Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting

research/k8-coordinated-owners/CLAIM.json

@@ -0,0 +1,52 @@
+{
+  "status": "FROZEN_CANDIDATE_REQUIRES_VERIFY_PY",
+  "baseline_pr": 1018,
+  "baseline_commit": "eac7547cb191f875d5f5ea5f9bbb1d2b8c51c4ef",
+  "baseline_kappa": "0.00167166528321877",
+  "kappa_decimal": "0.001672196274581061",
+  "gain_percent": "0.0317642154575695298353261990653697672265824378100",
+  "gain_over_previous_pushed_u10_t37_percent": "0.6111286406103019880837965694577492917132467559300",
+  "complex_lower": "0.001674997198656588841754",
+  "bit_lower": "0.001733427039589844234749",
+  "changed_owner_rows": 31939,
+  "calls": 72,
+  "R": 480,
+  "replicas": 8,
+  "live": 7168,
+  "physical": 7658,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "local_profile": {
+    "1": 2412,
+    "2": 418,
+    "3": 432,
+    "4": 142,
+    "5": 82,
+    "8": 8
+  },
+  "idle_profile": {
+    "1": 1110,
+    "3": 247,
+    "23": 2,
+    "32": 4,
+    "39": 1,
+    "48": 2426
+  },
+  "global_profile": {
+    "1": 174774,
+    "2": 30096,
+    "3": 31351,
+    "4": 10224,
+    "5": 5904,
+    "8": 576,
+    "23": 2,
+    "32": 4,
+    "39": 1,
+    "48": 2426
+  },
+  "files": {
+    "SPEC.json": "21d605679db7c2e2801ee0d3ef9c262e71319fc49cb98a01b2d05c8a491aa569",
+    "OWNERS.json.gz": "681670248da5ffe1504fab103855b6d0b8e91d176f31963fe88efa1d9d8bc2bd"
+  },
+  "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."
+}

research/k8-coordinated-owners/MANIFEST.json

@@ -0,0 +1,31 @@
+{
+  "CLAIM.json": "721457ddf32e3a418bf7e23e5e3009626d49eb0108c9f617263d8f5028a8e180",
+  "NOTICE.md": "442756fc1c5ecfd7b7b7694b53b1ecc70aa525004cd80f7d748ccd7270555189",
+  "OWNERS.json.gz": "681670248da5ffe1504fab103855b6d0b8e91d176f31963fe88efa1d9d8bc2bd",
+  "README.md": "7df766fd7fe3e7f0435eb2190e4a199ab6698b509499e3c0004168a66d78184f",
+  "SOURCE-PINS.json": "80b0357d714181f36476c34f9242ae21d72839c4afad9318b4228b78889fd676",
+  "SPEC.json": "21d605679db7c2e2801ee0d3ef9c262e71319fc49cb98a01b2d05c8a491aa569",
+  "discovery/SEARCH-LOG.json": "a7b4082ce270d84fcdea6dfcc7ae0836610f41d67183156fcd5f81bffb2ef096",
+  "discovery/SEARCH-TRACE.json.gz": "04be238ac938f38f77327e6e83efe0ea6e2cb29ee3d95a5b783bcdf7bda3b861",
+  "discovery/STAGES-RELAXATION.json": "165bf9204534944b44762109bbf35ba4bdedbc867fa1dde63a90bdf593cecaa2",
+  "discovery/screen_stages.py": "e78a0ee907b4ee97f90b7b66a8f8da7a0044474dab7c27845b24ffbf01dede14",
+  "discovery/search_calls.py": "5df48ab7775bfee767d71dd8c47585977922568b532c29f4528f2c8ca5ab364d",
+  "evidence/ADMISSION-CONTROLS.json": "31218c75b7a28d4f5397195bad9ba7e5750366ae7b73d010a749f358ce4adda4",
+  "evidence/ALL-T-BOUND.json": "07cc98bd055bc3f351de2c460364dc9fae25c1b728b90d6dc3ce9b5d9da32381",
+  "evidence/ASSEMBLY.json": "8634e3ce597619d6da631dcd1e40bd82f327a2b500bf6963b5961c945ab810b9",
+  "evidence/ASYNC-AUDIT.json": "abc1e11e3184371a41e4d73d56033e8e7ff608443085926a4e0037f7e335300b",
+  "evidence/BASELINE-CHAIN-STEPS.json": "9f5d3b0e72c92a4f5fda023685aab2e5f23dda6e079410824126c0802bc1710a",
+  "evidence/BASELINE-RESULT.json": "1d43f5f4a6d77f096182d9482eecb5313a0b79c4d3e12f4f70846c6f935287be",
+  "evidence/BIT-SUPPLIER-CONTROLS.json": "4f996bdd4802b0eea6187f01734d4e3f482b281952d6a923dac395a27bf93eb0",
+  "evidence/NATIVE-BINDING.json": "6059b4f78e63c818d52b72615e42d9b80269a3d69769a14a424af6fe19f22870",
+  "evidence/OWNERS-AND-PROFILE.json": "ee31a5ae84bcc6344b18c67ae828693ba92ec0328223c9b6af29b04d90c80b40",
+  "evidence/PREFIX-AND-INVOICE.json": "22cf5aa33d7c26708d1c8b5a5f88df9b330516e6ab9e5e8e10da5857c58e7961",
+  "evidence/PREPARATION.json": "23105d9e89bbf7e2a64e8ce391c6b3fc7a900e4e2d7351bbd0120d05ab52a2eb",
+  "evidence/REPLAY.json": "842986705a5ee84c969d5b58e831dd6cd8ddf549f2ee3bebbd9c6a5dcf566857",
+  "evidence/RESULT.json": "7bf23e92f06971315168cfe167a0ba923f8ba0c58a5f35d93ba53f58fcdb828e",
+  "independent/UPSTREAM.json": "46079c0178181f97b0d35cf2fb3a05e9d33a267bef31230a56dd5c84a7b3b385",
+  "independent/all_t_bound.py": "0ac15a2b2eaf72060924fcd33a43b2170a5c14ecfe4345ff5da041b81bd402df",
+  "prepare.py": "2a92b1a55cad73c0a5168f49f432a436db86111328228e300d3e8b72e9e994e6",
+  "verify.py": "960ad27c57416e061d907cb5f0de7acb4901b5232c29ca88224cc6284e60b496",
+  "verify_manifest.py": "723d726dbbe5b65a49caecae0f1aab664a1413fb639abfd3e826a5a538e14e5b"
+}

research/k8-coordinated-owners/NOTICE.md

@@ -0,0 +1,41 @@
+# Attribution and scope
+
+Prepared for Thomas DiFiore with OpenAI Codex assistance, October 13, 2026.
+Licensed under the repository's Apache-2.0 license.
+
+This contribution changes the whole-helper ownership map for the circuit from
+Jeremy Kothe's PR1018 (`eac7547cb191f875d5f5ea5f9bbb1d2b8c51c4ef`). The
+eight no-helper mutable-source cells, R480 circuit, frame optimization and
+construction controls come from Jeremy Kothe and the credited contributors to
+PR1005. The seven additional triangle slots come from PR1018 using Rohan Arun's
+PR987 search and NewBArch's PR869 builder. None of those circuit improvements
+are claimed as new here.
+
+The starting ownership map is G44Pack3's K8c8, descended from chafreaky's PR685
+and PR741 maps through G44Pack's relabeling and width changes. This package adds
+coordinated complete-call reassignment by grouped integer packing, with
+explicitly serialized owners and an unchanged independent admission verifier.
+
+The separate all-replica upper bound adapts jon314159's PR942 arithmetic
+implementation and proof, using chafreaky's PR795/890 signed-dual prices. Its
+new contribution is the application to PR1018's changed local profile and
+helper inventory. The two rational numerical engines retain their upstream
+authorship. `independent/UPSTREAM.json` records the source file and hash.
+
+All construction, controller, spectator, native phase, finite invoice, exact
+moment and outer-transfer implementations retain their upstream authorship
+and notices. The runtime copies PR1018's verifier files byte for byte. It
+changes the owner nomination, its derived PLAN fields, and expected-value SPEC.
+The original packages remain unchanged.
+
+The bit supplier is the unchanged PR589/PR555 punctured-star construction;
+this run reprices its pinned profile and reruns its admission controls. It does
+not rebuild the bit circuit. Earlier complex ancestry is inherited through the
+pinned PR741 initial word and PR622/PR558 reviewed parent artifacts. The run
+freshly rebuilds the k8 leaver circuit, all later layers, and the seven slots.
+
+This is a conditional finite construction, not an unconditional integer
+multiplication theorem. All-size compilation, common-label and mutable-source
+realization, whole-call hosting, precision/tape, analytic transfer and bit H1–H5
+assumptions remain. No independent human peer review is claimed. Optimizer
+outputs and floating relaxations are discovery evidence, not admission proofs.

research/k8-coordinated-owners/README.md

@@ -0,0 +1,134 @@
+# Coordinated k8 owners: conditional κ = 0.001672196274581061
+
+Coordinated reassignment of complete calls improves the conditional κ from
+PR1018's **0.001671665283218770** to **0.001672196274581061**, a **0.0317642%**
+gain. The circuit is PR1018's R480 k8 leaver word with seven additional
+triangle slots. This contribution improves its whole-helper ownership map.
+Larger κ is better in the bound `n (log n)^(1−κ)`.
+
+The fresh k8 and slot rebuild reproduced PR1018 before the changed ownership
+map was admitted. This is a conditional finite construction; the inherited
+all-size/compiler, mutable-source realization, hosting, precision/tape,
+analytic-transfer and bit H1–H5 assumptions remain. See [NOTICE.md](NOTICE.md)
+for attribution and precise reuse scope.
+
+| Quantity | Verified result |
+|---|---:|
+| κ | 0.001672196274581061 |
+| Complex saving lower endpoint | 0.001674997198656588841754 |
+| Bit saving lower endpoint, unchanged | 0.001733427039589844234749 |
+| Replicas / complete calls / helpers per call | 8 / 72 / 480 |
+| Serialized helper roles | 34,560 |
+| Live / physical families | 7,168 / 7,658 |
+| Rank mass / deficit | 520,704 / 2,560 |
+| Global coefficient prefix / charged bits | 253 / 512 |
+| Physical row coefficient / retained limit | 16,467 / 20,161 |
+
+The per-call profile is `{1:2412,2:418,3:432,4:142,5:82,8:8}`. The helper-width
+inventory is `{4:56,5:32,7:30,8:122,9:240}`. The idle remainder profile changes
+from `{1:1099,2:9,3:179,7:54,16:23,48:2419}` to
+`{1:1110,3:247,23:2,32:4,39:1,48:2426}`. The actual controller, spectator
+permutations and complete invoice are rebuilt from the serialized roles.
+
+## Search and verification
+
+A single-call min-cost reassignment found no improvement. The new search
+removes two, three or four complete calls, groups available bins by their
+remaining capacity and allowed calls, and solves an integer pattern assignment.
+Each pattern uses a bin at most once per call. Six-call searches specifically
+target occupied capacity-48 bins; these moves hold widths 5 and 7 fixed and
+jointly place widths 4, 8 and 9. A final four-call pass cleans up residuals.
+Stable prefix compaction emits the literal owner map.
+
+The objective uses floating arithmetic for discovery. Integer assignments are
+checked before use, and timed-out solves may contribute feasible incumbents.
+There is no claim that a neighborhood or the final map is globally optimal.
+The independent physical audit and two rational moment engines determine the
+claim, rather than the optimizer objective.
+
+The admission runtime copies PR1018's verifier files **byte for byte**. Only
+the owner file, derived PLAN fields and frozen expected-value SPEC change.
+There are no relaxed guards or special-case acceptance paths.
+
+The completed run includes the 21-stage k8 chain, five sets of 95 cold-end
+controls, 34 slot-control outcomes, fresh native forward/backward programs,
+exact local phases, independent local audit, and the strict global replay.
+The latter checks 15 controller mutants, 69 admission mutants, 12 bit-supplier
+mutants, both rational moment engines, 47 strict outer inequalities, and the
+next-grid and recurrence-model controls. The bit circuit is cited unchanged
+and repriced; it is not rebuilt by this run.
+
+## Reproduce
+
+Use Python 3.11+ and the repository's native verifier prerequisites, including
+Boost where required. The verifier itself does not need SciPy. From the
+repository root, choose fresh output directories:
+
+```sh
+python -B research/gauge44-slots/construction/reproduce.py \
+  --main . --pr635 research/complex-sw4-frame8/vendor/pr635 \
+  --out /tmp/k8-initial --until word
+
+python -B research/k8-coordinated-owners/verify.py \
+  --word-dir /tmp/k8-initial --work /tmp/k8-coordinated
+```
+
+The first command builds the historical shadow/hamming inputs; the verifier
+then constructs the k8 word and slot layer. A completed native rebuild may be
+explicitly reused with `--native-from /path/to/native` instead of `--word-dir`.
+That directory must contain completed `word/`, `chain/`, and `slots/` runs.
+The verifier rechecks their step coverage, pinned programs, canonical words,
+Clifford recipes, control counts and baseline result, then rebuilds the entire
+changed global controller and admission. The recorded run freshly built this
+native chain and subsequently used that explicit reuse path for final admission.
+
+The optional search requires NumPy and SciPy/HiGHS. It is not part of admission.
+Run `discovery/search_calls.py --help` from the repository root. The recorded
+sequence is `(block, passes, seed, seconds per solve)`:
+
+```text
+(1, 12, 13, 3)       negative single-call screen (stopped after 3 unchanged passes)
+(2, 240, 13, 2)      starting from the upstream owner map
+(3, 360, 27, 2)      starting from the preceding output
+(4, 240, 41, 3)
+(6, 24, 53, 5)      --target48
+(6, 48, 67, 3)      --target48
+(4, 160, 79, 2)
+```
+
+Use `--input previous-output --out fresh-output` to chain searches.
+Solver timing/version can change the nominated map. The frozen `OWNERS.json.gz`
+and `SPEC.json`, rather than a rerun optimizer, reproduce the certified result.
+`discovery/SEARCH-LOG.json` records accepted changes and solver statuses.
+
+## Exact limit of this packing family
+
+An independent extension of PR942's signed-dual argument proves that **every
+replica count** for this fixed local circuit, helper inventory and bin stock
+has κ-grid upper bound **0.001674097969905390**. This is an upper relaxation,
+not an attained construction. It leaves about **0.114%** improvement above the
+present result; a major increase must change assumptions of this packing family.
+
+With PR795/890 width prices `(-1,-20,-8,-2,4)` and capacity bonuses
+`(2,4,8,-13)`, two independently structured enumerations agree on all 1,163
+bin patterns. The remainder mass per replica is 14,814, the signed price is
+−1,084, and the required dual credit is 140,550. Thus the supporting rank-one
+solution has normalized remainders `{1:5622/37,48:11302/37}`. Both exact
+rational engines certify the supporting inequalities and the next-endpoint
+rejection. Every feasible physical owner map is subject to these necessary
+inequalities. Since the retained outer transfer has `κ < b/(1+b)`, the certified
+upper endpoint for `b` gives the stated grid ceiling.
+
+```sh
+python -B research/k8-coordinated-owners/independent/all_t_bound.py \
+  --out /tmp/k8-all-t-bound.json
+```
+
+The separate floating stage-count screen considers bank-free paired-chain
+relaxations with 5, 7, 9, 11 and 13 stages. It finds no improvement over nine
+stages in that search. It is not a proof against other circuits, banked
+constructions, helper splitting, or different recursion geometries.
+
+`CLAIM.json` contains the frozen numerical claim. `evidence/RESULT.json` and
+`evidence/ASSEMBLY.json` contain the completed strict admission;
+`evidence/ALL-T-BOUND.json` contains the separate exact upper-bound certificate.

research/k8-coordinated-owners/SOURCE-PINS.json

@@ -0,0 +1,27 @@
+{
+  "research/gauge44-slots/MANIFEST.json": "9a6f239b1618a43262e56735a99cc59b6f5a6e8816a794a34413e89cc33f4976",
+  "research/gauge44-leaver8/MANIFEST.json": "7c9637f06798b144274458efa145f701c61282f8b3aab1c0c900b53bdfbe1f0d",
+  "research/gauge44-slots/verify_global.py": "16bd5e54598592e92e210f99065348c5df261b8350fdc688072ce053d15b088a",
+  "research/gauge44-slots/verify_manifest.py": "723d726dbbe5b65a49caecae0f1aab664a1413fb639abfd3e826a5a538e14e5b",
+  "research/gauge44-slots/hosting/reuse_owners.py": "2106fe79bd89071e62a3a25c1e444531e14fb89f88b4bdeb72d7b40c91266402",
+  "research/gauge44-slots/data/PLAN.json": "1dec4ca3af6d45d82286005cae4c5e56e7253adefb117d797da55c55c891af08",
+  "research/gauge44-slots/data/OWNERS.json.gz": "32ca30cd1c652ef6ad43657273a08a157e1df3545e759ab36306a0d0b516fb4a",
+  "research/gauge44-slots/data/SPEC.json": "8e95ae8087124189cbd366d0e9d1c5ebededff536ff3501927b4b2a2e8dac70e",
+  "research/gauge44-slots/data/UPSTREAM-PINS.json": "ccc37ab7fbf78947fe02c7f57ea672d2e4eae8454cb1158ed964c75bf423869b",
+  "research/gauge44-slots/construction/leaver/PIVOT-SWAP-k8.json": "3ef7acf0cf67442a532f25b53d5fbeda76d3a84524118df8e003ca69b5cac0bb",
+  "research/gauge44-slots/construction/slots/verify_slots.py": "bc1c0e3e3d7c81dc1649f5be82cdd2399e543d46c24879cb975877bf9b7957be",
+  "research/gauge44-slots/construction/slots/SLOT-PINS-k8.json": "55dd229684febecb80638eff9c6b3986623e8539c6c956753b350209c3e0efe2",
+  "research/gauge44-slots/code/generated_identity.py": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708",
+  "research/gauge44-slots/code/witness.py": "779c5172894b992131e85be1e592ed2a1aec8c287b872ff42007d36a7291e444",
+  "research/gauge44-slots/code/assemble.py": "4c270a996b380ab712f72b81173ab24f1c73203a33578f261bfbaa7e67d75aec",
+  "research/gauge44-slots/code/prepare_global.py": "8c0dae301a8f34b77a5a462f840952d08ed120576212adf5051bc09bcad874dc",
+  "research/gauge44-slots/code/assembly_controls.py": "e4c0f7828af64fdaef1896e4448d0212bd3041805097140b8cfafd098f8a6162",
+  "research/gauge44-slots/code/restore_parent.py": "69b7b25ff85e9b8160e233c1d415cc6a0272019e5c486dcec14cb6c349e7024d",
+  "research/gauge44-slots/code/audit_allcold.py": "a87d7f4844ca963516637d249b14a0654f67f8047b6b265ae25b0cf30963e503",
+  "research/gauge44-slots/code/bind_providers_portable.py": "1d39bcc7b63ac158e021454beaae897d123e174360573762aecade3cd43193f6",
+  "research/gauge44-slots/code/invoice_allcold.py": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+  "research/gauge44-slots/code/bit_supplier_controls.py": "e6d33fb61a570c3f50669412acc467a3fd06ef0b806da6a75bc296c6ba2142a5",
+  "research/gauge44-slots/code/emit_allcold.py": "17c110c7c8d219e79e7dce36b19c4781e7effa800086cec03384387ad9acc7aa",
+  "research/gauge44-slots/code/freeze_spec.py": "f96c2b9cd886596bc7ab267f77abe9d16b6cbb5a724a5ad0a1d18d540369ed93",
+  "research/gauge44-slots/inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4"
+}