diff --git a/research/layered-joint-owners/LICENSE b/research/layered-joint-owners/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/layered-joint-owners/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/layered-joint-owners/MANIFEST.json b/research/layered-joint-owners/MANIFEST.json
new file mode 100644
index 0000000000..0c6255f4e2
--- /dev/null
+++ b/research/layered-joint-owners/MANIFEST.json
@@ -0,0 +1,57 @@
+{
+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "NOTICE.md": "da20040d266f100207b920a64df66e81056eded9e531c8ec07f596b613d400b7",
+  "PROOF.md": "6126320f3edee5ea6840f8491e623498b66953f75e2cdab3dee78ee06e8b4e2a",
+  "README.md": "259a352ff8e3bde0554af41428d1480ea4afb46d2b6c6d9999bbc1a288172b2b",
+  "SOURCES.json": "bd3bd1ec4ec6de3151871aa0333504e2d0ecb546007f87714e958ca04fee6153",
+  "VALIDATION.json": "4167bb5b7e15268c3fbf5d9257013dce5b5f4fda13cc3ba6102556d1f7faf344",
+  "audit_owners.py": "e4f002ad73825474b955ab19f037cdcf14eea8d4d945bde9956dd9d635d2467d",
+  "data/FIVES-RECEIPT.json.gz": "e60584bca424d4d2c7eb753a25415e4b0c0f0705d29f206653179ab4a40a3282",
+  "data/FIVES-SEARCH.json.gz": "065b64274ffc39405be1d86c66533da88b7bc7f26f77df6ff37ead26bff8eda8",
+  "data/OWNERS.json.gz": "5dde55d556840aea8746058124642b539502aac5f4084bfb72301e90e46a6f7c",
+  "data/PLAN-OWNER-FIELDS.json": "9b3bd259a096260e0917b9ba8b8f562d474b6d7437ced586ec42f6c3d2b28963",
+  "data/PR656-OWNERS.json.gz": "01a8f5c5cd54e13662f2fe40d16c2a1d443dfc664a6c988fffea6e0bacdfc937",
+  "data/PROFILE.json": "80f219e800298f27b1187c0f927f06963157ceee4ec5710df55a77fde9ccf561",
+  "data/QUADS-RECEIPT.json.gz": "d3ebeba20526ff063fdc81907e4a170461cbfbbe793f1e37ba06d2c40e70953b",
+  "data/QUADS-SEARCH.json.gz": "c0870d8a4d58319ff0bc50946a801cfddd3815f4e2c52c998243cf209cda50e9",
+  "data/RECEIPT.json": "a240d5d9206ca462aa18b0d6de6eb20ebc41a96fe8f86213deb1c67e4a5222fc",
+  "data/SPEC.json": "4521daacffc2d08ae8bed702a916312f7d8b1c75f34c59a9320072f0ae0ddb39",
+  "data/TRIPLES-OWNERS.json.gz": "08068f37b46adae98501116a94e7f40f075c61aaeac2a07de35b72f9bf565eb4",
+  "data/TRIPLES-RECEIPT.json.gz": "d56ed4886a7d35c763c036bc91f3019db9221b19a501162bbd769e5c6651e951",
+  "data/TRIPLES-SEARCH.json.gz": "c7133f58aa257cd395aaed57cc96c28b1554385662c9b68b56d5ed18fd26afb9",
+  "data/UPSTREAM-PINS.json": "ccc37ab7fbf78947fe02c7f57ea672d2e4eae8454cb1158ed964c75bf423869b",
+  "evidence/INDEPENDENT-OWNERS.json": "186af17da5152a18ac1cf44f65b9ac40d17fa41c490efeb588a6e9eb06e2b6c6",
+  "evidence/INDEPENDENT-SCALAR.json": "74137c74b7eadf40e6d43086ef17f926b523b4f242b16df4f0f32761fc2ee5fc",
+  "evidence/OWNERS-AUDIT.json": "da62381aec98303ca768b0294bf333efe8987a67a0672caba87f194ebeb1588d",
+  "evidence/PRICE.json": "f27703f3ea6a784988982bccd2718c1fee1e9dd95aa958abe77cde3879caf33a",
+  "evidence/PRIOR-BASE-CHECKS.json": "12e24b5d3f1217392609ae27660843f08d14083841832c1ecc70e383a58a9cb9",
+  "evidence/REPLAY.json": "7e001a83a90f7f2541dfbc568d981e5b72f62ec786304c036167da82fecda1d8",
+  "evidence/STEPS.json": "dc49aaa188fd5a0c68426bf4685ffa6267eee65110c49425e4a5308cfe73e972",
+  "evidence/baseline/REPLAY.json": "bd275d74d2a41e805ce1e8e44b915c1e82ac8c434999fec5361540970ba34e16",
+  "evidence/ceiling/CEILING.json": "ea6662a691f3dbdf95f187be626e0eb662761cee30656f07b7b80776d8d851f5",
+  "evidence/ceiling/PRICE.json": "b314a83858e854b787dfbfbdc4868c69b9f993d2f7de2e75de92cffe454d6057",
+  "evidence/ceiling/RELAXED-PROFILE.json": "86fcf0ad87afc89e794941d41e6ff7dcfb035ce11ba45fc7f62a5031536aff61",
+  "evidence/global/ADMISSION-CONTROLS.json": "fa3148257d239588e420bd48c227b95495bc306900b7fe06c8f4d8ee26c095aa",
+  "evidence/global/ASSEMBLY.json": "a90da9ca7616aaba8897dc34f1f67029a8418a854ff615edc3f9fdd6e9be3901",
+  "evidence/global/BIT-SUPPLIER-CONTROLS.json": "d70b133fbaa1e8455a4383a1208b12dfb25750e345229f6e80294424652d0751",
+  "evidence/global/REPLAY.json": "cf474658d832ebdd23f724d8301bf8e837ae8c3e6746a5873c342d2ab190a74f",
+  "evidence/global/global/audit/ASYNC-AUDIT.json": "c69c7afe6f36873aac3099b3dad1eebed3c1bbbe772724be33b308ed7b29987f",
+  "evidence/global/global/audit/OWNERS-AND-PROFILE.json": "1830c73cf9d336efc40dabbb9c460a056ce4dbe65a62425ae45f55ae775f6625",
+  "evidence/global/global/audit/PREFIX-AND-INVOICE.json": "162685645abeeb40dcd7be1cbbd0b8c34ce3c3279db85866fc0d7380e2c1d4aa",
+  "evidence/global/global/hosted/HOSTED.json": "cda459c20349605b9b0a5ae9ec02ea388498b4d53db3ad53c6ad686b9c47a29a",
+  "evidence/layered/STEPS.json": "02f8366c729908ea30fc03ad6548a7507eddbf8b669a8bbcd05986aae73806b8",
+  "evidence/layered/controls/COLD-END-CONTROLS.json": "9fc5d35856d2b88929465a784369e2811cfc7fa9f971dde8e344f92223231638",
+  "evidence/layered/local/CLIFFORD-REVIEW.json": "c17864a376f0f6293d2dd97436ea3cd4e9ba98762d5882e06ab0480613cf1ff3",
+  "evidence/layered/local/INDEPENDENT-LOCAL-REPLAY.json": "c7ec4af7ccdf4230a4e277913d30ee41f2cc592d2360e008a18d11abd975b630",
+  "evidence/layered/local/LOCAL-CHECKS.json": "b855ab7f3ea15a2d318bfc2f5aa4612ea76c019fa91cf64bd99903cf646b5e0c",
+  "evidence/prior-base-make-verify.log.gz": "5b862e6b6316b24ba7598c6c8dcc650872fa1b0808ff7d209c83bea44b17d0d2",
+  "evidence/replay-logs.tar.gz": "34ba9bcad0ae64c4fb4eabf0ceebbf2cebf88a3648d7b88c1731afa8e8f5c31d",
+  "evidence/word/STEPS.json": "899b3a978c602073cb9c14456b3564b22f073c72fd57dad002dd842c2732e55d",
+  "independent_owners.py": "f28c7571b42e1cfe95b4b1524c2bb08d8e598baf266b481f58b86cf157577b76",
+  "packing_ceiling.py": "913f36bbc8d0a68e1932baa7adee8153117d1f7c5c16407afb9a4acb62745852",
+  "prepare.py": "8176b7e56c94ba7a2fec5777aa689d4ff33cd44c22af575095dfa688ef078c0e",
+  "search/group_owner_search.py": "42224373262487efb1c0890ad03ef73325e66bb47e01896eac42f0abc96db42a",
+  "search/joint_owner_passes.py": "42689b421ce4cf88976601191e859743b03512af111ca3aecec6b16b7251da6f",
+  "search/joint_owner_search.py": "422ff08415dd4bfe1c37f2434eac319cbe45829cf2b53a9346109a7e792ed58c",
+  "verify.py": "c6633b028ad2f18cad75fba81fa1abbf48898168c68dba4335becacd54e033b7"
+}
diff --git a/research/layered-joint-owners/NOTICE.md b/research/layered-joint-owners/NOTICE.md
new file mode 100644
index 0000000000..083b0f7b28
--- /dev/null
+++ b/research/layered-joint-owners/NOTICE.md
@@ -0,0 +1,27 @@
+# Attribution and changes
+
+New contributions: Jeremy Diviney, with substantial OpenAI Codex assistance,
+under Apache-2.0. No separate human mathematical review is claimed here.
+
+`search/joint_owner_search.py`, `search/joint_owner_passes.py`, `prepare.py`,
+`audit_owners.py`, and `independent_owners.py` are adapted from Jay Mosley's
+PR653 (`db9cbf96b13621c940a2f9db019da3378b52ed51`), prepared with OpenAI Codex.
+Adaptations pin PR656, use its PR655 layered widths/profile, limit solver
+threads, and point the independent auditor at fresh baseline evidence.
+`search/group_owner_search.py` generalizes the two-call model to multiple calls.
+The package driver and fixed-provider packing-ceiling argument/check are new.
+
+The exact constructors, native/phase/controller/invoice/moment/outer verifiers,
+bit supplier, and frozen PR656 seed are retained from jeremykothe2's PR656
+(`0805e78f5fecc700804d4766d7e3e1d7d7e6a2ba`), prepared with Claude Code.
+Their parent notices and license are verified and retained in the staged
+package. PR655/656 extend icekylinx's PR645 Gauge44 construction and its
+GPT-6 Astra/Codex attribution. The inherited end-construction lineage includes
+PR601/604/617/627/635/637, DreamingOfClouds, jeremydiviney, CarrierBypass,
+and the other contributors recorded in the pinned parent notices.
+
+Earlier owner search includes vectorsss / Chi Zhao's PR638. The unchanged
+PR589 bit supplier is DreamingOfClouds's work, with its credited eumemic
+lineage and Claude assistance. PR635 and all retained compiler, controller,
+phase, exact-arithmetic and source contributors remain credited by their
+original notices. No ownership of those upstream contributions is claimed.
diff --git a/research/layered-joint-owners/PROOF.md b/research/layered-joint-owners/PROOF.md
new file mode 100644
index 0000000000..a7a38c0e31
--- /dev/null
+++ b/research/layered-joint-owners/PROOF.md
@@ -0,0 +1,78 @@
+# Fixed-provider joint owner improvement
+
+The local word, its 492 helper residual widths, all 72 indivisible calls, the
+literal controller, every admissible whole-family window and the bit supplier
+are unchanged from pinned PR656. These interfaces are independently replayed;
+they are not replaced by the optimizer's constraints.
+
+## Nomination and literal admission
+
+Choose a set of calls and release their present footprints. Group eligible
+families by remaining capacity and eligibility bitmask. For each bucket, a
+nonnegative integer variable counts families receiving a tuple of widths,
+one width or zero per selected call, with sum no greater than capacity.
+Bucket equalities preserve the number of families. Per-call equalities
+preserve each helper width multiplicity. The tuple enforces at most one helper
+from any selected call in a family. Existing calls outside the selected set
+retain their family and width.
+
+After solving, expand integer counts back to the literal family catalogue,
+assign distinct helpers with the required widths, and compact each family's
+disjoint offsets. Explicit checks cover every helper, call, family formula,
+capacity, idle window, active-data exclusion, and full footprint. The physical
+verifier then derives the actual frames and 73-column charts, checks the
+controller, phases and finite invoice, and admits the exact moment and outer
+parameters. A solver success alone establishes none of these physical claims.
+
+## Exact improvement for every native exponent
+
+Let `x` and `y` be old and new idle-remainder vectors, zero-padded to the same
+family catalogue. They have equal total rank. The submitted map satisfies
+
+`sum_i max(y_i-k,0) >= sum_i max(x_i-k,0)`
+
+for every integer `k` from 0 to 48, with at least one strict inequality.
+Coordinates are integers in `[0,48]`, so the difference of these stop-loss
+functions is affine between consecutive integers and zero beyond this range.
+Thus the same inequality holds at every real threshold. It is the usual
+equal-mass majorization condition: `y` majorizes `x` and is not a permutation.
+
+For every `0 < b < 1`, `r -> r^(1-b)` is strictly concave on the nonnegative
+axis. Majorization therefore strictly reduces its sum. The normalized native
+moment is `73^(b-1)/7168` times the sum of `r^(1-b)` over all paid children.
+The local contribution is fixed, so the new owner map strictly lowers this
+moment throughout that interval. The exact rational moment engines certify
+the new root bracket, and the unchanged outer admission separately certifies
+the stated κ. No conservative-surcharge claim is inferred solely from
+majorization; the complete conservative profile is separately priced.
+
+The total paid rank remains 520,704, so `73*7168 - 520704 = 2560` is unchanged.
+`audit_owners.py` and `independent_owners.py` check these integers without
+importing the optimizer. The latter derives windows from the freshly replayed
+literal schedule and phase recipe and reconstructs the actual chart columns.
+These are code-independent checks, not a claim of review by a separate person.
+
+## A ceiling on this owner-only search
+
+Keep the local paid profile and controller capacities fixed. The local profile
+is `{1:2542, 2:414, 3:434, 4:154, 5:56, 8:8}` per call. The idle rank is
+
+`520704 - 72*(2542 + 2*414 + 3*434 + 4*154 + 5*56 + 8*8) = 115200`.
+
+Every idle remainder has dimension at most `C=48`. For `0<p<1` and `0<=r<=C`,
+
+`r^p >= r*C^(p-1)`,
+
+with equality only for `r=0` or `r=C`. Summing gives the smallest possible idle
+moment after relaxing all placement constraints: 2,400 dimension-48 remainders
+and zeros. No assertion that an actual assignment realizes it is needed.
+
+`packing_ceiling.py` constructs that relaxed profile. The unchanged independent
+pricing program proves a rational root bracket with both exact moment engines.
+If `u` is its certified upper endpoint, every assignment using this fixed
+provider has complex saving below `u`. The retained outer transfer has
+`κ < b/(1+b)`, an increasing function of `b`, so `u/(1+u)` is an upper bound
+for every such owner assignment. The exact fraction and a decimal rendering
+are emitted in `CEILING.json`; the approximate ceiling is 0.001654249113130438.
+It constrains this fixed construction only, and makes no optimality claim
+for the submitted map or bound on different multiplication constructions.
diff --git a/research/layered-joint-owners/README.md b/research/layered-joint-owners/README.md
new file mode 100644
index 0000000000..a2becb008a
--- /dev/null
+++ b/research/layered-joint-owners/README.md
@@ -0,0 +1,147 @@
+# Joint three- and four-call owners: conditional κ = 0.001654192296855146
+
+This improves the pinned [PR #656](https://github.com/CrocSwap/integer-mult-bounds/pull/656)
+owner map from **0.001654108529511355** to **0.001654192296855146**, a
+0.0050642% gain. The circuit, controller, bit supplier, and every inherited
+verification and construction program are unchanged. This is an owner-only
+delta against PR656, staged by the verifier in a temporary directory.
+
+| Quantity | PR656 | This witness |
+| --- | ---: | ---: |
+| Conditional κ | 0.001654108529511355 | 0.001654192296855146 |
+| Conservative κ | 0.001654108526615491 | 0.001654192293959223 |
+| Helpers per call / calls | 492 / 72 | unchanged |
+| Live / physical families | 7,168 / 7,670 | unchanged |
+| Global paid rank / deficit | 520,704 / 2,560 | unchanged |
+
+The exact exponent is `827096148427573/500000000000000000`.
+The complex saving is `828466591481403378691/500000000000000000000000`;
+the cited PR589 bit saving is `1733427039589844234749/1000000000000000000000000`.
+The complex side binds.
+
+## Contribution
+
+Jay Mosley's [PR653](https://github.com/CrocSwap/integer-mult-bounds/pull/653)
+releases two complete calls together. We extend that integer nomination model
+to three and four calls: a family bucket records its free capacity and the
+subset of selected calls allowed to use it. Variables assign at most one helper
+of each selected call to a family. Exact width inventories and integer stop-loss
+inequalities are imposed, then every nominated literal owner is checked again.
+
+Starting at PR656, 180 three-call groups yielded eight strict improvements;
+120 four-call groups yielded four more. The final idle remainders are
+`{1:1, 3:1, 28:1, 32:2, 48:2398}`. Their distribution strictly majorizes PR656's
+distribution at fixed total rank, improving every native homogeneous moment
+with exponent in `(0,1)`. [PROOF.md](PROOF.md) gives the argument.
+This bounded search does not establish global or neighborhood optimality.
+
+The paid profile is:
+
+```json
+{"1":183025,"2":29808,"3":31249,"4":11088,"5":4032,"8":576,
+ "28":1,"32":2,"48":2398}
+```
+
+We also supply an exact **relaxed packing ceiling** for this fixed local
+profile and controller. Concentrating all 115,200 idle ranks into 2,400
+dimension-48 remainders minimizes their moment even when the actual assignment
+constraints are relaxed. Independent exact arithmetic bounds the corresponding
+κ above by approximately **0.001654249113130438**. Feasibility of this ideal
+packing is not claimed. This limits owner-only headroom; it does not bound
+other circuits, controllers, local profiles, or integer multiplication in general.
+
+## Reproduce
+
+Python 3.11+ with assertions enabled; verification uses only the standard library.
+Prepare the immutable inputs outside the checkout:
+
+```sh
+git fetch https://github.com/CrocSwap/integer-mult-bounds.git 0805e78f5fecc700804d4766d7e3e1d7d7e6a2ba
+mkdir -p /tmp/layered-pr656
+git archive FETCH_HEAD research/gauge44-layered-b | tar -x -C /tmp/layered-pr656
+git fetch https://github.com/CrocSwap/integer-mult-bounds.git a6895a69f8ad98ab45777b03e9e6f48888c39f6f
+mkdir -p /tmp/layered-pr635
+git archive FETCH_HEAD research/complex-571-cold14-st2 | tar -x -C /tmp/layered-pr635
+
+nice -n 15 python3 -B research/layered-joint-owners/verify.py \
+  --main . --parent /tmp/layered-pr656/research/gauge44-layered-b \
+  --pr635 /tmp/layered-pr635 --out /tmp/layered-joint-replay
+```
+
+The output directory must be new and outside input checkouts. Retained main
+dependencies are pinned by hashes; the submission is based on main commit
+`17ce0c79b7b51c2634b439ea5a2b754f09909693`. `SOURCES.json` pins the predecessor
+commits and parent manifest. All parent source files and notices remain in the
+staged copy. Only `data/PLAN.json`, `data/OWNERS.json.gz`, and `data/SPEC.json`
+change there; the added staging receipt is bookkeeping.
+
+Default verification rebuilds the scalar word and all layered ends, executes
+the 30 pivot-swap and 59 layer-end controls, emits both native ledgers,
+checks wrappers and phases, and independently audits all 716 scalar columns.
+It strictly replays PR656, then independently re-derives the owner windows and
+actual 73-column charts using that fresh baseline evidence. The owner audits
+include nine mutations. Finally it strictly replays the new controller,
+finite invoice, exact moments and outer assembly, including 15 controller,
+69 admission and 12 bit-supplier controls, and independently prices the profile.
+No optimizer or discovery mode runs during verification.
+
+For incremental replay, `--local /path/to/rebuilt/local` accepts an existing
+layered native directory including phases. The output explicitly records that
+the local construction was not rebuilt in that invocation. Historical PR645
+evidence retained by PR656 is never used as current local/owner evidence by
+the new driver. Generated gzip artifacts are compared by inherited semantic
+identities; immutable submitted inputs retain byte pins.
+
+Optional nomination uses NumPy/SciPy (discovery: 2.5.4/1.18.1):
+
+```sh
+GAUGE44_PARENT=/tmp/layered-pr656/research/gauge44-layered-b \
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 \
+nice -n 15 python3 -B research/layered-joint-owners/search/group_owner_search.py \
+  --owners research/layered-joint-owners/data/PR656-OWNERS.json.gz \
+  --size 3 --groups 180 --seconds 2 --out /tmp/layered-triples
+GAUGE44_PARENT=/tmp/layered-pr656/research/gauge44-layered-b \
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 \
+nice -n 15 python3 -B research/layered-joint-owners/search/group_owner_search.py \
+  --owners /tmp/layered-triples/OWNERS.json.gz \
+  --size 4 --groups 120 --seconds 3 --out /tmp/layered-quads
+```
+
+HiGHS is limited to one thread. Timing and solver choices can change nominations;
+the frozen owners and receipts, rather than repeatable optimizer decisions, are
+the submitted witness. Both discovery receipts, the intermediate triple owner map, and bounded search
+transcripts are retained under `data/`. A further bounded five-call pass
+(30 groups, six seconds per group) accepted no moves; its transcript is retained
+without a claim of neighborhood optimality. The final receipt compares to the triple endpoint;
+the independent audits compare directly to PR656.
+
+## Recorded validation
+
+`VALIDATION.json` records a complete fresh Linux/Python 3.12.3 replay of the
+default driver, including local construction and phases. Selected receipts and
+all replay logs are retained under `evidence/`. The earlier `make verify` run
+on the identical unchanged main base passed all 18 groups (including
+`gen4-bank-verify`) and 84 isolated test modules; its receipt and compressed
+log are retained with an explicit prior-run scope. The standalone addition is
+validated by its new full replay, not by that earlier repository check.
+
+## Scope and attribution
+
+This remains conditional on the retained all-size compiler,
+common-label/mutable-source realization, whole-call hosting, precision/tape,
+exact-recovery, analytic-transfer, and bit H1–H5 interfaces. It is a finite
+conditional witness, not an unconditional theorem or complete Lean proof.
+The PR589 bit circuit is cited unchanged; its exact profile and exceptional
+residue surcharge are freshly priced, but its circuit is not rebuilt here.
+
+Prepared by **Jeremy Diviney**, with substantial **OpenAI Codex** assistance.
+The multi-call search extends **Jay Mosley / jaymosley07's PR653** model; its
+solver-free auditors and staging pattern are adapted with attribution. The
+layered word and seed owners are **jeremykothe2's PR655/656**, prepared with
+Claude Code. They build on **icekylinx's PR645 Gauge44**, with GPT-6 Astra and
+Codex assistance, and the PR601/604/617/627/635/637 end-construction lineage,
+including DreamingOfClouds, Jeremy Diviney and CarrierBypass. Earlier packing
+work includes **vectorsss / Chi Zhao's PR638**. **DreamingOfClouds's PR589**
+bit supplier retains its eumemic lineage and Claude attribution. All earlier
+contributors, source-specific notices and Apache-2.0 licensing in the pinned
+packages remain in force; see [NOTICE.md](NOTICE.md).
diff --git a/research/layered-joint-owners/SOURCES.json b/research/layered-joint-owners/SOURCES.json
new file mode 100644
index 0000000000..7f4516a999
--- /dev/null
+++ b/research/layered-joint-owners/SOURCES.json
@@ -0,0 +1,12 @@
+{
+  "main": "17ce0c79b7b51c2634b439ea5a2b754f09909693",
+  "parent_pr": 656,
+  "parent_head": "0805e78f5fecc700804d4766d7e3e1d7d7e6a2ba",
+  "parent_manifest_sha256": "04934a9d42a1f078dd0b23c8b05570184cd664a99f13625a0ada5c41cb324d0e",
+  "local_construction_pr": 655,
+  "local_construction_head": "3e669dc7987cb2295a71664b77e110c0cd979a87",
+  "pr635": "a6895a69f8ad98ab45777b03e9e6f48888c39f6f",
+  "search_and_auditors_pr653": "db9cbf96b13621c940a2f9db019da3378b52ed51",
+  "author": "Jeremy Diviney",
+  "assistance": "Substantial OpenAI Codex assistance"
+}
diff --git a/research/layered-joint-owners/VALIDATION.json b/research/layered-joint-owners/VALIDATION.json
new file mode 100644
index 0000000000..f8e97b6b39
--- /dev/null
+++ b/research/layered-joint-owners/VALIDATION.json
@@ -0,0 +1,97 @@
+{
+  "status": "PASS_FRESH_COMPLETE_LAYERED_JOINT_REPLAY",
+  "archived_utc": "2026-10-13T02:32:48.686827+00:00",
+  "python": "3.12.3",
+  "command": "nice -n 15 ionice -c 3 env PYTHONDONTWRITEBYTECODE=1 OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python -B research/layered-joint-owners/verify.py --main . --parent /path/to/pr656/research/gauge44-layered-b --pr635 /path/to/pr635 --out /fresh/replay",
+  "fresh_output": "No reused local or global artifacts; default driver including exact layers and phases.",
+  "kappa_decimal": "0.001654192296855146",
+  "source_sha256": {
+    "audit_owners.py": "e4f002ad73825474b955ab19f037cdcf14eea8d4d945bde9956dd9d635d2467d",
+    "independent_owners.py": "f28c7571b42e1cfe95b4b1524c2bb08d8e598baf266b481f58b86cf157577b76",
+    "packing_ceiling.py": "913f36bbc8d0a68e1932baa7adee8153117d1f7c5c16407afb9a4acb62745852",
+    "prepare.py": "8176b7e56c94ba7a2fec5777aa689d4ff33cd44c22af575095dfa688ef078c0e",
+    "search/group_owner_search.py": "42224373262487efb1c0890ad03ef73325e66bb47e01896eac42f0abc96db42a",
+    "search/joint_owner_passes.py": "42689b421ce4cf88976601191e859743b03512af111ca3aecec6b16b7251da6f",
+    "search/joint_owner_search.py": "422ff08415dd4bfe1c37f2434eac319cbe45829cf2b53a9346109a7e792ed58c",
+    "verify.py": "c6633b028ad2f18cad75fba81fa1abbf48898168c68dba4335becacd54e033b7"
+  },
+  "archived_artifacts": {
+    "REPLAY.json": "7e001a83a90f7f2541dfbc568d981e5b72f62ec786304c036167da82fecda1d8",
+    "STEPS.json": "dc49aaa188fd5a0c68426bf4685ffa6267eee65110c49425e4a5308cfe73e972",
+    "INDEPENDENT-SCALAR.json": "74137c74b7eadf40e6d43086ef17f926b523b4f242b16df4f0f32761fc2ee5fc",
+    "OWNERS-AUDIT.json": "da62381aec98303ca768b0294bf333efe8987a67a0672caba87f194ebeb1588d",
+    "INDEPENDENT-OWNERS.json": "186af17da5152a18ac1cf44f65b9ac40d17fa41c490efeb588a6e9eb06e2b6c6",
+    "PRICE.json": "f27703f3ea6a784988982bccd2718c1fee1e9dd95aa958abe77cde3879caf33a",
+    "ceiling/CEILING.json": "ea6662a691f3dbdf95f187be626e0eb662761cee30656f07b7b80776d8d851f5",
+    "ceiling/PRICE.json": "b314a83858e854b787dfbfbdc4868c69b9f993d2f7de2e75de92cffe454d6057",
+    "ceiling/RELAXED-PROFILE.json": "86fcf0ad87afc89e794941d41e6ff7dcfb035ce11ba45fc7f62a5031536aff61",
+    "word/STEPS.json": "899b3a978c602073cb9c14456b3564b22f073c72fd57dad002dd842c2732e55d",
+    "layered/STEPS.json": "02f8366c729908ea30fc03ad6548a7507eddbf8b669a8bbcd05986aae73806b8",
+    "layered/controls/COLD-END-CONTROLS.json": "9fc5d35856d2b88929465a784369e2811cfc7fa9f971dde8e344f92223231638",
+    "layered/local/CLIFFORD-REVIEW.json": "c17864a376f0f6293d2dd97436ea3cd4e9ba98762d5882e06ab0480613cf1ff3",
+    "layered/local/LOCAL-CHECKS.json": "b855ab7f3ea15a2d318bfc2f5aa4612ea76c019fa91cf64bd99903cf646b5e0c",
+    "layered/local/INDEPENDENT-LOCAL-REPLAY.json": "c7ec4af7ccdf4230a4e277913d30ee41f2cc592d2360e008a18d11abd975b630",
+    "baseline/REPLAY.json": "bd275d74d2a41e805ce1e8e44b915c1e82ac8c434999fec5361540970ba34e16",
+    "global/REPLAY.json": "cf474658d832ebdd23f724d8301bf8e837ae8c3e6746a5873c342d2ab190a74f",
+    "global/ASSEMBLY.json": "a90da9ca7616aaba8897dc34f1f67029a8418a854ff615edc3f9fdd6e9be3901",
+    "global/ADMISSION-CONTROLS.json": "fa3148257d239588e420bd48c227b95495bc306900b7fe06c8f4d8ee26c095aa",
+    "global/BIT-SUPPLIER-CONTROLS.json": "d70b133fbaa1e8455a4383a1208b12dfb25750e345229f6e80294424652d0751",
+    "global/global/audit/ASYNC-AUDIT.json": "c69c7afe6f36873aac3099b3dad1eebed3c1bbbe772724be33b308ed7b29987f",
+    "global/global/audit/OWNERS-AND-PROFILE.json": "1830c73cf9d336efc40dabbb9c460a056ce4dbe65a62425ae45f55ae775f6625",
+    "global/global/audit/PREFIX-AND-INVOICE.json": "162685645abeeb40dcd7be1cbbd0b8c34ce3c3279db85866fc0d7380e2c1d4aa",
+    "global/global/hosted/HOSTED.json": "cda459c20349605b9b0a5ae9ec02ea388498b4d53db3ad53c6ad686b9c47a29a"
+  },
+  "logs": {
+    "baseline/admission-controls.log": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3",
+    "baseline/assembly.log": "b98bef079fe1a2f3b296f9546ffdbd47bb99680541cdfe0ac4ddf2883a3363f8",
+    "baseline/audit.log": "6bfc03daddbc4e7b6b5f82f7ff2c075bf507b80362ad8270c7400824694d3e48",
+    "baseline/bind.log": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a",
+    "baseline/bit-supplier-controls.log": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67",
+    "baseline/emit.log": "048b3817b3014017ebe5dbfa1b04ab20de7fecbe6780c331a08db8098e0921b7",
+    "baseline/invoice.log": "94fcce7faae261bed1f9e74b0a957a01f5ec5d3ba99d0071fc8dcae256c57e1c",
+    "baseline/restore-parent.log": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5",
+    "baseline-strict.log": "9160163b7c291dcc26212e185c72fe5153116e90ef8e5bcfbfeb071552aed9fb",
+    "global/admission-controls.log": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3",
+    "global/assembly.log": "6156e687737926264161f6e3f83ae4728181dd217b41642aa9fd158fa702ab07",
+    "global/audit.log": "c69c7afe6f36873aac3099b3dad1eebed3c1bbbe772724be33b308ed7b29987f",
+    "global/bind.log": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a",
+    "global/bit-supplier-controls.log": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67",
+    "global/emit.log": "cda459c20349605b9b0a5ae9ec02ea388498b4d53db3ad53c6ad686b9c47a29a",
+    "global/invoice.log": "94fcce7faae261bed1f9e74b0a957a01f5ec5d3ba99d0071fc8dcae256c57e1c",
+    "global/restore-parent.log": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5",
+    "global-strict.log": "f0a01750c6ce4fbd625f35a4f517159e50494b177e78cf69ebfcc90c823a0ee1",
+    "independent-owners.log": "7f8973e0aad35cbad2e43362a3a57beece8e65bb8335d88dcf3b71fe34ea2db9",
+    "independent-price.log": "db6a5f47d7a6cec6472d9055709882def6f2c5cfa18a6b0019ce2ea532b09679",
+    "independent-scalar.log": "d3f17a7125edd3d9d72bedb646b498f8791609d84403c8087b652c5a14316bdc",
+    "layered/cold44-exact.log": "907b7e6629aa828429f3af0744a0c7a2513132873bf8c139979841c05c4a0c7d",
+    "layered/layer-end-controls.log": "c1fc02e9a8d533fb45375e274e94275e3c1769f3ee7ba2a559e45663bb94be8e",
+    "layered/ledgers.log": "171c61ffe5eb12bb2704ba6a1b576c587e0068da750d5cc33e47e7abe9924a85",
+    "layered/local-replay.log": "dd643a58258431c3b07d3b06d9060c49677fa23b4fafc9f10988ed1f6867bd9a",
+    "layered/native.log": "ee704349a6caee702ccd57192c5640ab2e73544ec1ce4500f684df8f2af2059a",
+    "layered/phases.log": "8e39e27c7348bfc869d625b8bc6ca89ca82598959b73f7ced05476d04f79e630",
+    "layered/pivot-swap.log": "74eebc64728dd960e3a68ff2db93ff8f88975bcead1581993a0d170fd319c3bc",
+    "layered/wrappers.log": "74b13cf8570ca2f32ce0018575b1b73e95af77a28e59d09556fec59260bdbba5",
+    "layers-and-native.log": "b353f5a30bc7bc16d1921582dfe23b1f390e2a12c2a45940e6ee9ab14ce229ba",
+    "owners.log": "abb351df7056714a45cc614208c62be5a4d0603f93987b3e605e0c428b801eae",
+    "packing-ceiling.log": "bf2fa9f2cdd5ddfb502bd1451cdbd2a896c9d854eb53d15779a480d0288eda52",
+    "parent-manifest.log": "84d3af581669219a35ce0807c2b9cc2b313bf07168760a80d8bb5eb220a99715",
+    "prepare.log": "987b51820faf4b3803bbe7f365b21ab266dde65ae17086988c18217804c38b74",
+    "word/cold44-exact.log": "3d8a1b6898fa650df131f953b461187fb3b6fdacba062ab82fb5ca2dd6614678",
+    "word/gauge-forward.log": "ba6767bc74e7e91330d27026fa81875d2b116f7a34b818a037d94f1bd519b778",
+    "word/port0.log": "051c88c14bf62d53703b37f1853e443bcdd76223d0f3c3ddb0c0d784bac39071",
+    "word/port1.log": "fa2deab44218bd23044f6457f4dde17c5f1defd02237451cf6eb5857cf6c0719",
+    "word/port2.log": "5b51ddfbd53e625eacabaeebfeb969c5090b735803d40e7351adbe61b8e58757",
+    "word/port3.log": "9ed3fb2baabff72a69fd679df55ad9671f03b83fe2047df99430607fffbecc2f",
+    "word/shadow-early.log": "7a13ad21a3e4e12710e37ab9d1c54a90b2b8741fc3f5f620c363844e9cd766fb",
+    "word/shadow-prefix.log": "9d4cf22962c6e9358f935ca7d6ea5bc0fb64b54112d6d8d3ce5ad63fb2fb037c",
+    "word.log": "b31877e807c4748ad59179231313b3c37181c6b4613afed99b4690ca9f75569f"
+  },
+  "previous_repository_checks": {
+    "base": "17ce0c79b7b51c2634b439ea5a2b754f09909693",
+    "groups": 18,
+    "isolated_test_modules": 84,
+    "gen4_bank_verify": true,
+    "scope": "Previously completed make verify on the identical unchanged main base; not rerun for this additive standalone package. The new package is covered by the fresh default replay archived here."
+  },
+  "scope": "Finite conditional witness. PR589 bit circuit cited unchanged and exact profile repriced. No GitHub CI, independent human review, unconditional theorem or global packing optimum claimed."
+}
diff --git a/research/layered-joint-owners/audit_owners.py b/research/layered-joint-owners/audit_owners.py
new file mode 100644
index 0000000000..973c467644
--- /dev/null
+++ b/research/layered-joint-owners/audit_owners.py
@@ -0,0 +1,97 @@
+"""Solver-free integer owner admission and rational native moment screen.
+Checks the explicit parent windows, not their physical derivation. Fresh global
+phase/controller/invoice/outer admission is a separate obligation.
+"""
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter,defaultdict
+from decimal import Decimal,localcontext,ROUND_FLOOR
+from functools import lru_cache
+import argparse,copy,gzip,hashlib,json
+
+if not __debug__:
+ raise RuntimeError('Assertions are required; do not use python -O.')
+BASELINE_HEAD='0805e78f5fecc700804d4766d7e3e1d7d7e6a2ba'
+BASELINE_SHA256='01a8f5c5cd54e13662f2fe40d16c2a1d443dfc664a6c988fffea6e0bacdfc937'
+
+read=lambda p:json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+packed=lambda x:json.dumps(x,sort_keys=True,separators=(',',':')).encode()
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+DYAD=1<<240
+floor=lambda x:F(x.numerator*DYAD//x.denominator,DYAD)
+ceil=lambda x:-floor(-x)
+@lru_cache(None)
+def log_bounds(x):
+ assert x>=1;k=0
+ while x>=2:x/=2;k+=1
+ def log_atanh(y):
+  z=(y-1)/(y+1);s=F(0);power=z
+  for j in range(150):s+=2*power/(2*j+1);power*=z*z
+  return s,s+2*power/(301*(1-z*z))
+ l,u=log_atanh(x);a,b=log_atanh(F(2));return floor(l+k*a),ceil(u+k*b)
+def exp_bounds(l,u):
+ assert 0<=l<=u<F(1,10)
+ def pol(x):
+  s=t=F(1)
+  for j in range(1,25):t*=x/j;s+=t
+  return s,t
+ lo,_=pol(l);hi,t=pol(u);return floor(lo),ceil(hi+t*u/25/(1-u/26))
+def moment(H,b):
+ lo=hi=F(0)
+ for r,n in H.items():
+  l,u=log_bounds(F(73,r));a,c=exp_bounds(b*l,b*u);lo+=F(r*n,73*7168)*a;hi+=F(r*n,73*7168)*c
+ return floor(lo),ceil(hi)
+def certificate(H):
+ with localcontext() as ctx:
+  ctx.prec=65;terms=[(Decimal(r*n)/Decimal(73*7168),(Decimal(73)/Decimal(r)).ln()) for r,n in H.items()];lo=Decimal(0);hi=Decimal('.01')
+  for _ in range(220):
+   mid=(lo+hi)/2
+   if sum(p*(mid*l).exp() for p,l in terms)<1:lo=mid
+   else:hi=mid
+  q=int((lo*10**24).to_integral_value(rounding=ROUND_FLOOR))
+ lo=F(q,10**24);hi=lo+F(1,10**24);lv=moment(H,lo);hv=moment(H,hi);assert lv[1]<1<hv[0]
+ return {'native_lower':str(lo),'native_upper':str(hi),'lower_endpoint_moment_upper':str(lv[1]),'upper_endpoint_moment_lower':str(hv[0]),'nominal_outer_ceiling_lower':str(lo/(1+lo)),'nominal_outer_ceiling_upper':str(hi/(1+hi)),'scope':'Native homogeneous moment only; outer ceiling is not an assembled witness.'}
+
+def audit(plan,roles,expected_widths):
+ assert (plan['K'],plan['T'],plan['M'],plan['L'],plan['live'])==(4,8,73,9,7168)
+ caps={};elig=defaultdict(set);families={};used=defaultdict(set);helpers=defaultdict(set);callfams=defaultdict(set)
+ for key,(cap,times) in plan['windows'].items():
+  rep,ch=map(int,key.split(','));assert 0<cap<=48 and len(times)==len(set(times))
+  for port in range(112):
+   g=(rep,ch,port);caps[g]=cap;families[g]=rep*896+(2*plan['pairs'][str(ch)]+plan['sides'][str(ch)])*112+port
+   for t in times:elig[t].add(g)
+ for t,gs in elig.items():assert len({families[g] for g in gs})==len(gs)
+ for z in roles:
+  t,h=z['time'],z['helper'];assert type(t) is int and 0<=t<72 and type(h) is int and 0<=h<492
+  s,rep=plan['order'][t];assert (z['stage'],z['replica'])==(s,rep)
+  g=(z['owner_replica'],z['child'],z['port']);assert g in elig[t]
+  assert z['family']==families[g] and z['copy']==g[0]*112+g[2]
+  assert h not in helpers[t] and z['family'] not in callfams[t];helpers[t].add(h);callfams[t].add(z['family'])
+  assert not(g[0]==rep and plan['pairs'][str(g[1])]==max(0,(s-1)//2))
+  w=z['width'];off=z['offset'];assert type(w) is int and w==expected_widths[h] and type(off) is int and off>=0 and off+w<=caps[g]
+  cells=set(range(off,off+w));assert not cells&used[g];used[g]|=cells
+ assert len(roles)==72*492 and all(helpers[t]==set(range(492)) for t in range(72))
+ assert all(cells==set(range(len(cells))) for cells in used.values())
+ idle=Counter(caps[g]-len(used[g]) for g in caps if caps[g]>len(used[g]))
+ local={1:2542,2:414,3:434,4:154,5:56,8:8};H=Counter({r:72*n for r,n in local.items()});H.update(idle)
+ assert sum(r*n for r,n in H.items())==520704 and 73*7168-sum(r*n for r,n in H.items())==2560
+ return idle,H
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--baseline-owners',type=Path,required=True);ap.add_argument('--package',type=Path,required=True);ap.add_argument('--nomination',type=Path,required=True);ap.add_argument('--output',type=Path,required=True);a=ap.parse_args()
+ assert sha(a.baseline_owners)==BASELINE_SHA256, 'Unexpected PR656 seed owner map'
+ p=a.package;plan=read(p/'data/PLAN.json');baseline=read(a.baseline_owners);roles=read(a.nomination/'OWNERS.json.gz');widths=plan['provider_registry']['gauge44']['widths'];assert Counter(widths)=={4:52,5:48,7:42,8:116,9:234}
+ old,oldH=audit(plan,baseline,widths);new,H=audit(plan,roles,widths)
+ profile={str(k):v for k,v in sorted(H.items())};assert profile==read(a.nomination/'PROFILE.json')
+ fields=read(a.nomination/'PLAN-OWNER-FIELDS.json');assert fields['profile']==profile and fields['assignment_sha256']==hashlib.sha256(packed(roles)).hexdigest()
+ assert fields['per_call_widths']==[{'stage':s,'replica':r,'widths':widths} for s,r in plan['order']]
+ margins=[sum(n*max(r-k,0) for r,n in new.items())-sum(n*max(r-k,0) for r,n in old.items()) for k in range(49)];assert margins[0]==margins[-1]==0 and min(margins)>=0 and max(margins)>0
+ controls=[]
+ for name,change in [('wrong_width',lambda x:x[0].update(width=x[0]['width']+1)),('wrong_call_time',lambda x:x[0].update(time=(x[0]['time']+1)%72)),('duplicate_helper',lambda x:x[1].update(helper=x[0]['helper']))]:
+  bad=copy.deepcopy(roles);change(bad)
+  try:audit(plan,bad,widths)
+  except (AssertionError,KeyError,IndexError):controls.append(name)
+  else:raise AssertionError('Corruption accepted: '+name)
+ result={'status':'PASS_SOLVER_FREE_JOINT_OWNER_COMBINATORICS_AND_NATIVE_MOMENT','source_baseline_head':BASELINE_HEAD,'geometry_and_native_head':'3e669dc7987cb2295a71664b77e110c0cd979a87','source_plan_sha256':sha(p/'data/PLAN.json'),'source_owners_sha256':sha(a.baseline_owners),'owners_sha256':sha(a.nomination/'OWNERS.json.gz'),'owners_semantic_sha256':hashlib.sha256(packed(roles)).hexdigest(),'baseline_idle':dict(sorted(old.items())),'candidate_idle':dict(sorted(new.items())),'global_profile':profile,'integer_stoploss_margins':margins,'exact_native_moment':certificate(H),'negative_controls_rejected':controls,'all_explicit_windows_and_capacities_checked':True,'all_families_distinct_and_outside_active_data':True,'all_helpers_and_offsets_checked':True,'remaining_admission':'Independently derive controller windows and actual73-column phase charts, finite invoice and complete outer witness. No new physical supplier claimed here.'}
+ a.output.write_text(json.dumps(result,indent=2)+'\n');print(json.dumps({'status':result['status'],'native_moment':result['exact_native_moment'],'profile':profile,'controls':controls},indent=2))
+if __name__=='__main__':main()
diff --git a/research/layered-joint-owners/data/FIVES-RECEIPT.json.gz b/research/layered-joint-owners/data/FIVES-RECEIPT.json.gz
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diff --git a/research/layered-joint-owners/data/FIVES-SEARCH.json.gz b/research/layered-joint-owners/data/FIVES-SEARCH.json.gz
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diff --git a/research/layered-joint-owners/data/OWNERS.json.gz b/research/layered-joint-owners/data/OWNERS.json.gz
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diff --git a/research/layered-joint-owners/data/PLAN-OWNER-FIELDS.json b/research/layered-joint-owners/data/PLAN-OWNER-FIELDS.json
new file mode 100644
index 0000000000..cfb8a797d1
--- /dev/null
+++ b/research/layered-joint-owners/data/PLAN-OWNER-FIELDS.json
@@ -0,0 +1 @@
+{"assignment_sha256":"6b4353a4de84c314b48d9a05aebddb1ab1fbfe33cbc8f109b6a06c4ef8002e28","assignment_sha256_semantics":"SHA256 sorted-key compact uncompressed OWNERS 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+    {
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+      "status": 0,
+      "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)",
+      "seconds": 0.35684475395828485,
+      "variables": 6549,
+      "buckets": 26,
+      "integer_equations_checked": true,
+      "mip_gap": 0.0,
+      "mip_nodes": 1,
+      "candidate": {
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+        "b": 0.0016569331829628066
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+      "gain_b": 1.7951763360557482e-08,
+      "integer_stoploss_margins": [
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+        4,
+        5,
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+        4,
+        3,
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+        1,
+        0,
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+        0,
+        0,
+        0
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+      "strict_majorization": true
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+  ],
+  "roles": 35424,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "live": 7168,
+  "M": 73,
+  "remaining_admission": "Fresh native-provider binding, all actual73-column charts/controller audit, finite invoice, exact moment and outer assembly. No supplier/global optimality claim."
+}
diff --git a/research/layered-joint-owners/data/SPEC.json b/research/layered-joint-owners/data/SPEC.json
new file mode 100644
index 0000000000..f9559fb998
--- /dev/null
+++ b/research/layered-joint-owners/data/SPEC.json
@@ -0,0 +1,1338 @@
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+      "strict_all_p_improvement": true
+    }
+  },
+  "scope": "Independent mapping/capacity/literal-bridge-window/active-family/spectator-map/profile and strict all-p moment proof against every named baseline. Does not replay unchanged local scalar/Clifford providers, global coefficient invoice, or outer admission.",
+  "mutation_controls_rejected": [
+    "wrong helper residual width",
+    "offset exceeds actual pending child",
+    "family formula alias",
+    "duplicate complete-call helper",
+    "overlapping footprints across complete calls",
+    "whole-family borrowing outside literal idle window"
+  ]
+}
diff --git a/research/layered-joint-owners/evidence/INDEPENDENT-SCALAR.json b/research/layered-joint-owners/evidence/INDEPENDENT-SCALAR.json
new file mode 100644
index 0000000000..2ccf2d6ff9
--- /dev/null
+++ b/research/layered-joint-owners/evidence/INDEPENDENT-SCALAR.json
@@ -0,0 +1,137 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+  "input_file": "FULL-WORD.json.gz",
+  "content_sha256": "0be48b1d8a6105059addf3f0d5e420c27ae3398b3a1186b6b11e9c4aa9e3f3d4",
+  "compressed_sha256": "c272d2992c2b5c003e35843d86b075ffcde5b9a7ee792ab0160aec50fabe6113",
+  "parent_center_interface": {
+    "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+    "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "transport_tau": 43,
+    "ordered_frame_bases_match": true,
+    "all_ports_match": true,
+    "transported_centers": [
+      92,
+      57,
+      81,
+      224,
+      11,
+      240,
+      9,
+      256
+    ],
+    "source_centers": [
+      92,
+      57,
+      81,
+      11,
+      9
+    ],
+    "ordered_frame_bases": [
+      [
+        256,
+        128,
+        64,
+        34,
+        16,
+        10,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        16,
+        8,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        17,
+        9,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ],
+      [
+        256,
+        128,
+        66,
+        32,
+        18,
+        8,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        17,
+        9,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        16,
+        8,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        68,
+        32,
+        16,
+        12,
+        2,
+        1
+      ]
+    ]
+  },
+  "v": 112,
+  "h": 9,
+  "R": 492,
+  "entering": 204,
+  "lowends": 96,
+  "coldends": 54,
+  "compensation_gates": 7268,
+  "local_profile": {
+    "1": 2542,
+    "2": 414,
+    "3": 434,
+    "4": 154,
+    "5": 56,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 52,
+    "5": 48,
+    "7": 42,
+    "8": 116,
+    "9": 234
+  },
+  "checked_columns": 716,
+  "elapsed_seconds": 0.6273348280228674,
+  "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+}
diff --git a/research/layered-joint-owners/evidence/OWNERS-AUDIT.json b/research/layered-joint-owners/evidence/OWNERS-AUDIT.json
new file mode 100644
index 0000000000..3771ad9782
--- /dev/null
+++ b/research/layered-joint-owners/evidence/OWNERS-AUDIT.json
@@ -0,0 +1,105 @@
+{
+  "status": "PASS_SOLVER_FREE_JOINT_OWNER_COMBINATORICS_AND_NATIVE_MOMENT",
+  "source_baseline_head": "0805e78f5fecc700804d4766d7e3e1d7d7e6a2ba",
+  "geometry_and_native_head": "3e669dc7987cb2295a71664b77e110c0cd979a87",
+  "source_plan_sha256": "2ea1d2e317e5dd943c30bb5432011824a2e15acc3e7313d150bd5c8430d0e255",
+  "source_owners_sha256": "01a8f5c5cd54e13662f2fe40d16c2a1d443dfc664a6c988fffea6e0bacdfc937",
+  "owners_sha256": "5dde55d556840aea8746058124642b539502aac5f4084bfb72301e90e46a6f7c",
+  "owners_semantic_sha256": "6b4353a4de84c314b48d9a05aebddb1ab1fbfe33cbc8f109b6a06c4ef8002e28",
+  "baseline_idle": {
+    "2": 4,
+    "3": 4,
+    "5": 1,
+    "7": 1,
+    "16": 2,
+    "32": 1,
+    "48": 2398
+  },
+  "candidate_idle": {
+    "1": 1,
+    "3": 1,
+    "28": 1,
+    "32": 2,
+    "48": 2398
+  },
+  "global_profile": {
+    "1": 183025,
+    "2": 29808,
+    "3": 31249,
+    "4": 11088,
+    "5": 4032,
+    "8": 576,
+    "28": 1,
+    "32": 2,
+    "48": 2398
+  },
+  "integer_stoploss_margins": [
+    0,
+    8,
+    17,
+    22,
+    24,
+    26,
+    27,
+    28,
+    28,
+    28,
+    28,
+    28,
+    28,
+    28,
+    28,
+    28,
+    28,
+    26,
+    24,
+    22,
+    20,
+    18,
+    16,
+    14,
+    12,
+    10,
+    8,
+    6,
+    4,
+    3,
+    2,
+    1,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0
+  ],
+  "exact_native_moment": {
+    "native_lower": "828466591481403378691/500000000000000000000000",
+    "native_upper": "1656933182962806757383/1000000000000000000000000",
+    "lower_endpoint_moment_upper": "883423532389192164791647813082715395697900278728624093524042002491564109/883423532389192164791648750371459257913741948437809479060803100646309888",
+    "upper_endpoint_moment_lower": "1766847064778384329583300858965949849690883370200586171631160615355764663/1766847064778384329583297500742918515827483896875618958121606201292619776",
+    "nominal_outer_ceiling_lower": "828466591481403378691/500828466591481403378691",
+    "nominal_outer_ceiling_upper": "1656933182962806757383/1001656933182962806757383",
+    "scope": "Native homogeneous moment only; outer ceiling is not an assembled witness."
+  },
+  "negative_controls_rejected": [
+    "wrong_width",
+    "wrong_call_time",
+    "duplicate_helper"
+  ],
+  "all_explicit_windows_and_capacities_checked": true,
+  "all_families_distinct_and_outside_active_data": true,
+  "all_helpers_and_offsets_checked": true,
+  "remaining_admission": "Independently derive controller windows and actual73-column phase charts, finite invoice and complete outer witness. No new physical supplier claimed here."
+}
diff --git a/research/layered-joint-owners/evidence/PRICE.json b/research/layered-joint-owners/evidence/PRICE.json
new file mode 100644
index 0000000000..20765f2365
--- /dev/null
+++ b/research/layered-joint-owners/evidence/PRICE.json
@@ -0,0 +1,156 @@
+{
+  "status": "PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK",
+  "profile_input_file": "PROFILE.json",
+  "profile_input_sha256": "80f219e800298f27b1187c0f927f06963157ceee4ec5710df55a77fde9ccf561",
+  "global_profile": {
+    "1": 183025,
+    "2": 29808,
+    "3": 31249,
+    "4": 11088,
+    "5": 4032,
+    "8": 576,
+    "28": 1,
+    "32": 2,
+    "48": 2398
+  },
+  "live": 7168,
+  "m": 73,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "prices": {
+    "native": {
+      "root": {
+        "lower": "0.001656933182962806757382",
+        "upper": "0.001656933182962806757383",
+        "lower_endpoint_residual_upper": "-1.060973258576604638575815877175516444274115876250957310930785418322809E-24",
+        "upper_endpoint_residual_lower": "1.900686877930255608273638414454963784979977200130979177368537375429010E-24",
+        "strict_rational_signs": true
+      },
+      "exact_moments": [
+        {
+          "endpoint": "828466591481403378691/500000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-28603782466498286183767980511033226351872399/26959946667150639794667015087019630673637144422540572481103610249216",
+            "-28603782466498286183767980511033226351872397/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "-530487/500000000000000000000000000000",
+            "-1060973/1000000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "1656933182962806757383/1000000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "25621208429976374812876319635112835345566277/13479973333575319897333507543509815336818572211270286240551805124608",
+            "12810604214988187406438159817556417672783139/6739986666787659948666753771754907668409286105635143120275902562304"
+          ],
+          "base_two_residual": [
+            "950343/500000000000000000000000000000",
+            "1900687/1000000000000000000000000000000"
+          ]
+        }
+      ],
+      "outer_with_bit": {
+        "complex_b": "828466591481403378691/500000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "827096148427573/500000000000000000",
+        "kappa_decimal": "0.001654192296855146",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    },
+    "conservative": {
+      "root": {
+        "lower": "0.001656933180057279686934",
+        "upper": "0.001656933180057279686935",
+        "lower_endpoint_residual_upper": "-6.992429964461360053702388619222120817058083000350372423969036432688089E-25",
+        "upper_endpoint_residual_lower": "2.262417140066028734391645960609064845648654445236305975615703479306451E-24",
+        "strict_rational_signs": true
+      },
+      "exact_moments": [
+        {
+          "endpoint": "828466590028639843467/500000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-2356444236445803883052132449317619651354319/3369993333393829974333376885877453834204643052817571560137951281152",
+            "-9425776945783215532208529797270478605417275/13479973333575319897333507543509815336818572211270286240551805124608"
+          ],
+          "base_two_residual": [
+            "-6992439195487836546339/10000000000000000000000000000000000000000000000",
+            "-1398485839097567309239/2000000000000000000000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "331386636011455937387/200000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "30497322717513806795559482934434527726390927/13479973333575319897333507543509815336818572211270286240551805124608",
+            "1906082669844612924722467683402157982899433/842498333348457493583344221469363458551160763204392890034487820288"
+          ],
+          "base_two_residual": [
+            "5656042701220341342537/2500000000000000000000000000000000000000000000",
+            "22624180804881365370291/10000000000000000000000000000000000000000000000"
+          ]
+        }
+      ],
+      "outer_with_bit": {
+        "complex_b": "828466590028639843467/500000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "1654192293959223/1000000000000000000",
+        "kappa_decimal": "0.001654192293959223",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    }
+  },
+  "bit_supplier_pr": 589,
+  "bit_deficit": 10272,
+  "bit_moments_with_surcharge": [
+    {
+      "endpoint": "1733427039589844234749/1000000000000000000000000",
+      "accept": true,
+      "mercator_residual": [
+        "-43100600330766044577088869872467188970742291/26959946667150639794667015087019630673637144422540572481103610249216",
+        "-43100600330766044577088869872467188970742289/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two_residual": [
+        "-799345163337715793503/500000000000000000000000000000000000000000000",
+        "-3197378653350863173989/2000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "endpoint": "6933708158359376939/4000000000000000000000",
+      "accept": false,
+      "mercator_residual": [
+        "22502934905675809315035333485365686073718547/13479973333575319897333507543509815336818572211270286240551805124608",
+        "5625733726418952328758833371341421518429637/3369993333393829974333376885877453834204643052817571560137951281152"
+      ],
+      "base_two_residual": [
+        "8346798366759439729359/5000000000000000000000000000000000000000000000",
+        "16693606733518879458833/10000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "gain_over_pr635_percent": "1.09707492820979314365832953500735265605280721777942151912118918284103344551",
+  "input_sha256": {
+    "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "package:inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4"
+  },
+  "scope": "Independent arithmetic for the exact nominated all72 profile. Complete local, controller and finite invoice admission are separately replayed by the package driver; this receipt does not replace them. The cited PR589 bit supplier is unchanged and its exceptional-residue surcharge is retained. Any alternative c is only a headroom comparison."
+}
diff --git a/research/layered-joint-owners/evidence/PRIOR-BASE-CHECKS.json b/research/layered-joint-owners/evidence/PRIOR-BASE-CHECKS.json
new file mode 100644
index 0000000000..7469d6ff33
--- /dev/null
+++ b/research/layered-joint-owners/evidence/PRIOR-BASE-CHECKS.json
@@ -0,0 +1,31 @@
+{
+  "exit_code": 0,
+  "gen4_bank_verify_included": true,
+  "log_sha256": "7b3471bc805cf836dd884e615b243f8708eed90224b5bd3095e7d335e7124292",
+  "base_commit": "17ce0c79b7b51c2634b439ea5a2b754f09909693",
+  "command": "nice -n 15 ionice -c 3 env PATH=\"/tmp/intmult-contribution-venv/bin:$PATH\" PYTHONDONTWRITEBYTECODE=1 OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 make verify",
+  "python": "3.12.3",
+  "groups": [
+    "verify-community",
+    "verify-producers",
+    "verify-partial-gauge",
+    "verify-three-stage-cover",
+    "verify-paired-cube",
+    "verify-recycled-bit",
+    "verify-entrance-banks",
+    "gen4-bank-verify",
+    "frontier626-verify",
+    "verify-certificates",
+    "verify-ternary",
+    "verify-research",
+    "verify-strips",
+    "verify-clones",
+    "verify-positive",
+    "verify-joint",
+    "verify-pair",
+    "verify-tests"
+  ],
+  "isolated_test_modules": 84,
+  "archived_utc": "2026-10-13T01:14:29.299696+00:00",
+  "scope": "Local repository-wide checks at the pinned base. The new K480 research package is separately verified by the archived complete fresh replay; no GitHub CI or full-theorem claim."
+}
diff --git a/research/layered-joint-owners/evidence/REPLAY.json b/research/layered-joint-owners/evidence/REPLAY.json
new file mode 100644
index 0000000000..654b354838
--- /dev/null
+++ b/research/layered-joint-owners/evidence/REPLAY.json
@@ -0,0 +1,114 @@
+{
+  "status": "PASS_LAYERED_JOINT_OWNER_STRICT_ADMISSION",
+  "kappa_decimal": "0.001654192296855146",
+  "parent_head": "0805e78f5fecc700804d4766d7e3e1d7d7e6a2ba",
+  "parent_manifest_sha256": "04934a9d42a1f078dd0b23c8b05570184cd664a99f13625a0ada5c41cb324d0e",
+  "owner_sha256": "5dde55d556840aea8746058124642b539502aac5f4084bfb72301e90e46a6f7c",
+  "unchanged_verifier_python_files": {
+    "verify_global.py": "16bd5e54598592e92e210f99065348c5df261b8350fdc688072ce053d15b088a",
+    "verify_manifest.py": "723d726dbbe5b65a49caecae0f1aab664a1413fb639abfd3e826a5a538e14e5b",
+    "hosting/reuse_owners.py": "2106fe79bd89071e62a3a25c1e444531e14fb89f88b4bdeb72d7b40c91266402",
+    "hosting/reproduce.py": "7551004d8d15cebcecc6793ebd17385830390935ccd1a8957f1c5472bce6ec82",
+    "hosting/audit_frozen.py": "a8d9c7c894cb44453aea93b33141559824f6c3ff81a85a6d066f4a10a2757659",
+    "hosting/expand_owners.py": "0f826377881d0c9405f90d9f5feac857c7c7cf8aef5bcf22d326bc274f038a70",
+    "independent/review_guards.py": "b83164d6c0122a055b3281f3381b305683a875760a2d727dd0188bb2aa59d67d",
+    "independent/audit_local.py": "03afcfc9da428b3f6edac81c1fee7f277ab81b64998efae78380b63498dec6cd",
+    "independent/price_profile.py": "d2f548ad6b99f64a8ca5fbaf822a89560bb99359957ce3420b497f6a46fc0acf",
+    "code/assemble.py": "4c270a996b380ab712f72b81173ab24f1c73203a33578f261bfbaa7e67d75aec",
+    "code/assembly_controls.py": "e4c0f7828af64fdaef1896e4448d0212bd3041805097140b8cfafd098f8a6162",
+    "code/bit_supplier_controls.py": "e6d33fb61a570c3f50669412acc467a3fd06ef0b806da6a75bc296c6ba2142a5",
+    "code/generated_identity.py": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+    "code/freeze_spec.py": "f96c2b9cd886596bc7ab267f77abe9d16b6cbb5a724a5ad0a1d18d540369ed93",
+    "code/audit_allcold.py": "a87d7f4844ca963516637d249b14a0654f67f8047b6b265ae25b0cf30963e503",
+    "code/invoice_allcold.py": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+    "code/witness.py": "779c5172894b992131e85be1e592ed2a1aec8c287b872ff42007d36a7291e444",
+    "code/bind_providers_portable.py": "1d39bcc7b63ac158e021454beaae897d123e174360573762aecade3cd43193f6",
+    "code/restore_parent.py": "69b7b25ff85e9b8160e233c1d415cc6a0272019e5c486dcec14cb6c349e7024d",
+    "code/prepare_global.py": "8c0dae301a8f34b77a5a462f840952d08ed120576212adf5051bc09bcad874dc",
+    "code/emit_allcold.py": "17c110c7c8d219e79e7dce36b19c4781e7effa800086cec03384387ad9acc7aa",
+    "construction/build_gauge_cold44.py": "ec730a4d3ff12fb058780718b1d5a7afe61243c532679ef347a5a48e2af0a3bb",
+    "construction/construct_gauge_xcentre.py": "d8d295566ef2399af2da0707a4adc83e07aa26d2344c01a66bd0ca7684cf9217",
+    "construction/reproduce.py": "047bb9b3536b0b16bb08a21cd9fd80404ca9d022345f1aeab34b21dffc281c92",
+    "construction/layers/build_pivot_swap.py": "8e8bced88be2e592ded40929499bac385ca92fcc1fa59183c22229dbf34093b8",
+    "construction/layers/layer_end_controls.py": "7829187bfc8f909948d5250e0ec00f02c89f5fe98306a3ed88daee36cb3c92ef",
+    "construction/layers/reproduce_layers.py": "435699f6f79c6c7fb8d6cc5a8382576d6ac88747583a975ff671e45440b93c4e"
+  },
+  "baseline_snapshot": {
+    "data/PLAN.json": "2ea1d2e317e5dd943c30bb5432011824a2e15acc3e7313d150bd5c8430d0e255",
+    "data/OWNERS.json.gz": "01a8f5c5cd54e13662f2fe40d16c2a1d443dfc664a6c988fffea6e0bacdfc937",
+    "evidence/local/CANONICAL-WORD.json.gz": "72a4952751383e2a5e84b967f1e76fdfda003fe5592df357a599232e586817e3",
+    "evidence/global/GLOBAL-TEMPLATE.json.gz": "fa2b5d8873b063355e7b59402d0a9ab4d698b1d26801cf6c93eb84a5ad9bd9ce",
+    "evidence/global/HOSTED.json": "048b3817b3014017ebe5dbfa1b04ab20de7fecbe6780c331a08db8098e0921b7",
+    "evidence/audit/OWNERS-AND-PROFILE.json": "87b57ed694889b840d568e21110bb28b808698281f56d2c32dc11e95d8231c2c"
+  },
+  "rebuilt_local": true,
+  "steps": [
+    {
+      "name": "parent-manifest",
+      "exit_code": 0,
+      "seconds": 0.054,
+      "log_sha256": "84d3af581669219a35ce0807c2b9cc2b313bf07168760a80d8bb5eb220a99715"
+    },
+    {
+      "name": "word",
+      "exit_code": 0,
+      "seconds": 3.332,
+      "log_sha256": "b31877e807c4748ad59179231313b3c37181c6b4613afed99b4690ca9f75569f"
+    },
+    {
+      "name": "layers-and-native",
+      "exit_code": 0,
+      "seconds": 149.55,
+      "log_sha256": "b353f5a30bc7bc16d1921582dfe23b1f390e2a12c2a45940e6ee9ab14ce229ba"
+    },
+    {
+      "name": "independent-scalar",
+      "exit_code": 0,
+      "seconds": 0.655,
+      "log_sha256": "d3f17a7125edd3d9d72bedb646b498f8791609d84403c8087b652c5a14316bdc"
+    },
+    {
+      "name": "baseline-strict",
+      "exit_code": 0,
+      "seconds": 15.433,
+      "log_sha256": "9160163b7c291dcc26212e185c72fe5153116e90ef8e5bcfbfeb071552aed9fb"
+    },
+    {
+      "name": "owners",
+      "exit_code": 0,
+      "seconds": 0.831,
+      "log_sha256": "abb351df7056714a45cc614208c62be5a4d0603f93987b3e605e0c428b801eae"
+    },
+    {
+      "name": "independent-owners",
+      "exit_code": 0,
+      "seconds": 13.412,
+      "log_sha256": "7f8973e0aad35cbad2e43362a3a57beece8e65bb8335d88dcf3b71fe34ea2db9"
+    },
+    {
+      "name": "prepare",
+      "exit_code": 0,
+      "seconds": 0.114,
+      "log_sha256": "987b51820faf4b3803bbe7f365b21ab266dde65ae17086988c18217804c38b74"
+    },
+    {
+      "name": "global-strict",
+      "exit_code": 0,
+      "seconds": 15.431,
+      "log_sha256": "f0a01750c6ce4fbd625f35a4f517159e50494b177e78cf69ebfcc90c823a0ee1"
+    },
+    {
+      "name": "independent-price",
+      "exit_code": 0,
+      "seconds": 0.325,
+      "log_sha256": "db6a5f47d7a6cec6472d9055709882def6f2c5cfa18a6b0019ce2ea532b09679"
+    },
+    {
+      "name": "packing-ceiling",
+      "exit_code": 0,
+      "seconds": 0.29,
+      "log_sha256": "bf2fa9f2cdd5ddfb502bd1451cdbd2a896c9d854eb53d15779a480d0288eda52"
+    }
+  ],
+  "scope": "Conditional finite owner witness under the unchanged PR655/656 local construction, controller and admission interfaces. PR589 bit circuit cited unchanged and its profile repriced; no unconditional theorem, full Lean proof or packing optimality claim."
+}
diff --git a/research/layered-joint-owners/evidence/STEPS.json b/research/layered-joint-owners/evidence/STEPS.json
new file mode 100644
index 0000000000..19572face6
--- /dev/null
+++ b/research/layered-joint-owners/evidence/STEPS.json
@@ -0,0 +1,68 @@
+[
+  {
+    "name": "parent-manifest",
+    "exit_code": 0,
+    "seconds": 0.054,
+    "log_sha256": "84d3af581669219a35ce0807c2b9cc2b313bf07168760a80d8bb5eb220a99715"
+  },
+  {
+    "name": "word",
+    "exit_code": 0,
+    "seconds": 3.332,
+    "log_sha256": "b31877e807c4748ad59179231313b3c37181c6b4613afed99b4690ca9f75569f"
+  },
+  {
+    "name": "layers-and-native",
+    "exit_code": 0,
+    "seconds": 149.55,
+    "log_sha256": "b353f5a30bc7bc16d1921582dfe23b1f390e2a12c2a45940e6ee9ab14ce229ba"
+  },
+  {
+    "name": "independent-scalar",
+    "exit_code": 0,
+    "seconds": 0.655,
+    "log_sha256": "d3f17a7125edd3d9d72bedb646b498f8791609d84403c8087b652c5a14316bdc"
+  },
+  {
+    "name": "baseline-strict",
+    "exit_code": 0,
+    "seconds": 15.433,
+    "log_sha256": "9160163b7c291dcc26212e185c72fe5153116e90ef8e5bcfbfeb071552aed9fb"
+  },
+  {
+    "name": "owners",
+    "exit_code": 0,
+    "seconds": 0.831,
+    "log_sha256": "abb351df7056714a45cc614208c62be5a4d0603f93987b3e605e0c428b801eae"
+  },
+  {
+    "name": "independent-owners",
+    "exit_code": 0,
+    "seconds": 13.412,
+    "log_sha256": "7f8973e0aad35cbad2e43362a3a57beece8e65bb8335d88dcf3b71fe34ea2db9"
+  },
+  {
+    "name": "prepare",
+    "exit_code": 0,
+    "seconds": 0.114,
+    "log_sha256": "987b51820faf4b3803bbe7f365b21ab266dde65ae17086988c18217804c38b74"
+  },
+  {
+    "name": "global-strict",
+    "exit_code": 0,
+    "seconds": 15.431,
+    "log_sha256": "f0a01750c6ce4fbd625f35a4f517159e50494b177e78cf69ebfcc90c823a0ee1"
+  },
+  {
+    "name": "independent-price",
+    "exit_code": 0,
+    "seconds": 0.325,
+    "log_sha256": "db6a5f47d7a6cec6472d9055709882def6f2c5cfa18a6b0019ce2ea532b09679"
+  },
+  {
+    "name": "packing-ceiling",
+    "exit_code": 0,
+    "seconds": 0.29,
+    "log_sha256": "bf2fa9f2cdd5ddfb502bd1451cdbd2a896c9d854eb53d15779a480d0288eda52"
+  }
+]
diff --git a/research/layered-joint-owners/evidence/baseline/REPLAY.json b/research/layered-joint-owners/evidence/baseline/REPLAY.json
new file mode 100644
index 0000000000..0aba4b9fdd
--- /dev/null
+++ b/research/layered-joint-owners/evidence/baseline/REPLAY.json
@@ -0,0 +1,86 @@
+{
+  "status": "PASS_GAUGE44_STRICT_GLOBAL_REPLAY",
+  "kappa": "330821705902271/200000000000000000",
+  "kappa_decimal": "0.001654108529511355",
+  "complex_lower": "1656849137802307980933/1000000000000000000000000",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_supplier": {
+    "pr": 589,
+    "repository": "CrocSwap/integer-mult-bounds",
+    "commit": "a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46",
+    "merged_as": "b3eb785ac5b4b1ca2beea0f80db078a505626a90",
+    "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "git_blob_sha1": "e293ddc557742637f9f679f083a1a282d87b1b13",
+    "word": {
+      "v": 111,
+      "decoder_constant": 63,
+      "copy_ranks": [
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7
+      ]
+    },
+    "derived_deficit": 10272,
+    "deficit_formula": "T(2Kv-L*cst), L=9 T=32 K=4 M=64",
+    "replay_scope": "Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit."
+  },
+  "gain_over_pr635_percent": "1.091955430647220818316176963276019114058189320358907321234709427485771",
+  "spec_sha256": "d7d2a719481e9a8125e0982f957efe3b0ddef64450d71554d4476a5b5eee21e7",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 1.037,
+      "exit_code": 0,
+      "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.204,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "emit",
+      "seconds": 2.536,
+      "exit_code": 0,
+      "log_sha256": "048b3817b3014017ebe5dbfa1b04ab20de7fecbe6780c331a08db8098e0921b7"
+    },
+    {
+      "name": "audit",
+      "seconds": 10.03,
+      "exit_code": 0,
+      "log_sha256": "6bfc03daddbc4e7b6b5f82f7ff2c075bf507b80362ad8270c7400824694d3e48"
+    },
+    {
+      "name": "invoice",
+      "seconds": 0.577,
+      "exit_code": 0,
+      "log_sha256": "94fcce7faae261bed1f9e74b0a957a01f5ec5d3ba99d0071fc8dcae256c57e1c"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.244,
+      "exit_code": 0,
+      "log_sha256": "b98bef079fe1a2f3b296f9546ffdbd47bb99680541cdfe0ac4ddf2883a3363f8"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 0.292,
+      "exit_code": 0,
+      "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+    },
+    {
+      "name": "bit-supplier-controls",
+      "seconds": 0.48,
+      "exit_code": 0,
+      "log_sha256": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67"
+    }
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; this bit composition is unreviewed. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/layered-joint-owners/evidence/ceiling/CEILING.json b/research/layered-joint-owners/evidence/ceiling/CEILING.json
new file mode 100644
index 0000000000..d980194c40
--- /dev/null
+++ b/research/layered-joint-owners/evidence/ceiling/CEILING.json
@@ -0,0 +1,13 @@
+{
+  "status": "PASS_EXACT_FIXED_PROVIDER_RELAXED_PACKING_CEILING",
+  "max_idle_dimension": 48,
+  "fixed_idle_rank": 115200,
+  "relaxed_idle": {
+    "48": 2400
+  },
+  "native_root_upper": "1656990187678871312389/1000000000000000000000000",
+  "kappa_upper_rational": "1656990187678871312389/1001656990187678871312389",
+  "kappa_upper_decimal": "0.001654249113130437701999323091781377471424000301759803157906768862937181",
+  "feasible_assignment_claimed": false,
+  "scope": "Upper bound for fixed local profile and controller capacities with retained outer transfer; not a universal multiplication bound. Exact root upper endpoint is independently signed. The retained outer transfer has kappa < b/(1+b)."
+}
diff --git a/research/layered-joint-owners/evidence/ceiling/PRICE.json b/research/layered-joint-owners/evidence/ceiling/PRICE.json
new file mode 100644
index 0000000000..4dd3885544
--- /dev/null
+++ b/research/layered-joint-owners/evidence/ceiling/PRICE.json
@@ -0,0 +1,154 @@
+{
+  "status": "PASS_FROZEN_PROFILE_TWO_EXACT_ENGINE_AND_OUTER47_CROSSCHECK",
+  "profile_input_file": "RELAXED-PROFILE.json",
+  "profile_input_sha256": "86fcf0ad87afc89e794941d41e6ff7dcfb035ce11ba45fc7f62a5031536aff61",
+  "global_profile": {
+    "1": 183024,
+    "2": 29808,
+    "3": 31248,
+    "4": 11088,
+    "5": 4032,
+    "8": 576,
+    "48": 2400
+  },
+  "live": 7168,
+  "m": 73,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "prices": {
+    "native": {
+      "root": {
+        "lower": "0.001656990187678871312388",
+        "upper": "0.001656990187678871312389",
+        "lower_endpoint_residual_upper": "-8.741674213356410630861964365637486788266953190221093923404088549064405E-25",
+        "upper_endpoint_residual_lower": "2.087391285875233072298784912364865655399780370115273070588381924586977E-24",
+        "strict_rational_signs": true
+      },
+      "exact_moments": [
+        {
+          "endpoint": "414247546919717828097/250000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-23567507057369485367913633386857277537454593/26959946667150639794667015087019630673637144422540572481103610249216",
+            "-23567507057369485367913633386857277537454591/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "-109271/125000000000000000000000000000",
+            "-874167/1000000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "1656990187678871312389/1000000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "28137978870335639120031879013083105167898859/13479973333575319897333507543509815336818572211270286240551805124608",
+            "7034494717583909780007969753270776291974715/3369993333393829974333376885877453834204643052817571560137951281152"
+          ],
+          "base_two_residual": [
+            "2087391/1000000000000000000000000000000",
+            "65231/31250000000000000000000000000"
+          ]
+        }
+      ],
+      "outer_with_bit": {
+        "complex_b": "414247546919717828097/250000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "1654249113130437/1000000000000000000",
+        "kappa_decimal": "0.001654249113130437",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    },
+    "conservative": {
+      "root": {
+        "lower": "0.001656990184773277268828",
+        "upper": "0.001656990184773277268829",
+        "lower_endpoint_residual_upper": "-2.712653381334333817250232665413338046094365933144254394358920741914784E-24",
+        "upper_endpoint_residual_lower": "2.489053258818442267550534323543413367445278719689172423106998588452788E-25",
+        "strict_rational_signs": true
+      },
+      "exact_moments": [
+        {
+          "endpoint": "414247546193319317207/250000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-18283247621809871639351946368861868497183977/6739986666787659948666753771754907668409286105635143120275902562304",
+            "-36566495243619743278703892737723736994367953/13479973333575319897333507543509815336818572211270286240551805124608"
+          ],
+          "base_two_residual": [
+            "-13563267576373431980619/5000000000000000000000000000000000000000000000",
+            "-5425305030549372792219/2000000000000000000000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "1656990184773277268829/1000000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "6710474310944270144100462499269533079903213/26959946667150639794667015087019630673637144422540572481103610249216",
+            "6710474310944270144100462499269533079903215/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "2489044847622333820929/10000000000000000000000000000000000000000000000",
+            "2489054847622333821073/10000000000000000000000000000000000000000000000"
+          ]
+        }
+      ],
+      "outer_with_bit": {
+        "complex_b": "414247546193319317207/250000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "103390569389653/62500000000000000",
+        "kappa_decimal": "0.001654249110234448",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    }
+  },
+  "bit_supplier_pr": 589,
+  "bit_deficit": 10272,
+  "bit_moments_with_surcharge": [
+    {
+      "endpoint": "1733427039589844234749/1000000000000000000000000",
+      "accept": true,
+      "mercator_residual": [
+        "-43100600330766044577088869872467188970742291/26959946667150639794667015087019630673637144422540572481103610249216",
+        "-43100600330766044577088869872467188970742289/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two_residual": [
+        "-799345163337715793503/500000000000000000000000000000000000000000000",
+        "-3197378653350863173989/2000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "endpoint": "6933708158359376939/4000000000000000000000",
+      "accept": false,
+      "mercator_residual": [
+        "22502934905675809315035333485365686073718547/13479973333575319897333507543509815336818572211270286240551805124608",
+        "5625733726418952328758833371341421518429637/3369993333393829974333376885877453834204643052817571560137951281152"
+      ],
+      "base_two_residual": [
+        "8346798366759439729359/5000000000000000000000000000000000000000000000",
+        "16693606733518879458833/10000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "gain_over_pr635_percent": "1.10054729309213245950373431820903409770935229107692816773918969755623129657",
+  "input_sha256": {
+    "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "package:inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4"
+  },
+  "scope": "Independent arithmetic for the exact nominated all72 profile. Complete local, controller and finite invoice admission are separately replayed by the package driver; this receipt does not replace them. The cited PR589 bit supplier is unchanged and its exceptional-residue surcharge is retained. Any alternative c is only a headroom comparison."
+}
diff --git a/research/layered-joint-owners/evidence/ceiling/RELAXED-PROFILE.json b/research/layered-joint-owners/evidence/ceiling/RELAXED-PROFILE.json
new file mode 100644
index 0000000000..10ce76406c
--- /dev/null
+++ b/research/layered-joint-owners/evidence/ceiling/RELAXED-PROFILE.json
@@ -0,0 +1,9 @@
+{
+  "1": 183024,
+  "2": 29808,
+  "3": 31248,
+  "4": 11088,
+  "5": 4032,
+  "8": 576,
+  "48": 2400
+}
diff --git a/research/layered-joint-owners/evidence/global/ADMISSION-CONTROLS.json b/research/layered-joint-owners/evidence/global/ADMISSION-CONTROLS.json
new file mode 100644
index 0000000000..3e4e08ac65
--- /dev/null
+++ b/research/layered-joint-owners/evidence/global/ADMISSION-CONTROLS.json
@@ -0,0 +1,102 @@
+{
+  "status": "PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS",
+  "valid_receipt_kappa": "827096148427573/500000000000000000",
+  "input_sha256": {
+    "owner_audit": "1830c73cf9d336efc40dabbb9c460a056ce4dbe65a62425ae45f55ae775f6625",
+    "fresh_invoice": "162685645abeeb40dcd7be1cbbd0b8c34ce3c3279db85866fc0d7380e2c1d4aa",
+    "package:inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+  },
+  "assembler_sha256": "4c270a996b380ab712f72b81173ab24f1c73203a33578f261bfbaa7e67d75aec",
+  "rejected_controls": [
+    "empty_certification_maps",
+    "failed_invoice_status",
+    "nonboolean_precision_check",
+    "wrong_owner_role_count",
+    "understated_physical_stock",
+    "changed_profile_same_rank_mass",
+    "insufficient_finite_C0",
+    "missing_finite_check",
+    "wrong_reflected_orientation_selfconsistent_totals",
+    "missing_selected_call",
+    "wrong_selected_primitive_sum",
+    "wrong_selected_coefficient_work_sum",
+    "unpaid_wrapper_factors",
+    "wrong_global_compiler",
+    "wrong_global_adapter_maximum",
+    "understated_exact_prefix_and_global_sum",
+    "wrong_global_prefix_sum",
+    "wrong_row_prefix_reserve",
+    "wrong_parent_geometry_charge",
+    "wrong_rebased_geometry_charge",
+    "wrong_complete_pervertex_envelope",
+    "wrong_prior_added_complete_invoice",
+    "wrong_finite_router_bits",
+    "wrong_finite_literal_bits",
+    "wrong_finite_physical_stock_bits",
+    "wrong_finite_row_coefficient",
+    "reordered_complete_calls",
+    "understated_explicit_idle_remainders",
+    "understated_actual_chart_types",
+    "wrong_cross_replica_role_count",
+    "old_no_cold_wrapper_counts_selfconsistent",
+    "gauge44:missing_provider",
+    "gauge44:missing_backward_orientation",
+    "gauge44:unpaid_scalar_primitive",
+    "gauge44:wrong_local_artifact_binding",
+    "gauge44:false_dirty_restoration",
+    "gauge44:wrong_declared_provider_count",
+    "gauge44:wrong_local_compiler",
+    "gauge44:wrong_local_adapter_charge",
+    "gauge44:wrong_local_primitive_bound",
+    "gauge44:forged_provider_and_call_program_hash",
+    "gauge44:provider_at_wrong_call",
+    "gauge44:synchronized_forged_source_recipe_hash",
+    "gauge44:synchronized_forged_phase_review_semantics",
+    "gauge44:width_order_swap_4_5",
+    "gauge44:width_inventory_shift_4_5",
+    "gauge44:width_order_swap_4_7",
+    "gauge44:width_inventory_shift_4_7",
+    "gauge44:width_order_swap_4_8",
+    "gauge44:width_inventory_shift_4_8",
+    "gauge44:width_order_swap_4_9",
+    "gauge44:width_inventory_shift_4_9",
+    "gauge44:width_order_swap_5_7",
+    "gauge44:width_inventory_shift_5_7",
+    "gauge44:width_order_swap_5_8",
+    "gauge44:width_inventory_shift_5_8",
+    "gauge44:width_order_swap_5_9",
+    "gauge44:width_inventory_shift_5_9",
+    "gauge44:width_order_swap_7_8",
+    "gauge44:width_inventory_shift_7_8",
+    "gauge44:width_order_swap_7_9",
+    "gauge44:width_inventory_shift_7_9",
+    "gauge44:width_order_swap_8_9",
+    "gauge44:width_inventory_shift_8_9",
+    "gauge44:cold_helper_width_swap_264",
+    "gauge44:cold_helper_width_swap_276",
+    "gauge44:cold_helper_width_swap_288",
+    "gauge44:cold_helper_width_swap_300",
+    "wrong_owner_receipt_hash"
+  ],
+  "discovery_accepted_controls": [],
+  "exact_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "conservative_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "recurrence_model_controls": [
+    "native_complex_endpoint_rejected_with_old_surcharge",
+    "omitting_bit_surcharge_would_fail_next_endpoint_rejection"
+  ],
+  "scope": "Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay."
+}
diff --git a/research/layered-joint-owners/evidence/global/ASSEMBLY.json b/research/layered-joint-owners/evidence/global/ASSEMBLY.json
new file mode 100644
index 0000000000..e582ae08d1
--- /dev/null
+++ b/research/layered-joint-owners/evidence/global/ASSEMBLY.json
@@ -0,0 +1,346 @@
+{
+  "status": "PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY",
+  "kappa": "827096148427573/500000000000000000",
+  "kappa_decimal": "0.001654192296855146",
+  "complex_lower": "828466591481403378691/500000000000000000000000",
+  "complex_decimal": "0.001656933182962806757382",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_decimal": "0.001733427039589844234749",
+  "binding": "complex",
+  "gain_over_pr635_percent": "1.097074928209793143658329535007352656052807217779421519121189182841033",
+  "complex_profile": {
+    "1": 183025,
+    "2": 29808,
+    "3": 31249,
+    "4": 11088,
+    "5": 4032,
+    "8": 576,
+    "28": 1,
+    "32": 2,
+    "48": 2398
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "surcharge_model": {
+    "complex": false,
+    "bit": true
+  },
+  "conservative_complex_lower": "828466590028639843467/500000000000000000000000",
+  "conservative_complex_decimal": "0.001656933180057279686934",
+  "conservative_kappa": "1654192293959223/1000000000000000000",
+  "conservative_kappa_decimal": "0.001654192293959223",
+  "conservative_moments": [
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "828466590028639843467/500000000000000000000000",
+      "accept": true,
+      "mercator": [
+        "-2356444236445803883052132449317619651354319/3369993333393829974333376885877453834204643052817571560137951281152",
+        "-9425776945783215532208529797270478605417275/13479973333575319897333507543509815336818572211270286240551805124608"
+      ],
+      "base_two": [
+        "-6992439195487836546339/10000000000000000000000000000000000000000000000",
+        "-1398485839097567309239/2000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "331386636011455937387/200000000000000000000000",
+      "accept": false,
+      "mercator": [
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+        "1906082669844612924722467683402157982899433/842498333348457493583344221469363458551160763204392890034487820288"
+      ],
+      "base_two": [
+        "5656042701220341342537/2500000000000000000000000000000000000000000000",
+        "22624180804881365370291/10000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "conservative_bootstrap": [
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+    "beta_positive": "1/1000000000000000000000000",
+    "beta_below_one": "999999999999999999999999/1000000000000000000000000",
+    "leaf_saving_above_bit": "216774582247366152310031456467204101605803362241081463567013219664707608385007367468836206619142507327401601739154755602772342826734140164584476962829742767663377901467813340560816131152087628176812618032152697189514499638431687418223944444481577185173087235374559893361420810766088085362866407902469008971994448038668925778066604261229852040653533173502822241/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+  },
+  "controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; this bit composition is unreviewed. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/layered-joint-owners/evidence/global/BIT-SUPPLIER-CONTROLS.json b/research/layered-joint-owners/evidence/global/BIT-SUPPLIER-CONTROLS.json
new file mode 100644
index 0000000000..d0a091cd7a
--- /dev/null
+++ b/research/layered-joint-owners/evidence/global/BIT-SUPPLIER-CONTROLS.json
@@ -0,0 +1,49 @@
+{
+  "status": "PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS",
+  "kappa": "0.001654192296855146",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_decimal": "0.001733427039589844234749",
+  "binding": "complex",
+  "bit_supplier": {
+    "pr": 589,
+    "repository": "CrocSwap/integer-mult-bounds",
+    "commit": "a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46",
+    "merged_as": "b3eb785ac5b4b1ca2beea0f80db078a505626a90",
+    "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "git_blob_sha1": "e293ddc557742637f9f679f083a1a282d87b1b13",
+    "word": {
+      "v": 111,
+      "decoder_constant": 63,
+      "copy_ranks": [
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7
+      ]
+    },
+    "derived_deficit": 10272,
+    "deficit_formula": "T(2Kv-L*cst), L=9 T=32 K=4 M=64",
+    "replay_scope": "Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit."
+  },
+  "derived_deficit": 10272,
+  "rejected_controls": [
+    "revert_hardcoded_9984",
+    "ports_112",
+    "decoder_constant_64_copy_ranks_unchanged",
+    "decoder_constant_64_with_one_copy_rank_8",
+    "eight_retained_totals",
+    "live_minus_one",
+    "profile_rank_mass_plus_one",
+    "profile_rank_mass_receipt_mismatch",
+    "bit_lower_next_grid",
+    "not_nine_stage_record",
+    "tampered_bytes_next_grid",
+    "pr543_file_under_pr589_pin"
+  ],
+  "assembler_sha256": "4c270a996b380ab712f72b81173ab24f1c73203a33578f261bfbaa7e67d75aec"
+}
diff --git a/research/layered-joint-owners/evidence/global/REPLAY.json b/research/layered-joint-owners/evidence/global/REPLAY.json
new file mode 100644
index 0000000000..8b8daf04b2
--- /dev/null
+++ b/research/layered-joint-owners/evidence/global/REPLAY.json
@@ -0,0 +1,86 @@
+{
+  "status": "PASS_GAUGE44_STRICT_GLOBAL_REPLAY",
+  "kappa": "827096148427573/500000000000000000",
+  "kappa_decimal": "0.001654192296855146",
+  "complex_lower": "828466591481403378691/500000000000000000000000",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_supplier": {
+    "pr": 589,
+    "repository": "CrocSwap/integer-mult-bounds",
+    "commit": "a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46",
+    "merged_as": "b3eb785ac5b4b1ca2beea0f80db078a505626a90",
+    "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "git_blob_sha1": "e293ddc557742637f9f679f083a1a282d87b1b13",
+    "word": {
+      "v": 111,
+      "decoder_constant": 63,
+      "copy_ranks": [
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7
+      ]
+    },
+    "derived_deficit": 10272,
+    "deficit_formula": "T(2Kv-L*cst), L=9 T=32 K=4 M=64",
+    "replay_scope": "Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit."
+  },
+  "gain_over_pr635_percent": "1.097074928209793143658329535007352656052807217779421519121189182841033",
+  "spec_sha256": "4521daacffc2d08ae8bed702a916312f7d8b1c75f34c59a9320072f0ae0ddb39",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 1.082,
+      "exit_code": 0,
+      "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.223,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "emit",
+      "seconds": 2.473,
+      "exit_code": 0,
+      "log_sha256": "cda459c20349605b9b0a5ae9ec02ea388498b4d53db3ad53c6ad686b9c47a29a"
+    },
+    {
+      "name": "audit",
+      "seconds": 10.084,
+      "exit_code": 0,
+      "log_sha256": "c69c7afe6f36873aac3099b3dad1eebed3c1bbbe772724be33b308ed7b29987f"
+    },
+    {
+      "name": "invoice",
+      "seconds": 0.564,
+      "exit_code": 0,
+      "log_sha256": "94fcce7faae261bed1f9e74b0a957a01f5ec5d3ba99d0071fc8dcae256c57e1c"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.244,
+      "exit_code": 0,
+      "log_sha256": "6156e687737926264161f6e3f83ae4728181dd217b41642aa9fd158fa702ab07"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 0.275,
+      "exit_code": 0,
+      "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+    },
+    {
+      "name": "bit-supplier-controls",
+      "seconds": 0.458,
+      "exit_code": 0,
+      "log_sha256": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67"
+    }
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, 44 cold dimension-four ends, and explicit all72 whole-owner dispatch are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; this bit composition is unreviewed. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/layered-joint-owners/evidence/global/global/audit/ASYNC-AUDIT.json b/research/layered-joint-owners/evidence/global/global/audit/ASYNC-AUDIT.json
new file mode 100644
index 0000000000..bd0fe5ad53
--- /dev/null
+++ b/research/layered-joint-owners/evidence/global/global/audit/ASYNC-AUDIT.json
@@ -0,0 +1,76 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "2f11d6588a4014dbc12b7459c4c5f87869a826dc0b236db122342d9ffccb5678",
+  "complex_template_sha256": "2f11d6588a4014dbc12b7459c4c5f87869a826dc0b236db122342d9ffccb5678",
+  "complex_live": 7168,
+  "complex_profile": {
+    "1": 183025,
+    "2": 29808,
+    "3": 31249,
+    "4": 11088,
+    "5": 4032,
+    "8": 576,
+    "28": 1,
+    "32": 2,
+    "48": 2398
+  },
+  "complex_hosted_residuals": 35424,
+  "physical": 7670,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "entering_helper_roles": 18576,
+  "cross_replica_helper_roles": 26449,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 35424,
+  "complete_invocations": 72,
+  "actual_orthogonal_73column_maps": 8428,
+  "actual_sigma_stream_sha256": "ef0744394ad29fbf24782ebc5e06bf9b7dbf0430356c1a3d7f2b225a2357fd70",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 2403,
+  "mutations_rejected": [
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit idle remainder",
+    "understate physical reserve",
+    "gauge44: wrong provider at its invocation",
+    "gauge44: stale per-call local program hash",
+    "gauge44: stale serialized provider program",
+    "gauge44: unbound residual adapter hash",
+    "gauge44: wrong provider width registry",
+    "gauge44: wrong per-call residual width",
+    "gauge44: wrong sweep provider",
+    "gauge44: entering helper width silently restored to nine"
+  ],
+  "mutation_controls_run": true,
+  "provider_phase_semantic_sha256": {
+    "gauge44": "f74b565a63708431a6432fc422397a91617ed7796aa8d07452bd3bc49b858be7"
+  },
+  "provider_artifact_semantic_sha256": {
+    "gauge44": {
+      "CANONICAL-WORD.json.gz": "94fc985d6ab90967bfe995de41581690bcdb6dbade69e594b0130ef3da0c6314",
+      "LOCAL-PROGRAMS.json.gz": "fbecd226314c5f547582546843447fc1d366be5af5ace1acebe3b7a778aa9ce5",
+      "LOCAL-CHECKS.json": "b23622ee9c3d2bf2524464cd81480ca05a69171cfc5b93b122c33e565a8c3242",
+      "INDEPENDENT-LOCAL-REPLAY.json": "566ef5011c55c1ab4c6f829d1ef41a7fbec923db74c17f67c91abdf0f067b7c2",
+      "CLIFFORD-RECIPES.json": "b23cb8aac87f19a27ac5c982022bec10bcb7f02774182b8c3ef8e529a167c1b0",
+      "CLIFFORD-REVIEW.json": "f74b565a63708431a6432fc422397a91617ed7796aa8d07452bd3bc49b858be7",
+      "RESIDUAL-ADAPTERS.json": "8b792e77a8eb993e48374aae4b98f22ced30f6deda3b05d0a753e0538ff3f32d"
+    }
+  },
+  "widths_by_provider": {
+    "gauge44": {
+      "4": 52,
+      "5": 48,
+      "7": 42,
+      "8": 116,
+      "9": 234
+    }
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "all_provider_program_phase_and_wrapper_bindings": true,
+  "scope": "Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations."
+}
diff --git a/research/layered-joint-owners/evidence/global/global/audit/OWNERS-AND-PROFILE.json b/research/layered-joint-owners/evidence/global/global/audit/OWNERS-AND-PROFILE.json
new file mode 100644
index 0000000000..6591b015c6
--- /dev/null
+++ b/research/layered-joint-owners/evidence/global/global/audit/OWNERS-AND-PROFILE.json
@@ -0,0 +1,53 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE",
+  "template_sha256": "2f11d6588a4014dbc12b7459c4c5f87869a826dc0b236db122342d9ffccb5678",
+  "paid_profile": {
+    "1": 183025,
+    "2": 29808,
+    "3": 31249,
+    "4": 11088,
+    "5": 4032,
+    "8": 576,
+    "28": 1,
+    "32": 2,
+    "48": 2398
+  },
+  "live": 7168,
+  "physical": 7670,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "hosted_residuals": 35424,
+  "banked_residuals": 0,
+  "all_live_owners_per_call_distinct": true,
+  "owners_per_call": 716,
+  "actual_helper_owner_charts": 35424,
+  "actual_73column_sigmas": 8428,
+  "cross_replica_helper_roles": 26449,
+  "explicit_idle_remainder_children": 2403,
+  "source_idle_children_charged": 16128,
+  "source_artifacts": {
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "providers/gauge44/CANONICAL-WORD.json.gz": "72a4952751383e2a5e84b967f1e76fdfda003fe5592df357a599232e586817e3",
+    "providers/gauge44/LOCAL-PROGRAMS.json.gz": "61a30dfb8f63a7d1b5d8ef5b7ded2b2440d8998151ee5686defc01fcc93088e3",
+    "providers/gauge44/LOCAL-CHECKS.json": "b855ab7f3ea15a2d318bfc2f5aa4612ea76c019fa91cf64bd99903cf646b5e0c",
+    "providers/gauge44/INDEPENDENT-LOCAL-REPLAY.json": "c7ec4af7ccdf4230a4e277913d30ee41f2cc592d2360e008a18d11abd975b630",
+    "providers/gauge44/RESIDUAL-ADAPTERS.json": "0f2f39d58e7fb0844369dc0ea25e98ba35f0da9de4ee815015df66fad94af936",
+    "providers/gauge44/CLIFFORD-RECIPES.json": "b23cb8aac87f19a27ac5c982022bec10bcb7f02774182b8c3ef8e529a167c1b0",
+    "providers/gauge44/CLIFFORD-REVIEW.json": "c17864a376f0f6293d2dd97436ea3cd4e9ba98762d5882e06ab0480613cf1ff3"
+  },
+  "provider_phase_semantic_sha256": {
+    "gauge44": "f74b565a63708431a6432fc422397a91617ed7796aa8d07452bd3bc49b858be7"
+  },
+  "provider_artifact_semantic_sha256": {
+    "gauge44": {
+      "CANONICAL-WORD.json.gz": "94fc985d6ab90967bfe995de41581690bcdb6dbade69e594b0130ef3da0c6314",
+      "LOCAL-PROGRAMS.json.gz": "fbecd226314c5f547582546843447fc1d366be5af5ace1acebe3b7a778aa9ce5",
+      "LOCAL-CHECKS.json": "b23622ee9c3d2bf2524464cd81480ca05a69171cfc5b93b122c33e565a8c3242",
+      "INDEPENDENT-LOCAL-REPLAY.json": "566ef5011c55c1ab4c6f829d1ef41a7fbec923db74c17f67c91abdf0f067b7c2",
+      "CLIFFORD-RECIPES.json": "b23cb8aac87f19a27ac5c982022bec10bcb7f02774182b8c3ef8e529a167c1b0",
+      "CLIFFORD-REVIEW.json": "f74b565a63708431a6432fc422397a91617ed7796aa8d07452bd3bc49b858be7",
+      "RESIDUAL-ADAPTERS.json": "8b792e77a8eb993e48374aae4b98f22ced30f6deda3b05d0a753e0538ff3f32d"
+    }
+  },
+  "controller_audit_sha256": "c69c7afe6f36873aac3099b3dad1eebed3c1bbbe772724be33b308ed7b29987f"
+}
diff --git a/research/layered-joint-owners/evidence/global/global/audit/PREFIX-AND-INVOICE.json b/research/layered-joint-owners/evidence/global/global/audit/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..337e372726
--- /dev/null
+++ b/research/layered-joint-owners/evidence/global/global/audit/PREFIX-AND-INVOICE.json
@@ -0,0 +1,1746 @@
+{
+  "status": "PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "2f11d6588a4014dbc12b7459c4c5f87869a826dc0b236db122342d9ffccb5678",
+  "parent_template_sha256": "7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3",
+  "owner_audit_sha256": "1830c73cf9d336efc40dabbb9c460a056ce4dbe65a62425ae45f55ae775f6625",
+  "controller_audit_sha256": "c69c7afe6f36873aac3099b3dad1eebed3c1bbbe772724be33b308ed7b29987f",
+  "providers": {
+    "gauge44": {
+      "local": {
+        "backward": {
+          "events": 25250,
+          "macros": 20038,
+          "real_component_primitives": 200978,
+          "prefix_l1": "5318217944347079857738781/16",
+          "prefix_bits": 79,
+          "coefficient_work_primitive_count": 99399,
+          "all_exact_columns": 716,
+          "dirty_helper_columns": 492,
+          "all_dirty_helper_columns_restored": true,
+          "private_centres_and_coefficient_work_cleared": true,
+          "pre_wrappers": 258,
+          "post_wrappers": 258,
+          "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+        },
+        "forward": {
+          "events": 25250,
+          "macros": 20038,
+          "real_component_primitives": 200930,
+          "prefix_l1": "8008832819811317/2",
+          "prefix_bits": 52,
+          "coefficient_work_primitive_count": 99367,
+          "all_exact_columns": 716,
+          "dirty_helper_columns": 492,
+          "all_dirty_helper_columns_restored": true,
+          "private_centres_and_coefficient_work_cleared": true,
+          "pre_wrappers": 258,
+          "post_wrappers": 258,
+          "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+        }
+      },
+      "helpers": 492,
+      "centres": 8,
+      "v": 112,
+      "h": 9,
+      "n": 716,
+      "entering_helpers": 204,
+      "entrance_rank": 380,
+      "terminal_codimension": 272,
+      "hyperplane_ended_helpers": 96,
+      "cold_hyperplane_ended_helpers": 54,
+      "width_inventory": {
+        "4": 52,
+        "5": 48,
+        "7": 42,
+        "8": 116,
+        "9": 234
+      },
+      "widths": [
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+  "selected_scalar_macros": 1442736,
+  "global_prefix_bits": 264,
+  "charged_prefix_bits": 512,
+  "complete_invocation_sweeps": 72,
+  "bridge_sweeps": 72,
+  "row_prefix_extra": 1024,
+  "helpers": 492,
+  "centres": 8,
+  "live": 7168,
+  "physical": 7670,
+  "physical_stock_identity": {
+    "data_and_owner_families": 7168,
+    "local_helpers": 492,
+    "private_centres": 8,
+    "coefficient_work": 2
+  },
+  "local_adapters": 394592,
+  "local_primitive_bound": 10233481711890,
+  "wrapper_elementary_factors_charged": 5349888,
+  "factors_per_wrapper": 144,
+  "compiler": 25934336,
+  "unhosted_pervertex": 1886463200979656,
+  "hosted_rebased_pervertex": 1886463200679500,
+  "conservative_pervertex_used": 4764410190704224,
+  "retained_prior_overcharge": {
+    "sha256": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+    "previous_pervertex_allowance": 2877946989724568,
+    "added_complete_new_pervertex": 1886463200979656,
+    "policy": "Retain old allowance and add entire fresh mixed recount."
+  },
+  "finite": {
+    "physical_stock_bits": 2641,
+    "router_bits": 7985,
+    "literal_bits": 35282,
+    "physical_row_coefficient": 16467,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. All three providers use fresh hash-bound independent all-column/frame/phase/normalization admission. Shared compiler uses conservative maxima; parent is geometry/overcharge only. All-size compiler, hosting, precision/tape and analytic transfer remain conditional."
+}
diff --git a/research/layered-joint-owners/evidence/global/global/hosted/HOSTED.json b/research/layered-joint-owners/evidence/global/global/hosted/HOSTED.json
new file mode 100644
index 0000000000..21cfb9cd96
--- /dev/null
+++ b/research/layered-joint-owners/evidence/global/global/hosted/HOSTED.json
@@ -0,0 +1,52 @@
+{
+  "status": "EMITTED_MIXED_PROVIDER_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE",
+  "template_sha256": "2f11d6588a4014dbc12b7459c4c5f87869a826dc0b236db122342d9ffccb5678",
+  "parent_template_sha256": "7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3",
+  "live": 7168,
+  "physical": 7670,
+  "global_profile": {
+    "1": 183025,
+    "2": 29808,
+    "3": 31249,
+    "4": 11088,
+    "5": 4032,
+    "8": 576,
+    "28": 1,
+    "32": 2,
+    "48": 2398
+  },
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "hosted_residuals": 35424,
+  "banks_per_stage": [
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0
+  ],
+  "entering_helper_roles": 18576,
+  "unique_actual_73column_sigmas": 8428,
+  "sigma_stream_sha256": "ef0744394ad29fbf24782ebc5e06bf9b7dbf0430356c1a3d7f2b225a2357fd70",
+  "cross_replica_helper_roles": 26449,
+  "asynchronous_order_sha256": "2acd6b2004be3d3ef6645f3c968feb22b5167c400bb49eb446821e5cb7af6eee",
+  "source_artifacts": {
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "providers/gauge44/CANONICAL-WORD.json.gz": "72a4952751383e2a5e84b967f1e76fdfda003fe5592df357a599232e586817e3",
+    "providers/gauge44/LOCAL-PROGRAMS.json.gz": "61a30dfb8f63a7d1b5d8ef5b7ded2b2440d8998151ee5686defc01fcc93088e3",
+    "providers/gauge44/LOCAL-CHECKS.json": "b855ab7f3ea15a2d318bfc2f5aa4612ea76c019fa91cf64bd99903cf646b5e0c",
+    "providers/gauge44/INDEPENDENT-LOCAL-REPLAY.json": "c7ec4af7ccdf4230a4e277913d30ee41f2cc592d2360e008a18d11abd975b630",
+    "providers/gauge44/RESIDUAL-ADAPTERS.json": "0f2f39d58e7fb0844369dc0ea25e98ba35f0da9de4ee815015df66fad94af936",
+    "providers/gauge44/CLIFFORD-RECIPES.json": "b23cb8aac87f19a27ac5c982022bec10bcb7f02774182b8c3ef8e529a167c1b0",
+    "providers/gauge44/CLIFFORD-REVIEW.json": "c17864a376f0f6293d2dd97436ea3cd4e9ba98762d5882e06ab0480613cf1ff3"
+  },
+  "provider_counts": {
+    "gauge44": 72
+  },
+  "scope": "Two actual verified plain/width-seven providers dispatched per complete invocation; independent controller/spectator/normalization and complete finite invoice admission required."
+}
diff --git a/research/layered-joint-owners/evidence/layered/STEPS.json b/research/layered-joint-owners/evidence/layered/STEPS.json
new file mode 100644
index 0000000000..391cd84f7b
--- /dev/null
+++ b/research/layered-joint-owners/evidence/layered/STEPS.json
@@ -0,0 +1,42 @@
+[
+  {
+    "step": "pivot-swap",
+    "exit_code": 0,
+    "seconds": 6.842
+  },
+  {
+    "step": "cold44-exact",
+    "exit_code": 0,
+    "seconds": 1.317
+  },
+  {
+    "step": "layer-end-controls",
+    "exit_code": 0,
+    "seconds": 38.077
+  },
+  {
+    "step": "native",
+    "exit_code": 0,
+    "seconds": 0.935
+  },
+  {
+    "step": "ledgers",
+    "exit_code": 0,
+    "seconds": 0.626
+  },
+  {
+    "step": "local-replay",
+    "exit_code": 0,
+    "seconds": 5.326
+  },
+  {
+    "step": "wrappers",
+    "exit_code": 0,
+    "seconds": 1.537
+  },
+  {
+    "step": "phases",
+    "exit_code": 0,
+    "seconds": 94.682
+  }
+]
diff --git a/research/layered-joint-owners/evidence/layered/controls/COLD-END-CONTROLS.json b/research/layered-joint-owners/evidence/layered/controls/COLD-END-CONTROLS.json
new file mode 100644
index 0000000000..42fbc86ee0
--- /dev/null
+++ b/research/layered-joint-owners/evidence/layered/controls/COLD-END-CONTROLS.json
@@ -0,0 +1,65 @@
+{
+ "status": "PASS_COLD_END_RAW_WORD_CONTROLS",
+ "word": "/home/jeremydiviney/intmult/build/contribution/layered-joint-full-replay/layered/layers/FULL-WORD.json.gz",
+ "rejected": [
+  "premix placed in the zero-frame precondition (before the cold wrappers)",
+  "one premix gate dropped (the compensation then reads a cold-ended helper)",
+  "one lower-frame cleanup gate dropped (gate and its early_cleanup entry)",
+  "one FULL-remainder gate dropped",
+  "lower-frame gate coefficient changed",
+  "lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)",
+  "lower-frame gate frame below its registers' frames",
+  "cold end at another dim-4 frame",
+  "profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)",
+  "extra cold end on a premixed partner (the compensation reads it before its wrapper)",
+  "refactored-cleanup marker removed (literal-inverse rule applies)",
+  "remainder gate retargeted to a target register",
+  "non-dyadic remainder coefficient",
+  "profile not updated (paid climbs misreported)",
+  "entering end 537: lower-frame gate dropped (gate and its early_cleanup entry)",
+  "entering end 537: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)",
+  "entering end 537: end at another hyperplane",
+  "entering end 549: lower-frame gate dropped (gate and its early_cleanup entry)",
+  "entering end 549: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)",
+  "entering end 549: end at another hyperplane",
+  "entering end 560: premix gate dropped",
+  "entering end 560: premix gate at frame [] instead of its entrance E",
+  "entering end 560: premix gate moved into the zero-frame precondition",
+  "entering end 560: lower-frame gate dropped (gate and its early_cleanup entry)",
+  "entering end 560: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)",
+  "entering end 560: end at another hyperplane",
+  "entering end 561: lower-frame gate dropped (gate and its early_cleanup entry)",
+  "entering end 561: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)",
+  "entering end 561: end at another hyperplane",
+  "entering end 572: lower-frame gate dropped (gate and its early_cleanup entry)",
+  "entering end 572: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)",
+  "entering end 572: end at another hyperplane",
+  "entering end 573: lower-frame gate dropped (gate and its early_cleanup entry)",
+  "entering end 573: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)",
+  "entering end 573: end at another hyperplane",
+  "entering end 597: premix gate dropped",
+  "entering end 597: premix gate at frame [] instead of its entrance E",
+  "entering end 597: premix gate moved into the zero-frame precondition",
+  "entering end 597: lower-frame gate dropped (gate and its early_cleanup entry)",
+  "entering end 597: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)",
+  "entering end 597: end at another hyperplane",
+  "entering end 599: premix gate dropped",
+  "entering end 599: premix gate at frame [] instead of its entrance E",
+  "entering end 599: premix gate moved into the zero-frame precondition",
+  "entering end 599: lower-frame gate dropped (gate and its early_cleanup entry)",
+  "entering end 599: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)",
+  "entering end 599: end at another hyperplane",
+  "dim-8 cold end 310 (frame [256, 128, 66, 34, 16, 8, 6, 1]) at another dim-8 frame",
+  "dim-8 cold end 310 (frame [256, 128, 66, 34, 16, 8, 6, 1]): one lower-frame gate dropped (gate and its early_cleanup entry)",
+  "dim-8 cold end 310 (frame [256, 128, 66, 34, 16, 8, 6, 1]): profile pin (end dropped)",
+  "dim-8 cold end 311 (frame [256, 128, 72, 40, 24, 4, 2, 1]) at another dim-8 frame",
+  "dim-8 cold end 311 (frame [256, 128, 72, 40, 24, 4, 2, 1]): one lower-frame gate dropped (gate and its early_cleanup entry)",
+  "dim-8 cold end 311 (frame [256, 128, 72, 40, 24, 4, 2, 1]): profile pin (end dropped)",
+  "dim-8 cold end 327 (frame [256, 128, 66, 34, 18, 10, 6, 1]) at another dim-8 frame",
+  "dim-8 cold end 327 (frame [256, 128, 66, 34, 18, 10, 6, 1]): one lower-frame gate dropped (gate and its early_cleanup entry)",
+  "dim-8 cold end 327 (frame [256, 128, 66, 34, 18, 10, 6, 1]): profile pin (end dropped)",
+  "dim-8 cold end 518 (frame [256, 128, 96, 16, 8, 4, 2, 1]) at another dim-8 frame",
+  "dim-8 cold end 518 (frame [256, 128, 96, 16, 8, 4, 2, 1]): one lower-frame gate dropped (gate and its early_cleanup entry)",
+  "dim-8 cold end 518 (frame [256, 128, 96, 16, 8, 4, 2, 1]): profile pin (end dropped)"
+ ]
+}
diff --git a/research/layered-joint-owners/evidence/layered/local/CLIFFORD-REVIEW.json b/research/layered-joint-owners/evidence/layered/local/CLIFFORD-REVIEW.json
new file mode 100644
index 0000000000..7e95b65805
--- /dev/null
+++ b/research/layered-joint-owners/evidence/layered/local/CLIFFORD-REVIEW.json
@@ -0,0 +1,19 @@
+{
+  "status": "PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES",
+  "canonical_word_sha256": "72a4952751383e2a5e84b967f1e76fdfda003fe5592df357a599232e586817e3",
+  "frames": 1041,
+  "directed_edges": 3017,
+  "ranks": {
+    "1": 2035,
+    "2": 406,
+    "3": 398,
+    "8": 16,
+    "4": 148,
+    "5": 14
+  },
+  "endpoint_adapters": 224,
+  "all_child_equalities_include_global_phase": true,
+  "recipe_sha256": "b23cb8aac87f19a27ac5c982022bec10bcb7f02774182b8c3ef8e529a167c1b0",
+  "seconds": 94.64054721395951,
+  "scope": "Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations."
+}
diff --git a/research/layered-joint-owners/evidence/layered/local/INDEPENDENT-LOCAL-REPLAY.json b/research/layered-joint-owners/evidence/layered/local/INDEPENDENT-LOCAL-REPLAY.json
new file mode 100644
index 0000000000..2738599bff
--- /dev/null
+++ b/research/layered-joint-owners/evidence/layered/local/INDEPENDENT-LOCAL-REPLAY.json
@@ -0,0 +1,71 @@
+{
+  "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY",
+  "canonical_word_sha256": "72a4952751383e2a5e84b967f1e76fdfda003fe5592df357a599232e586817e3",
+  "local_programs_sha256": "61a30dfb8f63a7d1b5d8ef5b7ded2b2440d8998151ee5686defc01fcc93088e3",
+  "v": 112,
+  "helpers": 492,
+  "local": {
+    "forward": {
+      "all_exact_columns": 716,
+      "prefix_l1_upper": "8008832819811317/2",
+      "prefix_bits_upper": 52,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    },
+    "backward": {
+      "all_exact_columns": 716,
+      "prefix_l1_upper": "5318217944347079857738781/16",
+      "prefix_bits_upper": 79,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    }
+  },
+  "paid_profiles": {
+    "forward": {
+      "1": 2542,
+      "4": 154,
+      "8": 8,
+      "3": 434,
+      "2": 414,
+      "5": 56
+    },
+    "backward": {
+      "1": 2542,
+      "4": 154,
+      "8": 8,
+      "3": 434,
+      "2": 414,
+      "5": 56
+    }
+  },
+  "entering_helpers": 204,
+  "cold_hyperplane_ended_helpers": 54,
+  "negative_controls_rejected": [
+    "wrong_scale",
+    "missing_center",
+    "wrong_common_frame",
+    "wrong_child_rank",
+    "missing_pre_wrapper",
+    "missing_post_wrapper",
+    "wrapper_with_wrong_frame",
+    "wrapper_in_wrong_phase",
+    "wrapper_on_a_data_register",
+    "wrapper_on_a_target_register",
+    "wrapper_on_a_centre_register",
+    "hpe_pre_wrapper_resolved_to_full_recipe",
+    "hpe_post_wrapper_without_terminal_frame",
+    "hpe_post_wrapper_wrong_terminal_frame",
+    "hpe_tail_gate_at_full_frame",
+    "hpe_tail_climb_dropped",
+    "hpe_helper_exit_adapter_to_full",
+    "hpe_tail_gate_moved_into_full_cleanup",
+    "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter",
+    "cold_hpe_pre_wrapper_dropped",
+    "cold_hpe_post_wrapper_replaced_by_exit_adapter",
+    "cold_hpe_pre_wrapper_resolved_to_cold_full_convention",
+    "cold_hpe_wrapper_with_nonzero_entrance",
+    "cold_hpe_post_wrapper_wrong_terminal_frame",
+    "cold_hpe_premix_gate_before_pre_wrapper"
+  ],
+  "scope": "Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate."
+}
diff --git a/research/layered-joint-owners/evidence/layered/local/LOCAL-CHECKS.json b/research/layered-joint-owners/evidence/layered/local/LOCAL-CHECKS.json
new file mode 100644
index 0000000000..9ea1585a9d
--- /dev/null
+++ b/research/layered-joint-owners/evidence/layered/local/LOCAL-CHECKS.json
@@ -0,0 +1,36 @@
+{
+  "forward": {
+    "sha256": "23078c4401a226135bbf3839da45829a779ca741390eb9636ae062bd57585223",
+    "events": 25250,
+    "scalar_macros": 20038,
+    "real_component_primitive_bound": 200930,
+    "paid_profile": {
+      "1": 2542,
+      "2": 414,
+      "3": 434,
+      "4": 154,
+      "5": 56,
+      "8": 8
+    },
+    "all_columns": 716,
+    "private_centers_cleared": true,
+    "private_coefficient_stream_cleared_after_each_macro": true
+  },
+  "backward": {
+    "sha256": "be4fa2d2da35651905d8e5cab54eb607bee66018adbbe9bff8eca446298de1be",
+    "events": 25250,
+    "scalar_macros": 20038,
+    "real_component_primitive_bound": 200978,
+    "paid_profile": {
+      "1": 2542,
+      "2": 414,
+      "3": 434,
+      "4": 154,
+      "5": 56,
+      "8": 8
+    },
+    "all_columns": 716,
+    "private_centers_cleared": true,
+    "private_coefficient_stream_cleared_after_each_macro": true
+  }
+}
diff --git a/research/layered-joint-owners/evidence/prior-base-make-verify.log.gz b/research/layered-joint-owners/evidence/prior-base-make-verify.log.gz
new file mode 100644
index 0000000000..ecb5258412
Binary files /dev/null and b/research/layered-joint-owners/evidence/prior-base-make-verify.log.gz differ
diff --git a/research/layered-joint-owners/evidence/replay-logs.tar.gz b/research/layered-joint-owners/evidence/replay-logs.tar.gz
new file mode 100644
index 0000000000..fca0e7cbb1
Binary files /dev/null and b/research/layered-joint-owners/evidence/replay-logs.tar.gz differ
diff --git a/research/layered-joint-owners/evidence/word/STEPS.json b/research/layered-joint-owners/evidence/word/STEPS.json
new file mode 100644
index 0000000000..4293dff0e8
--- /dev/null
+++ b/research/layered-joint-owners/evidence/word/STEPS.json
@@ -0,0 +1,42 @@
+[
+  {
+    "step": "shadow-early",
+    "exit_code": 0,
+    "seconds": 0.195
+  },
+  {
+    "step": "shadow-prefix",
+    "exit_code": 0,
+    "seconds": 0.251
+  },
+  {
+    "step": "gauge-forward",
+    "exit_code": 0,
+    "seconds": 0.285
+  },
+  {
+    "step": "port0",
+    "exit_code": 0,
+    "seconds": 0.244
+  },
+  {
+    "step": "port1",
+    "exit_code": 0,
+    "seconds": 0.257
+  },
+  {
+    "step": "port2",
+    "exit_code": 0,
+    "seconds": 0.255
+  },
+  {
+    "step": "port3",
+    "exit_code": 0,
+    "seconds": 0.251
+  },
+  {
+    "step": "cold44-exact",
+    "exit_code": 0,
+    "seconds": 1.44
+  }
+]
diff --git a/research/layered-joint-owners/independent_owners.py b/research/layered-joint-owners/independent_owners.py
new file mode 100644
index 0000000000..2e7baa0135
--- /dev/null
+++ b/research/layered-joint-owners/independent_owners.py
@@ -0,0 +1,146 @@
+"""Independent solver-free whole-owner and all-p moment audit.
+No import from optimizer, emitter, or source checker. Discovery is not admission.
+"""
+from pathlib import Path
+from collections import Counter,defaultdict
+import argparse,json,gzip,hashlib,tempfile,copy
+if not __debug__:
+ raise RuntimeError('Assertions must remain enabled')
+
+read=lambda p:json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+
+def audit(main,parent,owners_path,comparison_paths=None):
+ pkg=parent;t=read(pkg/'evidence/global/GLOBAL-TEMPLATE.json.gz');plan=read(pkg/'data/PLAN.json');canon=read(pkg/'evidence/local/CANONICAL-WORD.json.gz')
+ phasefile=main/'research/frame-sa504/inputs/data-base/work/complex-nine-native/DATA-PHASES.json';ph=read(phasefile)
+ assert sha(phasefile)==t['exact_data_phase_recipe_sha256']=='c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa'
+ assert (t['m'],t['live'],t['physical'],canon['v'],canon['h'],canon['R'])==(73,7168,7670,112,9,492)
+ assert sha(pkg/'evidence/local/CANONICAL-WORD.json.gz')==t['local_providers']['gauge44']['canonical_word_sha256']
+ widths=[len(canon['frames'][canon['final'][224+h]])-len(canon['frames'][canon['start'][224+h]]) for h in range(492)]
+ assert widths==plan['provider_registry']['gauge44']['widths']==t['local_providers']['gauge44']['widths']
+ assert Counter(widths)==Counter({4:52,5:48,7:42,8:116,9:234})
+ localprofile={int(r):n for r,n in canon['local_profile'].items()}
+ assert localprofile=={int(r):n for r,n in plan['provider_registry']['gauge44']['actual_paid_profile'].items()}
+ # Establish indivisible call blocks and all literal replica-local touches.
+ order=[tuple(x) for x in plan['order']]
+ assert order==[(c['stage'],c['replica']) for c in t['calls']] and len(set(order))==72
+ assert all([s for s,r in order if r==rep]==list(range(9)) for rep in range(8))
+ stagepair={e['stage']:e['pair'] for e in t['recipe'] if e['kind']=='local'}
+ positive_children={i for i,x in enumerate(ph['recipes'][0]['idle_children']) if x['rank']};assert positive_children==set(range(18))
+ last={};windows={};callpos={};pairs={};sides={};block=-1
+ for pos,e in enumerate(t['execution_schedule']):
+  if 'replica' not in e:continue
+  rep=e['replica']
+  if e['kind']=='local_cover_sweep':
+   block+=1;assert e['time']==block and order[block]==(e['stage'],rep)
+   callpos[e['time']]=pos;last[rep,stagepair[e['stage']]]=pos
+  assert e['time']==block
+  if e['kind']=='bridge':last[rep,e['src']]=last[rep,e['dst']]=pos
+  elif e['kind']=='idle_cover_sweep':
+   for side,ch in enumerate(e['child_indices']):
+    if ch not in positive_children:continue
+    pairs[ch]=e['pair'];sides[ch]=side;windows[rep,ch]=(last.get((rep,e['pair']),-1),pos)
+ assert block==71 and len(windows)==8*18
+ caps={}
+ for rep in range(8):
+  for ch in range(18):
+   dims={int(x['idle_children'][ch]['rank']) for x in ph['recipes']};assert len(dims)==1;cap=dims.pop()
+   lo,hi=windows[rep,ch];allowed=[tm for tm,pos in callpos.items() if lo<pos<hi]
+   assert plan['windows'][f'{rep},{ch}']==[cap,allowed]
+   for port in range(112):caps[rep,ch,port]=cap
+ assert plan['pairs']=={str(k):v for k,v in pairs.items()} and plan['sides']=={str(k):v for k,v in sides.items()}
+ bases={}
+ for port,q in enumerate(canon['ports']):
+  assert ph['recipes'][port]['port']==port and q==ph['recipes'][port]['q']
+  z=next(i for i in range(9) if not(q>>i)&1);u=q^(1<<z);ix=list(range(9));ix[0],ix[z]=ix[z],ix[0]
+  B=[(1<<i)^(u if u>>i&1 else 0) for i in ix]+[1<<i for i in range(9,73)]
+  assert len(set(B))==73 and all((x&y).bit_count()%2==int(i==j) for i,x in enumerate(B) for j,y in enumerate(B))
+  bases[port]=B
+ def mapping(path):
+  roles=read(path);seen=set();percall=defaultdict(set);used=defaultdict(set);occupied=[];cross=0;small=0;sigmas=set();dig=hashlib.sha256()
+  for z in sorted(roles,key=lambda z:(z['time'],z['helper'])):
+   tm,h=z['time'],z['helper'];assert 0<=tm<72 and 0<=h<492
+   s,r=order[tm];assert (z['stage'],z['replica'])==(s,r);assert (tm,h) not in seen;seen.add((tm,h))
+   rep,ch,port=z['owner_replica'],z['child'],z['port'];assert 0<=rep<8 and 0<=ch<18 and 0<=port<112
+   assert z['copy']==rep*112+port
+   f=rep*896+(2*pairs[ch]+sides[ch])*112+port;assert f==z['family'] and 0<=f<7168
+   assert f not in percall[tm];percall[tm].add(f)
+   datafamilies={v[0] for v in t['calls'][tm]['owners'][:224]};assert f not in datafamilies
+   assert windows[rep,ch][0]<callpos[tm]<windows[rep,ch][1]
+   w=widths[h];assert z['width']==w and 0<=z['offset'] and z['offset']+w<=caps[rep,ch,port]
+   cells=set(range(z['offset'],z['offset']+w));g=rep,ch,port;assert not cells&used[g];used[g]|=cells
+   B=bases[port];pending=list(map(int,ph['recipes'][port]['idle_children'][ch]['orthogonal_axes']));assert len(pending)==caps[g]
+   assert len(set(pending))==len(pending) and all(x in B for x in pending)
+   active=[B.index(x) for x in pending[z['offset']:z['offset']+w]];spectators=[i for i in range(73) if i not in active][:9-w]
+   perm=active+spectators+[i for i in range(73) if i not in active and i not in spectators]
+   assert sorted(perm)==list(range(73)) and len(set(active+spectators))==9
+   sigma=tuple(B[i] for i in perm);assert sigma[:w]==tuple(pending[z['offset']:z['offset']+w])
+   sigmas.add(sigma);d=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();dig.update(json.dumps([s,r,h,f,d],separators=(',',':')).encode()+b'\n')
+   cross+=r!=rep;small+=w<9
+  assert len(roles)==len(seen)==35424 and all(len(v)==492 for v in percall.values())
+  assert all(v==set(range(len(v))) for v in used.values())
+  idle=Counter(caps[g]-len(used[g]) for g in caps) # zero-pad every same catalog coordinate
+  profile=Counter({r:72*n for r,n in localprofile.items()})+Counter({r:n for r,n in idle.items() if r})
+  assert sum(r*n for r,n in profile.items())==520704 and 73*7168-520704==2560 and 73**2>2*max(profile)**2
+  return {'owners_sha256':sha(path),'idle':dict(sorted(idle.items())),'profile':dict(sorted(profile.items())),'cross_replica':cross,'entering_or_cold_lower_width':small,'sigmas':len(sigmas),'sigma_digest':dig.hexdigest(),'roles':roles}
+ old=mapping(pkg/'data/OWNERS.json.gz');new=mapping(owners_path)
+ assert old['profile']=={int(k):v for k,v in read(pkg/'evidence/audit/OWNERS-AND-PROFILE.json')['paid_profile'].items()}
+ assert old['sigma_digest']==read(pkg/'evidence/global/HOSTED.json')['sigma_stream_sha256']
+ def compare(base):
+  om={(z['time'],z['helper']):z for z in base['roles']}
+  changed=[z for z in new['roles'] if z!=om[z['time'],z['helper']]]
+  di={k:new['profile'].get(k,0)-base['profile'].get(k,0) for k in sorted(set(new['profile'])|set(base['profile']))};di={k:v for k,v in di.items() if v}
+  assert sum(k*v for k,v in di.items())==0
+  margins=[sum(n*max(r-k,0) for r,n in new['idle'].items())-sum(n*max(r-k,0) for r,n in base['idle'].items()) for k in range(74)]
+  assert margins[0]==margins[-1]==0 and min(margins)>=0 and max(margins)>0
+  return {'baseline':{k:v for k,v in base.items() if k!='roles'},'profile_delta':di,'stoploss_delta':margins,'changed_records':len(changed),'changed_by_call':dict(Counter(z['time'] for z in changed)),'strict_all_p_improvement':True}
+ comparisons={'PR656':compare(old)}
+ for name,path in (comparison_paths or {}).items():
+  assert name not in comparisons and name
+  comparisons[name]=compare(mapping(path))
+ reference=comparisons['PR656']
+ return {'status':'PASS_SOLVER_FREE_LITERAL_WHOLE_FAMILY_AND_ALL_P_MOMENT_AUDIT','source_plan_sha256':sha(pkg/'data/PLAN.json'),'source_template_sha256':sha(pkg/'evidence/global/GLOBAL-TEMPLATE.json.gz'),'canonical_word_sha256':sha(pkg/'evidence/local/CANONICAL-WORD.json.gz'),'data_phases_sha256':sha(phasefile),'candidate_input':owners_path.name,'baseline':reference['baseline'],'candidate':{k:v for k,v in new.items() if k!='roles'},'profile_delta':reference['profile_delta'],'stoploss_delta':reference['stoploss_delta'],'changed_records':reference['changed_records'],'changed_by_call':reference['changed_by_call'],'comparisons':comparisons,'scope':'Independent mapping/capacity/literal-bridge-window/active-family/spectator-map/profile and strict all-p moment proof against every named baseline. Does not replay unchanged local scalar/Clifford providers, global coefficient invoice, or outer admission.'}
+
+def mutation_controls(main,parent,owners_path,work):
+ rows=read(owners_path);tests=[]
+ def reject(name,fn):
+  x=copy.deepcopy(rows);fn(x)
+  with tempfile.TemporaryDirectory(prefix='owner-mutation-',dir=work) as td:
+   q=Path(td)/'OWNERS.json.gz';q.write_bytes(gzip.compress(json.dumps(x,separators=(',',':')).encode(),mtime=0))
+   try:audit(main,parent,q)
+   except (AssertionError,IndexError,KeyError,ValueError):tests.append(name);return
+   raise AssertionError('Mutation accepted: '+name)
+ reject('wrong helper residual width',lambda x:x[0].__setitem__('width',x[0]['width']-1))
+ reject('offset exceeds actual pending child',lambda x:x[0].__setitem__('offset',73))
+ reject('family formula alias',lambda x:x[0].__setitem__('family',x[0]['family']^1))
+ reject('duplicate complete-call helper',lambda x:x[1].__setitem__('helper',x[0]['helper']))
+ def overlap(x):
+  groups=defaultdict(list)
+  for z in x:groups[z['owner_replica'],z['child'],z['port']].append(z)
+  zs=next(v for v in groups.values() if len(v)>1)
+  zs[1]['offset']=zs[0]['offset']
+ reject('overlapping footprints across complete calls',overlap)
+ # Preserve named family but borrow it after its literal idle window ends.
+ def window(x):
+  z=x[0];plan=read(parent/'data/PLAN.json');allowed=plan['windows'][f"{z['owner_replica']},{z['child']}"][1]
+  tm=next(t for t in range(72) if t not in allowed);z.update(time=tm,stage=plan['order'][tm][0],replica=plan['order'][tm][1])
+ reject('whole-family borrowing outside literal idle window',window)
+ return tests
+
+def main():
+ a=argparse.ArgumentParser(description=__doc__)
+ a.add_argument('--main',type=Path,required=True,help='Pinned main checkout containing the exact DATA-PHASES artifact')
+ a.add_argument('--parent',type=Path,required=True,help='Pinned PR656 baseline snapshot from a fresh PR656 replay')
+ a.add_argument('--owners',type=Path,required=True)
+ a.add_argument('--out',type=Path,required=True)
+ a.add_argument('--compare',action='append',default=[],metavar='NAME=OWNERS_PATH',help='Additional baseline owner map, independently checked under the same literal controller and provider')
+ a.add_argument('--mutation-controls',action='store_true')
+ x=a.parse_args();comparisons={}
+ for value in x.compare:
+  name,sep,path=value.partition('=');assert sep and name and path and name not in comparisons and name!='PR656'
+  comparisons[name]=Path(path)
+ r=audit(x.main,x.parent,x.owners,comparisons)
+ if x.mutation_controls:r['mutation_controls_rejected']=mutation_controls(x.main,x.parent,x.owners,x.out.parent)
+ x.out.write_text(json.dumps(r,indent=2)+'\n')
+ print(json.dumps({k:r[k] for k in ('status','candidate_input','profile_delta','changed_records','scope')},indent=2))
+if __name__=='__main__':main()
diff --git a/research/layered-joint-owners/packing_ceiling.py b/research/layered-joint-owners/packing_ceiling.py
new file mode 100644
index 0000000000..b23cdac114
--- /dev/null
+++ b/research/layered-joint-owners/packing_ceiling.py
@@ -0,0 +1,58 @@
+"""Exact relaxed ceiling for owner changes with fixed local profile/capacities.
+
+For 0<p<1 and 0<=x<=C, x**p >= x*C**(p-1). Thus concentrating the
+fixed idle rank in C-dimensional remainders minimizes its homogeneous moment.
+This relaxation need not have a feasible assignment. It bounds only this fixed
+local provider and controller, not other circuits or multiplication algorithms.
+"""
+import argparse
+from collections import Counter
+from decimal import Decimal, localcontext
+from fractions import Fraction
+import json
+from pathlib import Path
+import subprocess
+import sys
+
+
+def main():
+    if not __debug__:
+        raise RuntimeError('Assertions required')
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--parent', type=Path, required=True)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args(); a.out.mkdir(exist_ok=False)
+    plan = json.loads((a.parent / 'data/PLAN.json').read_text())
+    assert (plan['M'], plan['live'], plan['deficit']) == (73, 7168, 2560)
+    local = {int(r): n for r, n in plan['provider_registry']['gauge44']['actual_paid_profile'].items()}
+    profile = Counter({r: 72*n for r, n in local.items()})
+    maximum = max(cap for cap, _ in plan['windows'].values())
+    assert maximum == 48 and len(plan['order']) == 72
+    idle = 73*7168-2560-sum(r*n for r, n in profile.items())
+    assert idle == 115200 and idle % maximum == 0
+    profile[maximum] += idle // maximum
+    (a.out / 'RELAXED-PROFILE.json').write_text(json.dumps(dict(sorted(profile.items())), indent=2)+'\n')
+    subprocess.run([sys.executable, '-B', str(a.parent / 'independent/price_profile.py'),
+                    '--main', str(a.main), '--profile', str(a.out / 'RELAXED-PROFILE.json'),
+                    '--output', str(a.out / 'PRICE.json')], check=True)
+    price = json.loads((a.out / 'PRICE.json').read_text())
+    upper = Fraction(price['prices']['native']['root']['upper'])
+    assert 0 < upper < 1
+    ceiling = upper/(1+upper)
+    with localcontext() as ctx:
+        ctx.prec = 70
+        decimal = str(Decimal(ceiling.numerator)/Decimal(ceiling.denominator))
+    result = dict(status='PASS_EXACT_FIXED_PROVIDER_RELAXED_PACKING_CEILING',
+                  max_idle_dimension=maximum, fixed_idle_rank=idle, relaxed_idle={str(maximum): idle//maximum},
+                  native_root_upper=str(upper), kappa_upper_rational=str(ceiling),
+                  kappa_upper_decimal=decimal, feasible_assignment_claimed=False,
+                  scope='Upper bound for fixed local profile and controller capacities with retained outer transfer; '
+                        'not a universal multiplication bound. Exact root upper endpoint is independently signed. '
+                        'The retained outer transfer has kappa < b/(1+b).')
+    (a.out / 'CEILING.json').write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], decimal)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/layered-joint-owners/prepare.py b/research/layered-joint-owners/prepare.py
new file mode 100644
index 0000000000..61484fce7d
--- /dev/null
+++ b/research/layered-joint-owners/prepare.py
@@ -0,0 +1,67 @@
+"""Stage an owner-only delta for the unchanged, pinned Gauge44 verifier.
+
+This staging command does not admit a result. Run discovery, freeze the
+independently recomputed expectations, and then run strict admission.
+"""
+import argparse
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import shutil
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def digest(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def write(path, value):
+    path.write_text(json.dumps(value, indent=2) + '\n')
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--parent', type=Path, required=True)
+    parser.add_argument('--candidate', type=Path, required=True)
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    assert not args.out.exists()
+    shutil.copytree(args.parent, args.out, ignore=shutil.ignore_patterns('__pycache__'))
+    data = args.out / 'data'
+    plan = read(data / 'PLAN.json')
+    owners = args.candidate / 'OWNERS.json.gz'
+    roles = read(owners)
+    profile = read(args.candidate / 'PROFILE.json')
+    assert len(roles) == 72 * 492
+    assert sum(int(r) * n for r, n in profile.items()) == 520704
+    plan['profile'] = profile
+    plan['source_plan_sha256'] = digest(args.parent / 'data/PLAN.json')
+    fields = read(args.candidate / 'PLAN-OWNER-FIELDS.json')
+    plan['source_owners_sha256'] = fields['source_owners_sha256']
+    plan['assignment_sha256'] = hashlib.sha256(
+        json.dumps(roles, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+    plan['solver_status'] = 'frozen joint-call nomination from PR656; full global admission required'
+    # No dispatch, schedule, local provider, width or phase field changes.
+    write(data / 'PLAN.json', plan)
+    shutil.copyfile(owners, data / 'OWNERS.json.gz')
+    spec = read(data / 'SPEC.json')
+    spec['name'] = 'gauge44-joint-call-owners'
+    spec['data']['plan_sha256'] = digest(data / 'PLAN.json')
+    spec['data']['owners_sha256'] = digest(data / 'OWNERS.json.gz')
+    write(data / 'SPEC.json', spec)
+    write(args.out / 'DELTA-PROVENANCE.json', {
+        'parent_plan_sha256': digest(args.parent / 'data/PLAN.json'),
+        'parent_owners_sha256': digest(args.parent / 'data/OWNERS.json.gz'),
+        'candidate_owners_sha256': digest(owners),
+        'candidate_profile_sha256': digest(args.candidate / 'PROFILE.json'),
+        'scope': 'Only PLAN owner/profile bookkeeping, explicit OWNERS, and expected SPEC change. All verifier code is copied unchanged.'})
+    print(args.out)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/layered-joint-owners/search/group_owner_search.py b/research/layered-joint-owners/search/group_owner_search.py
new file mode 100644
index 0000000000..a171161be8
--- /dev/null
+++ b/research/layered-joint-owners/search/group_owner_search.py
@@ -0,0 +1,143 @@
+"""Joint multi-call nominations extending Jay Mosley's PR653 two-call model.
+
+Every accepted move passes the inherited literal owner checks and exact integer
+stop-loss inequalities. Solver output is not global admission. Apache-2.0.
+Prepared by Jeremy Diviney with substantial OpenAI Codex assistance.
+"""
+from joint_owner_search import *
+from joint_owner_passes import write_outputs
+
+
+def solve_group(inst, calls, seconds):
+    buckets = defaultdict(list)
+    oldmaps = {t: {g: (h, w) for h, (g, w) in inst.bycall[t].items()} for t in calls}
+    groups = set().union(*(inst.eligible[t] for t in calls))
+    for g in sorted(groups):
+        capacity = inst.caps[g] - inst.used[g] + sum(oldmaps[t].get(g, (None, 0))[1] for t in calls)
+        mask = sum((1 << i) for i, t in enumerate(calls) if g in inst.eligible[t])
+        buckets[capacity, mask].append(g)
+    cats = sorted(buckets)
+    widths = sorted(set(inst.widths))
+    inventory = Counter(inst.widths)
+    rhs = [len(buckets[key]) for key in cats] + [inventory[w] for _ in calls for w in widths]
+    equalrows = len(rhs)
+    oldremainders = [inst.caps[g] - inst.used[g] for g in groups]
+    rhs += [sum(max(r-k, 0) for r in oldremainders) for k in range(1, 48)]
+    columns, rows, cols, values, objective, bounds = [], [], [], [], [], []
+    for ci, (capacity, mask) in enumerate(cats):
+        options = [[0] + widths if mask & (1 << i) else [0] for i in range(len(calls))]
+        for assignment in itertools.product(*options):
+            if sum(assignment) > capacity:
+                continue
+            j = len(columns)
+            columns.append((ci, assignment))
+            rows.append(ci); cols.append(j); values.append(1)
+            for side, w in enumerate(assignment):
+                if w:
+                    rows.append(len(cats) + side * len(widths) + widths.index(w))
+                    cols.append(j); values.append(1)
+            remainder = capacity - sum(assignment)
+            for k in range(1, remainder):
+                rows.append(equalrows+k-1); cols.append(j); values.append(remainder-k)
+            objective.append((remainder * math.expm1(inst.baseline['b'] * math.log(73/remainder)) if remainder else 0) * 1e6)
+            bounds.append(len(buckets[capacity, mask]))
+    matrix = coo_matrix((values, (rows, cols)), shape=(len(rhs), len(columns))).tocsc()
+    rhs = np.asarray(rhs)
+    upper = np.concatenate((rhs[:equalrows], np.full(len(rhs)-equalrows, np.inf)))
+    started = time.monotonic()
+    result = milp(objective, integrality=np.ones(len(columns)), bounds=Bounds(np.zeros(len(columns)), bounds),
+                  constraints=LinearConstraint(matrix, rhs, upper),
+                  options={'time_limit': seconds, 'mip_rel_gap': 0.0, 'threads': 1})
+    report = dict(calls=list(calls), status=int(result.status), message=str(result.message),
+                  seconds=time.monotonic()-started, variables=len(columns), buckets=len(cats))
+    if result.x is None:
+        return report, None
+    x = np.rint(result.x).astype(np.int64)
+    assert np.max(np.abs(result.x-x)) < 1e-5
+    assert np.all(x >= 0) and np.all(x <= bounds)
+    assert np.all((matrix @ x)[:equalrows] == rhs[:equalrows])
+    assert np.all((matrix @ x)[equalrows:] >= rhs[equalrows:])
+    report.update(integer_equations_checked=True, mip_gap=float(result.mip_gap), mip_nodes=int(result.mip_node_count))
+    choices = defaultdict(Counter)
+    for count, (ci, assignment) in zip(x, columns):
+        choices[ci][assignment] += int(count)
+    assigned = {t: defaultdict(list) for t in calls}
+    for ci, key in enumerate(cats):
+        pending = []
+        for g in buckets[key]:
+            assignment = tuple(oldmaps[t].get(g, (None, 0))[1] for t in calls)
+            if not choices[ci][assignment]:
+                pending.append(g)
+                continue
+            choices[ci][assignment] -= 1
+            for t, w in zip(calls, assignment):
+                if w: assigned[t][w].append(g)
+        remaining = deque(a for a, count in sorted(choices[ci].items()) for _ in range(count))
+        assert len(remaining) == len(pending)
+        for g in pending:
+            for t, w in zip(calls, remaining.popleft()):
+                if w: assigned[t][w].append(g)
+    roles = [dict(z) for z in inst.roles if z['time'] not in calls]
+    for t in calls:
+        stage, replica = inst.plan['order'][t]
+        available = {w: set(gs) for w, gs in assigned[t].items()}
+        nominated = {}
+        for h, (g, w) in sorted(inst.bycall[t].items()):
+            if g in available[w]:
+                available[w].remove(g); nominated[h] = g
+        for h, w in enumerate(inst.widths):
+            if h not in nominated:
+                g = min(available[w]); available[w].remove(g); nominated[h] = g
+            g = nominated[h]; owner_replica, child, port = g
+            roles.append(dict(child=child, copy=owner_replica*112+port, family=inst.families[g], helper=h,
+                              offset=0, owner_replica=owner_replica, port=port, replica=replica, stage=stage, time=t, width=w))
+        assert not any(available.values())
+    grouped = defaultdict(list)
+    for role in roles: grouped[role['owner_replica'], role['child'], role['port']].append(role)
+    for group in grouped.values():
+        offset = 0
+        for role in sorted(group, key=lambda z: (z['time'], z['helper'])):
+            role['offset'] = offset; offset += role['width']
+    roles.sort(key=lambda z: (z['time'], z['helper']))
+    checked = inst.check(roles)
+    old, new = Counter(inst.baseline['idle']), Counter(checked['idle'])
+    margins = [sum(n*max(r-k, 0) for r, n in new.items()) - sum(n*max(r-k, 0) for r, n in old.items()) for k in range(49)]
+    assert margins[0] == margins[-1] == 0 and min(margins) >= 0
+    report.update(candidate=checked, gain_b=checked['b']-inst.baseline['b'], integer_stoploss_margins=margins,
+                  strict_majorization=max(margins)>0)
+    return report, roles
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--owners', type=Path, required=True)
+    ap.add_argument('--groups', type=int, default=120)
+    ap.add_argument('--size', type=int, choices=(2, 3, 4, 5), default=3)
+    ap.add_argument('--seconds', type=float, default=2)
+    ap.add_argument('--out', type=Path, required=True)
+    args = ap.parse_args(); args.out.mkdir(exist_ok=False)
+    inst = Instance(args.owners); inst.source_owners_path = args.owners
+    inst.source_head = '0805e78f5fecc700804d4766d7e3e1d7d7e6a2ba'
+    original = inst.baseline; steps = []; reports = []
+    defect = {g for g in inst.caps if 0 < inst.caps[g]-inst.used[g] < inst.caps[g]}
+    overlap = {(a,b): len(inst.eligible[a] & inst.eligible[b] & defect) for a,b in itertools.combinations(range(72), 2)}
+    pool = range(72)
+    if args.size == 5:
+        nonmax = {g for g in inst.caps if 0 < inst.caps[g]-inst.used[g] < 48}
+        pool = sorted(range(72), key=lambda t: (len(inst.eligible[t] & nonmax), -t), reverse=True)[:16]
+        overlap = {(a,b): len(inst.eligible[a] & inst.eligible[b] & nonmax) for a,b in itertools.combinations(range(72), 2)}
+    scored = [(sum(overlap[p] for p in itertools.combinations(calls, 2)), calls) for calls in itertools.combinations(sorted(pool), args.size)]
+    for _, calls in sorted(scored, reverse=True)[:args.groups]:
+        report, roles = solve_group(inst, calls, args.seconds); reports.append(report)
+        if roles is not None and report['strict_majorization']:
+            assert report['gain_b'] > 0
+            steps.append(report); inst.roles = roles; inst.used = Counter(); inst.bycall = defaultdict(dict)
+            for z in roles:
+                g = z['owner_replica'], z['child'], z['port']
+                inst.used[g] += z['width']; inst.bycall[z['time']][z['helper']] = g, z['width']
+            inst.baseline = inst.check(roles)
+            write_outputs(args.out, inst, original, steps)
+            print(json.dumps(dict(calls=calls, accepted=len(steps), b=inst.baseline['b'], gain=inst.baseline['b']-original['b'])), flush=True)
+        (args.out/'SEARCH.json').write_text(json.dumps(dict(groups=len(reports), reports=reports), indent=2)+'\n')
+    write_outputs(args.out, inst, original, steps)
+    print('DONE', len(reports), 'groups;', len(steps), 'accepted;', inst.baseline['b'], flush=True)
diff --git a/research/layered-joint-owners/search/joint_owner_passes.py b/research/layered-joint-owners/search/joint_owner_passes.py
new file mode 100644
index 0000000000..06785bb555
--- /dev/null
+++ b/research/layered-joint-owners/search/joint_owner_passes.py
@@ -0,0 +1,38 @@
+"""Finite paired-call majorization passes. Solver proposes; integers admit."""
+from joint_owner_search import *
+
+def write_outputs(out,inst,original,steps):
+ out.mkdir(parents=True,exist_ok=True);raw=packed(inst.roles);owner=out/'OWNERS.json.gz';owner.write_bytes(gzip.compress(raw,mtime=0))
+ profile={str(r):n for r,n in inst.baseline['profile'].items()}
+ (out/'PROFILE.json').write_text(json.dumps(profile,indent=2)+'\n')
+ fields={'profile':profile,'per_call_widths':[{'stage':s,'replica':r,'widths':inst.widths} for s,r in inst.plan['order']], 'assignment_sha256':hashlib.sha256(raw).hexdigest(),'assignment_sha256_semantics':'SHA256 sorted-key compact uncompressed OWNERS array','source_owners_sha256':sha(inst.source_owners_path),'provider_signatures':{'gauge44':{'widths':inst.widths,'profile':{int(r):n for r,n in inst.sig['actual_paid_profile'].items()},'source':'Frozen PR655 layered native signature'}}}
+ (out/'PLAN-OWNER-FIELDS.json').write_text(json.dumps(fields,indent=2)+'\n')
+ before=Counter(original['idle']);after=Counter(inst.baseline['idle'])
+ margins=[sum(n*max(r-k,0) for r,n in after.items())-sum(n*max(r-k,0) for r,n in before.items()) for k in range(49)]
+ assert min(margins)>=0 and margins[0]==margins[-1]==0
+ receipt={'status':'PASS_FINITE_JOINT_OWNER_NOMINATION_PENDING_GLOBAL_ADMISSION','source_head':inst.source_head,'geometry_and_native_head':'3e669dc7987cb2295a71664b77e110c0cd979a87','source_plan_sha256':sha(PKG/'data/PLAN.json'),'source_owners_sha256':sha(inst.source_owners_path),'owners_semantic_sha256':hashlib.sha256(raw).hexdigest(),'owners_sha256':sha(owner),'baseline':original,'candidate':inst.baseline,'integer_stoploss_margins':margins,'strict_majorization':max(margins)>0,'accepted_steps':steps,'roles':len(inst.roles),'rank_mass':520704,'deficit':2560,'live':7168,'M':73,'remaining_admission':'Fresh native-provider binding, all actual73-column charts/controller audit, finite invoice, exact moment and outer assembly. No supplier/global optimality claim.'}
+ (out/'RECEIPT.json').write_text(json.dumps(receipt,indent=2)+'\n')
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--owners',type=Path,required=True);ap.add_argument('--source-head',required=True);ap.add_argument('--pairs',type=int,default=120);ap.add_argument('--passes',type=int,default=3);ap.add_argument('--seconds',type=float,default=3);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args()
+ inst=Instance(a.owners);inst.source_owners_path=a.owners;inst.source_head=a.source_head;original=inst.baseline;steps=[];allreports=[]
+ for passno in range(a.passes):
+  scores=[]
+  for x,y in itertools.combinations(range(72),2):
+   score=sum(1 for g in inst.eligible[x]&inst.eligible[y] if 0<inst.caps[g]-inst.used[g]<inst.caps[g]);scores.append((score,x,y))
+  accepted=0
+  for _,x,y in sorted(scores,reverse=True)[:a.pairs]:
+   report,roles=inst.solve(x,y,a.seconds);report['pass']=passno+1;allreports.append(report)
+   if roles is not None and report['strict_majorization']:
+    assert report['gain_b']>0
+    steps.append(report);inst.roles=roles;inst.used=Counter();inst.bycall=defaultdict(dict)
+    for z in roles:
+     g=z['owner_replica'],z['child'],z['port'];inst.used[g]+=z['width'];inst.bycall[z['time']][z['helper']]=(g,z['width'])
+    inst.baseline=inst.check(inst.roles);accepted+=1;write_outputs(a.out,inst,original,steps)
+    print(json.dumps({'pass':passno+1,'pair':[x,y],'accepted':accepted,'b':inst.baseline['b'],'gain':inst.baseline['b']-original['b']}),flush=True)
+  (a.out/'SEARCH.json').write_text(json.dumps({'per_pass_pair_limit':a.pairs,'pass_limit':a.passes,'time_limit_per_pair':a.seconds,'reports':allreports,'accepted':len(steps),'source_owners_sha256':sha(inst.source_owners_path),'source_plan_sha256':sha(PKG/'data/PLAN.json'),'source_head':inst.source_head,'geometry_and_native_head':'3e669dc7987cb2295a71664b77e110c0cd979a87'},indent=2)+'\n')
+  print(json.dumps({'pass_completed':passno+1,'accepted':accepted,'b':inst.baseline['b']}),flush=True)
+  if not accepted:break
+ write_outputs(a.out,inst,original,steps)
+
+if __name__=='__main__':main()
diff --git a/research/layered-joint-owners/search/joint_owner_search.py b/research/layered-joint-owners/search/joint_owner_search.py
new file mode 100644
index 0000000000..8dacd26e0b
--- /dev/null
+++ b/research/layered-joint-owners/search/joint_owner_search.py
@@ -0,0 +1,147 @@
+"""Bounded two-call owner nomination, with full integer footprint checks.
+The optimizer is discovery only. A nomination needs fresh global admission.
+"""
+from pathlib import Path
+from collections import Counter, defaultdict, deque
+import argparse, gzip, hashlib, itertools, json, math, os, time
+import numpy as np
+from scipy.optimize import milp, Bounds, LinearConstraint
+from scipy.sparse import coo_matrix
+
+# Optional discovery only. Verification never imports NumPy, SciPy, or this file.
+PKG=Path(os.environ['GAUGE44_PARENT']).resolve()
+read=lambda p:json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+packed=lambda x:json.dumps(x,sort_keys=True,separators=(',',':')).encode()
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+
+def rate(profile):
+ lo,hi=0.,.02
+ for _ in range(60):
+  b=(lo+hi)/2
+  if sum(n*r*math.expm1(b*math.log(73/r)) for r,n in profile.items())<2560:lo=b
+  else:hi=b
+ return lo
+
+class Instance:
+ def __init__(self, owners=None):
+  self.plan=read(PKG/'data/PLAN.json');self.roles=read(owners or PKG/'data/OWNERS.json.gz')
+  self.sig=self.plan['provider_registry']['gauge44'];self.widths=self.sig['widths'];assert Counter(self.widths)=={4:52,5:48,7:42,8:116,9:234}
+  self.caps={};self.eligible=defaultdict(set);self.families={}
+  for key,(cap,times) in self.plan['windows'].items():
+   rep,ch=map(int,key.split(','))
+   for port in range(112):
+    g=rep,ch,port;self.caps[g]=cap
+    self.families[g]=rep*896+(2*self.plan['pairs'][str(ch)]+self.plan['sides'][str(ch)])*112+port
+    for t in times:self.eligible[t].add(g)
+  self.used=Counter();self.bycall=defaultdict(dict)
+  for z in self.roles:
+   g=z['owner_replica'],z['child'],z['port'];self.used[g]+=z['width'];self.bycall[z['time']][z['helper']]=(g,z['width'])
+  self.baseline=self.check(self.roles)
+ def check(self,roles):
+  used=defaultdict(set);seen=defaultdict(set);fams=defaultdict(set)
+  for z in roles:
+   t,h=z['time'],z['helper'];s,rep=self.plan['order'][t];g=z['owner_replica'],z['child'],z['port'];w=self.widths[h]
+   assert (z['stage'],z['replica'])==(s,rep) and z['width']==w and h not in seen[t];seen[t].add(h)
+   assert g in self.eligible[t] and z['family']==self.families[g] and z['copy']==g[0]*112+g[2]
+   assert z['family'] not in fams[t];fams[t].add(z['family'])
+   assert not(g[0]==rep and self.plan['pairs'][str(g[1])]==max(0,(s-1)//2))
+   cells=set(range(z['offset'],z['offset']+w));assert z['offset']>=0 and z['offset']+w<=self.caps[g] and not cells&used[g];used[g]|=cells
+  assert len(roles)==72*492 and all(seen[t]==set(range(492)) for t in range(72))
+  assert all(v==set(range(len(v))) for v in used.values())
+  idle=Counter(self.caps[g]-len(used[g]) for g in self.caps if self.caps[g]>len(used[g]))
+  profile=Counter({int(r):72*n for r,n in self.sig['actual_paid_profile'].items()});profile.update(idle)
+  assert sum(r*n for r,n in profile.items())==520704 and 73*7168-520704==2560
+  return {'idle':dict(sorted(idle.items())),'profile':dict(sorted(profile.items())),'b':rate(profile)}
+ def model(self,a,b):
+  gs=self.eligible[a]|self.eligible[b];buckets=defaultdict(list)
+  olda={g:w for g,w in self.bycall[a].values()};oldb={g:w for g,w in self.bycall[b].values()}
+  for g in sorted(gs):
+   c=self.caps[g]-self.used[g]+olda.get(g,0)+oldb.get(g,0)
+   typ=int(g in self.eligible[a])+2*int(g in self.eligible[b]);buckets[c,typ].append(g)
+  cats=sorted(buckets);widths=sorted(set(self.widths));columns=[];row=[];col=[];val=[];obj=[];ub=[]
+  constraints=[len(buckets[x]) for x in cats]+[Counter(self.widths)[w] for _ in range(2) for w in widths]
+  equalrows=len(constraints)
+  oldres=[self.caps[g]-self.used[g] for g in gs]
+  constraints.extend(sum(max(r-k,0) for r in oldres) for k in range(1,48))
+  for ci,(c,typ) in enumerate(cats):
+   for wa in ([0]+widths if typ&1 else [0]):
+    for wb in ([0]+widths if typ&2 else [0]):
+     if wa+wb>c:continue
+     j=len(columns);columns.append((ci,wa,wb));row.append(ci);col.append(j);val.append(1)
+     for side,w in enumerate((wa,wb)):
+      if w:row.append(len(cats)+side*len(widths)+widths.index(w));col.append(j);val.append(1)
+     r=c-wa-wb
+     for k in range(1,48):
+      if r>k:row.append(equalrows+k-1);col.append(j);val.append(r-k)
+     # Minimize exact same scalar pressure, scaled for solver conditioning.
+     obj.append((r*math.expm1(.0016522089943684118*math.log(73/r)) if r else 0)*1e6);ub.append(len(buckets[c,typ]))
+  A=coo_matrix((val,(row,col)),shape=(len(constraints),len(columns))).tocsc()
+  return cats,buckets,columns,np.asarray(obj),np.asarray(ub),A,np.asarray(constraints),equalrows
+ def solve(self,a,b,seconds):
+  cats,buckets,columns,obj,ub,A,rhs,equalrows=self.model(a,b);start=time.monotonic()
+  upper=np.concatenate((rhs[:equalrows],np.full(len(rhs)-equalrows,np.inf)))
+  res=milp(obj,integrality=np.ones(len(obj)),bounds=Bounds(np.zeros(len(obj)),ub),constraints=LinearConstraint(A,rhs,upper),options={'time_limit':seconds,'mip_rel_gap':0.0,'threads':1})
+  report={'pair':[a,b],'calls':[self.plan['order'][a],self.plan['order'][b]],'status':int(res.status),'message':str(res.message),'seconds':time.monotonic()-start,'variables':len(obj),'buckets':len(cats)}
+  if res.x is None:return report,None
+  x=np.rint(res.x).astype(np.int64);assert np.max(np.abs(res.x-x))<1e-5 and np.all((A@x)[:equalrows]==rhs[:equalrows]) and np.all((A@x)[equalrows:]>=rhs[equalrows:]) and np.all(x>=0) and np.all(x<=ub)
+  report.update({'integer_equations_checked':True,'mip_gap':float(res.mip_gap),'mip_nodes':int(res.mip_node_count)})
+  assigned={a:defaultdict(list),b:defaultdict(list)}
+  choices=defaultdict(Counter)
+  for count,(ci,wa,wb) in zip(x,columns):choices[ci][wa,wb]+=int(count)
+  oldmaps={t:{g:(h,w) for h,(g,w) in self.bycall[t].items()} for t in (a,b)}
+  for ci,key in enumerate(cats):
+   pending=[]
+   for g in buckets[key]:
+    pair=tuple(oldmaps[t].get(g,(None,0))[1] for t in (a,b))
+    if choices[ci][pair]:choices[ci][pair]-=1
+    else:pending.append(g);continue
+    for t,w in zip((a,b),pair):
+     if w:assigned[t][w].append(g)
+   left=deque(pair for pair,n in sorted(choices[ci].items()) for _ in range(n))
+   assert len(left)==len(pending)
+   for g in pending:
+    pair=left.popleft()
+    for t,w in zip((a,b),pair):
+     if w:assigned[t][w].append(g)
+  assert all(sum(len(v) for v in assigned[t].values())==492 for t in (a,b))
+  roles=[dict(z) for z in self.roles if z['time'] not in (a,b)]
+  for t in (a,b):
+   s,rep=self.plan['order'][t]
+   nominated={};available={w:set(gs) for w,gs in assigned[t].items()}
+   for h,(g,w) in sorted(self.bycall[t].items()):
+    if g in available[w]:available[w].remove(g);nominated[h]=g
+   for h,w in enumerate(self.widths):
+    if h not in nominated:g=min(available[w]);available[w].remove(g);nominated[h]=g
+    g=nominated[h];orp,ch,port=g
+    roles.append(dict(child=ch,copy=orp*112+port,family=self.families[g],helper=h,offset=0,owner_replica=orp,port=port,replica=rep,stage=s,time=t,width=w))
+   assert not any(available.values())
+  groups=defaultdict(list)
+  for z in roles:groups[z['owner_replica'],z['child'],z['port']].append(z)
+  for g,zs in groups.items():
+   off=0
+   for z in sorted(zs,key=lambda z:(z['time'],z['helper'])):z['offset']=off;off+=z['width']
+  roles.sort(key=lambda z:(z['time'],z['helper']))
+  checked=self.check(roles);report['candidate']=checked;report['gain_b']=checked['b']-self.baseline['b']
+  old=Counter(self.baseline['idle']);new=Counter(checked['idle']);ks=list(range(49))
+  margins=[sum(n*max(r-k,0) for r,n in new.items())-sum(n*max(r-k,0) for r,n in old.items()) for k in ks]
+  assert margins[0]==margins[-1]==0
+  report['integer_stoploss_margins']=margins;report['strict_majorization']=min(margins)>=0 and max(margins)>0
+  return report,roles
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--owners',type=Path);ap.add_argument('--pairs',type=int,default=50);ap.add_argument('--seconds',type=float,default=5);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();a.out.mkdir(parents=True,exist_ok=True)
+ inst=Instance(a.owners);scores=[]
+ for x,y in itertools.combinations(range(72),2):
+  common=inst.eligible[x]&inst.eligible[y]
+  score=sum(1 for g in common if 0<inst.caps[g]-inst.used[g]<inst.caps[g])
+  scores.append((score,x,y))
+ reports=[];best=inst.baseline['b'];beg=time.monotonic()
+ for _,x,y in sorted(scores,reverse=True)[:a.pairs]:
+  report,roles=inst.solve(x,y,a.seconds);reports.append(report)
+  print(json.dumps({k:report[k] for k in ('pair','status','seconds','gain_b','strict_majorization') if k in report}),flush=True)
+  if roles is not None and report['candidate']['b']>best+1e-16:
+   best=report['candidate']['b'];raw=packed(roles);(a.out/'BEST-OWNERS.json.gz').write_bytes(gzip.compress(raw,mtime=0));(a.out/'BEST-RECEIPT.json').write_text(json.dumps(report,indent=2)+'\n')
+  result={'status':'BOUNDED_TWO_CALL_NOMINATION_SEARCH','source_head':'3e669dc7987cb2295a71664b77e110c0cd979a87','source_plan_sha256':sha(PKG/'data/PLAN.json'),'source_owners_sha256':sha(PKG/'data/OWNERS.json.gz'),'baseline':inst.baseline,'pairs_requested':a.pairs,'pairs_checked':len(reports),'per_pair_time_limit':a.seconds,'reports':reports,'best_b':best,'seconds':time.monotonic()-beg,'scope':'Discovery only. Every returned integer owner nomination passes capacity/window/active-family/unique-helper/compacted-footprint checks. Requires fresh provider/global phase/finite invoice/moment/outer admission.'}
+  (a.out/'SEARCH.json').write_text(json.dumps(result,indent=2)+'\n')
+
+if __name__=='__main__':main()
diff --git a/research/layered-joint-owners/verify.py b/research/layered-joint-owners/verify.py
new file mode 100644
index 0000000000..5ce14e13b0
--- /dev/null
+++ b/research/layered-joint-owners/verify.py
@@ -0,0 +1,138 @@
+"""Replay the owner delta using every PR656 verifier and constructor unchanged.
+
+Standard library only; Python 3.11+ with assertions enabled. The optional search
+is never imported. Prepared by Jeremy Diviney with OpenAI Codex assistance.
+"""
+import argparse
+import hashlib
+import json
+import os
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import time
+
+HERE = Path(__file__).resolve().parent
+
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def read(path):
+    return json.loads(path.read_text())
+
+
+def dump(path, value):
+    path.write_text(json.dumps(value, indent=2) + '\n')
+
+
+def baseline_snapshot(parent, local, global_work, out):
+    """Give the independent auditor fresh baseline evidence, not historical #645 files."""
+    paths = {
+        'data/PLAN.json': parent / 'data/PLAN.json',
+        'data/OWNERS.json.gz': parent / 'data/OWNERS.json.gz',
+        'evidence/local/CANONICAL-WORD.json.gz': local / 'CANONICAL-WORD.json.gz',
+        'evidence/global/GLOBAL-TEMPLATE.json.gz': global_work / 'global/hosted/GLOBAL-TEMPLATE.json.gz',
+        'evidence/global/HOSTED.json': global_work / 'global/hosted/HOSTED.json',
+        'evidence/audit/OWNERS-AND-PROFILE.json': global_work / 'global/audit/OWNERS-AND-PROFILE.json',
+    }
+    for relative, source in paths.items():
+        target = out / relative
+        target.parent.mkdir(parents=True, exist_ok=True)
+        shutil.copyfile(source, target)
+    return {relative: sha(source) for relative, source in paths.items()}
+
+
+def main():
+    if not __debug__:
+        raise RuntimeError('Assertions are required; do not use python -O.')
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, required=True)
+    ap.add_argument('--parent', type=Path, required=True, help='Pinned PR656 research/gauge44-layered-b')
+    ap.add_argument('--pr635', type=Path, required=True)
+    ap.add_argument('--out', type=Path, required=True)
+    ap.add_argument('--local', type=Path, help='Optional rebuilt layered local directory, including phases')
+    a = ap.parse_args()
+    main_root, parent, pr635, out = [p.resolve() for p in (a.main, a.parent, a.pr635, a.out)]
+    assert not out.exists() and not any(out.is_relative_to(p) for p in (main_root, parent, pr635, HERE))
+    actual = {p.relative_to(HERE).as_posix(): sha(p) for p in HERE.rglob('*')
+              if p.is_file() and '__pycache__' not in p.parts and p != HERE / 'MANIFEST.json'}
+    assert actual == read(HERE / 'MANIFEST.json'), 'Package inventory or hashes changed'
+    sources = read(HERE / 'SOURCES.json')
+    assert sha(parent / 'MANIFEST.json') == sources['parent_manifest_sha256'], 'Unexpected PR656 package'
+    assert sha(parent / 'data/OWNERS.json.gz') == sha(HERE / 'data/PR656-OWNERS.json.gz')
+    out.mkdir(parents=True)
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0')
+    for key in ('PYTHONOPTIMIZE', 'WITNESS_DISCOVER', 'WITNESS_RECORD'):
+        env.pop(key, None)
+    steps = []
+
+    def run(name, script, *args):
+        started = time.monotonic()
+        log = out / (name + '.log')
+        with log.open('w') as stream:
+            result = subprocess.run([sys.executable, '-B', str(script), *map(str, args)],
+                                    env=env, stdout=stream, stderr=subprocess.STDOUT)
+        steps.append(dict(name=name, exit_code=result.returncode,
+                          seconds=round(time.monotonic()-started, 3), log_sha256=sha(log)))
+        dump(out / 'STEPS.json', steps)
+        if result.returncode:
+            raise RuntimeError(name + '\n' + log.read_text()[-6000:])
+        print('PASS', name, flush=True)
+
+    run('parent-manifest', parent / 'verify_manifest.py')
+    if a.local:
+        local = a.local.resolve()
+    else:
+        run('word', parent / 'construction/reproduce.py', '--main', main_root,
+            '--pr635', pr635, '--out', out / 'word', '--until', 'word')
+        run('layers-and-native', parent / 'construction/layers/reproduce_layers.py',
+            '--main', main_root, '--pr635', pr635, '--word-dir', out / 'word', '--out', out / 'layered')
+        local = out / 'layered/local'
+        run('independent-scalar', parent / 'independent/audit_local.py', '--main', main_root,
+            '--word', out / 'layered/layers/FULL-WORD.json.gz', '--output', out / 'INDEPENDENT-SCALAR.json')
+    run('baseline-strict', parent / 'verify_global.py', '--main', main_root,
+        '--local', local, '--work', out / 'baseline')
+    assert read(out / 'baseline/REPLAY.json')['kappa_decimal'] == '0.001654108529511355'
+    snapshot = baseline_snapshot(parent, local, out / 'baseline', out / 'baseline-snapshot')
+    run('owners', HERE / 'audit_owners.py', '--package', parent,
+        '--baseline-owners', HERE / 'data/PR656-OWNERS.json.gz',
+        '--nomination', HERE / 'data', '--output', out / 'OWNERS-AUDIT.json')
+    run('independent-owners', HERE / 'independent_owners.py', '--main', main_root,
+        '--parent', out / 'baseline-snapshot', '--owners', HERE / 'data/OWNERS.json.gz',
+        '--out', out / 'INDEPENDENT-OWNERS.json', '--mutation-controls')
+    staged = out / 'staged-parent'
+    run('prepare', HERE / 'prepare.py', '--parent', parent, '--candidate', HERE / 'data', '--out', staged)
+    shutil.copyfile(HERE / 'data/SPEC.json', staged / 'data/SPEC.json')
+    unchanged = {p.relative_to(parent).as_posix(): sha(p) for p in parent.rglob('*.py')
+                 if '__pycache__' not in p.parts}
+    assert all(sha(staged / rel) == digest for rel, digest in unchanged.items())
+    changed = {p.relative_to(parent).as_posix() for p in parent.rglob('*')
+               if p.is_file() and '__pycache__' not in p.parts and sha(p) != sha(staged / p.relative_to(parent))}
+    assert changed == {'data/PLAN.json', 'data/OWNERS.json.gz', 'data/SPEC.json'}
+    run('global-strict', staged / 'verify_global.py', '--main', main_root,
+        '--local', local, '--work', out / 'global')
+    run('independent-price', staged / 'independent/price_profile.py', '--main', main_root,
+        '--profile', HERE / 'data/PROFILE.json', '--output', out / 'PRICE.json')
+    run('packing-ceiling', HERE / 'packing_ceiling.py', '--parent', staged, '--main', main_root,
+        '--out', out / 'ceiling')
+    admitted = read(out / 'global/REPLAY.json')
+    kappa = read(HERE / 'data/SPEC.json')['expected']['kappa_decimal']
+    assert admitted['status'] == 'PASS_GAUGE44_STRICT_GLOBAL_REPLAY' and admitted['kappa_decimal'] == kappa
+    assert read(out / 'PRICE.json')['prices']['native']['outer_with_bit']['kappa_decimal'] == kappa
+    receipt = dict(status='PASS_LAYERED_JOINT_OWNER_STRICT_ADMISSION', kappa_decimal=kappa,
+                   parent_head=sources['parent_head'], parent_manifest_sha256=sources['parent_manifest_sha256'],
+                   owner_sha256=sha(HERE / 'data/OWNERS.json.gz'),
+                   unchanged_verifier_python_files=unchanged, baseline_snapshot=snapshot,
+                   rebuilt_local=a.local is None, steps=steps,
+                   scope='Conditional finite owner witness under the unchanged PR655/656 local construction, '
+                         'controller and admission interfaces. PR589 bit circuit cited unchanged and its '
+                         'profile repriced; no unconditional theorem, full Lean proof or packing optimality claim.')
+    dump(out / 'REPLAY.json', receipt)
+    print(receipt['status'], kappa)
+
+
+if __name__ == '__main__':
+    main()