Mister-Meeseeks · Oct 16, 2026 · Oct 13, 2026
diff --git a/research/complex-t37-owners/DEPENDENCY-PINS.json b/research/complex-t37-owners/DEPENDENCY-PINS.json
@@ -0,0 +1,38 @@
+{
+  "scripts/verify_frontier741.py": "215ee6a12de8dc2392e6811a1b8f2140035f6b2d2a0d2100ff4bd2fdcb8bb39b",
+  "scripts/verify_frontier741_bindings.py": "eff455167e2fd0bc9a67d35241d0e69d8edc58f3a23e776dcfe8f500ca8e8d67",
+  "scripts/verify_frontier799.py": "19fe1b32079095160dc00fe2f7df75e0fcbc82cff37f7159b755c8a63bd5ce99",
+  "scripts/verify_frontier799_bindings.py": "43897b3c99212d6134870898a1840f32898aa1b3679b299e654901568ad7e19b",
+  "research/complex-sw4-frame8/MANIFEST.json": "b9b39c206fcd2613382b0dcbda23a371e8781d1bedaf8e2f8e7df1e79dc1fa89",
+  "research/gauge44-frames-x/MANIFEST.json": "e1b7998c8f7cb24f8674d250d0510f2b5b351b2ed0b35f17a17e6bacf3d9824b",
+  "research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py": "322d29d43dbee8130cde15d4bf05396698b5e3dfe3735813899db91cc0ba7955",
+  "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",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-RECIPES.json": "534ace870cabe515987e00f50f71550030965006ea18978e0924590ac6944345",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-REVIEW.json": "ee9b86428278392d2c933f76d60e51f5af90d4ab67e4d3937ed2fa416e7755ab",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-LOCAL-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INTEGRATION.json": "5c14538134dfffbc58fa4b4d2f26b270ec5f56d17d4bf23752c82964f45171db",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-CHECKS.json": "79177449e404403964ce1b2f4a9a8bd49e1916daba3123d7fd7f5cfd1f1ac0ea",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-PROGRAMS.json.gz": "99a18eede965accf65943e490b8d2b2ffb9f1c9bc6babdb825413a80cbea2cde",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/RESIDUAL-ADAPTERS.json": "baafef737acc16dafbe1150896feb16744f3d669fa123bb2bff19ecc4e71b275",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/SCALAR-FRAME-AUDIT.json": "73b3601a6239502475a272ea0c46945fd42034486aaf43e66a212eb4f012ca44",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/WRAPPER-CHECKS.json": "9a09146e686c4f535b04fdef3753fe01dad8f5e8881a69408a91394acb5b48f5",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+  "research/complex-k492-owner-repair/vendor/multicold/inputs/PR543-EXPECTED.json": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz": "025448abdf2012d327e50a009084e1501690d05e650300d2982836aa0350ae00",
+  "research/community-k492-audit/pr622/replay/baseline558/complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz": "de2be0f4b6d24ace368fd5b834b7a00f9625d0a1824c4ff969f2db5f115db667",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/prepare_supplier_base.py": "f5eae94aca965d0008bc07cff8245ccb7509042ccad457d3bcb7d51c1e9409f0",
+  "research/gauge44-frames-x/data/PLAN.json": "5f40e7ccfca61f298539b4f41286d2a9d62caf947057f9cec82aa53f73f707fd",
+  "research/gauge44-frames-x/data/OWNERS.json.gz": "99d1c4caf85855c353d30f122d9efbd9e51562914facded13027f347b18a6082",
+  "research/complex-t21-owners/build_owners.py": "d1e6bbab8ea0de09048fc9737dd4a4713289ca69328efe71855e16fc55abfa57",
+  "research/complex-t21-owners/common.py": "41a2e8a4cc69251e7e31dd82b4776ccfe46033afa8dca59f45f5d3c377541ea7",
+  "research/complex-t21-owners/independent_check.py": "9d8c86bf45cdaef37f223c88704055ced503ee295645611e13f3fb9059a00e55",
+  "research/complex-t21-owners/VENDOR-PINS.json": "578100c9ed4812a161271a1b5c8036673f4b27d6cc1df560715ff2ea9a598f6d",
+  "research/complex-t21-owners/MANIFEST.json": "663a4300ec3abe2278ac6c8e49dd13dc58694c33bfadaa278c5406539e113a31",
+  "research/complex-t21-owners/data/T5-OWNERS.json.gz": "676e91f0ab18bdc93b3da067082506b779969dde32a38baacfc8576c327a3c54",
+  "research/complex-t21-owners/data/EDITS.json": "a3bdecb4899af794427458eec0b7b13b404e2c822c1e8e152d4a4eb92cb10638"
+}
diff --git a/research/complex-t37-owners/MANIFEST.json b/research/complex-t37-owners/MANIFEST.json
@@ -0,0 +1,20 @@
+{
+  "DEPENDENCY-PINS.json": "8ce67d5bdb1ae2643908606d6123a05f12df4c547e1c78366b9ee724d9e037c0",
+  "NOTICE.md": "ae6f2c4c31c5a9ec0433bc13d16522e195397eb5081552c54870f61d1700a0fb",
+  "PROOF.md": "46ef4ec5e2e2727928e89dfd95ae018a26c9a6d75371fdd5c26ed976e62aba3f",
+  "README.md": "ed58a37440fc10a84baa27ec3d460d3da68bdb34bcaf7dca5b8adf46d4642645",
+  "build_owners.py": "fd0f0a24c34f8927890038e12c375642ad91e5d1ae28bfaea50b60b53e3339a3",
+  "build_parent.py": "f86610b5ba77144980257d1e2a3addf6a4bdfad2cfdc72fb99d22765fbae6ebc",
+  "check_parent.py": "56e923ba05ddab3414a531e2d8455f8fe04e03c60f0d0c707cd42e3a3383924f",
+  "common.py": "41a2e8a4cc69251e7e31dd82b4776ccfe46033afa8dca59f45f5d3c377541ea7",
+  "data/ADAPTER-EDITS.json": "82f4efc903789dcfd046e7bd26e72a9a5904cf909f03edd1e8812a2bfc990211",
+  "data/CLAIM.json": "e610d96b7ec0a79aefe5b31e424710715497fae326672ea3eec73ddda37895eb",
+  "data/EDITS.json": "43923636f076bda0c6c9087dee6b0bd3118b79d7317306de563a8ffc52567ff9",
+  "data/SPEC.json": "9dbaac1043821ece044f6aac9afb531c52d38fcb2367f31c2c8eacd4d455a19c",
+  "freeze.py": "154667b513a640bd96ca91da58bc065fd31dabaab109452e38812935cbaf54de",
+  "independent_check.py": "07216c2d7d6e46f08af649c1f30c8fe1fcd48a35257291ae9548358726ca61bb",
+  "owner_controls.py": "2241e3958b732f5cc03a24b7d972e942b036ef324d8c99a5002f6afe00136fe9",
+  "price.py": "af05621b2232ce22e2dda0c4d610e4606c7d584ae439b081df9a842ac4402f90",
+  "source_adapters.py": "2423752102e0b4c0e8d329586868cfe55869682e76cc392decc3f99273d320f7",
+  "verify.py": "f52c1a9f8e69a52113efc2003ab7fb37769bb5e1e38f17a8222cab6a69fb1fc5"
+}
diff --git a/research/complex-t37-owners/NOTICE.md b/research/complex-t37-owners/NOTICE.md
@@ -0,0 +1,30 @@
+# Attribution and source boundaries
+
+Prepared for Joel Pulikkan (GamingPuzzled) with Claude Opus 5.5 (Anthropic)
+assistance via Claude Code, Apache-2.0.
+
+- New in this package: the observation that PR890's fixed-family bound becomes
+  replica-unbounded once the charged prefix payload is raised (its row cost is
+  explicit), the T37 = T21 + T16 composition and proportional merge, the
+  eight-role (44,3,2) -> (48,1) trade, the 8+8+8+8+5 bank lift and its audit,
+  the 1024-bit charged-prefix adaptation, and the strict T37 composition.
+- Chafik Boukhalfa (chafreaky), PR890: the T21 owner map (T5 witness, T16+T5
+  interleaving, nine-role trade), 8+8+5 bank lift, independent checks, owner
+  bound (whose signed-price relaxation identifies T37's target profile) and the
+  verification driver this package adapts. Used unchanged from
+  `research/complex-t21-owners` by path and hash pin.
+- Hao Yan (@FanPUYen), PR858: T16 duplication and eleven-role correction,
+  physical source-event windows, independent owner/chart audit and the
+  replication-parameterization approach. Its constructor is used unchanged
+  (twice: inside T21 and as the second T16 component).
+- PR869/PR870: the unchanged U8 local word, builder and controller chain
+  (NewBArch triangle-hybrid B; ColdWitness/icekylinx driver), vendored in PR890.
+- Jeremy Kothe's PR799, Chafik Boukhalfa's PR741, the gauge44/PR645, PR635,
+  PR514/PR484/PR507 controller lineage and the PR589 bit supplier remain
+  dependencies, covered by the ancestral replay. PR795's signed dual (Chafik
+  Boukhalfa) is the relaxation used to locate the T37 optimum.
+
+`DEPENDENCY-PINS.json` pins every PR890 and repository file read by path.
+`data/ADAPTER-EDITS.json` lists every literal source edit applied to PR890's
+vendored PR870 code with its required multiplicity. `MANIFEST.json` binds this
+package.
diff --git a/research/complex-t37-owners/PROOF.md b/research/complex-t37-owners/PROOF.md
@@ -0,0 +1,95 @@
+# The T37 owner composition
+
+## What changes, and what does not
+
+The complex local supplier (PR869/PR870 U8 word: paid profile
+`{1:2548,2:338,3:446,4:162,5:72,8:8}`, helper widths
+`{4:80,5:32,7:54,8:122,9:216}`), the PR589 bit supplier, both rational moment
+engines and the seven-step outer recipe are PR890's, unchanged. Only the
+replica count, the whole-owner map and one charged finite constant change.
+
+## Why PR890's bound stops at T21
+
+PR890's exhaustive relaxation (PR795 signed dual) is stated for
+`T <= 22`, because the retained prefix charge is `113+18T < 512`. The 512 is
+the *charged* global prefix payload. In the inherited finite invoice it is
+paid in exactly two places: the prefix reserve `prefix < payload` and the
+physical row coefficient `row = 2*bitlen(stock)+9909+252+2*payload < 20161`;
+the outer bootstrap additionally checks finite cutoffs `cut*gap >= 2*(4+payload)`.
+None of the moment, deficit or 47 outer inequalities depends on it (the outer
+row gap uses the retained bound 20161, not the actual row). Charging
+`payload = 1024` costs `row = 17495 < 20161` and leaves every other inequality
+unchanged; the bootstrap cutoffs are recomputed at `2*(4+1024)`. The retained
+PR531 invoice is still required to have been charged at 512 and its allowance
+is retained in full, as before. Precedent: earlier packages raised other
+charged allocations (192 -> 256) after recomputing their reserves.
+
+## The relaxed optimum over all T
+
+Running PR890's own relaxation without the `T <= 22` cap (same dual, same
+price table): per replica the excess over all-48 is mass `30 (mod 48)` and
+signed credit `150`. Rank-one remainders have the best credit per cost
+(credit 925). Six rank-one remainders give credit `5550 = 150*37` and mass
+`6 = 30*37 (mod 48)`, so T37 with idle `{48:11086, 1:6}` meets the dual with
+equality and is the unique-shape normalized optimum for every T (multiples of
+37 repeat it). Its normalized penalty `6c(1)/37` is below T21's
+`(3c(1)+c(3))/21`.
+
+## Construction
+
+1. PR890's T21 map (PR858 T16 + literal T5 + nine edits) is rebuilt by its own
+   unchanged constructor; its own independent checker is rerun on it.
+2. PR858's T16 map is rebuilt unchanged and relabelled into replicas 21..36
+   (replica, owner, copy and family offsets `+21`, `+21*112`, `+21*896`).
+3. The 189 T21 calls and 144 T16 calls are merged by the key `(i+1)/189`
+   versus `(j+1)/144` (ties: T21 first). Each component keeps its own order,
+   so every component role keeps its window.
+4. Before the trade the idle profile is `{48:11085,44:1,3:1,2:1,1:5}`, which
+   is worse than T21. Eight frozen edits (`data/EDITS.json`) apply the
+   credit-neutral trade `(44,3,2) -> (48,1)`:
+   - the lone width-4 role of the cap-48 bin (owner 29, child 8, port 0)
+     moves into a full bin of owner 20; the width-4 role it displaces (a later
+     T21 call) moves on to bin (20,14,111);
+   - bins (20,14,111) and (27,15,0) (fills 29 and 30) are repacked as
+     `{8,4,4,4,4,4,4} = 32` and `{9,9,9,4} = 31`, moving one width-9 role
+     (T21 call) into owner 27 and two width-4 roles (second-T16 calls) into
+     owner 20.
+   All moves are cross-component, so no moved role is hosted by its own
+   replica. The result is `{48:11086, 1:6}`.
+
+## Checks
+
+The independent checker (PR858/PR890 code, `T = 37`, payload 1024) checks all
+`333*504 = 167832` roles against the actual source-event windows, families,
+per-call distinctness, whole widths, contiguous slices, all 73-axis charts,
+exact per-replica projections, idle profile, deficit `320*37 = 11840`,
+prefix `72+37+333+333+4 = 779 < 1024`, row `17495 < 20161` and halving.
+Every omitted edit is rejected, and so is the same map under the sequential
+(non-interleaved) schedule. The partial bank envelope 8+8+8+8+5 is audited
+literally with eight mutations. The PR870 controller chain (bind, emit,
+asynchronous audit with mutations, invoice, assembly, 69 admission and 12 bit
+controls) runs with cardinality edits and the payload edits listed in
+`data/ADAPTER-EDITS.json`.
+
+## Price
+
+Live `33152`, rank mass `73*33152-11840 = 2408256`. Both engines certify
+
+```
+b = 1664727258740678855772 / 10^24
+```
+
+(accept at b, reject b+10^-24); bit `c` unchanged. The outer recipe gives
+
+```
+kappa = 1661960547713947 / 10^18 = 0.001661960547713947
+```
+
+which is `2.773066918e-9` above PR890.
+
+## Scope
+
+Inherited hypotheses are unchanged (all-size compiler, common-label/mutable
+source realization, whole-call hosting, precision/tape, analytic transfer, bit
+H1-H5). The new explicit premise is that the charged global prefix payload is
+a finite constant priced only through the reserves listed above.
diff --git a/research/complex-t37-owners/README.md b/research/complex-t37-owners/README.md
@@ -0,0 +1,59 @@
+# Thirty-seven replicas on the U8 word
+
+The retained conditional framework admits
+
+```
+kappa = 1661960547713947 / 10^18 = 0.001661960547713947
+```
+
+This is **2.773066918e-9 above PR890** (0.001661957774647029). The U8 local
+word, its 504 helper widths, the PR589 bit supplier, both moment engines and the
+outer recipe are unchanged. The owner map has **37 replicas, 333 complete calls
+and 167,832 whole-helper roles**; its idle profile is `{48:11086, 1:6}`.
+
+## Idea
+
+PR890 proves that no replica count `T <= 22` or whole-owner placement improves
+T21 for this word. The cap `T <= 22` comes only from the charged 512-bit global
+prefix payload (`113+18T < 512`). That payload is a finite constant paid in the
+invoice's row reserve (`2*payload`), the prefix reserve and the bootstrap
+cutoffs; the moments and the 47 outer inequalities do not see it. This package
+charges **1024 bits** (row coefficient `17495 < 20161`, prefix `779 < 1024`).
+
+Rerunning PR890's own signed-price relaxation without the cap shows that
+`{48:11086, 1:6}` at T37 attains the dual with equality and is the best
+normalized profile for every replica count. It is constructed as PR890's T21
+plus a second PR858 T16 (replicas 21..36), merged proportionally, plus an
+eight-role credit-neutral trade `(44,3,2) -> (48,1)`. See [PROOF.md](PROOF.md).
+
+## Reproduce
+
+From the repository root, with Python 3.11+ and the existing frontier replay's
+NumPy/SymPy/SciPy, C++17 and Boost dependencies (set `CPATH` to the Boost
+include directory if needed):
+
+```sh
+python -B research/complex-t37-owners/verify.py --work /tmp/t37-cold
+```
+
+It rebuilds PR589, PR741 and PR799, rebuilds U8 and its controls, constructs
+T37 (rerunning PR890's T21 and PR858's T16 constructors and audits), lifts the
+8+8+8+8+5 bank envelope and audits it with eight mutations, runs PR890's
+unchanged independent checker on the T21 component and the T37-parameterized
+checker on all roles, rejects all eight omitted edits and the sequential
+schedule, then runs bind, emit, asynchronous audit (15 mutations), invoice,
+assembly, 69 admission and 12 bit-supplier controls and two exact moment
+engines with all 47 outer inequalities. No optimizer runs. Reuse of a verified
+PR799 replay works as in PR890 (`--baseline799 DIR --ancestor741 DIR/ancestor`).
+
+`freeze.py` is the discovery path used once to write `data/SPEC.json`; it is not
+a verification premise.
+
+## Scope
+
+Finite conditional witness. All-size compilation, common-label and
+mutable-source realization, whole-call hosting, precision/tape, analytic
+transfer and bit H1-H5 remain inherited hypotheses. The explicit new premise is
+the 1024-bit charged prefix payload, priced through the reserves above. Not an
+unconditional multiplication theorem or an optimality claim beyond the
+relaxation stated in PROOF.md.