MA (actPoint (g1 K.Mt) u)
+/-- after the scatter: phase B, then the slot rows of the inverse. -/
+def f2 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint (g8 K.Mti) (actPoint K.MB u)
+/-- the same for the backward word (transposed inverses). -/
+def b1 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint K.MAiᵀ (actPoint (g1i K.Mt)ᵀ u)
+def b2 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint (h8 K.Mt)ᵀ (actPoint K.MBiᵀ u)
+
+lemma fwd_live (u : L3 T Sl → ℂ) :
+    K.f2 (actPoint (scatM (K.Jr * K.Cc)) (K.f1 u)) = actPoint (1 + PY * K.Mt * PX) u := by
+  rw [← K.hF]
+  show actPoint (g8 K.Mti) (actPoint K.MB (actPoint (scatM (K.Jr * K.Cc))
+      (actPoint K.MA (actPoint (g1 K.Mt) u))))
+    = actPoint (g8 K.Mti * (K.MB * scatM (K.Jr * K.Cc) * K.MA) * g1 K.Mt) u
+  rw [actPoint_mul, actPoint_mul, actPoint_mul, actPoint_mul]
+
+lemma bwd_live (u : L3 T Sl → ℂ) :
+    K.b2 (actPoint ((scatMi (K.Jr * K.Cc))ᵀ) (K.b1 u))
+      = actPoint ((1 - PY * K.Mt * PX)ᵀ) u := by
+  rw [← K.hB]
+  show actPoint (h8 K.Mt)ᵀ (actPoint K.MBiᵀ (actPoint (scatMi (K.Jr * K.Cc))ᵀ
+      (actPoint K.MAiᵀ (actPoint (g1i K.Mt)ᵀ u))))
+    = actPoint ((g1i K.Mt * (K.MAi * scatMi (K.Jr * K.Cc) * K.MBi) * h8 K.Mt)ᵀ) u
+  rw [Matrix.transpose_mul, Matrix.transpose_mul, Matrix.transpose_mul, Matrix.transpose_mul,
+    actPoint_mul, actPoint_mul, actPoint_mul, actPoint_mul]
+
+lemma liveAct_glue (φ : (L3 T Sl → ℂ) → (L3 T Sl → ℂ)) (u : L3 T Sl → ℂ) (c : C → ℂ) :
+    liveAct φ (glue u c) = glue (φ u) c :=
+  congrArg (fun v => glue (φ v) c) (glue_up u c)
+
+/-- **Scalar identity of the forward word**: `y += x`, slots restored, for ARBITRARY slot
+contents (the copies are erased before and after). -/
+theorem fwd_scalar (z : Box T Sl C → ℂ) :
+    eraseC (liveAct K.f2 (gateS bY bC K.Jr (gateS bC bS K.Cc (liveAct K.f1 (eraseC z)))))
+      = shearF z := by
+  have h1 : liveAct K.f1 (eraseC z) = glue (K.f1 (z ∘ upE)) (fun _ => 0) := by
+    rw [erase_glue z, liveAct_glue]
+  have hs : gateS bY bC K.Jr (gateS bC bS K.Cc (glue (K.f1 (z ∘ upE)) (fun _ => 0))) ∘ upE
+      = actPoint (scatM (K.Jr * K.Cc)) (K.f1 (z ∘ upE)) := by
+    have h := scat_glue K.Jr K.Cc (glue (K.f1 (z ∘ upE)) (fun _ => 0)) rfl
+    rw [glue_up] at h
+    exact h
+  rw [h1]
+  unfold liveAct
+  rw [erase_of_glue, hs, K.fwd_live, act_shear K.Mt K.hid]
+  exact glue_shearF z
+
+/-- **Scalar identity of the backward word**: `x -= y`, slots restored. -/
+theorem bwd_scalar (z : Box T Sl C → ℂ) :
+    eraseC (liveAct K.b2 (gateS bS bC (-K.Ccᵀ) (gateS bC bY K.Jrᵀ (liveAct K.b1 (eraseC z)))))
+      = shearB z := by
+  have h1 : liveAct K.b1 (eraseC z) = glue (K.b1 (z ∘ upE)) (fun _ => 0) := by
+    rw [erase_glue z, liveAct_glue]
+  have hs : gateS bS bC (-K.Ccᵀ) (gateS bC bY K.Jrᵀ (glue (K.b1 (z ∘ upE)) (fun _ => 0))) ∘ upE
+      = actPoint ((scatMi (K.Jr * K.Cc))ᵀ) (K.b1 (z ∘ upE)) := by
+    have h := scat_glueT K.Jr K.Cc (glue (K.b1 (z ∘ upE)) (fun _ => 0)) rfl
+    rw [glue_up] at h
+    exact h
+  rw [h1]
+  unfold liveAct
+  rw [erase_of_glue, hs, K.bwd_live, act_shearT K.Mt K.hid]
+  exact glue_shearB z
+
+end Scal
+end Alg
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.Scal.fwd_scalar
+#print axioms OAI.PowerSaving.GX.Scal.bwd_scalar
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__WinB.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__WinB.lean
new file mode 100644
index 0000000000..951edde5cf
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Chain__WinB.lean
@@ -0,0 +1,132 @@
+import Work.GCert.Chain.Win
+import Work.BridgeGeom.Stage
+
+/-!
+# (key: gx-chain) THE WINDOW LIFT (spec statement 3): the windows of the bridged geometry
+
+For the block frame map `BG.fmapB hB hH d q` of a stage of the bridged word (label space
+`LB B H = H ⊕ (B × H)`, old frame of the projector `P`: `PhiB d q P`) the stage-B frame map is
+`BXMap.ofConj d q` (`U ↦ d (U ⊕ span q)`, arbitrary subspaces `U` of `H`).  At a coordinate
+subspace of an orthonormal basis `A` of `H` the two name the SAME subspace of the address space
+(`insub_old_new`), so the old frame and the representative of any label of that subspace
+differ by a free factor (`frame_core_free`, `rep_change`): `old_to_new`, `new_to_old`.
+
+`gwinB hB hH d q : GWin H (LB B H)` with `(gwinB hB hH d q).Xm = fmapB hB hH d q` (`rfl`).
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR BG GF
+noncomputable section
+
+section
+variable {B H : Type} [Fintype B] [DecidableEq B] [Fintype H] [DecidableEq H]
+
+lemma blkT_mulVec (A : OBase H) (z : Space (LB B H)) (k : LB B H) :
+    ((blkB B A)ᵀ *ᵥ z) k = Sum.elim (fun i => dot (A.v i) (fun j => z (Sum.inl j)))
+      (fun b => z (Sum.inr b)) k := by
+  cases k with
+  | inl i =>
+    simp [blkB, Matrix.fromBlocks_transpose, Matrix.mulVec, dotProduct, Fintype.sum_sum_type,
+      cmat, dot]
+  | inr b =>
+    simp [blkB, Matrix.fromBlocks_transpose, Matrix.mulVec, dotProduct, Fintype.sum_sum_type,
+      Matrix.one_apply]
+
+/-- coordinates of `y` in the basis `d (A ⊕ std)`. -/
+lemma dot_cols (d : Orth (LB B H)) (A : OBase H) (y : Space (LB B H)) (k : LB B H) :
+    dot ((ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A))).v k) y
+      = Sum.elim (fun i => dot (A.v i) (fun j => (d.1ᵀ *ᵥ y) (Sum.inl j)))
+          (fun b => (d.1ᵀ *ᵥ y) (Sum.inr b)) k := by
+  rw [← blkT_mulVec A (d.1ᵀ *ᵥ y) k, Matrix.mulVec_mulVec, ← Matrix.transpose_mul]
+  rfl
+
+/-- **the old frame and the lifted label name the same subspace of the address space.** -/
+theorem insub_old_new (d : Orth (LB B H)) (q : Finset (B × H)) (A : OBase H) (s : Finset H)
+    (U : SLbl H) (h : ∀ x, U.Mem x ↔ InSub (coordPerm A) s x) (y : Space (LB B H)) :
+    InSub (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q) y ↔
+      InSub (conjPerm d.1 d.2 (Orth.orth' d) U.G) (U.s.disjSum q) y := by
+  rw [insub_conj, insub_coordPerm]
+  have hU := h (fun i => (d.1ᵀ *ᵥ y) (Sum.inl i))
+  constructor
+  · intro hk
+    refine ⟨hU.mpr ((insub_coordPerm A s _).mpr (fun i hi => ?_)), fun b hb => ?_⟩
+    · have h1 := hk (Sum.inl i) (fun hm => hi (Finset.inl_mem_disjSum.mp hm))
+      rw [dot_cols] at h1
+      exact h1
+    · have h1 := hk (Sum.inr b) (fun hm => hb (Finset.inr_mem_disjSum.mp hm))
+      rw [dot_cols] at h1
+      exact h1
+  · rintro ⟨h1, h2⟩ k hk
+    rw [dot_cols]
+    cases k with
+    | inl i =>
+      exact (insub_coordPerm A s _).mp (hU.mp h1) i
+        (fun hm => hk (Finset.inl_mem_disjSum.mpr hm))
+    | inr b => exact h2 b (fun hm => hk (Finset.inr_mem_disjSum.mpr hm))
+
+/-- old frame of a coordinate subspace → representative of any label naming it: FREE. -/
+theorem old_to_new (d : Orth (LB B H)) (q : Finset (B × H)) (A : OBase H) (s : Finset H)
+    (U : SLbl H) (h : ∀ x, U.Mem x ↔ InSub (coordPerm A) s x) :
+    GReach (PhiB d q (A.mat s)) ((BXMap.ofConj d.1 d.2 (Orth.orth' d) q).Φ U) (fun _ => 0) := by
+  rw [PhiB_eq]
+  obtain ⟨N, hN, e⟩ := repChange (LB B H) _ _ _ _ (insub_old_new d q A s U h)
+  have a : GReach (frame (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A))) (JB s q))
+      (core (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q))
+      (fun φ => rcost φ []) :=
+    GReach.ofReach (fmv_old_to_core _ _).reach
+  have b : GReach
+      (core (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q))
+      (core (conjPerm d.1 d.2 (Orth.orth' d) U.G) (U.s.disjSum q)) (fun φ => rcost φ []) :=
+    GReach.ofReach (fmv_of_free hN e).reach
+  exact (a.trans b).cast (fun φ => by simp [rcost])
+
+/-- the same, backwards. -/
+theorem new_to_old (d : Orth (LB B H)) (q : Finset (B × H)) (A : OBase H) (s : Finset H)
+    (U : SLbl H) (h : ∀ x, U.Mem x ↔ InSub (coordPerm A) s x) :
+    GReach ((BXMap.ofConj d.1 d.2 (Orth.orth' d) q).Φ U) (PhiB d q (A.mat s)) (fun _ => 0) := by
+  rw [PhiB_eq]
+  obtain ⟨N, hN, e⟩ := repChange (LB B H) _ _ _ _
+    (fun y => (insub_old_new d q A s U h y).symm)
+  have a : GReach (core (conjPerm d.1 d.2 (Orth.orth' d) U.G) (U.s.disjSum q))
+      (core (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q))
+      (fun φ => rcost φ []) :=
+    GReach.ofReach (fmv_of_free hN e).reach
+  have b : GReach
+      (core (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q))
+      (frame (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A))) (JB s q))
+      (fun φ => rcost φ []) :=
+    GReach.ofReach (fmv_core_to_old _ _).reach
+  exact (a.trans b).cast (fun φ => by simp [rcost])
+
+/-- **The window of a stage of the bridged geometry.** -/
+def gwinB (hB : 1 ≤ Fintype.card B) (hH : 1 ≤ Fintype.card H) (d : Orth (LB B H))
+    (q : Finset (B × H)) : GWin H (LB B H) where
+  Xm := fmapB hB hH d q
+  X := BXMap.ofConj d.1 d.2 (Orth.orth' d) q
+  big := by
+    rw [card_LB]
+    have := Nat.mul_le_mul_right (Fintype.card H) (show 2 ≤ Fintype.card B + 1 by omega)
+    omega
+  toNew := fun A s U h => old_to_new d q A s U h
+  toOld := fun A s U h => new_to_old d q A s U h
+
+@[simp] lemma gwinB_Xm (hB : 1 ≤ Fintype.card B) (hH : 1 ≤ Fintype.card H) (d : Orth (LB B H))
+    (q : Finset (B × H)) : (gwinB hB hH d q).Xm = fmapB hB hH d q := rfl
+
+end
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.insub_old_new
+#print axioms OAI.PowerSaving.GX.old_to_new
+#print axioms OAI.PowerSaving.GX.new_to_old
+#print axioms OAI.PowerSaving.GX.gwinB
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__B2Gp193Main.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__B2Gp193Main.lean
new file mode 100644
index 0000000000..d7ecfebcea
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__B2Gp193Main.lean
@@ -0,0 +1,33 @@
+import Work.GCert.Scalar.Main
+import Work.GCert.Data.P193ScalOK
+import Work.GCert.Data.B2Gp193
+
+/-!
+# (key: gx-data) Bridged word B_2 with the gcert/1 circuit `P193`: THE CLOSED THEOREMS
+GENERATED by checks/wht26/gx-data/py/gxrate.py.  No `sorry`.
+`wht_B2Gp193_of_ids` (label half, price, unit list, rate fact, gx-chain's end theorem) applied to the scalar half
+`GXD.P193.scalOK : GS.ScalOK GXD.P193.raw` (kernel checks `scal<i>_ok`, `ychk_ok`; soundness: gx-scalar).
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace WHT
+open BlockWHT
+
+/-- **Walsh-Hadamard transform in `O(n (log n)^(1 - 74745/10^8))`-type time bounds: whole-block recursion on the bridged
+word B_2 with the kernel-checked gcert/1 circuit `P193`.** -/
+theorem wht_main_B2Gp193 :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - 74745/(10:ℝ)^8) W :=
+  wht_B2Gp193_of_ids GXD.P193.scalOK.hv GXD.P193.scalOK.hAi GXD.P193.scalOK.hBi GXD.P193.scalOK.hx GXD.P193.scalOK.hy GXD.P193.scalOK.hid
+
+/-- **Walsh-Hadamard transform in `O(n (log n)^(1 - 7474547/10^10))`-type time bounds: whole-block recursion on the bridged
+word B_2 with the kernel-checked gcert/1 circuit `P193`.** -/
+theorem wht_main_B2Gp193x :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - 7474547/(10:ℝ)^10) W :=
+  wht_B2Gp193x_of_ids GXD.P193.scalOK.hv GXD.P193.scalOK.hAi GXD.P193.scalOK.hBi GXD.P193.scalOK.hx GXD.P193.scalOK.hy GXD.P193.scalOK.hid
+
+end WHT
+end PowerSaving
+end OAI
+#print axioms OAI.PowerSaving.WHT.wht_main_B2Gp193
+#print axioms OAI.PowerSaving.WHT.wht_main_B2Gp193x
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__Glue.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__Glue.lean
new file mode 100644
index 0000000000..c6cbac38e3
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__Glue.lean
@@ -0,0 +1,97 @@
+import Work.GCert.Scalar.Roles
+import Work.GCert.Labels.Main
+
+/-!
+# (key: gx-data) Glue between the scalar half (gx-scalar) and the label half (gx-labels)
+
+For ANY `c : GXD.Raw` (nothing is evaluated here):
+
+* `roles`   gx-scalar's numbering `GS.emb` / `GS.unemb` is gx-labels' `GLab.Roles`;
+* `scalOf`  gx-chain's record `GX.Scal (Fin v) (Fin R) (Fin ret.length)` from the FIVE scalar
+            identities of the matrices `GS.MA`, `GS.MAi`, `GS.MB`, `GS.MBi`, `GS.Jrm`, `GS.Ccm`;
+* `scalOf_MA .. scalOf_MBi`  its gate matrices are the ordered products of the adds of `c`, in
+            the form asked by `GLab.Valid.lab` (`GLab.mic GS.toCoef`);
+* `reg`, `reg_slot`, `reg_mem`  copy `k` reads the retained register `(c.ret.getD k (0,0)).1`.
+
+So a generated instance needs from the scalar side exactly `hAi hBi hx hy hid` (see
+`wht_<Inst>_of_ids` in `Work/GCert/Data/<Inst>.lean`).  No `sorry`.
+-/
+
+namespace GXD
+open SSC OAI.PowerSaving OAI.PowerSaving.CR Matrix
+
+/-- the numbering of the roles: `x_t = t`, `y_t = v + t`, slot `q = 2 v + q` -/
+theorem roles (c : Raw) (hv : 0 < c.v) : GLab.Roles c.v c.R (GS.emb c) (GS.unemb c hv) where
+  hun := GS.unemb_emb hv
+  hin := GS.emb_unemb hv
+  hlt := fun q => by
+    rcases q with (t | S) | q
+    · have := t.isLt; show t.val < 2 * c.v + c.R; omega
+    · have := S.isLt; show c.v + S.val < 2 * c.v + c.R; omega
+    · have := q.isLt; show 2 * c.v + q.val < 2 * c.v + c.R; omega
+  eX := fun _ => rfl
+  eY := fun _ => rfl
+  eS := fun _ => rfl
+
+/-- **the scalar half as gx-chain's record**, from the five scalar identities -/
+noncomputable def scalOf (c : Raw) (hv : 0 < c.v)
+    (hAi : GS.MAi c hv * GS.MA c hv = 1) (hBi : GS.MBi c hv * GS.MB c hv = 1)
+    (hx : ∀ (t : Fin c.v) (j : GS.Rl c), (GS.MB c hv * scatM (GS.Jrm c * GS.Ccm c) * GS.MA c hv)
+      (lX t) j = if lX t = j then 1 else 0)
+    (hy : ∀ (i : GS.Rl c) (t : Fin c.v), (GS.MB c hv * scatM (GS.Jrm c * GS.Ccm c) * GS.MA c hv)
+      i (lY t) = if i = lY t then 1 else 0)
+    (hid : ∀ S t : Fin c.v, (GS.MB c hv * scatM (GS.Jrm c * GS.Ccm c) * GS.MA c hv)
+      (lY S) (lX t) = if S = t then 1 else 0) :
+    GX.Scal (Fin c.v) (Fin c.R) (Fin c.ret.length) where
+  Cc := GS.Ccm c
+  Jr := GS.Jrm c
+  MA := GS.MA c hv
+  MAi := GS.MAi c hv
+  MB := GS.MB c hv
+  MBi := GS.MBi c hv
+  hAi := hAi
+  hBi := hBi
+  hx := hx
+  hy := hy
+  hid := hid
+
+section
+variable (c : Raw) (hv : 0 < c.v) (hAi) (hBi) (hx) (hy) (hid)
+
+theorem scalOf_MA : (scalOf c hv hAi hBi hx hy hid).MA
+    = matP (GS.unemb c hv) (GLab.mic GS.toCoef (c.gatesA.flatMap Gate.adds)) := rfl
+
+theorem scalOf_MAi : (scalOf c hv hAi hBi hx hy hid).MAi
+    = matPinv (GS.unemb c hv) (GLab.mic GS.toCoef (c.gatesA.flatMap Gate.adds)) := rfl
+
+theorem scalOf_MB : (scalOf c hv hAi hBi hx hy hid).MB
+    = matP (GS.unemb c hv) (GLab.mic GS.toCoef (c.gatesB.flatMap Gate.adds)) := rfl
+
+theorem scalOf_MBi : (scalOf c hv hAi hBi hx hy hid).MBi
+    = matPinv (GS.unemb c hv) (GLab.mic GS.toCoef (c.gatesB.flatMap Gate.adds)) := rfl
+
+end
+
+/-- the register read by copy `k` (the slot of the retained total `k`) -/
+def reg (c : Raw) (k : Fin c.ret.length) : Nat := (c.ret.getD k.val (0, 0)).1
+
+theorem reg_slot (c : Raw) (hv : 0 < c.v) (hAi) (hBi) (hx) (hy) (hid) (k : Fin c.ret.length)
+    (q : Fin c.R) (h : (scalOf c hv hAi hBi hx hy hid).Cc k q ≠ 0) :
+    reg c k = 2 * c.v + q.val := by
+  have h' : (if 2 * c.v + q.val = (c.ret.getD k.val (0, 0)).1 then (1:ℚ) else 0) ≠ 0 := h
+  by_cases e : 2 * c.v + q.val = (c.ret.getD k.val (0, 0)).1
+  · exact e.symm
+  · rw [if_neg e] at h'; exact absurd rfl h'
+
+theorem reg_mem (c : Raw) (k : Fin c.ret.length) : reg c k ∈ c.ret.map Prod.fst := by
+  unfold reg
+  rw [List.getD_eq_getElem _ _ k.isLt]
+  exact List.mem_map.mpr ⟨_, List.getElem_mem k.isLt, rfl⟩
+
+end GXD
+
+#print axioms GXD.roles
+#print axioms GXD.scalOf
+#print axioms GXD.scalOf_MA
+#print axioms GXD.reg_slot
+#print axioms GXD.reg_mem
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__InstB2Gp193.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__InstB2Gp193.lean
new file mode 100644
index 0000000000..9b9925ce26
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__InstB2Gp193.lean
@@ -0,0 +1,55 @@
+import Work.BridgeGeom.B2
+import Work.FoldRate.Group
+import Work.GCert.Data.RateB2Gp193
+import Work.GCert.Data.RateB2Gp193x
+
+/-!
+# (key: gx-data) Bridged word B_2 with the gcert/1 circuit `P193`, h = 22: the unit price is the price of the block list
+
+GENERATED by checks/wht26/gx-data/py/gxrate.py.  No `sorry`.  Arithmetic only (no certificate is imported).
+
+One unit: `W = 14692` live roles (`4 v + R`, `v = 1320`, `R = 9412`), label dimension `m = 110`, deficit `D = 3080`.
+`invPrice φ` = the price of the blocks of ONE invocation (the kernel-counted list `GXD.P193.hist`, by rank);
+`unitPrice φ = 5 * invPrice φ + v * BG.bankPrice h φ = listCost φ BlockAccounting.blocksB2Gp193` (`unit_cost`).
+Whole-block `1 - 74745/10^8` (fails at 74746), ten decimals `1 - 7474547/10^10` (fails at 7474550).
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace BridgeRate
+namespace B2Gp193
+open Finset Binary Matrix RAM CB FoldRate
+noncomputable section
+
+/-- price of the blocks of ONE invocation of `P193` (all roles and scratch copies), by rank -/
+def invPrice (φ : ℕ → ℝ) : ℝ := 29178 * φ 1 + 12398 * φ 2 + 9923 * φ 3 + 4209 * φ 4 + 1950 * φ 5 + 1605 * φ 6 + 706 * φ 7 + 1531 * φ 8 + 429 * φ 9 + 930 * φ 10 + 354 * φ 11 + 1197 * φ 12 + 127 * φ 13 + 742 * φ 14 + 1879 * φ 15 + 88 * φ 16 + 81 * φ 17 + 2653 * φ 18 + 167 * φ 19 + 22 * φ 20
+
+/-- price of ONE unit of the bridged word B_2 -/
+def unitPrice (φ : ℕ → ℝ) : ℝ := 5 * invPrice φ + ((1320:ℕ):ℝ) * BG.bankPrice 22 φ
+
+/-- **The unit price is the price of the unit block list.** -/
+theorem unit_cost (φ : ℕ → ℝ) : unitPrice φ = listCost φ BlockAccounting.blocksB2Gp193 := by
+  unfold unitPrice invPrice
+  simp only [BG.bankPrice, listCost, BlockAccounting.blocksB2Gp193, List.map_cons, List.map_nil,
+    List.sum_cons, List.sum_nil]
+  norm_num [bcost]
+  try ring
+
+theorem blocks_x : BlockAccounting.blocksB2Gp193 = BlockAccounting.blocksB2Gp193x := rfl
+
+theorem unit_cost_x (φ : ℕ → ℝ) : unitPrice φ = listCost φ BlockAccounting.blocksB2Gp193x := by
+  rw [unit_cost, blocks_x]
+
+/-- one unit stands for `W * m - D` unit moves -/
+theorem unit_tally : unitPrice (fun r => (r:ℝ)) = ((14692:ℕ):ℝ) * ((110:ℕ):ℝ) - ((3080:ℕ):ℝ) := by
+  rw [unit_cost]
+  exact BlockAccounting.blocksB2Gp193_tally
+
+end
+end B2Gp193
+end BridgeRate
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.BridgeRate.B2Gp193.unit_cost
+#print axioms OAI.PowerSaving.BridgeRate.B2Gp193.unit_tally
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__P193Cert.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__P193Cert.lean
new file mode 100644
index 0000000000..3c3250279e
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__P193Cert.lean
@@ -0,0 +1,81 @@
+import Work.GCert.Labels.Main
+import Work.GCert.Data.P193Price
+import Work.GCert.Data.Gen.P193Tab0
+import Work.GCert.Data.Gen.P193Tab1
+import Work.GCert.Data.Gen.P193Tab2
+import Work.GCert.Data.Gen.P193Tab3
+import Work.GCert.Data.Gen.P193Seg0
+import Work.GCert.Data.Gen.P193Seg1
+import Work.GCert.Data.Gen.P193Seg2
+import Work.GCert.Data.Gen.P193Seg3
+import Work.GCert.Data.Gen.P193Seg4
+import Work.GCert.Data.Gen.P193SegF
+import Work.GCert.Data.Gen.P193End
+/-! # (key: gx-data) gcert/1 certificate `P193` (h = 22): THE LABEL HALF and its price
+GENERATED by checks/wht26/gx-data/py/gxgen.py from gcert1-p11-pr193.json.gz.  No `sorry`.
+`v = 1320` ports, `R = 9412` slots, 22 scratch copies of rank 20, copy cost `cst = 440`, `N = 262944` unit moves.
+* `aux : GLab.Aux`, `valid : GLab.Valid raw aux`: frame table (`tab<i>_ok` composed by `tabK_node`), the replays of phase A
+  and phase B (`seg<i>_ok` composed by `Run.append`), the final climbs (`segF_ok`, `fin_ok`), the ends (`end_ok`);
+* `lab_cost`, `lab_price`: for ANY scalar half `S` the label half `valid.lab S ..` costs
+  `rcost rA + card C * bcost 20 + rcost rB + rcost rF` = `invPrice φ` = 29178 * φ 1 + 12398 * φ 2 + 9923 * φ 3 + 4209 * φ 4 + 1950 * φ 5 + 1605 * φ 6 + 706 * φ 7 + 1531 * φ 8 + 429 * φ 9 + 930 * φ 10 + 354 * φ 11 + 1197 * φ 12 + 127 * φ 13 + 742 * φ 14 + 1879 * φ 15 + 88 * φ 16 + 81 * φ 17 + 2653 * φ 18 + 167 * φ 19 + 22 * φ 20
+  (`Gen.P193Hist`, `P193Price`) when there are 22 copies. -/
+set_option maxRecDepth 100000
+namespace GXD.P193
+open GXD OAI.PowerSaving OAI.PowerSaving.CB
+theorem raw_h : raw.h = 22 := rfl
+theorem raw_v : raw.v = 1320 := rfl
+theorem raw_R : raw.R = 9412 := rfl
+/-- what the label checks read next to `raw` -/
+noncomputable def aux : GLab.Aux := ⟨par, st0, st2, st5, st6, fins, rA, rB, rF⟩
+theorem fin_ok : GLab.noAdds fins = true := by decide +kernel
+theorem cen_ok : (raw.ret.map Prod.fst).all (fun r => Nat.beq (GLab.cdim (par.tab.get (st2.get r))) 20) = true := by
+  decide +kernel
+theorem tab_ok : GLab.tabK par.h par.tab = true := (GLab.tabK_node _ _ _ (GLab.tabK_node _ _ _ tab0_ok tab1_ok) (GLab.tabK_node _ _ _ tab2_ok tab3_ok))
+theorem gatesA_eq : raw.gatesA = seg0 ++ (seg1) := by
+  show List.flatten [seg0, seg1] = _
+  simp only [List.flatten_cons, List.flatten_nil, List.append_nil]
+/-- the replay of phase A, composed from its kernel-checked segments -/
+theorem runA : GLab.Run par st0 raw.gatesA st2 rA := by
+  rw [gatesA_eq]
+  exact GLab.Run.append (GLab.Run.of_seg seg0_ok) (GLab.Run.of_seg seg1_ok)
+theorem gatesB_eq : raw.gatesB = seg2 ++ (seg3 ++ (seg4)) := by
+  show List.flatten [seg2, seg3, seg4] = _
+  simp only [List.flatten_cons, List.flatten_nil, List.append_nil]
+/-- the replay of phase B, composed from its kernel-checked segments -/
+theorem runB : GLab.Run par st2 raw.gatesB st5 rB := by
+  rw [gatesB_eq]
+  exact GLab.Run.append (GLab.Run.of_seg seg2_ok) (GLab.Run.append (GLab.Run.of_seg seg3_ok) (GLab.Run.of_seg seg4_ok))
+/-- **the kernel-checked label facts** of the certificate -/
+theorem valid : GLab.Valid raw aux where
+  hn := rfl
+  tab := tab_ok
+  runA := runA
+  runB := runB
+  runF := GLab.Run.of_seg segF_ok
+  fin := fin_ok
+  ends := end_ok
+theorem cen_dim (r : Nat) (hr : r ∈ raw.ret.map Prod.fst) : GLab.cdim (par.tab.get (st2.get r)) = 20 :=
+  Nat.eq_of_beq_eq_true (List.all_eq_true.mp cen_ok r hr)
+/-- price of the label half over ANY scalar half -/
+theorem lab_cost {C : Type} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin raw.v) (Fin raw.R) C)
+    {emb : CR.L3 (Fin raw.v) (Fin raw.R) → Nat} {un : Nat → CR.L3 (Fin raw.v) (Fin raw.R)}
+    (Ro : GLab.Roles raw.v raw.R emb un) (cf : Co → SSC.Coef) (hMA) (hMAi) (hMB) (hMBi)
+    (reg : C → Nat) (hCc) (hreg) (φ : ℕ → ℝ) :
+    (valid.lab S Ro cf hMA hMAi hMB hMBi reg hCc hreg).cost φ
+      = rcost φ rA + (Fintype.card C : ℝ) * bcost φ 20 + rcost φ rB + rcost φ rF := by
+  obtain ⟨h1, h2, h3, h4⟩ := valid.lab_ranks S Ro cf hMA hMAi hMB hMBi reg hCc hreg
+  have h5 : ∀ k, bcost φ (((valid.lab S Ro cf hMA hMAi hMB hMBi reg hCc hreg).cen k).dim) = bcost φ 20 :=
+    fun k => by rw [h4 k]; exact congrArg (bcost φ) (cen_dim _ (hreg k))
+  rw [GX.Lab.cost, h1, h2, h3, Finset.sum_congr rfl (fun k _ => h5 k), Finset.sum_const, Finset.card_univ, nsmul_eq_mul]
+  rfl
+/-- **the label half costs one invocation price** (`invPrice`, by rank, from the kernel counts) -/
+theorem lab_price {C : Type} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin raw.v) (Fin raw.R) C)
+    {emb : CR.L3 (Fin raw.v) (Fin raw.R) → Nat} {un : Nat → CR.L3 (Fin raw.v) (Fin raw.R)}
+    (Ro : GLab.Roles raw.v raw.R emb un) (cf : Co → SSC.Coef) (hMA) (hMAi) (hMB) (hMBi)
+    (reg : C → Nat) (hCc) (hreg) (hC : Fintype.card C = 22) (φ : ℕ → ℝ) :
+    (valid.lab S Ro cf hMA hMAi hMB hMBi reg hCc hreg).cost φ = invPrice φ := by
+  rw [lab_cost S Ro cf hMA hMAi hMB hMBi reg hCc hreg φ, hC, ← inv_cost φ]
+  norm_num [bcost]
+end GXD.P193
+#print axioms GXD.P193.valid
+#print axioms GXD.P193.lab_price
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__P193Price.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__P193Price.lean
new file mode 100644
index 0000000000..eeed011d64
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__P193Price.lean
@@ -0,0 +1,54 @@
+import Work.GCert.Data.Price
+import Work.GCert.Data.Gen.P193Hist
+
+/-!
+# (key: gx-data) gcert/1 certificate `P193` (h = 22): the price of one invocation
+
+GENERATED by checks/wht26/gx-data/py/gxgen.py from gcert1-p11-pr193.json.gz.  No `sorry`.
+`rA_cost`, `rB_cost`, `rF_cost`: the price of the block rank lists of phase A, phase B and the final climbs
+(lists `GXD.P193.rA / rB / rF`, counted by the kernel in `Gen.P193Hist`);
+`inv_cost`: with the 22 scratch copies (22 * φ 20) the blocks of ONE invocation cost
+`invPrice φ` = 29178 * φ 1 + 12398 * φ 2 + 9923 * φ 3 + 4209 * φ 4 + 1950 * φ 5 + 1605 * φ 6 + 706 * φ 7 + 1531 * φ 8 + 429 * φ 9 + 930 * φ 10 + 354 * φ 11 + 1197 * φ 12 + 127 * φ 13 + 742 * φ 14 + 1879 * φ 15 + 88 * φ 16 + 81 * φ 17 + 2653 * φ 18 + 167 * φ 19 + 22 * φ 20;  `inv_moves`: they stand for `R h + 2 v (h - 1) + cst = 262944` unit moves.
+-/
+
+namespace GXD.P193
+open GXD OAI.PowerSaving.CB
+
+/-- price of the blocks of phase A, from the kernel counts -/
+theorem rA_cost (φ : ℕ → ℝ) : rcost φ rA = 9900 * φ 1 + 500 * φ 2 + 2402 * φ 3 + 82 * φ 4 + 242 * φ 5 + 175 * φ 6 + 88 * φ 7 + 68 * φ 8 + 110 * φ 9 + 132 * φ 10 + 10 * φ 11 + 67 * φ 12 + 3 * φ 13 + 19 * φ 15 := by
+  rw [GXD.rcost_wsumK φ rA 19 rankBoundA]
+  simp only [Finset.sum_range_succ, Finset.sum_range_zero, rankA0_ok, rankA1_ok, rankA2_ok, rankA3_ok, rankA4_ok, rankA5_ok, rankA6_ok, rankA7_ok, rankA8_ok, rankA9_ok, rankA10_ok, rankA11_ok, rankA12_ok, rankA13_ok, rankA14_ok, rankA15_ok, rankA16_ok, rankA17_ok, rankA18_ok, rankA19_ok]
+  norm_num [bcost]
+
+/-- price of the blocks of phase B, from the kernel counts -/
+theorem rB_cost (φ : ℕ → ℝ) : rcost φ rB = 16638 * φ 1 + 10380 * φ 2 + 4111 * φ 3 + 3476 * φ 4 + 1531 * φ 5 + 1137 * φ 6 + 531 * φ 7 + 1346 * φ 8 + 293 * φ 9 + 629 * φ 10 + 343 * φ 11 + 1067 * φ 12 + 123 * φ 13 + 712 * φ 14 + 1860 * φ 15 + 81 * φ 16 + 39 * φ 17 + 2640 * φ 18 := by
+  rw [GXD.rcost_wsumK φ rB 19 rankBoundB]
+  simp only [Finset.sum_range_succ, Finset.sum_range_zero, rankB0_ok, rankB1_ok, rankB2_ok, rankB3_ok, rankB4_ok, rankB5_ok, rankB6_ok, rankB7_ok, rankB8_ok, rankB9_ok, rankB10_ok, rankB11_ok, rankB12_ok, rankB13_ok, rankB14_ok, rankB15_ok, rankB16_ok, rankB17_ok, rankB18_ok, rankB19_ok]
+  norm_num [bcost]
+
+/-- price of the blocks of the final climbs, from the kernel counts -/
+theorem rF_cost (φ : ℕ → ℝ) : rcost φ rF = 2640 * φ 1 + 1518 * φ 2 + 3410 * φ 3 + 651 * φ 4 + 177 * φ 5 + 293 * φ 6 + 87 * φ 7 + 117 * φ 8 + 26 * φ 9 + 169 * φ 10 + 1 * φ 11 + 63 * φ 12 + 1 * φ 13 + 30 * φ 14 + 7 * φ 16 + 42 * φ 17 + 13 * φ 18 + 167 * φ 19 := by
+  rw [GXD.rcost_wsumK φ rF 19 rankBoundF]
+  simp only [Finset.sum_range_succ, Finset.sum_range_zero, rankF0_ok, rankF1_ok, rankF2_ok, rankF3_ok, rankF4_ok, rankF5_ok, rankF6_ok, rankF7_ok, rankF8_ok, rankF9_ok, rankF10_ok, rankF11_ok, rankF12_ok, rankF13_ok, rankF14_ok, rankF15_ok, rankF16_ok, rankF17_ok, rankF18_ok, rankF19_ok]
+  norm_num [bcost]
+
+/-- price of the blocks of ONE invocation (x roles, y roles, slots, scratch copies), by rank -/
+def invPrice (φ : ℕ → ℝ) : ℝ := 29178 * φ 1 + 12398 * φ 2 + 9923 * φ 3 + 4209 * φ 4 + 1950 * φ 5 + 1605 * φ 6 + 706 * φ 7 + 1531 * φ 8 + 429 * φ 9 + 930 * φ 10 + 354 * φ 11 + 1197 * φ 12 + 127 * φ 13 + 742 * φ 14 + 1879 * φ 15 + 88 * φ 16 + 81 * φ 17 + 2653 * φ 18 + 167 * φ 19 + 22 * φ 20
+
+/-- **Price of ONE invocation** in the shape of `GX.Lab.cost`: phase A, the scratch copies, phase B, final climbs. -/
+theorem inv_cost (φ : ℕ → ℝ) : rcost φ rA + (22 * φ 20) + rcost φ rB + rcost φ rF = invPrice φ := by
+  rw [rA_cost, rB_cost, rF_cost]
+  unfold invPrice
+  ring
+
+theorem inv_moves : invPrice (fun r => (r:ℝ)) = 9412 * 22 + 2 * 1320 * (22 - 1) + 440 := by
+  unfold invPrice
+  norm_num
+
+theorem inv_count : invPrice (fun _ => (1:ℝ)) = 70169 := by
+  unfold invPrice
+  norm_num
+
+end GXD.P193
+#print axioms GXD.P193.inv_cost
+#print axioms GXD.P193.inv_moves
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__P193ScalOK.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__P193ScalOK.lean
new file mode 100644
index 0000000000..3539192ac1
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__P193ScalOK.lean
@@ -0,0 +1,17 @@
+import Work.GCert.Scalar.Main
+import Work.GCert.Data.Gen.P193Scal0
+import Work.GCert.Data.Gen.P193Scal1
+import Work.GCert.Data.Gen.P193YChk
+/-! # (key: gx-data) gcert/1 certificate `P193` (h = 22): THE SCALAR HALF `scalOK : GS.ScalOK raw`
+GENERATED by checks/wht26/gx-data/py/gxgen.py from gcert1-p11-pr193.json.gz.  No `sorry`.
+Kernel checks `scal<i>_ok` (2 source batches) and `ychk_ok`. -/
+namespace GXD.P193
+open GXD
+theorem scalOK : GS.ScalOK raw where
+  hv := by decide
+  hs := fun t ht =>
+    if h0 : t < 660 then ⟨0, 660, Nat.zero_le t, h0, GS.XRun.of_check scal0_ok⟩ else
+    ⟨660, 660, Nat.le_of_not_lt h0, Nat.lt_of_lt_of_le ht (by decide), GS.XRun.of_check scal1_ok⟩
+  hyc := fun t ht => ⟨0, 1320, Nat.zero_le t, Nat.lt_of_lt_of_le ht (by decide), GS.YRun.of_check ychk_ok⟩
+end GXD.P193
+#print axioms GXD.P193.scalOK
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__RateB2Gp193x.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__RateB2Gp193x.lean
new file mode 100644
index 0000000000..df563cde73
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__RateB2Gp193x.lean
@@ -0,0 +1,327 @@
+import Work.BlockAccounting.Moment
+import Work.BlockAccounting.Sharp
+import Work.FoldRate.RankTools
+
+/-!
+# (key: gx-data) Rate lemmas for one unit of the bridged word B_2 with the gcert/1 circuit `P193` (h = 22)
+
+GENERATED by checks/wht26/gx-data/py/gxrate.py with the text generators of checks/wht9/bridge-rate/py
+(used read-only).  No `sorry`.  Arithmetic only.
+
+One unit: `W = 14692` live roles, label dimension `m = 110`, deficit `D = 3080`.
+
+* `blocksB2Gp193x`            the block list (rank, count) of ONE unit;
+* `fold_B2Gp193x`             whole-block fact at `1 - 7474547/10^10`, fill parameter `s = 40` (slack 2.37e-12);
+* `fold_B2Gp193x_sharp`       `W ≤ moment` at `1 - 7474550/10^10`: fails for every table (excess 1.40e-10);
+* `foldRank_B2Gp193x`         per-rank fact at `1 - 4058344/10^10`, `s = 40` (slack 1.10e-07);
+* `foldRank_B2Gp193x_sharp`   per-rank: fails for every table at `1 - 4058349/10^10`.
+
+That a Lean word has `G` times this list as its block histogram is NOT proved here.
+-/
+
+set_option maxRecDepth 4000
+
+namespace OAI.PowerSaving.BlockAccounting
+open Finset
+
+/-- Block list `(rank, count)` of ONE unit of the bridged five-stage word B_2 with the gcert/1 circuit `P193` (h = 22, m = 110): five invocations (ALL blocks of one invocation: x roles, y roles, slots, scratch copies; the kernel-counted list `GXD.P193.hist`), and for each of the v = 1320 ports the idle climbs of its two twins (2 blocks each of rank h-1, 2h-2, 2h+2, 4); R = 9412 slots shared by the five stages. -/
+def blocksB2Gp193x : List (ℕ × ℕ) := [(1, 145890), (2, 61990), (3, 49615), (4, 23685), (5, 9750), (6, 8025), (7, 3530), (8, 7655), (9, 2145), (10, 4650), (11, 1770), (12, 5985), (13, 635), (14, 3710), (15, 9395), (16, 440), (17, 405), (18, 13265), (19, 835), (20, 110), (21, 2640), (42, 2640), (46, 2640)]
+
+/-- total rank of one unit (= number of unit moves it stands for): `W * m - D` -/
+theorem blocksB2Gp193x_rank : (blocksB2Gp193x.map fun b => b.1 * b.2).sum = 14692 * 110 - 3080 := by
+  norm_num [blocksB2Gp193x]
+
+/-- the same as a price: the unit list at the price list `r ↦ r` (shape of `hPid` in `RAM.engine_program_group_perRank`) -/
+theorem blocksB2Gp193x_tally : (blocksB2Gp193x.map fun b => (b.2:ℝ) * ((b.1:ℕ):ℝ)).sum = ((14692:ℕ):ℝ) * ((110:ℕ):ℝ) - ((3080:ℕ):ℝ) := by
+  norm_num [blocksB2Gp193x]
+
+theorem blocksB2Gp193x_count : (blocksB2Gp193x.map fun b => b.2).sum = 361405 := by
+  norm_num [blocksB2Gp193x]
+
+theorem blocksB2Gp193x_proper : ∀ b ∈ blocksB2Gp193x, 1 ≤ b.1 ∧ b.1 < 110 := by
+  decide
+
+/-- **whole-block fact** of `blocksB2Gp193x` at exponent `1 - 7474547/10^10`, fill parameter `s = 40`: the hypothesis `hnum` of `RAM.engine_program_group_list` (u = 110, W = 14692).  Relative slack of the rational certificate: 2.37e-12. -/
+theorem fold_B2Gp193x :
+    ((2:ℝ)^40 - 1) * moment 110 (1 - 7474547/(10:ℝ)^10) blocksB2Gp193x
+      + ((14692:ℕ):ℝ) * (T 110 (1 - 7474547/(10:ℝ)^10) (110 - 1) 1 + T 110 (1 - 7474547/(10:ℝ)^10) 1 1)
+      < (2:ℝ)^40 * ((14692:ℕ):ℝ) := by
+  have hsum : moment 110 (1 - 7474547/(10:ℝ)^10) blocksB2Gp193x
+      = T 110 (1 - 7474547/(10:ℝ)^10) 1 145890 + (T 110 (1 - 7474547/(10:ℝ)^10) 2 61990 + (T 110 (1 - 7474547/(10:ℝ)^10) 3 49615 + (T 110 (1 - 7474547/(10:ℝ)^10) 4 23685 + (T 110 (1 - 7474547/(10:ℝ)^10) 5 9750 + (T 110 (1 - 7474547/(10:ℝ)^10) 6 8025 + (T 110 (1 - 7474547/(10:ℝ)^10) 7 3530 + (T 110 (1 - 7474547/(10:ℝ)^10) 8 7655 + (T 110 (1 - 7474547/(10:ℝ)^10) 9 2145 + (T 110 (1 - 7474547/(10:ℝ)^10) 10 4650 + (T 110 (1 - 7474547/(10:ℝ)^10) 11 1770 + (T 110 (1 - 7474547/(10:ℝ)^10) 12 5985 + (T 110 (1 - 7474547/(10:ℝ)^10) 13 635 + (T 110 (1 - 7474547/(10:ℝ)^10) 14 3710 + (T 110 (1 - 7474547/(10:ℝ)^10) 15 9395 + (T 110 (1 - 7474547/(10:ℝ)^10) 16 440 + (T 110 (1 - 7474547/(10:ℝ)^10) 17 405 + (T 110 (1 - 7474547/(10:ℝ)^10) 18 13265 + (T 110 (1 - 7474547/(10:ℝ)^10) 19 835 + (T 110 (1 - 7474547/(10:ℝ)^10) 20 110 + (T 110 (1 - 7474547/(10:ℝ)^10) 21 2640 + (T 110 (1 - 7474547/(10:ℝ)^10) 42 2640 + (T 110 (1 - 7474547/(10:ℝ)^10) 46 2640 + 0)))))))))))))))))))))) := rfl
+  have b0 : T 110 (1 - 7474547/(10:ℝ)^10) 1 145890 ≤ ((16636758090767:ℝ)/12500000000) :=
+    term_le 110 1 145890 (7474547/(10:ℝ)^10) ((2350240182897:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 27 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b1 : T 110 (1 - 7474547/(10:ℝ)^10) 2 61990 ≤ ((22609438945563:ℝ)/20000000000) :=
+    term_le 110 2 61990 (7474547/(10:ℝ)^10) ((2003666592617:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 26 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b2 : T 110 (1 - 7474547/(10:ℝ)^10) 3 49615 ≤ ((135678423202471:ℝ)/100000000000) :=
+    term_le 110 3 49615 (7474547/(10:ℝ)^10) ((1800934038563:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 24 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b3 : T 110 (1 - 7474547/(10:ℝ)^10) 4 23685 ≤ ((43170446048157:ℝ)/50000000000) :=
+    term_le 110 4 23685 (7474547/(10:ℝ)^10) ((1657093002337:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 24 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b4 : T 110 (1 - 7474547/(10:ℝ)^10) 5 9750 ≤ ((44420693582197:ℝ)/100000000000) :=
+    term_le 110 5 9750 (7474547/(10:ℝ)^10) ((38638030667:ℝ)/12500000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 23 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b5 : T 110 (1 - 7474547/(10:ℝ)^10) 6 8025 ≤ ((43867998737293:ℝ)/100000000000) :=
+    term_le 110 6 8025 (7474547/(10:ℝ)^10) ((1454360448283:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 22 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b6 : T 110 (1 - 7474547/(10:ℝ)^10) 7 3530 ≤ ((2250993477097:ℝ)/10000000000) :=
+    term_le 110 7 3530 (7474547/(10:ℝ)^10) ((2754570216739:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 22 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b7 : T 110 (1 - 7474547/(10:ℝ)^10) 8 7655 ≤ ((55781903078171:ℝ)/100000000000) :=
+    term_le 110 8 7655 (7474547/(10:ℝ)^10) ((1310519412057:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 21 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b8 : T 110 (1 - 7474547/(10:ℝ)^10) 9 2145 ≤ ((17582868029823:ℝ)/100000000000) :=
+    term_le 110 9 2145 (7474547/(10:ℝ)^10) ((1251627894229:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 21 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b9 : T 110 (1 - 7474547/(10:ℝ)^10) 10 4650 ≤ ((10587140349809:ℝ)/25000000000) :=
+    term_le 110 10 4650 (7474547/(10:ℝ)^10) ((2997369091:ℝ)/1250000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 21 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b10 : T 110 (1 - 7474547/(10:ℝ)^10) 11 1770 ≤ ((17730489316207:ℝ)/100000000000) :=
+    term_le 110 11 1770 (7474547/(10:ℝ)^10) ((575646273249:ℝ)/250000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 20 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b11 : T 110 (1 - 7474547/(10:ℝ)^10) 12 5985 ≤ ((65399123107589:ℝ)/100000000000) :=
+    term_le 110 12 5985 (7474547/(10:ℝ)^10) ((1107786858003:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 20 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b12 : T 110 (1 - 7474547/(10:ℝ)^10) 13 635 ≤ ((3758266936203:ℝ)/50000000000) :=
+    term_le 110 13 635 (7474547/(10:ℝ)^10) ((533882752083:ℝ)/250000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 20 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b13 : T 110 (1 - 7474547/(10:ℝ)^10) 14 3710 ≤ ((47290992642379:ℝ)/100000000000) :=
+    term_le 110 14 3710 (7474547/(10:ℝ)^10) ((2061423036179:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 19 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b14 : T 110 (1 - 7474547/(10:ℝ)^10) 15 9395 ≤ ((128304571925681:ℝ)/100000000000) :=
+    term_le 110 15 9395 (7474547/(10:ℝ)^10) ((498107541173:ℝ)/250000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 19 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b15 : T 110 (1 - 7474547/(10:ℝ)^10) 16 440 ≤ ((6409229123791:ℝ)/100000000000) :=
+    term_le 110 16 440 (7474547/(10:ℝ)^10) ((963945821777:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 19 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b16 : T 110 (1 - 7474547/(10:ℝ)^10) 17 405 ≤ ((1253566561349:ℝ)/20000000000) :=
+    term_le 110 17 405 (7474547/(10:ℝ)^10) ((933633510869:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 19 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b17 : T 110 (1 - 7474547/(10:ℝ)^10) 18 13265 ≤ ((217357516651669:ℝ)/100000000000) :=
+    term_le 110 18 13265 (7474547/(10:ℝ)^10) ((905054303949:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 18 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b18 : T 110 (1 - 7474547/(10:ℝ)^10) 19 835 ≤ ((14441670418763:ℝ)/100000000000) :=
+    term_le 110 19 835 (7474547/(10:ℝ)^10) ((1756041386627:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 18 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b19 : T 110 (1 - 7474547/(10:ℝ)^10) 20 110 ≤ ((2002550068509:ℝ)/100000000000) :=
+    term_le 110 20 110 (7474547/(10:ℝ)^10) ((21309351153:ℝ)/12500000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 18 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b20 : T 110 (1 - 7474547/(10:ℝ)^10) 21 2640 ≤ ((25231210703361:ℝ)/50000000000) :=
+    term_le 110 21 2640 (7474547/(10:ℝ)^10) ((165595792807:ℝ)/100000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 18 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b21 : T 110 (1 - 7474547/(10:ℝ)^10) 42 2640 ≤ ((100872567578631:ℝ)/100000000000) :=
+    term_le 110 42 2640 (7474547/(10:ℝ)^10) ((962810747511:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 15 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b22 : T 110 (1 - 7474547/(10:ℝ)^10) 46 2640 ≤ ((22094393345401:ℝ)/20000000000) :=
+    term_le 110 46 2640 (7474547/(10:ℝ)^10) ((174367793861:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 14 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b23 : T 110 (1 - 7474547/(10:ℝ)^10) 109 1 ≤ ((198183171:ℝ)/200000000) :=
+    term_le 110 109 1 (7474547/(10:ℝ)^10) ((1826496713:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 5 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b24 : T 110 (1 - 7474547/(10:ℝ)^10) 1 1 ≤ ((456145263:ℝ)/50000000000) :=
+    term_le 110 1 1 (7474547/(10:ℝ)^10) ((2350240182897:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 27 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have e1 : ((2:ℝ)^40 - 1) = 1099511627775 := by norm_num
+  have e2 : (2:ℝ)^40 = 1099511627776 := by norm_num
+  have e3 : ((14692:ℕ):ℝ) = 14692 := by norm_num
+  have e4 : T 110 (1 - 7474547/(10:ℝ)^10) (110 - 1) 1 = T 110 (1 - 7474547/(10:ℝ)^10) 109 1 := rfl
+  rw [e1, e2, e3, e4, hsum]
+  linarith
+
+/-- **sharpness**: at exponent `1 - 7474550/10^10` the moment of one unit is at least its number of live roles `14692`, so the moment criterion fails for EVERY table made of copies of the unit and idle roles (`FoldRate.block_fails`).  Relative excess of the rational certificate: 1.40e-10. -/
+theorem fold_B2Gp193x_sharp : ((14692:ℕ):ℝ) ≤ moment 110 (1 - 7474550/(10:ℝ)^10) blocksB2Gp193x := by
+  have hsum : moment 110 (1 - 7474550/(10:ℝ)^10) blocksB2Gp193x
+      = T 110 (1 - 7474550/(10:ℝ)^10) 1 145890 + (T 110 (1 - 7474550/(10:ℝ)^10) 2 61990 + (T 110 (1 - 7474550/(10:ℝ)^10) 3 49615 + (T 110 (1 - 7474550/(10:ℝ)^10) 4 23685 + (T 110 (1 - 7474550/(10:ℝ)^10) 5 9750 + (T 110 (1 - 7474550/(10:ℝ)^10) 6 8025 + (T 110 (1 - 7474550/(10:ℝ)^10) 7 3530 + (T 110 (1 - 7474550/(10:ℝ)^10) 8 7655 + (T 110 (1 - 7474550/(10:ℝ)^10) 9 2145 + (T 110 (1 - 7474550/(10:ℝ)^10) 10 4650 + (T 110 (1 - 7474550/(10:ℝ)^10) 11 1770 + (T 110 (1 - 7474550/(10:ℝ)^10) 12 5985 + (T 110 (1 - 7474550/(10:ℝ)^10) 13 635 + (T 110 (1 - 7474550/(10:ℝ)^10) 14 3710 + (T 110 (1 - 7474550/(10:ℝ)^10) 15 9395 + (T 110 (1 - 7474550/(10:ℝ)^10) 16 440 + (T 110 (1 - 7474550/(10:ℝ)^10) 17 405 + (T 110 (1 - 7474550/(10:ℝ)^10) 18 13265 + (T 110 (1 - 7474550/(10:ℝ)^10) 19 835 + (T 110 (1 - 7474550/(10:ℝ)^10) 20 110 + (T 110 (1 - 7474550/(10:ℝ)^10) 21 2640 + (T 110 (1 - 7474550/(10:ℝ)^10) 42 2640 + (T 110 (1 - 7474550/(10:ℝ)^10) 46 2640 + 0)))))))))))))))))))))) := rfl
+  have c0 : ((665470322971:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 1 145890 :=
+    term_ge 110 1 145890 (7474550/(10:ℝ)^10) ((4700480365791:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 4 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c1 : ((565235973477:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 2 61990 :=
+    term_ge 110 2 61990 (7474550/(10:ℝ)^10) ((4007333185231:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 4 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c2 : ((1356784232023:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 3 49615 :=
+    term_ge 110 3 49615 (7474550/(10:ℝ)^10) ((3601868077123:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c3 : ((431704460547:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 4 23685 :=
+    term_ge 110 4 23685 (7474550/(10:ℝ)^10) ((3314186004671:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c4 : ((44420693593:ℝ)/100000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 5 9750 :=
+    term_ge 110 5 9750 (7474550/(10:ℝ)^10) ((3091042453357:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c5 : ((87735997501:ℝ)/200000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 6 8025 :=
+    term_ge 110 6 8025 (7474550/(10:ℝ)^10) ((2908720896563:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c6 : ((112549673893:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 7 3530 :=
+    term_ge 110 7 3530 (7474550/(10:ℝ)^10) ((86080319273:ℝ)/31250000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c7 : ((557819030987:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 8 7655 :=
+    term_ge 110 8 7655 (7474550/(10:ℝ)^10) ((2621038824111:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c8 : ((87914340183:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 9 2145 :=
+    term_ge 110 9 2145 (7474550/(10:ℝ)^10) ((500651157691:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c9 : ((423485614161:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 10 4650 :=
+    term_ge 110 10 4650 (7474550/(10:ℝ)^10) ((2397895272797:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c10 : ((88652446617:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 11 1770 :=
+    term_ge 110 11 1770 (7474550/(10:ℝ)^10) ((2302585092993:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c11 : ((130798246269:ℝ)/200000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 12 5985 :=
+    term_ge 110 12 5985 (7474550/(10:ℝ)^10) ((2215573716003:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c12 : ((15033067751:ℝ)/200000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 13 635 :=
+    term_ge 110 13 635 (7474550/(10:ℝ)^10) ((2135531008329:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c13 : ((23645496331:ℝ)/50000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 14 3710 :=
+    term_ge 110 14 3710 (7474550/(10:ℝ)^10) ((128838939761:ℝ)/62500000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c14 : ((320761429947:ℝ)/250000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 15 9395 :=
+    term_ge 110 15 9395 (7474550/(10:ℝ)^10) ((1992430164689:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 12 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c15 : ((1001442051:ℝ)/15625000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 16 440 :=
+    term_ge 110 16 440 (7474550/(10:ℝ)^10) ((1927891643551:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c16 : ((62678328093:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 17 405 :=
+    term_ge 110 17 405 (7474550/(10:ℝ)^10) ((373453404347:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c17 : ((1086787583699:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 18 13265 :=
+    term_ge 110 18 13265 (7474550/(10:ℝ)^10) ((362021721579:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c18 : ((28883340849:ℝ)/200000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 19 835 :=
+    term_ge 110 19 835 (7474550/(10:ℝ)^10) ((13719073333:ℝ)/7812500000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c19 : ((20025500693:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 20 110 :=
+    term_ge 110 20 110 (7474550/(10:ℝ)^10) ((1704748092237:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c20 : ((63078026783:ℝ)/125000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 21 2640 :=
+    term_ge 110 21 2640 (7474550/(10:ℝ)^10) ((1655957928067:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c21 : ((126090709507:ℝ)/125000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 42 2640 :=
+    term_ge 110 42 2640 (7474550/(10:ℝ)^10) ((240702686877:ℝ)/250000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 1 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c22 : ((552359833771:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 46 2640 :=
+    term_ge 110 46 2640 (7474550/(10:ℝ)^10) ((435919484651:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 1 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have e3 : ((14692:ℕ):ℝ) = 14692 := by norm_num
+  rw [e3, hsum]
+  linarith
+
+/-- **per-rank fact** at exponent `1 - 4058344/10^10`, fill parameter `s = 40`: the hypothesis `hnum` of `RAM.engine_program_group_perRank` (u = 110, W = 14692, D = 3080).  Relative slack: 1.10e-07. -/
+theorem foldRank_B2Gp193x :
+    (2:ℝ)^40 * ((14692:ℕ):ℝ) * (((110:ℕ):ℝ) - ((110:ℕ):ℝ)^(1 - 4058344/(10:ℝ)^10)) < ((2:ℝ)^40 - 1) * ((3080:ℕ):ℝ) :=
+  FoldRate.rank_fact3 110 14692 3080 40 (4058344/(10:ℝ)^10) ((2350240182897:ℝ)/500000000000) (by norm_num) (by norm_num) (by norm_num)
+    (log_le_of_le_expsum _ _ 27 (by norm_num) (by norm_num)
+      (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+    (by norm_num) (by norm_num)
+
+/-- **per-rank sharpness**: at exponent `1 - 4058349/10^10` the deficit of one unit is at most `W (m - m^z)`, so the per-rank inequality fails for EVERY table made of copies of the unit and idle roles (`FoldRate.rank_fails`). -/
+theorem foldRank_B2Gp193x_sharp :
+    ((3080:ℕ):ℝ) ≤ ((14692:ℕ):ℝ) * (((110:ℕ):ℝ) - ((110:ℕ):ℝ)^(1 - 4058349/(10:ℝ)^10)) :=
+  FoldRate.rank_fact_sharp 110 14692 3080 (4058349/(10:ℝ)^10) ((4700480365791:ℝ)/1000000000000) (by norm_num) (by norm_num) (by norm_num)
+    (le_log_of_expbound _ _ 4 10 (by norm_num) (by norm_num) (by norm_num)
+      (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+    (by norm_num) (by norm_num)
+
+end OAI.PowerSaving.BlockAccounting
+
+#print axioms OAI.PowerSaving.BlockAccounting.fold_B2Gp193x
+#print axioms OAI.PowerSaving.BlockAccounting.fold_B2Gp193x_sharp
+#print axioms OAI.PowerSaving.BlockAccounting.foldRank_B2Gp193x
+#print axioms OAI.PowerSaving.BlockAccounting.foldRank_B2Gp193x_sharp
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__Raw.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__Raw.lean
new file mode 100644
index 0000000000..499fa67e88
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__Raw.lean
@@ -0,0 +1,93 @@
+/-!
+# (key: gx-data) Raw Lean form of a `gcert/1` file (EXTENDED-CERT-SPEC section 1)
+
+Core Lean only (no Mathlib): the generated data modules import nothing else, so they elaborate
+cheaply.  Field order and meaning are those of the JSON; `pairs` and `cuts` are DERIVED by the
+generator (`checks/wht26/gx-data/py/gxgen.py`) and must be tested by the label check.
+
+Registers: `x_t = t`, `y_t = v + t`, slot `k = 2 v + k`.  Vectors are bit masks.
+-/
+
+namespace GXD
+
+/-- the rational `(-1)^neg * num / den` (`den > 0`) -/
+structure Co where
+  neg : Bool
+  num : Nat
+  den : Nat
+  deriving DecidableEq, Repr
+
+/-- a gate: every register named (extras too) first moves to `frame`; then the adds happen in order -/
+inductive Gate where
+  /-- `tgt += co * src` for each `(tgt, co)` -/
+  | out (frame src : Nat) (tgts : List (Nat × Co)) (extra : List Nat)
+  /-- `tgt += co * src` for each `(src, co)` -/
+  | inn (frame tgt : Nat) (srcs : List (Nat × Co))
+  deriving Repr
+
+/-- the scatter `y_t += sum over k of coef(t, k) * total k` -/
+inductive Scat where
+  /-- star rule: `inside` if coordinate `k` is in port `t`, else `outside` -/
+  | star (inside outside : Co)
+  /-- explicit rows: row `t` = `[(total k, coef)]` -/
+  | table (rows : List (List (Nat × Co)))
+  deriving Repr
+
+/-- a `gcert/1` file -/
+structure Raw where
+  h : Nat
+  v : Nat
+  R : Nat
+  N : Nat
+  cst : Nat
+  /-- `v` masks: the unit vectors of the ports -/
+  ports : List Nat
+  /-- CHUNKED frame table (`flatten` = the table); an entry is a reduced echelon basis, leading bits descending -/
+  frames : List (List (List Nat))
+  /-- frame id per register at the start -/
+  start : List Nat
+  /-- frame id per register at the end -/
+  final : List Nat
+  /-- position `k` = retained total `k`: (slot REGISTER, frame id) -/
+  ret : List (Nat × Nat)
+  scat : Scat
+  /-- CHUNKED gates before the scatter -/
+  A : List (List Gate)
+  /-- CHUNKED gates after the scatter -/
+  B : List (List Gate)
+  /-- CHUNKED, derived: the distinct climbs `(a, b)`, `a ≠ b`, in order of first use -/
+  pairs : List (List (Nat × Nat))
+  /-- derived: replay cut points `(gates of A ++ B before the cut, frame id per register there)` -/
+  cuts : List (Nat × List Nat)
+  /-- slots that start off the zero frame `(slot REGISTER, frame id)` (rule 2); EMPTY on the path -/
+  ext : List (Nat × Nat)
+  /-- derived (questions.md Q1): per port `h` masks, the first is the port, pairwise dots = delta
+  (an orthonormal basis of `F_2^h` through the port) -/
+  obase : List (List Nat)
+
+/-- registers of a gate, in the order they are moved -/
+def Gate.regs : Gate → List Nat
+  | .out _ s ts ex => s :: (ts.map Prod.fst ++ ex)
+  | .inn _ t ss => t :: ss.map Prod.fst
+
+/-- frame of a gate -/
+def Gate.frame : Gate → Nat
+  | .out f _ _ _ => f
+  | .inn f _ _ => f
+
+/-- single adds `(tgt, src, co)` of a gate, in order -/
+def Gate.adds : Gate → List (Nat × Nat × Co)
+  | .out _ s ts _ => ts.map fun p => (p.1, s, p.2)
+  | .inn _ t ss => ss.map fun p => (t, p.1, p.2)
+
+/-- the frame table -/
+def Raw.frameTab (c : Raw) : List (List Nat) := c.frames.flatten
+
+/-- all gates of phase A / phase B -/
+def Raw.gatesA (c : Raw) : List Gate := c.A.flatten
+def Raw.gatesB (c : Raw) : List Gate := c.B.flatten
+
+/-- number of registers -/
+def Raw.nreg (c : Raw) : Nat := 2 * c.v + c.R
+
+end GXD
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__SolutionB2Gp193x.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__SolutionB2Gp193x.lean
new file mode 100644
index 0000000000..0392e1f05b
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GCert__Data__SolutionB2Gp193x.lean
@@ -0,0 +1,38 @@
+import Work.GCert.Data.B2Gp193Main
+
+/-!
+Comparator solution `Work.GCert.Data.SolutionB2Gp193x` (not part of github.com/openai/math).
+
+The whole proof is in `Work.GCert.Data.B2Gp193Main` (and its imports), which ends with
+
+    theorem wht_main_B2Gp193x :
+        ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - 7474547/(10:ℝ)^10) W
+
+This module adds nothing mathematical: it defines `WHT.WHTTimeBoundsAt` with the text of the
+challenge (the same definition as `BlockWHT.WHTTimeBoundsAt` of `Work.Block.WHT`) and restates
+the theorem under the name the challenge uses.  Its proof is that single term.
+`WHTProgram`, `wht`, `whtInKind`, `whtOutKind` come from `WHTCheck.Solution`.
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace WHT
+open Filter Asymptotics
+
+/-- `W = O(2^k (k+1)^β)` and `W = o(2^k k)` (`WHTTimeBounds` is the case `β = 1 - 2/10^11`). -/
+def WHTTimeBoundsAt (β : ℝ) (W : ℕ → ℕ) : Prop :=
+  let W' := fun k : ℕ => (W k : ℝ)
+  W' =O[atTop] (fun k : ℕ => (2:ℝ)^k * ((k:ℝ)+1)^β) ∧
+  W' =o[atTop] (fun k : ℕ => (2:ℝ)^k * (k:ℝ))
+
+/-- **Walsh-Hadamard transform with the improved exponent**: the statement `WHTGoal` of
+`WHTCheck/Challenge.lean` with `1 - 2/10^11` replaced by `1 - 7474547/10^10`. -/
+theorem wht_main_block_B2Gp193x :
+    ∃ solve W, WHTProgram solve W ∧ WHTTimeBoundsAt (1 - 7474547/(10:ℝ)^10) W :=
+  wht_main_B2Gp193x
+
+end WHT
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.WHT.wht_main_block_B2Gp193x
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GFrame__Engine__Adapt.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GFrame__Engine__Adapt.lean
new file mode 100644
index 0000000000..24e261ad08
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GFrame__Engine__Adapt.lean
@@ -0,0 +1,183 @@
+import Work.GFrame.Engine.Letters
+
+/-!
+# GFrame engine, part 2: the free adapter letters in the RAM (agent key: eng-ram)
+
+One free adapter on the array of one role is ONE linear pass, no recursive call:
+
+* `Gear.permuted`     the address of `x ↦ G.π x` (columnwise), O(1) per entry with the XOR table
+                      (as `Gear.shifted`, through `Gear.body_additive` of `Work/Block/Address.lean`);
+* `Gear.phase_row`    the `f`-bit row `(z·x_j + c)_j` of an entry, O(1);
+* `GRig`              a rig together with the table of `lum` over `Bits f` (`i^popcount`);
+* `Rig.perm_cost`, `GRig.phase_cost`   the two letters, work = length of the role table.
+-/
+
+set_option linter.unusedSectionVars false
+
+namespace OAI
+namespace PowerSaving.GF
+open Binary Matrix Finset
+noncomputable section
+section
+variable {α : Type*} [Fintype α] [DecidableEq α]
+
+/-- An address permutation acts on an array with `f` columns by moving the address. -/
+lemma act_perm (G : APerm α) (f : ℕ) (x : Sky α f → ℂ) (j : Sky α f) :
+    matAct f (permMat G) x j = x (fun k => G.π (j k)) := by
+  change ∑ i, digitProd (fun _ : Fin f => permMat G) j i * x i = _
+  have h (i : Sky α f) : digitProd (fun _ : Fin f => permMat G) j i =
+      if (fun k => G.π (j k)) = i then 1 else 0 :=
+    prod_delta (κ:=fun _ : Fin f => Space α) _ _
+  simp_rw [h]
+  simp [ite_mul]
+
+/-- A diagonal phase acts by the scalar `lum` of the row of phase bits. -/
+lemma act_phase (z : Space α) (c : F) (f : ℕ) (x : Sky α f → ℂ) (j : Sky α f) :
+    matAct f (phaseMat z c) x j = lum (fun k : Fin f => dot z (j k) + c) * x j := by
+  unfold matAct phaseMat
+  rw [digitProd_diagonal, Matrix.mulVec_diagonal]
+  rfl
+
+end
+end
+end PowerSaving.GF
+
+namespace PowerSaving.RAM
+open Binary Ty Finset GF
+noncomputable section
+universe U V
+variable {ι : Type U}
+
+namespace Gear
+variable {m : Bool} {B f : ι → ℕ} {s t : Ty} {x : ι → T s}
+variable (g : Gear m B f s x)
+include g
+variable {α : Type*} [Fintype α] [DecidableEq α] (X : Layout α) (r : ℕ)
+
+/-- Address moved by an additive bijection (across the `f` columns). -/
+lemma permuted (G : APerm α) (v : ∀ i, Grid α r (f i))
+    (h : Knows m B s x (fun i => (book X r (f i)).loc (v i))) :
+    Knows m B s x (fun i => (book X r (f i)).loc ((v i).1,
+      fun j => G.π ((v i).2 j))) := by
+  obtain ⟨hg, hh⟩ := g.grid_fetch X r (v:=v) h
+  let K (i : ι) : Grid α r (f i) := ((v i).1, fun j => G.π ((v i).2 j))
+  apply g.grid_combine X r (v:=K) hg (g.body_set X (fun i => (K i).2) _)
+  intro a
+  exact g.body_additive X (fun y => G.π y a) (fun p q => by rw [G.add]; rfl)
+    (fun i => (v i).2) hh
+
+/-- The row of phase bits `(z·x_j + c)_j` of an address. -/
+lemma phase_row (z : Space α) (c : F) (v : ∀ i, Grid α r (f i))
+    (h : Knows m B s x (fun i => (book X r (f i)).loc (v i))) :
+    Knows m B s x (fun i => (bits (f i)).loc (fun l : Fin (f i) => dot z ((v i).2 l) + c)) := by
+  obtain ⟨_, hh⟩ := g.grid_fetch X r (v:=v) h
+  have hv := g.body_additive X (fun y => dot z y) (fun p q => dot_add_right z p q)
+    (fun i => (v i).2) hh
+  rcases bit_cases c with hc|hc
+  · refine hv.cong (fun _ => rfl) (fun i => ?_)
+    simp [hc]
+  · let q i : Bits (f i) × Bits (f i) := (fun l => dot z ((v i).2 l), fun _ => 1)
+    have hf : Knows m B s x (fun i => (bits (f i)).loc (q i).2) :=
+      (g.power.minus (Can.wc 1) g.bound).cong (fun _ => rfl) (fun i => by
+        change 2^f i-1=(bits _).loc (fun _ => 1)
+        rw [← bits_lit]
+        simp)
+    refine (g.addr_xor q hv hf).cong (fun _ => rfl) (fun i => ?_)
+    apply congr_arg (bits (f i)).loc
+    ext k; simp [q,hc]
+
+end Gear
+
+/-- A rig together with the table of `lum` over `Bits f` (the fourth roots `i^popcount`). -/
+structure GRig {α ρ : Type*} (m : Bool) (B f : ι → ℕ) (s : Ty) (x : ι → T s)
+    (cl : Paint) (X : Layout α) (R : Layout ρ) (r : ℕ) (v : ∀ i, Grain α ρ r (f i)) : Prop where
+  rig : Rig m B f s x cl X R r v
+  lumT : Has m B s (a sc) x fun i => (bits (f i)).tape (fun y : Bits (f i) => lum y)
+
+section
+variable {α ρ : Type*} [Fintype α] [DecidableEq α] [Fintype ρ] [DecidableEq ρ]
+variable {m : Bool} {B f : ι → ℕ} {s t : Ty} {x : ι → T s}
+    {cl : Paint} {X : Layout α} {R : Layout ρ} {r : ℕ} {v : ∀ i, Grain α ρ r (f i)}
+
+omit [Fintype α] [DecidableEq α] [Fintype ρ] [DecidableEq ρ] in
+lemma GRig.gather (h : GRig m B f s x cl X R r v) {κ : Type V} (j : κ → ι) (y : κ → T t)
+    (g : Has m (fun k => B (j k)) t s y (fun k => x (j k))) :
+    GRig m (fun k => B (j k)) (fun k => f (j k)) t y cl X R r (fun k => v (j k)) :=
+  ⟨h.rig.gather j y g, g.then_do (h.lumT.reindex j)⟩
+
+lemma Rig.ferry_perm (h : Rig m B f s x cl X R r v) (l : ρ) (G : APerm α)
+    (q : ∀ i, Beach α ρ r (f i))
+    (g : Knows m B s x fun i => (fleet X R r (f i)).loc (q i)) :
+    Has m B s (c cl) x fun i => ferryM r (f i) l (permMat G) (v i) (q i) := by
+  obtain ⟨hl,hk⟩ := h.addrs q g
+  have hb := h.read q hl hk
+  let t i : Beach α ρ r (f i) := ((q i).1,(q i).2.1,fun j => G.π ((q i).2.2 j))
+  have hh := h.read t hl (h.gear.permuted X r G _ hk)
+  apply Can.cases_code (q:=fun i => (q i).1) R hl
+  intro p
+  by_cases he : p=l
+  · refine (hh.reindex (fun i : {i // (q i).1=p} => i.1)).cong (fun _ => rfl)
+      (fun i => ?_)
+    have hql : (q i.val).1 = l := i.property.trans he
+    change v i.val ((q i.val).1,(q i.val).2.1,fun j => G.π ((q i.val).2.2 j)) = _
+    simp only [ferryM, roleAct, hql, if_true, act_perm]
+  · refine (hb.reindex (fun i : {i // (q i).1=p} => i.1)).cong (fun _ => rfl)
+      (fun i => ?_)
+    have H : (q i.val).1≠l := fun hh => he (i.property.symm.trans hh)
+    simp only [ferryM, roleAct, H, ite_false, Prod.mk.eta]
+
+/-- **Free address permutation**: one pass over the role table. -/
+lemma Rig.perm_cost (h : Rig m B f s x cl X R r v) (l : ρ) (G : APerm α) :
+    Can m B s (a (c cl)) x
+      (fun i => (fleet X R r (f i)).tape (ferryM r (f i) l (permMat G) (v i)))
+      (fun i => (fleet X R r (f i)).n) := by
+  refine h.chart _ ?_
+  let S := Σ i, Beach α ρ r (f i)
+  have hg := h.gather (fun d : S => d.1)
+    (fun d => ((x d.1, (fleet X R r (f d.1)).loc d.2):T (p s w))) (t:=p s w) Can.first
+  exact hg.ferry_perm l G (fun d => d.2) Can.second
+
+lemma GRig.ferry_phase (h : GRig m B f s x cl X R r v) (l : ρ) (z : Space α) (c' : F)
+    (q : ∀ i, Beach α ρ r (f i))
+    (g : Knows m B s x fun i => (fleet X R r (f i)).loc (q i)) :
+    Has m B s (c cl) x fun i => ferryM r (f i) l (phaseMat z c') (v i) (q i) := by
+  obtain ⟨hl,hk⟩ := h.rig.addrs q g
+  have hb := h.rig.read q hl hk
+  have hrow := h.rig.gear.phase_row X r z c' (fun i => (q i).2) hk
+  have hs : Has m B s sc x
+      (fun i => lum (fun k : Fin (f i) => dot z ((q i).2.2 k) + c')) :=
+    Can.fetch (t:=sc) (L:=fun i => bits (f i)) (v:=fun i (y : Bits (f i)) => lum y)
+      (i:=fun i => (fun k : Fin (f i) => dot z ((q i).2.2 k) + c')) h.lumT hrow
+  have hh := hs.mul hb
+  apply Can.cases_code (q:=fun i => (q i).1) R hl
+  intro p
+  by_cases he : p=l
+  · refine (hh.reindex (fun i : {i // (q i).1=p} => i.1)).cong (fun _ => rfl)
+      (fun i => ?_)
+    have hql : (q i.val).1 = l := i.property.trans he
+    change lum (fun k : Fin (f i.val) => dot z ((q i.val).2.2 k) + c') *
+      v i.val ((q i.val).1,(q i.val).2.1,(q i.val).2.2) = _
+    simp only [ferryM, roleAct, hql, if_true, act_phase]
+  · refine (hb.reindex (fun i : {i // (q i).1=p} => i.1)).cong (fun _ => rfl)
+      (fun i => ?_)
+    have H : (q i.val).1≠l := fun hh => he (i.property.symm.trans hh)
+    simp only [ferryM, roleAct, H, ite_false, Prod.mk.eta]
+
+/-- **Free diagonal phase**: one pass over the role table (one table look-up per entry). -/
+lemma GRig.phase_cost (h : GRig m B f s x cl X R r v) (l : ρ) (z : Space α) (c' : F) :
+    Can m B s (a (c cl)) x
+      (fun i => (fleet X R r (f i)).tape (ferryM r (f i) l (phaseMat z c') (v i)))
+      (fun i => (fleet X R r (f i)).n) := by
+  refine h.rig.chart _ ?_
+  let S := Σ i, Beach α ρ r (f i)
+  have hg := h.gather (fun d : S => d.1)
+    (fun d => ((x d.1, (fleet X R r (f d.1)).loc d.2):T (p s w))) (t:=p s w) Can.first
+  exact hg.ferry_phase l z c' (fun d => d.2) Can.second
+
+end
+end
+end PowerSaving.RAM
+end OAI
+
+#print axioms OAI.PowerSaving.RAM.Rig.perm_cost
+#print axioms OAI.PowerSaving.RAM.GRig.phase_cost
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GFrame__Engine__Letters.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GFrame__Engine__Letters.lean
new file mode 100644
index 0000000000..2eca6e713b
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GFrame__Engine__Letters.lean
@@ -0,0 +1,199 @@
+import Work.Block.Bridge
+
+/-!
+# GFrame engine, part 1: the generalised word language (agent key: eng-ram)
+
+Letters = the letters of `BWord` (`localM`, `shift`, `block`) plus TWO FREE ADAPTER letters on
+one role:
+
+* `perm l G`      address permutation by an additive bijection `G` of the label space
+                  (matrix `permMat G`, `(permMat G) x y = 1` iff `G.π x = y`);
+* `phase l z c`   the diagonal phase `i^[z·x + c]` IN THE STANDARD BASIS
+                  (matrix `phaseMat z c = diagonal (fun x => tint (dot z x + c))`).
+
+Products of `phaseMat` are exactly the diagonal matrices `i^Q(x)`, `Q` a `ℤ/4`-valued quadratic
+form plus a constant; with the old free letter `shift` the free letters generate every affine
+address permutation times such a phase.  A "twisted block" is NOT a primitive letter: it is the
+word `free adapters ++ [block] ++ free adapters` (see `Free.lean`, `gstep_of_factor`).
+
+The semantics is `gwalk` (no unit-move word behind it: the new letters are not Walsh-diagonal).
+Old words embed by `GWord.ofB`, and `gwalk f (ofB w) = walk f w.flat`.
+-/
+
+set_option linter.unusedSectionVars false
+
+namespace OAI
+namespace PowerSaving.GF
+open Binary Matrix Finset
+noncomputable section
+
+/-- An additive bijection of the label space. -/
+structure APerm (α : Type*) where
+  π : Space α ≃ Space α
+  add : ∀ x y, π (x + y) = π x + π y
+
+section Mats
+variable {α : Type*} [Fintype α] [DecidableEq α]
+
+/-- Permutation matrix of an additive bijection: `(permMat G *ᵥ v) x = v (G.π x)`. -/
+def permMat (G : APerm α) : CMat α := fun x y => if G.π x = y then 1 else 0
+
+/-- Elementary diagonal phase in the standard basis: `i^[z·x + c]`. -/
+def phaseMat (z : Space α) (c : F) : CMat α := Matrix.diagonal fun x => tint (dot z x + c)
+
+end Mats
+
+/-- Letters of the generalised word language. -/
+inductive GMove (α ρ : Type*)
+  | old (mv : BMove α ρ)
+  | perm (l : ρ) (G : APerm α)
+  | phase (l : ρ) (z : Space α) (c : F)
+
+abbrev GWord (α ρ : Type*) := List (GMove α ρ)
+
+namespace GMove
+variable {α ρ : Type*}
+
+/-- The letter of `BWord` with the same price (free adapters ↦ a free letter). -/
+def shadow : GMove α ρ → BMove α ρ
+  | .old mv => mv
+  | .perm _ _ => .localM 0
+  | .phase _ _ _ => .localM 0
+
+/-- Rank paid by a letter (`none` = free). -/
+def rk? (mv : GMove α ρ) : Option ℕ := mv.shadow.rk?
+def costR (φ : ℕ → ℝ) (mv : GMove α ρ) : ℝ := mv.shadow.costR φ
+def Proper (u : ℕ) (mv : GMove α ρ) : Prop := mv.shadow.Proper u
+
+@[simp] lemma costR_perm (φ : ℕ → ℝ) (l : ρ) (G : APerm α) :
+    (GMove.perm l G : GMove α ρ).costR φ = 0 := rfl
+@[simp] lemma costR_phase (φ : ℕ → ℝ) (l : ρ) (z : Space α) (c : F) :
+    (GMove.phase l z c : GMove α ρ).costR φ = 0 := rfl
+@[simp] lemma costR_old (φ : ℕ → ℝ) (mv : BMove α ρ) : (GMove.old mv).costR φ = mv.costR φ := rfl
+lemma proper_perm (u : ℕ) (l : ρ) (G : APerm α) : (GMove.perm l G : GMove α ρ).Proper u :=
+  trivial
+lemma proper_phase (u : ℕ) (l : ρ) (z : Space α) (c : F) :
+    (GMove.phase l z c : GMove α ρ).Proper u := trivial
+@[simp] lemma proper_old (u : ℕ) (mv : BMove α ρ) : (GMove.old mv).Proper u ↔ mv.Proper u :=
+  Iff.rfl
+
+end GMove
+
+namespace GWord
+variable {α ρ : Type*}
+
+def shadow (w : GWord α ρ) : BWord α ρ := w.map GMove.shadow
+def costR (φ : ℕ → ℝ) (w : GWord α ρ) : ℝ := (w.map (GMove.costR φ)).sum
+def Proper (u : ℕ) (w : GWord α ρ) : Prop := ∀ mv ∈ w, mv.Proper u
+def hist (w : GWord α ρ) (r : ℕ) : ℕ := w.shadow.hist r
+/-- Natural-number cost when a block of rank `rk` costs `g rk`. -/
+def cost (g : ℕ → ℕ) (w : GWord α ρ) : ℕ := w.shadow.cost g
+/-- An old block word as a generalised word. -/
+def ofB (w : BWord α ρ) : GWord α ρ := w.map GMove.old
+
+@[simp] lemma shadow_nil : shadow ([] : GWord α ρ) = [] := rfl
+@[simp] lemma shadow_cons (mv : GMove α ρ) (w : GWord α ρ) :
+    shadow (mv :: w) = mv.shadow :: shadow w := rfl
+@[simp] lemma shadow_ofB (w : BWord α ρ) : shadow (ofB w) = w := by
+  simp [shadow, ofB, List.map_map, Function.comp_def, GMove.shadow]
+
+lemma costR_shadow (φ : ℕ → ℝ) (w : GWord α ρ) : costR φ w = BWord.costR φ w.shadow := by
+  unfold costR BWord.costR shadow
+  rw [List.map_map]
+  rfl
+@[simp] lemma costR_nil (φ : ℕ → ℝ) : costR φ ([] : GWord α ρ) = 0 := rfl
+lemma costR_cons (φ : ℕ → ℝ) (mv : GMove α ρ) (w : GWord α ρ) :
+    costR φ (mv :: w) = mv.costR φ + costR φ w := by simp [costR]
+lemma costR_append (φ : ℕ → ℝ) (w w' : GWord α ρ) :
+    costR φ (w ++ w') = costR φ w + costR φ w' := by simp [costR]
+lemma costR_ofB (φ : ℕ → ℝ) (w : BWord α ρ) : costR φ (ofB w) = BWord.costR φ w := by
+  rw [costR_shadow, shadow_ofB]
+@[simp] lemma cost_nil (g : ℕ → ℕ) : cost g ([] : GWord α ρ) = 0 := rfl
+lemma cost_cons (g : ℕ → ℕ) (mv : GMove α ρ) (w : GWord α ρ) :
+    cost g (mv :: w) = mv.shadow.cost g + cost g w := BWord.cost_cons g _ _
+
+lemma Proper.shadow {u : ℕ} {w : GWord α ρ} (h : Proper u w) : BWord.Proper u w.shadow := by
+  intro mv hmv
+  obtain ⟨g, hg, rfl⟩ := List.mem_map.mp hmv
+  exact h g hg
+lemma Proper.tail {u : ℕ} {mv : GMove α ρ} {w : GWord α ρ} (h : Proper u (mv :: w)) :
+    Proper u w := fun x hx => h x (List.mem_cons_of_mem _ hx)
+lemma Proper.head {u : ℕ} {mv : GMove α ρ} {w : GWord α ρ} (h : Proper u (mv :: w)) :
+    mv.Proper u := h mv List.mem_cons_self
+lemma Proper.append {u : ℕ} {w w' : GWord α ρ} (h : Proper u w) (h' : Proper u w') :
+    Proper u (w ++ w') := by
+  intro mv hmv
+  rcases List.mem_append.mp hmv with h1|h1
+  · exact h mv h1
+  · exact h' mv h1
+lemma proper_nil (u : ℕ) : Proper u ([] : GWord α ρ) := fun _ h => by simp at h
+lemma proper_ofB {u : ℕ} {w : BWord α ρ} (h : w.Proper u) : Proper u (ofB w) := by
+  intro mv hmv
+  obtain ⟨g, hg, rfl⟩ := List.mem_map.mp hmv
+  exact h g hg
+
+lemma costR_eq_sum (u : ℕ) (φ : ℕ → ℝ) (w : GWord α ρ) (hw : Proper u w) :
+    costR φ w = ∑ r : Fin u, (w.hist r:ℝ) * φ r := by
+  rw [costR_shadow]; exact BWord.costR_eq_sum u φ _ hw.shadow
+lemma cost_eq_sum (u : ℕ) (g : ℕ → ℕ) (w : GWord α ρ) (hw : Proper u w) :
+    cost g w = ∑ r : Fin u, hist w r * g r := BWord.cost_eq_sum u g _ hw.shadow
+lemma hist_zero (u : ℕ) (w : GWord α ρ) (hw : Proper u w) : hist w 0 = 0 :=
+  BWord.hist_zero u _ hw.shadow
+lemma hist_large (u : ℕ) (w : GWord α ρ) (hw : Proper u w) (r : ℕ) (hr : u ≤ r) :
+    hist w r = 0 := BWord.hist_large u _ hw.shadow r hr
+
+end GWord
+
+section Sem
+variable {α ρ σ : Type*} [Fintype α] [DecidableEq α] [Fintype ρ] [DecidableEq ρ]
+
+/-- The action of one letter. -/
+def GMove.act (f : ℕ) : GMove α ρ → Data α ρ f → Data α ρ f
+  | .old mv => mv.act f
+  | .perm l G => roleAct f l (permMat G)
+  | .phase l z c => roleAct f l (phaseMat z c)
+
+/-- **Semantics of a generalised word.** -/
+def gwalk (f : ℕ) (w : GWord α ρ) (x : Data α ρ f) : Data α ρ f :=
+  w.foldl (fun y mv => mv.act f y) x
+
+@[simp] lemma gwalk_nil (f : ℕ) (x : Data α ρ f) : gwalk f ([] : GWord α ρ) x = x := rfl
+lemma gwalk_cons (f : ℕ) (mv : GMove α ρ) (w : GWord α ρ) (x : Data α ρ f) :
+    gwalk f (mv :: w) x = gwalk f w (mv.act f x) := rfl
+lemma gwalk_append (f : ℕ) (p q : GWord α ρ) (x : Data α ρ f) :
+    gwalk f (p ++ q) x = gwalk f q (gwalk f p x) := by simp [gwalk]
+
+/-- Old words keep their meaning. -/
+lemma gwalk_ofB (f : ℕ) (w : BWord α ρ) (x : Data α ρ f) :
+    gwalk f (GWord.ofB w) x = walk f w.flat x := by
+  induction w generalizing x with
+  | nil => rfl
+  | cons mv w ih =>
+    rw [walk_flat_cons, ← ih]
+    rfl
+
+/-- The scratch certificate for the generalised language (cf. `RAM.LiveKernel`). -/
+def GLiveKernel (e : σ → ρ) (w : GWord α ρ) : Prop :=
+  ∀ (f : ℕ) (v : Data α ρ f), (∀ s, (∀ l, e l ≠ s) → v s = 0) →
+    ∀ l, gwalk f w v (e l) = matAct f (kernel α) (v (e l))
+
+/-- Every old certificate is a generalised certificate. -/
+theorem GLiveKernel.ofB {e : σ → ρ} {w : BWord α ρ} (h : RAM.LiveKernel e w.flat) :
+    GLiveKernel e (GWord.ofB w) := by
+  intro f v hv l
+  rw [gwalk_ofB]
+  exact h f v hv l
+
+/-- One role goes from matrix `M` to `N` by a generalised word (cf. `XStep`). -/
+def GStep (l : ρ) (M N : CMat α) (c : (ℕ → ℝ) → ℝ) : Prop :=
+  ∃ (w : GWord α ρ) (U : CMat α), w.Proper (Fintype.card α) ∧ (∀ φ, w.costR φ = c φ) ∧
+    U * M = N ∧ ∀ (f : ℕ) (x : Data α ρ f), gwalk f w x = roleAct f l U x
+
+end Sem
+end
+end PowerSaving.GF
+end OAI
+
+#print axioms OAI.PowerSaving.GF.gwalk_ofB
+#print axioms OAI.PowerSaving.GF.GLiveKernel.ofB
+#print axioms OAI.PowerSaving.GF.GWord.costR_eq_sum
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GFrame__Engine__Level.lean b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GFrame__Engine__Level.lean
new file mode 100644
index 0000000000..6bd7cfa0c3
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/Work__GFrame__Engine__Level.lean
@@ -0,0 +1,163 @@
+import Work.GFrame.Engine.Sweep
+import WHTCheck.Solution
+
+/-!
+# GFrame engine, part 4: one level of the recursion for generalised words (agent key: eng-ram)
+
+Copy of `amplifyB` (`Work/Block/Recursion.lean`) with two changes:
+
+* the word is a `GWord` with certificate `GLiveKernel e w` (semantics `gwalk`);
+* after the XOR table the level also builds the table of `lum` over `Bits f`
+  (`WHT.lum_tables`, doubling construction, `O(2^f)` work), which the free diagonal phases
+  read; it is part of the environment of the sweep (`GRig`).
+
+Cost: the same `2^k` linear term and the same recursive calls as `amplifyB`.
+-/
+
+set_option linter.unusedSectionVars false
+
+namespace OAI
+namespace PowerSaving.RAM
+open Binary Matrix Ty Finset GF
+noncomputable section
+
+section
+universe U
+variable {α ρ σ : Type*} [Fintype α] [DecidableEq α] [Fintype ρ] [DecidableEq ρ]
+  [Fintype σ] [DecidableEq σ]
+variable {ι : Type U} {m : Bool}
+    {k f : ι → ℕ} {cl : Paint} {b : Bank (hatch cl) ι}
+    {v : ∀ i, Sim σ (k i)→ℂ}
+
+/-- **One level of the recursion for a generalised word** (replaces `amplifyB`). -/
+lemma gamplify (m : Bool) (b : Bank (hatch cl) ι) (v : ∀ i, Sim σ (k i) → ℂ)
+    (X : Layout α) (R : Layout ρ) (Q : Layout σ) (e : σ → ρ) (he : Function.Injective e)
+    (r : ℕ) (hr : 3 ≤ X.n) (hq : ∀ i, X.n*f i+r=k i) (hd : r < X.n) (hQ : 0<Q.n)
+    (n τ : ℕ → ι → ℕ)
+    (hc : ∀ rk, 1 ≤ rk → rk < X.n → ∀ i, n rk i*(sim Q (rk * f i)).n=2^k i)
+    (hk : ∀ rk, 1 ≤ rk → rk < X.n → Contract cl b (fun i => rk * f i) (τ rk) Q)
+    (hB : Small b.B (fun i => 2^k i))
+    (w : GWord α ρ) (hw : GLiveKernel e w) (hP : w.Proper X.n) :
+    Able m b (simIn cl) (bundle cl) (fun i => loaded cl Q (k i) (v i))
+      (fun i => (sim Q (k i)).tape (whole (k i) (v i)))
+      (fun i => 2^k i) (fun i => w.cost (fun rk => n rk i * τ rk i)) := by
+  let W i := 2^k i
+  let s := simIn cl
+  let eQ (i : ι) := ebb X r (f i) (k i) (hq i) (v i)
+  let zQ (i : ι) : Grain α σ r (f i) :=
+    fun j => chords r (f i) (fun l => eQ i (j.1,l)) j.2
+  let Z (i : ι) : Grain α ρ r (f i) := crossAct r (f i) (embM e) (zQ i)
+  let O (i : ι) : Grain α σ r (f i) :=
+    crossAct r (f i) (extM e) (gcoast r (f i) w (Z i))
+  let szQ i := (fleet X Q r (f i)).n
+  let szR i := (fleet X R r (f i)).n
+  have hszQ : Dom W szQ := by
+    refine ⟨Q.n+1, fun i => ?_⟩
+    unfold W szQ fleet
+    rw [Layout.pair_len, book_len,hq]
+    simp only [mul_add,add_mul,mul_one,one_mul]
+    gcongr <;> simp
+  have hszR : Dom W szR := by
+    refine ⟨R.n+1, fun i => ?_⟩
+    unfold W szR fleet
+    rw [Layout.pair_len, book_len,hq]
+    simp only [mul_add,add_mul,mul_one,one_mul]
+    gcongr <;> simp
+  have hn (i : ι) : 0 < W i := pow_pos (by decide) _
+  have hf (i) : f i ≤ k i := by
+    have g := hq i
+    have h := Nat.le_mul_of_pos_left (f i) (show 0 < X.n by omega)
+    omega
+  have hy (i) : k i ≤ W i := Nat.lt_two_pow_self.le
+  have sd := hB.mono hy
+  have sq := sd.mono hf
+  let p2 i := 2^f i
+  have hm : Small b.B p2 :=
+    hB.mono (fun i => Nat.pow_le_pow_right (by omega) (hf i))
+  have hcube (i) : p2 i ^ 3 ≤ W i := by
+    unfold p2 W
+    rw [← pow_mul]
+    apply Nat.pow_le_pow_right (by omega)
+    have hh : 3*f i ≤ X.n*f i := Nat.mul_le_mul_right _ hr
+    have hg := hq i
+    rw [mul_comm]
+    omega
+  let env (i : ι) := loaded cl Q (k i) (v i)
+  -- construct fields (f,p2)
+  have hmf : Can m b.B s Ty.w env f W := by
+    have ht : Can m b.B s Ty.w env k W := Can.first
+    refine (ht.dvdW (Can.wc X.n) sd).cong (fun _ => rfl) ?_
+    intro i
+    rw [← hq,mul_comm X.n]
+    exact Layout.div_join hd
+  have hmp : Can m b.B s (Ty.p Ty.w Ty.w) env (fun i => (f i,p2 i)) W :=
+    hmf.pair (hmf.wTwo sq hm (Dom.of_le (fun i => (hf i).trans (hy i))))
+  let T1 := Ty.p s (Ty.p Ty.w Ty.w)
+  let Y (i : ι) : T T1 := (env i,f i,p2 i)
+  have hmx : Can m b.B T1 (Ty.a Ty.w) Y (fun i => xorTab (f i)) W :=
+    (Can.xor_prepare (m:=m) (f:=f) (B:=b.B) (s:=T1) (x:=Y)
+      (Can.fst Can.second) (Can.snd Can.second) sq hm).mono hcube
+  let T2 := Ty.p T1 (Ty.a Ty.w)
+  let Y' (i : ι) : T T2 := (Y i,xorTab (f i))
+  -- NEW: the table of `lum` over `Bits f`
+  have hE2 : Has m b.B T2 s Y' env := Can.fst Can.first
+  have hml : Can m b.B T2 (Ty.a sc) Y'
+      (fun i => (bits (f i)).tape (fun y : Bits (f i) => lum y)) W :=
+    (WHT.lum_tables (k:=f) (Can.fst (Can.snd Can.first)) sq hm hE2.snd.fst).1.mono
+      (fun i => Nat.pow_le_pow_right (by omega) (hf i))
+  let T2' := Ty.p T2 (Ty.a sc)
+  let Y'' (i : ι) : T T2' := (Y' i,(bits (f i)).tape (fun y : Bits (f i) => lum y))
+  -- the input, read as a table on the slots
+  have hG0 : Rig m b.B f T2 Y' cl X Q r eQ := by
+    refine ⟨⟨?_,?_,Can.second,hm⟩,?_,?_⟩
+    · exact Can.snd (Can.snd Can.first)
+    · exact Can.fst (Can.snd Can.first)
+    · exact hE2.snd.fst
+    · exact hE2.snd.snd.cong (fun _ => rfl) (fun i => (ebb_eq ..).symm)
+  have hG : Rig m b.B f T2' Y'' cl X Q r eQ := hG0.gather id Y'' (t:=T2') Can.first
+  -- leftover bits, still on the slots
+  have HH : Can m b.B T2' (bundle cl) Y'' (fun i => (fleet X Q r (f i)).tape (zQ i)) W :=
+    hG.dots_cost.weaken hszQ
+  let T3 := Ty.p T2' (bundle cl)
+  let A (i) : T T3 := (Y'' i,(fleet X Q r (f i)).tape (zQ i))
+  have Hg := hG.gather id A (t:=T3) Can.first
+  have G : Rig m b.B f T3 A cl X Q r zQ := ⟨Hg.gear,Hg.imag,Can.second⟩
+  -- embed the slots into the table of roles; scratch roles are created as zero
+  have HE : Can m b.B T3 (bundle cl) A (fun i => (fleet X R r (f i)).tape (Z i)) W :=
+    (G.cross_point R (embM e)).weaken hszR
+  let T4 := Ty.p T3 (bundle cl)
+  let A4 (i) : T T4 := (A i,(fleet X R r (f i)).tape (Z i))
+  have Hg4 := G.gather id A4 (t:=T4) Can.first
+  have hL4 : Has m b.B T4 (Ty.a sc) A4
+      (fun i => (bits (f i)).tape (fun y : Bits (f i) => lum y)) :=
+    Can.snd (Can.fst Can.first)
+  have G4 : GRig m b.B f T4 A4 cl X R r Z := ⟨⟨Hg4.gear,Hg4.imag,Can.second⟩,hL4⟩
+  -- the GENERALISED word on the table of roles
+  have Hy := G4.gsweep n τ Q hQ hk
+    (fun rk h1 h2 i => by rw [book_len,hq]; exact hc rk h1 h2 i) w hP
+  -- extract the slots; scratch roles are dropped
+  let T5 := Ty.p T4 (bundle cl)
+  let A5 (i) : T T5 := (A4 i,(fleet X R r (f i)).tape (gcoast r (f i) w (Z i)))
+  have Hg5 := G4.rig.gather id A5 (t:=T5) Can.first
+  have G5 : Rig m b.B f T5 A5 cl X R r (fun i => gcoast r (f i) w (Z i)) :=
+    ⟨Hg5.gear,Hg5.imag,Can.second⟩
+  have HX : Can m b.B T5 (bundle cl) A5 (fun i => (fleet X Q r (f i)).tape (O i)) W :=
+    (G5.cross_point Q (extM e)).weaken hszQ
+  have heq (i) : O i = ebb X r (f i) (k i) (hq i) (whole (k i) (v i)) :=
+    gamplifies X r (f i) (k i) (hq i) e he w hw (v i)
+  have ha (i) : (fleet X Q r (f i)).tape (O i) =
+      (sim Q (k i)).tape (whole (k i) (v i)) := by
+    rw [heq]; exact ebb_eq ..
+  have Ho := ((Hy.weaken hszR (fun _ => le_rfl)).save_keep
+    (Able.of_can (b:=b) HX)).cong (fun _ => rfl) ha
+  have Hx := (Able.of_can (b:=b) hmp).save_keep
+    ((Able.of_can (b:=b) hmx).save_keep ((Able.of_can (b:=b) hml).save_keep
+      ((Able.of_can (b:=b) HH).save_keep ((Able.of_can (b:=b) HE).save_keep Ho))))
+  simpa only [Nat.zero_add,Nat.add_zero] using Hx
+
+end
+end
+end PowerSaving.RAM
+end OAI
+
+#print axioms OAI.PowerSaving.RAM.gamplify
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__ORIGIN.md b/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__ORIGIN.md
new file mode 100644
index 0000000000..e28b355d0a
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__ORIGIN.md
@@ -0,0 +1,64 @@
+# tools/gx/ and tools/certificate/gcert1-p11-pr193.json.gz: where they come from
+
+Everything in this directory is Python 3 (standard library only). No Lean is run by these scripts.
+"The outside repository" means github.com/CrocSwap/integer-mult-bounds (Apache-2.0, `LICENSE` and `NOTICE`
+of that repository; `NOTICE`: "A sharper exponent for integer multiplication, Copyright 2026 Douglas Colkitt").
+
+## The scripts (this project)
+
+| file | what it is |
+|---|---|
+| `gxcore.py` | loads a certificate of format gcert/1, brings it to normal form, and is a Python mirror of both Lean checks (labels and scalars); cut points and label data for the generator |
+| `gxunit.py` | split plan of the kernel evaluations, the unit of the word, expected exponents |
+| `gxbind.py` | the texts of the generated Lean modules (check, histogram, price, certificate and final modules) |
+| `gxgen.py` | certificate -> Lean data modules and one module per kernel evaluation |
+| `gxrate.py` | rate lemmas, unit price list, final theorem modules, comparator challenge / solution / configuration |
+| `gxdry.py`, `gxmut.py` | dry run (mirror, sizes, plan, exponents); mutants that the mirror must reject |
+| `gxconv.py` | converts the earlier format gcert/0 to gcert/1 when a step scales its target (the in-place pair step of #193) |
+| `gsmirror.py` | a second, separately written Python mirror of the scalar check `GS.scalCheck` / `GS.yCheck`; `gxbind.py` calls it for the check parameters |
+| `gx.py`, `gxrun.py` | the reference checker of the format (`gx.check1`: labels and exact scalar identity) and its command line |
+| `gxpaths.py`, `regen_check.py`, `refcheck.py` | written for this repository: relative paths; regenerate and compare; `gx.check1` on a gcert/1 file |
+
+The scripts are the working copies with path edits only (absolute paths of the author's machine replaced through
+`gxpaths.py`; templates read from `tools/gen/templates/`; `foldlib.py` / `foldgen.py` taken from `tools/gen/`).
+The sentences "Generated by checks/..." that the generators print into Lean files name the scripts by their
+working paths; they are kept so that the generated modules come out byte for byte.
+No script of the outside repository is included, imported or executed.
+
+## The certificate `tools/certificate/gcert1-p11-pr193.json.gz`
+
+sha256 of the file: `15251deb0c11e0504d7b297c9786818888a93f08b92b03c6c122784b70488633`
+(gzip stores a time stamp; sha256 of the uncompressed JSON: `c64d2a95431c3cf24452de7391cce780bd71521da44ce23923ebb235f6c7962c`).
+
+It is ONE explicit program (numbered registers, every addition, every frame) for the helper circuit at
+h = 22: 1,320 ports, 9,412 slots, 262,944 unit moves. **The design of that circuit is not this project's.** It is the
+"paired-cube" circuit of the outside repository as of pull request #193 (which builds on #191, #184, #168 and #144).
+The outside repository publishes the design as generator scripts, frozen data files and a ledger; it has no file
+of this kind. This file was produced by this project's own code, which
+
+1. loaded the following files of the outside repository **as data** (JSON; nothing was executed):
+   - at pull request #168, commit `4a3c769e5c5430e7114c4d3e099ff34664677f17`:
+     `references/paired-cube/sources/local_L1.json`,
+     `references/paired-cube/sources/tmod_TE_TD_TB3_1_1_4_full_6.0617964e-4.json`,
+     `references/paired-cube/sources/pmod_J0_full_6.0666810e-4.json`,
+     `references/paired-cube/sources/qmod_climb3u_best.json` (the local modules),
+     `references/paired-cube/selected-module/matching-arcs.json` (carrier arcs),
+     `references/paired-cube/physical/frames.json` (moved frames);
+   - at pull request #193, commit `187e1010ac8b259af8e9b5166f68b64bc27b4b47`:
+     `research/source-assisted-v4/data/physical-pairs.json` (the hand-over pairs);
+2. rebuilt the circuit from them step by step, following the algorithms of the outside scripts (read as text),
+   and checked the result exactly (every published count reproduced; the scalar identity as an identity of
+   linear maps with arbitrary contents of the helper registers);
+3. converted it to gcert/1 with `gxconv.py` (tested by `gx.check1`).
+
+Step 1 and step 2 (the rebuild scripts and the outside inputs they read) are NOT part of this repository;
+the inputs can be fetched from the outside repository at the two commits above.
+What this repository proves about the file does not depend on how it was made: the Lean kernel checks the
+generated modules (labels, scalar identity, price), and `regen_check.py` shows that those modules are exactly
+what `gxgen.py` / `gxrate.py` produce from this file.
+
+## Check it yourself
+
+    python3 tools/gx/regen_check.py                       # regenerates the Lean modules and compares
+    python3 tools/gx/gxdry.py tools/certificate/gcert1-p11-pr193.json.gz      # Python mirror of both checks
+    python3 tools/gx/refcheck.py                          # the reference checker gx.check1 on the certificate
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__gx.py b/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__gx.py
new file mode 100644
index 0000000000..6d14c0a976
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__gx.py
@@ -0,0 +1,296 @@
+#!/usr/bin/python3 -I
+"""gx.py.  OWN code (imports nothing of port-producer, nothing outside).
+(1) convert(c0): gcert/0 (port-producer's event list) -> gcert/1, the LEAN-FACING NORMAL FORM:
+    only the main phase (no read0 / undo / uninj: the invocation theorem derives the dirt gate and the undo
+    gate from the product), every gate an elementary fan-out or fan-in add, the 4x4 K block written as three
+    such adds plus a sign carried by one register, the star scatter as a table.
+(2) check1(c1): the local decidable conditions of EXTENDED-CERT-SPEC.md on a gcert/1 file:
+    E0 sizes, E1 labels (nested subspaces by containment, equal frame at a gate), E2 scatter cut,
+    E3 shape (kinds of gates; X1; S1), E4 bracket rule S2, E5 scalar (x-content replay: hid and X3),
+    E6 price data (block histograms, N), E7 exterior gauges only (Q2).  Raises AssertionError("<rule>: ...").
+"""
+from fractions import Fraction as Fr
+from collections import Counter
+from math import lcm
+
+
+def need(c, msg):
+    if not c:
+        raise AssertionError(msg)
+
+
+def reduce(u, basis):
+    """basis: reduced echelon, pivot = leading bit, descending.  Returns u modulo the span."""
+    for b in basis:
+        if u >> (b.bit_length() - 1) & 1:
+            u ^= b
+    return u
+
+
+def echelon_ok(f):
+    piv = [b.bit_length() - 1 for b in f]
+    if any(b == 0 for b in f) or piv != sorted(piv, reverse=True) or len(set(piv)) != len(piv):
+        return False
+    return all(not (b >> p & 1) for i, b in enumerate(f) for j, p in enumerate(piv) if i != j)
+
+
+def inside(a, b):
+    return all(reduce(u, b) == 0 for u in a)
+
+
+def par(x):
+    return bin(x).count("1") & 1
+
+
+KJ = [[[1, 2] if i == j else [-1, 2] for j in range(4)] for i in range(4)]
+
+
+def convert(c0):
+    need(c0["format"] == "gcert/0", "input is not gcert/0")
+    v, h, R = c0["v"], c0["h"], c0["R"]
+    ev = c0["events"]
+    cen = [n for n, e in enumerate(ev) if e[0] == "centre"]
+    need(cen == list(range(cen[0], cen[0] + len(cen))), "centres are not contiguous: no single scatter cut")
+    A, B, ret = [], [], []
+    neg = set()            # x registers currently holding MINUS their value (between the two K blocks)
+    openq = {}
+    for n, e in enumerate(ev):
+        k = e[0]
+        out = A if n < cen[0] else B
+        if k in ("read0", "undo", "uninj"):
+            continue
+        if k == "inj":
+            need(e[2] not in neg, "inj reads a negated x register")
+            out.append(["out", e[3], e[2], [[e[1], 1, 1]], []])
+        elif k == "op":
+            if e[3] == -1:
+                out.append(["neg", e[5], e[1]])
+            else:
+                need(e[3] == 1, "op ca")
+            out.append(["out", e[5], e[2], [[e[1], e[4], 1]], []])
+        elif k == "centre":
+            ret.append([e[2], e[1], e[3]])
+        elif k == "gread":
+            hit = set(t for t, _, _ in e[3])
+            out.append(["out", e[2], e[1], [[v + t, a, b] for t, a, b in e[3]], [v + t for t in e[4] if t not in hit]])
+        elif k == "rread":
+            out.append(["out", e[2], e[1], [[v + t, a, b] for t, a, b in e[3]], []])
+        elif k == "ysh":
+            out.append(["out", e[4], e[2], [[e[1], e[3], 1]], []])
+        elif k == "yw":
+            out.append(["out", e[4], e[2], [[e[1], e[3][0], e[3][1]]], []])
+        elif k == "kd":
+            out.append(["out", e[3], e[2], [[e[1], -1 if e[2] in neg else 1, 1]], []])
+        elif k == "ktr":
+            q = tuple(e[1])
+            need(e[2] == KJ, "ktr matrix is not 1 - J/2")
+            x1, rest = q[0], list(q[1:])
+            if q not in openq:          # first block: x := M x, register x1 keeps the sign
+                out.append(["in", e[3], x1, [[r, 1, 1] for r in rest]])
+                out.append(["out", e[3], x1, [[r, -1, 2] for r in rest], []])
+                out.append(["in", e[3], x1, [[r, 1, 1] for r in rest]])
+                openq[q] = n
+                neg.add(x1)
+            else:                       # second block: the three adds undone in reverse order
+                out.append(["in", e[3], x1, [[r, -1, 1] for r in rest]])
+                out.append(["out", e[3], x1, [[r, 1, 2] for r in rest], []])
+                out.append(["in", e[3], x1, [[r, -1, 1] for r in rest]])
+                del openq[q]
+                neg.discard(x1)
+        else:
+            raise AssertionError("unknown event kind %r" % k)
+    need(not openq and not neg, "a K block is not closed")
+    ext = sorted([z[3], z[1]] for z in c0["gauge"] if z[5])
+    c1 = dict(format="gcert/1", derived_from=c0["name"] + " (gcert/0)", p=c0["p"], h=h, v=v, R=R, cst=c0["cst"],
+              N=c0["N"], ports=c0["ports"], frames=c0["frames"], start=c0["start"], final=c0["final"],
+              ext=ext, ret=sorted(ret), scat=dict(inside=c0["scat"]["inside"], outside=c0["scat"]["outside"]),
+              A=A, B=B, blocks=c0["blocks"])
+    return c1
+
+
+def scat_row(c, t):
+    """the scatter of target t: [(k, coefficient)], from the table or from the star rule"""
+    sc = c["scat"]
+    if "table" in sc:
+        return [(k, Fr(a, b)) for k, a, b in sc["table"][t]]
+    sin, sout = Fr(*sc["inside"]), Fr(*sc["outside"])
+    return [(k, sin if c["ports"][t] >> k & 1 else sout) for k in range(c["h"])]
+
+
+def gate_regs(g):
+    if g[0] == "neg":
+        return [g[2]], [], []
+    if g[0] == "out":
+        return [g[2]] + [t for t, _, _ in g[3]] + list(g[4]), [(t, g[2], Fr(a, b)) for t, a, b in g[3]], g[4]
+    if g[0] == "in":
+        return [g[2]] + [s for s, _, _ in g[3]], [(g[2], s, Fr(a, b)) for s, a, b in g[3]], []
+    raise AssertionError("E0: unknown gate kind %r" % (g[0],))
+
+
+def check1(c, scalar=True, stats=None):
+    need(c.get("format") == "gcert/1", "E0: format")
+    h, v, R = c["h"], c["v"], c["R"]
+    nreg = 2 * v + R
+    ports, fr = c["ports"], [tuple(f) for f in c["frames"]]
+    need(len(ports) == v == len(set(ports)) and all(par(q) and 0 < q < 1 << h for q in ports), "E0: ports")
+    need(fr[0] == () and fr[1] == tuple(1 << i for i in range(h - 1, -1, -1)), "E0: frames 0 and 1")
+    need(all(echelon_ok(f) for f in fr) and len(set(fr)) == len(fr), "E0: frame table not reduced echelon / repeats")
+    dim = [len(f) for f in fr]
+    start, final = c["start"], c["final"]
+    need(len(start) == len(final) == nreg, "E0: start / final")
+    ext = {r: f for r, f in c["ext"]}
+    for t in range(v):
+        need(fr[start[t]] == (ports[t],) and final[t] == 1, "E1: x start / final")
+        f = fr[final[v + t]]
+        need(start[v + t] == 0 and len(f) == h - 1 and all(par(u & ports[t]) == 0 for u in f), "E1: y start / final")
+    for r in range(2 * v, nreg):
+        need(start[r] == ext.get(r, 0) and final[r] == 1, "E1: slot start / final")
+    cls = lambda r: "x" if r < v else "y" if r < 2 * v else "s"
+    cur = list(start)
+    H = {"x": Counter(), "y": Counter(), "s": Counter(), "c": Counter()}
+    steps = set()
+
+    def climb(r, f, where):
+        o = cur[r]
+        if o != f:
+            if (o, f) not in steps:
+                need(dim[o] < dim[f] and inside(fr[o], fr[f]), "E1: step not nested (%s, register %d)" % (where, r))
+                steps.add((o, f))
+            H[cls(r)][dim[f] - dim[o]] += 1
+            cur[r] = f
+    okind = {("x", "s"), ("s", "s"), ("s", "y"), ("x", "y"), ("x", "x"), ("y", "y")}
+    ysum, piv, ytg = Counter(), set(), set()
+    inc = 0
+    for ph, gates in (("A", c["A"]), ("B", c["B"])):
+        if ph == "B":      # ---- E2: the scatter cut
+            need(sorted(k for k, _, _ in c["ret"]) == list(range(len(c["ret"]))), "E2: retained totals numbered 0..")
+            if "table" in c["scat"]:
+                need(len(c["scat"]["table"]) == v and all(0 <= k < len(c["ret"]) for row in c["scat"]["table"] for k, _, _ in row),
+                     "E2: scatter table")
+            else:
+                need(len(c["ret"]) == h, "E2: one retained total per coordinate (star rule)")
+            for k, s, f in c["ret"]:
+                need(cls(s) == "s" and cur[s] == f, "E2: retained slot %d is not at its frame" % s)
+                H["c"][dim[f]] += 1
+            need(all(cur[v + t] == 0 for t in range(v)), "E2: a y role left frame 0 before the scatter")
+        for i, g in enumerate(gates):
+            regs, pairs, _ = gate_regs(g)
+            need(all(0 <= r < nreg for r in regs) and len(set(regs)) == len(regs), "E3: registers of gate %s%d" % (ph, i))
+            inc += len(regs)
+            for r in regs:
+                climb(r, g[1], "%s%d" % (ph, i))
+            for t, s, co in pairs:
+                kd = (cls(s), cls(t))
+                need(kd in okind, "E3: gate kind %s -> %s (gate %s%d)" % (kd + (ph, i)))
+                need(ph == "B" or kd in {("x", "s"), ("s", "s")}, "E3: bank gate before the scatter (gate A%d)" % i)
+                if kd == ("y", "y"):
+                    ysum[s, t] += co
+                    piv.add(s)
+                    ytg.add(t)
+            need(ph == "B" or all(cls(r) != "y" for r in regs), "E2: y role named in phase A")
+    for r in range(nreg):
+        climb(r, final[r], "final")
+    need(not (piv & ytg), "E4: a pivot is the target of a gate reading y")
+    need(all(x == 0 for x in ysum.values()), "E4: y-reads of a (pivot, target) pair do not cancel")
+    Hs = {k: {str(r): n for r, n in sorted(w.items())} for k, w in H.items()}
+    need(Hs == c["blocks"], "E6: block histograms")
+    N = sum(r * n for w in H.values() for r, n in w.items())
+    tails = sum(dim[f] for f in ext.values())
+    need(N == c["N"] and N + tails == R * h + 2 * v * (h - 1) + c["cst"], "E6: N")
+    if stats is not None:
+        stats.update(steps=len(steps), incidences=inc, blocks=sum(sum(w.values()) for w in H.values()),
+                     step_work=sum(dim[a] * dim[b] for a, b in steps), ysh_pairs=len(ysum))
+    if scalar:
+        scal(c, stats)
+        q2(c)
+    return True
+
+
+def scal(c, stats=None):
+    """E5: exact replay of the x-content of every register through A, scatter, B."""
+    h, v, R = c["h"], c["v"], c["R"]
+    nreg = 2 * v + R
+    reg = [({r: Fr(1)} if r < v else {}) for r in range(nreg)]
+    den = {"x": 1, "y": 1, "s": 1}
+    mx = {"x": Fr(0), "y": Fr(0), "s": Fr(0)}
+    cls = lambda r: "x" if r < v else "y" if r < 2 * v else "s"
+
+    def axpy(t, src, co):
+        d = reg[t]
+        for k, u in src.items():
+            w = d.get(k, 0) + co * u
+            if w:
+                d[k] = w
+                kk = cls(t)
+                if w.denominator != 1:
+                    den[kk] = lcm(den[kk], w.denominator)
+                if abs(w) > mx[kk]:
+                    mx[kk] = abs(w)
+            else:
+                d.pop(k, None)
+
+    def run(gates):
+        for g in gates:
+            if g[0] == "neg":
+                reg[g[2]] = {k: -u for k, u in reg[g[2]].items()}
+            elif g[0] == "out":
+                src = dict(reg[g[2]])
+                for t, a, b in g[3]:
+                    axpy(t, src, Fr(a, b))
+            else:
+                for s, a, b in g[3]:
+                    axpy(g[2], reg[s], Fr(a, b))
+    run(c["A"])
+    tot = {k: dict(reg[s]) for k, s, _ in c["ret"]}
+    for t in range(v):
+        for k, co in scat_row(c, t):
+            axpy(v + t, tot[k], co)
+    run(c["B"])
+    need(all(reg[t] == {t: 1} for t in range(v)), "E5: an x role is not restored (X3)")
+    need(all(reg[v + t] == {t: 1} for t in range(v)), "E5: a target does not receive exactly its source (hid)")
+    if stats is not None:
+        stats.update(den=dict(den), maxabs={k: str(x) for k, x in mx.items()},
+                     gates_A=len(c["A"]), gates_B=len(c["B"]))
+
+
+def q2(c):
+    """E7 (only for files with exterior gauges, rule (2)): for every slot q that starts off the zero frame, the
+    column of q in the y rows of the product is zero (its dirt is removed in line, the derived dirt gate at
+    frame 0 does not touch it).  Replay with the gauged slots as variables, x = 0."""
+    h, v, R = c["h"], c["v"], c["R"]
+    ext = [r for r, _ in c["ext"]]
+    if not ext:
+        return True
+    reg = [dict() for _ in range(2 * v + R)]
+    for r in ext:
+        reg[r] = {r: Fr(1)}
+
+    def axpy(t, src, co):
+        d = reg[t]
+        for k, u in src.items():
+            w = d.get(k, 0) + co * u
+            if w:
+                d[k] = w
+            else:
+                d.pop(k, None)
+
+    def run(gates):
+        for g in gates:
+            if g[0] == "neg":
+                reg[g[2]] = {k: -u for k, u in reg[g[2]].items()}
+            elif g[0] == "out":
+                src = dict(reg[g[2]])
+                for t, a, b in g[3]:
+                    axpy(t, src, Fr(a, b))
+            else:
+                for s, a, b in g[3]:
+                    axpy(g[2], reg[s], Fr(a, b))
+    run(c["A"])
+    tot = {k: dict(reg[s]) for k, s, _ in c["ret"]}
+    for t in range(v):
+        for k, co in scat_row(c, t):
+            if tot[k]:
+                axpy(v + t, tot[k], co)
+    run(c["B"])
+    need(all(not reg[v + t] for t in range(v)), "E7: the dirt of an exterior-gauged slot reaches a y role (Q2)")
+    return True
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__gxbind.py b/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__gxbind.py
new file mode 100644
index 0000000000..fcb625619c
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__gxbind.py
@@ -0,0 +1,438 @@
+"""gxbind.py: THE BINDING of the generator to the Lean terms of gx-scalar / gx-labels /
+gx-chain.  Everything that names somebody else's definition is in this file (tables SCAL, LAB, CHAIN)."""
+import os, re, subprocess
+import gxpaths
+ROOT = gxpaths.OUT
+GSM = gxpaths.HERE + '/gsmirror.py'
+
+# gx-scalar (gcert-interface.md, SCALAR v1): GS.scalCheck c p lo n, GS.yCheck c p lo n, p : GS.SPar = <d, sw, ux, us, uy>
+SCAL = dict(imports=['Work.GCert.Scalar.Seg'], scal='GS.scalCheck raw ⟨%(d)d, %(sw)d, %(ux)d, %(us)d, %(uy)d⟩ %(lo)d %(n)d',
+            ychk='GS.yCheck raw ⟨%(d)d, %(sw)d, %(ux)d, %(us)d, %(uy)d⟩ 0 %(v)d')
+# gx-labels (gcert-interface.md LABELS v1 + questions.md N1): namespace GLab; frame = code, table and states = SSC.Trie,
+# GLab.Par = <h, n, d, K, tab>.  `end` = GLab.endK of Labels/EndDef.lean (questions.md N2; no obaseK: Q1 closed).
+LAB = dict(imports=['Work.GCert.Labels.Def'], end_imports=['Work.GCert.Labels.EndDef'], par='⟨%(h)d, %(n)d, %(d)d, %(K)d, tab⟩', ns='GLab',
+           tab='GLab.tabK %(h)d %(sub)s', seg='GLab.segK par %(gs)s st%(i)d st%(j)d %(rs)s',
+           end='GLab.endK par %(v)d ports (raw.ret.map Prod.fst) st0 st%(a)d st%(f)d', noadds='GLab.noAdds fins')
+# gx-chain (CHAIN v1): GX.wht_of_halves; the terms below are PLACEHOLDERS until Labels/Main and Scalar/Main compile
+CHAIN = dict(imports=['Work.GCert.Chain.End', 'Work.GCert.Labels.Main'], scal='(GS.ScalOK.scal GXD.%(c)s.scalOK)',
+             lab='(GXD.%(c)s.valid.lab GXD.%(c)s.scalOK)', lab_cost='GXD.%(c)s.lab_cost')
+
+
+def code(h, basis):
+    """gx-labels' code of a reduced echelon basis: dim + 2^8 M + 2^(8+h) P (M = pivot mask, vector of pivot p at digit p)"""
+    M = P = 0
+    for b in basis:
+        p = b.bit_length() - 1
+        M |= 1 << p
+        P |= b << (h * p)
+    return len(basis) + (M << 8) + (P << (8 + h))
+
+
+MOD = '''import %(imports)s
+/-! Kernel check (%(doc)s) of the gcert/1 certificate `GXD.%(name)s.raw`.  Source: %(src)s.
+Generated by checks/wht26/gx-data/py/gxgen.py (do not edit). -/
+set_option maxRecDepth 100000
+namespace GXD.%(name)s
+open GXD
+theorem %(thm)s : %(stmt)s := by decide +kernel
+end GXD.%(name)s
+#print axioms GXD.%(name)s.%(thm)s
+'''
+
+
+def spar(D, path):
+    """scalar parameters: from gx-scalar's mirror when it exists, else from my own replay (sw is then a GUESS)"""
+    import gxcore as gc
+    n, d = 2 * D['v'] + D['R'], 0
+    while (1 << d) < n:
+        d += 1
+    dg = gc.digits(D)
+    S = dict(d=d, sw=16, ux=dg['x'][0], us=dg['s'][0], uy=dg['y'][0], source='gx-data replay; sw = 16 is a GUESS', digits=dg)
+    if os.path.exists(GSM):
+        try:
+            o = subprocess.run(['python3', '-B', GSM, path], capture_output=True, text=True, timeout=1800).stdout
+            m = re.search(r'SPar[^\d]*(\d+)[, ]+(\d+)[, ]+(\d+)[, ]+(\d+)[, ]+(\d+)', o)
+            if m:
+                S.update(zip(('d', 'sw', 'ux', 'us', 'uy'), map(int, m.groups())), source='gsmirror.py')
+        except Exception as e:
+            S['source'] += ' (gsmirror.py failed: %r)' % (e,)
+    return S
+
+
+def write_checks(D, M, name, src, out, L, S, plan):
+    base = out[len(ROOT):].replace('/', '.')
+    raw = '%s.Gen.%s' % (base, name)
+    h, v, n = D['h'], D['v'], 2 * D['v'] + D['R']
+    res = []
+
+    def mod(suffix, imports, thm, stmt, doc):
+        m = '%s.Gen.%s%s' % (base, name, suffix)
+        open('%s/Gen/%s%s.lean' % (out, name, suffix), 'w').write(MOD % dict(
+            imports='\nimport '.join(imports), doc=doc, name=name, src=src, thm=thm, stmt=stmt))
+        res.append((m, thm, stmt))
+    for i, (lo, hi) in enumerate(M['scal']['batches']):
+        mod('Scal%d' % i, SCAL['imports'] + [raw], 'scal%d_ok' % i, SCAL['scal'] % dict(S, lo=lo, n=hi - lo) + ' = true',
+            'scalar identity E3 E5 for the sources %d .. %d' % (lo, hi - 1))
+    mod('YChk', SCAL['imports'] + [raw], 'ychk_ok', SCAL['ychk'] % dict(S, v=v) + ' = true', 'the y -> y adds, E4')
+    par = '%s.Gen.%sPar' % (base, name)
+    open('%s/Gen/%sPar.lean' % (out, name), 'w').write(
+        'import %s\nimport %s\n/-! Parameters `GLab.Par` of the label check of `GXD.%s.raw` (h, registers, trie depth, K, frame table).\n'
+        'Generated by checks/wht26/gx-data/py/gxgen.py (do not edit). -/\nnamespace GXD.%s\nopen GXD\n'
+        'noncomputable def par : GLab.Par := %s\nend GXD.%s\n'
+        % (LAB['imports'][0], raw, name, name, LAB['par'] % dict(h=h, n=n, d=L['d'], K=L['K']), name))
+    paths = [format(i, '0%db' % L['ts']) for i in range(1 << L['ts'])] if L['ts'] else ['']
+    for i, pth in enumerate(paths):
+        mod('Tab%d' % i, LAB['imports'] + [raw], 'tab%d_ok' % i,
+            LAB['tab'] % dict(h=h, sub='tab_n' + pth if pth else 'tab') + ' = true',
+            'E0: subtrie %d of %d of the frame table (codes of reduced echelon bases)' % (i, len(paths)))
+    for i in range(L['nseg']):
+        mod('Seg%d' % i, [par], 'seg%d_ok' % i,
+            LAB['seg'] % dict(gs='seg%d' % i, i=i, j=i + 1, rs='rs%d' % i) + ' = true',
+            'E1: replay of the gates %d .. %d (phase %s) and their block ranks' % (
+                M['cuts'][i], M['cuts'][i + 1] - 1, 'A' if i < L['nsegA'] else 'B'))
+    mod('SegF', [par], 'segF_ok', LAB['seg'] % dict(gs='fins', i=L['nseg'], j=L['nseg'] + 1, rs='rF') + ' = true',
+        'E1: the final climbs and their block ranks')
+    if LAB['end']:
+        mod('End', LAB['end_imports'] + [par], 'end_ok', LAB['end'] % dict(v=v, a=L['nsegA'], f=L['nseg'] + 1) + ' = true',
+            'E1 E2: frames at the start, at the scatter, at the end')
+    return res
+
+
+def nest(xs):
+    return ' ++ ('.join(xs) + ')' * (len(xs) - 1) if xs else '[]'
+
+
+def write_hist(D, M, name, src, out, L):
+    """kernel counts of the block ranks on the EXPLICIT rank lists rA, rB, rF (no replay)"""
+    base = out[len(ROOT):].replace('/', '.')
+    h, rs = D['h'], M['lab']['rs']
+    ph = {'A': sum(rs[:L['nsegA']], []), 'B': sum(rs[L['nsegA']:], []), 'F': M['lab']['rF']}
+    top = max(max(x) if x else 0 for x in ph.values())
+    cop = [M['dim'][f] for _, f in D['ret']]
+    tot = {r: sum(x.count(r) for x in ph.values()) + cop.count(r) for r in range(1, max(top, max(cop)) + 1)}
+    assert {r: c for r, c in tot.items() if c} == M['hist'], 'histogram of the rank lists differs from the mirror'
+    lines = ['/-- block ranks of phase A / phase B, in order (the lists of the replay segments) -/',
+             'noncomputable def rA : List Nat := ' + nest(['rs%d' % i for i in range(L['nsegA'])]),
+             'noncomputable def rB : List Nat := ' + nest(['rs%d' % i for i in range(L['nsegA'], L['nseg'])])]
+    names = []
+    for X, lst in sorted(ph.items()):
+        l = 'r' + X
+        lines.append('theorem rankBound%s : wsumK (SSC.wGt %d) %s 0 = 0 := by decide +kernel' % (X, top, l))
+        lines += ['theorem rank%s%d_ok : wsumK (SSC.wEq %d) %s 0 = %d := by decide +kernel' % (X, r, r, l, lst.count(r))
+                  for r in range(top + 1)]
+        names += ['rankBound' + X] + ['rank%s%d_ok' % (X, r) for r in range(top + 1)]
+    txt = ('import Work.GCert.Data.Count\nimport %s.Gen.%s\n' % (base, name) +
+           '/-! Kernel count of the BLOCK RANKS of the gcert/1 certificate `GXD.%s.raw` (h = %d) on the explicit rank lists\n'
+           '`rA`, `rB`, `rF` (phase A, phase B, final climbs): `wsumK (SSC.wEq r) l 0` blocks of rank `r`, none above %d\n'
+           '(`GXD.sum_of_wsumK` turns a count into `(l.map wt).sum` = `SSC.wsum wt l`).\n'
+           'The %d scratch copies (ranks %s) are not in these lists.  Whole invocation, by rank: %s.\n'
+           'Source: %s.  Generated by checks/wht26/gx-data/py/gxgen.py (do not edit). -/\n'
+           'set_option maxRecDepth 100000\nnamespace GXD.%s\nopen GXD\n' % (
+               name, h, top, len(cop), sorted(set(cop)), M['hist'], src, name) + '\n'.join(lines) +
+           '\nend GXD.%s\n' % name + '\n'.join('#print axioms GXD.%s.%s' % (name, x) for x in names[:2]) + '\n')
+    open('%s/Gen/%sHist.lean' % (out, name), 'w').write(txt)
+    return '%s.Gen.%sHist' % (base, name)
+
+
+def write_price(D, M, name, src, out, L):
+    """Mathlib module: the price of the rank lists rA, rB, rF from the kernel counts, and of one whole invocation"""
+    base = out[len(ROOT):].replace('/', '.')
+    rs = M['lab']['rs']
+    ph = {'A': sum(rs[:L['nsegA']], []), 'B': sum(rs[L['nsegA']:], []), 'F': M['lab']['rF']}
+    top = max(max(x) if x else 0 for x in ph.values())
+    cop = [M['dim'][f] for _, f in D['ret']]
+    tm = lambda cnt: ' + '.join('%d * φ %d' % (n, r) for r, n in sorted(cnt.items()) if n) or '0'
+    thms = ''
+    for X in 'ABF':
+        cnt = {r: ph[X].count(r) for r in range(1, top + 1)}
+        thms += '''
+/-- price of the blocks of %s, from the kernel counts -/
+theorem r%s_cost (φ : ℕ → ℝ) : rcost φ r%s = %s := by
+  rw [GXD.rcost_wsumK φ r%s %d rankBound%s]
+  simp only [Finset.sum_range_succ, Finset.sum_range_zero, %s]
+  norm_num [bcost]
+''' % ({'A': 'phase A', 'B': 'phase B', 'F': 'the final climbs'}[X], X, X, tm(cnt), X, top, X,
+       ', '.join('rank%s%d_ok' % (X, r) for r in range(top + 1)))
+    copies = tm({r: cop.count(r) for r in set(cop)})
+    txt = '''import Work.GCert.Data.Price
+import %(base)s.Gen.%(name)sHist
+
+/-!
+# (key: gx-data) gcert/1 certificate `%(name)s` (h = %(h)d): the price of one invocation
+
+GENERATED by checks/wht26/gx-data/py/gxgen.py from %(src)s.  No `sorry`.
+`rA_cost`, `rB_cost`, `rF_cost`: the price of the block rank lists of phase A, phase B and the final climbs
+(lists `GXD.%(name)s.rA / rB / rF`, counted by the kernel in `Gen.%(name)sHist`);
+`inv_cost`: with the %(nc)d scratch copies (%(copies)s) the blocks of ONE invocation cost
+`invPrice φ` = %(terms)s;  `inv_moves`: they stand for `R h + 2 v (h - 1) + cst = %(N)d` unit moves.
+-/
+
+namespace GXD.%(name)s
+open GXD OAI.PowerSaving.CB
+%(thms)s
+/-- price of the blocks of ONE invocation (x roles, y roles, slots, scratch copies), by rank -/
+def invPrice (φ : ℕ → ℝ) : ℝ := %(terms)s
+
+/-- **Price of ONE invocation** in the shape of `GX.Lab.cost`: phase A, the scratch copies, phase B, final climbs. -/
+theorem inv_cost (φ : ℕ → ℝ) : rcost φ rA + (%(copies)s) + rcost φ rB + rcost φ rF = invPrice φ := by
+  rw [rA_cost, rB_cost, rF_cost]
+  unfold invPrice
+  ring
+
+theorem inv_moves : invPrice (fun r => (r:ℝ)) = %(R)d * %(h)d + 2 * %(v)d * (%(h)d - 1) + %(cst)d := by
+  unfold invPrice
+  norm_num
+
+theorem inv_count : invPrice (fun _ => (1:ℝ)) = %(count)d := by
+  unfold invPrice
+  norm_num
+
+end GXD.%(name)s
+#print axioms GXD.%(name)s.inv_cost
+#print axioms GXD.%(name)s.inv_moves
+''' % dict(base=base, name=name, h=D['h'], src=src, nc=len(cop), copies=copies, terms=tm(M['hist']), N=D['N'], thms=thms,
+           R=D['R'], v=D['v'], cst=D['cst'], count=sum(M['hist'].values()))
+    open('%s/%sPrice.lean' % (out, name), 'w').write(txt)
+    return '%s.%sPrice' % (base, name)
+
+
+def write_cert(D, M, name, src, out, chk, L):
+    """<Name>Cert: THE LABEL HALF (aux, valid : GLab.Valid raw aux, lab_cost, lab_price) -- compiles without the scalar half;
+    <Name>ScalOK: the scalar half `scalOK : GS.ScalOK raw` (needs Work/GCert/Scalar/Main)."""
+    base = out[len(ROOT):].replace('/', '.')
+    bs = M['scal']['batches']
+    hs = ''
+    for i, (lo, hi) in enumerate(bs):
+        lo_pf = 'Nat.zero_le t' if i == 0 else 'Nat.le_of_not_lt h%d' % (i - 1)
+        if i + 1 < len(bs):
+            hs += '    if h%d : t < %d then ⟨%d, %d, %s, h%d, GS.XRun.of_check scal%d_ok⟩ else\n' % (i, hi, lo, hi - lo, lo_pf, i, i)
+        else:
+            hs += '    ⟨%d, %d, %s, Nat.lt_of_lt_of_le ht (by decide), GS.XRun.of_check scal%d_ok⟩' % (lo, hi - lo, lo_pf, i)
+    terms = ' + '.join('%d * φ %d' % (n, r) for r, n in M['hist'].items())
+    info = dict(base=base, name=name, h=D['h'], src=src, v=D['v'], R=D['R'], nc=len(D['ret']), cst=D['cst'], N=D['N'],
+                nb=len(bs), terms=terms, hs=hs)
+    txt = '''import Work.GCert.Scalar.Main
+import %(imps)s
+/-! # (key: gx-data) gcert/1 certificate `%(name)s` (h = %(h)d): THE SCALAR HALF `scalOK : GS.ScalOK raw`
+GENERATED by checks/wht26/gx-data/py/gxgen.py from %(src)s.  No `sorry`.
+Kernel checks `scal<i>_ok` (%(nb)d source batches) and `ychk_ok`. -/
+namespace GXD.%(name)s
+open GXD
+theorem scalOK : GS.ScalOK raw where
+  hv := by decide
+  hs := fun t ht =>
+%(hs)s
+  hyc := fun t ht => ⟨0, %(v)d, Nat.zero_le t, Nat.lt_of_lt_of_le ht (by decide), GS.YRun.of_check ychk_ok⟩
+end GXD.%(name)s
+#print axioms GXD.%(name)s.scalOK
+''' % dict(info, imps='\nimport '.join(c[0] for c in chk if 'Scal' in c[0] or 'YChk' in c[0]))
+    open('%s/%sScalOK.lean' % (out, name), 'w').write(txt)
+    # ---- the label half
+    nA, ns, ts = L['nsegA'], L['nseg'], L['ts']
+    cop = sorted(set(M['dim'][f] for _, f in D['ret']))
+    assert len(cop) == 1, 'scratch copies of several ranks %s: lab_cost of gxbind.py assumes one' % cop
+
+    def tabpf(path):
+        if len(path) == ts:
+            return 'tab%d_ok' % (int(path, 2) if path else 0)
+        return '(GLab.tabK_node _ _ _ %s %s)' % (tabpf(path + '0'), tabpf(path + '1'))
+
+    def runpf(a, b):
+        return 'GLab.Run.of_seg seg%d_ok' % a if a + 1 == b else 'GLab.Run.append (GLab.Run.of_seg seg%d_ok) (%s)' % (a, runpf(a + 1, b))
+
+    def run(X, a, b):
+        segs = ['seg%d' % i for i in range(a, b)]
+        return '''theorem gates%(X)s_eq : raw.gates%(X)s = %(cat)s := by
+  show List.flatten %(lst)s = _
+  simp only [List.flatten_cons, List.flatten_nil, List.append_nil]
+/-- the replay of phase %(X)s, composed from its kernel-checked segments -/
+theorem run%(X)s : GLab.Run par st%(a)d raw.gates%(X)s st%(b)d r%(X)s := by
+  rw [gates%(X)s_eq]
+  exact %(pf)s
+''' % dict(X=X, cat=nest(segs), lst=ll_(segs), a=a, b=b, pf=runpf(a, b))
+    lab = 'valid.lab S Ro cf hMA hMAi hMB hMBi reg hCc hreg'
+    txt = '''import Work.GCert.Labels.Main
+import %(base)s.%(name)sPrice
+import %(imps)s
+/-! # (key: gx-data) gcert/1 certificate `%(name)s` (h = %(h)d): THE LABEL HALF and its price
+GENERATED by checks/wht26/gx-data/py/gxgen.py from %(src)s.  No `sorry`.
+`v = %(v)d` ports, `R = %(R)d` slots, %(nc)d scratch copies of rank %(c)d, copy cost `cst = %(cst)d`, `N = %(N)d` unit moves.
+* `aux : GLab.Aux`, `valid : GLab.Valid raw aux`: frame table (`tab<i>_ok` composed by `tabK_node`), the replays of phase A
+  and phase B (`seg<i>_ok` composed by `Run.append`), the final climbs (`segF_ok`, `fin_ok`), the ends (`end_ok`);
+* `lab_cost`, `lab_price`: for ANY scalar half `S` the label half `valid.lab S ..` costs
+  `rcost rA + card C * bcost %(c)d + rcost rB + rcost rF` = `invPrice φ` = %(terms)s
+  (`Gen.%(name)sHist`, `%(name)sPrice`) when there are %(nc)d copies. -/
+set_option maxRecDepth 100000
+namespace GXD.%(name)s
+open GXD OAI.PowerSaving OAI.PowerSaving.CB
+theorem raw_h : raw.h = %(h)d := rfl
+theorem raw_v : raw.v = %(v)d := rfl
+theorem raw_R : raw.R = %(R)d := rfl
+/-- what the label checks read next to `raw` -/
+noncomputable def aux : GLab.Aux := ⟨par, st0, st%(a)d, st%(n)d, st%(f)d, fins, rA, rB, rF⟩
+theorem fin_ok : GLab.noAdds fins = true := by decide +kernel
+theorem cen_ok : (raw.ret.map Prod.fst).all (fun r => Nat.beq (GLab.cdim (par.tab.get (st%(a)d.get r))) %(c)d) = true := by
+  decide +kernel
+theorem tab_ok : GLab.tabK par.h par.tab = true := %(tabpf)s
+%(runA)s%(runB)s/-- **the kernel-checked label facts** of the certificate -/
+theorem valid : GLab.Valid raw aux where
+  hn := rfl
+  tab := tab_ok
+  runA := runA
+  runB := runB
+  runF := GLab.Run.of_seg segF_ok
+  fin := fin_ok
+  ends := end_ok
+theorem cen_dim (r : Nat) (hr : r ∈ raw.ret.map Prod.fst) : GLab.cdim (par.tab.get (st%(a)d.get r)) = %(c)d :=
+  Nat.eq_of_beq_eq_true (List.all_eq_true.mp cen_ok r hr)
+/-- price of the label half over ANY scalar half -/
+theorem lab_cost {C : Type} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin raw.v) (Fin raw.R) C)
+    {emb : CR.L3 (Fin raw.v) (Fin raw.R) → Nat} {un : Nat → CR.L3 (Fin raw.v) (Fin raw.R)}
+    (Ro : GLab.Roles raw.v raw.R emb un) (cf : Co → SSC.Coef) (hMA) (hMAi) (hMB) (hMBi)
+    (reg : C → Nat) (hCc) (hreg) (φ : ℕ → ℝ) :
+    (%(lab)s).cost φ
+      = rcost φ rA + (Fintype.card C : ℝ) * bcost φ %(c)d + rcost φ rB + rcost φ rF := by
+  obtain ⟨h1, h2, h3, h4⟩ := valid.lab_ranks S Ro cf hMA hMAi hMB hMBi reg hCc hreg
+  have h5 : ∀ k, bcost φ (((%(lab)s).cen k).dim) = bcost φ %(c)d :=
+    fun k => by rw [h4 k]; exact congrArg (bcost φ) (cen_dim _ (hreg k))
+  rw [GX.Lab.cost, h1, h2, h3, Finset.sum_congr rfl (fun k _ => h5 k), Finset.sum_const, Finset.card_univ, nsmul_eq_mul]
+  rfl
+/-- **the label half costs one invocation price** (`invPrice`, by rank, from the kernel counts) -/
+theorem lab_price {C : Type} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin raw.v) (Fin raw.R) C)
+    {emb : CR.L3 (Fin raw.v) (Fin raw.R) → Nat} {un : Nat → CR.L3 (Fin raw.v) (Fin raw.R)}
+    (Ro : GLab.Roles raw.v raw.R emb un) (cf : Co → SSC.Coef) (hMA) (hMAi) (hMB) (hMBi)
+    (reg : C → Nat) (hCc) (hreg) (hC : Fintype.card C = %(nc)d) (φ : ℕ → ℝ) :
+    (%(lab)s).cost φ = invPrice φ := by
+  rw [lab_cost S Ro cf hMA hMAi hMB hMBi reg hCc hreg φ, hC, ← inv_cost φ]
+  norm_num [bcost]
+end GXD.%(name)s
+#print axioms GXD.%(name)s.valid
+#print axioms GXD.%(name)s.lab_price
+''' % dict(info, imps='\nimport '.join(c[0] for c in chk if 'Scal' not in c[0] and 'YChk' not in c[0]), c=cop[0], a=nA, n=ns,
+           f=ns + 1, tabpf=tabpf(''), runA=run('A', 0, nA), runB=run('B', nA, ns), lab=lab)
+    open('%s/%sCert.lean' % (out, name), 'w').write(txt)
+    return ['%s.%sCert' % (base, name), '%s.%sScalOK' % (base, name)]
+
+
+def ll_(xs):
+    return '[' + ', '.join(xs) + ']'
+
+
+def final_module(name, cname, d, dx, g, out):
+    """<Inst>.lean: the final theorems OVER ANY SCALAR HALF (compiles as soon as <C>Cert does): label half, price,
+    unit list, rate fact and gx-chain's `GX.wht_of_halves` are all closed; what is left is `S : GX.Scal` with its
+    gate matrices = the ordered products of the adds of `raw` (gx-scalar)."""
+    h, v, R, W, m, nc = g['h'], g['v'], g['R'], d['W'], d['m'], g['nc']
+    X = 'GXD.%s' % cname
+    args = 'S Ro cf hMA hMAi hMB hMBi reg hCc hreg'
+
+    def thm(nm, rate, A, B, s, ux):
+        return f'''
+/-- **Walsh-Hadamard transform, whole-block recursion on the bridged word B_2 with the gcert/1 circuit `{cname}`**,
+over any scalar half of `{X}.raw`: the statement `WHTGoal` of `WHTCheck/Challenge.lean` with `1 - 2/10^11`
+replaced by `1 - {A}/10^{B}`. -/
+theorem {nm} (Ro : GLab.Roles {X}.raw.v {X}.raw.R emb un)
+    (hMA : S.MA = SSC.matP un (GLab.mic cf ({X}.raw.gatesA.flatMap GXD.Gate.adds)))
+    (hMAi : S.MAi = SSC.matPinv un (GLab.mic cf ({X}.raw.gatesA.flatMap GXD.Gate.adds)))
+    (hMB : S.MB = SSC.matP un (GLab.mic cf ({X}.raw.gatesB.flatMap GXD.Gate.adds)))
+    (hMBi : S.MBi = SSC.matPinv un (GLab.mic cf ({X}.raw.gatesB.flatMap GXD.Gate.adds)))
+    (reg : C → Nat) (hCc : ∀ k (q : Fin {X}.raw.R), S.Cc k q ≠ 0 → reg k = 2 * {X}.raw.v + q.val)
+    (hreg : ∀ k, reg k ∈ {X}.raw.ret.map Prod.fst) (hC : Fintype.card C = {nc}) :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - {A}/(10:ℝ)^{B}) W :=
+  GX.wht_of_halves S ({X}.valid.lab {args})
+    (by rw [Fintype.card_fin]; decide) {m} {W} (by rw [Fintype.card_fin]; rfl)
+    (by rw [Fintype.card_fin, Fintype.card_fin]; rfl) (by norm_num) BlockAccounting.blocks{rate}
+    (fun φ => by
+      rw [{X}.lab_price {args} hC φ, Fintype.card_fin, Fintype.card_fin]
+      exact BridgeRate.{name}.unit_cost{ux} φ)
+    {s} (1 - {A}/(10:ℝ)^{B}) (by norm_num) (by norm_num) BlockAccounting.fold_{rate}
+
+/-- the same from the FIVE scalar identities of gx-scalar's matrices of `{X}.raw` (`Work/GCert/Data/Glue.lean`) -/
+theorem {nm.replace('_of_scal', '_of_ids')} (hv : 0 < {X}.raw.v)
+    (hAi : GS.MAi {X}.raw hv * GS.MA {X}.raw hv = 1) (hBi : GS.MBi {X}.raw hv * GS.MB {X}.raw hv = 1)
+    (hx : ∀ (t : Fin {X}.raw.v) (j : GS.Rl {X}.raw), (GS.MB {X}.raw hv * CR.scatM (GS.Jrm {X}.raw * GS.Ccm {X}.raw)
+      * GS.MA {X}.raw hv) (CR.lX t) j = if CR.lX t = j then 1 else 0)
+    (hy : ∀ (i : GS.Rl {X}.raw) (t : Fin {X}.raw.v), (GS.MB {X}.raw hv * CR.scatM (GS.Jrm {X}.raw * GS.Ccm {X}.raw)
+      * GS.MA {X}.raw hv) i (CR.lY t) = if i = CR.lY t then 1 else 0)
+    (hid : ∀ S t : Fin {X}.raw.v, (GS.MB {X}.raw hv * CR.scatM (GS.Jrm {X}.raw * GS.Ccm {X}.raw)
+      * GS.MA {X}.raw hv) (CR.lY S) (CR.lX t) = if S = t then 1 else 0) :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - {A}/(10:ℝ)^{B}) W :=
+  {nm} (GXD.scalOf {X}.raw hv hAi hBi hx hy hid) GS.toCoef (GXD.roles {X}.raw hv)
+    (GXD.scalOf_MA _ hv hAi hBi hx hy hid) (GXD.scalOf_MAi _ hv hAi hBi hx hy hid)
+    (GXD.scalOf_MB _ hv hAi hBi hx hy hid) (GXD.scalOf_MBi _ hv hAi hBi hx hy hid)
+    (GXD.reg {X}.raw) (GXD.reg_slot {X}.raw hv hAi hBi hx hy hid) (GXD.reg_mem {X}.raw)
+    (by rw [Fintype.card_fin]; decide)
+'''
+    txt = f'''import Work.GCert.Chain.End
+import Work.GCert.Data.Glue
+import Work.GCert.Data.{cname}Cert
+import Work.GCert.Data.Inst{name}
+
+/-!
+# (key: gx-data) Bridged word B_2 with the gcert/1 circuit `{cname}` (h = {h}, m = {m}): final theorems over a scalar half
+GENERATED by checks/wht26/gx-data/py/gxrate.py.  No `sorry`.
+`GX.wht_of_halves` (gx-chain) on the label half `{X}.valid` (kernel checks of `Work/GCert/Data/Gen/{cname}*`), its
+price `{X}.lab_price`, the unit list `BlockAccounting.blocks{name}` (`W = {W}` live roles) and the rate facts
+`fold_{name}` (`1 - {d['A']}/10^{d['B']}`), `fold_{name}x` (`1 - {dx['A']}/10^{dx['B']}`).
+The ONLY hypothesis left is the scalar half: `S : GX.Scal (Fin {v}) (Fin {R}) C` whose gate matrices are the ordered
+products of the adds of `raw` (`hMA .. hMBi`), with `{nc}` copies read from the retained registers (`reg`, `hCc`, `hreg`, `hC`);
+`wht_{name}_of_ids`, `wht_{name}x_of_ids`: the same from the five identities `hAi hBi hx hy hid` of gx-scalar's matrices
+`GS.MA GS.MAi GS.MB GS.MBi GS.Jrm GS.Ccm` of `raw` (the fields of the planned `GS.ScalOK`).
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace WHT
+open BlockWHT
+
+variable {{C : Type}} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin {X}.raw.v) (Fin {X}.raw.R) C)
+  {{emb : CR.L3 (Fin {X}.raw.v) (Fin {X}.raw.R) → Nat}} {{un : Nat → CR.L3 (Fin {X}.raw.v) (Fin {X}.raw.R)}}
+  (cf : GXD.Co → SSC.Coef)
+''' + thm('wht_' + name + '_of_scal', name, d['A'], d['B'], d['s'], '') + thm('wht_' + name + 'x_of_scal', name + 'x', dx['A'], dx['B'], dx['s'], '_x') + f'''
+end WHT
+end PowerSaving
+end OAI
+#print axioms OAI.PowerSaving.WHT.wht_{name}_of_scal
+#print axioms OAI.PowerSaving.WHT.wht_{name}x_of_scal
+#print axioms OAI.PowerSaving.WHT.wht_{name}_of_ids
+#print axioms OAI.PowerSaving.WHT.wht_{name}x_of_ids
+'''
+    open(out + '%s.lean' % name, 'w').write(txt)
+
+
+def main_module(name, cname, d, dx, out):
+    """<Inst>Main.lean: the CLOSED theorems (what the comparator solution cites).  WRITTEN against gx-scalar's planned
+    `GS.ScalOK` (fields / theorems hv hAi hBi hx hy hid, SCALAR v2); compiles when Work/GCert/Scalar/Main.lean exists."""
+    K = 'GXD.%s.scalOK' % cname
+
+    def thm(sfx, A, B):
+        return f'''
+/-- **Walsh-Hadamard transform in `O(n (log n)^(1 - {A}/10^{B}))`-type time bounds: whole-block recursion on the bridged
+word B_2 with the kernel-checked gcert/1 circuit `{cname}`.** -/
+theorem wht_main_{name}{sfx} :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - {A}/(10:ℝ)^{B}) W :=
+  wht_{name}{sfx}_of_ids {K}.hv {K}.hAi {K}.hBi {K}.hx {K}.hy {K}.hid
+'''
+    txt = f'''import Work.GCert.Scalar.Main
+import Work.GCert.Data.{cname}ScalOK
+import Work.GCert.Data.{name}
+
+/-!
+# (key: gx-data) Bridged word B_2 with the gcert/1 circuit `{cname}`: THE CLOSED THEOREMS
+GENERATED by checks/wht26/gx-data/py/gxrate.py.  No `sorry`.
+`wht_{name}_of_ids` (label half, price, unit list, rate fact, gx-chain's end theorem) applied to the scalar half
+`{K} : GS.ScalOK GXD.{cname}.raw` (kernel checks `scal<i>_ok`, `ychk_ok`; soundness: gx-scalar).
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace WHT
+open BlockWHT
+''' + thm('', d['A'], d['B']) + thm('x', dx['A'], dx['B']) + f'''
+end WHT
+end PowerSaving
+end OAI
+#print axioms OAI.PowerSaving.WHT.wht_main_{name}
+#print axioms OAI.PowerSaving.WHT.wht_main_{name}x
+'''
+    open(out + '%sMain.lean' % name, 'w').write(txt)
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__gxconv.py b/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__gxconv.py
new file mode 100644
index 0000000000..49ebb65973
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__gxconv.py
@@ -0,0 +1,131 @@
+"""gxconv.py: gcert/0 -> gcert/1 for files whose in-place pair op SCALES its target
+(`op dest ctrl ca cb`: dest := ca dest + cb ctrl with ca not in {1}; #193 has ca = -2), questions.md D2.
+COPY of `convert` of gx.py with ONE change: a scaling is not a gate, it changes the
+UNIT in which the register is stored.  wanted(r) = lam[r] * stored(r), lam = 1 at the start;
+    op dest ctrl ca cb :  lam[dest] *= ca ;  stored(dest) += (cb lam[ctrl] / lam[dest]) stored(ctrl)
+    any other add t += k s :  stored(t) += (k lam[s] / lam[t]) stored(s)
+    scatter y_t += coef(t, k) total_k :  coefficient coef(t, k) * lam[slot of total k]   (a TABLE if some lam != 1)
+Only slots may be scaled (tested: lam = 1 on every x and y register, always), so the x / y rows and columns of
+the product (E5: hx, hy, hid) are those of the unscaled circuit; frames, blocks and N are untouched.
+The result is tested by the reference checker `gx.check1` (labels and scalars) before it is written.
+
+usage: gxconv.py <gcert0.json[.gz]> out=<gcert1.json[.gz]> [noext]
+"""
+import sys, time
+from fractions import Fraction as Fr
+import gxpaths
+import gx
+import gxrun
+need = gx.need
+
+
+def convert(c0):
+    need(c0["format"] == "gcert/0", "input is not gcert/0")
+    v, h, R = c0["v"], c0["h"], c0["R"]
+    ev = c0["events"]
+    cen = [n for n, e in enumerate(ev) if e[0] == "centre"]
+    need(cen == list(range(cen[0], cen[0] + len(cen))), "centres are not contiguous: no single scatter cut")
+    A, B, ret = [], [], []
+    neg, openq, lam, nsc = set(), {}, {}, 0
+    L = lambda r: lam.get(r, Fr(1))
+
+    def co(t, s, a, b=1):                       # stored coefficient of the wanted add t += (a/b) s
+        w = Fr(a, b) * L(s) / L(t)
+        return [w.numerator, w.denominator]
+
+    def o(f, s, tg, ex=()):
+        return ["out", f, s, [[t] + co(t, s, a, b) for t, a, b in tg], list(ex)]
+
+    def i(f, t, sr):
+        return ["in", f, t, [[s] + co(t, s, a, b) for s, a, b in sr]]
+    scat_lam = None
+    for n, e in enumerate(ev):
+        k = e[0]
+        out = A if n < cen[0] else B
+        if k in ("read0", "undo", "uninj"):
+            continue
+        if k == "inj":
+            need(e[2] not in neg, "inj reads a negated x register")
+            out.append(o(e[3], e[2], [[e[1], 1, 1]]))
+        elif k == "op":
+            if e[3] != 1:
+                need(e[3] != 0 and e[1] >= 2 * v, "op scales a register that is not a slot (or by 0)")
+                lam[e[1]] = L(e[1]) * e[3]
+                nsc += 1
+            out.append(o(e[5], e[2], [[e[1], e[4], 1]]))
+        elif k == "centre":
+            ret.append([e[2], e[1], e[3]])
+            if scat_lam is None:
+                scat_lam = dict(lam)
+        elif k == "gread":
+            hit = set(t for t, _, _ in e[3])
+            out.append(o(e[2], e[1], [[v + t, a, b] for t, a, b in e[3]], [v + t for t in e[4] if t not in hit]))
+        elif k == "rread":
+            out.append(o(e[2], e[1], [[v + t, a, b] for t, a, b in e[3]]))
+        elif k == "ysh":
+            out.append(o(e[4], e[2], [[e[1], e[3], 1]]))
+        elif k == "yw":
+            out.append(o(e[4], e[2], [[e[1], e[3][0], e[3][1]]]))
+        elif k == "kd":
+            out.append(o(e[3], e[2], [[e[1], -1 if e[2] in neg else 1, 1]]))
+        elif k == "ktr":
+            q = tuple(e[1])
+            need(e[2] == gx.KJ, "ktr matrix is not 1 - J/2")
+            x1, rest = q[0], list(q[1:])
+            if q not in openq:
+                out.append(i(e[3], x1, [[r, 1, 1] for r in rest]))
+                out.append(o(e[3], x1, [[r, -1, 2] for r in rest]))
+                out.append(i(e[3], x1, [[r, 1, 1] for r in rest]))
+                openq[q] = n
+                neg.add(x1)
+            else:
+                out.append(i(e[3], x1, [[r, -1, 1] for r in rest]))
+                out.append(o(e[3], x1, [[r, 1, 2] for r in rest]))
+                out.append(i(e[3], x1, [[r, -1, 1] for r in rest]))
+                del openq[q]
+                neg.discard(x1)
+        else:
+            raise AssertionError("unknown event kind %r" % k)
+        need(all(r >= 2 * v for r, x in lam.items() if x != 1), "an x or y register is scaled")
+    need(not openq and not neg, "a K block is not closed")
+    ret = sorted(ret)
+    need([z[0] for z in ret] == list(range(len(ret))), "retained totals are not 0 .. n-1")
+    sin, sout = Fr(*c0["scat"]["inside"]), Fr(*c0["scat"]["outside"])
+    sl = [(scat_lam or {}).get(z[1], Fr(1)) for z in ret]
+    if all(x == 1 for x in sl):
+        scat = dict(inside=c0["scat"]["inside"], outside=c0["scat"]["outside"])
+    else:
+        need(len(ret) == h, "star rule with a number of totals other than h")
+        scat = dict(table=[[[kk, (w * sl[kk]).numerator, (w * sl[kk]).denominator]
+                            for kk in range(h) for w in [sin if c0["ports"][t] >> kk & 1 else sout]] for t in range(v)])
+    ext = sorted([z[3], z[1]] for z in c0["gauge"] if z[5])
+    c1 = dict(format="gcert/1", derived_from=c0["name"] + " (gcert/0; %d scalings as units, gxconv.py)" % nsc, p=c0["p"],
+              h=h, v=v, R=R, cst=c0["cst"], N=c0["N"], ports=c0["ports"], frames=c0["frames"], start=c0["start"],
+              final=c0["final"], ext=ext, ret=ret, scat=scat, A=A, B=B, blocks=c0["blocks"])
+    return c1, nsc, sorted(set(str(x) for x in lam.values())), sum(1 for x in sl if x != 1)
+
+
+if __name__ == "__main__":
+    t0 = time.time()
+    opt = dict(a.split("=", 1) for a in sys.argv[2:] if "=" in a)
+    c0 = gxrun.load(sys.argv[1])
+    c1, nsc, lams, nsl = convert(c0)
+    c1["two_hosts"] = sorted(2 * c0["v"] + i for i, hs in enumerate(c0["hosts"]) if len(hs) > 1)
+    if "noext" in sys.argv and c1["ext"]:        # as gxrun.py: exterior gauges become first blocks
+        for r, f in c1["ext"]:
+            d = str(len(c1["frames"][f]))
+            c1["start"][r] = 0
+            c1["blocks"]["s"][d] = c1["blocks"]["s"].get(d, 0) + 1
+            c1["N"] += int(d)
+        c1["blocks"]["s"] = {k: c1["blocks"]["s"][k] for k in sorted(c1["blocks"]["s"], key=int)}
+        c1["derived_from"] += ", exterior gauges turned into first blocks"
+        c1["ext"] = []
+    st = {}
+    gx.check1(c1, scalar=True, stats=st)
+    print("ACCEPTED by gx.check1: %s h=%d v=%d R=%d N=%d gates A=%d B=%d ext=%d; scalings %d, final units %s, scaled totals %d, "
+          "scatter %s, stats %s (%.1fs)" % (c0["name"], c1["h"], c1["v"], c1["R"], c1["N"], len(c1["A"]), len(c1["B"]),
+                                           len(c1["ext"]), nsc, lams, nsl, "table" if "table" in c1["scat"] else "star", st,
+                                           time.time() - t0))
+    if "out" in opt:
+        gxrun.dump(c1, opt["out"])
+        print("written", opt["out"])
diff --git a/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__gxcore.py b/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__gxcore.py
new file mode 100644
index 0000000000..3e3f0a3076
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/inputs/complex/sources/tools__gx__gxcore.py
@@ -0,0 +1,375 @@
+"""gxcore.py: gcert/1 JSON -> normal data D, PYTHON MIRROR of the two Lean checks
+(label side: E0 frames, E1 pairs, E1/E2/E6 replay in segments; scalar side: E3 kinds, E4 bracket, E5 replay
+in source batches, E7), derived data (distinct climbs, cut states, block histogram) and kernel sizes.
+Own code; the reference is gx.py (check1), not imported.  Python 3, standard library only."""
+import json, gzip
+from collections import Counter
+from math import gcd
+
+
+class Reject(Exception):
+    pass
+
+
+def need(c, msg):
+    if not c:
+        raise Reject(msg)
+
+
+def load(path):
+    c = json.load(gzip.open(path, "rt") if path.endswith(".gz") else open(path))
+    need(c.get("format") == "gcert/1", "E0: format is not gcert/1")
+    return c
+
+
+def co(num, den):
+    need(den > 0, "E0: denominator")
+    return (num < 0, abs(num), den)
+
+
+def normal(c):
+    """the Lean-facing data: gates as tuples, coefficients (neg, num, den), ret by total"""
+    def gate(g):
+        if g[0] == "out":
+            return ("out", g[1], g[2], [(t, co(a, b)) for t, a, b in g[3]], list(g[4]))
+        need(g[0] == "in", "E0: unknown gate kind %r" % (g[0],))
+        return ("in", g[1], g[2], [(s, co(a, b)) for s, a, b in g[3]])
+    ret = sorted(c["ret"])
+    need([k for k, _, _ in ret] == list(range(len(ret))), "E2: retained totals numbered 0..")
+    sc = c["scat"]
+    scat = ("table", [[(k, co(a, b)) for k, a, b in row] for row in sc["table"]]) if "table" in sc else \
+        ("star", co(*sc["inside"]), co(*sc["outside"]))
+    return dict(h=c["h"], v=c["v"], R=c["R"], N=c["N"], cst=c["cst"], ports=list(c["ports"]),
+                frames=[list(f) for f in c["frames"]], start=list(c["start"]), final=list(c["final"]),
+                ext=[tuple(e) for e in c.get("ext", [])], ret=[(s, f) for _, s, f in ret], scat=scat,
+                A=[gate(g) for g in c["A"]], B=[gate(g) for g in c["B"]],
+                blocks={k: {int(r): n for r, n in c["blocks"][k].items()} for k in "xysc"})
+
+
+def regs(g):
+    return [g[2]] + [t for t, _ in g[3]] + (g[4] if g[0] == "out" else [])
+
+
+def adds(g):
+    """single adds (tgt, src, coef) in order"""
+    return [(t, g[2], k) for t, k in g[3]] if g[0] == "out" else [(g[2], s, k) for s, k in g[3]]
+
+
+def reduce(u, basis):
+    for b in basis:
+        if u >> (b.bit_length() - 1) & 1:
+            u ^= b
+    return u
+
+
+def echelon_ok(f):
+    piv = [b.bit_length() - 1 for b in f]
+    if any(b == 0 for b in f) or any(piv[i] <= piv[i + 1] for i in range(len(piv) - 1)):
+        return False
+    return all(not (b >> p & 1) for i, b in enumerate(f) for j, p in enumerate(piv) if i != j)
+
+
+def par(x):
+    return bin(x).count("1") & 1
+
+
+def cls(D, r):
+    return "x" if r < D["v"] else "y" if r < 2 * D["v"] else "s"
+
+
+# ---- label side ------------------------------------------------------------------------------------------
+def chk_frames(D):
+    """E0: ports; frame table reduced echelon, no repeats, zero first, full second"""
+    h, v, fr = D["h"], D["v"], D["frames"]
+    p = D["ports"]
+    need(len(p) == v == len(set(p)) and all(par(q) and 0 < q < 1 << h for q in p), "E0: ports")
+    need(len(fr) >= 2 and fr[0] == [] and fr[1] == [1 << i for i in range(h - 1, -1, -1)], "E0: frames 0 and 1")
+    need(all(echelon_ok(f) and all(b < 1 << h for b in f) for f in fr), "E0: frame table not reduced echelon")
+    need(len(set(map(tuple, fr))) == len(fr), "E0: frame table has repeats")
+    return [len(f) for f in fr]
+
+
+def derive(D):
+    """distinct climbs in order of first use (NOT a check: plain replay of the frame ids)"""
+    cur, seen, pairs = list(D["start"]), set(), []
+
+    def go(r, f):
+        o = cur[r]
+        if o != f:
+            if (o, f) not in seen:
+                seen.add((o, f))
+                pairs.append((o, f))
+            cur[r] = f
+    for g in D["A"] + D["B"]:
+        for r in regs(g):
+            go(r, g[1])
+    for r, f in enumerate(D["final"]):
+        go(r, f)
+    return pairs
+
+
+def chk_pairs(D, dim, pairs):
+    """E1, level 2: every listed pair is a nested pair of the table; returns the mask-operation count"""
+    fr, n, work = D["frames"], len(D["frames"]), 0
+    for a, b in pairs:
+        need(a < n and b < n and dim[a] < dim[b], "E1: pair (%d, %d) does not climb" % (a, b))
+        need(all(reduce(u, fr[b]) == 0 for u in fr[a]), "E1: pair (%d, %d) is not nested" % (a, b))
+        work += dim[a] * dim[b]
+    return work
+
+
+def cut_points(D, gmax, wmax=210000):
+    """replay segments: each phase (A, B) is cut into k pieces of equal gate count, k = the least number with at
+    most `gmax` gates AND at most `wmax` work per piece on average (work = sum over gates of the dimension of the
+    gate's frame; measured at h = 22: about 1 ms of kernel time per unit, NOTES.md).
+    Cut points = gate counts in A ++ B (always 0, |A| and the end)."""
+    nA, nB = len(D["A"]), len(D["B"])
+    cuts = [0]
+    for off, gs in ((0, D["A"]), (nA, D["B"])):
+        n = len(gs)
+        k = max(1, -(-n // gmax), -(-sum(len(D["frames"][g[1]]) for g in gs) // wmax))
+        cuts += [off + (n * i) // k for i in range(1, k + 1)]
+    return sorted(set(cuts))
+
+
+def label_data(D, dim, cuts):
+    """for gx-labels (gcert-interface.md LABELS v1): ordered block ranks per replay segment, the final climbs as
+    gates without adds (same final frame, at most 32 registers, only registers that still climb), their ranks,
+    the largest number of registers named by one gate.  Plain replay (the mirror has accepted the file)."""
+    cur, G = list(D["start"]), D["A"] + D["B"]
+    rs, most = [], 0
+    for a, b in zip(cuts, cuts[1:]):
+        r = []
+        for g in G[a:b]:
+            most = max(most, len(regs(g)))
+            for x in regs(g):
+                if cur[x] != g[1]:
+                    r.append(dim[g[1]] - dim[cur[x]])
+                    cur[x] = g[1]
+        rs.append(r)
+    by = {}
+    for x, f in enumerate(D["final"]):
+        if cur[x] != f:
+            by.setdefault(f, []).append(x)
+    fins, rF = [], []
+    for f in sorted(by):
+        for i in range(0, len(by[f]), 32):
+            xs = by[f][i:i + 32]
+            fins.append(("out", f, xs[0], [], xs[1:]))
+            rF += [dim[f] - dim[cur[x]] for x in xs]
+    return dict(rs=rs, fins=fins, rF=rF, most=max(most, 32 if fins else 0))
+
+
+def chk_replay(D, dim, pairs, cuts):
+    """E1 (labels), E2 (scatter cut), E6 (price), in the segments given by `cuts`.
+    Returns (states at the cuts, histogram by class, visits per segment)."""
+    h, v, R, fr = D["h"], D["v"], D["R"], D["frames"]
+    n = 2 * v + R
+    start, final, ext = D["start"], D["final"], dict(D["ext"])
+    need(len(start) == len(final) == n, "E0: start / final")
+    for t in range(v):
+        need(fr[start[t]] == [D["ports"][t]] and final[t] == 1, "E1: x start / final")
+        f = fr[final[v + t]]
+        need(start[v + t] == 0 and len(f) == h - 1 and all(par(u & D["ports"][t]) == 0 for u in f), "E1: y start / final")
+    for r in range(2 * v, n):
+        need(start[r] == ext.get(r, 0) and final[r] == 1, "E1: slot start / final")
+    ok = set(pairs)
+    need(len(ok) == len(pairs), "E1: pair list has repeats")
+    cur = list(start)
+    H = {k: Counter() for k in "xysc"}
+
+    def climb(r, f, where):
+        o = cur[r]
+        if o != f:
+            need((o, f) in ok, "E1: climb (%d, %d) is not a tested pair (%s, register %d)" % (o, f, where, r))
+            H[cls(D, r)][dim[f] - dim[o]] += 1
+            seg[dim[f] - dim[o]] += 1
+            cur[r] = f
+    seg, segs = Counter(), []
+    G, nA = D["A"] + D["B"], len(D["A"])
+    states, visits = [], []
+    need(cuts[0] == 0 and cuts[-1] == len(G) and cuts == sorted(cuts), "cut points")
+    for a, b in zip(cuts, cuts[1:]):
+        states.append(list(cur))
+        vs = 0
+        for i in range(a, b):
+            if i == nA:
+                scatter_cut(D, cur, dim, H, seg)
+            g = G[i]
+            rs = regs(g)
+            need(all(0 <= r < n for r in rs) and len(set(rs)) == len(rs), "E3: registers of gate %d" % i)
+            need(i >= nA or all(r < v or r >= 2 * v for r in rs), "E2: y role named in phase A (gate %d)" % i)
+            vs += len(rs)
+            for r in rs:
+                climb(r, g[1], "gate %d" % i)
+        visits.append(vs)
+        if b < len(G):
+            segs.append(seg)
+            seg = Counter()
+    if nA == len(G):
+        scatter_cut(D, cur, dim, H, seg)
+    states.append(list(cur))
+    for r in range(n):
+        climb(r, final[r], "final")
+    segs.append(seg)
+    Hb = {k: dict(sorted(w.items())) for k, w in H.items()}
+    need(Hb == D["blocks"], "E6: block histogram differs from `blocks`")
+    N = sum(r * c for w in H.values() for r, c in w.items())
+    need(N == D["N"] and N + sum(dim[f] for f in ext.values()) == R * h + 2 * v * (h - 1) + D["cst"], "E6: N")
+    need(sum(r * c for r, c in H["c"].items()) == D["cst"], "E6: cst")
+    return states, Hb, visits, [[w[r] for r in range(h + 1)] for w in segs]
+
+
+def scatter_cut(D, cur, dim, H, seg):
+    v = D["v"]
+    if D["scat"][0] == "table":
+        need(len(D["scat"][1]) == v and all(k < len(D["ret"]) for row in D["scat"][1] for k, _ in row), "E2: scatter table")
+    else:
+        need(len(D["ret"]) == D["h"], "E2: one retained total per coordinate (star rule)")
+    for s, f in D["ret"]:
+        need(s >= 2 * v and cur[s] == f, "E2: retained slot %d is not at its frame" % s)
+        H["c"][dim[f]] += 1
+        seg[dim[f]] += 1
+    need(all(cur[v + t] == 0 for t in range(v)), "E2: a y role left frame 0 before the scatter")
+
+
+# ---- scalar side -----------------------------------------------------------------------------------------
+SC = 6            # all scalar entries are kept as integers in units of 1/6
+KINDS = {("x", "s"), ("s", "s"), ("s", "y"), ("x", "y"), ("x", "x"), ("y", "y")}
+
+
+def chk_shape(D):
+    """E3 kinds, E4 bracket"""
+    ysum, piv, ytg = Counter(), set(), set()
+    for ph in "AB":
+        for i, g in enumerate(D[ph]):
+            for t, s, (ng, a, b) in adds(g):
+                kd = (cls(D, s), cls(D, t))
+                need(kd in KINDS and t != s, "E3: gate kind %s -> %s (gate %s%d)" % (kd + (ph, i)))
+                need(ph == "B" or kd in {("x", "s"), ("s", "s")}, "E3: bank gate before the scatter (gate A%d)" % i)
+                if kd == ("y", "y"):
+                    need(SC % b == 0, "E4: denominator beyond sixths")
+                    ysum[s, t] += (-a if ng else a) * (SC // b)
+                    piv.add(s)
+                    ytg.add(t)
+    need(not (piv & ytg), "E4: a pivot is the target of a gate reading y")
+    need(all(x == 0 for x in ysum.values()), "E4: y-reads of a (pivot, target) pair do not cancel")
+    return len(ysum)
+
+
+def scat_row(D, t):
+    sc = D["scat"]
+    if sc[0] == "table":
+        return sc[1][t]
+    return [(k, sc[1] if D["ports"][t] >> k & 1 else sc[2]) for k in range(D["h"])]
+
+
+
+def replay(D, init, count=None):
+    """exact replay through A, scatter, B of sparse vectors with entries in sixths; `init` = register -> {key: 6}"""
+    v = D["v"]
+    reg = [dict(init.get(r, ())) for r in range(2 * v + D["R"])]
+
+    def axpy(t, src, k):
+        ng, a, b = k
+        d = reg[t]
+        for key, u in src.items():
+            w = u * a
+            need(w % b == 0, "E5: an entry needs a denominator beyond sixths (register %d)" % t)
+            w = w // b
+            w = d.get(key, 0) + (-w if ng else w)
+            if count is not None:
+                count[key] += 1
+            if w:
+                d[key] = w
+            else:
+                d.pop(key, None)
+
+    def run(gates):
+        for g in gates:
+            if g[0] == "out":
+                src = dict(reg[g[2]])
+                for t, k in g[3]:
+                    axpy(t, src, k)
+            else:
+                for s, k in g[3]:
+                    axpy(g[2], reg[s], k)
+    run(D["A"])
+    afterA = sum(len(d) for d in reg)
+    tot = [dict(reg[s]) for s, _ in D["ret"]]
+    for t in range(v):
+        for k, cf in scat_row(D, t):
+            if tot[k]:
+                axpy(v + t, tot[k], cf)
+    run(D["B"])
+    return reg, afterA
+
+
+def chk_scalar(D, batches=1):
+    """E5 (+ E7 when `ext` is non-empty).  Returns stats: denominators and largest numerators per class in the
+    units of the spec (x halves, y sixths, slots integers), updates per source batch, entries after A."""
+    v = D["v"]
+    count = Counter()
+    reg, afterA = replay(D, {t: {t: SC} for t in range(v)}, count)
+    need(all(reg[t] == {t: SC} for t in range(v)), "E5: an x role is not restored (X3)")
+    need(all(reg[v + t] == {t: SC} for t in range(v)), "E5: a target does not receive exactly its source (hid)")
+    if D["ext"]:
+        rg, _ = replay(D, {r: {r: SC} for r, _ in D["ext"]})
+        need(all(not rg[v + t] for t in range(v)), "E7: the dirt of an exterior-gauged slot reaches a y role")
+    step = -(-v // batches)
+    per = [sum(count[k] for k in range(lo, min(lo + step, v))) for lo in range(0, v, step)]
+    return dict(updates=sum(count.values()), per_batch=per, afterA=afterA,
+                batches=[(lo, min(lo + step, v)) for lo in range(0, v, step)])
+
+
+def digits(D):
+    """largest |entry| met and denominators per class, by a second replay that watches every write (slow path
+    kept separate from the check): returns {class: (lcm of denominators, largest |numerator| in units 1/den)}"""
+    v = D["v"]
+    den = {"x": 1, "y": 1, "s": 1}
+    mx = {"x": 0, "y": 0, "s": 0}
+    reg = [({r: SC} if r < v else {}) for r in range(2 * v + D["R"])]
+
+    def axpy(t, src, k):
+        ng, a, b = k
+        d, kk = reg[t], cls(D, t)
+        for key, u in src.items():
+            w = d.get(key, 0) + (-(u * a // b) if ng else u * a // b)
+            if w:
+                d[key] = w
+                q = SC // gcd(w, SC)
+                if den[kk] % q:
+                    den[kk] = den[kk] * q // gcd(den[kk], q)
+                if abs(w) > mx[kk]:
+                    mx[kk] = abs(w)
+            else:
+                d.pop(key, None)
+    for g in D["A"]:
+        for t, s, k in adds(g):
+            axpy(t, reg[s], k)
+    tot = [dict(reg[s]) for s, _ in D["ret"]]
+    for t in range(v):
+        for k, cf in scat_row(D, t):
+            axpy(v + t, tot[k], cf)
+    for g in D["B"]:
+        for t, s, k in adds(g):
+            axpy(t, reg[s], k)
+    return {k: (den[k], mx[k] * den[k] // SC if (mx[k] * den[k]) % SC == 0 else "%d/6" % mx[k]) for k in "xys"}
+
+
+def mirror(D, gmax=12000, batches=1, pairs=None, cuts=None):
+    """both checks; returns everything the generator and the dry run need"""
+    dim = chk_frames(D)
+    pairs = derive(D) if pairs is None else pairs
+    work = chk_pairs(D, dim, pairs)
+    cuts = cut_points(D, gmax) if cuts is None else cuts
+    states, H, visits, segH = chk_replay(D, dim, pairs, cuts)
+    ysh = chk_shape(D)
+    S = chk_scalar(D, batches)
+    hist = Counter()
+    for k in "xysc":
+        for r, n in H[k].items():
+            hist[r] += n
+    return dict(dim=dim, pairs=pairs, pair_work=work, cuts=cuts, states=states, H=H, visits=visits, ysh=ysh,
+                scal=S, hist=dict(sorted(hist.items())), segH=segH,
+                lab=label_data(D, dim, cuts))
diff --git a/research/five-stage-p10-transcript-stages/kernel-selection.json b/research/five-stage-p10-transcript-stages/kernel-selection.json
new file mode 100644
index 0000000000..5039105df5
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/kernel-selection.json
@@ -0,0 +1,44315 @@
+{
+ "status": "P10_SHARED_DONOR_KERNEL_ENTRIES",
+ "tag": "kernel",
+ "provenance": "discovery/coll (lines.py/planes.py + closure_pack.py: per-entrance maximum-weight closure over alternate response bases; shared donors after PR319) on the p = 10 word after descent/target; prepared with Anthropic Claude assistance",
+ "n": 10150,
+ "v": 960,
+ "input_raw_sha256": "3c81e8c478ccfad3dec11ff56424e40c3dfa19808ef4982bfdb4eca5da611b4b",
+ "input_scalar_sha256": "8bed15b704381cb833e54eebb5899af8a418291cba4045ecb2573ac2ef7db8f2",
+ "selected_pairs": 0,
+ "selected_families": 1047,
+ "expected_local_delta": {
+  "1": 2086,
+  "2": -184,
+  "3": -867,
+  "4": 59,
+  "5": -55,
+  "6": -12,
+  "7": 3,
+  "8": 5,
+  "10": 4,
+  "11": 4,
+  "12": -26,
+  "13": 3,
+  "14": 3,
+  "15": -8
+ },
+ "pairs": [],
+ "families": [
+  {
+   "pivot": 5476,
+   "donors": [
+    5478
+   ],
+   "cut_read": [
+    1222,
+    5478,
+    -1
+   ],
+   "rank": 1,
+   "basis": [
+    [
+     1,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     -1
+    ]
+   ],
+   "kind": "shared-donor-rank1"
+  },
+  {
+   "pivot": 5467,
+   "donors": [
+    5469
+   ],
+   "cut_read": [
+    1166,
+    5469,
+    -1
+   ],
+   "rank": 1,
+   "basis": [
+    [
+     1,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     -1
+    ]
+   ],
+   "kind": "shared-donor-rank1"
+  },
+  {
+   "pivot": 5449,
+   "donors": [
+    5451
+   ],
+   "cut_read": [
+    1078,
+    5451,
+    -1
+   ],
+   "rank": 1,
+   "basis": [
+    [
+     1,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     -1
+    ]
+   ],
+   "kind": "shared-donor-rank1"
+  },
+  {
+   "pivot": 5422,
+   "donors": [
+    5424
+   ],
+   "cut_read": [
+    1022,
+    5424,
+    -1
+   ],
+   "rank": 1,
+   "basis": [
+    [
+     1,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     -1
+    ]
+   ],
+   "kind": "shared-donor-rank1"
+  },
+  {
+   "pivot": 5386,
+   "donors": [
+    5388
+   ],
+   "cut_read": [
+    1222,
+    5388,
+    -1
+   ],
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+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ]
+   ],
+   "kind": "shared-donor-rank2"
+  },
+  {
+   "pivot": 8766,
+   "donors": [
+    8757,
+    8760,
+    8763
+   ],
+   "cut_read": [
+    1903,
+    8766,
+    -1
+   ],
+   "rank": 8,
+   "basis": [
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0
+    ],
+    [
+     0,
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     1,
+     1,
+     1,
+     1,
+     1,
+     1,
+     1,
+     1,
+     1,
+     0,
+     -3,
+     1,
+     1
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     -1,
+     0,
+     0
+    ]
+   ],
+   "kind": "shared-donor-rank8"
+  },
+  {
+   "pivot": 6994,
+   "donors": [
+    6974,
+    6976,
+    6992
+   ],
+   "cut_read": [
+    1822,
+    6994,
+    -1
+   ],
+   "rank": 2,
+   "basis": [
+    [
+     0,
+     0,
+     1,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     1,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ]
+   ],
+   "kind": "shared-donor-rank2"
+  },
+  {
+   "pivot": 8729,
+   "donors": [
+    8720,
+    8723,
+    8726
+   ],
+   "cut_read": [
+    1015,
+    8729,
+    -1
+   ],
+   "rank": 8,
+   "basis": [
+    [
+     1,
+     1,
+     1,
+     1,
+     1,
+     1,
+     1,
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -3,
+     1,
+     1,
+     1,
+     1
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     -1,
+     0,
+     0,
+     0,
+     0
+    ]
+   ],
+   "kind": "shared-donor-rank8"
+  },
+  {
+   "pivot": 7945,
+   "donors": [
+    7889,
+    7891,
+    7943
+   ],
+   "cut_read": [
+    1567,
+    7945,
+    -1
+   ],
+   "rank": 2,
+   "basis": [
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     -1,
+     0,
+     0,
+     0,
+     0
+    ]
+   ],
+   "kind": "shared-donor-rank2"
+  }
+ ],
+ "entrance_rank_histogram": {
+  "1": 1007,
+  "2": 20,
+  "4": 5,
+  "5": 3,
+  "7": 1,
+  "8": 3,
+  "10": 6,
+  "13": 1,
+  "14": 1
+ },
+ "total_entrance_rank": 1200,
+ "donor_sharing_histogram": {
+  "1": 466,
+  "2": 135,
+  "3": 141,
+  "4": 97,
+  "5": 63,
+  "6": 35,
+  "7": 14,
+  "8": 7,
+  "9": 10,
+  "11": 7,
+  "12": 2,
+  "13": 1,
+  "14": 2,
+  "16": 5,
+  "17": 4,
+  "18": 4,
+  "20": 3,
+  "21": 6,
+  "22": 2,
+  "23": 3,
+  "24": 1,
+  "25": 3,
+  "27": 2,
+  "28": 1,
+  "30": 1
+ }
+}
diff --git a/research/five-stage-p10-transcript-stages/kernel_transform.py b/research/five-stage-p10-transcript-stages/kernel_transform.py
new file mode 100644
index 0000000000..9e8c791df8
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/kernel_transform.py
@@ -0,0 +1,221 @@
+"""Response-kernel entries (twin pairs and multi-donor families) with per-entry cuts on the gen4 word.
+
+Generalizes the per-pair-cut adaptation of #268's kernel_transform.py (PR254 pairs, eumemic / OpenAI Codex)
+to entries with a pivot p, donors D (one donor: twin pair; two or three: collective family, #272-style) and an
+entrance E of rank e >= 1 (basis rows), nondegenerate for 9I-J and inside every member's first frame. The entry
+cut is the later of the members' last initial (frame-ZERO) compensation reads, bound by content. At the cut each
+donor pays d += p at E (kernel_setup); at the end each pays d -= p at the full frame (kernel_restore); the pivot
+starts at E and loses its initial reads. A donor may serve several entries along a nested entrance chain (the
+emitted MOVEs are checked nested). Correctness is the F2 replay of every formal column, forward and inverse, with
+both omission controls; the prefix relation (pivot response = XOR of donor responses) is checked on the literal
+prefix; every required frame path is rebuilt from scalar/COPY events independently of the emitted MOVEs.
+Prepared with Anthropic Claude assistance; Apache-2.0.
+p = 10 port (Chafik Boukhalfa (chafreaky), Anthropic Claude assistance): h, v, centre copies and scatter reads come
+from word_pins.shape and the stage counts are pinned in word-pins.json; the mechanism and checks are unchanged.
+"""
+from array import array
+from collections import Counter
+from copy import copy
+from pathlib import Path
+import gzip,hashlib,json,time,sys
+sys.dont_write_bytecode=True
+if not __debug__:raise SystemExit('assertions required')
+HERE=Path(__file__).resolve().parent
+from word_pins import shape as _shape
+_S=_shape();_H=_S['h'];_V=_S['v'];_M=_S['m'];_CR=_S['center_rank'];_NC=_S['centers'];_SCAT=_S['scatter_reads'];_DEF=_S['deficit']
+sha=lambda b:hashlib.sha256(b).hexdigest()
+
+def transform(producer,selection,tag='kernel'):
+    W,C=producer['W'],producer['C'];old=producer['records'];initial=dict(producer['initial_state']);context=producer['context'];v=W.v;n=2*v+len(context['regs']);ZERO=producer['ZERO'];FULL=producer['FULL']
+    assert n==selection['n'] and v==selection['v']
+    assert sha(old.tobytes())==selection['input_raw_sha256']
+    assert producer['physical']['scalar_projection_sha256']==selection['input_scalar_sha256']
+    cats=list(producer['physical']['category_names']);readcat=cats.index('dirty_read')
+    assert tag+'_setup' not in cats and tag+'_restore' not in cats
+    setupcat=len(cats);restorecat=setupcat+1;cats+=[tag+'_setup',tag+'_restore']
+    final=dict(initial)
+    for k in range(0,len(old),6):
+        if old[k]==0:final[old[k+1]]=old[k+3]
+    raw_entries=[dict(pivot=p['a'],donors=[p['b']],cut_read=p['cut_read'],rank=p['rank'],basis=p['basis'],kind='pair')for p in selection['pairs']]
+    raw_entries+=[dict(pivot=f['pivot'],donors=list(f['donors']),cut_read=f['cut_read'],rank=f['rank'],basis=f['basis'],kind=f.get('kind','family'))for f in selection.get('families',[])]
+    assert len(raw_entries)==selection['selected_pairs']+selection.get('selected_families',0)
+    members=set();pivots=set();donorset=set()
+    for e in raw_entries:
+        p=e['pivot'];assert p not in pivots and 2*v<=p<n;pivots.add(p);members.add(p)
+        for d in e['donors']:assert d!=p and 2*v<=d<n;donorset.add(d);members.add(d)
+    assert not(pivots&donorset),'pivot used as a donor (non-nilpotent support)'
+    # Literal prefix facts: last initial read and first other use of every member.
+    lastread={};firsttouch={};reads=Counter()
+    for k in range(0,len(old),6):
+        op,a,b,c,f,z=old[k:k+6];i=k//6
+        if op==1:
+            if b in members and z==readcat and f==ZERO and v<=a<2*v and c%2:lastread[b]=i;reads[b]+=1;continue
+            for s in (a,b):
+                if s in members and s not in firsttouch:firsttouch[s]=(i,f)
+        elif op==2:
+            if a in members and a not in firsttouch:firsttouch[a]=(i,c)
+    entries=[];bycut={};memcut={};chosen={}
+    for e in raw_entries:
+        ms=[e['pivot']]+e['donors']
+        for s in ms:
+            r=context['regs'][s-2*v];assert r not in W.gauge and r not in W.donor and r not in context['borrow'] and initial[s]==ZERO and final[s]==FULL and reads[s]>0
+        cut=max(lastread[s]for s in ms);assert [old[6*cut+j]for j in(1,2,3)]==e['cut_read'],('cut read differs',e['pivot'])
+        assert cut<min(firsttouch[s][0]for s in ms),('a member is touched before the entry cut',e['pivot'])
+        f=W.register(e['basis']);assert C.dimf[f]==e['rank']==len(e['basis'])>=1 and C.nondeg(f),('entrance',e['pivot'])
+        for s in ms:assert C.sub(f,firsttouch[s][1]),('entrance not inside first frame',s)
+        row=dict(e,cut=cut,frame=f,role=context['regs'][e['pivot']-2*v],first_frames={str(s):firsttouch[s][1]for s in ms},removed_reads=reads[e['pivot']])
+        entries.append(row);chosen[e['pivot']]=row;bycut.setdefault(cut,[]).append(row);initial[e['pivot']]=f
+        for s in ms:memcut[s]=max(memcut.get(s,-1),cut)
+    for cut in bycut:bycut[cut].sort(key=lambda r:(r['rank'],r['pivot']))
+    # Prefix relation on the literal prefix up to the latest cut: pivot response = XOR of donor responses, confined
+    # to targets and own coordinates.
+    latest=max(bycut);bit={s:1<<i for i,s in enumerate(sorted(members))};columns=[bit.get(i,0)for i in range(n+1)];temporary=None
+    for k in range(0,6*latest+6,6):
+        op,a,b,c,f,z=old[k:k+6]
+        if op==1:
+            source=temporary if b==n else b;assert source is not None
+            if c%2:columns[a]^=columns[source]
+        elif op==2:assert temporary is None;temporary=a
+        elif op==3:assert temporary==a;temporary=None
+    for i,col in enumerate(columns):
+        if not v<=i<2*v:assert col==bit.get(i,0),'selected response escapes targets or own coordinate'
+    relations=0
+    for row in entries:
+        p=row['pivot'];support=[]
+        for t in range(v):
+            col=columns[v+t];x=(col>>sorted(members).index(p))&1 if False else bool(col&bit[p])
+            y=0
+            for d in row['donors']:y^=bool(col&bit[d])
+            assert x==y,('prefix relation fails',p,t)
+            if x:support.append(t)
+        assert support;row['prefix_response_targets']=support;relations+=1
+    state=dict(initial);out=array('i');temporary=None;skipped=[]
+    def move(s,f):
+        before=state[s]
+        if before==f:return
+        assert C.sub(before,f),('kernel nonnested actual use',s,before,f)
+        gap=C.dimf[f]-C.dimf[before];assert gap>=0;out.extend((0,s,before,f,gap,0));state[s]=f
+    def add(a,b,c,f,z):
+        move(a,f);move(b,f);out.extend((1,a,b,c,f,z))
+    for k in range(0,len(old),6):
+        op,a,b,c,f,z=old[k:k+6];i=k//6
+        if op==1:
+            if b in chosen and f==ZERO and z==readcat:
+                assert i<=chosen[b]['cut'];skipped.append(i)
+            else:
+                if not(b in members and z==readcat and f==ZERO and v<=a<2*v):
+                    for s in (a,b):
+                        if s in members:assert i>memcut[s],('touched before cut',s)
+                add(a,b,c,f,z)
+        elif op==2:
+            assert temporary is None;move(a,c);state[b]=f;temporary=(a,b,c);out.extend((op,a,b,c,f,z))
+            if a in members:assert i>memcut[a]
+        elif op==3:
+            assert temporary==(a,b,c)and state[a]==c and state[b]==f;out.extend((op,a,b,c,f,z));del state[b];temporary=None
+        if i in bycut:
+            assert temporary is None
+            for row in bycut[i]:
+                for d in row['donors']:add(d,row['pivot'],1,row['frame'],setupcat)
+    assert len(skipped)==sum(r['removed_reads']for r in entries)and temporary is None
+    for s in sorted(final):move(s,final[s])
+    for row in entries:
+        for d in row['donors']:add(d,row['pivot'],-1,FULL,restorecat)
+    assert state==final
+    project=lambda aa:[tuple(aa[k+j]for j in(0,1,2,3,5))for k in range(0,len(aa),6)if aa[k]]
+    drop=set(skipped);expected=[]
+    for k in range(0,len(old),6):
+        i=k//6
+        if old[k] and i not in drop:expected.append(tuple(old[k+j]for j in(0,1,2,3,5)))
+        if i in bycut:expected.extend((1,d,r['pivot'],1,setupcat)for r in bycut[i]for d in r['donors'])
+    expected.extend((1,d,r['pivot'],-1,restorecat)for r in entries for d in r['donors']);assert project(out)==expected
+    ew=copy(W);ew.gauge=dict(W.gauge);ew.w=dict(W.w);ew.w['gauges']=list(W.w['gauges'])
+    for row in entries:
+        g=dict(role=row['role'],frame=row['frame'],dim=row['rank'],targets=[]);ew.gauge[row['role']]=g;ew.w['gauges'].append(g)
+    execution=dict(context);execution['W']=ew
+    gates=sum(len(r['donors'])for r in entries);shared=Counter(Counter(d for r in entries for d in r['donors']).values())
+    proof=dict(selected_entries=len(entries),kinds=dict(Counter(r['kind']for r in entries)),selected_helpers=len(members),distinct_cuts=len(bycut),earliest_cut=min(bycut),latest_cut=latest,entrance_rank_histogram=dict(Counter(r['rank']for r in entries)),total_entrance_rank=sum(r['rank']for r in entries),donor_sharing_histogram={str(k):c for k,c in sorted(shared.items())},prefix_relations_checked=relations,prefix_target_comparisons=len(entries)*v,removed_initial_reads=len(skipped),added_setup_and_restores=2*gates,selected_helpers_untouched_before_own_cut=True,no_prefix_response_outside_targets_and_own_helper=True,all_old_surviving_scalar_and_copy_events_in_order=True,source_context_preserved=True)
+    return out,initial,final,entries,execution,cats,proof,n,v
+
+def replay(records,n,v,reverse=False,omit_category=None):
+    columns=[1<<i for i in range(n+1)];wanted=[1<<i for i in range(n)];norm=[1]*(n+1);largest=1;temporary=None;count=0;coeff=Counter();digest=hashlib.sha256()
+    for t in range(v):wanted[v+t]^=1<<t
+    for k in(range(len(records)-6,-1,-6)if reverse else range(0,len(records),6)):
+        op,a,b,c,f,z=records[k:k+6]
+        if op==1:
+            if z==omit_category:continue
+            assert c%2 and (b!=n or temporary is not None)
+            columns[a]^=columns[b];norm[a]+=abs(c)*norm[b];largest=max(largest,norm[a]);count+=1;coeff[abs(c)]+=1
+            digest.update(json.dumps([a,temporary if b==n else b,-c if reverse else c],separators=(',',':')).encode());digest.update(b'\n')
+        elif op==(3 if reverse else 2):
+            assert temporary is None and b==n;temporary=a;columns[b]=columns[a];norm[b]=norm[a]
+        elif op==(2 if reverse else 3):
+            assert temporary==a and b==n and columns[a]==columns[b];temporary=None
+    assert temporary is None
+    wrong=[i for i in range(n)if columns[i]!=wanted[i]]
+    if omit_category is None:assert not wrong,('kernel scalar failure',reverse,wrong[:20])
+    else:assert wrong,'vacuous kernel omitted-gate control'
+    return dict(reverse=reverse,formal_columns=n,wrong_rows=len(wrong),all_sources_and_dirty_restored=not wrong,scalar_additions=count,coefficient_counts=dict(coeff),event_sha256=digest.hexdigest(),max_intermediate_row_l1=largest)
+
+def run(producer,output_dir=None,selection_path=None,tag='kernel'):
+    start=time.monotonic();W,C=producer['W'],producer['C'];path=Path(selection_path)if selection_path else HERE/(tag+'-selection.json');selection=json.loads(path.read_text())
+    out,initial,final,entries,context,cats,proof,n,v=transform(producer,selection,tag);ZERO=producer['ZERO'];FULL=producer['FULL']
+    forward=replay(out,n,v);inverse=replay(out,n,v,True);controls=[replay(out,n,v,omit_category=cats.index(tag+'_setup')),replay(out,n,v,omit_category=cats.index(tag+'_restore'))]
+    needs={s:[]for s in initial};copies=Counter();temporary=None
+    for k in range(0,len(out),6):
+        op,a,b,c,f,z=out[k:k+6]
+        if op==1:
+            needs[a].append(f)
+            if b!=n:needs[b].append(f)
+            else:assert temporary is not None and f==ZERO
+        elif op==2:assert temporary is None;temporary=(a,b,c);needs[a].append(c);copies[z]+=1
+        elif op==3:assert temporary==(a,b,c);temporary=None
+    assert temporary is None and copies=={_CR:_NC}
+    per_role={};pairs=set();census=Counter(copies);reflected=Counter(copies)
+    for s,startframe in initial.items():
+        H=Counter();pathframes=[startframe]+needs[s]+[final[s]]
+        for a,b in zip(pathframes,pathframes[1:]):
+            assert C.sub(a,b);gap=C.dimf[b]-C.dimf[a];assert gap>=0;pairs.add((a,b))
+            if gap:H[gap]+=1
+        for a,b in zip(reversed(pathframes),list(reversed(pathframes))[1:]):
+            assert all(not W.module.dot(x,y)for x in C.A[a]for y in C.B[b]);gap=len(C.A[b])-len(C.A[a]);assert gap>=0
+            if gap:reflected[gap]+=1
+        per_role[s]=H;census.update(H)
+    assert reflected==census
+    for f in {x for pair in pairs for x in pair}:assert C.nondeg(f)and len(C.B[f])+len(C.A[f])==_H
+    state=dict(initial);hist=Counter();cat=Counter();coeff=Counter();used=set(state.values());temporary=None;centers=[];count=0;tagged=hashlib.sha256()
+    for k in range(0,len(out),6):
+        op,a,b,c,f,z=out[k:k+6]
+        if op==0:
+            assert state[a]==b and C.sub(b,c)and C.dimf[c]-C.dimf[b]==f and len(C.A[b])-len(C.A[c])==f
+            state[a]=c;used.update((b,c))
+            if f:hist[f]+=1
+        elif op==1:
+            assert state[a]==state[b]==f and a!=b and c%2;count+=1;cat[cats[z]]+=1;coeff[abs(c)]+=1;used.add(f)
+            tagged.update(json.dumps([a,b,c,f,cats[z]],separators=(',',':')).encode());tagged.update(b'\n')
+        elif op==2:
+            assert temporary is None and b==n and state[a]==c and f==ZERO and z==_CR
+            state[b]=f;hist[z]+=1;temporary=dict(source=a,frame=c,rank=z,temporary=b,first_event=count,copy_output_frame=f)
+        else:
+            assert op==3 and temporary is not None and (a,b,c)==(temporary['source'],temporary['temporary'],temporary['frame'])and state[a]==c and state[b]==f==ZERO
+            temporary.update(after_event=count,scatter_reads=count-temporary['first_event']);assert temporary['scatter_reads']==_SCAT;centers.append(temporary);temporary=None;del state[b]
+    assert state==final and temporary is None and hist==census and len(centers)==_NC
+    old=Counter({int(r):c for r,c in producer['physical']['paid_histogram'].items()});delta=Counter(hist);delta.subtract(old);delta={r:c for r,c in delta.items()if c}
+    assert delta=={int(k):v for k,v in selection['expected_local_delta'].items()}
+    assert count==producer['physical']['weighted_scalar_events']-proof['removed_initial_reads']+proof['added_setup_and_restores'] and sum(r*c for r,c in hist.items())==producer['physical']['paid_rank_mass']-proof['total_entrance_rank']
+    # Physical inventory: frames consumed by the preceding stages stay in the determinant inventory.
+    inherited=set()
+    for inventory in (producer['physical'],producer.get('producer_physical')):
+        if isinstance(inventory,dict):inherited.update(row['frame_id']for row in inventory.get('used_frames',[]))
+    sourceH=Counter();targetH=Counter();internalH=Counter(copies)
+    for s,H in per_role.items():(sourceH if s<v else targetH if s<2*v else internalH).update(H)
+    receipt=dict(status='PASS_GEN4_PER_ENTRY_CUT_KERNEL_ON_ACTUAL_WORD_AND_BOTH_REFLECTED_LEDGERS',tag=tag,proof=proof,scalar=dict(forward=forward,inverse=inverse,controls=controls),selected_pairs=proof['kinds'].get('pair',0),selected_entries=len(entries),rank_drop=proof['total_entrance_rank'],local_histogram_delta=delta,unchanged_data_input_output_and_dirty_output_frames=True,unchanged_copy_lifetimes=True,both_reflected_ledgers=True,unique_required_frame_pairs=len(pairs),source_histogram=dict(sourceH),target_histogram=dict(targetH),internal_histogram_including_copies=dict(internalH),copied_center_histogram=dict(copies),input_raw_sha256=sha(producer['records'].tobytes()),output_raw_sha256=sha(out.tobytes()),selection_sha256=sha(path.read_bytes()),transform_sha256=sha(Path(__file__).read_bytes()),seconds=time.monotonic()-start)
+    meta=dict(producer['physical']);meta.update(status='PASS_PHYSICAL_GEN4_KERNEL_ENTRIES',scalar_projection_sha256=forward['event_sha256'],tagged_scalar_sha256=tagged.hexdigest(),weighted_scalar_events=count,coefficient_histogram=dict(coeff),categories=dict(cat),category_names=cats,copied_center_blocks=centers,paid_histogram=dict(sorted(hist.items())),paid_rank_mass=sum(r*c for r,c in hist.items()),positive_rank_moves=sum(hist.values())-_NC,used_frames=[dict(frame_id=f,dimension=C.dimf[f],basis_sha256=sha(json.dumps(C.B[f],separators=(',',':')).encode()))for f in sorted(used|inherited)],**{tag+'_transform':receipt},initial_independent_entrances=dict(Counter(C.dimf[initial[s]]for s in range(2*v,n)if C.dimf[initial[s]])),producer_physical_emitter_sha256=producer['physical'].get('physical_emitter_sha256'),physical_emitter_sha256=receipt['transform_sha256'])
+    # A later kernel round (tag kernel2, ...) appends its entrances to the earlier rounds' list.
+    result=dict(producer);result.update(records=out,physical=meta,result=meta,initial_state=initial,context=context,W=context['W'],kernel_entrances=list(producer.get('kernel_entrances',[]))+entries)
+    result[tag+'_census']=receipt
+    if output_dir is not None:
+        p=Path(output_dir);p.mkdir(parents=True,exist_ok=True);(p/(tag+'-records.bin.gz')).write_bytes(gzip.compress(out.tobytes(),mtime=0))
+        for name,value in [(tag,receipt),(tag+'-initial',initial),(tag+'-entrances',[{k:v for k,v in e.items()if k!='prefix_response_targets'}for e in entries])]:
+            (p/(name+'.json')).write_text(json.dumps(value,indent=2)+'\n')
+    print('PASS',tag,'entries',len(entries),dict(proof['kinds']),'rank',proof['total_entrance_rank'],count,'scalar ADDs',sum(hist.values()),'paid calls',len(out)//6,'records',flush=True)
+    return result
diff --git a/research/five-stage-p10-transcript-stages/math_check.py b/research/five-stage-p10-transcript-stages/math_check.py
new file mode 100644
index 0000000000..e22f96400f
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/math_check.py
@@ -0,0 +1,98 @@
+"""Source-bound banked five-stage moments and all47outerconstraints.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+Uses PR234 five-stage architecture and complex baseline, the p = 10 helper and
+PR197-derived actual five-stage entrance banks. Inputs must be live verifier outputs.
+p = 10 port (DreamingOfClouds, Anthropic Claude assistance): the bit profile is the p = 10 word's (m = 5h = 100,
+deficit 4v - 5h(h-2), counts pinned in word-pins.json). The complex supplier is isolated in complex_supplier().
+Complex-bound assembly (draft by DreamingOfClouds with Anthropic Claude assistance, adopted unchanged in logic):
+the bit is certified at its true root c with the adjacent grid point rejected; the saving fed to the bootstrap
+and the 47 outer constraints is s = min(c, floor((1-beta)b - 10^-18)), re-checked exactly at s (the moment is
+increasing in the saving). When s < c the complex supplier binds, and outer.assembly at the cap (1-beta)b itself
+must fail on leaf_saving_above_bit.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+import importlib.util
+from word_pins import expect,shape
+HERE=Path(__file__).resolve().parent
+
+def load(name):
+ p=HERE/(name+'.py');s=importlib.util.spec_from_file_location('banked527_'+name,p);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+
+def serial(x):
+ if isinstance(x,Q):return str(x)
+ if isinstance(x,dict):return {str(k):serial(v)for k,v in x.items()}
+ if isinstance(x,(list,tuple)):return list(map(serial,x))
+ return x
+
+def hist(x):return Counter({int(k):v for k,v in x.items()if v})
+
+def complex_supplier(cost,other,complex_histogram):
+ """The retained complex supplier: profile pins, coarse b and its exact moment certificate (adjacent grid point
+ rejected). This is the only complex-specific block of math_check; a transplanted complex chain replaces it.
+ b is certified like the bit side: WITH the 10^-16 bad-class fallback envelope (32 m^2 rank-one calls per paid
+ child), by both rational moment engines, adjacent 10^-18 grid point rejected. The inherited PR234/PR193
+ convention priced the complex side without the fallback; that larger root b0 is re-certified and recorded only."""
+ # the centre-sharing complex supplier built with PR #304's pipeline (inputs/complex/centre-mw/).
+ CH=hist(complex_histogram);assert sum(CH.values())==351820 and sum(k*n for k,n in CH.items())==1571680
+ m,W,grid=110,14316,Q(1,10**18)
+ cp=dict(m=m,W=W,histogram=dict(CH),calls=sum(CH.values()),rank_mass=sum(k*n for k,n in CH.items()),deficit=3080,maxchild=max(CH))
+ root=cost.certify(dict(CH),m,W,True);b=Q(int(Q(root['lower'])*10**18),10**18);assert b==Q(772714351296671,10**18)
+ cm=cost.moment(dict(CH),m,W,b,True);nextcm=cost.moment(dict(CH),m,W,b+grid,True);assert cm[1]<1<nextcm[0]
+ fallback=32*m*m*sum(CH.values())
+ _,upper=other.moment(m,W,list(CH.items()),b);_,bad=other.moment(m,W,[(1,fallback)],b)
+ lower,_=other.moment(m,W,list(CH.items()),b+grid);badlower,_=other.moment(m,W,[(1,fallback)],b+grid);assert upper+Q(1,10**16)*bad<1<lower+Q(1,10**16)*badlower
+ b0=Q(772714354722691,10**18);cm0=cost.moment(dict(CH),m,W,b0,False);nextcm0=cost.moment(dict(CH),m,W,b0+grid,False);assert cm0[1]<1<nextcm0[0] and b<b0
+ return dict(profile=cp,coarse=b,moment_interval=cm,next_grid_excluded=nextcm,coarse_without_fallback=b0,moment_interval_without_fallback=cm0)
+
+def run(raw,complex_histogram,banks,global_result):
+ cost=load('moment');other=load('base_two_moment');outer=load('outer');S=shape();m=S['m'];T=S['replicas']
+ assert raw['source_aliases']==0 and raw['physical_R']==expect('final_physical_R',raw['physical_R']) and raw['h']==S['h'] and raw['v']==S['v']
+ H=hist(raw['five_stage_profile']['histogram']);assert H==hist(global_result['paid_histogram'])
+ assert global_result['paid_rank_mass']==sum(k*n for k,n in H.items())==expect('final_five_stage_rank_mass',global_result['paid_rank_mass'])
+ gauges=hist(raw['auxiliary_entrance_rank_histogram']);expect('final_entrance_ranks',gauges)
+ completions=hist(raw.get('completion_rank_histogram',gauges));expect('completion_rank_histogram',completions);assert sum(completions.values())==sum(gauges.values())
+ assert banks['assignments']==5*T*raw['physical_R'] and banks['physical_roles']==raw['physical_R'] and banks['physical_replicas']==T
+ assert banks['literal_stock']==expect('literal_stock',banks['literal_stock']) and banks['banks_total']==5*expect('banks_per_stage',banks['banks_total']//5) and banks['charts']==expect('final_charts',banks['charts'])
+ for a,n in completions.items():
+  assert H[5*a]>=n;H[5*a]-=n
+  if not H[5*a]:del H[5*a]
+ assert len(H)>0 and min(H.values())>0 and max(H)==S['idle'][2]
+ literal={k:n*T for k,n in H.items()};literal_mass=sum(k*n for k,n in literal.items());literal_W=banks['literal_stock']
+ assert m*literal_W-literal_mass==T*S['deficit']
+ # Divide the literal profile by5 to an integer normalization. The executed
+ # realization is still60replicas, and finite accounting uses its literalstock.
+ assert literal_W%5==0 and all(n%5==0 for n in literal.values())
+ normalized={k:n//5 for k,n in literal.items()};W=literal_W//5;mass=sum(k*n for k,n in normalized.items())
+ bp=dict(m=m,W=W,histogram=normalized,calls=sum(normalized.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(normalized),normalization=T//5,physical_replicas=T,literal_stock=literal_W,literal_children=sum(literal.values()),literal_rank_mass=literal_mass)
+ root=cost.certify(normalized,m,W,True);c=Q(int(Q(root['lower'])*10**18),10**18);bm=cost.moment(normalized,m,W,c,True);nextbm=cost.moment(normalized,m,W,c+Q(1,10**18),True);assert bm[1]<1<nextbm[0]
+ fallback=32*m*m*sum(normalized.values())
+ _,upper=other.moment(m,W,list(normalized.items()),c);_,bad=other.moment(m,W,[(1,fallback)],c)
+ lower,_=other.moment(m,W,list(normalized.items()),c+Q(1,10**18));badlower,_=other.moment(m,W,[(1,fallback)],c+Q(1,10**18));assert upper+Q(1,10**16)*bad<1<lower+Q(1,10**16)*badlower
+ expect('bit_root',c)
+ supplier=complex_supplier(cost,other,complex_histogram);cp,b,cm=supplier['profile'],supplier['coarse'],supplier['moment_interval']
+ # Bit saving fed to the bootstrap: the certified root c, capped below the complex leaf cap (1-beta)*b of outer.py
+ # (leaf_saving_above_bit, complex_above_bit). The moment is monotone in the saving, so any grid point s<=c is
+ # certified too; it is re-checked exactly. c, bm and nextbm stay the record of the uncapped root.
+ grid=Q(1,10**18);eta=Q(1,10**12);beta=Q(1,10**9);cap=(1-beta)*b
+ s=min(c,Q(((cap-grid)*10**18).__floor__(),10**18));binding='bit' if s==c else 'complex'
+ sm=bm if s==c else cost.moment(normalized,m,W,s,True);assert 0<s<=c and sm[1]<1
+ if binding=='complex':assert s+grid>cap-grid   # tight against the complex cap: the next grid point exceeds (1-beta)*b-grid
+ chain=[Q(384599,10**10)]
+ for _ in range(3):
+  a=(1-s)*s+s*chain[-1];assert chain[-1]<a<s<1-a;chain.append(a)
+ bit=chain[-1];assert bit<s<=cap-grid<cap
+ bridge=dict(proof='PROOF.md',representation='Exact powers with source-bound finite overcharges',semantic=dict(G=dict(base=2,exponent=30000),E=dict(base=2,exponent=100000),B_upper=dict(base=2,exponent=100001),C0=dict(base=2,exponent=210000),C1=1,strict_literal_gap=1,induction_gap_lower=1),rows=dict(coefficient=20161,degree=10**6,suffix_slope=4*10**6,degree_gap=Q(10**6)-Q(51*20161,25)))
+ assert bridge['rows']['degree_gap']>0
+ q=bit*(1-2*eta);minimum=(1-eta)*q/(1+q);ticks=minimum*10**18;k=Q((ticks.numerator-1)//ticks.denominator,10**18)
+ assembly=outer.assembly(bit,b,bridge,k,eta=eta,beta=beta);assert len(assembly['strict_constraints'])==47 and len(assembly['margins'])==7 and min(assembly['strict_constraints'].values())>0
+ try:outer.assembly(bit,b,bridge,k+Q(1,10**18),eta=eta,beta=beta)
+ except AssertionError:pass
+ else:raise AssertionError('Adjacentkappaadmitted')
+ if binding=='complex':   # the cap is the outer constraint: a bit saving at (1-beta)*b itself fails leaf_saving_above_bit
+  try:outer.assembly(cap,b,bridge,k,eta=eta,beta=beta)
+  except AssertionError as e:assert 'leaf_saving_above_bit' in str(e)
+  else:raise AssertionError('Complexleafcapadmitted')
+ expect('binding',binding);expect('kappa',k)
+ return serial(dict(status='PASS_BANKED_FIVE_STAGE_P10_EXACT_MOMENTS_AND_OUTER47',mathematics=dict(bit_profile=bp,complex_profile=cp,bit_coarse=s,bit_root=c,bit_root_moment_interval=bm,complex_coarse=b,complex_coarse_without_fallback=supplier['coarse_without_fallback'],complex_leaf_cap=cap,bit_moment_interval=sm,complex_moment_interval=cm,next_complex_grid_excluded=supplier['next_grid_excluded'],next_bit_grid_excluded=nextbm,independent_base_two_pass=True,ordinary_bootstrap_chain=chain,finite_bridge=bridge,assembly=assembly,kappa=k,kappa_decimal=cost.decimal(k),kappa_scientific=format(float(k),'.15e'),binding=binding),adjacent_grid_point_rejected=True))
diff --git a/research/five-stage-p10-transcript-stages/moment.py b/research/five-stage-p10-transcript-stages/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/five-stage-p10-transcript-stages/notices/PR210-coordinated-crossover-NOTICE b/research/five-stage-p10-transcript-stages/notices/PR210-coordinated-crossover-NOTICE
new file mode 100644
index 0000000000..d08cb66ac7
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/notices/PR210-coordinated-crossover-NOTICE
@@ -0,0 +1,431 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Stopped product-ring extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The opposite-bank generic projector factorization, componentwise atom-ring
+adapters, stopped recurrence and outer ordinary-interchange conversion,
+aligned pair-star producer with rational centers, exact denominator-21
+grid and selected (23,23)/(24,24) composition are contributed by icekylinx
+with substantial OpenAI GPT-6 Astra and Codex assistance. This extension
+builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is
+integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37.
+
+The retained ordinary leaf uses the preceding projector, corner and
+copied-center proofs. The selected two-stage topology retains Aurel Prosz
+(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly
+retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching,
+original source notices and each imported license remain unchanged.
+
+Partial-gauge extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The pair-first cube assembly, compatible backward frame enlargement,
+partial source-gauge schedule and stopped whole-projector composition are
+contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834.
+
+The physical deferred bit word, reflected event accounting, fan-order
+clarification and signed two-stage endpoint are adopted from Zhihao Chen
+(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with
+Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen
+witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38,
+with the original Claude disclosure retained. Cyclic interval and core-aware
+pair primitives build on Avi Eisenberg (ikeboy), PR #62,
+ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance.
+Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and
+precision credits remain in force. Imported source notices and licenses
+are preserved under references/partial-gauge/; see SOURCES.json.
+
+Three-stage cover extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry,
+weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring
+fallback, uniform batching, internal row borrowing and exact composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This
+repository integration uses Codex assistance and extends
+PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86.
+
+The selected local complex DAG and support/label replay are adopted from
+Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf,
+with its original Apache-2.0 terms and Claude assistance disclosure.
+The unchanged bit physical word retains Zhihao Chen (jacklightChen),
+PR #97, and Swapnil Jain's underlying witness and assistance notices.
+The prior opposite-bank, stopped ordinary-leaf, copied-center, topology,
+semantic/bulk, precision and analytic credits remain applicable.
+Original source notices and license bytes are preserved in
+references/three-stage-cover/pr117/ and references/partial-gauge/.
+
+Paired-cube and shared-core extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The paired-coordinate triple-cube identity, signed overlap channels,
+original-source involution, coordinate-star centers, concrete frame/carrier
+compiler, chronological source gauges, PR97 gauge-subset selection,
+orthogonal cross-stage routing and exact supplier/assembly integration
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance.
+Repository integration uses Codex assistance and extends PR #130 at
+6a9970a530119174507904e23592fd59ede19a5d.
+
+The substantial completed-core workspace-sharing principle is credited to
+an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported
+OpenAI Codex assistance. No source code, partition or serialized witness
+from that PR is imported. The new routing and paired-motif integration
+are described separately and claim no exclusive priority for broad sharing,
+paired-coordinate, Fourier or carrier-matching ideas.
+
+Selected coarse queries restrict the retained eumemic PR #117 positive DAG;
+its original Apache-2.0 and Claude assistance notices remain unchanged.
+The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil
+Jain's frozen witness, notices and historical assistance disclosures.
+Earlier generalized Clifford, three-stage, uniform weighted recursion,
+ordinary-leaf, semantic/bulk, precision and analytic credits remain in force.
+Source-specific license bytes are preserved under references/.
+
+Source-assisted common-frame extension (2026-10-09)
+Copyright 2026 icekylinx. Apache-2.0.
+Research construction and local certificates: OpenAI GPT-6 Astra assistance.
+Repository integration and independent complex scalar replay: Codex assistance.
+Substantial dependency: eumemic PR168, fd25adb7fbaa12ee761d02c733c54d1d2a7687ee;
+its byte-preserved sources, licenses and original Claude assistance disclosure
+are retained in research/source-assisted/public/pr168_fd25adb7.tar.gz.
+Additional inherited contributions are recorded in research/source-assisted/CREDITS.md.
+The new work concerns source-assisted invertible common-frame lifts, controlled
+affine cleanup and compatible zero-fresh reuse; no exclusive claim is made for
+broad register reuse, paired cubes, frame theory or ordinary linear elimination.
+
+Fourth finite bootstrap refinement (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+This arithmetic refinement builds on PR207 at
+cd14825023b75af4f5919a30e5e6d548b6ade5bc by adding one finite ordinary-leaf
+level. The 302 frame overrides, completed banks, scalar words and upstream
+assistance disclosures are inherited, not newly attributed to this work.
+The Apache-2.0 license and all preceding notices remain applicable.
+
+PR211 plateau frame refinement (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+The additional seven equal-frame component moves build directly on Rohan
+Arun's PR211 cascade witness at c63e50a5dde96fe1459d6b29e55e47f42f104347,
+prepared with Anthropic Claude assistance. Its original notice is preserved
+byte-for-byte in search/PR211-NOTICE. The offline certificate package and
+independent stage-private bank admission derive from Dugongue's PR207 at
+cd14825023b75af4f5919a30e5e6d548b6ade5bc. Original contributor notices,
+licenses, source pins and all upstream AI disclosures remain applicable.
+
+The final refinement also includes seeded bidirectional cascade search after
+the seven initial component moves. Exact canonical subspace comparison
+records 274 changed operations beyond PR211. Search, integration and replay
+were prepared with substantial OpenAI Codex assistance.
+
+Shared rank-18 gauges and two donor substitutions (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+The new actual gauge/read chronology, gauged-donor handoff, shared target
+transitions, rank6 residual banks and donor substitutions extend the same
+PR200/PR211 word and PR207/PR197 completed-bank framework. All original
+licenses, notices, authorship and upstream AI disclosures remain in force.
+
+Nested-gauge extension: three rank-19 physical entrances compose with thirteen shared rank-18 entrances; all target transitions and mixed4/5/6/24 banks are explicit. Prepared by eumemic with substantial OpenAI Codex assistance. All retained authorship, licenses and AI disclosures remain applicable.
diff --git a/research/five-stage-p10-transcript-stages/notices/PR230-NOTICE b/research/five-stage-p10-transcript-stages/notices/PR230-NOTICE
new file mode 100644
index 0000000000..bc1cfc52a1
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/notices/PR230-NOTICE
@@ -0,0 +1,441 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Stopped product-ring extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The opposite-bank generic projector factorization, componentwise atom-ring
+adapters, stopped recurrence and outer ordinary-interchange conversion,
+aligned pair-star producer with rational centers, exact denominator-21
+grid and selected (23,23)/(24,24) composition are contributed by icekylinx
+with substantial OpenAI GPT-6 Astra and Codex assistance. This extension
+builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is
+integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37.
+
+The retained ordinary leaf uses the preceding projector, corner and
+copied-center proofs. The selected two-stage topology retains Aurel Prosz
+(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly
+retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching,
+original source notices and each imported license remain unchanged.
+
+Partial-gauge extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The pair-first cube assembly, compatible backward frame enlargement,
+partial source-gauge schedule and stopped whole-projector composition are
+contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834.
+
+The physical deferred bit word, reflected event accounting, fan-order
+clarification and signed two-stage endpoint are adopted from Zhihao Chen
+(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with
+Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen
+witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38,
+with the original Claude disclosure retained. Cyclic interval and core-aware
+pair primitives build on Avi Eisenberg (ikeboy), PR #62,
+ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance.
+Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and
+precision credits remain in force. Imported source notices and licenses
+are preserved under references/partial-gauge/; see SOURCES.json.
+
+Three-stage cover extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry,
+weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring
+fallback, uniform batching, internal row borrowing and exact composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This
+repository integration uses Codex assistance and extends
+PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86.
+
+The selected local complex DAG and support/label replay are adopted from
+Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf,
+with its original Apache-2.0 terms and Claude assistance disclosure.
+The unchanged bit physical word retains Zhihao Chen (jacklightChen),
+PR #97, and Swapnil Jain's underlying witness and assistance notices.
+The prior opposite-bank, stopped ordinary-leaf, copied-center, topology,
+semantic/bulk, precision and analytic credits remain applicable.
+Original source notices and license bytes are preserved in
+references/three-stage-cover/pr117/ and references/partial-gauge/.
+
+Paired-cube and shared-core extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The paired-coordinate triple-cube identity, signed overlap channels,
+original-source involution, coordinate-star centers, concrete frame/carrier
+compiler, chronological source gauges, PR97 gauge-subset selection,
+orthogonal cross-stage routing and exact supplier/assembly integration
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance.
+Repository integration uses Codex assistance and extends PR #130 at
+6a9970a530119174507904e23592fd59ede19a5d.
+
+The substantial completed-core workspace-sharing principle is credited to
+an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported
+OpenAI Codex assistance. No source code, partition or serialized witness
+from that PR is imported. The new routing and paired-motif integration
+are described separately and claim no exclusive priority for broad sharing,
+paired-coordinate, Fourier or carrier-matching ideas.
+
+Selected coarse queries restrict the retained eumemic PR #117 positive DAG;
+its original Apache-2.0 and Claude assistance notices remain unchanged.
+The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil
+Jain's frozen witness, notices and historical assistance disclosures.
+Earlier generalized Clifford, three-stage, uniform weighted recursion,
+ordinary-leaf, semantic/bulk, precision and analytic credits remain in force.
+Source-specific license bytes are preserved under references/.
+
+Source-assisted common-frame extension (2026-10-09)
+Copyright 2026 icekylinx. Apache-2.0.
+Research construction and local certificates: OpenAI GPT-6 Astra assistance.
+Repository integration and independent complex scalar replay: Codex assistance.
+Substantial dependency: eumemic PR168, fd25adb7fbaa12ee761d02c733c54d1d2a7687ee;
+its byte-preserved sources, licenses and original Claude assistance disclosure
+are retained in research/source-assisted/public/pr168_fd25adb7.tar.gz.
+Additional inherited contributions are recorded in research/source-assisted/CREDITS.md.
+The new work concerns source-assisted invertible common-frame lifts, controlled
+affine cleanup and compatible zero-fresh reuse; no exclusive claim is made for
+broad register reuse, paired cubes, frame theory or ordinary linear elimination.
+
+Fourth finite bootstrap refinement (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+This arithmetic refinement builds on PR207 at
+cd14825023b75af4f5919a30e5e6d548b6ade5bc by adding one finite ordinary-leaf
+level. The 302 frame overrides, completed banks, scalar words and upstream
+assistance disclosures are inherited, not newly attributed to this work.
+The Apache-2.0 license and all preceding notices remain applicable.
+
+PR211 plateau frame refinement (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+The additional seven equal-frame component moves build directly on Rohan
+Arun's PR211 cascade witness at c63e50a5dde96fe1459d6b29e55e47f42f104347,
+prepared with Anthropic Claude assistance. Its original notice is preserved
+byte-for-byte in search/PR211-NOTICE. The offline certificate package and
+independent stage-private bank admission derive from Dugongue's PR207 at
+cd14825023b75af4f5919a30e5e6d548b6ade5bc. Original contributor notices,
+licenses, source pins and all upstream AI disclosures remain applicable.
+
+The final refinement also includes seeded bidirectional cascade search after
+the seven initial component moves. Exact canonical subspace comparison
+records 274 changed operations beyond PR211. Search, integration and replay
+were prepared with substantial OpenAI Codex assistance.
+
+Shared rank-18 gauges and two donor substitutions (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+The new actual gauge/read chronology, gauged-donor handoff, shared target
+transitions, rank6 residual banks and donor substitutions extend the same
+PR200/PR211 word and PR207/PR197 completed-bank framework. All original
+licenses, notices, authorship and upstream AI disclosures remain in force.
+
+Nested-gauge extension: three rank-19 physical entrances compose with thirteen shared rank-18 entrances; all target transitions and mixed4/5/6/24 banks are explicit. Prepared by eumemic with substantial OpenAI Codex assistance. All retained authorship, licenses and AI disclosures remain applicable.
+
+Equal-frame plateau refinement on PR210's 471-source word (2026-10-10)
+Prepared by sennemmi with substantial OpenAI Codex assistance. The deterministic
+frame search, 19 operation retimings, exact price update and repository
+integration extend eumemic's PR210 head
+df95878d11190518e45ef9717c9ee05011f88ace. They do not claim the inherited
+source word, shared gauges, completed banks or upstream proof framework.
+All PR200, PR197, PR202/193, PR207, PR211, PR216 and PR210 attributions,
+licenses and AI disclosures remain in force; the repository's Apache-2.0
+license is unchanged.
diff --git a/research/five-stage-p10-transcript-stages/notices/PR230-PROVENANCE.json b/research/five-stage-p10-transcript-stages/notices/PR230-PROVENANCE.json
new file mode 100644
index 0000000000..ff39579387
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/notices/PR230-PROVENANCE.json
@@ -0,0 +1,27 @@
+{
+  "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/230",
+  "author": "sennemmi",
+  "assistance": "Substantial OpenAI Codex assistance, as disclosed by the original contributor.",
+  "imported_head": "fee4c05b91d4cdebc0b9d8cbb266a98069928a9a",
+  "scope": "Nineteen operation-frame changes inherited from the independently verified492-source composition and replayed with493sourcealiases,82equal-response groups,seven integer-response groups andfour signed echelon groups. Original search,result,framewitness andnotice remain byte-preserved.",
+  "original_files": {
+    "NOTICE": "7dfbad087ee49b74fd5075d517eaa263c5dd3d4fbd4c69bfba34ee1cb55e837f",
+    "joint-plateau-result-prdf958.json": "cd5731260af0daa62952c3b82debdb26cfb79e62a5c615688d8ccac6f7a95fcc",
+    "joint-plateau-search-prdf958.py": "80f3f9e8ba1972b911b701a4de4f811d6d25c9b4c0bc6282d640c2f44caafd0d",
+    "opframe-bases.json": "387ae1b5e69004426d094f4947b29c532d60fdf31f727f5e8830468278fe0f92"
+  },
+  "final_frame_sha256": "9a2bba5c72aebc9ee4f21e59b10ce810b2da98a1fa1748fbc44c50a080e584ff",
+  "raw_child_delta": {
+    "1": -27,
+    "2": -36,
+    "3": 51,
+    "4": -30,
+    "7": 30,
+    "8": -15,
+    "9": -15,
+    "10": 24,
+    "11": -24,
+    "12": 30,
+    "15": -15
+  }
+}
diff --git a/research/five-stage-p10-transcript-stages/notices/README.md b/research/five-stage-p10-transcript-stages/notices/README.md
new file mode 100644
index 0000000000..5a8ac3990a
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/notices/README.md
@@ -0,0 +1,15 @@
+# Retained upstream notices
+
+These notices are retained verbatim from eumemic's source527 package. They carry the contributor credits and
+AI-assistance disclosures for the package machinery reused here: the scalar program, emitters, parity fusion,
+census, banks, and the moment, prime and finite checks.
+
+| File | Origin |
+| --- | --- |
+| `source527-loader-NOTICE.md` | source527's source loader |
+| `PR230-NOTICE`, `PR230-PROVENANCE.json` | sennemmi's PR230 operation-frame witnesses, including the PR211 and PR216/207 lineage |
+| `base-bit-PR200-PR202-NOTICE` | Chafik Boukhalfa's PR200/PR202 base bit package |
+| `PR210-coordinated-crossover-NOTICE` | eumemic's PR210 coordinated-crossover package |
+
+The source471/source527 helper data they describe is not used by the p = 10 word. The notices are kept for the
+inherited code and attribution.
diff --git a/research/five-stage-p10-transcript-stages/notices/base-bit-PR200-PR202-NOTICE b/research/five-stage-p10-transcript-stages/notices/base-bit-PR200-PR202-NOTICE
new file mode 100644
index 0000000000..ba5ea80dd7
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/notices/base-bit-PR200-PR202-NOTICE
@@ -0,0 +1,399 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Stopped product-ring extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The opposite-bank generic projector factorization, componentwise atom-ring
+adapters, stopped recurrence and outer ordinary-interchange conversion,
+aligned pair-star producer with rational centers, exact denominator-21
+grid and selected (23,23)/(24,24) composition are contributed by icekylinx
+with substantial OpenAI GPT-6 Astra and Codex assistance. This extension
+builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is
+integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37.
+
+The retained ordinary leaf uses the preceding projector, corner and
+copied-center proofs. The selected two-stage topology retains Aurel Prosz
+(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly
+retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching,
+original source notices and each imported license remain unchanged.
+
+Partial-gauge extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The pair-first cube assembly, compatible backward frame enlargement,
+partial source-gauge schedule and stopped whole-projector composition are
+contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834.
+
+The physical deferred bit word, reflected event accounting, fan-order
+clarification and signed two-stage endpoint are adopted from Zhihao Chen
+(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with
+Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen
+witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38,
+with the original Claude disclosure retained. Cyclic interval and core-aware
+pair primitives build on Avi Eisenberg (ikeboy), PR #62,
+ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance.
+Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and
+precision credits remain in force. Imported source notices and licenses
+are preserved under references/partial-gauge/; see SOURCES.json.
+
+Three-stage cover extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry,
+weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring
+fallback, uniform batching, internal row borrowing and exact composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This
+repository integration uses Codex assistance and extends
+PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86.
+
+The selected local complex DAG and support/label replay are adopted from
+Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf,
+with its original Apache-2.0 terms and Claude assistance disclosure.
+The unchanged bit physical word retains Zhihao Chen (jacklightChen),
+PR #97, and Swapnil Jain's underlying witness and assistance notices.
+The prior opposite-bank, stopped ordinary-leaf, copied-center, topology,
+semantic/bulk, precision and analytic credits remain applicable.
+Original source notices and license bytes are preserved in
+references/three-stage-cover/pr117/ and references/partial-gauge/.
+
+Paired-cube and shared-core extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The paired-coordinate triple-cube identity, signed overlap channels,
+original-source involution, coordinate-star centers, concrete frame/carrier
+compiler, chronological source gauges, PR97 gauge-subset selection,
+orthogonal cross-stage routing and exact supplier/assembly integration
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance.
+Repository integration uses Codex assistance and extends PR #130 at
+6a9970a530119174507904e23592fd59ede19a5d.
+
+The substantial completed-core workspace-sharing principle is credited to
+an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported
+OpenAI Codex assistance. No source code, partition or serialized witness
+from that PR is imported. The new routing and paired-motif integration
+are described separately and claim no exclusive priority for broad sharing,
+paired-coordinate, Fourier or carrier-matching ideas.
+
+Selected coarse queries restrict the retained eumemic PR #117 positive DAG;
+its original Apache-2.0 and Claude assistance notices remain unchanged.
+The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil
+Jain's frozen witness, notices and historical assistance disclosures.
+Earlier generalized Clifford, three-stage, uniform weighted recursion,
+ordinary-leaf, semantic/bulk, precision and analytic credits remain in force.
+Source-specific license bytes are preserved under references/.
+
+Source-assisted common-frame extension (2026-10-09)
+Copyright 2026 icekylinx. Apache-2.0.
+Research construction and local certificates: OpenAI GPT-6 Astra assistance.
+Repository integration and independent complex scalar replay: Codex assistance.
+Substantial dependency: eumemic PR168, fd25adb7fbaa12ee761d02c733c54d1d2a7687ee;
+its byte-preserved sources, licenses and original Claude assistance disclosure
+are retained in research/source-assisted/public/pr168_fd25adb7.tar.gz.
+Additional inherited contributions are recorded in research/source-assisted/CREDITS.md.
+The new work concerns source-assisted invertible common-frame lifts, controlled
+affine cleanup and compatible zero-fresh reuse; no exclusive claim is made for
+broad register reuse, paired cubes, frame theory or ordinary linear elimination.
diff --git a/research/five-stage-p10-transcript-stages/notices/source527-loader-NOTICE.md b/research/five-stage-p10-transcript-stages/notices/source527-loader-NOTICE.md
new file mode 100644
index 0000000000..47090d6e93
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/notices/source527-loader-NOTICE.md
@@ -0,0 +1,11 @@
+# Attribution
+
+This focused preparation adapter is distributed under Apache-2.0. It preserves the original source files, headers and notices in the supplied source roots.
+
+- eumemic: the current PR210 operation frames, joint gauges, donor assignments, source borrowing and retimed source471 schedule at df95878d11190518e45ef9717c9ee05011f88ace; original OpenAI Codex assistance disclosure retained.
+- Chafik Boukhalfa (chafreaky): the PR200 physical bit construction and terminal interfaces, carried by the consumed PR202 base at 8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d.
+- Rohan Arun, Dugongue, evmckinney9, icekylinx, James Chang, eumemic, Douglas Colkitt, OpenAI, and preceding contributors retain the attribution and assistance disclosures recorded in the supplied original notices.
+
+The new contribution here is the explicit public-root binding, source-derived terminal records, exact semantic comparison and independent raw-path recount. It does not claim authorship of the inherited helper, frames, compiler or theorem interfaces, nor review or endorsement by the named contributors.
+
+Assisted with ChatGPT.
diff --git a/research/five-stage-p10-transcript-stages/outer.py b/research/five-stage-p10-transcript-stages/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/five-stage-p10-transcript-stages/parity_transform.py b/research/five-stage-p10-transcript-stages/parity_transform.py
new file mode 100644
index 0000000000..c9e688b54c
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/parity_transform.py
@@ -0,0 +1,146 @@
+"""F2 payload identity elision and exact nested address-MOVE fusion.
+The inherited signed source decoder is retained as producer evidence.
+All odd-prime address projectors and routes remain unchanged.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+p = 10 port (DreamingOfClouds, Anthropic Claude assistance): h, copies and scatter reads from word_pins.shape,
+word counts pinned in word-pins.json; the unused-stream census ranges over the actual 2v+R streams.
+"""
+from array import array
+from collections import Counter
+from pathlib import Path
+import gzip,hashlib,json,time
+from word_pins import expect,shape
+if not __debug__:raise SystemExit('assertions required')
+
+def transform(records, nstreams):
+    out = array('i')
+    pending = {}
+    chains = []
+    removed = Counter()
+    hist = Counter()
+    merged = 0
+    maxchain = 0
+    uses = Counter()
+
+    def flush(a):
+        nonlocal merged, maxchain
+        if a in pending:
+            old, new, rank, count, first, last = pending.pop(a)
+            if rank:
+                hist[rank] += 1
+            out.extend((0, a, old, new, rank, 0))
+            merged += count - 1
+            maxchain = max(maxchain, count)
+            if count > 1:
+                chains.append(dict(stream=a, old=old, new=new, rank=rank, moves=count, first=first, last=last))
+    for index in range(0, len(records), 6):
+        op, a, b, c, f, z = records[index:index + 6]
+        if op == 1 and c % 2 == 0:
+            removed[c] += 1
+            continue
+        if op == 0:
+            assert z == 0
+            if a in pending:
+                old, prev, rank, count, first, last = pending[a]
+                assert prev == b, ('disconnected movechain', a, prev, b)
+                pending[a] = (old, c, rank + f, count + 1, first, index // 6)
+            else:
+                pending[a] = (b, c, f, 1, index // 6, index // 6)
+            continue
+        assert op in (1, 2, 3)
+        flush(a)
+        flush(b)
+        if op == 1:
+            uses[a] += 1
+            uses[b] += 1
+        elif op == 2:
+            hist[z] += 1
+            uses[a] += 1
+            uses[b] += 1
+        out.extend((op, a, b, c, f, z))
+    for a in sorted(pending):
+        flush(a)
+    return (out, dict(removed_even_adds=dict(removed), removed_even_add_count=sum(removed.values()), merged_move_count=merged, max_chain=maxchain, fused_chains=len(chains), paid_histogram=dict(sorted(hist.items())), paid_calls=sum(hist.values()), paid_rank_mass=sum((r * n for r, n in hist.items())), surviving_additions=sum((out[k] == 1 for k in range(0, len(out), 6))), output_records=len(out) // 6, unused_streams=[i for i in range(nstreams) if not uses[i]], stream_use_counts=dict(uses)), chains)
+
+def run(producer,output_dir=None):
+    begun=time.monotonic();W,C=producer['W'],producer['C'];v=W.v;S=shape();h=W.h;assert h==S['h'] and v==S['v'];n=2*v+len(producer['context']['regs'])
+    old=producer['records'];out,stats,chains=transform(old,n);oldmeta=producer['physical']
+    expect('removed_even_adds',stats['removed_even_add_count']);expect('surviving_additions',stats['surviving_additions'])
+    expect('local_paid_rank_mass',stats['paid_rank_mass']);assert stats['merged_move_count']==0
+    initial=producer['initial_state'];ZERO,FULL=producer['ZERO'],producer['FULL']
+    # Independent required-frame census: ignore all original MOVE instructions.
+    # Use only surviving gate operands, copy sources and mathematical endpoints.
+    needs={i:[] for i in initial};copies=Counter();copy=None
+    for k in range(0,len(old),6):
+        op,a,b,c,f,z=old[k:k+6]
+        if op==1 and c%2:
+            needs[a].append(f)
+            if b!=n:needs[b].append(f)
+            else:assert copy is not None
+        elif op==2:
+            assert copy is None;copy=(a,b,c);needs[a].append(c);copies[z]+=1
+        elif op==3:assert copy==(a,b,c);copy=None
+    assert copy is None and copies=={S['center_rank']:S['centers']}
+    final={i:FULL for i in initial}
+    for t in range(v):final[v+t]=W.register(W.module.kernel([C.cov[t]],W.h)[0])
+    census=Counter(copies);per_role={};pairs=set()
+    for i,oldf in initial.items():
+        H=Counter()
+        for f in needs[i]+[final[i]]:
+            assert C.sub(oldf,f);rank=C.dimf[f]-C.dimf[oldf]
+            if rank:H[rank]+=1
+            pairs.add((oldf,f));oldf=f
+        per_role[i]=H;census.update(H)
+    assert census==Counter({int(r):c for r,c in stats['paid_histogram'].items()})
+    # Read back the actual annihilator rows as a separate reflected ledger.
+    # A(new) annihilating B(old) states new^perp <= old^perp exactly.
+    reflected_pairs=0;endpoint_frames={f for pair in pairs for f in pair};nondeg_bases=set()
+    for f in endpoint_frames:
+        assert len(C.B[f])==C.dimf[f] and len(C.A[f])+C.dimf[f]==h
+        key=tuple(map(tuple,C.B[f]))
+        if key not in nondeg_bases:
+            assert C.nondeg(f),'singular required endpoint frame'
+            nondeg_bases.add(key)
+    for oldf,newf in sorted(pairs):
+        assert len(C.A[newf])<=len(C.A[oldf])
+        assert all(W.module.dot(a,b)==0 for a in C.A[newf]for b in C.B[oldf])
+        reflected_pairs+=1
+    # Validate the actual transformed instruction stream against its own frames.
+    state=dict(initial);copy=None;used=set(initial.values());hist=Counter();cat=Counter();coeff=Counter();centers=[];count=0
+    scalar=hashlib.sha256();tagged=hashlib.sha256();category_names=oldmeta['category_names']
+    def event(d,row):d.update(json.dumps(row,separators=(',',':')).encode());d.update(b'\n')
+    for k in range(0,len(out),6):
+        op,a,b,c,f,z=out[k:k+6]
+        if op==0:
+            assert state[a]==b and C.sub(b,c) and C.dimf[c]-C.dimf[b]==f
+            # Complement reflection reverses containment and preserves the gap.
+            assert (h-C.dimf[b])-(h-C.dimf[c])==f
+            state[a]=c;used.update((b,c))
+            if f:hist[f]+=1
+        elif op==1:
+            assert c%2 and state[a]==state[b]==f and a!=b
+            kind=category_names[z];source=copy['source']if b==n else b
+            event(scalar,[a,source,c]);event(tagged,[a,b,c,f,kind]);count+=1;cat[kind]+=1;coeff[abs(c)]+=1;used.add(f)
+        elif op==2:
+            assert copy is None and b==n and state[a]==c and f==ZERO and z==S['center_rank']
+            state[b]=f;hist[z]+=1;copy=dict(source=a,frame=c,rank=z,temporary=b,first_event=count,copy_output_frame=f)
+        else:
+            assert op==3 and copy is not None and (a,b,c)==(copy['source'],copy['temporary'],copy['frame']) and state[b]==f==ZERO
+            copy.update(after_event=count,scatter_reads=count-copy['first_event']);assert copy['scatter_reads']==S['scatter_reads']
+            centers.append(copy);copy=None;del state[b]
+    assert copy is None and state==final and hist==census
+    assert count==expect('surviving_additions',count) and coeff==expect('surviving_coefficients',dict(coeff)) and len(centers)==S['centers']
+    delta=Counter(hist);delta.subtract(Counter({int(r):c for r,c in oldmeta['paid_histogram'].items()}));delta={r:c for r,c in delta.items()if c}
+    assert delta=={}
+    sourceH=Counter();targetH=Counter();internalH=Counter(copies)
+    for i,H in per_role.items():(sourceH if i<v else targetH if i<2*v else internalH).update(H)
+    receipt=dict(status='PASS_FRESH_PARITY_FUSION_AND_INDEPENDENT_REQUIRED_FRAME_CENSUS',removed_even_add_count=stats['removed_even_add_count'],remaining_payload_additions=count,merged_moves=stats['merged_move_count'],chains=chains,local_histogram_delta=delta,both_reflected_ledgers=True,unchanged_all_input_output_frames=True,unique_required_frame_pairs=len(pairs),explicit_reflected_annihilator_pairs=reflected_pairs,nondegenerate_endpoint_bases=len(nondeg_bases),source_histogram=dict(sourceH),target_histogram=dict(targetH),internal_histogram_including_copies=dict(internalH),copied_center_histogram=dict(copies),producer_scalar_sha256=oldmeta['scalar_projection_sha256'],producer_tagged_sha256=oldmeta['tagged_scalar_sha256'],transform_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest())
+    meta=dict(oldmeta);meta.update(status='PASS_PHYSICAL_P10_PARITY_FUSED_EXACT_FRAME_AND_SCALAR_PROJECTION',scalar_projection_sha256=scalar.hexdigest(),tagged_scalar_sha256=tagged.hexdigest(),weighted_scalar_events=count,coefficient_histogram=dict(coeff),categories=dict(cat),copied_center_blocks=centers,paid_histogram=dict(sorted(hist.items())),paid_rank_mass=sum(r*c for r,c in hist.items()),positive_rank_moves=sum(hist.values())-S['centers'],used_frames=[dict(frame_id=f,dimension=C.dimf[f],basis_sha256=hashlib.sha256(json.dumps(C.B[f],separators=(',',':')).encode()).hexdigest())for f in sorted(used)],parity_transform=receipt,producer_physical_emitter_sha256=oldmeta['physical_emitter_sha256'],physical_emitter_sha256=receipt['transform_sha256'])
+    result=dict(producer);result.update(records=out,physical=meta,result=meta,producer_physical=oldmeta,parity_census=receipt)
+    if output_dir is not None:
+        p=Path(output_dir);p.mkdir(parents=True,exist_ok=True)
+        (p/'records.bin.gz').write_bytes(gzip.compress(out.tobytes(),mtime=0))
+        (p/'physical.json').write_text(json.dumps(meta,indent=2)+'\n')
+        (p/'parity.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    print('PASS parity fusion',count,'ADDs',len(out)//6,'records',flush=True)
+    return result
diff --git a/research/five-stage-p10-transcript-stages/portable_bit.py b/research/five-stage-p10-transcript-stages/portable_bit.py
new file mode 100644
index 0000000000..e03029be32
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/portable_bit.py
@@ -0,0 +1,95 @@
+"""Fresh p = 10 local physical and complete five-stage global lowering (source527 integration, rebound).
+
+Inherited source-bound PR234 lowering, integrated with source527 using
+substantial OpenAI Codex assistance. Cover expansion is phase-major.
+"""
+from pathlib import Path
+import hashlib,importlib.util,sys,time,json
+sys.dont_write_bytecode=True
+if not __debug__:raise SystemExit('assertions required')
+HERE=Path(__file__).resolve().parent
+
+def load(name,path):
+ spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);sys.modules[name]=m;spec.loader.exec_module(m);return m
+
+def phase_major_templates(lower):
+ """Expand all cover classes for each yielded phase before advancing."""
+ for stage in range(5):
+  yield('helper',stage,lambda s=stage:lower.iter_stage(s))
+  if stage in(1,2,4):
+   i={1:0,2:1,4:2}[stage]
+   yield('idle',i,lambda i=i:lower.iter_idle(i))
+   yield('bridge',i,lambda i=i:lower.iter_bridges(i))
+ yield('completion',0,lower.iter_completions)
+ yield('terminal_exchange',0,lower.iter_exchanges)
+
+# Transcript stages, in order (each binds to the exact output word of the previous one). A second descent and a
+# second reorder round were searched on this word and found nothing (discovery/README.md), so they are not stages.
+STAGES=('descent','target','kernel','restore','sink','reorder')
+
+def completion_census(run):
+ """Five-stage completion rank per independent entrance: dim(sigma) + h - dim(endpoint) (endpoint FULL unless restored early)."""
+ from collections import Counter
+ C=run['C'];W=run['W'];v=W.v;regs=run['context']['regs'];init=run['initial_state'];ends=run.get('helper_endpoints',{});H=Counter()
+ for j in range(len(regs)):
+  s=2*v+j;a=C.dimf[init[s]]
+  if s in ends:assert a and C.sub(init[s],ends[s])
+  if a:H[a+W.h-C.dimf[ends.get(s,run["FULL"])]]+=1
+ return H
+
+def run(prepared_context=None,raw=None,output_dir=None,run_geometry=True,package_root=None):
+ begun=time.monotonic();package=Path(package_root or HERE).resolve()
+ if prepared_context is None:prepared_context=load('portable527_prepare',package/'prepare.py').prepare()
+ if raw is None:raw=load('portable527_raw_ledger',package/'raw_ledger.py').run(prepared_context)
+ physical_module=load('portable527_physical',package/'code/physical527.py')
+ context=dict(prepared_context);source=context['SOURCE_TEXT']
+ producer_output=Path(output_dir)/'producer-bit' if output_dir is not None else None
+ producer=physical_module.run(context,source,output_dir=producer_output)
+ physical_run=load('portable527_parity',package/'parity_transform.py').run(producer,output_dir=output_dir)
+ raw=load('portable527_parity_raw',package/'raw_ledger.py').rebind_parity(raw,physical_run['parity_census'])
+ for name in STAGES:
+  if name=='descent':
+   physical_run=load('portable527_descent',package/'descent_transform.py').run(physical_run,output_dir=output_dir)
+   raw=load('portable527_descent_raw',package/'raw_ledger.py').rebind_descent(raw,physical_run['descent_census'])
+  elif name=='target':
+   targetmod=load('portable527_target',package/'target_transform.py');physical_run=targetmod.run(physical_run,output_dir=output_dir)
+   raw=targetmod.rebind(raw,physical_run['target_census'])
+  elif name=='kernel':
+   physical_run=load('portable527_kernel',package/'kernel_transform.py').run(physical_run,output_dir=output_dir)
+   raw=load('portable527_kernel_raw',package/'raw_ledger.py').rebind_kernel(raw,physical_run['kernel_census'])
+  elif name=='restore':
+   physical_run=load('portable527_restore',package/'restore_transform.py').run(physical_run,output_dir=output_dir)
+   raw=load('portable527_restore_raw',package/'raw_ledger.py').rebind_restore(raw,physical_run['restore_census'],completion_census(physical_run))
+  elif name=='sink':
+   physical_run=load('portable527_sink',package/'sink_transform.py').run(physical_run,output_dir=output_dir)
+   raw=load('portable527_sink_raw',package/'raw_ledger.py').rebind_sink(raw,physical_run['sink_census'],completion_census(physical_run))
+  else:
+   assert name in('reorder','reorder2')
+   physical_run=load('portable527_reorder',package/'reorder_transform.py').run(physical_run,output_dir=output_dir,tag=name)
+   raw=load('portable527_'+name+'_raw',package/'raw_ledger.py').rebind_reorder(raw,physical_run[name+'_census'],completion_census(physical_run),name)
+ raw['transcript_stages']=list(STAGES)
+ # The global lowering binds the final register count of the emitted word (after terminal sinks).
+ from word_pins import expect
+ assert expect('final_physical_R',len(physical_run['context']['regs']))==raw['physical_R']
+ global_module=load('portable527_global',package/'code/global_lowering.py')
+ context=physical_run['context']
+ physical=physical_run['physical'];physical['source_head']=raw['source_head']
+ assert physical['source_heads']==raw['source_aliases']and physical['independent_dirty_registers']==raw['physical_R']
+ assert physical['paid_histogram']=={int(k):v for k,v in raw['one_stage_helper_histogram_including_copies'].items()}
+ assert physical['initial_independent_entrances']=={int(k):v for k,v in raw['auxiliary_entrance_rank_histogram'].items()}
+ lower=global_module.Lowerer(physical_run['records'],physical_run);global_result=global_module.verify(lower,raw)
+ assert global_result['paid_histogram']=={int(k):v for k,v in raw['five_stage_profile']['histogram'].items()}
+ global_result.update(source_head=raw['source_head'],scalar_projection_sha256=physical['scalar_projection_sha256'],local_tagged_sha256=physical['tagged_scalar_sha256'],weighted_stage_additions=global_result['opcode_counts'][global_module.ADD],bridge_additions=global_result['opcode_counts'][global_module.BRIDGE],total_weighted_additions=global_result['opcode_counts'][global_module.ADD]+global_result['opcode_counts'][global_module.BRIDGE],m=global_module.M,global_live=global_module.LIVE,external_work_family=global_module.WORK)
+ phases=[(name,index)for name,index,method in phase_major_templates(lower)]
+ assert phases==[('helper',0),('helper',1),('idle',0),('bridge',0),('helper',2),('idle',1),('bridge',1),('helper',3),('helper',4),('idle',2),('bridge',2),('completion',0),('terminal_exchange',0)]
+ geometry=None
+ if run_geometry:geometry=load('portable527_geometry',package/'code/geometry527.py').run(context,global_module)
+ result=dict(context=context,helper_endpoints=physical_run.get('helper_endpoints',{}),**{name+'_census':physical_run[name+'_census']for name in STAGES},W=context['W'],C=context['C'],records=physical_run['records'],lower=lower,raw=raw,physical=physical,global_result=global_result,geometry=geometry,phase_major_schedule=phases,scalar_observer_result=physical_run['scalar_result'],kernel_entrances=physical_run.get('kernel_entrances',[]),seconds=time.monotonic()-begun)
+ if output_dir is not None:
+  out=Path(output_dir);out.mkdir(parents=True,exist_ok=True)
+  for name in('physical','global_result','geometry','raw'):
+   if result[name]is not None:(out/(name+'.json')).write_text(json.dumps(result[name],indent=2)+'\n')
+ return result
+
+def summary(result):
+ return dict(status='PASS_PORTABLE_P10_FRESH_PHYSICAL_GLOBAL_AND_GEOMETRY',source_head=result['raw']['source_head'],local_record_count=len(result['records'])//6,scalar_projection_sha256=result['physical']['scalar_projection_sha256'],physical_tagged_sha256=result['physical']['tagged_scalar_sha256'],global_result=result['global_result'],geometry=result['geometry'],phase_major_schedule=result['phase_major_schedule'],seconds=result['seconds'])
diff --git a/research/five-stage-p10-transcript-stages/portable_complex.py b/research/five-stage-p10-transcript-stages/portable_complex.py
new file mode 100644
index 0000000000..7594dc70fe
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/portable_complex.py
@@ -0,0 +1,155 @@
+#!/usr/bin/env python3
+"""Fresh complex label, scalar, splice and finite-guard checks from primary inputs.
+No saved PASS receipts, workstation paths, network or Lean rebuild are required.
+p = 10 packages: the complex program itself is admitted by Sussman's gx.check1 with the exact scalar identity and by
+his gxcore mirror (code/complex_gx.py), added by DreamingOfClouds with Anthropic Claude assistance.
+"""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as Q
+from hashlib import sha256
+from math import prod
+from pathlib import Path
+import gzip, importlib.util, json, sys
+sys.dont_write_bytecode = True
+
+PIN='f010392c923279e3dd59ef3aa5fedad23affc5fd'
+CHRONOLOGY=['stage0','stage1','climbA','bridgeA','stage2','climbB','bridgeB','stage3','stage4','final_climbs','bridgeC','terminal_shifts','signed_exchange']
+
+def need(ok, why):
+    if not ok: raise ValueError(why)
+
+def module(root, name):
+    spec=importlib.util.spec_from_file_location('portable_'+name,root/'code'/(name+'.py'))
+    result=importlib.util.module_from_spec(spec);spec.loader.exec_module(result)
+    return result
+
+def finite_guard(m, b, basis):
+    p=m['parameters'];l=m['ledger'];dim=p['m'];R=p['R'];h=p['h'];W=p['W_live']
+    need((dim,R,h,W)==(110,9036,22,14316),'complex family changed')
+    scalar=max(b[o]['totals']['real_component_primitive_steps'] for o in ['forward','backward'])
+    macros=max(b[o]['totals']['scalar_macros'] for o in ['forward','backward'])
+    scalar5=3*b['forward']['totals']['real_component_primitive_steps']+2*b['backward']['totals']['real_component_primitive_steps']
+    physical=W+R+h+1
+    adapters=8*(macros+m['checks']['invocation_calls']+p['invocation_live']+h)+32*dim
+    outside=8*(l['idle_calls']+6*p['v']+physical)+32*dim
+    compiler=64*(dim+1)**3
+    local=scalar+adapters*compiler
+    pervertex=scalar5+12*p['v']+(5*adapters+outside)*compiler+64*physical
+    group=(1<<(dim-1+(dim//2-1)**2))*prod((1<<(2*i))-1 for i in range(1,dim//2))
+    live_stock=group*W;physical_stock=group*physical;s=group*l['rank_mass']
+    K=group*pervertex+64;router=compiler*(K+1)*(physical_stock+1)**2
+    G,E,C0=1<<30000,1<<100000,1<<210000;B=s+E
+    literal=2*G*physical_stock**2+8*s+4*physical_stock+4+32*dim
+    need(local==234625086804828 and local<1<<48 and K<1<<6050,'fresh local/global bill')
+    need((group.bit_length(),live_stock.bit_length(),physical_stock.bit_length(),s.bit_length())==(5995,6009,6009,6016),'fresh cover/work stock')
+    need(router<G and literal<E and B<1<<100001,'fresh router/literal guard')
+    need(2*B*(dim-l['max_child'])-s-E==127*B,'completed-child induction')
+    need(32*dim*B*B<C0 and 2*B+18<C0 and 2*l['max_child']<dim,'semantic and half-shrink guard')
+    row=live_stock.bit_length()+9909+252;rowphysical=physical_stock.bit_length()+9909+252
+    need(row<=rowphysical<20161,'external rows')
+    gap=Q(10**6)-Q(51,25)*20161;need(gap>0,'row reserve gap')
+    need(2*(dim*(dim-1)+3*dim+dim+3*dim*(dim-1)//2+dim+1)+2*dim<compiler,'explicit quadratic-phase lowering')
+    for e in range(1,100001):need((e-1).bit_length()+1<=2*e,'grid-depth endpoint')
+    def validate(c):
+        need(c['physical']==c['live']+R+h+1,'missing work stock')
+        need(dim*c['live']-l['rank_mass']==l['deficit'],'wrong live normalization')
+        need(c['copy_calls']==5*h,'missing center child')
+        need(c['denominators']==[1,2,3,6],'unrecorded denominator')
+        need(physical_stock<1<<c['stock_exponent'],'false stock bound')
+    original=dict(physical=physical,live=W,copy_calls=5*h,denominators=[1,2,3,6],stock_exponent=6009)
+    validate(original);controls={}
+    for name,key,value in [('missing_tableau','physical',physical-R),('scratch_in_live','live',physical),('dropped_center','copy_calls',5*h-1),('unrecorded_divisor','denominators',[1,2,3,5,6]),('stale_stock_bound','stock_exponent',5208)]:
+        bad=dict(original);bad[key]=value
+        try:validate(bad)
+        except ValueError:controls[name]=True
+        else:raise ValueError('finite guard mutation accepted: '+name)
+    return dict(status='PASS_FRESH_EXACT_COMPLEX_GUARD',m=dim,live_per_vertex=W,physical_per_vertex=physical,
+        coefficient_denominators=[1,2,3,6],semantic_C1=1,complete_local_group_upper=local,
+        complete_local_group_bits=local.bit_length(),global_logical_groups_bits=K.bit_length(),
+        simple_global_logical_bound_exponent=6050,router_bits=router.bit_length(),G_exponent=30000,
+        literal_charge_bits=literal.bit_length(),E_exponent=100000,required_C0_bits=(32*dim*B*B).bit_length(),
+        C0_exponent=210000,induction_gap_multiple_of_B=127,group_bits=group.bit_length(),
+        live_stock_bits=live_stock.bit_length(),physical_stock_bits=physical_stock.bit_length(),
+        rank_mass_bits=s.bit_length(),live_row_coefficient=row,physical_row_overcharge_coefficient=rowphysical,
+        retained_row_coefficient=20161,retained_row_gap=str(gap),controls=controls,
+        binary_basis_count_tests=basis.gl_count_test(),
+        odd_denominator_grid='2^(-P)3^(-G(D+1)); no return rounding')
+
+def run(package_root=None, progress=lambda text:None):
+    root=Path(package_root).resolve() if package_root else Path(__file__).resolve().parent
+    labels=module(root,'complex_labels');scalar=module(root,'complex_scalars')
+    splice=module(root,'complex_splice');basis=module(root,'complex_basis')
+    pinpath=root/'inputs/complex/source-pins.json'
+    if not pinpath.is_file():pinpath=root/'inputs/complex-source-pins.json'
+    pins=json.loads(pinpath.read_text());verified={};by_upstream={}
+    for relative,spec in pins['files'].items():
+        path=root/relative;got=sha256(path.read_bytes()).hexdigest()
+        need(got==spec['sha256'],'primary proof input changed: '+relative)
+        verified[relative]=got;by_upstream[spec['upstream']]=(path,spec)
+    cp=pins['certificate'];z=(root/cp['path']).read_bytes()
+    need(sha256(z).hexdigest()==cp['compressed_sha256'],'compressed certificate binding')
+    raw=gzip.decompress(z);need(sha256(raw).hexdigest()==cp['uncompressed_sha256'],'expanded certificate binding')
+    verified[cp['path']]=sha256(z).hexdigest();c=json.loads(raw)
+    progress('Checking the complex program: gx.check1 with the exact scalar identity, and the gxcore mirror.')
+    program_check=module(root,'complex_gx').check(root,raw)
+    progress('Checking every complex source label and paid child.')
+    checks=labels.replay_label_counts(c)
+    H=Counter({int(k):5*n for k,n in checks['invocation_histogram'].items()})
+    v,R,h=c['v'],c['R'],c['h'];dim=5*h;W=4*v+R
+    for rank in [2*h-2,h-1,2*h+2,4]:H[rank]+=2*v
+    ledger=dict(histogram={str(k):n for k,n in sorted(H.items())},calls=sum(H.values()),
+        rank_mass=sum(k*n for k,n in H.items()),max_child=max(H),deficit=dim*W-sum(k*n for k,n in H.items()),
+        copy_calls=5*h,idle_calls=8*v)
+    need((ledger['calls'],ledger['rank_mass'],ledger['deficit'],ledger['max_child'])==(351820,1571680,3080,46),'fresh five-stage ledger')
+    source_path,source_spec=by_upstream['Work/GCert/Chain/NetDef.lean'];lines=source_path.read_text().splitlines();refs={}
+    for name in ['x01','y01','x12','y12','x23','y23','x34','y34','sfin','term']:
+        indices=[i for i,line in enumerate(lines) if name+' :' in line];need(indices,'missing exact matrix field '+name)
+        i=indices[-1] if name=='sfin' else indices[0]
+        text=' '.join(x.strip() for x in lines[i:i+(2 if name=='sfin' else 1)])
+        refs[name]=dict(source='Work/GCert/Chain/NetDef.lean',anchor=name+' :',line=i+1,declaration_line=text,
+            url='https://github.com/jacobalansussman/wht-power-saving-lean/blob/'+PIN+'/Work/GCert/Chain/NetDef.lean#L'+str(i+1))
+    m=dict(source_pin=PIN,parameters=dict(h=h,m=dim,v=v,R=R,W_live=W,invocation_live=2*v+R),
+        ledger=ledger,checks=checks,chronology=CHRONOLOGY,source_frame_equalities=refs)
+    progress('Deriving both complex scalar words and temporary lifetimes.')
+    A=scalar.flat(c['A']);B=scalar.flat(c['B']);b={};life={}
+    for orientation in ['forward','backward']:
+        b[orientation]=scalar.bill(scalar.inv_schedule(orientation,A,B,c))
+        life[orientation]=scalar.lifecycle(scalar.inv_schedule(orientation,A,B,c))
+    need((b['forward']['totals']['real_component_primitive_steps'],b['backward']['totals']['real_component_primitive_steps'])==(1735572,1789788),'fresh scalar expansion')
+    b['scratch_lifecycle_checks']=life;b['template_tests']=scalar.toy_checks()
+    b['five_invocation_scalar_primitives_per_vertex']=3*b['forward']['totals']['real_component_primitive_steps']+2*b['backward']['totals']['real_component_primitive_steps']
+    b['scratch']=dict(live_roles=W,physical_roles_per_cover=W+R+h+1,additional_recursive_calls=0,extra_external_row_coordinate=False)
+    progress('Merging scalar events, exact frames and all final climbs.')
+    programs={};controls=[]
+    for orientation in ['forward','backward']:
+        events=list(splice.emit(c,orientation));programs[orientation]=splice.validate(events,c,orientation,m,b)
+        controls.extend(splice.controls(events,c,orientation,m,b))
+    g=splice.global_contract(m);splice.validate_global(g,m)
+    mutations=[('wrong_helper_owner',lambda x:x['stage_recipe'][1].__setitem__('helper_owner','s1^(-1)(d)')),
+        ('rank_only_frame',lambda x:x['exact_frame_bindings']['x23'].__setitem__('declaration_line','same rank only')),
+        ('scratch_alias',lambda x:x['scratch_namespace'].__setitem__('centers',[14315,14337])),
+        ('wrong_live_normalization',lambda x:x.__setitem__('recursive_volume_denominator',23375)),
+        ('free_RAM',lambda x:x.__setitem__('primitive_policy','free_RAM')),
+        ('missing_tableau',lambda x:x.__setitem__('physical',14339))]
+    for name,fn in mutations:
+        bad=deepcopy(g);fn(bad)
+        try:splice.validate_global(bad,m)
+        except ValueError as error:controls.append(dict(name=name,rejected=True,reason=str(error)))
+        else:raise ValueError('global mutation accepted: '+name)
+    progress('Recomputing complex cover, router, precision and row inequalities.')
+    precision=finite_guard(m,b,basis)
+    need(labels.scalar_word([(1,0,1),(0,1,-1),(0,2,1),(3,1,-1),(1,0,1),(3,1,1),(0,2,-1),(2,3,-1),(3,2,1),(1,3,-1),(2,0,1)])==[[0,-1,0,0],[1,0,0,0],[0,0,0,-1],[0,0,1,0]],'global scalar signed exchange')
+    return dict(status='PASS_FRESH_COMPLEX_LABEL_SCALAR_SPLICE_PRECISION',five_stage_histogram=ledger['histogram'],
+        label_checks=checks,ledger=ledger,scalar_bill=b,
+        splice=dict(program=programs,global_contract=g,controls=controls,source_pin=PIN,certificate_sha256=cp['compressed_sha256']),
+        precision_guard=precision,input_pins=verified,program_check=program_check,
+        inherited_theorem_dependencies=[
+            'The pinned gcert/1 program is accepted, fresh in this run, by Sussman\'s reference checker gx.check1 with the exact scalar identity (E5) and by his gxcore mirror of the two Lean checks; a flipped scalar sign is rejected by both. No Lean check of this program is pinned in this package.',
+            'Pinned Lab.inv dirty lifting, exact gwinB/G0..G4 geometry, owner bijections and NetCert composition are inherited source theorems.',
+            'Retained general Clifford synthesis, compact complete-stream tape primitives, common-grid precision and complete-row proofs remain analytic dependencies.',
+            'The finite operational recipe is regenerated and checked; no astronomical cover enumeration or universal tape-machine execution is claimed.'])
+
+if __name__=='__main__':
+    result=run(progress=lambda text:print(text,file=sys.stderr))
+    print(json.dumps(result,indent=2))
diff --git a/research/five-stage-p10-transcript-stages/prepare.py b/research/five-stage-p10-transcript-stages/prepare.py
new file mode 100644
index 0000000000..1348c80f5e
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/prepare.py
@@ -0,0 +1,66 @@
+"""Clean p = 10 preparation: the gen5-generator paired-cube bit word at cube size p = 10 with its physical layer.
+
+The bit word (bitword/selected/bit) is admitted by PR200's physical-word classes (bitword/bit/word.py, whose
+only change is the pP input file names, and base_word.py, unmodified) over PR168-v4's unmodified exact checker. The context exposes
+the interface of the retained source527 scalar program (scalar/word.py, byte-identical); every
+source527-specific selection (source loans, aggregation/rank/echelon groups, fresh and paired
+source reads, terminal sinks, early mixes, retimed prefixes) is empty for this word.
+No payload execution occurs here.
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+p = 10 port: constants derived from the cube size (word_pins.shape) or pinned in word-pins.json.
+"""
+from pathlib import Path
+from collections import Counter,defaultdict
+from types import SimpleNamespace
+import hashlib,importlib.util,json,sys
+from word_pins import expect,shape
+sys.dont_write_bytecode=True
+HERE=Path(__file__).resolve().parent
+WORD_SHA='e675d4eb9d90ff0b44279fae0b46f1a8b39f65421cc38454b70a6b75d0e10b42'
+
+def prepare():
+ G=HERE/'bitword';S=shape()
+ spec=importlib.util.spec_from_file_location('p10_pr200_physical_word',G/'bit/word.py');module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module)
+ W=module.Candidate();C=W.C
+ # Exact decoder/geometry of the virtual graph, and every changed operation frame and alias handoff.
+ C.decoder();C.geometry();W.exact_frames()
+ W.changed_frames=[i for i,(a,b)in enumerate(zip(W.original_opframe,W.opframe))if a!=b]
+ W.endframe={r:W.opframe[ii[-1]]for r,ii in W.role_ops.items()}
+ assert W.v==S['v'] and W.h==S['h']
+ expect('virtual_R',W.R);expect('reuse_pairs',len(W.pairs));expect('virtual_gauges',len(W.gauge));expect('changed_operation_frames',len(W.changed_frames))
+ assert all(0<=W.readtime[s]<=W.first[s]for s in W.gauge)
+ assert all(W.last[d]<W.readtime[b]and C.sub(W.endframe[d],W.gauge[b]['frame'])for b,d in W.pairs)
+ assert all(not(set(W.gauge)&set(W.ops[i][:2]))for i in W.phase1)
+ # The centre prefix is exactly phase one, executed in its listed order.
+ schedule=dict(events=[dict(kind='gate',op=i)for i in W.phase1],center_prefix_events=list(range(len(W.phase1))),deferred_ops=[],new_phase1=list(W.phase1),new_untouched_roles=[])
+ selection=[];gauge_selection=[];new_gauge_selection=[];extra_selection=[];new_phase_roles=set()
+ borrow={};by_source={};omitted=set();early={};gauge_borrow={}
+ kpair={e['passive']:e for e in W.k['entries']};assert len(kpair)==W.v//2  # every source lies in exactly one partner pair
+ adj=[{}for _ in range(W.R)]
+ for r,s in zip(W.g['roots'],W.w['rootroles']):
+  for t in r['targets']:adj[s][t]=adj[s].get(t,0)+1
+ for i in reversed(W.phase1+W.rest):
+  a,b,_=W.ops[i]
+  for t,c in adj[a].items():adj[b][t]=adj[b].get(t,0)+c
+ assert adj==W.adjoint()
+ assert all(set(adj[s])==set(z['targets'])for s,z in W.gauge.items()),'gauge targets are exact response supports'
+ terminal=[];removed=set();deletedroots=set();bywrite={};afterwrite={}
+ regs=sorted(set(W.phys.values())-set(borrow)-removed);idx={r:2*W.v+j for j,r in enumerate(regs)}
+ assert len(regs)==W.R-len(W.pairs);expect('physical_R',len(regs))
+ at=defaultdict(list)
+ for b in W.order:at[W.readtime[b]].append(b)
+ deliveries=defaultdict(list)
+ for e in W.k['entries']:deliveries[e['deliver_after_root']].append(e)
+ m=SimpleNamespace(W=W,C=C,schedule=schedule,selection=selection,gauge_selection=gauge_selection,new_gauge_selection=new_gauge_selection,
+  extra_selection=extra_selection,new_phase_roles=new_phase_roles,borrow=borrow,by_source=by_source,omitted=omitted,early=early,
+  gauge_borrow=gauge_borrow,kpair=kpair,adj=adj,terminal=terminal,removed=removed,deletedroots=deletedroots,bywrite=bywrite,
+  afterwrite=afterwrite,regs=regs,idx=idx,at=at,deliveries=deliveries,deferred=[],
+  agg=[],role_groups={},target_group={},read_frames={},extra_byrole={},rankgroups=[],rankowner={},echelon=[],eowner={},
+  fresh={},pair_byalias={},pair_bydirty={},pair_selection=[],zero=W.register([]),source_head='p10')
+ # Names the retained scalar program reads from its preparation namespace.
+ m.Counter,m.defaultdict,m.json,m.sys,m.hashlib,m.Path=Counter,defaultdict,json,sys,hashlib,Path
+ m.SOURCE_TEXT=(HERE/'scalar/word.py').read_text()
+ assert hashlib.sha256(m.SOURCE_TEXT.encode()).hexdigest()==WORD_SHA
+ m.input_pins={str(p.relative_to(HERE)):hashlib.sha256(p.read_bytes()).hexdigest()for p in sorted(G.rglob('*'))if p.is_file()}
+ m.portable_source_pins=dict(m.input_pins)
+ return dict(m.__dict__)
diff --git a/research/five-stage-p10-transcript-stages/prime_check.py b/research/five-stage-p10-transcript-stages/prime_check.py
new file mode 100644
index 0000000000..aef6c5e80c
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/prime_check.py
@@ -0,0 +1,75 @@
+"""Recompute exact determinants for every physically consumed basis of the p = 10 word.
+Based on PR234's prime coverage check; substantial OpenAI Codex assistance.
+p = 10 port (DreamingOfClouds, Anthropic Claude assistance): m from the cube size, entrance census pinned.
+"""
+from collections import Counter
+from pathlib import Path
+import hashlib,importlib.util,json,time
+from word_pins import expect,shape
+HERE=Path(__file__).resolve().parent
+
+def basis_hash(basis):return hashlib.sha256(json.dumps(basis,separators=(',',':')).encode()).hexdigest()
+
+def validate_record(row,dimension,determinant,allowed_primes):
+    assert type(row['dimension'])is int and type(row['determinant'])is int and type(row['residual'])is int,'exact integer witness fields'
+    assert row['dimension']==dimension and row['determinant']==determinant!=0,'exact determinant mismatch or singular basis'
+    assert 0<row['residual']<2**80,'retained prime lower bound'
+    product=row['residual']
+    for prime,exponent in row['factors'].items():
+        p=int(prime);assert p in allowed_primes and type(exponent)is int and exponent>0,'factor shape';product*=p**exponent
+    assert product==abs(determinant),'factor identity'
+
+def run(context,physical,progress=lambda text:None):
+    started=time.monotonic();w,c=context['W'],context['C']
+    p=HERE/'prime_witnesses.py';spec=importlib.util.spec_from_file_location('source527_exact_prime_validator',p);module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module)
+    required=set(w.opframe)|set(w.w['source_frame'])|set(w.w['root_frame'])|{w.w['full_frame'],w.register([])}
+    required.update(g['frame']for g in w.gauge.values())
+    for e in w.k['entries']:required.update((e['mix_frame'],e['deliver_frame']))
+    for t in range(w.v):required.add(w.register(w.module.kernel([c.cov[t]],w.h)[0]))
+    required.update(g['frame']for g in context['agg']+context['rankgroups']+context['echelon'])
+    required.update(r['mix_frame']for r in context['pair_selection'])
+    used=set();groups={}
+    for row in physical['used_frames']:
+        f=row['frame_id'];assert f not in used;used.add(f)
+        h=basis_hash(c.B[f]);assert h==row['basis_sha256'] and len(c.B[f])==c.dimf[f]==row['dimension'],'fresh physical basis identity'
+        groups.setdefault(h,f)
+    # Retiming may remove a producer frame from the executed word. Retain its
+    # determinant obligation as well as every fresh physically consumed basis.
+    actual_basis_hashes=set(groups)
+    for f in required:groups.setdefault(basis_hash(c.B[f]),f)
+    assert actual_basis_hashes<=set(groups)
+    assert {basis_hash(c.B[f])for f in required}<=set(groups),'base and added transform coverage'
+    determinants={};largest=0;prime_factors=set();witnesses={}
+    for j,(h,f)in enumerate(sorted(groups.items())):
+        B=c.B[f];s=list(map(sum,B))
+        gram=[[9*sum(a*b for a,b in zip(x,y))-s[i]*s[k]for k,y in enumerate(B)]for i,x in enumerate(B)]
+        det=module.det(gram);powers,residual=module.factor_witness(det)
+        row=dict(dimension=len(B),determinant=det,residual=residual,factors={p:e for p,e in powers.items()if e})
+        validate_record(row,len(B),det,module.PRIMES);prime_factors.update(map(int,row['factors']));witnesses[h]=row
+        determinants[h]=det;largest=max(largest,abs(det).bit_length())
+        if j and j%5000==0:progress('Validated '+str(j)+' exact basis determinants')
+    ranks=Counter();bundle_bases=set();M=shape()['m']
+    for role,g in w.gauge.items():
+        if role in w.donor or role in context['borrow']:continue
+        a=g['dim'];h=basis_hash(c.B[g['frame']]);d=determinants[h]
+        assert 0<5*a<M and d!=0;ranks[a]+=1;bundle_bases.add(h)
+        assert abs(d**5)==abs(d)**5
+    expect('final_entrance_ranks',ranks);expect('final_entrance_bases',len(bundle_bases))
+    assert 2*M**3*10**16<2**80
+    from copy import deepcopy
+    controls=[]
+    def reject(name,call):
+        try:call()
+        except AssertionError:controls.append(name)
+        else:raise AssertionError('invalid witness accepted: '+name)
+    first=next(iter(groups));row=witnesses[first];det=determinants[first]
+    missing=dict(witnesses);missing.pop(first)
+    def coverage(actual,wanted):assert set(actual)==set(wanted),'complete current basis coverage'
+    reject('missing current basis',lambda:coverage(groups,missing))
+    changed=deepcopy(row);changed['determinant']=det+1;reject('incorrect determinant',lambda:validate_record(changed,row['dimension'],det,module.PRIMES))
+    changed_factor=deepcopy(row);changed_factor['residual']+=1;reject('incorrect factor identity',lambda:validate_record(changed_factor,row['dimension'],det,module.PRIMES))
+    singular=deepcopy(row);singular['determinant']=0;reject('singular basis',lambda:validate_record(singular,row['dimension'],module.det([[1,2],[1,2]]),module.PRIMES))
+    huge=deepcopy(row);huge['residual']=2**80;reject('residual at prime lower bound',lambda:validate_record(huge,row['dimension'],det,module.PRIMES))
+    noninteger=deepcopy(row);noninteger['residual']=float(row['residual']);reject('noninteger residual',lambda:validate_record(noninteger,row['dimension'],det,module.PRIMES))
+    expect('unique_bases',len(groups));expect('maximum_determinant_bits',largest)
+    return dict(status='PASS_FRESH_ALL_ACTUAL_P10_BASIS_DETERMINANTS_AND_FIVEFOLD_BUNDLES',unique_bases=len(groups),current_frame_ids=len(used),basis_inventory_sha256=hashlib.sha256(json.dumps(sorted(groups),separators=(',',':')).encode()).hexdigest(),maximum_determinant_bits=largest,prime_factors=sorted(prime_factors),all_remaining_factors_below_2_power_80=True,independent_entrances=sum(ranks.values()),bundled_unique_bases=len(bundle_bases),entrance_rank_counts=dict(ranks),controls=controls,physical_inventory_bound=True,seconds=time.monotonic()-started,scope='Every actual physical basis of the p = 10 word is freshly evaluated over exact integers; all source, gauge, operation, root, partner-mix, delivery and cap frames are covered. Five disjoint copies inherit nondegeneracy; compiler and prime supply remain theorem dependencies.')
diff --git a/research/five-stage-p10-transcript-stages/prime_witnesses.py b/research/five-stage-p10-transcript-stages/prime_witnesses.py
new file mode 100644
index 0000000000..7f16d93030
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/prime_witnesses.py
@@ -0,0 +1,99 @@
+"""Exact finite prime exclusions for the selected new rational bit frames.
+
+For integer basis B and G=I-J/9, det(9 B G B^t) is a nonzero integer.
+Excluding its prime divisors and 2,3,5 makes the reduced frame nondegenerate
+over every odd local ring Z/q^w. Projector denominators divide this determinant
+times fixed powers of 3. Retained frames retain their old exclusion witnesses.
+The selected q is an arbitrarily large fixed prime chosen after this finite
+set; this is not verification at a preselected numeric q.
+"""
+from pathlib import Path
+import argparse,gzip,hashlib,json,sys
+
+HERE=Path(__file__).resolve().parent
+
+def det(A):
+    A=[list(r) for r in A];n=len(A)
+    if not n:return 1
+    sign=1;previous=1
+    for k in range(n-1):
+        pivot=next((i for i in range(k,n) if A[i][k]),None)
+        if pivot is None:return 0
+        if pivot!=k:A[k],A[pivot]=A[pivot],A[k];sign=-sign
+        p=A[k][k]
+        for i in range(k+1,n):
+            for j in range(k+1,n):
+                v=A[i][j]*p-A[i][k]*A[k][j]
+                assert v%previous==0
+                A[i][j]=v//previous
+            A[i][k]=0
+        previous=p
+    return sign*A[-1][-1]
+
+PRIMES=(2,3,5,7,11,13,17,19,23,29,31)
+
+def factor_witness(determinant):
+    assert type(determinant) is int and determinant != 0
+    residual=abs(determinant);powers={}
+    for prime in PRIMES:
+        power=0
+        while residual%prime==0:residual//=prime;power+=1
+        powers[str(prime)]=power
+    validate_factor(determinant,powers,residual)
+    return powers,residual
+
+def validate_factor(determinant,powers,residual):
+    assert type(determinant) is int and determinant != 0
+    assert set(powers)==set(map(str,PRIMES))
+    assert all(type(x) is int and x>=0 for x in powers.values())
+    assert type(residual) is int and 0<residual<2**80
+    reconstructed=residual
+    for p in PRIMES:reconstructed*=p**powers[str(p)]
+    assert reconstructed==abs(determinant)
+
+def certificate(word=None):
+    if word is None:
+        from word import Candidate
+        word=Candidate()
+    C=word.C;h=word.h
+    used=set(word.opframe)|set(word.w['source_frame'])|set(word.w['root_frame'])|{word.w['full_frame']}
+    used.update(z['frame'] for z in word.w['gauges'])
+    for e in word.k['entries']:used.update((e['mix_frame'],e['deliver_frame']))
+    groups={}
+    for frame in sorted(used):
+        B=C.B[frame]
+        key=json.dumps(B,separators=(',',':'));groups.setdefault(key,[]).append(frame)
+    records=[]
+    for key,frames in sorted(groups.items()):
+        B=json.loads(key);s=list(map(sum,B))
+        gram=[[9*sum(a*b for a,b in zip(x,y))-s[i]*s[j] for j,y in enumerate(B)] for i,x in enumerate(B)]
+        determinant=det(gram);powers,residual=factor_witness(determinant)
+        records.append(dict(basis_sha256=hashlib.sha256(key.encode()).hexdigest(),
+            frame_ids=frames,dimension=len(B),cleared_gram_determinant=determinant,
+            small_prime_powers=powers,remaining_factor=residual,gram_denominator_power_of_9=len(B)))
+    controls=[];zeros={str(p):0 for p in PRIMES}
+    for name,args in (('zero determinant',(0,zeros,1)),('incorrect factor identity',(15,zeros,1)),
+        ('residual above retained prime lower bound',(2**80+7,zeros,2**80+7))):
+        try:validate_factor(*args)
+        except AssertionError:controls.append(name)
+        else:raise ValueError('Invalid prime witness accepted: '+name)
+    return dict(status='PASS exact prime witnesses for every used physical frame',h=h,
+        source_commit='4a3c769e5c5430e7114c4d3e099ff34664677f17',
+        input_sha256={str(p.relative_to(HERE.parents[2])):hashlib.sha256(p.read_bytes()).hexdigest() for p in word.input_paths},
+        script_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(),
+        stripped_primes=list(PRIMES),frame_witnesses=records,unique_used_bases=len(records),
+        total_used_frames=len(used),total_operation_frames=len(word.changed_frames),
+        maximum_determinant_bits=max(abs(z['cleared_gram_determinant']).bit_length() for z in records),
+        all_remaining_factors_below_retained_prime_lower_bound=True,adverse_controls=controls,
+        rule='Every q>2^80 avoids every nonzero used-frame determinant, so the original prime range is unchanged.',
+        scope='Exact integer cleared-Gram factors for all physical frames including every changed operation, gauge, source, root, partner-mix, delivery and ambient frame. Uniform split-rank and fallback arguments remain the retained local-ring interface.')
+
+def main():
+    assert not sys.flags.optimize
+    ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');args=ap.parse_args()
+    record=certificate();target=HERE/'prime-witnesses.json.gz'
+    if args.write:target.write_bytes(gzip.compress((json.dumps(record,sort_keys=True,separators=(',',':'))+'\n').encode(),mtime=0))
+    else:assert record==json.loads(gzip.decompress(target.read_bytes())),'Exact prime witnesses changed'
+    print(json.dumps({k:v for k,v in record.items() if k!='frame_witnesses'}))
+
+if __name__=='__main__':main()
diff --git a/research/five-stage-p10-transcript-stages/proof/FINITE_BIT_ACCOUNTING.md b/research/five-stage-p10-transcript-stages/proof/FINITE_BIT_ACCOUNTING.md
new file mode 100644
index 0000000000..42a585d742
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/proof/FINITE_BIT_ACCOUNTING.md
@@ -0,0 +1,126 @@
+# Portable five-stage BIT finite bill
+
+The executable `finite_check.run` accepts the freshly reconstructed source
+ledger, physical tags, independently checked scalar projection, exact current
+basis-prime result, exact moment calculation and optional global lowering
+result. It reads no saved execution receipt. Source expectations are checked
+against those computed objects, not substituted for them. The complete
+package runner is responsible for generating its inputs before this call.
+
+## Quantifiers and inherited primitive hypotheses
+
+Fix this candidate and an eligible odd prime q>2^80 before the input widths
+n,w are chosen. All represented determinant and route exclusions lie in
+{2,3,5,7}. The primitive constant C may depend on q, the fixed source recipe,
+the finite bootstrap level and the retained primitive implementations. It
+does not depend on n,w, ancestor values or unrelated spectator widths except
+through logical volume V.
+
+The three byte-pinned public sources supplied here are
+`three-stage-cover-bit.tex`, `three-stage-cover-rows.tex`, and
+`copied-centers-lemma.tex`. Their exact-tape, completed ordinary-leaf and
+complete-stream hypotheses are retained. All high matrix fibers are batched;
+prefix descriptor preparation has fixed polynomial cost in w and is paid
+over the complete q^w target fiber. Unrelated spectators use ripple counters.
+Fresh child role fields never enter the ancestor weight descriptor. Finite
+low-type tables, initialization and sequential scans are charged in C.
+There is no unit-cost random-access oracle or new numerical Turing-machine
+constant requirement.
+
+## Actual finite recipe
+
+Let m=120, W=23,683, E=495,304, v=1,760, R=16,643, d=m^2 and
+J=20v+10R+4v=208,670. The last 4v=7,040 families pay the explicit final
+complete-stream exchange; they are not equal-frame payload shears.
+
+The check derives from the fresh word 12,858,690 weighted additions or
+21,787,770 unit additions, including all six bridge families. Its
+cancellation-free prefix lift is
+64*37,623^3*9,430,154^2=303,094,329,841,208,644,962,256,113,408<2^98.
+No old defining-integer endpoint is imposed on the F2 supplier.
+
+The actual rational 48-dimensional route is reconstructed, eliminated and
+inversely replayed: 195 additions, 44 swaps and 27 scalings, with denominator
+set {1,2,3,6}. A missing addition fails reconstruction. Coordinate
+permutations and embedding give the other ports and stages.
+
+Per route, pay at most 23,707*|GL_120(F_q)| low-role transpositions and
+16*(d+1)^2 high affine factors. Per good edge, pay at most 8m^2+8 elementary
+normalizer wrappers. The same compiler pays all exterior completions.
+There are 120 copied-center episodes. Their recursive rank-22 calls and
+their scalar reads are already included in E and the scalar count; their
+copy/erase and parking passes are separately paid by the complete-stream
+primitive, using one additional work stream.
+
+For a bad edge with N=2m=240, the exact inherited Gaussian fallback uses at
+most 6N(N-1)+3N+6(N-1)=346,314<32m^2=460,800 children. Keep the entire
+larger allowance in the moment. Coefficient preparation uses only unit
+pivot inversions. Allocate 128N^3 ring operations per edge per low class:
+four 8N^3 elimination/inversion allocations and sixteen 2N^3 matrix products
+give 64N^3; the remaining 64N^3 pays extraction, copying, generic tests,
+factor output and the bad-branch elimination. Matrix bit costs and descriptor
+arithmetic are paid by the inherited primitive theorem. Invertibility testing
+of each candidate low matrix additionally gets 16m^3 operations.
+
+Overcharging every finite recipe item over every low matrix gives
+
+    B(q) <= [unit+J*16(d+1)^2+J*(W+24)+E*(8m^2+8)
+             +E*128(2m)^3+16m^3+120+E+1]*q^14400
+         = 1,568,901,757,016,837*q^14400 < q^14401.
+
+These are explicit ring/recipe counts, not single-step machine costs. All
+fixed-tape, table, setup and selector constants stay in C_primitive, giving
+the normalized toll C*n+C*w^(1-a_old) after increasing one finite C.
+No recursive child is absorbed into this nonrecursive constant.
+
+## Weighted induction and rows
+
+Set c=704197288590873/10^18 and tau=1-c. Exact interval recomputation,
+adding the entire 10^-16*32m^2 fallback envelope per edge, proves
+
+    1-mu_tau > 774/10^21,
+    1-mu_1 = 107421874442783/69383789062500000 > 0.
+
+For the retained recurrence
+T(n,w)<=sum_r c_r*T(r*floor(n/120),w)+C*n+C*w^(1-a_old),
+take A=C*(1+1/(1-mu_1)+1/(1-mu_tau)). Induction bounds T by
+A*(n+n^tau*w^(1-a_old)): the linear and stopped gaps separately pay the
+two tolls; the leaves follow A>=C. Floors only decrease the child sizes.
+
+The maximum ratio is 5/6, so four levels halve. The depth bound
+4*ceil(log2(max(2,n))) changes stock, not the one-level moment. Paying all
+24 temporary roles gives per-level log_q stock below 14400w+1. Add the
+inherited old-leaf reserve. The new contribution is at most
+57,604w*ceil(log2(max(2,n))). Borrow and restore these complete high digits;
+successive residuals and the two-call ordinary wrapper reuse the reserve.
+One outer row padding factor is below two; binary-radix padding costs less
+than q^2 in logical volume. The temporary roles never enter the denominator W.
+
+## Finite ordinary bootstrap and cutoff
+
+Starting with completed ordinary a0=384599/10^10, set beta=c and repeat
+a_(j+1)=(1-c)c+c*a_j exactly three times. The finite result is
+
+    a3=704197288358392787581160456097840009769165126434639147437106139267359/10^72.
+
+At each stage, the paid exponents are 1-c, 1-a_(j+1), c with a logarithm,
+and c(1-a_j). The exact positive gaps are c-a_(j+1),
+1-a_(j+1)-c, 1-a_(j+1)-c(1-a_j), and 1-c (for row fitting).
+
+Choose a finite integer C>=1 dominating that stage's already fixed primitive,
+recurrence, wrapper, row, setup, padding and previous ordinary constants.
+Let delta be the minimum positive gap and
+
+    L=ceil(max(1,36/delta^2,2*(4+ceil(log2 C))/delta)), e0=2^L.
+
+For e>=e0, C(1+log2 e)e^(-delta)<=1/16. Indeed for t=log2 e,
+log2(1+t)<=3sqrt(t)<=delta*t/2 and log2 C+4<=delta*t/2.
+Thus every lower-order toll is covered and the borrowed high part fits.
+Below e0 use the previously completed ordinary algorithm. A finite next
+constant is C_large+C_old*2^(L*(a_(j+1)-a_j)). This choice is sequential,
+not circular, and uniform in the input and complete spectators.
+
+This proves the finite-accounting and ordinary-bootstrap step at the same
+conditional theorem level as the retained public baseline. It does not claim
+an independent proof of those inherited primitives, a measured universal
+machine constant, or execution at every input width.
diff --git a/research/five-stage-p10-transcript-stages/proof/INTEGRATED_PROOF.md b/research/five-stage-p10-transcript-stages/proof/INTEGRATED_PROOF.md
new file mode 100644
index 0000000000..c624da6c5c
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/proof/INTEGRATED_PROOF.md
@@ -0,0 +1,87 @@
+# Source-bound five-stage compositional candidate
+
+9 October 2026. This is an isolated research admission branch. Its executable checks immutable finite receipts and recomputes exact scalar moments, a finite ordinary bootstrap, and all 47 balanced outer inequalities. It additionally binds fresh public-source bit preparation, raw-ledger construction, and the complete globally lowered physical event stream. It does not repeat the exhaustive F2 column proof, run the Lean kernel or universal tape machine, or claim Mac qualification or publication.
+
+## 1. Meaning of admission here
+
+The branch is an explicit conjunction of constructive source theorems and finite source-bound evidence. It does not replace any proof with a numerical root or infer source correctness from a PASS string. The new family names are `new5stageF2` and `baseline5stageComplex`; the old dimension-72 entry point and written bounds are kept byte-identical. The branch has no general-purpose dimension override.
+
+The executable's semantic guards reject a wrong source, omitted copied centers, a rank-only complex frame contract, a work/live denominator substitution, omitted final climbs, incorrect reverse-copy lowering, and a one-level bit-halving substitution. The source lock identifies the exact evidence, code, and primary proof files consumed. The more detailed emitted-program verifiers exercise local chronology and addresses, beyond these top-level schema controls.
+
+## 2. Raw source471 provenance
+
+The saved raw helper ledger pins an older screen.py. The older screen bytes are unavailable; no byte-delta assertion is made. The rebind verifier reruns the current exact geometry/ledger construction with all writes suppressed and a hash-verified cached certificate in place of its redundant network fetch. Every semantic field, all 471 source paths, and all 1,760 target paths agree. The saved ledger is not rewritten.
+
+The apparent target-prefix duplication is resolved by the actual chronology: screen.py removes the two latest loan prefixes for its predecessor positive controls; raw_ledger.py puts those two prefixes back. There are exactly eight restored target reads. Current-source dependency hashes and the canonical semantic-payload digest make this equivalence independently inspectable. The sole historical pin exception is specifically this screen.py field and is allowed only with the exact rebind witness.
+
+## 3. Local bit helper and global lowering
+
+The source is PR210 df95878d11190518e45ef9717c9ee05011f88ace. The independently recorded local scalar word has 2,569,626 weighted events. Its projection is fixed by SHA256 e74e43692685ad5f716b41b363acb8b443c2c90096634a55f0e3728980713944. Both literal forward and signed inverse pass all 20,163 F2 columns, including arbitrary targets and 16,643 independent dirty helpers. The 471 borrowed sources are source aliases, never extra independent dirty coordinates.
+
+The tagged physical word has digest 614f19da4288021cd5c10a575ec7759c069962a6030bf30edb047573ed76edf6 and realizes the telescope Dout M Din^-1. Its input frames are X:Pq, Y:0, Z:sigma and output frames X:H, Y:H-Pq, Z:H. Thus a completed invocation has no data/helper cross blocks and each independent helper residual is D_(H-sigma). This is a full arbitrary-input operator identity, not just zero-dirt testing.
+
+The five-stage compiler maps every local live index through the stage owner injection, maps every local temporary to external family 23,683, and applies the stage's data or helper cover bijection. The active source/target pairs are (X1,Y1), (Y1,X1), (X1,Y1), (Y2,X2), (X2,Y2). The unused pair stays parked. A data route is right multiplication by the exact rational rho_i,S; a helper route is the whole-block exchange tau_i. Both are bijections of the eligible GL cover. They are charged address movements, not dense payload arithmetic.
+
+Cover expansion is strictly phase-major: complete every cover class in stage i before starting the next routed stage or boundary phase. The same rule applies separately to idle, bridge, completion and terminal-exchange phases. Running all five stages for one class before proceeding to another class would be incorrect because rho and tau refer to other classes. The callable stage and boundary iterators specify the phases; a flattened one-class-per-phase template is not a class-major execution schedule. The admission contract rejects that alternative loop ordering.
+
+For backward stages the compiler reverses the complete local event order, negates scalar coefficients, and replaces local P by H-P. A copied-center block is lowered afresh: copy the original at H-U, transform the copy to H, perform reverse signed scatter, and erase it. It is forbidden to invert an erased temporary. Every original center also retains its complementary live climb. Copy/live index injectivity is checked for all stage orientations.
+
+The global lowering artifact must emit bridges, idle children, independent gauge completions, and the final signed bank exchange. That exchange is an explicitly paid complete-stream role permutation, not a same-frame shear. A stage-descriptor string alone does not meet this obligation.
+
+## 4. Rational five-window geometry and prime eligibility
+
+Take H=Q^24, G=I-J/9 and a triple line q*. Its projector has denominator 6; coordinate permutations supply the port isometries. The two-block involution rho_i,S fixes the two port lines and exchanges their complementary spaces. With Q_i the direct sum of the first i copied complements, the frame is D_[g rho_i,S(P direct_sum Q_i)rho_i,S^-1 g^-1]. The four elementary two-block projector identities imply all eight bank boundary equalities. Rational complements are I-P.
+
+The exact rational partial swap is D_P=[[I-P,P],[P,I-P]]. It is involutory. Every same-frame scalar gate telescopes exactly, all idle transitions are nested actual projectors, and D_I D_Pq=D_(I-Pq) gives the terminal all-data address endpoint after the scalar exchange. No Pauli or Fourier phase claim is imported from the complex compiler into this bit proof.
+
+For each independent physical helper, the five routed residuals occupy different H_i. Their supported projectors have pairwise zero products. Their product is D_(I-sum_i sigma_i), so one paid child D_(sum_i sigma_i) completes D_I. This is one correction for each helper, not a packing of unrelated dirty rows. The 2,279 independent entrances have ranks {12:18,13:48,18:13,20:2200}; the 31 source-owned gauge entrances receive no extra completion.
+
+All 26,750 used physical frame IDs (26,380 distinct bases) have exact determinant witnesses. Their factors lie in {2,3,5,7}; the 231 distinct gauge-bundle bases use {2,3,5}. Window-map denominators also use {2,3,5}. Hence every retained q>2^80 preserves these ranks. General GL charts use gPg^-1, not a recomputed Euclidean orthogonal projection.
+
+The weighted generic normalizer allows every proper rank, including 60,65,90,100 in dimension120. Its cleared pivot-polynomial degree is at most m r(r+1)/2 < m^3. Thus the bad fraction is at most2m^3/q<10^-16. Each bad edge retains the full invertible local-ring residual and is paid 32m^2=460,800 rank-one fallback children. No field elimination at nonunit pivots is substituted.
+
+## 5. Exact bit ledger and ordinary finite recurrence
+
+One invocation has 95,789 positive-rank children and rank mass435,846. Its24 rank22 center copies are included once, as are each original center's live climbs. With H this histogram,
+
+n5 = 5H + 3520(delta4+delta23+delta46+delta50)
+     +18delta60+48delta65+13delta90+2200delta100.
+
+Thus m=120, W=23,683, calls495,304, mass2,837,560, deficit4,400. Work streams do not enlarge the live moment denominator. Five invocations retain all120 rank22 centers.
+
+The counted finite-bit adapter pays the literal scalar word, six bridge families, weighted good-edge wrappers, bad-class residuals, copy/read/erase, class routing, selector arithmetic, and fixed-tape movement. Its retained primitive theorem fixes the eligible prime and finite source recipe before varying width, so its finite constant may depend on that prime and recipe. It cannot depend on width, ancestor payload values or unrelated spectators except through complete volume. This is the correct quantifier order; an invented numerical Turing-machine constant is unnecessary.
+
+The largest child ratio is5/6. Three levels do not halve and four do: (5/6)^4=625/1296<1/2. The same one-level weighted moment induction remains valid; the factor4 is used only in depth/descriptor/borrowed-row bounds. Even paying24 simultaneous temporaries gives physical stock23,707 per GL cover vertex and log_q Wphysical(w)<14400w+1. The resulting internal log_q row charge is at most4ceil(log2(max(2,n)))(14400w+1), plus the old-leaf reserve. High digits are borrowed and restored internally; this is not a new external q-adic group factor.
+
+The defining-integer lift need not equal the older supplier's decoder endpoint. A safe cancellation-free prefix bound is64*37623^3*9430154^2<2^98. It uses neither signed integer restoration nor commutation between stage-dependent decoder channels. F2 payload exactness does not require complex floating precision.
+
+Let c=704197288590873/10^18. The freshly enclosed full bit moment, including all bad fallback charges, has a strictly positive gap. Start from the retained completed ordinary leaf a0=384599/10^10. Three finite levels with atom exponent beta=c give
+
+a_(j+1)=(1-c)c+c a_j,
+a3=.000704197288358392787581160456097840009769165126434639147437106139267359.
+
+At every level a_j<a_(j+1)<c<1-a_(j+1). The actual finite-cutoff witness binds the positive moment and lower-order toll gaps to the new finite recipe. This is not an infinite limiting bootstrap or a packed-profile substitution.
+
+## 6. Complex source, complete splice and finite guard
+
+The complex source is f010392c923279e3dd59ef3aa5fedad23affc5fd. The published gcert/1 gzip and expanded JSON identities are checked directly. Its pinned scalar identities and GBridge2 matrix equalities are reused as source theorems, including phases; no same-rank substitute or changed-185 helper is admitted.
+
+The source-defined old-response and cleanup maps are realized by filtered, reversed and transposed literal helper words. Their scalar projections are checked against complete schedule hashes. Old-response uses a9,412-stream temporary tableau, cleared before all recursive children. The coefficient work stream is also cleared after use. The emitted label/scalar splice preserves13,798 phaseA transitions,46,937 phaseB transitions, and9,412 final climbs, totaling70,147 live transitions. It retains22 center children. Final climbs occur after B, followed by exact final-frame adapters and then cleanup.
+
+The five-stage source theorem supplies all ten exact matrix fields x01/y01 through x34/y34, sfin and term, the actual cover owner bijections, all idle banks and final signed exchange. The complete finite compiler uses the retained two-rank-zero-factor construction around each exact recursive C^r child. Rank-zero phase/permutation operations are charged selected-bit and complete-stream tape primitives, not free RAM lookups.
+
+The exact scalar primitive counts are1,492,984 forward and1,549,456 backward, totaling7,577,864 for three forward plus two backward invocations. All361,405 recursive children, including110 rank20 centers, remain charged. The profile has m110, W14692, mass1,613,040, deficit3,080 and maxchild46.
+
+Physical work stock is24,127|O(110,2)|, with6010 bits; live recursion stock has6009 bits. The proved local operation bill is below2^48 and the complete fixed-program bound below2^6050. Router and literal guards fit G=2^30000 and E=2^100000. Coefficients use only denominators1,2,3,6, so the exact common grid2^-P 3^-G(D+1) introduces no return rounding. Completed child semantics give C1=1, induction gap127B, and C0=2^210000>32mB^2. The complex half-shrink requirement is preserved:2*46<110.
+
+The physical row overcharge16,171 remains below20,161. Degree1,000,000 and suffix slope4,000,000 retain exact row gap23,971,789/25. These constants come from the changed stock and counted program, not from simply replacing72 by110 in the old guard.
+
+## 7. Fresh outer47 arithmetic and completion boundary
+
+Use complex saving747454944651775/10^18, strictly inside its freshly re-enclosed moment. The bit saving is the exact finite a3 above. Both moment gaps exceed7.7e-19. With eta=10^-12 and stopping fraction10^-9, the unchanged retained balanced assembly produces47 positive strict constraints and7 margins.
+
+The isolated candidate is kappa=703701743496697/10^18, or.000703701743496697. The minimum outer margin exceeds it by approximately7.3899e-19. This arithmetic value exceeds the retained frontier. Exact rational gaps, rather than printed decimals, are the evidence.
+
+The certificate remains a receipt-bound compositional research candidate with explicit source-theorem dependencies. The clean loader consumes 22 pinned public files and agrees in 23 exact semantic components with the audited context. Its fresh raw ledger and complete five-stage histogram agree; an empty-directory extraction passes all 10 focused tests. The clean-root global emitter regenerates all 12,858,690 weighted additions, 495,304 paid children, 120 fresh copies and erasures, 2,279 helper completions, and 3,520 final pair exchanges. Source-bound global lowering, exact h24 geometry, clean-loader qualification, and finite closure supplements are all mandatory before the entry point emits its PASS certificate.
+
+These fresh computations do not pretend that the inherited exhaustive F2 columns, exact determinant archive, or complex source theorems were independently reproved. Full portable packaging and Mac qualification remain separate delivery checks. The pinned comparison frontier is df95878's .000694782719690783; the subsequently reported public head31f4ccc1c16c538749845f9244b24747f1cf93dd claims .000695191451687307, which is a separate comparator pending independent validation and is not substituted into this source freeze.
diff --git a/research/five-stage-p10-transcript-stages/proof/PARITY-CONTRACT.md b/research/five-stage-p10-transcript-stages/proof/PARITY-CONTRACT.md
new file mode 100644
index 0000000000..fad6150b1f
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/proof/PARITY-CONTRACT.md
@@ -0,0 +1,45 @@
+# Parity-even payload gate removal: inherited contract audit
+
+Conclusion: removing an even-coefficient pointwise payload ADD is valid for the bit supplier. The odd-prime address arithmetic remains unchanged. A new paid profile still requires the actual filtered word and full frame schedule; this conclusion alone does not certify a new kappa value.
+
+## Primary source evidence
+
+The bundled, unmodified primary section [`primary/03-motifs.tex`](primary/03-motifs.tex) states the following. Its exact source, attribution, and file hashes are recorded in [`primary/PROVENANCE.md`](primary/PROVENANCE.md).
+
+* Line50: in the bit construction scalars lie in F2.
+* Lines149–177: replace a scalar by an array in R^Omega, with R the scalar ring of the network. Common R-linear frames give the exact operator `D_out S_Omega D_in^-1`.
+* Around line223: the scalar domain need not equal the label field. Bit labels are rational subspaces even though the payload scalars are binary.
+* Lines483–493: rational-address frames are F2-linear permutations of array entries; the bit network uses pointwise XOR gates.
+
+The byte-pinned [`copied-centers-lemma.tex`](copied-centers-lemma.tex) in this package opens with its scalar restoration identity explicitly over F2. Its copy contract preserves the complete role stream, controls and spectators; each copy's frame change and erasure remain paid.
+
+The retained PR234 [`INTEGRATED_PROOF.md`](INTEGRATED_PROOF.md), line56, explicitly says: "The defining-integer lift need not equal the older supplier's decoder endpoint" and the majorant "uses neither signed integer restoration nor commutation between stage-dependent decoder channels." The package's signed integer decoder checks are stronger supplier evidence; the inherited bit interface does not impose their particular integer endpoint on a newly synthesized F2-equivalent word.
+
+The retained weighted bit theorem, [`three-stage-cover-bit.tex`](three-stage-cover-bit.tex), uses the odd-prime local ring Z/q^w for address fields and weighted address interchanges. Its rational projectors, unit-pivot tests, route matrices and fallback coefficients are address geometry. They are not the F2 payload ADD coefficients.
+
+## Operator proof
+
+Fix the finite complete address set Omega and let one stream be a vector in F2^Omega. A payload gate is `x_a <- x_a + (c mod2) x_b`. For even c this is the identity on every input, including arbitrary correlated dirty streams and spectators. Removing any number of these identity gates leaves the complete scalar operator S_Omega unchanged. Negative odd coefficients and coefficient3 also reduce to1, though the simplest experimental witness can retain their original signed integer representatives.
+
+Retain each original input/output frame and every remaining gate's original common frame. The common-frame identity then gives the same `D_out S_Omega D_in^-1` for the filtered word. In particular, every independent helper still has its required partial-swap residual and the existing completed-bank proof still applies. No integer identity of the new lift is needed to conclude this F2 operator identity.
+
+## Safe frame compression
+
+Deleting an ADD removes its operand-frame alignment requirement. For a given stream, collect successive MOVE operations between surviving uses. A use includes any surviving ADD, COPY read/write, ERASE or required phase/endpoint boundary. No use may be crossed merely because another stream is idle.
+
+Suppose the original local frames form a nested chain U0 <= U1 <= ... <= Uk. Their exact address changes telescope to `D_Uk D_U0^-1`. Their orthogonal increments are disjoint commuting projectors, so this is one allowed residual of rank dim(Uk)-dim(U0). In the reflected orientation the chain is the reversed complementary chain; the same endpoint difference and rank follow exactly. The ambient stage background cancels. Rebuild both ledgers from the actual surviving uses and actual basis inclusions; do not infer this from summed ranks alone.
+
+Keep every physical input/output family and its endpoint, all stage boundaries, all data routes/bridges, and every copied-center lifetime. For source527 the120 center copies in the five-stage construction have odd scatter coefficients, so parity filtering does not itself remove those episodes. The shared work stream cannot be used before COPY or after ERASE. A COPY is a barrier even if its original register has no intervening ADD.
+
+## Required finite admission
+
+1. Filter actual emitted ADD records by the literal coefficient modulo2; retain all odd-coefficient records in their original order. Check all20107 formal F2 source, target and dirty columns against the admitted shear. The expected local event counts before any further resynthesis are1,783,196 removed and786,621 retained.
+2. Generate the actual complemented inverse schedule, with fresh reverse copies as before, and verify every formal F2 column again. Do not reverse an erasure.
+3. Compute cancellation-free prefix bounds for the new literal signed forward/inverse projections. Recompute the five-stage bound and finite bill. Failure to reproduce the previous integer decoder is not itself a contract failure; a missing F2 dirty restoration is.
+4. Regenerate exact monotone forward/reflected physical paths and the complete paid histogram. Every fused residual's actual endpoints must be checked. Keep all remaining recursive children, copied-center calls, fallback allowance, data idle edges and stock.
+5. Rebind the completed banks and final global address lowering to the new word and tags. Their actual rational address projectors, odd-q routes and normalizers must not be reduced modulo2.
+6. Rerun actual basis/prime coverage, finite ordinary-leaf assembly, both rational moment engines and all47 outer inequalities before claiming a result.
+
+For simple monotone MOVE fusion the paid rank mass and physical stock remain unchanged; combining positive increments can improve the concave moment while reducing the number of children. Any different deficit or stock must be explained by a separate exact endpoint change. The displayed bound is still conditional on the retained all-size compiler, selectors, common ancestor charts, restored rows, routing, prime and analytic interfaces.
+
+Prepared with OpenAI Codex assistance. This audit is independent of the physical parity-filter/fusion implementation owned by the complex research lane.
diff --git a/research/five-stage-p10-transcript-stages/proof/README.md b/research/five-stage-p10-transcript-stages/proof/README.md
new file mode 100644
index 0000000000..e6bb06c84e
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/proof/README.md
@@ -0,0 +1,8 @@
+# Retained proof documents
+
+The `.tex` files are byte-pinned theorem sources. `finite_check.py` checks their hashes and phrases.
+
+`INTEGRATED_PROOF.md`, `FINITE_BIT_ACCOUNTING.md` and `PARITY-CONTRACT.md` are retained verbatim from the
+PR234 and source527 packages. Their arguments apply to this package unchanged. Their numerical instances,
+such as R, W, stock, bills and digests, describe the earlier source471 and source527 helpers, not this package's p = 10 word.
+The p = 10 values are recomputed by `verify.py` and stated in `../PROOF.md` and `../BANK-PROOF.md`.
diff --git a/research/five-stage-p10-transcript-stages/proof/copied-centers-lemma.tex b/research/five-stage-p10-transcript-stages/proof/copied-centers-lemma.tex
new file mode 100644
index 0000000000..8933aaf508
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/proof/copied-centers-lemma.tex
@@ -0,0 +1,103 @@
+\subsection{Scalar, frame and temporary-stream contracts}
+The retained source-copy, reversible mixer and scatter maps satisfy
+$JLV=I$. Over $\mathbb F_2$ the chronological word
+\[
+ L,\ J,\ L^{-1},\ V,\ L,\ J,\ L^{-1},\ V
+\]
+adds the input to the target and restores every arbitrary auxiliary.
+Over Gaussian dyadics use its corresponding old-value subtraction and
+new-value addition. A designated retained output has a distinct terminal
+output-use carrier: a matching may feed that carrier, but cannot merge
+two designated terminals or append a later middle-producer consumer.
+Its remaining uses before cleanup are its scatter reads, all of which
+leave its scalar value unchanged.
+
+Within one tensor invocation suppress the fixed future line and put
+\[
+ D_0=B\otimes F_h,\quad D_1=A\otimes F_h,\quad
+ A=B\mathbin{\perp}P,\quad D_U=D_0\mathbin{\perp}(P\otimes U),
+\]
+where $P$ and the suppressed future factor are one-dimensional and
+$U$ is a nondegenerate retained-center space of dimension $r$.
+Thus a local change of rank $d$ has ambient rank $d$.
+Write $\mathcal F_Q$ for the address frame: it is the rational partial
+swap $D_Q$ in the bit construction, and the binary phase $C_Q$ in the
+complex construction. Changing a copy from frame $Q_1$ to $Q_2$ means
+applying $\mathcal F_{Q_2}\mathcal F_{Q_1}^{-1}$ to its physical stream.
+Orthogonal backgrounds cancel in this quotient.
+
+Copies use Paureel's retained copy/transform/read/discard interface
+\cite{paureel,pr29}. A copy has precisely the original complete role
+stream, including all control and spectator ranges, and volume $V/W$.
+It is processed while inactive original streams are parked on the fixed
+depth-first stack tapes. Copying, pointwise reads and erasure are linear
+in that stream's volume. Sequential processing needs one additional
+fixed work stream, not an independently varying row coordinate.
+
+\begin{lemma}[Copied retained-center schedule]
+In either invocation orientation a designated retained center's
+physical rank profile can be changed from $z^r+z^h$ to
+$z^r+z^{h-r}$, with the same scalar action, original role endpoints,
+and arbitrary-scratch restoration. The rank-$r$ transform on the copy
+is included in the recursive call list.
+\end{lemma}
+\begin{proof}
+In the forward orientation the original center has scalar value $w$
+at frame $D_U$ after the middle mixer. Its old sequence was
+$D_U\to D_0\to D_1$: scatter at $D_0$, then cleanup at $D_1$,
+with ranks $r,h$.
+Keep the original at $D_U$, copy its physical stream, and transform
+only the copy to $D_0$, paying rank $r$. Supply every scatter read
+from that transformed copy while its data targets remain at their
+unchanged common frame $D_0$, then erase the temporary. The reads
+are exactly those of $w$ in the old schedule. Since they do not change
+$w$, move the original directly from $D_U$ to $D_1$ before its first
+cleanup incidence; this costs $h-r$. Every subsequent original gate
+therefore receives the same scalar value at its required frame.
+
+In the reverse complementary orientation the old sequence was
+$D_0\to D_1\to D_{U^\perp}$, with ranks $h,r$ and scatter at $D_1$.
+After the preceding all-$D_0$ operations, advance the original directly
+to $D_{U^\perp}=D_0\mathbin{\perp}(P\otimes U^\perp)$, paying
+$h-r$. Copy it and transform the copy to $D_1$, paying $r$.
+Use that copy for all early scatter reads, then erase it. The original
+already has the exact frame and unchanged scalar value required by the
+following inverse mixer. Terminal output-use separation ensures no
+intervening producer consumer has been bypassed.
+
+For partial swaps either direction of the rank-$r$ change is the same
+involution. For complex phases the forward copy uses $C_U^{-1}$,
+the direct original growth uses $C_{U^\perp}$, and the reverse copy
+uses $C_FC_{U^\perp}^{-1}=C_U$. These are the same charged ranks,
+implemented by the retained forward/inverse residual interface.
+All tensor backgrounds cancel as stated. Every original scalar
+incidence, final source-copy cancellation and auxiliary source/sink
+operator is unchanged. Thus the scalar identity and all endpoints
+remain exact on arbitrary initial auxiliary values.
+\end{proof}
+
+For the selected centers $r=h-1$, and there are $h$ distinct retained
+output uses per invocation. Their old histogram has rank mass
+$hR_h+2\ell_h$, where $\ell_h=h(h-1)$. The new histogram is exactly
+\[
+ H'_{h,1}=H_{h,1}+h,\qquad H'_{h,h}=H_{h,h}-h,
+ \qquad H'_{h,r}=H_{h,r}\quad(r\ne1,h),
+\]
+and hence $\sum_r rH'_{h,r}=hR_h+\ell_h$.
+Every old rank-$(h-1)$ residual remains as a paid transform of a copy;
+its projector and ordinary bit pivot profile are unchanged. Only the
+full-rank original transition becomes the rank-one complement.
+The physical role count $R_h$ is unchanged.
+
+For two factors, put $N=v_av_b$, $B_a=v_bR_a$, $B_b=v_aR_b$,
+$W=2N+B_a+B_b$ and $L=v_b\ell_a+v_a\ell_b$.
+All exterior, data-front and endpoint-correction calls remain in place.
+The resulting complete rank mass is
+\[
+ s=Wm-N+L,\qquad Wm-s=N-L.
+\]
+This follows by subtracting exactly $L$ from the retained two-stage
+physical mass $Wm-N+2L$. The $N$ rank-one endpoint-copy calls are
+separate and remain fully charged. Because center copies retain the
+same complete role-volume fraction $1/W$, the existing complete-row,
+integer-width remainder and fixed-tape recurrence proofs apply.
diff --git a/research/five-stage-p10-transcript-stages/proof/primary/03-motifs.tex b/research/five-stage-p10-transcript-stages/proof/primary/03-motifs.tex
new file mode 100644
index 0000000000..cdb0ba527a
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/proof/primary/03-motifs.tex
@@ -0,0 +1,700 @@
+\section{Two finite networks with a rank saving}
+\label{sec:finite-networks}
+
+We construct two fixed linear networks that exchange two banks of values
+while restoring every auxiliary value.  When the values are replaced by
+arrays, a common representation on all wires at a gate lets that gate act
+pointwise without disturbing the representation.  We explain this invariant
+before constructing the subspace labels that make changes of representation
+cheap.  The first network uses bit values and rational subspaces; the second
+uses Gaussian dyadic values and binary subspaces.  The scalar domain specifies
+the values combined at a gate, while the subspace labels are used to construct operators
+on each wire's address-indexed array.
+
+Put
+\[
+ h=100,\qquad v=\binom h3=161700,\qquad
+ N=v^3=4227952113000000,\qquad m=h^3=1000000.
+\]
+Let $\mathcal T$ be the set of three-element subsets of $[h]$.
+There are two data banks $X_a,Y_a$, indexed by
+$a=(a_1,a_2,a_3)\in\mathcal T^3$.
+A wire carries one scalar.  A gate is a fixed linear map on a specified
+set of wires; untouched wires retain their values.  The vertices on a
+wire are its source, the gates that touch it in time order, and its sink;
+its edges join consecutive vertices.  We call the name of a wire its
+\emph{role}, so that we can distinguish a fixed place in the network
+from the value currently carried there.
+
+\subsection{Scalar operations and restored auxiliary values}
+
+There are three stages.  At stage $j$, fix the other two coordinates and
+operate on the $v$ values in each bank obtained by varying coordinate $j$.  Thus
+there are $v^2$ separate invocations at each stage.
+Each such invocation has its own auxiliary wires, distinct from all
+other invocations, including those in other stages.  There are
+\[
+ I=3v^2=78440670000
+\]
+invocations.  In a forward invocation, write $x_T$ for the data used as
+controls and $y_S$ for the data to be updated; $S,T\in\mathcal T$ are
+their varying $j$th coordinates.  These are the logical source and
+target banks of the invocation.  For each ordered pair $(S,T)$ that is
+neighboring under the rule below, there is an auxiliary wire $A_{ST}$.
+There are also central wires $C_i$, $i\in[h]$, and in the second
+construction a wire $C_\ast$.  We call all these auxiliary wires
+\emph{scratch wires}; their initial values may be arbitrary.
+
+The following maps specify the construction.
+\begin{itemize}
+\item In the bit construction, scalars lie in $\mathbb F_2$, and
+$S,T$ are neighbors when $|S\cap T|=1$.
+The copy map adds $x_T$ to $A_{ST}$ for each neighbor pair.
+The side injection adds $\sum_{T:\,|S\cap T|=1}A_{ST}$ to $y_S$.
+The gather adds $\sum_{T\ni i}x_T$ to $C_i$, and the scatter adds
+$\sum_{i\in S}C_i$ to $y_S$.
+\item In the complex construction, scalars lie in
+$\mathbb Z[i,1/2]$, and neighbors are distinct triples with even
+intersection.  Copy is unchanged.  Side injection adds
+\[
+ -\sum_{T\text{ neighboring }S}\frac{|S\cap T|-1}{2}A_{ST}
+\]
+to $y_S$.  Gather adds $\sum_{T\ni i}x_T$ to $C_i$ and
+$\sum_Tx_T$ to $C_\ast$.  Scatter adds
+$(\sum_{i\in S}C_i-C_\ast)/2$ to $y_S$.
+\end{itemize}
+Each update leaves its control wires unchanged.  The first two rows of
+the following schedule remove the effect of the old scratch values;
+the next four introduce the source values and add their effect to the
+target; the last two restore the scratch values.
+This cancellation of arbitrary initial scratch values is a linear
+instance of the restoration construction for transparent computation in
+Buhrman, Cleve, Kouck\'y, Loff and Speelman~\cite[Section~3]{BuhrmanCleveKouckyLoffSpeelman2014}.
+The forward schedule is
+\begin{equation}
+\begin{array}{c|l|l}
+\text{row}&\text{operation}&\text{gate grouping}\\ \hline
+0&\text{subtract side injection}&\text{one gate per target}\\
+1&\text{subtract scatter}&\text{one gate on targets and center}\\
+2&\text{copy}&\text{one gate per source}\\
+3&\text{gather}&\text{one gate on sources and center}\\
+4&\text{scatter}&\text{one gate on targets and center}\\
+5&\text{side injection}&\text{one gate per target}\\
+6&\text{undo gather}&\text{one gate on sources and center}\\
+7&\text{undo copy}&\text{one gate per source}.
+\end{array}
+\label{eq:motif-schedule}
+\end{equation}
+
+\begin{lemma}\label{lem:scalar-motifs}
+For arbitrary initial values of its auxiliary wires, a forward
+invocation changes $y_S$ to $y_S+x_S$ and leaves every other value
+unchanged.  Performing a forward invocation from $X$ to $Y$ at stage 1,
+the inverse forward schedule from $Y$ to $X$ at stage 2, and a forward
+invocation from $X$ to $Y$ at stage 3 sends
+\[
+ (X_a,Y_a)\longmapsto(-Y_a,X_a)
+\]
+and restores every auxiliary value.  In the bit construction this is the
+permutation exchanging $X_a$ and $Y_a$.
+\end{lemma}
+
+\begin{proof}
+Write $\mathcal V$ for copy, $\mathcal G$ for gather,
+$\mathcal J$ for side injection and $\mathcal R$ for scatter.
+If the initial side and central vectors are $a,c$, the first two rows
+subtract $\mathcal J a+\mathcal R c$ from $y$.  Rows 2 and 3 change
+them to $a+\mathcal Vx,c+\mathcal Gx$.  Rows 4 and 5 therefore add
+$\mathcal R(c+\mathcal Gx)+\mathcal J(a+\mathcal Vx)$.
+Rows 6 and 7 restore $c,a$.  The net target change is
+$(\mathcal J\mathcal V+\mathcal R\mathcal G)x$, independently of
+$a,c$.
+
+In the bit case, the central coefficient from $x_T$ to $y_S$ is
+$|S\cap T|\bmod2$.  The side contribution cancels exactly the
+intersection-one cases; distinct triples with intersection zero or two
+already have coefficient zero, and the self coefficient is one.
+In the complex case, the central coefficient is $(|S\cap T|-1)/2$.
+The side cancels it for distinct triples with intersection zero or two;
+intersection one contributes zero, and the self coefficient is one.
+Thus both net maps are $y\gets y+x$.
+
+The inverse schedule with logical source $Y$ and target $X$ effects
+$X\gets X-Y$.  Starting from $(x,y)$, the three stages give
+$(x,y+x)$, then $(-y,y+x)$, then $(-y,x)$.
+Each invocation restores its own auxiliary wires.
+\end{proof}
+
+A fixed triple has
+\[
+ z_{\rm b}=3\binom{97}{2}=13968,\qquad
+ z_{\rm c}=\binom{97}{3}+3\cdot97=147731
+\]
+neighbors in the two constructions, respectively.  The second count
+separates intersection zero and intersection two.  Ordered pairs must
+be counted: there are $vz$ side wires in each invocation, not $vz/2$.
+With $c_{\rm b}=100$ and $c_{\rm c}=101$ central wires per invocation,
+the total wire counts are
+\begin{align}
+ W_{\rm b}&=2N+I(vz_{\rm b}+c_{\rm b})
+          =177176569091445000000,\label{eq:bit-wire-count}\\
+ W_{\rm c}&=2N+I(vz_{\rm c}+c_{\rm c})
+          =1873807244643542670000.\label{eq:complex-wire-count}
+\end{align}
+All these numbers are fixed, independently of any eventual input length.
+
+\subsection{From scalar values to arrays}
+
+We record the representation principle before choosing the labels.  Let
+$R$ be the scalar ring of either network and let $\Omega$ be a finite address
+set common to all wires.  Replace each scalar by an array in $R^\Omega$, and
+apply each scalar gate pointwise at every address.  Write $\mathsf S_\Omega$
+for the resulting network on the vector of wire arrays.
+
+At each source, gate and sink $v$, assign an invertible $R$-linear operator
+$D_v$ on $R^\Omega$, called its \emph{frame}.  A frame acts on the values
+indexed by addresses within one wire's array and may mix them; a gate instead
+combines wire values at each fixed address.  All incoming and outgoing
+incidences of one gate use the same $D_v$.  On an edge from $u$ to $v$, apply
+$D_vD_u^{-1}$ to that wire's array.  Define the operators on all input and
+output roles by
+\[
+ D_{\rm in}=\bigoplus_w D_{\mathrm{source}(w)},\qquad
+ D_{\rm out}=\bigoplus_w D_{\mathrm{sink}(w)}.
+\]
+For a supplied physical input $f$, define its logical interpretation to be
+$g=D_{\rm in}^{-1}f$; this definition requires no physical preprocessing.
+At a vertex $v$, the invariant is that the stored array equals $D_v$ applied
+to the logical array there.  It holds at the sources by definition.  On an
+edge whose logical array is $\varphi$, the edge operator changes $D_u\varphi$
+to $D_v\varphi$.  At a gate with logical input arrays $\varphi_j$,
+$R$-linearity gives
+$\sum_j c_jD_v\varphi_j=D_v(\sum_j c_j\varphi_j)$ for each output combination, with
+$c_j\in R$.  Thus the common frame commutes with the pointwise gate, and
+the invariant continues to the sinks.  The implemented operator is therefore
+\begin{equation}
+ D_{\rm out}\,\mathsf S_\Omega\,D_{\rm in}^{-1}.
+ \label{eq:common-frame-identity}
+\end{equation}
+In particular, if the scalar network is a signed role permutation that
+sends input role $w$ to output role $\rho(w)$ with scalar sign
+$\varepsilon_w$, that route applies
+$\varepsilon_wD_{\mathrm{sink}(\rho(w))}
+D_{\mathrm{source}(w)}^{-1}$ to its input array.  All roles, including
+the auxiliary roles, enter this identity.  Once the scalar routing is fixed,
+the endpoint frames determine the array operator on each route; the
+intermediate frames can then be chosen to make each edge change inexpensive.
+
+Figure~\ref{fig:frame-compatibility} summarizes this invariant.
+\begin{figure}[ht]
+\centering
+\input{figures/proof-map.tex}
+\caption{An edge changes the representation of one role's logical array
+$g_w$. At the next gate $G$, all $t$ input arrays have the common frame
+$D_v$, so the pointwise linear gate commutes with that frame. The same
+$D_v$ acts on each output component.}
+\label{fig:frame-compatibility}
+\end{figure}
+
+\subsection{Subspaces attached to the gates}
+
+The scalar network already has the required signed exchange. We now
+choose its intermediate labels to make the changes of frame inexpensive.
+A label is a nondegenerate subspace of a fixed bilinear space. On every
+edge one label will contain the other. For such an edge, the
+\emph{orthogonal residual} is the orthogonal complement of the smaller label inside
+the larger one; its dimension is the absolute change in label dimension.
+The saving will come from keeping the total dimension lost on decreasing
+edges small relative to $N$.
+
+For the bit network, let $F=\mathbb Q^h$ with bilinear form
+\[
+ \langle x,y\rangle=x^{\mathsf T}(I-J/9)y,
+\]
+where $J$ is the all-one matrix.  This form has eigenvalues $1$ and
+$1-h/9=-91/9$, so it is nondegenerate.  For a triple $T$ let $t_T$ be
+its indicator vector.  Then
+\[
+ \langle t_S,t_T\rangle=|S\cap T|-1,
+ \qquad \langle t_T,t_T\rangle=2.
+\]
+For the complex network, take instead $F=\mathbb F_2^h$ with the
+ordinary dot product; here $t_T\cdot t_T=1$.
+Thus every triple line is nondegenerate, and neighboring triple lines
+are orthogonal, in the label field belonging to either construction.
+The scalar domain need not equal the label field.
+These degree-one intersection formulas specialize the construction
+described by Alon~\cite[Section~3, remark after Theorem~1.1]{Alon1998}
+to the prime $2$, with the ground-set size changed to $h=100$.
+
+The ambient label space is $\mathcal F=F^{\otimes3}$ with its tensor
+bilinear form.  It has dimension $m$ and is nondegenerate.  Write
+\[
+ u_a=t_{a_1}\otimes t_{a_2}\otimes t_{a_3},\qquad U_a=\langle u_a\rangle.
+\]
+The prescribed terminal labels are
+\[
+\begin{array}{c|cc}
+\text{role}&\text{source label}&\text{sink label}\\ \hline
+X_a&U_a&\mathcal F\\
+Y_a&0&U_a^\perp\\
+\text{each scratch role}&0&\mathcal F.
+\end{array}
+\]
+Write $W$ for the wire count in the construction under consideration.
+The source dimensions sum to $N$ and the sink dimensions to $Wm-N$.
+Thus the signed dimension changes will sum to $Wm-2N$, because the
+contributions at gates cancel. If decreasing edges lose a total
+dimension $L$, the sum of absolute changes is $Wm-2N+2L$.
+We will obtain $L<N/2$. The rational interface below will require
+an additional $N$ source ranks, so this inequality will leave a strict
+saving in both constructions.
+
+At stage $j$, fix an invocation.  Put
+\[
+ A=F^{\otimes(j-1)},\qquad
+ P=\langle t_{a_1}\otimes\cdots\otimes t_{a_{j-1}}\rangle,
+ \qquad B=P^\perp\subset A.
+\]
+An empty tensor product is the one-dimensional ground field; thus
+$B=0$ at stage 1.  Let
+$Q=\langle t_{a_{j+1}}\otimes\cdots\otimes t_{a_3}\rangle
+\subset F^{\otimes(3-j)}$, again using the empty tensor product at
+stage 3.  Since $P$ is nondegenerate,
+$A=B\mathbin{\perp}P$.  
+We prescribe the following transition for each data wire in the stage,
+where $t$ is the indicator of that wire's $j$th triple:
+\[
+\begin{array}{c|c|c}
+ &\text{incoming label}&\text{outgoing label}\\ \hline
+ X&A\otimes\langle t\rangle\otimes Q&(A\otimes F)\otimes Q\\
+ Y&B\otimes\langle t\rangle\otimes Q&
+ \bigl((B\otimes F)\mathbin{\perp}(P\otimes t^\perp)\bigr)\otimes Q.
+\end{array}
+\]
+The outgoing $Y$ label can also be written
+$(P\otimes\langle t\rangle)^\perp_{A\otimes F}\otimes Q$.
+These transitions expose one tensor factor at each stage. To see that
+they fit together, for $j<3$ write
+$Q=\langle t_{a_{j+1}}\rangle\otimes Q'$. The next stage has
+\[
+ A'=A\otimes F,\qquad
+ P'=P\otimes\langle t\rangle,\qquad
+ B'=(P')^\perp_{A'}
+    =(B\otimes F)\mathbin{\perp}(P\otimes t^\perp).
+\]
+Thus the prescribed outgoing labels are
+$A'\otimes\langle t_{a_{j+1}}\rangle\otimes Q'$ on $X$ and
+$B'\otimes\langle t_{a_{j+1}}\rangle\otimes Q'$ on $Y$, exactly
+the next incoming labels. At stage 1 they start at $U_a$ on $X_a$
+and zero on $Y_a$; at stage 3 they end at $\mathcal F$ on $X_a$
+and $U_a^\perp$ on $Y_a$, as prescribed at the terminals.
+
+The gate labels are organized by the decomposition
+\[
+ A\otimes F=(B\otimes F)\mathbin{\perp}(P\otimes F),
+\]
+with the common summand $B\otimes F$ and the remaining summand
+$P\otimes F$ of dimension $h$. Suppress the one-dimensional factor
+$Q$ for the moment. On a side wire joining neighboring physical triples
+with indicators $t_X,t_Y$, the common component grows to $B\otimes F$,
+while the remaining component passes through
+\[
+ P\otimes\langle t_X\rangle
+ \ \subset\ P\otimes t_Y^\perp
+ \ \subset\ P\otimes F.
+\]
+The first inclusion is possible because $t_X\perp t_Y$.
+For the central gates we assign $A\otimes F$ on the physical $X$
+bank and $B\otimes F$ on the physical $Y$ bank. A central wire
+returns once from the former label to the latter, losing exactly
+$P\otimes F$. The gate order below confines all decreases to this
+return, while the other edges realize the prescribed stage transitions.
+
+Number the successive times in an invocation by
+$r=0,\ldots,7$. At stages 1 and 3, time $r$ uses row $r$ of the scalar
+schedule~\eqref{eq:motif-schedule}. At stage 2 it uses the inverse of
+row $7-r$, with the logical banks exchanged. In either case the gates
+touch the physical wires in the order
+\[
+ Y\text{-side},\quad Y\text{-center},\quad X\text{-side},\quad
+ X\text{-center},\quad Y\text{-center},\quad Y\text{-side},\quad
+ X\text{-center},\quad X\text{-side}.
+\]
+A side wire still joins neighboring physical triples in stage 2 because
+the neighbor relation is symmetric. The following table assigns the
+common gate labels. It suppresses the tensor factor $Q$; for a gate
+indexed by a physical bank triple, $t$ denotes that triple's indicator.
+
+\begin{equation}
+\begin{array}{c|l|l}
+\text{time}&\text{physical wires}&\text{common gate label}\\ \hline
+0&Y,\ \text{its side wires}&B\otimes\langle t\rangle\\
+1&Y,\ \text{all center wires}&B\otimes F\\
+2&X,\ \text{its side wires}&(B\otimes F)\mathbin{\perp}(P\otimes\langle t\rangle)\\
+3&X,\ \text{all center wires}&A\otimes F\\
+4&Y,\ \text{all center wires}&B\otimes F\\
+5&Y,\ \text{its side wires}&(B\otimes F)\mathbin{\perp}(P\otimes t^\perp)\\
+6&X,\ \text{all center wires}&A\otimes F\\
+7&X,\ \text{its side wires}&A\otimes F.
+\end{array}
+\label{eq:motif-labels}
+\end{equation}
+All labels are tensored by $Q$ and viewed as subspaces of $\mathcal F$.
+Every displayed summand is nondegenerate.
+
+All scratch sources have label zero and all scratch sinks have label
+$\mathcal F$, as prescribed above. The next lemma verifies the stage
+boundaries and all intervening edge changes, including these scratch
+edges.
+
+\begin{lemma}\label{lem:motif-residuals}
+Every edge joins comparable nondegenerate labels.  The only decreasing
+edges are the central-wire edges from time 3 to time 4; their dimension
+loss is $h$.  Consequently, if $c$ is the number of central wires per
+invocation and $W$ the total number of wires, then
+\begin{equation}
+ L=Ich,\qquad
+ \sum_{e}\bigl|\dim U_{\mathrm{head}(e)}-
+                       \dim U_{\mathrm{tail}(e)}\bigr|
+ =Wm-2N+2L.                                      \label{eq:rank-budget-labels}
+\end{equation}
+For the binary label space, every nonzero orthogonal residual of an
+edge has an orthonormal basis.
+\end{lemma}
+
+\begin{proof}
+Write $a=\dim A=h^{j-1}$ and $f=h^{3-j}$.  In the table below,
+$\mathrm{in}$ denotes the preceding vertex on that data wire: its source
+at stage 1, and its last gate in the preceding stage otherwise.  The
+interstage calculation above gives its label.  The table lists the
+orthogonal residual and its dimension for every edge except the final
+data edges to their sinks, whose labels agree and whose residuals are zero.
+Tensor each residual by $Q$, except in the last row.  The symbols $t_X,t_Y$ are
+the indicators of the neighboring physical triples joined by a side wire.
+\[
+\begin{array}{l|l|r}
+\text{wire and edge}&\text{orthogonal residual}&\text{dimension}\\ \hline
+X:\ \mathrm{in}\to2&B\otimes t_X^\perp&(a-1)(h-1)\\
+X:\ 2\to3&P\otimes t_X^\perp&h-1\\
+X:\ 3\to6,\ 6\to7&0&0\\
+Y:\ \mathrm{in}\to0&0&0\\
+Y:\ 0\to1&B\otimes t_Y^\perp&(a-1)(h-1)\\
+Y:\ 1\to4&0&0\\
+Y:\ 4\to5&P\otimes t_Y^\perp&h-1\\
+\mathrm{center}:\ \mathrm{source}\to1&B\otimes F&(a-1)h\\
+\mathrm{center}:\ 1\to3&P\otimes F&h\\
+\mathrm{center}:\ 3\to4&P\otimes F&h\\
+\mathrm{center}:\ 4\to6&P\otimes F&h\\
+\mathrm{side}:\ \mathrm{source}\to0&B\otimes\langle t_Y\rangle&a-1\\
+\mathrm{side}:\ 0\to2&(B\otimes t_Y^\perp)\mathbin{\perp}(P\otimes\langle t_X\rangle)
+ &(a-1)(h-1)+1\\
+\mathrm{side}:\ 2\to5&P\otimes\langle t_X,t_Y\rangle^\perp&h-2\\
+\mathrm{side}:\ 5\to7&P\otimes\langle t_Y\rangle&1\\
+\mathrm{scratch}:\ \mathrm{last}\to\mathrm{sink}
+ &(A\otimes F)\otimes Q^\perp&ah(f-1).
+\end{array}
+\]
+The last gate on a central wire is at time 6, and the last gate on a side
+wire is at time 7.  Both have label $(A\otimes F)\otimes Q$.  Enlarging it
+to $\mathcal F$ at the sink gives the last residual in the table, with
+$Q^\perp$ taken in the entire future tensor space.
+The side edge $2\to5$ uses the neighbor relation
+essentially.  Since $t_X\perp t_Y$, we have
+$\langle t_X\rangle\subset t_Y^\perp$.  Hence its two labels satisfy
+\[
+ (B\otimes F)\mathbin{\perp}(P\otimes\langle t_X\rangle)
+ \ \subset\
+ (B\otimes F)\mathbin{\perp}(P\otimes t_Y^\perp).
+\]
+The complement of $\langle t_X\rangle$ inside $t_Y^\perp$ is
+$\langle t_X,t_Y\rangle^\perp$, of dimension $h-2$; tensoring by
+$P$ and then by $Q$ gives the residual in the table.  The other entries
+follow directly by splitting $A=B\mathbin{\perp}P$ and
+$F=\langle t\rangle\mathbin{\perp}t^\perp$.
+Label dimension is nondecreasing along every edge except center $3\to4$, which removes
+$P\otimes F\otimes Q$.  The table includes the interstage edges through
+$\mathrm{in}$, and the initial and final data labels match their terminals,
+so no other dimension changes occur.
+
+The signed sum of dimension changes telescopes at every gate: each
+touched wire has one incoming and one outgoing incidence with the same
+gate label.  The sum of source dimensions is $N$, while the sum of
+sink dimensions is $Wm-N$.  The signed increase is therefore $Wm-2N$.
+There are $Ic$ decreasing edges, each of loss $h$; replacing signed
+changes by absolute changes adds $2L$.
+
+Now work over $\mathbb F_2$.  A nondegenerate symmetric bilinear space
+is nonalternating precisely when it contains a vector of norm one.
+The lines $P,Q$ have such vectors.  If $B\ne0$, a coordinate unit
+outside the support of the earlier tensor vector belongs to $B$:
+that support has size $3^{j-1}<h^{j-1}$ when $j>1$.
+The same argument gives a unit vector in $Q^\perp$ when it is nonzero.
+A triple complement, and the complement of two neighboring triple
+lines, contain coordinate units outside supports of sizes at most
+three and six, respectively.  Full tensor spaces contain coordinate
+units as well.  In each nonzero tensor summand, tensoring these chosen
+norm-one vectors gives a norm-one vector; placing it in that orthogonal
+summand gives one in the whole residual.  Each residual is nondegenerate
+by the decompositions above.  Thus every nonzero residual is nonalternating.
+
+For completeness, every nondegenerate nonalternating binary symmetric
+space has an orthonormal basis.  Split off unit lines until the
+remaining space is alternating.  A nonzero nondegenerate alternating
+space splits into planes with bases $a,b$ satisfying
+$a\cdot a=b\cdot b=0$, $a\cdot b=1$; this follows by choosing a
+nonzero $a$, choosing $b$ with $a\cdot b=1$, and taking the orthogonal
+complement of their nondegenerate plane.  Retain one unit vector $w$
+from the lines already split off.  A plane orthogonal to $w$ can be
+absorbed into that line: the three vectors
+\[
+ w+a,\qquad w+b,\qquad w+a+b
+\]
+are independent, pairwise orthogonal, and have norm one.
+Use one of these new unit vectors in place of $w$ for the next plane;
+the remaining planes are still orthogonal to it.  Repeating this
+operation absorbs every alternating plane.
+\end{proof}
+
+The loss ratios have the exact values
+\[
+ \frac{L_{\rm b}}{N}=\frac{100}{539},\qquad
+ \frac{L_{\rm c}}{N}=\frac{101}{539}.
+\]
+In particular, both are smaller than $1/2$.  We now turn the dimension
+count into the two interfaces needed later.
+
+\subsection{The rational matrix interface}
+
+For a nondegenerate rational subspace $U\subset\mathcal F$, write
+$P_U$ for the projection onto $U$ along $U^\perp$.  Assign $P_U$ to
+each gate or sink with label $U$.  Assign the source matrix $-P_{U_a}$
+to $X_a$ and zero to every other source.
+These are fixed rational $m\times m$ matrices; write $M_v$ for the matrix
+at vertex $v$.  Define
+$\rho(X_a)=Y_a$, $\rho(Y_a)=X_a$, and let $\rho$ fix every auxiliary
+wire.
+
+In the tape application, two address chunks are written as vectors $H,D$
+of $m$ fields.  For a matrix $M$, the frame $\Phi_M$ moves the array entry
+at $(H,D)$ to $(H+MD,D)$, leaving the other address fields unchanged.
+The fields use a radix coprime to the fixed denominators, and addition is
+modulo their common range.  Hence $\Phi_M$ is an invertible
+$\mathbb F_2$-linear permutation of array entries, and
+$\Phi_{M'}\Phi_M=\Phi_{M'+M}$.  Using $D_v=\Phi_{M_v}$
+in \eqref{eq:common-frame-identity}, the endpoint matrix difference on each
+routed role is exactly the shear applied to that role.  The following identity
+makes it the same shear $H\gets H+D$ on every role;
+Section~\ref{sec:tape-interchange} turns that shear into a field interchange
+and implements an edge change with one smaller interchange per unit of its
+rational rank.
+
+\begin{proposition}\label{prop:bit-motif-interface}
+The bit network has $W_{\rm b}$ wires, uses only pointwise XOR gates,
+and sends its input vector to the permutation $\rho$ of that vector.
+Its rational matrices are common to all incidences of a gate and obey
+\[
+ M_{\mathrm{sink}(\rho(w))}-M_{\mathrm{source}(w)}=I_m
+ \quad\text{for every input role }w.
+\]
+The sum of the rational ranks of all edge differences is
+\begin{align}
+ s_{\rm b}
+ &=\sum_{e}\operatorname{rank}_{\mathbb Q}
+      (M_{\mathrm{head}(e)}-M_{\mathrm{tail}(e)})\\
+ &=W_{\rm b}m-N+2L_{\rm b}
+  =177176569088785861287000000<W_{\rm b}m.
+\end{align}
+\end{proposition}
+
+\begin{proof}
+Lemma~\ref{lem:scalar-motifs} gives the scalar permutation, including
+all auxiliary roles.  For $U\subset V$ nondegenerate,
+$P_V-P_U$ is the identity on $V\cap U^\perp$ and zero on its
+orthogonal complement.  Its rank is $\dim V-\dim U$; reversing the
+edge negates the matrix without changing its rank.
+The only exceptions are the $N$ negative source projections.
+At stage 1, $B=0$, and the first gate on $X_a$ has label exactly $U_a$.
+Its first edge matrix is therefore $2P_{U_a}$, of rational rank one,
+where the corresponding dimension change was zero.
+Lemma~\ref{lem:motif-residuals} consequently gives the stated rank sum.
+Its deficit from $W_{\rm b}m$ is $N-2L_{\rm b}>0$.
+
+For an input $X_a$ the endpoint difference is
+$P_{U_a^\perp}-(-P_{U_a})=I_m$.  Every other role has zero source
+matrix and identity sink matrix.  This proves the interface.
+\end{proof}
+
+\subsection{The binary phase interface}
+
+Use the complex scalar network and binary labels.  For a binary vector
+$x$, let $\operatorname{wt}(x)$ denote its integer Hamming weight, and
+write $[b]\in\{0,1\}$ for the integer representative of $b\in\mathbb F_2$.
+For a label $U$, let
+\[
+ q_U(x)=\operatorname{wt}(P_Ux)\pmod4.
+\]
+The projection here is over $\mathbb F_2$.
+Let
+\[
+ H=\frac1{\sqrt2}\begin{pmatrix}1&1\\1&-1\end{pmatrix},\quad
+ C=H\begin{pmatrix}1&0\\0&i\end{pmatrix}H
+   =aI+bX,\qquad a=\frac{1+i}{2},\quad b=\frac{1-i}{2},
+\]
+where $X$ interchanges the two coordinates.  On functions of
+$x\in\mathbb F_2^m$ define
+\[
+ \mathcal C_U=H^{\otimes m}\operatorname{diag}_x(i^{q_U(x)})H^{\otimes m}.
+\]
+The use of $H$ in this definition is an identity of matrices.  Each entry
+of $\mathcal C_U$ and its inverse is a Gaussian integer divided by $2^m$,
+so both preserve arrays over $\mathbb Z[i,1/2]$.  The kernels implemented
+below have Gaussian dyadic coefficients.
+
+To apply the scalar network to these functions, replace the scalar on
+each wire $w$ by an array
+$f_w:\mathbb F_2^m\to\mathbb Z[i,1/2]$.  At each address, a gate
+applies its scalar linear map to the values on the wires it touches.
+The frame in \eqref{eq:common-frame-identity} is $D_v=\mathcal C_U$ at a
+vertex with label $U$.  On an edge from label $U$ to label $V$, apply
+$\mathcal C_V\mathcal C_U^{-1}$ to that wire's array.
+All frames are diagonalized by the same matrix $H^{\otimes m}$.
+For an integer $k\ge1$, an address for $k$ columns is
+$(x^{(1)},\ldots,x^{(k)})\in(\mathbb F_2^m)^k$; every frame and edge
+operator is then the tensor product of its one-column version over
+these $k$ coordinates.  Each scalar gate is still applied once at each
+joint address, to the vector of values on the roles it touches.
+
+\begin{proposition}\label{prop:complex-motif-interface}
+For each edge of the complex network, write $U,V$ for its tail and
+head labels.  Its phase-frame difference
+$\mathcal C_V\mathcal C_U^{-1}$ is a product of one translation
+kernel $aI+bX_v$, or its inverse, per vector in an orthonormal basis
+of the edge residual.  Here $(X_vf)(x)=f(x+v)$.
+The sum of these basis lengths is
+\[
+ s_{\rm c}=W_{\rm c}m-2N+2L_{\rm c}
+ =1873807244636671267308000000<W_{\rm c}m.
+\]
+After source and sink diagonal corrections, and undoing the signed
+bank exchange, telescoping these phase frames gives $C^{\otimes m}$
+on every role, including auxiliary roles.  The same assertion holds
+on any positive number of columns by taking tensor products over columns.
+\end{proposition}
+
+\begin{proof}
+For binary vectors $z,w$,
+\[
+ \operatorname{wt}(z+w)
+ =\operatorname{wt}(z)+\operatorname{wt}(w)
+       -2|\operatorname{supp}(z)\cap\operatorname{supp}(w)|.
+\]
+If $z\cdot w=0$, the intersection cardinality is even, so weight is
+additive modulo four.  If $V=U\mathbin{\perp}E$ and $\mathcal B$
+is an orthonormal basis of $E$, it follows that
+\[
+ q_V(x)-q_U(x)=\sum_{v\in\mathcal B}
+                 \operatorname{wt}(v)[v\cdot x]\pmod4.
+\]
+For a decreasing edge the right side is negated.
+Each $v$ has norm one, so $\operatorname{wt}(v)$ is odd.  Its
+coefficient in the phase, including the sign for the edge direction,
+is therefore some $\varepsilon\in\{1,-1\}$ modulo four.  The function
+$i^{\varepsilon[v\cdot x]}$ equals
+\[
+ \frac{1+i^\varepsilon}{2}
+ +\frac{1-i^\varepsilon}{2}(-1)^{v\cdot x}.
+\]
+The identity $H\operatorname{diag}(1,-1)H=X$, tensored over the
+coordinates in $\operatorname{supp}(v)$, sends the diagonal character
+$(-1)^{v\cdot x}$ to translation $X_v$.  The displayed phase therefore
+becomes $aI+bX_v$ or its inverse.  The nonzero residuals have such
+bases by Lemma~\ref{lem:motif-residuals}; for a zero residual use the
+empty basis.  The same lemma gives the count $s_{\rm c}$.
+The deficit is $2N-2L_{\rm c}>0$.
+
+For an edge $e$, write $\mathcal B_e$ for its residual basis and
+$K_{e,v}$ for the forward or inverse translation kernel associated
+with $v\in\mathcal B_e$.  Taking tensor products preserves their
+product, so on $k$ columns
+\[
+ \bigl(\mathcal C_V\mathcal C_U^{-1}\bigr)^{\otimes k}
+ =\prod_{v\in\mathcal B_e}K_{e,v}^{\otimes k}.
+\]
+Thus each residual vector contributes one factor acting on all $k$
+columns, and there are $s_{\rm c}$ such factors over the network.
+
+Let $\rho$ denote the underlying permutation of the complex roles: it
+exchanges $X_a,Y_a$ and fixes each scratch role.
+By Lemma~\ref{lem:scalar-motifs}, the pointwise scalar network sends an input array at
+$X_a$ to $Y_a$ with sign $+1$, an input at $Y_a$ to $X_a$ with sign
+$-1$, and each scratch input to its own output with sign $+1$.
+Applying \eqref{eq:common-frame-identity} with $D_v=\mathcal C_{U_v}$,
+where $U_v$ is the label at vertex $v$, shows that an input role $w$ reaches
+output role $\rho(w)$ with that sign and with operator
+$\mathcal C_{U_{\mathrm{sink}(\rho(w))}}
+ \mathcal C_{U_{\mathrm{source}(w)}}^{-1}$.
+For $k$ columns, use $D_v=\mathcal C_{U_v}^{\otimes k}$ on the joint
+address set in the same identity.  The route operator is then the $k$th
+tensor power of the displayed address operator, multiplied by its scalar
+route sign once.
+The zero label has frame $I$, while the full label has frame
+$C^{\otimes m}$ because $q_{\mathcal F}(x)=\operatorname{wt}(x)$.
+Every pair except $X_a\to Y_a$ has these zero and full labels.
+For the remaining pair, write $u=u_a$.  Its binary norm is one and
+its weight is $3^3=27$.  Orthogonal weight additivity yields
+\begin{align*}
+ q_{U_a^\perp}(x)-q_{U_a}(x)
+ &=\operatorname{wt}(x)-2\operatorname{wt}(u)[u\cdot x]\\
+ &=\operatorname{wt}(x)+2[u\cdot x]\pmod4.
+\end{align*}
+Since $2[u\cdot x]\equiv2\sum_{j\in\operatorname{supp}(u)}x_j
+\pmod4$, the operator on $X_a\to Y_a$ is the tensor of $C^{-1}$ on the
+27 coordinates of $\operatorname{supp}(u)$ and $C$ elsewhere.
+Put $Z=\operatorname{diag}(1,-1)$.  Direct multiplication gives
+\[
+ C=iZC^{-1}Z,\qquad C^{-1}=-iZCZ.
+\]
+For $k$ columns, let $Z_{a,k}$ be the tensor product of $Z$ on
+those 27 coordinates in every column and the identity elsewhere.
+Apply $Z_{a,k}$ before the network at $X_a$, and apply
+$i^{27k}Z_{a,k}$ after the network at $Y_a$; the latter scalar is
+applied once to the whole role.  There are $27k$ inverse factors, so
+the identity $C=iZC^{-1}Z$ turns each of them into $C$.  The operator
+on this pair is therefore $C^{\otimes mk}$ as well.
+Only the physical $X$ outputs still carry the minus sign of the
+scalar exchange.  Negate those outputs and send output role $\rho(w)$
+back to role $w$.  Every role, including every scratch role, now has
+the required forward tensor product.
+\end{proof}
+
+\subsection{Explicit rational bounds for the two recurrences}
+
+The relative rank deficits are
+\[
+ \eta_{\rm b}=\frac{W_{\rm b}m-s_{\rm b}}{W_{\rm b}m}
+       =\frac{339}{22587335000000},\qquad
+ \eta_{\rm c}=\frac{W_{\rm c}m-s_{\rm c}}{W_{\rm c}m}
+       =\frac{73}{19906842167500}.
+\]
+For both recurrences we may use the fixed rational exponent
+\begin{equation}
+ \tau=\sigma=1-2^{-50}.
+ \label{eq:explicit-motif-exponents}
+\end{equation}
+Both exact deficits displayed above are greater than $20\cdot2^{-50}$.
+Since $m<2^{20}$ and $\log 2<1$, we have $\log m<20$, whence
+\[
+ m^{1-2^{-50}}
+ =m\exp(-2^{-50}\log m)
+ >m(1-20\cdot2^{-50})>m(1-\eta)
+\]
+for either $\eta=\eta_{\rm b}$ or $\eta=\eta_{\rm c}$.
+Consequently
+\[
+ \frac{s_{\rm b}}{W_{\rm b}}<m^\tau,
+ \qquad \frac{s_{\rm c}}{W_{\rm c}}<m^\sigma,
+ \qquad 0<\tau=\sigma<1.
+\]
+Here $\sigma$ is a rational upper bound for the logarithmic exponent
+of the complex recurrence.
diff --git a/research/five-stage-p10-transcript-stages/proof/primary/LICENSE b/research/five-stage-p10-transcript-stages/proof/primary/LICENSE
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@@ -0,0 +1,201 @@
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diff --git a/research/five-stage-p10-transcript-stages/proof/primary/PROVENANCE.md b/research/five-stage-p10-transcript-stages/proof/primary/PROVENANCE.md
new file mode 100644
index 0000000000..bebdb72910
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/proof/primary/PROVENANCE.md
@@ -0,0 +1,23 @@
+# Primary bit-scalar and common-frame contract
+
+The three unmodified source files in this directory are carried by Henry Grant / hcg890's PR234 snapshot:
+
+- Repository: https://github.com/hcg890/integer-mult-bounds
+- PR: https://github.com/CrocSwap/integer-mult-bounds/pull/234
+- Exact snapshot commit: `af3fe331ca60c936229e060681ffccbc1c208678`
+- Primary section path in that snapshot: `upstream/build/sections/03-motifs.tex`
+- Accompanying source paths: `upstream/README.md` and `upstream/LICENSE`
+
+The accompanying README identifies the primary work as **OpenAI, Integer multiplication below n log n, September 23, 2026** and records its original citation and publication link. It is retained as `UPSTREAM-README.md`. This is attribution to the primary source; the snapshot commit above belongs to the carrying repository and is not asserted to be an original OpenAI commit. These credits do not imply review or endorsement of this contribution.
+
+The accompanying Apache-2.0 license is retained without modification as `LICENSE`. These files have not been edited, excerpted, or reformatted. The exact content hashes are:
+
+| Bundled file | SHA256 |
+| --- | --- |
+| `03-motifs.tex` | `ed76761194988a01af77ead0ea6469cb5dcd29690ab985a0b5a4006b0f2b69bb` |
+| `UPSTREAM-README.md` | `8d1ceff898a4e0e681679f91c4def485820be9e99f04e4861f2ce601a364723e` |
+| `LICENSE` | `c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4` |
+
+`03-motifs.tex` supplies the bit scalar ring at line50, the common-frame identity at lines149–177, the distinction between scalar and label fields at line225, and the rational-address bit frame contract at lines483–493. It is bundled as theorem evidence, not as a standalone compilable document. The accompanying [`../PARITY-CONTRACT.md`](../PARITY-CONTRACT.md) proves the parity-filter adaptation and records the finite verification obligations. No theorem dependency in that parity argument requires a machine-local path.
+
+This provenance note and the parity contract were prepared with substantial OpenAI Codex assistance. Original source authorship and assistance disclosures remain separate from that disclosure.
diff --git a/research/five-stage-p10-transcript-stages/proof/primary/UPSTREAM-README.md b/research/five-stage-p10-transcript-stages/proof/primary/UPSTREAM-README.md
new file mode 100644
index 0000000000..c8cb3c3857
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/proof/primary/UPSTREAM-README.md
@@ -0,0 +1,17 @@
+# [Integer multiplication below n log n](paper.pdf)
+
+**Author:** OpenAI
+
+**Date:** September 23, 2026
+
+## Citation
+
+```bibtex
+@misc{OAI:Integer-multiplication-below-n-log-n-September-23-2026,
+  author = {{OpenAI}},
+  title = {{Integer multiplication below $n\log n$}},
+  howpublished = {OpenAI Math Release preprint
+                  \href{https://github.com/openai/math/blob/main/preprints/Integer-multiplication-below-n-log-n-September-23-2026/paper.pdf}{OAI:Integer-multiplication-below-n-log-n-September-23-2026}},
+  year = {2026}
+}
+```
diff --git a/research/five-stage-p10-transcript-stages/proof/three-stage-cover-bit.tex b/research/five-stage-p10-transcript-stages/proof/three-stage-cover-bit.tex
new file mode 100644
index 0000000000..f05225d21f
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/proof/three-stage-cover-bit.tex
@@ -0,0 +1,264 @@
+\subsection{Atom contract and common endpoint}
+Fix an odd prime $q$, chosen below, and put $R_w=\mathbb Z/q^w\mathbb Z$.
+An atom is a complete consecutive $w$-digit address field. Write $C_n$ for
+reversal of the $n$ atom positions, without reversing digits inside an atom.
+The recursive contract is the involution
+\[
+ F_A(H,D)=(AC_nD,C_nA^{-1}H),
+\]
+where $A$ is a diagonal array of units on the head atoms. Its entries may
+depend on exposed ancestor row fields and the atom index, but not on the
+fresh role fields of this invocation or on the head/data values. Only the
+polynomial-time descriptors generated by the construction are required;
+no constant-cost oracle for arbitrary functions of a prefix is assumed.
+Every call preserves all complete spectator fields and restores its row
+coordinate. The original unweighted call has $A=I$.
+
+For a split idempotent $P$ on the head coordinates set
+\[
+ D_P=\begin{pmatrix}I-P&PC_n\\C_nP&I-C_nPC_n\end{pmatrix},
+ \qquad F=D_I.
+\]
+These are involutions, and $D_P-I$ has split rank $\operatorname{rank}P$.
+Nested commuting-projector identities are polynomial identities and require
+no symmetry of $P$. For $n=mf$ and $G=g\otimes I_f$ define
+\[
+ Q_g=\operatorname{diag}(G,C_nGC_n).
+\]
+Then $Q_gF=FQ_g$ and $Q_gD_PQ_g^{-1}=D_{GPG^{-1}}$.
+Consequently conjugating every base frame by any $g\in\operatorname{GL}_m(R_w)$
+leaves the same full physical endpoint $F$.
+
+Put $Q_A=\operatorname{diag}(A,I)$. Conjugate the entire completed scalar
+word by $Q_A$. Scalar gates mix roles having the same address map, so they
+commute with $Q_A$. A current role routing also commutes with $Q_A$, since
+it changes only fresh fields. Thus only address residuals change, and the
+completed endpoint is $Q_AFQ_A^{-1}=F_A$. More explicitly, when a port
+changes charts from $g$ to $gR_s$, its local label changes from $M$ to
+$R_s^{-1}MR_s$, and
+\[
+ (gR_s)(R_s^{-1}MR_s)(gR_s)^{-1}=gMg^{-1}.
+\]
+This routing is a change of row/chart, not an uncharged dense address map.
+The adapted chart $Q_AQ_gQ_A^{-1}$ commutes with $F_A$. None of these
+conjugations is executed as an extra normalization pass.
+
+\subsection{Explicit rational three-stage geometry}
+Use the retained PR97 local producer with
+\[
+ h=23,\qquad v=1771,\qquad R_{\rm loc}=28866,\qquad \ell=506.
+\]
+Its physical projector ranks and scalar word are unchanged. On
+$\mathcal A=\mathbb Q^{23}$ take the form $H_0=(I-J/9)/2$.
+For a triple $S$ let $q_S=\chi_S$; then $q_S^tH_0q_S=1$.
+Fix $q_0=\chi_{\{1,2,3\}}$ and $K=q_0^\perp$. A rational basis is
+\[
+ k_i=e_i-(e_i^tH_0q_0)q_0,\qquad 2\le i\le23.
+\]
+Projection along $q_0$ is injective on the span of $e_2,\ldots,e_{23}$,
+since $q_0$ has nonzero first coordinate. Thus this is indeed a basis.
+Let $\mathcal B,\mathcal C$ be orthogonal copies of $K$ and put
+$\mathcal E=\mathcal A\perp\mathcal B\perp\mathcal C$, of dimension $m=67$.
+
+Choose a coordinate permutation $\pi_S$ taking $\{1,2,3\}$ to $S$.
+It preserves $H_0$. The rational isometry $R_{12,S}$ fixes $q_S$ and
+$\mathcal C$, and exchanges $\pi_Sk_i\in q_S^\perp\subset\mathcal A$
+with $k_i\in\mathcal B$. Define $R_{23,S}$ by exchanging the same vectors
+with their copies in $\mathcal C$, fixing $q_S$ and $\mathcal B$.
+Both maps are involutions. A hyperedge $(g,S)$ uses the invocations
+$gR_{12,S},g,gR_{23,S}$, with active spaces
+\[
+ g(\mathcal B+\mathbb Qq_S),\qquad g\mathcal A,
+ \qquad g(\mathcal C+\mathbb Qq_S).
+\]
+Their projectors commute; their pairwise and common intersection is the
+projector $P_{gq_S}$, and their sum is $I+2P_{gq_S}$.
+This follows from the orthogonal decomposition
+$\mathbb Qq_S\perp q_S^\perp\perp\mathcal B\perp\mathcal C$ before
+conjugation. These are the cumulative-projector three-stage transfer
+identities: the three scalar shears complete the interchange, with zero
+interstage connectors and no rank-one endpoint correction. Each port
+family visits the full cover bijectively, by right multiplication with
+its displayed involution. The physical ledger is therefore three copies
+of the local auxiliary, data and center histograms, and three copies of
+the exterior histogram $m-\text{nullity}$.
+
+\subsection{One weighted child on a generic residue class}
+Work first on one atom column. Let $g$ be its weighted residual involution,
+of split rank $r$ relative to $I$. If the cross block has generic northeast
+rank profile, unit lower row and column elimination, without normalizing
+pivots, gives
+\[
+ Lg_{XY}R=ED_pF_0^t,
+ \quad E=(e_1,\ldots,e_r),\quad
+ F_0=(e_m,\ldots,e_{m-r+1}),
+\]
+with invertible diagonal $D_p$. Conjugate by $\operatorname{diag}(L,R^{-1})$.
+Split rank and the unit pivot minor give a factorization
+\[
+ g-I=\binom EB(A_0,D_pF_0^t),\qquad
+ A_0E+D_pF_0^tB=-2I_r.
+\]
+For clarity, if $g-I=UV$, then $g^2=I$ gives
+$U(VU+2I)V=0$. The unit minor supplies a left inverse of $U$ and a right
+inverse of $V$, proving the identity over the local ring itself.
+Set
+\[
+ K=-(B+F_0D_p^{-1})E^t+F_0D_p^{-1}A_0(I-EE^t),
+ \qquad S=\begin{pmatrix}I&0\\K&I\end{pmatrix}.
+\]
+The identities $KE=-B-F_0D_p^{-1}$ and
+$D_pF_0^tK=A_0+E^t$ give
+\[
+ SgS^{-1}=\begin{pmatrix}
+ I-EE^t&ED_pF_0^t\\F_0D_p^{-1}E^t&I-F_0F_0^t
+ \end{pmatrix}.
+\]
+This is one weighted reversed interchange on the first $r$ head and last
+$r$ tail coordinates. All other factors are unit lower intrabank maps or
+lower cross-bank additive maps. Thus variable diagonal units remain in
+the child's weight array rather than becoming unsupported routing passes.
+
+For $n=mf$, group atoms by coarse coordinate $i$ and column $j$.
+If $L_P,R_P,D_P$ are unweighted normalizers for the current projector and
+$A_j=\operatorname{diag}(A[if+j])$, then
+$L_j=A_jL_PA_j^{-1}$ and $R_j=R_P$ are unit lower normalizers for
+$A_jPC_m$. The child's exact contiguous index rule is
+\[
+ A_{\rm child}[kf+j]=A[i_kf+j]D_P[k].
+\]
+The cross-bank atom pairing is reversed, and $C_r\otimes C_f=C_{rf}$.
+Hence the middle operation is exactly one $rf$-atom call of the same
+contract, with no interleaving or gathering. Its coefficients depend only
+on parent prefix fields, which become ancestor spectators at the child;
+the child's fresh roles come from disjoint unused row stock.
+
+All unit lower adapters require $O(n)$ atom passes. The retained ordered
+affine lemma implements each later-target shear in $O(V)$, including
+prefix-controlled offsets. The generated descriptors have polynomial cost
+in $w$: good-class evaluation follows one ancestral index per level;
+fallback evaluation branches by a constant per level. Since depth is
+$O(\log e)$ and $w=\lceil e^{1/1000}\rceil$, this costs $e^{O(1)}=w^{O(1)}$.
+Stored ancestor data use $O(w\log e)$ bits. The proof of the ordered affine
+lemma still applies with these controls: polynomial preparation per prefix
+is absorbed by the complete $q^w$ target fiber. Unrelated spectator counters
+are incremented by ripple counting rather than read in their entirety.
+
+\subsection{Weighted leaves and a genuine local-ring fallback}
+At one atom write $J_a=\left(\begin{smallmatrix}0&a\\a^{-1}&0\end{smallmatrix}\right)$,
+$U(a)=\left(\begin{smallmatrix}1&a\\0&1\end{smallmatrix}\right)$ and
+$L(b)=\left(\begin{smallmatrix}1&0\\b&1\end{smallmatrix}\right)$.
+Then
+\[
+ J_a=\operatorname{diag}(1,-1)U(a)L(-a^{-1})U(a),
+ \qquad U(a)=J_1L(a)J_1.
+\]
+Thus a weighted leaf uses four old ordinary atom interchanges, three
+prefix-controlled shifts and one fixed sign. With
+$a_{\rm old}=384599/10^{10}$ it costs $O(Vw^{1-a_{\rm old}})$.
+This constant occurs only at stopped leaves.
+
+A bad residue class cannot be treated by field Bruhat elimination:
+an entry zero modulo $q$ need not vanish modulo $q^w$. Instead Gaussian
+eliminate the full invertible residual of size $N_0=2m$ with unit pivots.
+Each invertible Schur complement has a unit in its next pivot column;
+row swaps and unnormalized additions clear that column. There are at most
+$N_0(N_0-1)$ additions and $N_0$ swaps. Pivot choices are determined by
+the unweighted low residue class: diagonal conjugation scales every
+Schur-complement row and column by units and preserves its zero pattern.
+The final diagonal has product a fixed sign, since the residual has
+determinant $(-1)^r$ and row swaps change only the sign.
+
+A lower addition is a paid additive adapter. An upper addition is
+conjugated into a lower addition by two ordinary coarse-field swaps.
+For a field of $f$ atoms, let $R_{\rm tail}$ reverse the later field.
+Then the ordinary weighted swap is
+\[
+ J_A=R_{\rm tail}F_AR_{\rm tail},\qquad
+ J_A(H,D)=(AD,A^{-1}H).
+\]
+Each $R_{\rm tail}$ is one unweighted reversed call on the first and last
+$\lfloor f/2\rfloor$ atoms, fixing a possible middle atom. Thus $J_A$
+costs at most three children of widths $f,\lfloor f/2\rfloor,
+\lfloor f/2\rfloor$. A paired diagonal scaling is $J_aJ_1$, at most six
+children. The full diagonal is a product of $N_0-1$ such pairs and a fixed
+sign. Across the two banks the reversed pairing already makes the swaps
+and diagonal pairs directly reversed calls; the preceding ordinary bounds
+remain conservative. Reindexing a tail weight by $j\mapsto f-1-j$ changes
+only its descriptor. Charging every addition as upper therefore gives
+\[
+ 6N_0(N_0-1)+3N_0+6(N_0-1)<32m^2.
+\]
+Every child has width at most $f$, hence ratio at most $1/m$. Coefficients
+are computed from constant-sized local-ring matrices and parent weight
+descriptors; only units are inverted. This proves the fallback cost,
+including its actual reversals, rather than assuming nonunit pivots away.
+
+\subsection{Finite covers, batching, and the strict moment}
+Take $q>2^{80}$ avoiding all fixed rational denominators and rank witnesses.
+At atom width $w$ use the finite cover $\operatorname{GL}_m(R_w)$ and its
+right-multiplication edges $g\mapsto gR_s$. Every vertex has the unique chart
+\[
+ g=g_0+qG_1,\quad g_0\in\operatorname{GL}_m(\mathbb F_q),
+ \quad G_1\in(\mathbb Z/q^{w-1}\mathbb Z)^{m^2},
+\]
+using fixed representatives for $g_0$. Right multiplication permutes $g_0$
+and acts affinely on $G_1$, with a carry determined by $g_0$. Its fixed
+dimensional rational linear part factors into fixed scalings, ordered
+shifts and a constant number of old width-$O(w)$ interchanges. Thus each
+fixed port routing costs $O(Vw^{1-a_{\rm old}})$.
+
+Let $W_0=|\operatorname{GL}_m(\mathbb F_q)|(2v+3R_{\rm loc})$.
+The full role count is $W(w)=W_0q^{m^2(w-1)}$. Split preceding rows into
+low role type, high matrix and unused stock. Batch \emph{all} high matrices
+for each low type in one stream. A frame edge is one child on this whole
+batch, of volume $V/W_0$, and routing is executed once per fixed operation
+type. Consequently neither the number of tapes nor the number of child
+programs grows with $w$. High cardinality cancels in the normalized moment,
+but its $m^2(w-1)$ digits are charged in the row reserve.
+
+For each fixed projector require the leading minors of sizes $1$ through
+$r$ to be units. Each cleared minor polynomial in $g_0$ is nonzero:
+similarity to $\operatorname{diag}(I_r,0)$ supplies a witness after the
+fixed rank is preserved modulo $q$. Their total degree is at most $m^3$.
+The polynomial zero bound and conditioning on invertibility (a factor at
+most two) give bad fraction at most $2m^3/q<10^{-16}$ for each edge type.
+No simultaneous union bound over edge types is needed, since their moments
+are averaged separately. Good classes use the whole-rank child; bad
+classes use the full $32m^2$-child fallback just proved.
+
+Let $H_r$ be the three-stage histogram described above and
+$W=2v+3R_{\rm loc}=90140$. The retained ledger gives
+\[
+ \sum_r rH_r=6037356,\qquad Wm-\sum_r rH_r=2024=2v-3\ell,
+ \qquad \max\{r:H_r>0\}=66.
+\]
+For $a=747/2000000$, $\tau=1-a$, and $b=10^{-16}$ the conservative moment is
+\[
+ \mu_\tau\le
+ \sum_r\frac{H_r}{W}(r/m)^\tau+
+ b\frac{32m^2\sum_rH_r}{W}(1/m)^\tau<1.
+\]
+The entire fallback is added; no displaced good contribution is subtracted.
+The exact script \path{scripts/three_stage_cover_network.py} and certificate
+\path{certificates/three-stage-cover-network.json}, from the retained axis
+\path{certificates/three-stage-cover-bit-input.json}, give
+$1-\mu_\tau>6.3397366396\cdot10^{-7}$.
+The certificate uses the 32-term positive atanh logarithm series with its
+geometric tail, $\exp(u)\le1+u+u^2/(2(1-u/3))$, and upward rounding to
+the grid $2^{-120}$. All inputs have $0\le u<3$; these are rational upper
+bounds, not floating-point root estimates. Since every child ratio is at
+most one and $\tau<1$, this same strict bound implies $\mu_1<1$.
+
+With $T(n,w)$ denoting time divided by logical volume, the fixed low-type
+profile $\{c_r\}$, including fallback classes, satisfies
+\[
+ T(n,w)\le\sum_rc_rT(r\lfloor n/m\rfloor,w)+Cn+Cw^{1-a_{\rm old}}
+ \quad(n\ge m),\qquad
+ T(n,w)\le Cw^{1-a_{\rm old}}\quad(n<m).
+\]
+Peeling fewer than $m$ leftover atoms uses the weighted leaf algorithm.
+The constants are independent of $w,n$ and ancestor values. Induction,
+using $\mu_1<1$ for the linear term and $\mu_\tau<1$ for the stopped term,
+gives $T(n,w)=O(n+n^\tau w^{1-a_{\rm old}})$. The maximum proper ratio
+$66/67$ has halving degree $47$, so recursion depth is $O(\log n)$.
diff --git a/research/five-stage-p10-transcript-stages/proof/three-stage-cover-rows.tex b/research/five-stage-p10-transcript-stages/proof/three-stage-cover-rows.tex
new file mode 100644
index 0000000000..590da4b892
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/proof/three-stage-cover-rows.tex
@@ -0,0 +1,95 @@
+\subsection{Internal row reserve and ordinary conversion}
+The finite cover requires a row divisor $W(w)$ at each coarse level.
+All children have ratio at most $66/67$ and depth
+$D(n)\le47\lceil\log_2\max(2,n)\rceil+O(1)$.
+A sufficient common divisor is $W(w)^{D(n)}$ times the inherited old-leaf
+reserve. The old supplier has its retained complete-row contract and
+logarithmic reserve. Therefore a sufficient integer $S(e,w)$ satisfies
+\[
+ \log_qS(e,w)=O(w\log e).
+\]
+Unused stock is divided only into fresh descendant role fields; exposed
+parent low/high fields are spectator prefixes. Their weights cannot depend
+on those fresh roles. Every completed call restores its row coordinate,
+so successive residuals and the outer wrapper reuse one reserve instead
+of multiplying reserves for sequential calls.
+
+The unweighted reversed endpoint $F_n(H,D)=(C_nD,C_nH)$ converts to an
+ordinary interchange by the chronological sequence
+\[
+ D\leftarrow D-H;\quad F_n;\quad D\leftarrow D+H;\quad
+ F_n;\quad D\leftarrow H-D.
+\]
+Indeed the successive values are $(H,D-H)$, $(C_n(D-H),C_nH)$,
+$(C_n(D-H),C_nD)$, $(D,D-H)$, and $(D,H)$.
+The three additive maps cost $O(Vn)$ in the atom model. The two calls
+reuse restored rows; their constant multiplicity is outside the recursion
+and does not multiply its characteristic moment.
+
+\subsection{Borrowing and restoring the stock}
+Set $\beta=1/1000$, $w=\lceil e^\beta\rceil$, and
+$k=\lceil\log_qS(e,w)\rceil=O(w\log e)$, using the depth bound for the
+original width $e$. For sufficiently large $e$, $k<e/2$. Write the two
+original complete radix-$q$ chunks as $H=(H_{\rm hi},H_{\rm body})$ and
+$D=(D_{\rm hi},D_{\rm body})$, both high parts having $k$ digits. The
+physical order, including arbitrary original complete spectators $Z$, is
+\[
+ H_{\rm hi},\ H_{\rm body},\ Z,\ D_{\rm hi},\ D_{\rm body}.
+\]
+The complete $q^k$ range of $H_{\rm hi}$ already precedes both bodies.
+Reinterpret it as a preceding row field; $D_{\rm hi}$ remains an intervening
+spectator. Pad only this row range to $\lceil q^k/S\rceil S$. As $q^k\ge S$,
+the padding factor is less than two.
+
+Execute the completed \emph{ordinary} body wrapper with this row reserve,
+then remove the padding. Each row is restored, so the genuine row range
+is invariant at the completed endpoint. The order of values is now
+\[
+ H_{\rm hi},\ D_{\rm body},\ Z,\ D_{\rm hi},\ H_{\rm body}.
+\]
+One inherited ordinary width-$k$ interchange of the two high parts,
+with the bodies and $Z$ as spectators, gives
+\[
+ D_{\rm hi},\ D_{\rm body},\ Z,\ H_{\rm hi},\ H_{\rm body}.
+\]
+This is precisely the original full-chunk interchange. Its extra cost is
+$O(Vk^{1-a_{\rm old}})\le O(Vw\log e)$, conservatively. No full body is
+moved once per borrowed digit. Padding occurs only in this outer wrapper;
+it contributes one volume constant, not a recursive branching factor.
+The wrapper does not rely on a raw reversed call preserving borrowed high
+positions. Small widths use the retained supplier directly.
+
+\subsection{Uniform saving and return to binary addresses}
+Select atom width from the original $e$. Since $k=o(e)$, the body width
+$e-k$ has the same asymptotic powers as $e$. Apply the ordinary wrapper to
+its complete atom body and the old ordinary supplier to fewer than $w$
+remaining digits. The stopped recurrence and the borrowing cost give
+\[
+ O\!\left(V\left[e^{1-\beta}+
+ e^{(1-\beta)(1-a)+\beta(1-a_{\rm old})}+e^\beta\log e\right]\right).
+\]
+Here $a=747/2000000$ and $a_{\rm old}=384599/10^{10}$. Set
+\[
+ a_{\rm bit}=(1-\beta)a+\beta a_{\rm old}
+ =\frac{3731649599}{10^{13}}=0.0003731649599.
+\]
+The inequalities $\beta>a_{\rm bit}$ and $\beta<1-a_{\rm bit}$ make both
+the atom-adapter and borrowing terms lower order. The remainder cost
+$O(Vw^{1-a_{\rm old}})$ is also covered. Thus the ordinary radix-$q$
+interchange has cost $O(Ve^{1-a_{\rm bit}})$, without an externally supplied
+superpolynomial stock of rows.
+
+For an original binary chunk range $[2^e]$, let
+$t=\lceil e/\log_2q\rceil$ and embed it numerically into $[q^t]$.
+Pad both exchanged ranges while retaining every spectator. The total
+logical-volume increase is below $q^2$. Execute the completed ordinary
+radix-$q$ interchange, then remove the padding. Its endpoint preserves the
+rectangular genuine set $[2^e]\times[2^e]$; intermediate maps may mix genuine
+and padded addresses, which does not affect this endpoint justification.
+As $q$ is fixed and $t=\Theta(e)$, the binary interchange has the same
+saving exponent. All schedules use a fixed number of finite-alphabet
+tapes; low residue tables and port types are fixed independently of $w$.
+
+The conclusion retains the original local-producer, ordered-affine,
+ordinary-leaf and multiplication-framework hypotheses. It adds no free
+unit-scaling, dense chart transformation, or external row-stock primitive.
diff --git a/research/five-stage-p10-transcript-stages/raw_ledger.py b/research/five-stage-p10-transcript-stages/raw_ledger.py
new file mode 100644
index 0000000000..2a175c9bba
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/raw_ledger.py
@@ -0,0 +1,333 @@
+"""Independent fresh p = 10 physical path census, including both reflections.
+Derived from the source527 census (eumemic); constants rebound to the gen5 word, then generalized to any cube
+size (h, v, m, copies and deficits from word_pins.shape; word counts pinned in word-pins.json) for p = 10.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+No saved receipt, search script, or historical profile is consumed.
+"""
+from collections import Counter,defaultdict
+from types import SimpleNamespace
+from word_pins import expect,shape
+
+def run(context):
+ m=SimpleNamespace(**context);W=m.W;C=m.C;chosen=m.pair_selection;fresh=m.fresh;pair_byalias=m.pair_byalias;pair_bydirty=m.pair_bydirty
+ compact=lambda h:{str(k):v for k,v in sorted(h.items())if v}
+ zero=W.register([]);compact=lambda h:{str(k):v for k,v in sorted(h.items())if v}
+ # Exact raw event sequence, with every actual extra source included.
+ events=[]
+ for j,op in enumerate(W.rest):
+  for s in m.at[j]:events.append(dict(kind='gauge',ref=s,frame=W.gauge[s]['frame'],targets=list(m.adj[s])))
+  if op in m.bywrite:events.append(dict(kind='terminalwrite',ref=op,frame=W.opframe[op],targets=[m.bywrite[op]['pivot']]))
+  if op in m.afterwrite:events.append(dict(kind='terminalread',ref=op,frame=m.afterwrite[op]['root_frame'],targets=m.afterwrite[op]['targets']))
+ for s in m.at[len(W.rest)]:events.append(dict(kind='gauge',ref=s,frame=W.gauge[s]['frame'],targets=list(m.adj[s])))
+ endgauge=len(events)
+ for j,r in enumerate(W.g['roots']):
+  if r['kind']=='side'and j not in m.deletedroots:events.append(dict(kind='root',ref=j,frame=W.w['root_frame'][j],targets=r['targets']))
+  for e in m.deliveries[j]:events.append(dict(kind='K',ref=e['passive'],frame=e['deliver_frame'],targets=e['receivers']))
+ for t in range(W.v):events.append(dict(kind='endpoint',ref=t,frame=W.register(W.module.kernel([C.cov[t]],W.h)[0]),targets=[t]))
+ 
+ def histogram(t,path):
+  h=Counter();rev=Counter();assert path[0]==zero and C.dimf[path[-1]]==W.h-1
+  for f in path:assert C.nondeg(f)and all(W.module.dot(C.cov[t],b)==0 for b in C.B[f]),('cap/nondeg',t,f)
+  for a,b in zip(path,path[1:]):
+   assert C.sub(a,b),('forward inclusion',t,a,b)
+   d=C.dimf[b]-C.dimf[a];assert d>=0
+   if d:h[d]+=1
+  for a,b in zip(reversed(path),list(reversed(path))[1:]):
+   assert all(W.module.dot(x,y)==0 for x in C.A[a]for y in C.B[b]),('reflected inclusion',t,a,b)
+   d=len(C.A[b])-len(C.A[a]);assert d>=0
+   if d:rev[d]+=1
+  assert h==rev and sum(k*v for k,v in h.items())==W.h-1
+  return h
+ 
+ def paths(agg,readframes,echelon,rankgroups):
+  rankowner={t:k for k,g in enumerate(rankgroups)for t in g['targets']}
+  out=[[zero]for _ in range(W.v)];owner={t:k for k,g in enumerate(agg)for t in g['targets']};roles=defaultdict(list)
+  for k,g in enumerate(agg):
+   for s in g['roles']:roles[s].append(k)
+  active=set(range(len(agg)));rankactive=set(range(len(rankgroups)));echactive=set(range(len(echelon)));seen=[set()for _ in echelon];restores=[]
+  for j,e in enumerate(events):
+   if j>=endgauge:assert not active and not rankactive and not echactive
+   s=e['ref'];T=set(e['targets'])
+   if e['kind']=='gauge':
+    if s in pair_byalias:continue
+    if s in fresh:
+     for t,c in fresh[s]['transformed_response'].items():
+      if c:out[int(t)].append(W.gauge[s]['frame'])
+     continue
+    skip=set()
+    for k,g in enumerate(echelon):
+     if k not in echactive:continue
+     if s not in g['roles']:
+      if T&set(g['targets']):
+       assert seen[k]==g['roles'];restores.append(dict(group=k,before_role=s,event=j))
+       for t in g['targets']:out[t].append(g['frame'])
+       echactive.remove(k)
+      continue
+     seen[k].add(s);skip.update(g['targets'])
+     for t,a in g['response'].items():
+      if a.get(s,0):out[t].append(W.gauge[s]['frame'])
+    for k in sorted({rankowner[t]for t in T if t in rankowner}):
+     if k in rankactive and s not in rankgroups[k]['roles']:
+      for t in rankgroups[k]['targets']:out[t].append(rankgroups[k]['frame'])
+      rankactive.remove(k)
+    for k in sorted({owner[t]for t in T if t in owner}):
+     if k in active and s not in agg[k]['roles']:
+      for t in agg[k]['targets']:out[t].append(agg[k]['frame'])
+      active.remove(k)
+    for k in roles[s]:
+     assert k in active;g=agg[k];out[g['pivot']].append(readframes[s,k]);skip.update(g['targets'])
+    for t in e['targets']:
+     if t in skip:continue
+     rk=rankowner.get(t)
+     if rk in rankactive and t in rankgroups[rk]['dependent']:continue
+     out[t].append(e['frame'])
+   else:
+    assert not(T&{t for k in active for t in agg[k]['targets']})
+    assert not(T&{t for k in echactive for t in echelon[k]['targets']})
+    for t in e['targets']:out[t].append(e['frame'])
+  H=Counter()
+  for t,p in enumerate(out):H.update(histogram(t,p))
+  return out,H,restores
+ 
+ newpaths,target,restores=paths(m.agg,m.read_frames,m.echelon,m.rankgroups)
+ # Recover raw literal adjoint independently, respecting all omitted copies.
+ adj=[{}for _ in range(W.R)]
+ for root,role in zip(W.g['roots'],W.w['rootroles']):
+  for t in root['targets']:adj[role][t]=adj[role].get(t,0)+1
+ for i in reversed(W.phase1+W.rest):
+  if i in m.omitted:continue
+  a,b,_=W.ops[i]
+  for t,c in adj[a].items():adj[b][t]=adj[b].get(t,0)+c
+ assert adj==m.adj
+ oldused={r[k]for r in m.selection+m.gauge_selection if r['role']not in pair_byalias for k in('source','partner')}
+ assert len({r[k]for r in chosen for k in('source','partner')})==2*len(chosen)==0 and not oldused&{r[k]for r in chosen for k in('source','partner')}
+ for r in chosen:
+  b=r['aliased_role'];response=Counter(adj[b])
+  for a,c in r['retained_dirty_coefficients'].items():
+   for t,v in adj[a].items():response[t]+=c*v
+  assert not any(response.values())
+ # Complete physical source and auxiliary census, including all alias handoffs.
+ recipient={d:b for b,d in W.pairs};roots=defaultdict(list)
+ for j,s in enumerate(W.w['rootroles']):roots[s].append(W.w['root_frame'][j])
+ source_role={s:n for n,s in W.source.items()};plainborrow={r['role']:r for r in m.selection};gauges={r['role']:r for r in m.gauge_selection}
+ assert len(plainborrow)==0 and len(gauges)==0 and len(m.borrow)==0
+ seq={s:[('op',i,W.opframe[i])for i in W.role_ops[s]]+[('root',j,f)for j,f in enumerate(roots[s])]for s in range(W.R)}
+ def physical_path(s):
+  a=list(seq[s])
+  if s in pair_bydirty:a=[('paired-source-injection',s,pair_bydirty[s]['mix_frame'])]+a
+  if s in recipient:
+   b=recipient[s];a+=[('alias',b,W.gauge[b]['frame'])]+seq[b]
+  return a+[('full',s,W.w['full_frame'])]
+ count=0
+ 
+ def census_hist(start,events):
+  nonlocal count
+  count+=1;prev=start;dim=C.dimf[start]if start is not None else 0;out=Counter();chain=[]if start is None else[start]
+  for _,_,f in events:
+   assert C.nondeg(f)and(prev is None or C.sub(prev,f));d=C.dimf[f]-dim;assert d>=0
+   if d:out[d]+=1
+   prev=f;dim=C.dimf[f];chain.append(f)
+  assert dim==W.h;reflected=Counter()
+  for a,b in zip(reversed(chain),list(reversed(chain))[1:]):
+   assert all(W.module.dot(x,y)==0 for x in C.A[a]for y in C.B[b]);d=len(C.A[b])-len(C.A[a]);assert d>=0
+   if d:reflected[d]+=1
+  if start is None:
+   d=W.h-len(C.A[chain[0]])
+   if d:reflected[d]+=1
+  assert reflected==out
+  return out,chain
+ internal=Counter();sources=Counter();pathrows={};sourcepaths={};dirtypaths={}
+ for s in m.regs:
+  start=W.gauge[s]['frame']if s in W.gauge else W.w['source_frame'][source_role[s]]if s in source_role else None
+  H,chain=census_hist(start,physical_path(s))
+  if s in source_role:H[1]+=1
+  internal.update(H);pathrows['a'+str(s)]=compact(H)
+  if s in pair_bydirty:dirtypaths[str(s)]=[zero]+chain
+ for j,r in enumerate(W.g['roots']):
+  if r['kind']=='center':internal[C.dimf[W.w['root_frame'][j]]]+=1
+ for entry in W.k['entries']:
+  carrier,n=entry['carrier'],entry['passive'];H,chain=census_hist(entry['carrier_chain'][0],[('carrier',j,f)for j,f in enumerate(entry['carrier_chain'][1:])]);sources.update(H)
+  if n not in m.by_source:
+   H,chain=census_hist(entry['passive_chain'][0],[('passive',j,f)for j,f in enumerate(entry['passive_chain'][1:])]);sources.update(H);pathrows['s'+str(n)]=compact(H);continue
+  r=m.by_source[n];s=r['role'];events=physical_path(s)
+  if s in plainborrow:
+   r=plainborrow[s];events=[x for x in events if not(x[0]=='op'and x[1]==r['omit_copy'])];at=next(i for i,x in enumerate(events)if x[0]=='op'and x[1]==r['early']);events.insert(at,('mix',n,entry['mix_frame']))
+  else:
+   assert s in gauges;events=[('mix',n,entry['mix_frame']),('gauge',s,W.gauge[s]['frame'])]+events
+  H,chain=census_hist(W.w['source_frame'][n],events);sources.update(H);pathrows['s'+str(n)]=compact(H)
+  if s in m.extra_byrole:sourcepaths[str(s)]=chain
+ assert count==len(m.regs)+W.v and len(sourcepaths)==0 and len(dirtypaths)==0 and sum(k*v for k,v in sources.items())==W.v*(W.h-1)
+ gauges=Counter(z['dim']for s,z in W.gauge.items()if s not in W.donor and s not in m.borrow)
+ S=shape();expect('entrance_ranks',gauges)
+ copies=Counter(C.dimf[W.w['root_frame'][j]]for j,r in enumerate(W.g['roots'])if r['kind']=='center');assert copies=={S['center_rank']:S['centers']}
+ withoutcopies=internal.copy();withoutcopies.subtract(copies);assert min(withoutcopies.values())>=0
+ helper=internal+sources+target;h=S['h'];v=S['v'];R=len(m.regs);M=S['m'];stock=4*v+R
+ assert h==W.h and v==W.v and R==expect('physical_R',R) and len(m.borrow)==0
+ assert sum(k*n for k,n in helper.items())==h*R+2*v*(h-1)+sum(k*n for k,n in copies.items())-sum(k*n for k,n in gauges.items())
+ idle=Counter({r:2*v for r in S['idle']});five=Counter({r:5*n for r,n in helper.items()});five.update(idle)
+ for r,n in gauges.items():five[5*r]+=n
+ mass=sum(k*n for k,n in five.items());assert M*stock-mass==S['deficit']
+ raw=dict(schema='p10-fresh-raw-ledger/1',source_head=context.get('source_head','p10'),h=h,v=v,physical_R=R,source_aliases=len(m.borrow),terminal_sinks=len(m.terminal),physical_donor_recipient_identifications=len(W.pairs),physical_internal_excluding_center_copies=compact(withoutcopies),paid_center_copy_histogram=compact(copies),physical_source_histogram=compact(sources),physical_target_histogram=compact(target),one_stage_helper_histogram_including_copies=compact(helper),auxiliary_entrance_rank_histogram=compact(gauges),auxiliary_entrance_count=sum(gauges.values()),helper_rank_mass=sum(k*n for k,n in helper.items()),five_stage_profile=dict(m=M,W=stock,histogram=compact(five),idle_histogram=compact(idle),calls=sum(five.values()),rank_mass=mass,deficit=M*stock-mass,maxchild=max(five)),source_aux_paths=count,target_paths=v,extra_source_paths=len(sourcepaths),paired_dirty_paths=len(dirtypaths),all_reflected_ledgers=True,all_zero_response_relations=True,scope='Fresh complete p = 10 raw physical source/internal/target and copied-center ledger. Both reflected chains checked; no saved execution receipt consumed.')
+ expect('producer_five_stage_calls',raw['five_stage_profile']['calls']);expect('five_stage_rank_mass',mass)
+ return raw
+
+def rebind_parity(raw,receipt):
+ """Bind the fresh required-use census to the retained producer source ledger."""
+ from copy import deepcopy
+ def hist(x):return Counter({int(r):n for r,n in x.items()if n})
+ assert receipt['status']=='PASS_FRESH_PARITY_FUSION_AND_INDEPENDENT_REQUIRED_FRAME_CENSUS'
+ assert receipt['both_reflected_ledgers']and receipt['unchanged_all_input_output_frames']
+ source=hist(receipt['source_histogram']);target=hist(receipt['target_histogram']);internal=hist(receipt['internal_histogram_including_copies']);copies=hist(receipt['copied_center_histogram'])
+ assert source==hist(raw['physical_source_histogram'])
+ assert internal==hist(raw['physical_internal_excluding_center_copies'])+copies
+ delta=target.copy();delta.subtract(hist(raw['physical_target_histogram']));assert {r:n for r,n in delta.items()if n}=={}
+ producer=deepcopy(raw);helper=source+target+internal;five=Counter({r:5*n for r,n in helper.items()});five.update(hist(raw['five_stage_profile']['idle_histogram']))
+ for a,n in hist(raw['auxiliary_entrance_rank_histogram']).items():five[5*a]+=n
+ expect('five_stage_calls',sum(five.values()));assert sum(r*n for r,n in five.items())==expect('five_stage_rank_mass',raw['five_stage_profile']['rank_mass'])
+ raw['schema']='p10-parity-fused-fresh-raw-ledger/1';raw['producer_ledger']=producer
+ raw['physical_target_histogram']={str(r):n for r,n in sorted(target.items())};raw['one_stage_helper_histogram_including_copies']={str(r):n for r,n in sorted(helper.items())}
+ raw['five_stage_profile'].update(histogram={str(r):n for r,n in sorted(five.items())},calls=sum(five.values()))
+ raw['parity_transform']=receipt;raw['scope']='Fresh p = 10 producer ledger plus independently rebuilt actual surviving-use ledger after F2 payload identity elision and same-stream nested MOVE fusion. Both reflected endpoint inclusions checked. No address arithmetic reduced modulo2.'
+ return raw
+
+_S=shape();_H=_S['h'];_V=_S['v'];_M=_S['m'];_CR=_S['center_rank'];_NC=_S['centers'];_DEF=_S['deficit']
+pin=expect   # the stage rebinds pin their counts in word-pins.json
+
+def rebind_descent(raw,receipt):
+ """Recount the complete word after the concave-descent frame retiming of selected ADD gates."""
+ from copy import deepcopy
+ hist=lambda x:Counter({int(r):n for r,n in x.items()if n})
+ compact=lambda x:{str(r):n for r,n in sorted(x.items())if n}
+ assert receipt['status']=='PASS_CONCAVE_DESCENT_RETIMING_AND_BOTH_REFLECTED_LEDGERS'
+ assert receipt['both_reflected_ledgers']and receipt['unchanged_all_input_output_frames']and receipt['unchanged_copy_lifetimes']and receipt['operand_source_spans_contained']
+ pin('descent_selected_gates',receipt['selected_gate_count']);pin('descent_remaining_payload_additions',receipt['remaining_payload_additions']);pin('descent_removed_calls',receipt['removed_calls'])
+ source=hist(receipt['source_histogram']);target=hist(receipt['target_histogram']);internal=hist(receipt['internal_histogram_including_copies']);copies=hist(receipt['copied_center_histogram'])
+ assert copies==hist(raw['paid_center_copy_histogram'])=={_CR:_NC}
+ helper=source+target+internal;delta=helper.copy();delta.subtract(hist(raw['one_stage_helper_histogram_including_copies']))
+ pin('descent_local_delta',{r:n for r,n in delta.items()if n})
+ assert {r:n for r,n in delta.items()if n}==hist(receipt['local_histogram_delta'])
+ # Source, target and internal paths may each regroup; every endpoint mass is retained exactly.
+ assert sum(r*n for r,n in source.items())==sum(r*n for r,n in hist(raw['physical_source_histogram']).items())==_V*(_H-1)
+ assert sum(r*n for r,n in target.items())==sum(r*n for r,n in hist(raw['physical_target_histogram']).items())==_V*(_H-1)
+ assert sum(r*n for r,n in helper.items())==pin('descent_helper_rank_mass',sum(r*n for r,n in helper.items()))==raw['helper_rank_mass'] and sum(helper.values())==sum(hist(raw['one_stage_helper_histogram_including_copies']).values())-receipt['removed_calls']
+ original=deepcopy(raw);gauges=hist(raw['auxiliary_entrance_rank_histogram']);pin('entrance_ranks',gauges)
+ five=Counter({r:5*n for r,n in helper.items()});five.update(hist(raw['five_stage_profile']['idle_histogram']))
+ for a,n in gauges.items():five[5*a]+=n
+ pin('descent_five_stage_calls',sum(five.values()));assert sum(r*n for r,n in five.items())==raw['five_stage_profile']['rank_mass']
+ withoutcopies=internal.copy();withoutcopies.subtract(copies);assert min(withoutcopies.values())>=0
+ raw['schema']='p10-parity-descent-fresh-raw-ledger/1';raw['parity_fused_ledger']=original
+ raw['physical_source_histogram']=compact(source);raw['physical_target_histogram']=compact(target);raw['physical_internal_excluding_center_copies']=compact(withoutcopies)
+ raw['one_stage_helper_histogram_including_copies']=compact(helper);raw['helper_rank_mass']=sum(r*n for r,n in helper.items())
+ raw['five_stage_profile'].update(histogram=compact(five),calls=sum(five.values()))
+ raw['descent_transform']=receipt;raw['scope']='Fresh actual p10 word after the concave-descent retiming of '+str(receipt['selected_gate_count'])+' ADD gate frames. Every scalar column, operand source span, required frame path, reflected inclusion, data endpoint and copied-center lifetime is checked; '+str(receipt['removed_calls'])+' local recursive calls disappear at unchanged rank mass.'
+ return raw
+
+def rebind_kernel(raw,receipt):
+ """Complete physical census after the per-pair-cut kernel rewrite (adapted from #268's rebind_kernel)."""
+ from copy import deepcopy
+ from word_pins import expect as pin
+ hist=lambda x:Counter({int(k):v for k,v in x.items()if v})
+ compact=lambda x:{str(k):v for k,v in sorted(x.items())if v}
+ assert receipt['status']=='PASS_GEN4_PER_ENTRY_CUT_KERNEL_ON_ACTUAL_WORD_AND_BOTH_REFLECTED_LEDGERS'
+ assert receipt['both_reflected_ledgers']and receipt['unchanged_data_input_output_and_dirty_output_frames']and receipt['unchanged_copy_lifetimes']
+ pairs=pin('kernel_pairs',receipt['selected_pairs']);pin('kernel_entries',receipt['selected_entries']);ranks=hist(receipt['proof']['entrance_rank_histogram']);assert receipt['rank_drop']==sum(r*c for r,c in ranks.items())==pin('kernel_entrance_rank',receipt['rank_drop']) and receipt['proof']['source_context_preserved']
+ source=hist(receipt['source_histogram']);target=hist(receipt['target_histogram']);internal=hist(receipt['internal_histogram_including_copies']);copies=hist(receipt['copied_center_histogram'])
+ assert source==hist(raw['physical_source_histogram'])and target==hist(raw['physical_target_histogram'])and copies=={_CR:_NC}
+ helper=source+target+internal;delta=helper.copy();delta.subtract(hist(raw['one_stage_helper_histogram_including_copies']))
+ assert {k:v for k,v in delta.items()if v}==hist(receipt['local_histogram_delta'])==hist(pin('kernel_local_delta',{k:v for k,v in delta.items()if v}))
+ pin('kernel_helper_rank_mass',sum(k*v for k,v in helper.items()))
+ before=deepcopy(raw);gauges=hist(raw['auxiliary_entrance_rank_histogram']);gauges.update(ranks)
+ pin('entrance_rank_histogram',dict(gauges))
+ five=Counter({r:5*n for r,n in helper.items()});five.update(hist(raw['five_stage_profile']['idle_histogram']))
+ for a,n in gauges.items():five[5*a]+=n
+ pin('kernel_five_stage_calls',sum(five.values()));pin('kernel_five_stage_rank_mass',sum(r*n for r,n in five.items()))
+ without=internal.copy();without.subtract(copies);assert min(without.values())>=0
+ raw.update(schema='gen4-kernel-pairs-fresh-ledger/1',parity_ledger=before,physical_internal_excluding_center_copies=compact(without),one_stage_helper_histogram_including_copies=compact(helper),helper_rank_mass=sum(k*v for k,v in helper.items()),auxiliary_entrance_rank_histogram=compact(gauges),auxiliary_entrance_count=sum(gauges.values()),kernel_transform=receipt)
+ raw['five_stage_profile'].update(histogram=compact(five),calls=sum(five.values()),rank_mass=sum(r*n for r,n in five.items()))
+ raw['scope']='Fresh complete actual gen4 kernel-pair word, all scalar columns and both reflected ledgers; the rank-one pivot entrances are tracked beside the gen4 entrances.'
+ return raw
+
+def rebind_restore(raw,receipt,completions):
+ """Complete physical census after the early-restoration rewrite: helper histogram from the fresh path census;
+ entrances unchanged; five-stage completions charged at dim(sigma)+h-dim(endpoint) (P_sigma + I - P_E)."""
+ from copy import deepcopy
+ from word_pins import expect as pin
+ hist=lambda x:Counter({int(k):v for k,v in x.items()if v})
+ compact=lambda x:{str(k):v for k,v in sorted(x.items())if v}
+ assert receipt['status']=='PASS_GEN5_EARLY_RESTORATION_ON_ACTUAL_WORD_AND_BOTH_REFLECTED_LEDGERS'
+ assert receipt['both_reflected_ledgers']and receipt['unchanged_data_input_output_frames']and receipt['unchanged_copy_lifetimes']
+ pin('restore_helpers',receipt['selected']);saving=pin('restore_endpoint_saving',receipt['endpoint_rank_saving'])
+ source=hist(receipt['source_histogram']);target=hist(receipt['target_histogram']);internal=hist(receipt['internal_histogram_including_copies']);copies=hist(receipt['copied_center_histogram'])
+ assert source==hist(raw['physical_source_histogram'])and target==hist(raw['physical_target_histogram'])and copies=={_CR:_NC}
+ helper=source+target+internal;delta=helper.copy();delta.subtract(hist(raw['one_stage_helper_histogram_including_copies']))
+ assert {k:v for k,v in delta.items()if v}==hist(receipt['local_histogram_delta'])==hist(pin('restore_local_delta',{k:v for k,v in delta.items()if v}))
+ assert sum(k*v for k,v in helper.items())==raw['helper_rank_mass']-saving
+ gauges=hist(raw['auxiliary_entrance_rank_histogram']);completions=Counter(completions)
+ assert sum(completions.values())==sum(gauges.values()) and sum(r*n for r,n in completions.items())==sum(r*n for r,n in gauges.items())+saving
+ pin('completion_rank_histogram',dict(completions))
+ five=Counter({r:5*n for r,n in helper.items()});five.update(hist(raw['five_stage_profile']['idle_histogram']))
+ for c,n in completions.items():five[5*c]+=n
+ assert sum(r*n for r,n in five.items())==raw['five_stage_profile']['rank_mass'],'early restoration keeps the five-stage deficit'
+ pin('restore_five_stage_calls',sum(five.values()));pin('restore_five_stage_rank_mass',sum(r*n for r,n in five.items()))
+ without=internal.copy();without.subtract(copies);assert min(without.values())>=0
+ before=deepcopy(raw)
+ raw.update(schema='p10-early-restoration-fresh-ledger/1',kernel_ledger=before,physical_internal_excluding_center_copies=compact(without),one_stage_helper_histogram_including_copies=compact(helper),helper_rank_mass=sum(k*v for k,v in helper.items()),completion_rank_histogram=compact(completions),restore_transform=receipt)
+ raw['five_stage_profile'].update(histogram=compact(five),calls=sum(five.values()),rank_mass=sum(r*n for r,n in five.items()))
+ raw['scope']='Fresh complete actual p10 word after kernel entries and early helper restoration; helper endpoints below FULL are completed by P_sigma + I - P_E.'
+ return raw
+
+def rebind_sink(raw,receipt,completions):
+ """Complete physical census after terminal sinks: removed zero-to-full helpers free their whole h-rank path; the
+ register count, the stock and the five-stage profile are recomputed and the deficit 4v-5h(h-2) is rechecked."""
+ from copy import deepcopy
+ from word_pins import expect as pin
+ hist=lambda x:Counter({int(k):v for k,v in x.items()if v})
+ compact=lambda x:{str(k):v for k,v in sorted(x.items())if v}
+ assert receipt['status']=='PASS_GEN5_TERMINAL_SINKS_ON_ACTUAL_WORD_AND_BOTH_REFLECTED_LEDGERS'
+ assert receipt['both_reflected_ledgers']and receipt['unchanged_surviving_input_output_frames']and receipt['unchanged_copy_lifetimes']
+ k=pin('sink_count',receipt['selected']);R=receipt['physical_R'];assert R==raw['physical_R']-k
+ source=hist(receipt['source_histogram']);target=hist(receipt['target_histogram']);internal=hist(receipt['internal_histogram_including_copies']);copies=hist(receipt['copied_center_histogram'])
+ assert source==hist(raw['physical_source_histogram'])and copies=={_CR:_NC}
+ assert sum(r*n for r,n in target.items())==_V*(_H-1)
+ helper=source+target+internal;delta=helper.copy();delta.subtract(hist(raw['one_stage_helper_histogram_including_copies']))
+ assert {a:b for a,b in delta.items()if b}==hist(receipt['local_histogram_delta'])==hist(pin('sink_local_delta',{a:b for a,b in delta.items()if b}))
+ assert sum(a*b for a,b in helper.items())==raw['helper_rank_mass']-_H*k
+ completions=Counter(completions);assert completions==hist(raw['completion_rank_histogram']),'sinks are plain helpers: entrances unchanged'
+ five=Counter({r:5*n for r,n in helper.items()});five.update(hist(raw['five_stage_profile']['idle_histogram']))
+ for c,n in completions.items():five[5*c]+=n
+ stock=4*_V+R;mass=sum(r*n for r,n in five.items());assert _M*stock-mass==_DEF,'terminal sinks keep the five-stage deficit'
+ pin('sink_five_stage_calls',sum(five.values()));pin('sink_five_stage_rank_mass',mass)
+ without=internal.copy();without.subtract(copies);assert min(without.values())>=0
+ before=deepcopy(raw)
+ raw.update(schema='p10-terminal-sinks-fresh-ledger/1',restore_ledger=before,physical_R=R,terminal_sinks=k,physical_target_histogram=compact(target),physical_internal_excluding_center_copies=compact(without),one_stage_helper_histogram_including_copies=compact(helper),helper_rank_mass=sum(a*b for a,b in helper.items()),sink_transform=receipt)
+ raw['five_stage_profile'].update(W=stock,histogram=compact(five),calls=sum(five.values()),rank_mass=mass,deficit=_M*stock-mass)
+ raw['scope']='Fresh complete actual p10 word after kernel entries, early restoration and terminal sinks.'
+ return raw
+
+def rebind_reorder(raw,receipt,completions,tag='reorder'):
+ """Complete physical census after the reordering stage: the same registers, endpoints and rank mass; only the split
+ of the paid paths changes. The five-stage profile is recomputed and the deficit 4v-5h(h-2) is rechecked."""
+ from copy import deepcopy
+ from word_pins import expect as pin
+ hist=lambda x:Counter({int(k):v for k,v in x.items()if v})
+ compact=lambda x:{str(k):v for k,v in sorted(x.items())if v}
+ assert receipt['status']=='PASS_GEN5_REORDER_ON_ACTUAL_WORD_AND_BOTH_REFLECTED_LEDGERS'
+ assert receipt['tag']==tag and receipt['all_gate_frames_contain_operand_source_spans'] and receipt['both_reflected_ledgers']and receipt['unchanged_endpoints']and receipt['unchanged_copy_lifetimes']and receipt['integer_replay']['identical']
+ k=pin(tag+'_count',receipt['selected']);R=raw['physical_R']
+ source=hist(receipt['source_histogram']);target=hist(receipt['target_histogram']);internal=hist(receipt['internal_histogram_including_copies']);copies=hist(receipt['copied_center_histogram'])
+ assert copies=={_CR:_NC}
+ assert sum(r*n for r,n in target.items())==_V*(_H-1)
+ helper=source+target+internal;delta=helper.copy();delta.subtract(hist(raw['one_stage_helper_histogram_including_copies']))
+ assert {a:b for a,b in delta.items()if b}==hist(receipt['local_histogram_delta'])==hist(pin(tag+'_local_delta',{a:b for a,b in delta.items()if b}))
+ assert sum(a*b for a,b in helper.items())==raw['helper_rank_mass'],'reordering keeps the rank mass'
+ completions=Counter(completions);assert completions==hist(raw['completion_rank_histogram']),'reordering keeps every entrance and endpoint'
+ five=Counter({r:5*n for r,n in helper.items()});five.update(hist(raw['five_stage_profile']['idle_histogram']))
+ for c,n in completions.items():five[5*c]+=n
+ stock=4*_V+R;mass=sum(r*n for r,n in five.items());assert _M*stock-mass==_DEF,'reordering keeps the five-stage deficit'
+ pin(tag+'_five_stage_calls',sum(five.values()));pin(tag+'_five_stage_rank_mass',mass)
+ without=internal.copy();without.subtract(copies);assert min(without.values())>=0
+ before=deepcopy(raw)
+ raw.update(schema='p10-'+tag+'-fresh-ledger/1',**{'before_'+tag+'_ledger':before,tag+'_transform':receipt},physical_source_histogram=compact(source),physical_target_histogram=compact(target),physical_internal_excluding_center_copies=compact(without),one_stage_helper_histogram_including_copies=compact(helper),helper_rank_mass=sum(a*b for a,b in helper.items()))
+ raw['five_stage_profile'].update(W=stock,histogram=compact(five),calls=sum(five.values()),rank_mass=mass,deficit=_M*stock-mass)
+ raw['scope']='Fresh complete actual p10 word after kernel entries, early restoration, terminal sinks, post-sink descent and reordering.'
+ return raw
diff --git a/research/five-stage-p10-transcript-stages/reorder-selection.json b/research/five-stage-p10-transcript-stages/reorder-selection.json
new file mode 100644
index 0000000000..fea3800542
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/reorder-selection.json
@@ -0,0 +1 @@
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diff --git a/research/five-stage-p10-transcript-stages/reorder_transform.py b/research/five-stage-p10-transcript-stages/reorder_transform.py
new file mode 100644
index 0000000000..eff90cafc5
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/reorder_transform.py
@@ -0,0 +1,180 @@
+"""Reordering stage after the terminal sinks: an ADD a += c*b leaves its frame and joins a neighbouring incidence.
+
+Mechanism (toggle-detection view of Khattar-Gidney, arXiv:2407.17966, specialised to this word). On the post-sink word a
+delivery y += h of a root helper h at the root frame R (rank 21) is immediately followed, for the same target y, by a
+climb to a rank-22 frame F for the next side_root read, while h itself stays at R for its three sibling deliveries
+and then climbs R -> FULL for its cleanups. The delivery commutes with every gate between it and y's next incidence
+(none of them reads y, none writes h), so it is executed just before that incidence, inside F: y now climbs R' -> F in
+one step instead of R' -> R -> F, and h climbs R -> F -> FULL instead of R -> FULL (local delta {21:-1, 22:+1, 3:-1,
+2:+1} per move, rank mass unchanged). The same screen also moves 22 forward gates to an earlier incidence frame.
+Selection rule (discovery/build_reorder_selection.py): every ADD whose frame is a strict breakpoint of an operand's
+path is tried at the frame of each of the six previous/next incidences of either operand; the move is admitted when
+no gate on the crossed interval reads a or writes b (and no COPY/ERASE touches a), the rebuilt frame chains of a and b
+are nested and the phi ledger decreases; greedy by gain over disjoint operand sets.
+Checks here: the frozen moves are re-derived on the actual input word (record content, anchor frame, crossed-interval
+contract, disjoint operand sets); F2 replay of every formal column forward and inverse; omitting the moved ADDs fails;
+every MOVE rebuilt from operand frames with both reflected ledgers; an independent integer replay modulo 2^61-1 with
+pseudo-random dirty inputs gives identical final values for every register; local delta equals the frozen one.
+Prepared with Anthropic Claude assistance; Apache-2.0.
+p = 10 port (Chafik Boukhalfa (chafreaky), Anthropic Claude assistance): h, v, centre copies and scatter reads come
+from word_pins.shape and the stage counts are pinned in word-pins.json; the mechanism and checks are unchanged.
+"""
+from array import array
+from collections import Counter
+from pathlib import Path
+import gzip,hashlib,json,time,sys,importlib.util,bisect
+sys.dont_write_bytecode=True
+if not __debug__:raise SystemExit('assertions required')
+HERE=Path(__file__).resolve().parent
+from word_pins import shape as _shape
+_S=_shape();_H=_S['h'];_V=_S['v'];_M=_S['m'];_CR=_S['center_rank'];_NC=_S['centers'];_SCAT=_S['scatter_reads'];_DEF=_S['deficit']
+sha=lambda b:hashlib.sha256(b).hexdigest()
+
+def integer_replay(records,n,seed=20260710):
+    """Exact replay modulo the Mersenne prime 2^61-1 with fixed pseudo-random dirty inputs (all registers and the temporary)."""
+    import random
+    P=(1<<61)-1;rng=random.Random(seed);val=[rng.randrange(P)for _ in range(n+1)]
+    for k in range(0,len(records),6):
+        op,a,b,c,f,z=records[k:k+6]
+        if op==1:val[a]=(val[a]+c*val[b])%P
+        elif op==2:val[n]=val[a]
+    return val[:n]
+
+def span_violations(records,W,C,n,v):
+    """Exact integer source span of every non-target operand after each gate (PR #287/#291 rule), checked against the
+    gate frame for EVERY gate of the word: returns the violating (record, source) pairs."""
+    columns=[{i:1} if i<v else {} for i in range(n)];center=None;bad=[]
+    for k in range(0,len(records),6):
+        op,a,b,c,f,z=records[k:k+6]
+        if op==0:continue
+        if op==2:assert center is None;center=a;continue
+        if op==3:assert center==a;center=None;continue
+        source=center if b==n else b;ca=columns[a]
+        for s,x in columns[source].items():
+            y=ca.get(s,0)+c*x
+            if y:ca[s]=y
+            else:del ca[s]
+        need=set()
+        if not(v<=a<2*v):need.update(ca)
+        if not(v<=b<2*v) and b!=n:need.update(columns[b])
+        for s in need:
+            if any(W.module.dot(x,C.chi[s])for x in C.A[f]):bad.append((k//6,s));break
+    return bad
+
+def transform(producer,selection,tag='reorder'):
+    W,C=producer['W'],producer['C'];old=producer['records'];initial=dict(producer['initial_state']);final=dict(producer['final_state'])
+    v=W.v;n=2*v+len(producer['context']['regs'])
+    assert n==selection['n'] and v==selection['v'] and sha(old.tobytes())==selection['input_raw_sha256'],'reorder selection bound to a different word'
+    assert producer['physical']['scalar_projection_sha256']==selection['input_scalar_sha256']
+    cats=list(producer['physical']['category_names']);assert tag+'_moved' not in cats
+    MOVED=len(cats);cats+=[tag+'_moved']
+    moves={};ops=set()
+    for e in selection['moves']:
+        i,T,side=e['record'],e['anchor'],e['side'];op,a,b,c,f,z=old[6*i:6*i+6]
+        assert op==1 and [a,b,c]==e['incidence'] and b!=n and cats[z]==e['category'],'moved record content differs'
+        assert not({a,b}&ops),'operand sets of the moves must be disjoint';ops|={a,b}
+        aop,aa,ab,ac,af,az=old[6*T:6*T+6];assert aop==1 and ({aa,ab}&{a,b}),'anchor must be an ADD incidence of a or b'
+        F=af;assert C.dimf[F]==e['frame_rank'] and [list(x)for x in C.B[F]]==e['frame_basis'],'anchor frame differs from the frozen basis'
+        assert (side=='before' and T>i) or (side=='after' and T<i)
+        lo,hi=(i,T) if side=='before' else (T+1,i)
+        for k in range(lo,hi):
+            if k==i:continue
+            xo,x,y,_,_,_=old[6*k:6*k+6]
+            if xo==1:assert y!=a and x!=b,('crossed gate reads a or writes b',i,k)
+            elif xo in(2,3):assert x!=a,('crossed copy of a',i,k)
+        moves[i]=(a,b,c,F,T,side)
+    before={};after={}
+    for i,m in moves.items():(before if m[5]=='before' else after).setdefault(m[4],[]).append(i)
+    state=dict(initial);out=array('i');temporary=None
+    def move(s,f):
+        b0=state[s]
+        if b0==f:return
+        assert C.sub(b0,f),('reorder nonnested use',s,b0,f)
+        gap=C.dimf[f]-C.dimf[b0];assert gap>=0;out.extend((0,s,b0,f,gap,0));state[s]=f
+    def add(a,b,c,f,z):
+        move(a,f)
+        if b!=n:move(b,f)
+        out.extend((1,a,b,c,f,z))
+    def emit_moved(lst):
+        for i in sorted(lst):a,b,c,F,T,side=moves[i];add(a,b,c,F,MOVED)
+    for k in range(0,len(old),6):
+        op,a,b,c,f,z=old[k:k+6];i=k//6
+        emit_moved(before.get(i,()))
+        if op==1:
+            if i not in moves:add(a,b,c,f,z)
+        elif op==2:assert temporary is None;move(a,c);state[b]=f;temporary=(a,b,c);out.extend((op,a,b,c,f,z))
+        elif op==3:assert temporary==(a,b,c)and state[a]==c and state[b]==f;out.extend((op,a,b,c,f,z));del state[b];temporary=None
+        emit_moved(after.get(i,()))
+    assert temporary is None
+    for s in sorted(final):move(s,final[s])
+    assert state==final
+    project=lambda aa:sorted(tuple(aa[k+j]for j in(0,1,2,3))for k in range(0,len(aa),6)if aa[k]==1)
+    assert project(out)==project(old),'only the documented reordering (same multiset of scalar ADDs)'
+    proof=dict(selected=len(moves),operand_sets_disjoint=True,crossed_interval_contract=True,categories=dict(Counter(e['category']for e in selection['moves'])),
+        shapes=dict(Counter('%s:%d->%d'%(e['category'],e['old_frame_rank'],e['frame_rank'])for e in selection['moves'])))
+    return out,initial,final,cats,proof,n,v
+
+def run(producer,output_dir=None,selection_path=None,tag='reorder'):
+    start=time.monotonic()
+    spec=importlib.util.spec_from_file_location('reorder_kernel_replay',HERE/'kernel_transform.py');km=importlib.util.module_from_spec(spec);spec.loader.exec_module(km)
+    W,C=producer['W'],producer['C'];path=Path(selection_path)if selection_path else HERE/(tag+'-selection.json');selection=json.loads(path.read_text())
+    out,initial,final,cats,proof,n,v=transform(producer,selection,tag);ZERO=producer['ZERO']
+    forward=km.replay(out,n,v);inverse=km.replay(out,n,v,True);controls=[km.replay(out,n,v,omit_category=cats.index(tag+'_moved'))]
+    assert not span_violations(out,W,C,n,v),'a gate frame omits an operand source span'
+    old=producer['records'];iold=integer_replay(old,n);inew=integer_replay(out,n);assert iold==inew,'integer replay differs'
+    needs={s:[]for s in initial};copies=Counter();temporary=None
+    for k in range(0,len(out),6):
+        op,a,b,c,f,z=out[k:k+6]
+        if op==1:
+            needs[a].append(f)
+            if b!=n:needs[b].append(f)
+            else:assert temporary is not None and f==ZERO
+        elif op==2:assert temporary is None;temporary=(a,b,c);needs[a].append(c);copies[z]+=1
+        elif op==3:assert temporary==(a,b,c);temporary=None
+    assert temporary is None and copies=={_CR:_NC}
+    per_role={};pairs=set();census=Counter(copies);reflected=Counter(copies)
+    for s,startframe in initial.items():
+        H=Counter();pathframes=[startframe]+needs[s]+[final[s]]
+        for a,b in zip(pathframes,pathframes[1:]):
+            assert C.sub(a,b);gap=C.dimf[b]-C.dimf[a];assert gap>=0;pairs.add((a,b))
+            if gap:H[gap]+=1
+        for a,b in zip(reversed(pathframes),list(reversed(pathframes))[1:]):
+            assert all(not W.module.dot(x,y)for x in C.A[a]for y in C.B[b]);gap=len(C.A[b])-len(C.A[a]);assert gap>=0
+            if gap:reflected[gap]+=1
+        per_role[s]=H;census.update(H)
+    assert reflected==census
+    for f in {x for pair in pairs for x in pair}:assert C.nondeg(f)and len(C.B[f])+len(C.A[f])==_H
+    state=dict(initial);hist=Counter();cat=Counter();coeff=Counter();usedf=set(state.values());temporary=None;centers=[];count=0;tagged=hashlib.sha256()
+    for k in range(0,len(out),6):
+        op,a,b,c,f,z=out[k:k+6]
+        if op==0:
+            assert state[a]==b and C.sub(b,c)and C.dimf[c]-C.dimf[b]==f and len(C.A[b])-len(C.A[c])==f
+            state[a]=c;usedf.update((b,c))
+            if f:hist[f]+=1
+        elif op==1:
+            assert state[a]==state[b]==f and a!=b and c%2;count+=1;cat[cats[z]]+=1;coeff[abs(c)]+=1;usedf.add(f)
+            tagged.update(json.dumps([a,b,c,f,cats[z]],separators=(',',':')).encode());tagged.update(b'\n')
+        elif op==2:
+            assert temporary is None and b==n and state[a]==c and f==ZERO and z==_CR
+            state[b]=f;hist[z]+=1;temporary=dict(source=a,frame=c,rank=z,temporary=b,first_event=count,copy_output_frame=f)
+        else:
+            assert op==3 and temporary is not None and (a,b,c)==(temporary['source'],temporary['temporary'],temporary['frame'])and state[a]==c and state[b]==f==ZERO
+            temporary.update(after_event=count,scatter_reads=count-temporary['first_event']);assert temporary['scatter_reads']==_SCAT;centers.append(temporary);temporary=None;del state[b]
+    assert state==final and temporary is None and hist==census and len(centers)==_NC
+    oldH=Counter({int(r):c for r,c in producer['physical']['paid_histogram'].items()});delta=Counter(hist);delta.subtract(oldH);delta={r:c for r,c in delta.items()if c}
+    assert delta=={int(k):x for k,x in selection['expected_local_delta'].items()}
+    assert sum(r*c for r,c in hist.items())==producer['physical']['paid_rank_mass'],'reordering keeps the paid rank mass'
+    assert count==producer['physical']['weighted_scalar_events']
+    inherited=set()
+    for inventory in (producer['physical'],producer.get('producer_physical')):
+        if isinstance(inventory,dict):inherited.update(row['frame_id']for row in inventory.get('used_frames',[]))
+    sourceH=Counter();targetH=Counter();internalH=Counter(copies)
+    for s,H in per_role.items():(sourceH if s<v else targetH if s<2*v else internalH).update(H)
+    receipt=dict(status='PASS_GEN5_REORDER_ON_ACTUAL_WORD_AND_BOTH_REFLECTED_LEDGERS',proof=proof,scalar=dict(forward=forward,inverse=inverse,controls=controls),integer_replay=dict(modulus='2^61-1',registers=n,identical=True),all_gate_frames_contain_operand_source_spans=True,tag=tag,selected=proof['selected'],local_histogram_delta=delta,unchanged_endpoints=True,unchanged_copy_lifetimes=True,both_reflected_ledgers=True,unique_required_frame_pairs=len(pairs),source_histogram=dict(sourceH),target_histogram=dict(targetH),internal_histogram_including_copies=dict(internalH),copied_center_histogram=dict(copies),input_raw_sha256=sha(old.tobytes()),output_raw_sha256=sha(out.tobytes()),selection_sha256=sha(path.read_bytes()),transform_sha256=sha(Path(__file__).read_bytes()),seconds=time.monotonic()-start)
+    meta=dict(producer['physical']);meta.update(status='PASS_PHYSICAL_GEN5_REORDER',scalar_projection_sha256=forward['event_sha256'],tagged_scalar_sha256=tagged.hexdigest(),weighted_scalar_events=count,coefficient_histogram=dict(coeff),categories=dict(cat),category_names=cats,copied_center_blocks=centers,paid_histogram=dict(sorted(hist.items())),paid_rank_mass=sum(r*c for r,c in hist.items()),positive_rank_moves=sum(hist.values())-_NC,used_frames=[dict(frame_id=f,dimension=C.dimf[f],basis_sha256=sha(json.dumps(C.B[f],separators=(',',':')).encode()))for f in sorted(usedf|inherited)],**{tag+'_transform':receipt},physical_emitter_sha256=receipt['transform_sha256'])
+    result=dict(producer);result.update(records=out,physical=meta,result=meta,**{tag+'_census':receipt})
+    if output_dir is not None:
+        p=Path(output_dir);p.mkdir(parents=True,exist_ok=True);(p/(tag+'-records.bin.gz')).write_bytes(gzip.compress(out.tobytes(),mtime=0))
+        (p/(tag+'.json')).write_text(json.dumps(receipt,indent=2)+'\n')
+    print('PASS',tag,proof['selected'],'moved ADDs; source spans of every gate checked;',count,'scalar ADDs',sum(hist.values()),'paid calls',len(out)//6,'records',flush=True)
+    return result
diff --git a/research/five-stage-p10-transcript-stages/requirements.txt b/research/five-stage-p10-transcript-stages/requirements.txt
new file mode 100644
index 0000000000..1ca5fd0616
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/requirements.txt
@@ -0,0 +1 @@
+sympy==1.14.0
diff --git a/research/five-stage-p10-transcript-stages/restore-selection.json b/research/five-stage-p10-transcript-stages/restore-selection.json
new file mode 100644
index 0000000000..f48cb0cb7e
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/restore-selection.json
@@ -0,0 +1 @@
+{"status": "GEN5_EARLY_RESTORATION_PR280_SCREEN", "n": 10150, "v": 960, "input_raw_sha256": "6bc01e74a192787a9b075d1569fb974baffccd7014057fe0c394f92a9e3a3dcf", "input_scalar_sha256": "b2178b676b360cab0901efa0b2ec5ad873175e95079a55630f2aabaa3562c730", "cut": 353416, "selected": 240, "entries": [{"helper": 9507, "donor": 2924, "coefficient": -1, "incidence": [9507, 2924, -1], "rank": 19, "basis": [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], "dims": [16, 18, 18, 19]}, {"helper": 9515, "donor": 2929, "coefficient": -1, "incidence": [9515, 2929, -1], "rank": 19, "basis": [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 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0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]], "dims": [16, 18, 18, 19]}], "expected_local_delta": {"1": 720, "2": -480}}
diff --git a/research/five-stage-p10-transcript-stages/restore_transform.py b/research/five-stage-p10-transcript-stages/restore_transform.py
new file mode 100644
index 0000000000..444a0204fe
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/restore_transform.py
@@ -0,0 +1,197 @@
+"""Early helper restoration on the gen5 kernel word (port of PR #280's 440-helper cleanup to this Python pipeline).
+
+Mechanism and selection rule from PR #280 (utcorvusvolat-dotcom, code/cleanup_screen.py, cleanup_emit.py,
+docs/cleanup-proof.md) and its endpoint-aware composition in PR #283 (Dugongue, RESTORATION-PROOF.md). At the first
+cleanup ADD (the cut) every target already holds its required endpoint. A helper a qualifies when its formal row is
+untouched at the cut, its only remaining scalar incidence is a += c*b, b is not written between the cut and that
+incidence, and no COPY/ERASE follows the cut. All selected a and b are distinct and disjoint. The shear a += c*b then
+commutes over the integers with every crossed scalar gate (no crossed gate reads or writes a, none writes b), so it is
+executed at the cut, inside the exact rational join E of the current frames of a and b (dimension 23, nondegenerate
+for 9I-J), and a ends at E instead of FULL. The helper's residual projector becomes P_E - P_sigma (rank 3 for a rank-20
+entrance sigma); the five-stage completion becomes P_sigma + (I - P_E) and the banks are re-tiled for the actual
+residual. The screen is recomputed on the actual input word and must equal the frozen selection.
+Checks: integer commutation conditions on the actual suffix; F2 replay of every formal column forward and inverse;
+omission control (deleting the moved restorations must fail); every required frame path rebuilt from scalar/COPY
+events with both reflected ledgers; all used frames nondegenerate.
+Prepared with Anthropic Claude assistance; Apache-2.0.
+p = 10 port (Chafik Boukhalfa (chafreaky), Anthropic Claude assistance): h, v, centre copies and scatter reads come
+from word_pins.shape and the stage counts are pinned in word-pins.json; the mechanism and checks are unchanged.
+"""
+from array import array
+from collections import Counter
+from pathlib import Path
+import gzip,hashlib,json,time,sys
+sys.dont_write_bytecode=True
+if not __debug__:raise SystemExit('assertions required')
+HERE=Path(__file__).resolve().parent
+from word_pins import shape as _shape
+_S=_shape();_H=_S['h'];_V=_S['v'];_M=_S['m'];_CR=_S['center_rank'];_NC=_S['centers'];_SCAT=_S['scatter_reads'];_DEF=_S['deficit']
+sha=lambda b:hashlib.sha256(b).hexdigest()
+
+def screen(old,initial,n,v,C,W,cats,ZERO,FULL):
+    """Fresh PR280 screen on the actual word: returns cut and the qualifying (a,b,i,c) rows."""
+    cleanup=cats.index('cleanup_gate')
+    cut=next(k//6 for k in range(0,len(old),6)if old[k]==1 and old[k+5]==cleanup)
+    rows=[1<<j for j in range(n)]+[0];state=dict(initial);temporary=None
+    for k in range(0,6*cut,6):
+        op,a,b,c,f,z=old[k:k+6]
+        if op==0:state[a]=c
+        elif op==1:
+            if c%2:rows[a]^=rows[b]
+        elif op==2:assert temporary is None;temporary=a;rows[n]=rows[a]
+        elif op==3:assert temporary==a;temporary=None;rows[n]=0
+    assert temporary is None
+    assert all(rows[v+j]==(1<<(v+j))^(1<<j)for j in range(v)),'targets incomplete at the cut'
+    affected=set()
+    for a,x in enumerate(rows[:n]):
+        x^=1<<a
+        if v<=a<2*v:x^=1<<(a-v)
+        while x:k=(x&-x).bit_length()-1;x&=x-1;affected.add(k)
+    inc={};writes={};copies=0
+    for k in range(6*cut,len(old),6):
+        op,a,b,c,f,z=old[k:k+6];i=k//6
+        if op==1:inc.setdefault(a,[]).append(i);inc.setdefault(b,[]).append(i);writes.setdefault(a,[]).append(i)
+        elif op in(2,3):copies+=1
+    assert copies==0,'COPY/ERASE after the cut'
+    out=[]
+    for a in range(2*v,n):
+        if a in affected or len(inc.get(a,[]))!=1:continue
+        i=inc[a][0];op,x,b,c,f,z=old[6*i:6*i+6]
+        if x!=a or any(cut<=w<i for w in writes.get(b,[])):continue
+        if C.dimf[initial[a]]>=_H:continue
+        out.append((a,b,i,c,state[a],state[b]))
+    return cut,out,state
+
+def transform(producer,selection):
+    W,C=producer['W'],producer['C'];old=producer['records'];initial=dict(producer['initial_state']);context=producer['context'];v=W.v;n=2*v+len(context['regs']);ZERO=producer['ZERO'];FULL=producer['FULL']
+    assert n==selection['n'] and v==selection['v']
+    assert sha(old.tobytes())==selection['input_raw_sha256'],'restoration selection bound to a different word'
+    assert producer['physical']['scalar_projection_sha256']==selection['input_scalar_sha256']
+    cats=list(producer['physical']['category_names']);assert 'early_restore' not in cats
+    restorecat=len(cats);cats+=['early_restore']
+    final=dict(initial)
+    for k in range(0,len(old),6):
+        if old[k]==0:final[old[k+1]]=old[k+3]
+    cut,rows,state=screen(old,initial,n,v,C,W,cats,ZERO,FULL)
+    # Keep the screened rows whose exact join is a proper nondegenerate frame; compare with the frozen selection.
+    chosen={}
+    for a,b,i,c,fa,fb in rows:
+        E=W.register([list(x)for x in C.B[fa]]+[list(x)for x in C.B[fb]])
+        if C.dimf[E]==_H or not C.nondeg(E):continue
+        chosen[a]=dict(helper=a,donor=b,record=i,coefficient=c,frame=E,rank=C.dimf[E],helper_frame=fa,donor_frame=fb,entrance=initial[a])
+    frozen={e['helper']:e for e in selection['entries']};assert len(frozen)==len(selection['entries'])==selection['selected']
+    assert set(chosen)==set(frozen),'fresh screen differs from the frozen selection'
+    for a,e in chosen.items():
+        s=frozen[a];assert (s['donor'],s['coefficient'],s['rank'])==(e['donor'],e['coefficient'],e['rank'])
+        assert [old[6*e['record']+j]for j in(1,2,3)]==s['incidence'],'incidence content differs'
+        assert e['frame']==W.register(s['basis']),'frozen join basis differs'
+        assert (C.dimf[e['entrance']],C.dimf[e['helper_frame']],C.dimf[e['donor_frame']],e['rank'])==tuple(s['dims'])
+        assert C.sub(e['entrance'],e['helper_frame'])and C.sub(e['helper_frame'],e['frame'])and C.sub(e['donor_frame'],e['frame'])
+        assert final[a]==FULL and C.dimf[e['entrance']]<e['rank']
+    helpers=set(chosen);donors={e['donor']for e in chosen.values()}
+    assert len(donors)==len(chosen) and not(helpers&donors),'helpers and donors must be distinct and disjoint'
+    # Integer commutation contract on the crossed interval of each moved shear a += c*b.
+    moved={e['record']:e for e in chosen.values()};donorrecord={e['donor']:e['record']for e in chosen.values()};crossed=0;import bisect;records=sorted(moved)
+    for k in range(6*cut,len(old),6):
+        op,x,y,c,f,z=old[k:k+6];i=k//6
+        if op!=1 or i in moved:continue
+        assert x not in helpers and y not in helpers,'crossed gate touches a moved helper'
+        assert not(x in donorrecord and i<donorrecord[x]),'crossed gate writes a moved donor'
+        crossed+=len(records)-bisect.bisect_right(records,i)
+    state=dict(initial);out=array('i');temporary=None
+    def move(s,f):
+        before=state[s]
+        if before==f:return
+        assert C.sub(before,f),('restoration nonnested actual use',s,before,f)
+        gap=C.dimf[f]-C.dimf[before];assert gap>=0;out.extend((0,s,before,f,gap,0));state[s]=f
+    def add(a,b,c,f,z):move(a,f);move(b,f);out.extend((1,a,b,c,f,z))
+    order=sorted(chosen.values(),key=lambda e:e['helper'])
+    for k in range(0,len(old),6):
+        op,a,b,c,f,z=old[k:k+6];i=k//6
+        if i==cut:
+            assert temporary is None
+            for e in order:add(e['helper'],e['donor'],e['coefficient'],e['frame'],restorecat)
+        if op==1:
+            if i in moved:continue
+            add(a,b,c,f,z)
+        elif op==2:assert temporary is None;move(a,c);state[b]=f;temporary=(a,b,c);out.extend((op,a,b,c,f,z))
+        elif op==3:assert temporary==(a,b,c)and state[a]==c and state[b]==f;out.extend((op,a,b,c,f,z));del state[b];temporary=None
+    assert temporary is None
+    for e in order:final[e['helper']]=e['frame']
+    for s in sorted(final):move(s,final[s])
+    assert state==final
+    project=lambda aa:[tuple(aa[k+j]for j in(0,1,2,3,5))for k in range(0,len(aa),6)if aa[k]]
+    expected=[]
+    for k in range(0,len(old),6):
+        i=k//6
+        if i==cut:expected.extend((1,e['helper'],e['donor'],e['coefficient'],restorecat)for e in order)
+        if old[k] and i not in moved:expected.append(tuple(old[k+j]for j in(0,1,2,3,5)))
+    assert project(out)==expected,'only the documented reordering'
+    proof=dict(selected=len(order),cut=cut,crossed_gate_checks=crossed,dims=dict(Counter((C.dimf[e['entrance']],C.dimf[e['helper_frame']],C.dimf[e['donor_frame']],e['rank'])for e in order).most_common()).__repr__(),
+        helpers_and_donors_disjoint=True,single_remaining_incidence=True,donor_unwritten_on_crossed_interval=True,no_copy_after_cut=True,targets_complete_at_cut=True,
+        endpoint_rank_saving=sum(_H-e['rank']for e in order),residual_histogram=dict(Counter(e['rank']-C.dimf[e['entrance']]for e in order)))
+    return out,initial,final,order,cats,proof,n,v
+
+def run(producer,output_dir=None,selection_path=None):
+    start=time.monotonic();kt=__import__('importlib').util
+    spec=kt.spec_from_file_location('restore_kernel_replay',HERE/'kernel_transform.py');km=kt.module_from_spec(spec);spec.loader.exec_module(km)
+    W,C=producer['W'],producer['C'];path=Path(selection_path)if selection_path else HERE/'restore-selection.json';selection=json.loads(path.read_text())
+    out,initial,final,entries,cats,proof,n,v=transform(producer,selection);ZERO=producer['ZERO'];FULL=producer['FULL']
+    forward=km.replay(out,n,v);inverse=km.replay(out,n,v,True);controls=[km.replay(out,n,v,omit_category=cats.index('early_restore'))]
+    needs={s:[]for s in initial};copies=Counter();temporary=None
+    for k in range(0,len(out),6):
+        op,a,b,c,f,z=out[k:k+6]
+        if op==1:
+            needs[a].append(f)
+            if b!=n:needs[b].append(f)
+            else:assert temporary is not None and f==ZERO
+        elif op==2:assert temporary is None;temporary=(a,b,c);needs[a].append(c);copies[z]+=1
+        elif op==3:assert temporary==(a,b,c);temporary=None
+    assert temporary is None and copies=={_CR:_NC}
+    per_role={};pairs=set();census=Counter(copies);reflected=Counter(copies)
+    for s,startframe in initial.items():
+        H=Counter();pathframes=[startframe]+needs[s]+[final[s]]
+        for a,b in zip(pathframes,pathframes[1:]):
+            assert C.sub(a,b);gap=C.dimf[b]-C.dimf[a];assert gap>=0;pairs.add((a,b))
+            if gap:H[gap]+=1
+        for a,b in zip(reversed(pathframes),list(reversed(pathframes))[1:]):
+            assert all(not W.module.dot(x,y)for x in C.A[a]for y in C.B[b]);gap=len(C.A[b])-len(C.A[a]);assert gap>=0
+            if gap:reflected[gap]+=1
+        per_role[s]=H;census.update(H)
+    assert reflected==census
+    for f in {x for pair in pairs for x in pair}:assert C.nondeg(f)and len(C.B[f])+len(C.A[f])==_H
+    state=dict(initial);hist=Counter();cat=Counter();coeff=Counter();used=set(state.values());temporary=None;centers=[];count=0;tagged=hashlib.sha256()
+    for k in range(0,len(out),6):
+        op,a,b,c,f,z=out[k:k+6]
+        if op==0:
+            assert state[a]==b and C.sub(b,c)and C.dimf[c]-C.dimf[b]==f and len(C.A[b])-len(C.A[c])==f
+            state[a]=c;used.update((b,c))
+            if f:hist[f]+=1
+        elif op==1:
+            assert state[a]==state[b]==f and a!=b and c%2;count+=1;cat[cats[z]]+=1;coeff[abs(c)]+=1;used.add(f)
+            tagged.update(json.dumps([a,b,c,f,cats[z]],separators=(',',':')).encode());tagged.update(b'\n')
+        elif op==2:
+            assert temporary is None and b==n and state[a]==c and f==ZERO and z==_CR
+            state[b]=f;hist[z]+=1;temporary=dict(source=a,frame=c,rank=z,temporary=b,first_event=count,copy_output_frame=f)
+        else:
+            assert op==3 and temporary is not None and (a,b,c)==(temporary['source'],temporary['temporary'],temporary['frame'])and state[a]==c and state[b]==f==ZERO
+            temporary.update(after_event=count,scatter_reads=count-temporary['first_event']);assert temporary['scatter_reads']==_SCAT;centers.append(temporary);temporary=None;del state[b]
+    assert state==final and temporary is None and hist==census and len(centers)==_NC
+    old=Counter({int(r):c for r,c in producer['physical']['paid_histogram'].items()});delta=Counter(hist);delta.subtract(old);delta={r:c for r,c in delta.items()if c}
+    assert delta=={int(k):v for k,v in selection['expected_local_delta'].items()}
+    assert count==producer['physical']['weighted_scalar_events'] and sum(r*c for r,c in hist.items())==producer['physical']['paid_rank_mass']-proof['endpoint_rank_saving']
+    inherited=set()
+    for inventory in (producer['physical'],producer.get('producer_physical')):
+        if isinstance(inventory,dict):inherited.update(row['frame_id']for row in inventory.get('used_frames',[]))
+    sourceH=Counter();targetH=Counter();internalH=Counter(copies)
+    for s,H in per_role.items():(sourceH if s<v else targetH if s<2*v else internalH).update(H)
+    endpoints={e['helper']:e['frame']for e in entries}
+    receipt=dict(status='PASS_GEN5_EARLY_RESTORATION_ON_ACTUAL_WORD_AND_BOTH_REFLECTED_LEDGERS',proof=proof,scalar=dict(forward=forward,inverse=inverse,controls=controls),selected=len(entries),endpoint_rank_saving=proof['endpoint_rank_saving'],local_histogram_delta=delta,unchanged_data_input_output_frames=True,changed_helper_endpoints=len(endpoints),unchanged_copy_lifetimes=True,both_reflected_ledgers=True,unique_required_frame_pairs=len(pairs),source_histogram=dict(sourceH),target_histogram=dict(targetH),internal_histogram_including_copies=dict(internalH),copied_center_histogram=dict(copies),input_raw_sha256=sha(producer['records'].tobytes()),output_raw_sha256=sha(out.tobytes()),selection_sha256=sha(path.read_bytes()),transform_sha256=sha(Path(__file__).read_bytes()),seconds=time.monotonic()-start)
+    meta=dict(producer['physical']);meta.update(status='PASS_PHYSICAL_GEN5_EARLY_RESTORATION',scalar_projection_sha256=forward['event_sha256'],tagged_scalar_sha256=tagged.hexdigest(),weighted_scalar_events=count,coefficient_histogram=dict(coeff),categories=dict(cat),category_names=cats,copied_center_blocks=centers,paid_histogram=dict(sorted(hist.items())),paid_rank_mass=sum(r*c for r,c in hist.items()),positive_rank_moves=sum(hist.values())-_NC,used_frames=[dict(frame_id=f,dimension=C.dimf[f],basis_sha256=sha(json.dumps(C.B[f],separators=(',',':')).encode()))for f in sorted(used|inherited)],restore_transform=receipt,physical_emitter_sha256=receipt['transform_sha256'])
+    ctx=dict(producer['context']);ctx['restored_endpoints']={ctx['regs'][a-2*v]:f for a,f in endpoints.items()}
+    result=dict(producer);result.update(context=ctx,records=out,physical=meta,result=meta,restore_census=receipt,initial_state=initial,final_state=final,helper_endpoints=endpoints,restore_entries=entries)
+    if output_dir is not None:
+        p=Path(output_dir);p.mkdir(parents=True,exist_ok=True);(p/'restore-records.bin.gz').write_bytes(gzip.compress(out.tobytes(),mtime=0))
+        (p/'restore.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    print('PASS early restoration',len(entries),'helpers endpoint saving',proof['endpoint_rank_saving'],count,'scalar ADDs',sum(hist.values()),'paid calls',len(out)//6,'records',flush=True)
+    return result
diff --git a/research/five-stage-p10-transcript-stages/scalar/word.py b/research/five-stage-p10-transcript-stages/scalar/word.py
new file mode 100644
index 0000000000..95b9affd44
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/scalar/word.py
@@ -0,0 +1,263 @@
+def replay(mode='F2',direction=1,bits=24,mutation=None):
+ major=mode=='bound';binary=mode=='F2';v=W.v
+ unit=(lambda i:1)if major else(lambda i:1<<i)if binary else(lambda i:1<<(bits*i))
+ def add(x,c,y):return x+abs(c)*y if major else x^y if binary and c&1 else x if binary else x+c*y
+ target_frames=[None]*v;target_paths=[[]for _ in range(v)];center_reads=[];target_hist=Counter()
+ aggregation_active=[True]*len(agg);aggregation_read=[set()for _ in agg];aggregation_restores=[];aggregation_pivot_reads=0
+ rank_active=set(range(len(rankgroups)));rank_seen=[set()for _ in rankgroups];rank_restores=[];rank_skipped=0
+ echelon_active=set(range(len(echelon)));echelon_seen=[set()for _ in echelon];echelon_restores=[];echelon_reads=0
+ def target_move(t,f):
+  previous=target_frames[t];assert previous is None or C.sub(previous,f),('actual target chronology',t,previous,f)
+  assert all(W.module.dot(C.cov[t],b)==0 for b in C.B[f]),('actual target cap',t,f)
+  d=C.dimf[f]-(0 if previous is None else C.dimf[previous]);assert d>=0
+  if d:target_hist[d]+=1
+  target_frames[t]=f;target_paths[t].append(f)
+ X0=[unit(i)for i in range(v)];Y0=[unit(v+i)for i in range(v)];Z0={r:unit(idx[r])for r in regs};x=X0[:];y=Y0[:];z=Z0.copy();top=1;done=[]
+ def track(value):
+  nonlocal top
+  if major:top=max(top,value)
+  return value
+ def value(s):
+  s=W.phys[s];return x[borrow[s]]if s in borrow else z[s]
+ def assign(s,val):
+  s=W.phys[s]
+  if s in borrow:x[borrow[s]]=track(val)
+  else:z[s]=track(val)
+ source_paths={role:[W.w['source_frame'][r['source']],r['mix_frame']]for role,r in extra_byrole.items()}
+ pair_dirty_paths={r:[zero]for r in pair_bydirty}
+ def source_move(s,f):
+  role=W.phys[s]
+  if role in pair_dirty_paths:
+   assert C.sub(pair_dirty_paths[role][-1],f),('paired dirty chronology',role,pair_dirty_paths[role][-1],f)
+   pair_dirty_paths[role].append(f)
+  if role not in source_paths:return
+  assert C.sub(source_paths[role][-1],f),('orderedsource chronology',s,role,source_paths[role][-1],f)
+  source_paths[role].append(f)
+ responses=W.adjoint() if mutation=='old_adjoint' else adj
+ def aggregate_restore(k,trigger):
+  if not aggregation_active[k]:return
+  group=agg[k];pivot=group['pivot'];assert aggregation_read[k]==set(group['roles']),('early aggregation inverse',k,trigger,aggregation_read[k])
+  for t in group['targets']:target_move(t,group['frame'])
+  if mutation!='omit_aggregation_inverse' or k!=39:
+   for t in group['targets']:
+    if t!=pivot:y[t]=track(add(y[t],1,y[pivot]))
+  aggregation_active[k]=False;aggregation_restores.append(dict(group=k,before_role=trigger,frame=group['frame']))
+ def rank_restore(k,trigger):
+  group=rankgroups[k];assert k in rank_active and rank_seen[k]==group['roles']
+  for t in group['targets']:target_move(t,group['frame'])
+  if mutation!='omit_rank_inverse'or k!=0:
+   for t,cs in group['dependent'].items():
+    for p,c in cs.items():y[t]=track(add(y[t],c,y[p]))
+  rank_active.remove(k);rank_restores.append(dict(group=k,before_role=trigger,frame=group['frame']))
+ def echelon_restore(k,trigger):
+  group=echelon[k];assert echelon_seen[k]==group['roles']
+  for t in group['targets']:target_move(t,group['frame'])
+  if mutation!='omit_echelon_inverse'or k!=0:
+   for t,p,c in reversed(group['moves']):y[t]=track(add(y[t],-c,y[p]))
+  echelon_active.remove(k);echelon_restores.append(dict(group=k,before_role=trigger,frame=group['frame']))
+ def read(s):
+  nonlocal aggregation_pivot_reads,rank_skipped,echelon_reads
+  if s in pair_byalias:
+   if mutation=='subtract_paired_alias'and s==next(iter(pair_byalias)):
+    for t,c in adj[s].items():y[t]=track(add(y[t],-direction*c,value(s)))
+   return
+  if s in fresh:
+   if mutation=='omit_transformed_source_read'and s==next(iter(fresh)):return
+   for t,c in fresh[s]['transformed_response'].items():
+    t=int(t);source_move(s,W.gauge[s]['frame']);target_move(t,W.gauge[s]['frame']);y[t]=track(add(y[t],-direction*c,value(s)))
+   return
+  echelon_skip=set()
+  if s in W.gauge:
+   for k,group in enumerate(echelon):
+    if k not in echelon_active:continue
+    if s not in group['roles']:
+     if set(responses[s])&set(group['targets']):echelon_restore(k,s)
+     continue
+    echelon_seen[k].add(s);echelon_skip.update(group['targets'])
+    for t,a in group['response'].items():
+     c=a.get(s,0)
+     if not c:continue
+     if mutation=='flip_echelon_sign'and k==0 and c<0:c=-c
+     source_move(s,W.gauge[s]['frame']);target_move(t,W.gauge[s]['frame']);y[t]=track(add(y[t],-direction*c,value(s)));echelon_reads+=1
+  if s in W.gauge:
+   for k in sorted({rankowner[t]for t in responses[s]if t in rankowner}):
+    if k not in rank_active:continue
+    if s not in rankgroups[k]['roles']:rank_restore(k,s)
+    else:rank_seen[k].add(s)
+  if mutation=='omit_gauge_compensation'and s==new_gauge_selection[-1]['role']:return
+  if mutation=='omit_extra_compensation'and s==extra_selection[0]['role']:return
+  grouped=role_groups.get(s,[])
+  for k in sorted({target_group[t]for t in responses[s]if t in target_group}) if s in W.gauge else []:
+   if k not in grouped:aggregate_restore(k,s)
+  skipped=set()
+  for k in grouped:
+   group=agg[k];pivot=group['pivot'];assert aggregation_active[k]
+   assert set(group['targets'])<=set(responses[s])and len({responses[s][t]for t in group['targets']})==1
+   c=responses[s][pivot];source_move(s,read_frames[s,k]);target_move(pivot,read_frames[s,k]);y[pivot]=track(add(y[pivot],-direction*c,value(s)))
+   if mutation=='repeat_aggregation_read'and k==39:
+    t=next(t for t in group['targets']if t!=pivot);target_move(t,read_frames[s,k]);y[t]=track(add(y[t],-direction*c,value(s)))
+   skipped.update(group['targets']);aggregation_read[k].add(s);aggregation_pivot_reads+=1
+  for t,c in responses[s].items():
+   if t in skipped or t in echelon_skip:continue
+   rk=rankowner.get(t)
+   if s in W.gauge and rk in rank_active and t in rankgroups[rk]['dependent']:
+    rank_skipped+=1
+    if mutation!='repeat_rank_read'or rk!=0:continue
+   if s in W.gauge:source_move(s,W.gauge[s]['frame']);target_move(t,W.gauge[s]['frame'])
+   else:assert target_frames[t]is None,'initial correction leaves target atD0'
+   y[t]=track(add(y[t],-direction*c,value(s)))
+ def gate(i,sign):
+  a,b,_=W.ops[i]
+  if sign==1:
+   source_move(a,W.opframe[i]);source_move(b,W.opframe[i])
+  assign(a,add(value(a),sign,value(b)))
+ for s in range(W.R):
+  if s not in W.gauge and s not in borrow and s not in removed:read(s)
+ for n,s in W.source.items():assign(s,add(value(s),1,x[n]))
+ for r in gauge_selection:
+  if mutation=='omit_transformed_source_mix'and r is next(iter(fresh.values())):continue
+  if mutation=='omit_extra_mix'and r is extra_selection[0]:continue
+  if mutation!='omit_gauge_mix' or r is not new_gauge_selection[-1]:x[r['partner']]=track(add(x[r['partner']],1,x[r['source']]))
+ def forward(i):
+  if i not in omitted:gate(i,1);done.append(i)
+ for k in schedule['center_prefix_events']:
+  event=schedule['events'][k];i=event['op']
+  if event['kind']=='early_mix':
+   r=early[i];a,b=r['partner'],r['source']
+   if mutation!='omit_early_mix' or r is not selection[0]:x[a]=track(add(x[a],1,x[b]))
+  else:forward(i)
+ for r,s in zip(W.g['roots'],W.w['rootroles']):
+  if r['kind']=='center':
+   for t in r['targets']:
+    assert all(f is None for f in target_frames),'copied centers scatter before any nonzero target movement'
+    center_reads.append((s,t));y[t]=track(add(y[t],direction,value(s)))
+ for k,group in enumerate(echelon):
+  assert all(target_frames[t]is None for t in group['targets'])
+  if mutation!='omit_echelon_setup'or k!=0:
+   for t,p,c in group['moves']:y[t]=track(add(y[t],c,y[p]))
+ for k,group in enumerate(rankgroups):
+  assert all(target_frames[t]is None for t in group['targets'])
+  if mutation!='omit_rank_setup'or k!=0:
+   for t,cs in group['dependent'].items():
+    for p,c in cs.items():y[t]=track(add(y[t],-c,y[p]))
+ for k,group in enumerate(agg):
+  assert all(target_frames[t]is None for t in group['targets']), 'aggregation setup after all D0 center scatters'
+  if mutation!='omit_aggregation_setup'or k!=39:
+   for t in group['targets']:
+    if t!=group['pivot']:y[t]=track(add(y[t],-1,y[group['pivot']]))
+ for e in terminal:
+  assert all(target_frames[t]is None for t in e['targets']),'terminal setup afterD0center scatter'
+  for t in e['targets']:
+   if t!=e['pivot']:y[t]=track(add(y[t],-1,y[e['pivot']]))
+ # Original dirty compensation happened at D0 before these source injections.
+ for r in pair_selection:
+  b,f=r['aliased_role'],r['mix_frame']
+  for a,c in r['retained_dirty_coefficients'].items():
+   source_move(a,f);source_move(b,f)
+   if mutation=='omit_sparse_anchor'and r is pair_selection[14]and a==next(iter(r['retained_dirty_coefficients'])):continue
+   if mutation=='wrong_sparse_sign'and r is pair_selection[14]and a==next(iter(r['retained_dirty_coefficients'])):c=-c
+   if mutation!='omit_pair_initialization'or r is not pair_selection[0]:assign(a,add(value(a),c,value(b)))
+ for j,i in enumerate(W.rest):
+  for s in at[j]:
+   if mutation!='late_phase1_gauge' or s not in new_phase_roles:read(s)
+  if mutation=='late_phase1_gauge'and j==168:
+   for s in sorted(new_phase_roles):read(s)
+  if i in bywrite:
+   e=bywrite[i];a,b,n=W.ops[i];source_move(b,W.opframe[i]);target_move(e['pivot'],W.opframe[i]);y[e['pivot']]=track(add(y[e['pivot']],direction,value(b)))
+  else:forward(i)
+  if i in afterwrite:
+   e=afterwrite[i]
+   for t in e['targets']:
+    target_move(t,e['root_frame'])
+    if t!=e['pivot']:y[t]=track(add(y[t],1,y[e['pivot']]))
+ for s in at[len(W.rest)]:read(s)
+ assert not any(aggregation_active),'all quotient inverses precede original side/K reads'
+ assert not rank_active,'rank quotient inverses precede side/K reads'
+ assert not echelon_active,'echelon inverses precede side/K reads'
+ for j,(r,s)in enumerate(zip(W.g['roots'],W.w['rootroles'])):
+  if r['kind']=='side' and j not in deletedroots:
+   for k in sorted({target_group[t]for t in r['targets']if t in target_group}):aggregate_restore(k,('root',j))
+   source_move(s,W.w['root_frame'][j])
+   for t in r['targets']:target_move(t,W.w['root_frame'][j]);y[t]=track(add(y[t],direction,value(s)))
+  for e in deliveries[j]:
+   a,b=e['carrier'],e['passive']
+   if b not in by_source:x[a]=track(add(x[a],1,x[b]))
+   for k in sorted({target_group[t]for t in e['receivers']if t in target_group}):aggregate_restore(k,('K',j))
+   for t in e['receivers']:target_move(t,e['deliver_frame']);y[t]=track(add(y[t],direction,x[a]))
+ assert not any(aggregation_active),'all target inverses completed beforecleanup'
+ for e in W.k['entries']:
+  if e['passive']not in by_source:x[e['carrier']]=track(add(x[e['carrier']],-1,x[e['passive']]))
+ if mutation=='undo_before_restore':
+  for e in W.k['entries']:
+   if e['passive']in by_source:x[e['carrier']]=track(add(x[e['carrier']],-1,x[e['passive']]))
+ for role in source_paths:source_move(role,W.w['full_frame'])
+ for role in pair_dirty_paths:source_move(role,W.w['full_frame'])
+ for i in reversed(done):gate(i,-1)
+ for r in reversed(pair_selection):
+  b=r['aliased_role']
+  for a,c in reversed(list(r['retained_dirty_coefficients'].items())):
+   c=-c
+   if mutation=='wrong_pair_restore_sign'and r is pair_selection[0]:c=-c
+   if mutation!='omit_pair_restoration'or r is not pair_selection[0]:assign(a,add(value(a),c,value(b)))
+ if mutation!='undo_before_restore':
+  for e in W.k['entries']:
+   if e['passive']in by_source:x[e['carrier']]=track(add(x[e['carrier']],-1,x[e['passive']]))
+ for n,s in W.source.items():assign(s,add(value(s),-1,x[n]))
+ if binary:want=[Y0[t]^X0[t]for t in range(v)]
+ else:
+  want=Y0[:];cache={}
+  for root in W.g['roots']:
+   n=root['node']
+   if n not in cache:
+    mask=C.sup[n];val=0
+    while mask:low=mask&-mask;mask-=low;val=add(val,1,X0[low.bit_length()-1])
+    cache[n]=val
+   for t in root['targets']:want[t]=add(want[t],direction,cache[n])
+  for e in W.k['entries']:
+   val=add(X0[e['carrier']],1,X0[e['passive']])
+   for t in e['receivers']:want[t]=add(want[t],direction,val)
+ # Finish every local target at its codimension-one cap, then reverse the exact
+ # annihilator stream. All copied-center scatters lie before these movements,
+ # hence atD0 forward and atD1 after the complementary movements reverse.
+ reflected=Counter()
+ for t,chain in enumerate(target_paths):
+  assert chain
+  d=W.h-1-C.dimf[chain[-1]];assert d>=0
+  if d:target_hist[d]+=1
+  previous=[C.cov[t]];dimension=1
+  for f in reversed(chain):
+   assert all(W.module.dot(a,b)==0 for a in previous for b in C.B[f])
+   basis=C.A[f];step=len(basis)-dimension;assert step>=0
+   if step:reflected[step]+=1
+   previous=basis;dimension=len(basis)
+  if W.h>dimension:reflected[W.h-dimension]+=1
+ assert reflected==target_hist
+ assert len(center_reads)==sum(len(r['targets'])for r in W.g['roots']if r['kind']=='center')
+ assert sum(k*n for k,n in target_hist.items())==W.v*(W.h-1)
+ source_histogram=Counter();source_reflected=Counter()
+ for role,path in source_paths.items():
+  assert C.dimf[path[0]]==1 and C.dimf[path[-1]]==W.h
+  for a,b in zip(path,path[1:]):
+   assert C.sub(a,b)and C.nondeg(a)and C.nondeg(b)
+   step=C.dimf[b]-C.dimf[a]
+   if step:source_histogram[step]+=1
+  for a,b in zip(reversed(path),list(reversed(path))[1:]):
+   assert all(W.module.dot(x,y)==0 for x in C.A[a]for y in C.B[b]);step=len(C.A[b])-len(C.A[a]);assert step>=0
+   if step:source_reflected[step]+=1
+ assert source_histogram==source_reflected and sum(k*n for k,n in source_histogram.items())==len(source_paths)*(W.h-1)
+ paired_hist=Counter();paired_reflected=Counter()
+ for role,path in pair_dirty_paths.items():
+  assert C.dimf[path[0]]==0 and C.dimf[path[-1]]==W.h
+  for a,b in zip(path,path[1:]):
+   assert C.sub(a,b)and C.nondeg(a)and C.nondeg(b)
+   d=C.dimf[b]-C.dimf[a]
+   if d:paired_hist[d]+=1
+  for a,b in zip(reversed(path),list(reversed(path))[1:]):
+   assert all(W.module.dot(x,y)==0 for x in C.A[a]for y in C.B[b]);d=len(C.A[b])-len(C.A[a])
+   if d:paired_reflected[d]+=1
+ assert paired_hist==paired_reflected and sum(k*n for k,n in paired_hist.items())==len(pair_dirty_paths)*W.h
+ if major:return max(top,max(a+b for a,b in zip(y,want)),max(z[r]+Z0[r]for r in regs),max(a+b for a,b in zip(x,X0)))
+ assert y==want,('wrong targets',mode,[t for t in range(v)if y[t]!=want[t]][:10])
+ assert x==X0,('source restoration',mode,[s for s in range(v)if x[s]!=X0[s]][:10])
+ assert z==Z0,('dirty restoration',mode)
+ return dict(mode=mode,direction=direction,formal_columns=2*v+len(regs),sources=v,targets=v,dirty=len(regs),all_targets=True,all_source_and_dirty_restored=True,copied_center_target_reads=len(center_reads),all_forward_centers_at_D0=True,all_reflected_centers_at_D1=True,actual_target_histogram={str(k):n for k,n in sorted(target_hist.items())},actual_reflected_target_histogram={str(k):n for k,n in sorted(reflected.items())},aggregation_groups=len(agg),aggregation_pivot_reads=aggregation_pivot_reads,aggregation_restores=aggregation_restores,actual_extra_source_paths=source_paths,rank_groups=len(rankgroups),rank_targets=len(rankowner),rank_restores=rank_restores,rank_removed_reads=rank_skipped,actual_extra_source_histogram=dict(source_histogram),actual_extra_reflected_source_histogram=dict(source_reflected),echelon_restores=echelon_restores,echelon_reads=echelon_reads,paired_dirty_paths=pair_dirty_paths,paired_dirty_histogram=dict(paired_hist),paired_dirty_reflected_histogram=dict(paired_reflected))
diff --git a/research/five-stage-p10-transcript-stages/scalar_check.py b/research/five-stage-p10-transcript-stages/scalar_check.py
new file mode 100644
index 0000000000..8fab4fb8ed
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/scalar_check.py
@@ -0,0 +1,130 @@
+"""Fresh F2 source proof, independent literal projection/inverse and controls.
+No saved execution receipt is accepted. Uses the actual clean source context
+and freshly emitted local physical records. Assisted with ChatGPT (source527).
+Rebound to the gen5 word, then to the p = 10 word: 2v+R formal columns; the controls corrupt the actual
+context (responses, read chronology, alias reads, gates, centres, partner
+deliveries, injections and signs) instead of absent source527 selections.
+Gen5 rebinding and controls by DreamingOfClouds with Anthropic Claude assistance.
+p = 10 port: the event digest, counts and prefix bounds are pinned in word-pins.json; N and V from the word.
+"""
+from collections import Counter,defaultdict
+from copy import copy
+import hashlib,json,time
+from word_pins import expect,shape
+
+
+
+def events(records,N,reverse=False):
+    center=None
+    for k in (range(len(records)-6,-1,-6) if reverse else range(0,len(records),6)):
+        op,a,b,c,f,z=records[k:k+6]
+        if op==1:
+            if b==N:
+                assert center is not None
+                b=center
+            assert 0<=a<N and 0<=b<N and a!=b
+            yield a,b,-c if reverse else c
+        elif op==(3 if reverse else 2):
+            assert center is None and b==N
+            center=a
+        elif op==(2 if reverse else 3):
+            assert center==a and b==N
+            center=None
+    assert center is None
+
+
+def replay_projection(records,N,V,reverse=False,omit_event=None):
+    n=N;v=V
+    columns=[1<<i for i in range(n)];norms=[1]*n
+    wanted=columns[:]
+    for i in range(v):wanted[v+i]^=1<<i
+    largest=1;counts=Counter();digest=hashlib.sha256();count=0
+    for event_index,(a,b,c) in enumerate(events(records,N,reverse)):
+        if event_index==omit_event:continue
+        if c&1:columns[a]^=columns[b]
+        norms[a]+=abs(c)*norms[b];largest=max(largest,norms[a])
+        counts[abs(c)]+=1
+        digest.update(json.dumps([a,b,c],separators=(',',':')).encode());digest.update(b'\n');count+=1
+    assert columns==wanted,'independent literal all-column endpoint'
+    assert count==expect('weighted_scalar_events',count) and counts==expect('weighted_scalar_coefficients',dict(counts))
+    if not reverse:expect('scalar_event_sha256',digest.hexdigest())
+    return dict(all_formal_columns=n,all_source_and_dirty_restored=True,
+                arbitrary_target_contents_preserved=True,
+                event_sha256=digest.hexdigest(),weighted_additions=count,
+                coefficient_counts=dict(counts),literal_unit_additions=sum(c*n for c,n in counts.items()),
+                max_intermediate_row_l1=largest,final_source_row_l1=max(norms[:v]),
+                final_target_row_l1=max(norms[v:2*v]),final_dirty_row_l1=max(norms[2*v:]))
+
+
+def mutated_namespaces(context):
+    """Actual-context corruptions; each must make the unchanged scalar program fail."""
+    W=context['W'];adj=context['adj'];at=context['at']
+    recipients={b:d for b,d in W.pairs}
+    odd=lambda s:any(c%2 for c in adj[s].values())
+    plain_gauge=next(s for s in W.order if s not in recipients and odd(s))
+    recipient=next(b for b in W.order if b in recipients and odd(b))
+    dirty=next(s for s in range(W.R) if s not in W.gauge and s in set(W.phys.values()) and odd(s) and s not in context['borrow'])
+    def with_adj(role,row):
+        a=list(adj);a[role]=row;return dict(adj=a)
+    def drop_first(role):
+        # an odd coefficient: even responses vanish over F2 and would not test anything
+        t=next(u for u,c in adj[role].items() if c%2);return with_adj(role,{u:c for u,c in adj[role].items() if u!=t})
+    def move_read(role,time):
+        a=defaultdict(list,{k:list(v) for k,v in at.items()})
+        a[W.readtime[role]].remove(role);a[time].append(role);return dict(at=a)
+    def proxy(**changes):
+        P=copy(W);P.__dict__.update(changes);return dict(W=P)
+    yield 'omit_gauge_compensation','F2',drop_first(plain_gauge)
+    yield 'omit_dirty_compensation','F2',drop_first(dirty)
+    yield 'omit_alias_recipient_compensation','F2',drop_first(recipient)
+    t=next(u for u,c in adj[plain_gauge].items() if c%2);other=(t+1)%W.v
+    while other in adj[plain_gauge]:other=(other+1)%W.v
+    row=dict(adj[plain_gauge]);row[other]=row.pop(t)
+    yield 'misrouted_gauge_response','F2',with_adj(plain_gauge,row)
+    row=dict(adj[plain_gauge]);row[t]=-row[t]
+    yield 'flipped_gauge_compensation_sign','Z',with_adj(plain_gauge,row)
+    position={i:j for j,i in enumerate(W.rest)}
+    def last_write(d):
+        js=[position[i] for i in W.role_ops[d] if W.ops[i][0]==d and i in position]
+        return max(js) if js else None
+    written=next(b for b in W.order if b in recipients and odd(b) and last_write(recipients[b]) is not None)
+    yield 'alias_read_before_donor_last_write','F2',move_read(written,last_write(recipients[written]))
+    yield 'gauge_read_after_first_use','F2',move_read(plain_gauge,W.first[plain_gauge]+1)
+    gate=next(i for i in W.rest if W.ops[i][0] not in W.gauge)
+    yield 'omitted_gate','F2',dict(omitted={gate})
+    roots=[dict(r) for r in W.g['roots']];j=next(k for k,r in enumerate(roots) if r['kind']=='center');roots[j]['targets']=roots[j]['targets'][1:]
+    yield 'omitted_centre_scatter','F2',proxy(g=dict(W.g,roots=roots))
+    deliveries=defaultdict(list,{k:list(v) for k,v in context['deliveries'].items()});k=next(k for k,v in sorted(deliveries.items()) if v);deliveries[k]=deliveries[k][1:]
+    yield 'omitted_partner_delivery','F2',dict(deliveries=deliveries)
+    source=dict(W.source);source.pop(next(iter(source)))
+    yield 'omitted_source_injection','F2',proxy(source=source)
+
+
+def run(context,records,progress=lambda text:None,word_columns=None):
+    # Terminal sinks remove helper registers from the emitted word (word_columns); the retained source program keeps N.
+    import gc
+    started=time.monotonic();ns=dict(context);source=ns['SOURCE_TEXT'];W=context['W'];V=W.v;N=2*V+len(context['regs']);assert W.h==shape()['h'] and V==shape()['v']
+    assert hashlib.sha256(source.encode()).hexdigest()=='e675d4eb9d90ff0b44279fae0b46f1a8b39f65421cc38454b70a6b75d0e10b42'
+    exec(compile(source,'retained source527 exact scalar word','exec'),ns)
+    progress('Checking all '+str(N)+' source, target and arbitrary dirty F2 columns')
+    exact=ns['replay']('F2');assert exact['formal_columns']==N and exact['all_targets']and exact['all_source_and_dirty_restored']
+    progress('Checking independent literal physical projection and inverse')
+    NW=N if word_columns is None else word_columns;assert NW<=N;expect('word_formal_columns',NW)
+    progress('Checking independent literal physical projection and inverse on all '+str(NW)+' emitted-word columns')
+    forward=replay_projection(records,NW,V);inverse=replay_projection(records,NW,V,True)
+    expect('forward_max_row_l1',forward['max_intermediate_row_l1']);expect('inverse_max_row_l1',inverse['max_intermediate_row_l1'])
+    try:replay_projection(records,NW,V,omit_event=forward['weighted_additions']-1)
+    except AssertionError:filtered_control='omitted surviving odd payload ADD rejected'
+    else:raise AssertionError('filtered odd payload omission accepted')
+    bound=ns['replay']('bound');bits=8*((bound.bit_length()+2+7)//8);assert 1<<bits>2*bound
+    progress('Checking the signed integer source decoder and dirty restoration')
+    integer=[]
+    for direction in(1,-1):integer.append(ns['replay']('Z',direction,bits));gc.collect()
+    controls={}
+    for name,mode,changes in mutated_namespaces(context):
+        bad=dict(context);bad.update(changes);exec(compile(source,'retained source527 exact scalar word','exec'),bad)
+        try:bad['replay'](mode,bits=bits)
+        except AssertionError as error:controls[name]=dict(rejected=True,reason=str(error)[:200])
+        else:raise AssertionError('invalid p = 10 context mutation accepted: '+name)
+    assert len(controls)==11
+    return dict(status='PASS_FRESH_P10_PRODUCER_SIGNED_DECODER_AND_PARITY_FUSED_F2_INVERSE_AND_CONTROLS',filtered_control=filtered_control,F2=exact,integer=integer,majorant=dict(residual_bound=bound,packing_bits=bits),forward=forward,inverse=inverse,controls=controls,source_sha256=hashlib.sha256(source.encode()).hexdigest(),seconds=time.monotonic()-started,scope='The retained source527 scalar program, run on the p = 10 context, proves the signed defining-integer decoder in both directions and rejects11 actual-context corruptions. The emitted parity-filtered word is independently checked on all '+str(N)+' formal F2columns and literalreverse, with its own cancellation-free signed-lift prefix bounds. Its integer endpoint is not asserted equal to the producer decoder; F2payload identity supplies the bit contract. Odd-prime address arithmetic is unchanged.')
diff --git a/research/five-stage-p10-transcript-stages/sink-selection.json b/research/five-stage-p10-transcript-stages/sink-selection.json
new file mode 100644
index 0000000000..d027b30802
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/sink-selection.json
@@ -0,0 +1,2738 @@
+{
+ "status": "GEN5_TERMINAL_SINKS_PR283_SCREEN",
+ "n": 10150,
+ "v": 960,
+ "input_raw_sha256": "ec2bfcc1d1fd9227beeddb0afa78a2c2ff6e10d49bff55183bc77ac84f4b79fd",
+ "input_scalar_sha256": "81f0eebc4970ddb0a480b06097ac99365d53d3ed66732f23ec736e5209a802dc",
+ "entry": 304918,
+ "selected": 7,
+ "sinks": [
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+   "stream": 6439,
+   "targets": [
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+   "forward_writes": 3,
+   "cleanups": 3
+  },
+  {
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+   "stream": 6945,
+   "targets": [
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+    1329,
+    1330,
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+   ],
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+   "stream": 6949,
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+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     2,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0,
+     0,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     1,
+     1,
+     0,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1,
+     0
+    ],
+    [
+     1,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     0,
+     -1
+    ]
+   ],
+   "forward_writes": 4,
+   "cleanups": 4
+  }
+ ],
+ "expected_local_delta": {
+  "3": -7,
+  "17": -7
+ }
+}
diff --git a/research/five-stage-p10-transcript-stages/sink_transform.py b/research/five-stage-p10-transcript-stages/sink_transform.py
new file mode 100644
index 0000000000..7862531f26
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/sink_transform.py
@@ -0,0 +1,201 @@
+"""Terminal sinks on the gen5 word (port of PR #283's sink-transform.cpp / SINK-PROOF.md to this Python pipeline).
+
+Mechanism from PR #283 (Dugongue; terminal sinks are a credited public source527 mechanism). A zero-to-full helper r
+qualifies when its only scalar uses are: one initial dirty compensation read y_t += -r at ZERO for every target t of a
+set S (before the copied-centre discard), forward writes r += x (forward_gate) after that discard, one terminal delivery
+y_t += r at a common root frame for every t in S after the last forward write, and cleanup writes r -= x after the last
+delivery; r is never copied. If no target in S is ever a scalar or COPY source, and the pivot p in S is not written by
+anything else between the discard and the last forward write, the forward writes are redirected to y_p, y_t -= y_p
+(t in S, t != p) is inserted at ZERO right after the discard and y_t += y_p at the root frame right after the last
+forward write; the reads, deliveries and cleanups of r are deleted and the register r is removed. Over the integers
+every y_t still receives exactly X = sum of the redirected writes (the dirty value of r cancels in the original and is
+never read in the new word), and all other registers are unchanged: no gate reads a target in S, nothing else writes p
+in the interval, and r was read only by the deleted reads. Selected target sets are disjoint.
+Checks: fresh screen equals the frozen selection; the coefficient pattern (-1 reads, +1 deliveries, +1 writes, -1
+cleanups) and the commutation conditions above on the actual word; F2 replay of every remaining formal column forward
+and inverse; three omission controls (redirected writes, setup, restore) must fail; every MOVE rebuilt from the actual
+operand frames with both reflected ledgers; register IDs compacted (removed roles recorded in the context).
+Prepared with Anthropic Claude assistance; Apache-2.0.
+p = 10 port (Chafik Boukhalfa (chafreaky), Anthropic Claude assistance): h, v, centre copies and scatter reads come
+from word_pins.shape and the stage counts are pinned in word-pins.json; the mechanism and checks are unchanged.
+"""
+from array import array
+from collections import Counter
+from pathlib import Path
+import gzip,hashlib,json,time,sys,importlib.util
+sys.dont_write_bytecode=True
+if not __debug__:raise SystemExit('assertions required')
+HERE=Path(__file__).resolve().parent
+from word_pins import shape as _shape
+_S=_shape();_H=_S['h'];_V=_S['v'];_M=_S['m'];_CR=_S['center_rank'];_NC=_S['centers'];_SCAT=_S['scatter_reads'];_DEF=_S['deficit']
+sha=lambda b:hashlib.sha256(b).hexdigest()
+
+def screen(old,initial,final,n,v,cats,ZERO,FULL):
+    Z=cats.index;READ,ROOT,FWD,CLN=Z('dirty_read'),Z('side_root'),Z('forward_gate'),Z('cleanup_gate')
+    entry=max(k//6 for k in range(0,len(old),6)if old[k]==3)
+    inc={};treads=set();twrites={};copied=set()
+    for k in range(0,len(old),6):
+        op,a,b,c,f,z=old[k:k+6];i=k//6
+        if op==1:
+            inc.setdefault(a,[]).append(i)
+            if b!=n:inc.setdefault(b,[]).append(i)
+            if v<=b<2*v:treads.add(b)
+            if v<=a<2*v:twrites.setdefault(a,[]).append(i)
+        elif op in(2,3):inc.setdefault(a,[]).append(i);copied.add(a)
+    out=[]
+    for r in range(2*v,n):
+        if initial[r]!=ZERO or final[r]!=FULL:continue
+        pre=Counter();post=Counter();writes=[];cleanups=[];bad=False;rootf=set();coeff=Counter()
+        for i in inc.get(r,[]):
+            op,a,b,c,f,z=old[6*i:6*i+6]
+            if op!=1:bad=True;break
+            if b==r:
+                if not(v<=a<2*v):bad=True;break
+                if z==READ and i<entry and f==ZERO:pre[a]+=1;coeff['read',c]+=1
+                elif z==ROOT:post[a]+=1;rootf.add(f);coeff['deliver',c]+=1;last_delivery=i
+                else:bad=True;break
+            elif a==r:
+                if z==FWD:writes.append(i);coeff['write',c]+=1
+                elif z==CLN:cleanups.append(i);coeff['cleanup',c]+=1
+                else:bad=True;break
+        if bad or not writes or not pre:continue
+        S=set(pre)
+        if set(post)!=S or any(pre[t]!=1 or post[t]!=1 for t in S) or len(rootf)!=1:continue
+        first,last=min(writes),max(writes);deliveries=[i for i in inc[r]if old[6*i+2]==r and old[6*i+5]==ROOT]
+        if first<=entry or min(deliveries)<last or (cleanups and min(cleanups)<max(deliveries)):continue
+        if S&treads or S&copied:continue   # no target in S is ever a scalar or COPY source
+        pivots=[p for p in sorted(S)if not[i for i in twrites.get(p,[])if entry<i<=last and old[6*i+2]!=r]]
+        if not pivots:continue
+        assert coeff==Counter({('read',-1):len(S),('deliver',1):len(S),('write',1):len(writes),('cleanup',-1):len(cleanups)}),('sink coefficient pattern',r,coeff)
+        sources={old[6*i+2]for i in writes};assert not(sources&S) and r not in sources and all(s>=2*v for s in sources)
+        out.append(dict(stream=r,targets=sorted(S),pivot=pivots[0],first=first,last=last,writes=writes,cleanups=cleanups,root_frame=rootf.pop(),entry=entry))
+    return entry,out
+
+def transform(producer,selection):
+    W,C=producer['W'],producer['C'];old=producer['records'];initial=dict(producer['initial_state']);context=producer['context'];v=W.v;regs=list(context['regs']);n=2*v+len(regs);ZERO=producer['ZERO'];FULL=producer['FULL']
+    final=dict(producer['final_state']);ends=dict(producer.get('helper_endpoints',{}))
+    assert n==selection['n'] and v==selection['v'] and sha(old.tobytes())==selection['input_raw_sha256'],'sink selection bound to a different word'
+    assert producer['physical']['scalar_projection_sha256']==selection['input_scalar_sha256']
+    cats=list(producer['physical']['category_names']);assert not {'sink_redirect','sink_setup','sink_restore'}&set(cats)
+    REDIR,SETUP,RESTORE=len(cats),len(cats)+1,len(cats)+2;cats+=['sink_redirect','sink_setup','sink_restore']
+    entry,rows=screen(old,initial,final,n,v,cats,ZERO,FULL)
+    frozen=[(e['role'],tuple(e['targets']),e['pivot'])for e in selection['sinks']]
+    fresh=[(regs[r['stream']-2*v],tuple(r['targets']),r['pivot'])for r in rows]
+    assert sorted(fresh)==sorted(frozen)and len(frozen)==selection['selected'],'fresh sink screen differs from the frozen selection'
+    used=set()
+    for r in rows:assert not(used&set(r['targets'])),'overlapping target sets';used.update(r['targets'])
+    sinks={r['stream']:r for r in rows};assert not(set(sinks)&set(ends))
+    # Compaction of register IDs: helpers after a removed one shift down; the copy temporary is n -> n'.
+    mp={};k=0
+    for s in range(n):
+        if s not in sinks:mp[s]=k;k+=1
+    nn=k;mp[n]=nn
+    redirected={i:r for r in rows for i in r['writes']};dropped=set()
+    for r in rows:
+        dropped.update(r['cleanups'])
+    for k6 in range(0,len(old),6):
+        op,a,b,c,f,z=old[k6:k6+6]
+        if op==1 and b in sinks:dropped.add(k6//6)
+    lastw={r['last']:r for r in rows}
+    state={mp[s]:f for s,f in initial.items()if s not in sinks};out=array('i');temporary=None
+    def move(s,f):
+        before=state[s]
+        if before==f:return
+        assert C.sub(before,f),('sink nonnested actual use',s,before,f)
+        gap=C.dimf[f]-C.dimf[before];assert gap>=0;out.extend((0,s,before,f,gap,0));state[s]=f
+    def add(a,b,c,f,z):
+        move(a,f)
+        if b!=nn:move(b,f)
+        out.extend((1,a,b,c,f,z))
+    for k6 in range(0,len(old),6):
+        op,a,b,c,f,z=old[k6:k6+6];i=k6//6
+        if op==1:
+            if i in dropped:pass
+            elif i in redirected:add(mp[redirected[i]['pivot']],mp[b],c,f,REDIR)
+            else:assert a not in sinks;add(mp[a],mp[b],c,f,z)
+        elif op==2:assert temporary is None and a not in sinks;move(mp[a],c);state[nn]=f;temporary=(mp[a],nn,c);out.extend((op,mp[a],nn,c,f,z))
+        elif op==3:assert temporary==(mp[a],nn,c)and state[mp[a]]==c and state[nn]==f;out.extend((op,mp[a],nn,c,f,z));del state[nn];temporary=None
+        if i==entry:
+            assert temporary is None
+            for r in rows:
+                for t in r['targets']:
+                    if t!=r['pivot']:add(mp[t],mp[r['pivot']],-1,ZERO,SETUP)
+        if i in lastw:
+            r=lastw[i]
+            for t in r['targets']:
+                if t!=r['pivot']:add(mp[t],mp[r['pivot']],1,r['root_frame'],RESTORE)
+    assert temporary is None
+    nfinal={mp[s]:f for s,f in final.items()if s not in sinks}
+    for s in sorted(nfinal):move(s,nfinal[s])
+    assert state==nfinal
+    ninitial={mp[s]:f for s,f in initial.items()if s not in sinks}
+    nends={mp[s]:f for s,f in ends.items()}
+    ctx=dict(context);ctx['regs']=[x for j,x in enumerate(regs)if 2*v+j not in sinks];ctx['removed']=set(context['removed'])|{regs[s-2*v]for s in sinks}
+    if 'restored_endpoints' in context:ctx['restored_endpoints']=dict(context['restored_endpoints'])
+    assert len(ctx['regs'])==nn-2*v
+    proof=dict(selected=len(rows),entry=entry,removed_roles=sorted(regs[s-2*v]for s in sinks),targets=sum(len(r['targets'])for r in rows),redirected_writes=len(redirected),deleted_scalar_events=len(dropped),inserted_setups=sum(len(r['targets'])-1 for r in rows),
+        targets_never_sources=True,pivot_unwritten_on_interval=True,coefficient_pattern_checked=True,disjoint_target_sets=True,old_n=n,new_n=nn)
+    return out,ninitial,nfinal,nends,rows,ctx,cats,proof,nn,v,mp
+
+def run(producer,output_dir=None,selection_path=None):
+    start=time.monotonic()
+    spec=importlib.util.spec_from_file_location('sink_kernel_replay',HERE/'kernel_transform.py');km=importlib.util.module_from_spec(spec);spec.loader.exec_module(km)
+    W,C=producer['W'],producer['C'];path=Path(selection_path)if selection_path else HERE/'sink-selection.json';selection=json.loads(path.read_text())
+    out,initial,final,ends,rows,ctx,cats,proof,n,v,mp=transform(producer,selection);ZERO=producer['ZERO']
+    forward=km.replay(out,n,v);inverse=km.replay(out,n,v,True);controls=[km.replay(out,n,v,omit_category=cats.index(x))for x in('sink_redirect','sink_setup','sink_restore')]
+    needs={s:[]for s in initial};copies=Counter();temporary=None
+    for k in range(0,len(out),6):
+        op,a,b,c,f,z=out[k:k+6]
+        if op==1:
+            needs[a].append(f)
+            if b!=n:needs[b].append(f)
+            else:assert temporary is not None and f==ZERO
+        elif op==2:assert temporary is None;temporary=(a,b,c);needs[a].append(c);copies[z]+=1
+        elif op==3:assert temporary==(a,b,c);temporary=None
+    assert temporary is None and copies=={_CR:_NC}
+    per_role={};pairs=set();census=Counter(copies);reflected=Counter(copies)
+    for s,startframe in initial.items():
+        H=Counter();pathframes=[startframe]+needs[s]+[final[s]]
+        for a,b in zip(pathframes,pathframes[1:]):
+            assert C.sub(a,b);gap=C.dimf[b]-C.dimf[a];assert gap>=0;pairs.add((a,b))
+            if gap:H[gap]+=1
+        for a,b in zip(reversed(pathframes),list(reversed(pathframes))[1:]):
+            assert all(not W.module.dot(x,y)for x in C.A[a]for y in C.B[b]);gap=len(C.A[b])-len(C.A[a]);assert gap>=0
+            if gap:reflected[gap]+=1
+        per_role[s]=H;census.update(H)
+    assert reflected==census
+    for f in {x for pair in pairs for x in pair}:assert C.nondeg(f)and len(C.B[f])+len(C.A[f])==_H
+    state=dict(initial);hist=Counter();cat=Counter();coeff=Counter();usedf=set(state.values());temporary=None;centers=[];count=0;tagged=hashlib.sha256()
+    for k in range(0,len(out),6):
+        op,a,b,c,f,z=out[k:k+6]
+        if op==0:
+            assert state[a]==b and C.sub(b,c)and C.dimf[c]-C.dimf[b]==f and len(C.A[b])-len(C.A[c])==f
+            state[a]=c;usedf.update((b,c))
+            if f:hist[f]+=1
+        elif op==1:
+            assert state[a]==state[b]==f and a!=b and c%2;count+=1;cat[cats[z]]+=1;coeff[abs(c)]+=1;usedf.add(f)
+            tagged.update(json.dumps([a,b,c,f,cats[z]],separators=(',',':')).encode());tagged.update(b'\n')
+        elif op==2:
+            assert temporary is None and b==n and state[a]==c and f==ZERO and z==_CR
+            state[b]=f;hist[z]+=1;temporary=dict(source=a,frame=c,rank=z,temporary=b,first_event=count,copy_output_frame=f)
+        else:
+            assert op==3 and temporary is not None and (a,b,c)==(temporary['source'],temporary['temporary'],temporary['frame'])and state[a]==c and state[b]==f==ZERO
+            temporary.update(after_event=count,scatter_reads=count-temporary['first_event']);assert temporary['scatter_reads']==_SCAT;centers.append(temporary);temporary=None;del state[b]
+    assert state==final and temporary is None and hist==census and len(centers)==_NC
+    oldH=Counter({int(r):c for r,c in producer['physical']['paid_histogram'].items()});delta=Counter(hist);delta.subtract(oldH);delta={r:c for r,c in delta.items()if c}
+    assert delta=={int(k):x for k,x in selection['expected_local_delta'].items()}
+    assert sum(r*c for r,c in hist.items())==producer['physical']['paid_rank_mass']-_H*proof['selected'],'each removed zero-to-full helper frees exactly its h rank'
+    assert count==producer['physical']['weighted_scalar_events']-proof['deleted_scalar_events']+2*proof['inserted_setups']
+    inherited=set()
+    for inventory in (producer['physical'],producer.get('producer_physical')):
+        if isinstance(inventory,dict):inherited.update(row['frame_id']for row in inventory.get('used_frames',[]))
+    sourceH=Counter();targetH=Counter();internalH=Counter(copies)
+    for s,H in per_role.items():(sourceH if s<v else targetH if s<2*v else internalH).update(H)
+    receipt=dict(status='PASS_GEN5_TERMINAL_SINKS_ON_ACTUAL_WORD_AND_BOTH_REFLECTED_LEDGERS',proof=proof,scalar=dict(forward=forward,inverse=inverse,controls=controls),selected=proof['selected'],physical_R=n-2*v,local_histogram_delta=delta,unchanged_surviving_input_output_frames=True,unchanged_copy_lifetimes=True,both_reflected_ledgers=True,unique_required_frame_pairs=len(pairs),source_histogram=dict(sourceH),target_histogram=dict(targetH),internal_histogram_including_copies=dict(internalH),copied_center_histogram=dict(copies),input_raw_sha256=sha(producer['records'].tobytes()),output_raw_sha256=sha(out.tobytes()),selection_sha256=sha(path.read_bytes()),transform_sha256=sha(Path(__file__).read_bytes()),seconds=time.monotonic()-start)
+    meta=dict(producer['physical']);meta.update(status='PASS_PHYSICAL_GEN5_TERMINAL_SINKS',scalar_projection_sha256=forward['event_sha256'],tagged_scalar_sha256=tagged.hexdigest(),weighted_scalar_events=count,coefficient_histogram=dict(coeff),categories=dict(cat),category_names=cats,copied_center_blocks=centers,paid_histogram=dict(sorted(hist.items())),paid_rank_mass=sum(r*c for r,c in hist.items()),positive_rank_moves=sum(hist.values())-_NC,independent_dirty_registers=n-2*v,physical_registers=n,used_frames=[dict(frame_id=f,dimension=C.dimf[f],basis_sha256=sha(json.dumps(C.B[f],separators=(',',':')).encode()))for f in sorted(usedf|inherited)],sink_transform=receipt,physical_emitter_sha256=receipt['transform_sha256'])
+    result=dict(producer);result.update(context=ctx,records=out,physical=meta,result=meta,sink_census=receipt,initial_state=initial,final_state=final,helper_endpoints=ends,sink_entries=rows,sink_stream_map=mp)
+    if output_dir is not None:
+        p=Path(output_dir);p.mkdir(parents=True,exist_ok=True);(p/'sink-records.bin.gz').write_bytes(gzip.compress(out.tobytes(),mtime=0))
+        (p/'sink.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    print('PASS terminal sinks',proof['selected'],'removed roles',proof['removed_roles'],'n',n,count,'scalar ADDs',sum(hist.values()),'paid calls',len(out)//6,'records',flush=True)
+    return result
diff --git a/research/five-stage-p10-transcript-stages/target-selection.json b/research/five-stage-p10-transcript-stages/target-selection.json
new file mode 100644
index 0000000000..cd06638041
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/target-selection.json
@@ -0,0 +1,48733 @@
+{
+ "input_raw_sha256": "da0d6c0e045ac62006189adfebc87df82ae5e6fe9512879e71359c2837d32bd3",
+ "input_scalar_sha256": "d1599cc94b7800ba7b81030ab4100048dc307c42268604fd4c448bfb56191dec",
+ "cut_record": 326320,
+ "rebase_parent": "gen5 parity-fused word after the concave-descent retiming (groups re-derived by gen5/target_search.py)",
+ "expected_total_delta": {
+  "1": -120,
+  "16": -120,
+  "17": 120
+ },
+ "groups": [
+  {
+   "targets": [
+    4,
+    5,
+    6,
+    7
+   ],
+   "cut_record": 326320,
+   "close_after_record": 329185,
+   "dependent": {
+    "4": [
+     5,
+     6,
+     7
+    ]
+   },
+   "retained": [
+    5,
+    6,
+    7
+   ],
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diff --git a/research/five-stage-p10-transcript-stages/target_transform.py b/research/five-stage-p10-transcript-stages/target_transform.py
new file mode 100644
index 0000000000..820f80729b
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/target_transform.py
@@ -0,0 +1,171 @@
+N_STREAMS=None
+"""Exact F2 target-prefix compression, with fresh literal word and both ledgers.
+The retained signed producer is untouched. New signed-lift prefix bounds are
+computed from the emitted odd payload word. OpenAI Codex assistance; Apache-2.0.
+p = 10 port (Chafik Boukhalfa (chafreaky), Anthropic Claude assistance): h, v, centre copies and scatter reads come
+from word_pins.shape and the stage counts are pinned in word-pins.json; the mechanism and checks are unchanged.
+"""
+from array import array
+from collections import Counter,defaultdict
+from copy import deepcopy
+from pathlib import Path
+import gzip,hashlib,json,time
+if not __debug__:raise SystemExit('assertions required')
+HERE=Path(__file__).resolve().parent
+from word_pins import shape as _shape
+_S=_shape();_H=_S['h'];_V=_S['v'];_CR=_S['center_rank'];_NC=_S['centers'];_SCAT=_S['scatter_reads']
+
+def replay(records,reverse=False,omit=None):
+ v=_V;n=N_STREAMS;columns=[1<<i for i in range(n)];wanted=columns[:];norms=[1]*n;largest=1;center=None;count=0;coeff=Counter();digest=hashlib.sha256()
+ for t in range(v):wanted[v+t]^=1<<t
+ for k in(range(len(records)-6,-1,-6)if reverse else range(0,len(records),6)):
+  op,a,b,c,f,z=records[k:k+6]
+  if op==1:
+   if b==n:assert center is not None;b=center
+   if k//6==omit:continue
+   assert c%2 and a!=b;columns[a]^=columns[b];norms[a]+=abs(c)*norms[b];largest=max(largest,norms[a]);coeff[abs(c)]+=1;count+=1
+   digest.update(json.dumps([a,b,-c if reverse else c],separators=(',',':')).encode());digest.update(b'\n')
+  elif op==(3 if reverse else 2):assert center is None;center=a
+  elif op==(2 if reverse else 3):assert center==a;center=None
+ assert center is None and columns==wanted,'full all-column endpoint failure'
+ return dict(reverse=reverse,all_formal_columns=n,all_source_and_dirty_restored=True,arbitrary_target_contents_preserved=True,weighted_additions=count,event_sha256=digest.hexdigest(),coefficient_counts=dict(coeff),literal_unit_additions=sum(c*cnt for c,cnt in coeff.items()),max_intermediate_row_l1=largest,final_source_row_l1=max(norms[:v]),final_target_row_l1=max(norms[v:2*v]),final_dirty_row_l1=max(norms[2*v:]))
+
+def run(producer,output_dir=None,selection_path=None):
+ start=time.monotonic();path=Path(selection_path)if selection_path else HERE/'target-selection.json';selection=json.loads(path.read_text());old=producer['records'];oldmeta=producer['physical'];W,C=producer['W'],producer['C'];initial=dict(producer['initial_state']);ZERO=producer['ZERO'];v=W.v;n=len(initial);global N_STREAMS;N_STREAMS=n
+ assert hashlib.sha256(old.tobytes()).hexdigest()==selection['input_raw_sha256']
+ assert oldmeta['scalar_projection_sha256']==selection['input_scalar_sha256']
+ groups=[];owner={};atclose=defaultdict(list);cut=selection['cut_record'];all_dep={}
+ for j,row in enumerate(selection['groups']):
+  r=dict(row);r['dependent']={int(t):ps for t,ps in r['dependent'].items()};r['frame']=W.register(r['close_basis']);F=r['frame'];assert C.dimf[F]==r['close_rank']and C.nondeg(F)
+  assert r['cut_record']==cut and r['close_after_record']>cut
+  assert not(set(r['dependent'])&{p for ps in r['dependent'].values()for p in ps})
+  assert set(r['dependent'])|set(r['retained'])==set(r['targets'])
+  for t in r['targets']:
+   assert t not in owner;owner[t]=j
+   assert all(W.module.dot(C.cov[t],b)==0 for b in C.B[F])
+  for t,ps in r['dependent'].items():assert set(ps)<=set(r['retained']);all_dep[t]=j
+  atclose[r['close_after_record']].append(j);groups.append(r)
+ # Check the literal old prefix responses, rather than trusting selected dependencies.
+ columns=[1<<i for i in range(n)];center=None;responses={t:0 for t in owner};final=dict(initial)
+ for k in range(0,len(old),6):
+  op,a,b,c,f,z=old[k:k+6];i=k//6
+  if op==0:final[a]=c
+  elif op==1:
+   actual=center if b==n else b;assert actual is not None
+   if i>cut:
+    if actual-v in owner:assert i>groups[owner[actual-v]]['close_after_record'],'active target prefix used as a source'
+    if a-v in owner and i<=groups[owner[a-v]]['close_after_record']:
+     assert not(v<=actual<2*v);responses[a-v]^=columns[actual]
+   assert c%2;columns[a]^=columns[actual]
+  elif op==2:assert center is None;center=a
+  elif op==3:assert center==a;center=None
+  for j in atclose.get(i,[]):
+   r=groups[j]
+   for t,ps in r['dependent'].items():
+    result=responses[t]
+    for p in ps:result^=responses[p]
+    assert result==0,('literal prefix dependency',j,t)
+ assert center is None
+ # Emit a concrete new word and regenerate every MOVE from actual needs.
+ cats=list(oldmeta['category_names'])+['target_prefix_setup','target_prefix_restore'];out=array('i');state=dict(initial);center=None;deleted=[];inserted=[];first_setup=None
+ def move(s,f):
+  before=state[s]
+  if before==f:return
+  assert C.sub(before,f),('nonnested actual use',s,before,f);gap=C.dimf[f]-C.dimf[before];assert gap>=0;out.extend((0,s,before,f,gap,0));state[s]=f
+ def add(a,b,c,f,z):move(a,f);move(b,f);out.extend((1,a,b,c,f,z))
+ def batch(j,sign,f,z):
+  nonlocal first_setup
+  r=groups[j]
+  for t in r['targets']:move(v+t,f)
+  for t,ps in r['dependent'].items():
+   for p in ps:
+    if first_setup is None and sign<0:first_setup=len(out)//6
+    add(v+t,v+p,sign,f,z);inserted.append((v+t,v+p,sign,f,z))
+ for k in range(0,len(old),6):
+  op,a,b,c,f,z=old[k:k+6];i=k//6
+  if op==1:
+   j=all_dep.get(a-v)
+   if j is not None and cut<i<=groups[j]['close_after_record']:
+    assert not(v<=b<2*v);deleted.append(i)
+   else:add(a,b,c,f,z)
+  elif op==2:
+   assert center is None;move(a,c);out.extend((op,a,b,c,f,z));state[b]=f;center=(a,b,c)
+  elif op==3:
+   assert center==(a,b,c)and state[a]==c and state[b]==f;out.extend((op,a,b,c,f,z));del state[b];center=None
+  if i==cut:
+   assert center is None and all(state[v+t]==ZERO for t in owner)
+   for j in range(len(groups)):batch(j,-1,ZERO,len(cats)-2)
+  for j in atclose.get(i,[]):batch(j,1,groups[j]['frame'],len(cats)-1)
+ for s in sorted(final):move(s,final[s])
+ assert center is None and state==final
+ # Independent required-frame census ignores all emitted MOVEs.
+ needs={s:[]for s in initial};copies=Counter();center=None
+ for k in range(0,len(out),6):
+  op,a,b,c,f,z=out[k:k+6]
+  if op==1:
+   needs[a].append(f)
+   if b!=n:needs[b].append(f)
+   else:assert center is not None and f==ZERO
+  elif op==2:assert center is None;center=(a,b,c);needs[a].append(c);copies[z]+=1
+  elif op==3:assert center==(a,b,c);center=None
+ assert center is None and copies=={_CR:_NC}
+ census=Counter(copies);per_role={};pairs=set()
+ for s,before in initial.items():
+  H=Counter()
+  for f in needs[s]+[final[s]]:
+   assert C.sub(before,f);gap=C.dimf[f]-C.dimf[before]
+   if gap:H[gap]+=1
+   pairs.add((before,f));before=f
+  per_role[s]=H;census.update(H)
+ usedframes={f for pair in pairs for f in pair}
+ for f in usedframes:assert C.nondeg(f)and len(C.B[f])==C.dimf[f]and len(C.A[f])+C.dimf[f]==_H
+ for a,b in pairs:
+  assert len(C.A[a])-len(C.A[b])==C.dimf[b]-C.dimf[a]
+  assert all(W.module.dot(x,y)==0 for x in C.A[b]for y in C.B[a])
+ # Independently validate literal frames and build fresh physical hashes.
+ state=dict(initial);center=None;hist=Counter();cat=Counter();coeff=Counter();centers=[];count=0;scalar=hashlib.sha256();tagged=hashlib.sha256();used=set(initial.values())
+ def event(d,row):d.update(json.dumps(row,separators=(',',':')).encode());d.update(b'\n')
+ for k in range(0,len(out),6):
+  op,a,b,c,f,z=out[k:k+6]
+  if op==0:
+   assert state[a]==b and C.sub(b,c)and C.dimf[c]-C.dimf[b]==f;state[a]=c;used.update((b,c))
+   if f:hist[f]+=1
+  elif op==1:
+   assert c%2 and state[a]==state[b]==f and a!=b;kind=cats[z];source=center['source']if b==n else b
+   event(scalar,[a,source,c]);event(tagged,[a,b,c,f,kind]);count+=1;cat[kind]+=1;coeff[abs(c)]+=1;used.add(f)
+  elif op==2:
+   assert center is None and b==n and state[a]==c and f==ZERO and z==_CR;state[b]=f;hist[z]+=1;center=dict(source=a,frame=c,rank=z,temporary=b,first_event=count,copy_output_frame=f)
+  else:
+   assert op==3 and center is not None and(a,b,c)==(center['source'],center['temporary'],center['frame'])and state[a]==c and state[b]==f==ZERO
+   center.update(after_event=count,scatter_reads=count-center['first_event']);assert center['scatter_reads']==_SCAT;centers.append(center);center=None;del state[b]
+ assert center is None and state==final and hist==census
+ forward=replay(out);inverse=replay(out,True);assert forward['event_sha256']==scalar.hexdigest()
+ try:replay(out,omit=first_setup)
+ except AssertionError:negative='omitted target-prefix setup rejected'
+ else:raise AssertionError('missing target prefix setup admitted')
+ delta=Counter(hist);delta.subtract(Counter({int(k):v for k,v in oldmeta['paid_histogram'].items()}));delta={k:v for k,v in delta.items()if v}
+ expected=Counter()
+ for r in groups:expected.update({int(k):v for k,v in r['local_histogram_delta'].items()})
+ assert delta=={k:v for k,v in expected.items()if v}
+ assert sum(r*c for r,c in hist.items())==oldmeta['paid_rank_mass'];assert count==oldmeta['weighted_scalar_events']-len(deleted)+len(inserted)
+ sourceH=Counter();targetH=Counter();internalH=Counter(copies)
+ for s,H in per_role.items():(sourceH if s<v else targetH if s<2*v else internalH).update(H)
+ receipt=dict(status='PASS_EXACT_F2_TARGET_PREFIX_COMPRESSION',selected_groups=len(groups),targets=len(owner),deleted_prefix_adds=len(deleted),inserted_setup_restore_adds=len(inserted),cut_record=cut,literal_prefix_dependencies_checked=True,remaining_payload_additions=count,local_histogram_delta=delta,both_reflected_ledgers=True,unchanged_all_input_output_frames=True,unchanged_copy_lifetimes=True,producer_context_unchanged=True,source_histogram=dict(sourceH),target_histogram=dict(targetH),internal_histogram_including_copies=dict(internalH),copied_center_histogram=dict(copies),unique_required_frame_pairs=len(pairs),explicit_reflected_annihilator_pairs=len(pairs),forward=forward,inverse=inverse,negative_control=negative,selection_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),transform_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(),seconds=time.monotonic()-start)
+ meta=dict(oldmeta);meta.update(status='PASS_PHYSICAL527_TARGET_PREFIX_FRAME_AND_SCALAR_PROJECTION',category_names=cats,scalar_projection_sha256=scalar.hexdigest(),tagged_scalar_sha256=tagged.hexdigest(),weighted_scalar_events=count,coefficient_histogram=dict(coeff),categories=dict(cat),copied_center_blocks=centers,paid_histogram=dict(sorted(hist.items())),paid_rank_mass=sum(r*c for r,c in hist.items()),positive_rank_moves=sum(hist.values())-_NC,used_frames=[dict(frame_id=f,dimension=C.dimf[f],basis_sha256=hashlib.sha256(json.dumps(C.B[f],separators=(',',':')).encode()).hexdigest())for f in sorted(used)],target_transform=receipt,physical_emitter_sha256=receipt['transform_sha256'])
+ result=dict(producer);result.update(records=out,physical=meta,result=meta,target_census=receipt)
+ if output_dir is not None:
+  p=Path(output_dir);p.mkdir(parents=True,exist_ok=True);(p/'records.bin.gz').write_bytes(gzip.compress(out.tobytes(),mtime=0));(p/'physical.json').write_text(json.dumps(meta,indent=2)+'\n');(p/'target.json').write_text(json.dumps(receipt,indent=2)+'\n');(p/'target-used-bases.json').write_text(json.dumps({f:dict(basis=C.B[f],annihilator=C.A[f])for f in sorted(used)},separators=(',',':'))+'\n')
+ print('PASS target prefix',len(groups),'groups',count,'ADDs',flush=True)
+ return result
+
+def rebind(raw,receipt):
+ assert receipt['status']=='PASS_EXACT_F2_TARGET_PREFIX_COMPRESSION'and receipt['both_reflected_ledgers']and receipt['producer_context_unchanged']
+ hist=lambda x:Counter({int(k):v for k,v in x.items()if v});compact=lambda h:{str(k):v for k,v in sorted(h.items())if v}
+ source=hist(receipt['source_histogram']);target=hist(receipt['target_histogram']);internal=hist(receipt['internal_histogram_including_copies']);copies=hist(receipt['copied_center_histogram']);helper=source+target+internal
+ assert source==hist(raw['physical_source_histogram'])and internal==hist(raw['physical_internal_excluding_center_copies'])+copies
+ delta=helper.copy();delta.subtract(hist(raw['one_stage_helper_histogram_including_copies']));assert compact(delta)==compact(hist(receipt['local_histogram_delta']))
+ old=deepcopy(raw);five=Counter({r:5*n for r,n in helper.items()});five.update(hist(raw['five_stage_profile']['idle_histogram']))
+ for r,n in hist(raw['auxiliary_entrance_rank_histogram']).items():five[5*r]+=n
+ assert sum(r*n for r,n in five.items())==raw['five_stage_profile']['rank_mass']
+ raw['before_target_prefix_ledger']=old;raw['schema']='source527-target-prefix-fresh-raw-ledger/1';raw['physical_target_histogram']=compact(target);raw['one_stage_helper_histogram_including_copies']=compact(helper);raw['five_stage_profile'].update(histogram=compact(five),calls=sum(five.values()));raw['target_transform']=receipt
+ return raw
diff --git a/research/five-stage-p10-transcript-stages/verify.py b/research/five-stage-p10-transcript-stages/verify.py
new file mode 100644
index 0000000000..86410f57c8
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/verify.py
@@ -0,0 +1,100 @@
+#!/usr/bin/env python3
+"""Immutable p = 10 five-stage banks with the transcript stage stack: regenerate every mandatory finite stage.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+p = 10 port (DreamingOfClouds, Anthropic Claude assistance): word-dependent values are checked against the
+MANIFEST-pinned word-pins.json through word_pins.expect (always strict here; see discovery/repin.py).
+Transcript stages (descent, target squares, kernel entries, early restorations, terminal sinks, reorder) ported to
+p = 10 by Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; each is a mandatory stage with its own receipt.
+"""
+import sys
+if not __debug__:raise SystemExit('Assertions required; refusing-O')
+sys.dont_write_bytecode=True
+from pathlib import Path
+from datetime import datetime,timezone
+from fractions import Fraction
+import argparse,hashlib,importlib.util,json,time,traceback
+ROOT=Path(__file__).resolve().parent
+BASE_REQUIRED={'virtual','raw','bit','scalar','primes','banks','complex','math','finite'}
+
+def progress(message):print(datetime.now(timezone.utc).strftime('%H:%M:%S UTC')+'  '+message,flush=True)
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def serial(x):
+ if isinstance(x,Fraction):return str(x)
+ if isinstance(x,dict):return {str(k):serial(v)for k,v in x.items()}
+ if isinstance(x,(list,tuple)):return list(map(serial,x))
+ return x
+
+def load(name):
+ s=importlib.util.spec_from_file_location('source527_'+name,ROOT/(name+'.py'));m=importlib.util.module_from_spec(s);sys.modules[s.name]=m;s.loader.exec_module(m);return m
+
+# Every transcript stage of portable_bit.STAGES is a mandatory proof stage with its own receipt.
+REQUIRED=BASE_REQUIRED|set(load('portable_bit').STAGES)
+
+def integrity():
+ p=ROOT/'MANIFEST.json';m=json.loads(p.read_text());actual={}
+ for q in ROOT.rglob('*'):
+  assert not q.is_symlink(),'Symlink in package'
+  if q.is_file()and q.name!='MANIFEST.json':actual[q.relative_to(ROOT).as_posix()]=sha(q)
+ # Nested source manifests are also ordinary pinned inputs.
+ for q in ROOT.rglob('MANIFEST.json'):
+  if q!=p:actual[q.relative_to(ROOT).as_posix()]=sha(q)
+ assert actual==m['files'],'Missing, changed or unpinned package/source file'
+ return sha(p),len(actual)
+
+def validate_required(results):
+ assert set(results)==REQUIRED,'Missing mandatory proof stage'
+ assert all(isinstance(results[k],dict)and results[k]for k in REQUIRED)
+
+def controls():
+ out=[];good={k:{'present':True}for k in REQUIRED}
+ for k in sorted(REQUIRED):
+  bad=good.copy();bad.pop(k)
+  try:validate_required(bad)
+  except AssertionError:out.append('omitted '+k+' stage')
+  else:raise AssertionError('Missingstageaccepted')
+ return out
+
+def replay(output,results,timings,save):
+ """Every mandatory stage, in order. main() runs it under strict pins; discovery/repin.py reuses it to record."""
+ def stage(name,call):
+  t=time.monotonic();value=call();results[name]=value;timings[name]=time.monotonic()-t;save(name+'.json',value);progress(name+' PASS '+format(timings[name],'.1f')+'s');return value
+ progress('Admitting the pinned p = 10 physical bit word')
+ stage('virtual',lambda:load('virtual_check').run(output,progress))
+ context=load('prepare').prepare()
+ raw=stage('raw',lambda:load('raw_ledger').run(context))
+ portable=load('portable_bit');bit=portable.run(prepared_context=context,raw=raw,output_dir=output,run_geometry=True,package_root=ROOT);raw=bit['raw'];results['raw']=raw;save('raw.json',raw);results['bit']=portable.summary(bit);timings['bit']=bit['seconds'];save('bit.json',results['bit'])
+ for name in portable.STAGES:results[name]=bit[name+'_census'];timings[name]=bit[name+'_census']['seconds'];save(name+'.json',results[name])
+ progress('bit physical/'+'/'.join(portable.STAGES)+'/global/geometry PASS')
+ scalar=stage('scalar',lambda:load('scalar_check').run(context,bit['records'],progress,2*bit['W'].v+len(bit['context']['regs'])))
+ primes=stage('primes',lambda:load('prime_check').run(bit['context'],bit['physical'],progress))
+ bankresult=stage('banks',lambda:load('bank_check').run(bit['context'],bit['global_result'],bit['lower']))
+ banks=bankresult['banks'];banked=bankresult['banked_result']
+ complex_result=stage('complex',lambda:load('portable_complex').run(package_root=ROOT,progress=progress))
+ assert complex_result['precision_guard']['retained_row_coefficient']==20161
+ math=stage('math',lambda:load('math_check').run(raw,complex_result['five_stage_histogram'],banks,bit['global_result']))
+ finite=stage('finite',lambda:load('finite_check').run(raw,bit['physical'],scalar,primes,math,banks,banked,bit['global_result']))
+ assert math['mathematics']['finite_bridge']['rows']['coefficient']==complex_result['precision_guard']['retained_row_coefficient']==finite['row_reserve']['external_complex_coefficient']
+ validate_required(results);assert len(scalar['controls'])==11 and len(primes['controls'])==6
+ return math
+
+def main():
+ ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--output',type=Path,required=True);args=ap.parse_args()
+ import sympy
+ assert sys.version_info>=(3,11)and sympy.__version__=='1.14.0'
+ import word_pins
+ assert Path(word_pins.__file__).resolve()==ROOT/'word_pins.py' and word_pins.RECORD is None,'strict pins only'
+ digest,count=integrity();output=args.output.resolve();assert not output.is_relative_to(ROOT)and not output.exists(),'Output must be new and outside package';output.mkdir(parents=True)
+ results={};timings={};start=time.monotonic()
+ def save(name,value):(output/name).write_text(json.dumps(serial(value),sort_keys=True,indent=2)+'\n')
+ try:
+  math=replay(output,results,timings,save)
+  assert math['mathematics']['kappa']==word_pins.PINS['kappa'][1] and math['mathematics']['binding']==word_pins.PINS['binding']
+  assert word_pins.RECORD is None
+  after,_=integrity();assert after==digest,'Package changed during replay'
+  certificate=dict(schema='p10-transcript-stages-five-stage-banks/1',**math['mathematics'],scope='Conditionalfiniteconstruction; inheritedallsizecompiler,weightedselector,commonancestorchart,restoredrow,routing,prime,recovery,complexsymbolicandanalyticinterfacesremainassumptions.')
+  save('certificate.json',certificate)
+  report=dict(status='PASS_IMMUTABLE_P10_TRANSCRIPT_STAGES_FIVE_STAGE_BANKED_CONSTRUCTION',manifest_sha256=digest,files=count,kappa=math['mathematics']['kappa'],kappa_scientific=math['mathematics']['kappa_scientific'],binding=math['mathematics']['binding'],bit_root=math['mathematics']['bit_root'],bit_coarse=math['mathematics']['bit_coarse'],complex_coarse=math['mathematics']['complex_coarse'],fresh_stages=sorted(REQUIRED),inputs_unchanged=True,timings=timings,seconds=time.monotonic()-start,negative_controls=controls())
+  save('verification.json',report);print(json.dumps(report),flush=True)
+ except BaseException as exc:
+  save('failure.json',dict(status='FAIL',error=str(exc),completed_stages=sorted(results),timings=timings,traceback=traceback.format_exc()));raise
+if __name__=='__main__':main()
diff --git a/research/five-stage-p10-transcript-stages/virtual_check.py b/research/five-stage-p10-transcript-stages/virtual_check.py
new file mode 100644
index 0000000000..485a407f6b
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/virtual_check.py
@@ -0,0 +1,68 @@
+"""Retained admissions of the p = 10 bit word: PR168-v4 package checker and PR200 physical-word proof.
+
+1. eumemic's unmodified PR168-v4 check_paired_cube_bit.py on the virtual (node-frame, unaliased) word:
+   exact frames, mod-2 decoder with stars and side parts, geometry (source lines, root caps, operand
+   nesting, star spans), role and target chains, partner chronology, G-nondegeneracy, a literal F2
+   dirty-scratch replay and the ledger recount, with its five mutation controls.
+2. Chafik Boukhalfa's unmodified PR200 physical-word classes, run as PR200's bit/prove.py runs them:
+   exact changed operation frames and handoffs, the physical row (phase one = centre closure, actual
+   addition operands, gauge supports, partner chronology, nested physical role and target chains,
+   telescoping deficit), the physical word on every formal column over F2 and the defining integer
+   decoder, and its adverse controls (omitted compensation, missing partner delivery, stale recipient
+   read, zero operation frame).
+Gen4 integration by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+p = 10 port: honest pP file names, PR168's p argument, constants from word_pins (shape or pins).
+"""
+from pathlib import Path
+import gzip,hashlib,importlib.util,json,shutil,time
+from word_pins import P,expect,shape
+HERE=Path(__file__).resolve().parent
+
+def load(name,path):
+    spec=importlib.util.spec_from_file_location(name,path);mod=importlib.util.module_from_spec(spec);spec.loader.exec_module(mod);return mod
+
+def run(output_dir,progress=lambda text:None):
+    begun=time.monotonic();S=shape();sfx='_p%d.json'%P;src=HERE/'bitword/selected/bit';d=Path(output_dir)/'virtual-bit';d.mkdir(parents=True)
+    assert sorted(x.name for x in src.iterdir())==sorted([n+sfx for n in('graph','kchron','profile')]+[n+sfx+'.gz' for n in('frames','word')])
+    for name in ('graph','kchron','profile'):shutil.copyfile(src/(name+sfx),d/(name+sfx))
+    for name in ('word','frames'):(d/(name+sfx)).write_bytes(gzip.decompress((src/(name+sfx+'.gz')).read_bytes()))
+    p=HERE/'bitword/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py'
+    mod=load('p10_pr168_v4_checker',p)
+    progress('Running the PR168-v4 package checker on the p = 10 virtual word')
+    result=mod.Checker(d,P).run()
+    assert result['m']==S['virtual_m'] and result['deficit']==S['virtual_deficit'] and result['roles']==expect('virtual_R',result['roles'])
+    expect('pr168_result',result)
+    controls={}
+    for m in ('broken_mix','outside_cap','below_level','dropped_star','non_nested'):
+        try:mod.Checker(d,P,mutate=m).run()
+        except mod.Fail as error:controls[m]=str(error)
+        else:raise AssertionError('PR168 mutation control accepted: '+m)
+    assert len(controls)==5
+    progress('Running the PR200 physical-word proof on the p = 10 physical word')
+    word=load('p10_pr200_physical_word_admission',HERE/'bitword/bit/word.py').Candidate()
+    word.exact_frames();row=word.row()
+    reference=json.loads((src/('profile'+sfx)).read_text())
+    assert row['h']==S['h'] and row['v']==S['v']
+    assert row['reused_registers']==len(word.pairs)==expect('reuse_pairs',row['reused_registers']) and row['virtual_R']==reference['R']==expect('virtual_R',row['virtual_R'])
+    assert row['R']==expect('physical_R',row['R']) and row['W_per_vertex']==2*S['v']+row['R'] and row['deficit_per_vertex']==reference['deficit_per_vertex']==S['virtual_deficit'] and row['loss']==reference['loss']==S['ell']
+    expect('changed_operation_frames',row['changed_operation_frames']);expect('entrances',row['selected_roles']);expect('entrance_ranks',dict(row['selected_rank_histogram']))
+    formal=[word.formal(r) for r in (2,0)]
+    assert formal[0]['identity'] and all(f['defining_decoder'] and f['all_dirty_and_source_columns_restored'] and f['formal_variables']==2*S['v']+row['R'] for f in formal)
+    physical_controls=[]
+    for tamper in ('omit_compensation','missing_partner','stale'):
+        try:word.formal(2,tamper)
+        except ValueError:physical_controls.append(tamper)
+        else:raise AssertionError('PR200 adverse word control accepted: '+tamper)
+    i=word.changed_frames[0];old=word.opframe[i];word.opframe[i]=word.register([])
+    try:word.exact_frames()
+    except ValueError:physical_controls.append('zero_operation_frame')
+    else:raise AssertionError('zero operation frame accepted')
+    word.opframe[i]=old
+    assert len(physical_controls)==4
+    row={k:(dict(v) if isinstance(v,dict) else v) for k,v in row.items()}
+    return dict(status='PASS_PR168_V4_VIRTUAL_AND_PR200_PHYSICAL_ADMISSION_OF_P10_WORD',virtual=result,virtual_controls_rejected=controls,
+        physical_row=row,physical_formal=formal,physical_controls_rejected=physical_controls,
+        checker_sha256=hashlib.sha256(p.read_bytes()).hexdigest(),
+        pr200_classes_sha256={n:hashlib.sha256((HERE/'bitword/bit'/n).read_bytes()).hexdigest() for n in ('word.py','base_word.py')},
+        seconds=time.monotonic()-begun,
+        scope='The pinned word is admitted by both retained checkers exactly as PR200 admitted its own word (its terminal-sink and prime steps have no counterpart here; primes are rechecked by prime_check).')
diff --git a/research/five-stage-p10-transcript-stages/word-pins.json b/research/five-stage-p10-transcript-stages/word-pins.json
new file mode 100644
index 0000000000..f5a77db62d
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/word-pins.json
@@ -0,0 +1,754 @@
+{
+ "bank_patterns": [
+  [
+   [
+    19,
+    19,
+    19,
+    19,
+    20,
+    4
+   ],
+   15105
+  ],
+  [
+   [
+    18,
+    18,
+    18,
+    18,
+    20,
+    4,
+    4
+   ],
+   300
+  ],
+  [
+   [
+    16,
+    16,
+    16,
+    16,
+    16,
+    20
+   ],
+   60
+  ],
+  [
+   [
+    15,
+    15,
+    15,
+    15,
+    20,
+    20
+   ],
+   45
+  ],
+  [
+   [
+    13,
+    13,
+    13,
+    13,
+    20,
+    20,
+    4,
+    4
+   ],
+   15
+  ],
+  [
+   [
+    12,
+    12,
+    12,
+    12,
+    12,
+    20,
+    20
+   ],
+   36
+  ],
+  [
+   [
+    10,
+    10,
+    10,
+    10,
+    10,
+    10,
+    10,
+    10,
+    10,
+    10
+   ],
+   36
+  ],
+  [
+   [
+    7,
+    7,
+    7,
+    7,
+    7,
+    7,
+    7,
+    7,
+    20,
+    20,
+    4
+   ],
+   7
+  ],
+  [
+   [
+    7,
+    7,
+    7,
+    7,
+    20,
+    20,
+    20,
+    4,
+    4,
+    4
+   ],
+   1
+  ],
+  [
+   [
+    6,
+    6,
+    6,
+    6,
+    6,
+    6,
+    6,
+    6,
+    6,
+    6,
+    20,
+    20
+   ],
+   6
+  ],
+  [
+   [
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    3,
+    20,
+    20
+   ],
+   930
+  ],
+  [
+   [
+    20,
+    20,
+    20,
+    20,
+    4,
+    4,
+    4,
+    4,
+    4
+   ],
+   1
+  ],
+  [
+   [
+    20,
+    20,
+    20,
+    20,
+    20
+   ],
+   67362
+  ],
+  [
+   [
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4,
+    4
+   ],
+   1674
+  ]
+ ],
+ "banked_calls": 250195,
+ "banked_rank_mass": 1095110,
+ "banks_per_stage": 85578,
+ "binding": "bit",
+ "bit_root": [
+  "Fraction",
+  "385073284125967/500000000000000000"
+ ],
+ "changed_operation_frames": 998,
+ "completion_rank_histogram": [
+  "dict",
+  [
+   [
+    1,
+    1007
+   ],
+   [
+    10,
+    6
+   ],
+   [
+    13,
+    1
+   ],
+   [
+    14,
+    1
+   ],
+   [
+    16,
+    960
+   ],
+   [
+    17,
+    310
+   ],
+   [
+    2,
+    20
+   ],
+   [
+    4,
+    5
+   ],
+   [
+    5,
+    3
+   ],
+   [
+    7,
+    1
+   ],
+   [
+    8,
+    3
+   ]
+  ]
+ ],
+ "descent_five_stage_calls": 245960,
+ "descent_helper_rank_mass": 181050,
+ "descent_local_delta": [
+  "dict",
+  [
+   [
+    1,
+    -960
+   ],
+   [
+    16,
+    -480
+   ],
+   [
+    17,
+    960
+   ],
+   [
+    18,
+    -480
+   ],
+   [
+    2,
+    480
+   ]
+  ]
+ ],
+ "descent_remaining_payload_additions": 355400,
+ "descent_removed_calls": 480,
+ "descent_selected_gates": 480,
+ "entrance_rank_histogram": [
+  "dict",
+  [
+   [
+    1,
+    1007
+   ],
+   [
+    10,
+    6
+   ],
+   [
+    13,
+    1
+   ],
+   [
+    14,
+    1
+   ],
+   [
+    16,
+    1200
+   ],
+   [
+    17,
+    70
+   ],
+   [
+    2,
+    20
+   ],
+   [
+    4,
+    5
+   ],
+   [
+    5,
+    3
+   ],
+   [
+    7,
+    1
+   ],
+   [
+    8,
+    3
+   ]
+  ]
+ ],
+ "entrance_ranks": [
+  "dict",
+  [
+   [
+    16,
+    1200
+   ],
+   [
+    17,
+    70
+   ]
+  ]
+ ],
+ "entrances": 1270,
+ "extra_selector_calls": 295929593400,
+ "family_collisions": 86405,
+ "final_charts": 759,
+ "final_entrance_bases": 519,
+ "final_entrance_ranks": [
+  "dict",
+  [
+   [
+    1,
+    1007
+   ],
+   [
+    10,
+    6
+   ],
+   [
+    13,
+    1
+   ],
+   [
+    14,
+    1
+   ],
+   [
+    16,
+    1200
+   ],
+   [
+    17,
+    70
+   ],
+   [
+    2,
+    20
+   ],
+   [
+    4,
+    5
+   ],
+   [
+    5,
+    3
+   ],
+   [
+    7,
+    1
+   ],
+   [
+    8,
+    3
+   ]
+  ]
+ ],
+ "final_entrances": 2317,
+ "final_five_stage_rank_mass": 1204260,
+ "final_physical_R": 8223,
+ "finite_coefficient": 25485577221183401,
+ "five_stage_calls": 248360,
+ "five_stage_rank_mass": 1204960,
+ "forward_max_row_l1": 120183,
+ "inverse_max_row_l1": 1267036,
+ "kappa": [
+  "Fraction",
+  "769553898621543/1000000000000000000"
+ ],
+ "kernel_entrance_rank": 1200,
+ "kernel_entries": 1047,
+ "kernel_five_stage_calls": 251482,
+ "kernel_five_stage_rank_mass": 1204960,
+ "kernel_helper_rank_mass": 179850,
+ "kernel_local_delta": [
+  "dict",
+  [
+   [
+    1,
+    2086
+   ],
+   [
+    10,
+    4
+   ],
+   [
+    11,
+    4
+   ],
+   [
+    12,
+    -26
+   ],
+   [
+    13,
+    3
+   ],
+   [
+    14,
+    3
+   ],
+   [
+    15,
+    -8
+   ],
+   [
+    2,
+    -184
+   ],
+   [
+    3,
+    -867
+   ],
+   [
+    4,
+    59
+   ],
+   [
+    5,
+    -55
+   ],
+   [
+    6,
+    -12
+   ],
+   [
+    7,
+    3
+   ],
+   [
+    8,
+    5
+   ]
+  ]
+ ],
+ "kernel_pairs": 0,
+ "literal_stock": 658290,
+ "literal_unit_additions": 338173,
+ "local_paid_rank_mass": 181050,
+ "max_chart_factors": 400,
+ "maximum_determinant_bits": 97,
+ "normalizer_factor_bound": 599,
+ "physical_R": 8230,
+ "pr168_result": [
+  "dict",
+  [
+   [
+    "W",
+    11040
+   ],
+   [
+    "children",
+    151140
+   ],
+   [
+    "deficit",
+    840
+   ],
+   [
+    "frames",
+    12912
+   ],
+   [
+    "m",
+    60
+   ],
+   [
+    "roles",
+    9120
+   ]
+  ]
+ ],
+ "producer_five_stage_calls": 248360,
+ "removed_completion_histogram": [
+  "dict",
+  [
+   [
+    10,
+    20
+   ],
+   [
+    20,
+    5
+   ],
+   [
+    25,
+    3
+   ],
+   [
+    35,
+    1
+   ],
+   [
+    40,
+    3
+   ],
+   [
+    5,
+    1007
+   ],
+   [
+    50,
+    6
+   ],
+   [
+    65,
+    1
+   ],
+   [
+    70,
+    1
+   ],
+   [
+    80,
+    960
+   ],
+   [
+    85,
+    310
+   ]
+  ]
+ ],
+ "removed_even_adds": 581680,
+ "reorder_count": 133,
+ "reorder_five_stage_calls": 252512,
+ "reorder_five_stage_rank_mass": 1204260,
+ "reorder_local_delta": [
+  "dict",
+  [
+   [
+    17,
+    -113
+   ],
+   [
+    18,
+    113
+   ],
+   [
+    2,
+    73
+   ],
+   [
+    3,
+    -113
+   ],
+   [
+    4,
+    20
+   ]
+  ]
+ ],
+ "residual_families": [
+  "dict",
+  [
+   [
+    10,
+    6
+   ],
+   [
+    12,
+    3
+   ],
+   [
+    13,
+    1
+   ],
+   [
+    15,
+    3
+   ],
+   [
+    16,
+    5
+   ],
+   [
+    18,
+    20
+   ],
+   [
+    19,
+    1007
+   ],
+   [
+    20,
+    5906
+   ],
+   [
+    3,
+    310
+   ],
+   [
+    4,
+    960
+   ],
+   [
+    6,
+    1
+   ],
+   [
+    7,
+    1
+   ]
+  ]
+ ],
+ "restore_endpoint_saving": 240,
+ "restore_five_stage_calls": 252682,
+ "restore_five_stage_rank_mass": 1204960,
+ "restore_helpers": 240,
+ "restore_local_delta": [
+  "dict",
+  [
+   [
+    1,
+    720
+   ],
+   [
+    2,
+    -480
+   ]
+  ]
+ ],
+ "reuse_pairs": 890,
+ "route_factor_counts": [
+  "dict",
+  [
+   [
+    "add",
+    163
+   ],
+   [
+    "scale",
+    23
+   ],
+   [
+    "swap",
+    36
+   ]
+  ]
+ ],
+ "scalar_event_sha256": "647cf2c3ebb6902d863e704fc391422f5e6292de43e5f3d893ed0c4ad788ae9f",
+ "sink_count": 7,
+ "sink_five_stage_calls": 252612,
+ "sink_five_stage_rank_mass": 1204260,
+ "sink_local_delta": [
+  "dict",
+  [
+   [
+    17,
+    -7
+   ],
+   [
+    3,
+    -7
+   ]
+  ]
+ ],
+ "surviving_additions": 355400,
+ "surviving_coefficients": [
+  "dict",
+  [
+   [
+    1,
+    354440
+   ],
+   [
+    3,
+    960
+   ]
+  ]
+ ],
+ "target_groups": 120,
+ "unique_bases": 13912,
+ "virtual_R": 9120,
+ "virtual_gauges": 2160,
+ "weighted_scalar_coefficients": [
+  "dict",
+  [
+   [
+    1,
+    335293
+   ],
+   [
+    3,
+    960
+   ]
+  ]
+ ],
+ "weighted_scalar_events": 336253,
+ "word_formal_columns": 10143
+}
diff --git a/research/five-stage-p10-transcript-stages/word_pins.py b/research/five-stage-p10-transcript-stages/word_pins.py
new file mode 100644
index 0000000000..0d5232e8ec
--- /dev/null
+++ b/research/five-stage-p10-transcript-stages/word_pins.py
@@ -0,0 +1,64 @@
+"""Cube-size shape and pinned word-dependent constants of the p = 10 package.
+
+shape() derives every p-dependent constant of the five-stage layout from the cube size p (h = 2p ports per
+coordinate block, v = 8*C(p,3) sources, m = 5h). The PR234 five-stage layout is the same at every h: idle ranks
+(2h-2, h-1, 2h+2, 4) at 2v each, h copied centres of rank h-2 each read by 3v/h targets, and five-stage deficit
+4v - 5h(h-2).
+
+Word-dependent observed values (register counts, histograms, digests, kappa, ...) are pinned in word-pins.json,
+which MANIFEST.json pins like every other input. Every check calls expect(name, value), which asserts exact
+equality with the pinned value (in the canonical form canon() below; dictionaries keep their key types), so each
+check is exactly as strong as the literal it replaces. RECORD is None in every verification run; only
+discovery/repin.py, in its own process, switches it to a dictionary to collect the values of a new word.
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+from fractions import Fraction
+from math import comb
+from pathlib import Path
+import json
+
+HERE = Path(__file__).resolve().parent
+P = 10
+FILE = HERE / 'word-pins.json'
+PINS = json.loads(FILE.read_text())
+RECORD = None
+
+
+def shape(p=P):
+    h = 2 * p; v = 8 * comb(p, 3); m = 5 * h; ell = h * (h - 2)
+    assert v * 3 % h == 0
+    return dict(p=p, h=h, v=v, m=m, ell=ell, idle=(2 * h - 2, h - 1, 2 * h + 2, 4), center_rank=h - 2, centers=h,
+                scatter_reads=3 * v // h, center_reads=3 * v, deficit=4 * v - 5 * ell,
+                virtual_m=3 * h, virtual_deficit=2 * v - 3 * ell, replicas=60, stages=5)
+
+
+def canon(x):
+    """Injective JSON form: dicts become key-sorted [key, value] lists (key types kept), tuples become lists."""
+    if isinstance(x, bool) or x is None or isinstance(x, (int, str)):
+        return x
+    if isinstance(x, Fraction):
+        return ['Fraction', str(x)]
+    if isinstance(x, dict):
+        items = [[canon(k), canon(v)] for k, v in x.items()]
+        return ['dict', sorted(items, key=lambda kv: json.dumps(kv[0], sort_keys=True))]
+    if isinstance(x, (list, tuple)):
+        return [canon(y) for y in x]
+    raise AssertionError(('value type not pinnable', type(x)))
+
+
+def expect(name, value):
+    """Assert value equals the pinned value; returns value. (Records instead only inside discovery/repin.py.)"""
+    c = canon(value)
+    if RECORD is not None:
+        assert RECORD.setdefault(name, c) == c, ('one pin, two values', name)
+        return value
+    assert name in PINS, ('unpinned value', name)
+    assert PINS[name] == c, ('pinned value changed', name)
+    return value
+
+
+def pinned(name):
+    """A pinned value already asserted by an earlier expect() (needed by module-level constants)."""
+    table = PINS if RECORD is None else RECORD
+    assert name in table, ('pin read before it was checked', name)
+    return table[name]
diff --git a/research/joint-dual/SOURCE.json b/research/joint-dual/SOURCE.json
index e3a8386b17..e1fbf9c5aa 100644
--- a/research/joint-dual/SOURCE.json
+++ b/research/joint-dual/SOURCE.json
@@ -3,9 +3,9 @@
   "base_pr57_commit": "cd350f76c9bc01489ec83568bded532cb69be938",
   "base_pr58_commit": "bc2f7ed4c20dc18898305ab17165c0c995cbb804",
   "files": {
-    "Makefile": "768131bd4ce18433f6abccdc9812a38c92e11220e3a1019c6d95334b42f529d1",
+    "Makefile": "cd0fb59dc078d1fdf54a163ea13bb3660d03c8fe69c1a7f99fc8e5f476a3d5c2",
     "NOTICE": "b49022cb4104d90b182e4c335f670faf45529025b15db77bf0291835083c28bd",
-    "README.md": "d104c31d5b7e0d3a8d011a0e3517ab615e5b499b3dc05684f7ad3cadcd28bdae",
+    "README.md": "b81f8035b859007add6693c6d860371c9100a6766e494045495a28a457a5fcb9",
     "certificates/joint-dual-compiler.json": "516c4d85158553dabd0a98216a064b2a7397957a9d5dd0df1d6e5aec53a4e805",
     "certificates/joint-dual-profiles-23.json": "159fa8fee175fc1d24f63e72d3c2f1dc9f4fcd78b938c5e7d2f735fd0fd37209",
     "certificates/joint-dual-profiles-25.json": "8d190ce42d097e828c5756918c52f2963df576cf4c6600b0fc7f2b7fdb6ad223",