Repository navigation
Conversation
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>
rohanarun
marked this pull request as ready for review
October 8, 2026 10:36
Contributor
|
Thank you @rohanarun. This contribution is now recorded on main in the scoped reconciliation review and contributor credits. Contribution: Partial-swap ternary construction removes a legacy outer shear. Review and limits: Focused tests include nonsymmetric controls; source archive retains all alternative experiments with their stated scope. The complete original source, proof/research notes, notices and relevant replay/CI evidence are retained through the pinned source archive. The review distinguishes fresh runs, exact-head historical CI and prior integration evidence. Closing this historical PR as reconciled; its obsolete headline does not replace the current selected bound, and draft/retracted claims retain their explicit qualifications. Reviewed head: |
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
3 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Partial swaps on the ternary six-block network
Apply icekylinx's #18 partial-swap frames to our #17 ternary construction. This yields the conditional witness
about 11.09% above #18 in exponent saving, not practical runtime. Subsequently superseded by Zhihao Chen’s #21 (κ = 5.499e-6); this PR remains a checked research record.
The new frames remove exactly N exceptional source calls, giving
s=Wm-2N+2L. The h30 producer, physical role allocation, matching, nested basis and all six recursive block multiplicities remain unchanged. The source-relocated auxiliary exit keeps the same projector. The circuit now directly implements interchange; the legacy outer shear-conversion passes are explicitly removed.The bit saving is 4187/10^9. The unchanged h28 complex construction uses its stronger certified saving 4191487/10^12, beta=1/1000 and C1=3749/2500. All 29 constraints and seven margins are strict; the final absorption gap exceeds 6.16e-13.
Proof and validation
research/partial-swap-ternary/proof.tex.make verifypassed 308 tests and 21 inherited patch checks. Its source hashes are revalidated here.make verifyexited 0 at56d4216: all 312 published tests plus four unpublished follow-up tests passed (316 observed), and all 21 inherited patch checks passed. Physical producer regeneration completed. Seeresearch/partial-swap-ternary/validation.jsonfor scope and the log digest.The follow-up documentation correction names all 33 complex rank classes and explains the inverse early-copy split 27+729 already counted by the certificate. The full candidate witness, four tests, manuscript patch and PDF were rechecked; numerical bounds are unchanged.
Finite checks and an independent agent audit are not formal verification or independent expert mathematical review. The general basis, arbitrary-width tape, precision and inherited multiplication interfaces remain mathematical dependencies.
Attribution and review base
The partial-swap frame and triangular-conjugation identity are icekylinx's #18 contribution at
f2ab41aebad47861caf6316282c1793e5513845e; pinned unmodified sources, license, NOTICE and hashes are inreferences/pr18/. We claim this compatible ternary composition, not those underlying ideas.This branch is based on #17 (
c915b4117626a512dd470adbdbd76963108f5cb3), itself based on #15; the main-branch diff therefore includes those pending dependencies. Review the final composition commit for this addition.Credit to eumemic (#13/#15 producer, source frames and complex batching), Zhihao Chen (#16 nested basis and earlier five-subset work), icekylinx (#10 tape/batching and #18 partial swaps), Rohan Arun (#14/#17 geometry and composition), Douglas Colkitt, OpenAI and prior contributors. Prepared by Rohan Arun with substantial OpenAI Codex assistance and parallel proof/test reviews. No global-optimality or endorsement claim is made.