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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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κ = 0.001612719427075359 (conservative 0.001612719424224312). Independent clean replay of CrocSwap PR592; see certificates/frontier-20261012-592.json and certificates/pr592-independent-replay/. All required scalar, dirty-restoration, reflected-ledger, invoice, assembly and control checks pass. PR592's Claude Opus 5.5 disclosure and provenance are retained; this replay was prepared with OpenAI Codex assistance. Conditional assumptions remain as stated in PR592.