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Replace the complex motif's per-pair side wires with a shared-sum circuit (3,693,800 -> 108,195 side roles per invocation at h=25). Binary coordinate and pair-star labels give every frame residual an orthonormal basis; injected disjoint pieces must leave an outside point uncovered, since otherwise the residual is an alternating hyperbolic plane. The certified complex saving rises from 418/10^12 to 14/10^9, so the paired bit network becomes the only binding motif. With the compact-control recurrence this gives the conditional witness kappa = 59/10^11 > 2^-31, 590/83 (about 7.11) times the preceding 83/10^12. - scripts/complex_circuit.py: circuit, F2 label algebra, role compiler, both-direction frame checks, exact dirty-scratch simulator - scripts/complex_network.py: full h=25 checks, counts, guard, gate bound, parameter witness -> certificates/complex-network.json - scripts/make_complex_circuit_patch.py -> patches/complex-circuit-31.patch - notes/complex-circuit-*.tex and artifacts/complex-circuit-note.pdf - tests/test_complex_network.py; README, status and reproducibility docs Contributed by eumemic. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
The upstream workflow limits each job to ten minutes. Cache residual and label verdicts by canonical basis (same checks, entry/exit checks now also require full label validity), and let the patch generator recompute only the counts and witness instead of the full finite checks, which scripts/complex_network.py and the tests already run. The certificate drops its diagnostic count of distinct cached checks; the patch is unchanged. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
- Evaluate the Gaussian maps S' and E as chirped block correlations with the established multiplier: O(p^(1+delta)) per output - Bound powers of the resampling correction by a potential argument, so the Neumann series needs O(p/alpha^2 + 1/theta) terms - alpha = floor(sqrt(b/(8d))): Gaussian cost O(d^2 p^delta), epsilon may approach 1/2; beta = 19/25 fits the compressed complex saving - Conditional witness kappa = 1479/10^12 > 2^-30 (1479/590 above 59/10^11) Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
- Feed each center wire from its group total inside the side circuit: it rises only to the star span H_i, so it loses h-1 instead of h dimensions per invocation in both stage directions - Align the paired blocks across common points and share each top-level pair-star chain between its two groups: 494196 roles vs 509244 - Bit saving 296/10^11 -> 325/10^11; witness 1479 -> 1624/10^12 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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Thank you @eumemic. This contribution is now retained on main in the scoped 100-PR review and contributor credits. Contribution: Independent full replay report for PR604 cold ends. Review and limits: Original construction credit remains with its authors. Source-bound receipt auditing is distinct from a new maintainer full replay or all-size theorem proof. This round verifies identity and shipped receipt/result/assembly hashes; it does not recreate the contributor’s original replay. 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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κ = 0.00162128508944984 (conservative κ = 0.001621285086572193)
This PR independently replays the exact head of #604, a new cold_end architecture that lets 14 factory-scratch helpers per provider call finish at dimension-4 frames after an exact premix and guarded multi-gate cleanup. It records the fresh evidence without changing any published upstream head.
Evidence:
The full receipt, result, assembly controls, phase controls, owner/profile audit and independent audit summary are in certificates/pr604-independent-replay/. The replay remains conditional on the inherited all-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape/exact recovery, analytic transfer and bit H1–H5 assumptions. No Lean replay or unconditional theorem is claimed.
Provenance and AI disclosure: the upstream cold_end construction is credited to DreamingOfClouds with Claude Opus 5.5 assistance and its inherited contributors. This independent replay and certificate packaging were prepared with OpenAI Codex assistance.