Source-assisted v4 complex word with PR189's bit supplier: conditional κ = 6.674324e-4 by ikeboy · Pull Request #194 · CrocSwap/integer-mult-bounds

ikeboy · 2026-10-09T12:43:44Z

Result

Conditional κ = 1668581/2500000000 = 0.0006674324. This is about 0.838% above PR186 (0.000661885549259598) and 0.398% above PR193 (0.0006647872).

What changed

PR193's complex supplier has saving 219037/312500000 = 0.0007009184. That is far above every published bit supplier, so the bit side binds.

This PR keeps PR193's complex word and replaces PR184's bit supplier with PR189's face-diagonal bit word (chafreaky). assemble.py reads PR189's certified bit profile (R = 17,554, W = 21,074, rank mass 1,515,392, deficit 1,936, largest child 60). It prices that profile with PR184's own select(): bad-row allowance 10^-16 with fallback 32 m^2 per edge, coarse saving on the 10^-10 grid, least payable atom on the 10^-12 grid, ordinary leaf 384599/10^10. It then runs PR184's assemble() unchanged: finite bridge, 47 strict constraints and seven margins.

Version	Complex saving	Bit supplier	Bit effective saving	κ
PR191	6.630702e-4	PR184	6.652295e-4	6.626307e-4
PR193	7.009184e-4	PR184	6.652295e-4	6.647872e-4
this PR	7.009184e-4	PR189	6.678782e-4	6.674324e-4

The bit coarse saving on PR184's grid is 6682989/10^10. The script checks that this does not exceed PR189's own 10^-18 certificate value, 668298937775631/10^18.

Verify

python3 -m pip install -r research/source-assisted/requirements-round13.txt
python3 -B research/source-assisted-v4/verify.py
python3 -B research/paired-cube-twin-local-168/verify.py

The first command takes about one minute and regenerates the complex word, flow, exact lift, contract checks and assembly. The second is PR189's own verifier (about two minutes). It regenerates the bit certificate that assemble.py reads. The workflow .github/workflows/source-assisted-v4.yml runs both.

Branch

The branch is PR193 plus PR189's commit (cherry-picked) plus one commit. That commit adds assemble.py, updates the package, and updates nine stale hash values in PR189's manifest (README.md, Makefile, NOTICE, SOURCES.json, the verify workflow, docs/reproducibility.md and the joint-dual files). PR189's verifier passes on this branch.

Scope

The complex supplier keeps PR184's validation scope: exact local lifts and contract checks, no globally renumbered scalar transcript and no full Clifford/router replay. The bit supplier keeps PR189's scope. PR184's finite bridge needs m ≤ 72, W < 10^7 and the uniform bit interface, which PR189's word shares with PR168 v4. The analytic, recursion, precision, weighted frame, fixed-tape routing, restored-row and all-size interfaces stay as assumptions.

Credits

icekylinx (PR184, with GPT-6 Astra and Codex assistance) for the source-assisted method, tools, finite bridge and assembly. chafreaky (PR189, with Anthropic Claude and OpenAI Codex assistance) for the bit supplier. eumemic (PR168 v4, with Claude assistance) for the query modules and physical layer. Package by Avi Eisenberg with Claude assistance.

🤖 Generated with Claude Code

…s: kappa = 5.878747e-4 Complex: PR144's paired cubes at p = 11 with a searched triple module and an annealed pair module; the face-2 and edge-02 outputs of each port are merged into one signed node per (b0, b2); 7,880 operation frames moved by physical descent and 2,970 gauged roles placed in dead donors' slots with deadline reads (AC 5885669/10^10). Bit: the paired-cube bit word with an annealed pair module (COARSE 5936323/10^10). Phase stop 1e-9. The complex side binds and the 47-constraint assembly gives kappa = 5878747/10^10. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

…the balanced prefix on paired cubes: kappa = 6.096379e-4 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

… on paired cubes: kappa = 6.457084e-4 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

…es: kappa = 6.489120e-4 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

…derived terminal sinks: kappa = 6.558894e-4 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

…on PR168 v4: kappa = 6.602166e-4 Complex: the direction-0 shared-edge local circuit of PR181 (13,042 virtual roles, 44 terminal sinks). Bit: 556 connected-component endpoint frame changes on PR168 v4's physical bit layer and 34 PR166 terminal sinks on face0 roots, rechecked on the overridden word with exact prime witnesses for all 24,577 used frames. Both suppliers and the paid balanced composition are independently certified above PR168 at 4a3c769: kappa = 330108276030861/(5*10^17). The bit branch still binds. The exact four-file PR175 overlay is retained. Prepared by Chafik Boukhalfa with substantial Anthropic Claude and OpenAI Codex assistance.

PR184 edits README.md, Makefile, NOTICE, SOURCES.json, the verify workflow, docs/reproducibility.md and the joint-dual source manifest. PR182 and PR185 pin those files, so their manifests go stale after the merge. This commit updates only the stale hash values: - certificates/joint-dual-kappa.json: source_manifest_sha256 - certificates/joint-dual-validation.json: certificate_sha256 - research/paired-cube-local-bit-168/SOURCE.json: nine shared files - research/bit-leaf-bootstrap182/SOURCE.json: regenerated with its own pin_sources.py No certificate value, construction file or package file changes. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

Apply PR184's source-parity local word and source-assisted frame flow to PR168 v4's query modules and physical layer instead of the older fd25adb modules. The complex supplier now has R = 10,824, W = 13,464, 1,412 source-controlled erasures and 707 kernel reuses. Its saving is 3315351/(5*10^9) = 6.630702e-4, about 0.91% above PR184's complex saving and 0.113% above PR186's. PR184's bit supplier is larger, so the complex side binds. PR184's unchanged finite bridge and 47-constraint assembly give kappa = 6626307/10^10 = 6.626307e-4, about 0.1126% above PR186 (6.61885549259598e-4). verify.py regenerates the v4 cache, the new local word, the flow, the exact lift, the contract checks and the assembly, and compares the result with certificate.json. A workflow runs it in CI. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

PR184 pairs each live gauge with a donor by a plain maximum matching. source_aligned_local_v4.py --avoid-parity-erasure instead takes a minimum-weight full matching that avoids pairs PR184's parity purification would erase. With the frozen result in data/physical-pairs.json the flow has 8,116 dependent outgoing values instead of 10,364 and needs 1,412 fewer dirty births: R = 9,412, W = 12,052. PR184's exact lift and contract checks pass unchanged. The complex saving rises to 219037/312500000 = 7.009184e-4. PR184's effective bit saving (6.6523e-4) now binds, and the unchanged assembly gives kappa = 103873/156250000 = 6.647872e-4: +0.438% over PR186 and +0.325% over PR191. verify.py now records the binding supplier and rounds binary-float diagnostics in the certificate, so last-digit libm differences between platforms cannot change the comparison. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

… kappa = 6.617552e-4 Complex: the direction-0 shared-edge local circuit of PR181 (13,042 virtual roles, 44 terminal sinks). Bit: assemble A[2,0] and A[2,1] from the two face diagonals (19,348 virtual roles), with a fresh carrier matching and gauge selection by the retained generator rules, our own physical layer (6,138 descended frames, 1,760 compensated handoffs) and 34 PR166 terminal sinks on face0 roots. Both suppliers are independently certified above PR168 at 4a3c769 with the paid balanced composition: kappa = 330877589979561/(5*10^17); the complex branch binds. The exact four-file PR175 overlay is retained. Prepared by Chafik Boukhalfa with substantial Anthropic Claude and OpenAI Codex assistance.

…ppa = 6.674324e-4 The complex saving of the v4 source-assisted word (7.009184e-4) exceeds every published bit supplier, so the bit side binds. assemble.py prices PR189's certified face-diagonal bit profile (R = 17,554, W = 21,074) with PR184's unchanged select() and assemble(): coarse 6682989/10^10, effective 6.678782e-4, 47 strict constraints and seven margins. kappa = 1668581/2500000000 = 6.674324e-4: +0.398% over PR193 and +0.838% over PR186. PR189's manifest pins README.md, Makefile, NOTICE, SOURCES.json, the verify workflow, docs/reproducibility.md and the joint-dual files; this commit updates those nine stale hash values. PR189's verify.py passes on this branch, and the workflow now runs it. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

…sition This PR's kappa is superseded on CrocSwap#194's inputs by CrocSwap#198 (same recurrence on a descended CrocSwap#189 word) and CrocSwap#197 (a stronger bit word), so state the standing plainly instead of claiming a record. What remains is the reproduction harness, the two maximality proofs, and a supplier-agnostic pricing path: applied to CrocSwap#200's deferred composition with CrocSwap#193's complex it yields kappa = 1693287/2500000000 = 6.773148e-4, +0.1826% over CrocSwap#197's standing claim, and the depth-2/3 rows sit 3.4e-11 below that word's own C/(1+C) ceiling, so pricing on it is exhausted. verify.py now re-prices the vendored CrocSwap#200 certificate and fails if the composition stops beating CrocSwap#197.

…duction report - CrocSwap#197: the bank-endpoint identity is proved on paper in PROOF.md:81-93; the finite controls (95-98) do not cover the full cover. Point to the maintainer review of CrocSwap#186's comparable removal in BANK-SCHEDULE.md. - CrocSwap#202: the 7 differing leaves derive from one lift gzip hash; CrocSwap#194's CI passed under CPython 3.13.16; CrocSwap#202 is CrocSwap#194 plus one commit and its CI has not run because of the merge conflict. Remedy cites verify_inner.py:23 and 29-30. - CI runs for CrocSwap#197 and CrocSwap#207 exist and await maintainer approval. - certificate_diff.py: usage (copy into a CrocSwap#202 checkout at 8d8d67b) and its .work/ side effect; code unchanged. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

Two observations establish the failure mode: CrocSwap#202's canonical check requires the sha256 of a container it regenerates (exact_complex_flow_lift.py:409 and :419, required by source-assisted-v4/verify.py:162) and fails on unchanged inputs, while CrocSwap#194 passes in the same environment; and PR212's pinned archive rebuilds byte for byte as a tar payload but not as a container. The repository already has the fixes in use -- CrocSwap#194 decompresses before comparing, CrocSwap#217 pins payload hashes and CrocSwap#207 checks semantic fields -- so this adds a scanner that locates the pattern, the audit with file and line evidence, and one CONTRIBUTING.md paragraph stating the rule once. Generated with Codebuff Co-Authored-By: Codebuff <noreply@codebuff.com>

… DFT PR CrocSwap#233 keeps PR CrocSwap#194's source-assisted word and replaces only its physical layer by PR CrocSwap#200's descent; its certified complex moment root 7.0861e-4 transfers as before (Proposition D). Vendored certificate, pin, moment certificate and controls added; expected.json regenerated.

…d prices at theta = 1 - 7547/10^7 (priced transfer), PR CrocSwap#194's at 7474/10^7 (Lean figure recovered)

Two observations establish the failure mode: #202's canonical check requires the sha256 of a container it regenerates (exact_complex_flow_lift.py:409 and :419, required by source-assisted-v4/verify.py:162) and fails on unchanged inputs, while #194 passes in the same environment; and PR212's pinned archive rebuilds byte for byte as a tar payload but not as a container. The repository already has the fixes in use -- #194 decompresses before comparing, #217 pins payload hashes and #207 checks semantic fields -- so this adds a scanner that locates the pattern, the audit with file and line evidence, and one CONTRIBUTING.md paragraph stating the rule once. Generated with Codebuff Co-Authored-By: Codebuff <noreply@codebuff.com> (cherry picked from commit 24e51c7)

Mister-Meeseeks · 2026-10-14T00:25:19Z

Thank you @ikeboy. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Composition of the source-assisted complex word with PR189's bit supplier.

Review and limits: Prior exact-head review and source-bound Linux CI. Retain the diagnosed local serialization mismatch and inherited global interfaces.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: a8c87783785be6fe20c4a8bb2ac4b3eec295a179. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.

eumemic and others added 13 commits October 9, 2026 00:16

Nested-prefix all-but-one modules, extended arcs, bundle descent and …

98c115b

…the balanced prefix on paired cubes: kappa = 6.096379e-4 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

Annealed modules, local circuit, fused outputs and physical bit words…

91f6a05

… on paired cubes: kappa = 6.457084e-4 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

Final triple module, terminal sinks and the L1 bit word on paired cub…

fd25adb

…es: kappa = 6.489120e-4 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

Annealed pair, triple and all-but-one modules on both words, with re-…

4a3c769

…derived terminal sinks: kappa = 6.558894e-4 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

Add finite ordinary-leaf bootstrap above PR182

32daefe

Add source-assisted common-frame compression for kappa = 6.566436e-4

e9c2af2

M6LI mentioned this pull request Oct 9, 2026

Independently audit PR #186 and refine its conditional exponent #180

Draft

evmckinney9 mentioned this pull request Oct 9, 2026

Pack #187's bit residuals: conditional κ = 0.000676080316519385 #197

Closed

sennemmi mentioned this pull request Oct 9, 2026

Lower PR189 endpoint frames plus finite leaf bootstrap: conditional κ = 0.0006679123 #198

Closed

maxime-fleury mentioned this pull request Oct 9, 2026

Bit leaf bootstrap: queue standing + the deferred #200 composition at conditional κ = 6.773148e-4 #199

Closed

chafreaky mentioned this pull request Oct 9, 2026

A stronger bit supplier: fixed-coordinate and face-diagonal bit local circuit on PR168 v4 (effective bit saving 6.7734e-4) #200

Closed

DaysSky mentioned this pull request Oct 9, 2026

A κ ceiling of 2.5592e-3 for every word on #144's paired-cube design (no new κ) #201

Closed

maxime-fleury mentioned this pull request Oct 9, 2026

Composed diagonal-bit bootstrap: the pricing model that called PR205's banked row, audits the queue, and prices the next ladder of κ gains #204

Closed

antoine-olivier mentioned this pull request Oct 9, 2026

Replays of the verifiers of #207, #202, #197 and #199 (no new κ) #214

Closed

maxime-fleury mentioned this pull request Oct 9, 2026

Audit hashes of regenerated gzip containers and propose a one-paragraph rule (no κ) #220

Closed

maxime-fleury mentioned this pull request Oct 9, 2026

Rung 2 above #219: a complex-side bank ledger that raises κ to 7.0829157e-4, blocked on C1/C5 #224

Closed

chafreaky mentioned this pull request Oct 9, 2026

Build #208's bank-absorption target: rank-22 residual absorption — certified accounting κ = 7.00427501305159e-4 (R1–R4 open; not a completed witness) #219

Closed

DreamingOfClouds mentioned this pull request Oct 10, 2026

A stronger complex supplier: compile-cost-annealed complex modules, five-stage complex saving 7635/10⁷ (+1.17% over #233; no new κ) #304

Closed

RobGruhl mentioned this pull request Oct 10, 2026

Searched pair module in the paired-cube bit word at p = 11: conditional κ = 5.616446e-4 #160

Closed

LJH-217 mentioned this pull request Oct 10, 2026

κ = 7.92580093369946e-4: w3 cube layer on #325's p10b word with a stronger p = 10 complex supplier #346

Closed

chafreaky mentioned this pull request Oct 11, 2026

Conditional κ = 7.93392809291691·10⁻⁴: #346's w3 bit word with a per-point p = 10 complex supplier (+0.1025 % over #346) #348

Closed

eumemic mentioned this pull request Oct 11, 2026

κ = 7.93392809671713586967588e-4: complete native admission for #346/#348 #351

Closed

Mister-Meeseeks closed this Oct 14, 2026

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Source-assisted v4 complex word with PR189's bit supplier: conditional κ = 6.674324e-4 - #194

Source-assisted v4 complex word with PR189's bit supplier: conditional κ = 6.674324e-4#194
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ikeboy commented Oct 9, 2026

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