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…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>
…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.
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Reproducibility finding (verified this session, Linux / Python 3.12): A field-level diff of the recomputation against the frozen
Two independent full recomputations with different forced Consequence: every downstream |
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Thank you @ikeboy. This contribution is now retained on main in the scoped 100-PR review and contributor credits. Contribution: Paired donors avoiding parity erasure in source-assisted flow. Review and limits: Prior exact-head strict semantic-adapter replay plus source-bound Linux CI. The adapter validates mathematical payload, rather than ignoring arbitrary hash differences. 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: |
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Result
Conditional κ = 103873/156250000 = 0.0006647872. This is about 0.438% above PR186 (0.000661885549259598) and 0.325% above PR191 (0.0006626307).
The complex saving is b = 219037/312500000 = 0.0007009184. PR184's effective bit saving, about 0.00066522948, is now smaller, so the bit supplier binds.
What changed
This PR adds one commit to PR191. PR191 runs PR184's source-parity local word and source-assisted frame flow on PR168 v4's query modules and physical layer.
PR184 pairs each live gauge (recipient) with an earlier donor role by a plain maximum bipartite matching. Its flow then erases some donors with original-source X controls at cube parity frames. Here
source_aligned_local_v4.py --avoid-parity-erasuretakes a minimum-weight full matching of the recipients instead. A pair costs 2 if the parity purification could erase it, and 1 otherwise.With the frozen pairs in
data/physical-pairs.json, the flow erases no donor and reuses no kernel. It finds 8,116 dependent outgoing values instead of 10,364, so it needs 1,412 fewer dirty births.Any legal pairing is allowed.
paired_cube_physical.physical()checks the frozen pairs. PR184's exact lift and contract checks pass unchanged on the new flow: all fresh columns equal the identity over the integers, source controls sit at paid parity frames, centers finish in phase 1, target cap reads occur in phase 2, and target chains nest.The complex side now has about 5% of slack over the bit side. A stronger bit supplier would raise κ further, up to the complex saving.
Verify
It takes about one minute. It regenerates the v4 cache and the new local word with the frozen pairs, runs PR184's flow, exact lift and assembly unchanged, runs this package's copy of PR184's contract checker, and compares the result with
certificate.json. The workflow.github/workflows/source-assisted-v4.ymlruns it in CI.Branch
The branch stacks on PR191, which stacks on PR185's head
32daefe471e1e41926971747bb901e2839938b43with PR184's commit merged. A separate commit in PR191 only updates the shared-file hashes that the merge made stale.Scope
PR184's validation scope applies. The exact lift and the contract checks establish the local maps and the flow ledger. There is no globally renumbered scalar transcript of the new complex word and no full Clifford/router replay. The bit supplier and its scope are PR184's. The analytic, recursion, precision, weighted frame, fixed-tape routing, restored-row and all-size interfaces stay as assumptions. The PR192 frame ceiling covers only PR168's fixed word and pairs, so it does not apply to this word.
Credits
icekylinx (PR184, with GPT-6 Astra and Codex assistance) for the method, the tools and the bit supplier. eumemic (PR168 v4, with Claude assistance) for the query modules and the physical layer. Package by Avi Eisenberg with Claude assistance.
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