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…289348441e-5
Replace the ordinary prefix/suffix leave-one-out of each h24 pair star with the
PR55 dual-suffix identity s_j = (A_{j-1}+v_{j+1}) + B_{j+2}. The unchanged legal
carrier matcher joins 15,422 instead of 8,750 additions, so roles fall from
44,918 to 43,270 and the binding strict complex saving rises to 7989584037/10^14.
Conditional kappa = 7988289348441/10^17, 2.4348% above PR107.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
…55e-5 Replace the prefix/suffix leave-one-out strips of PR104's h23 retained-total bit producer and of the h24 rational-center PairedTriple recursion with cyclic interval strips (PR62's construction), keeping PR108's dual-suffix pair stars. Unchanged matchers join 30,197 (was 1,324) bit and 37,802 (was 15,422) complex additions: roles 38,776 -> 32,301 and 43,270 -> 38,506. Certified stopped coarse saving 898920417/10^13, strict complex saving 8579641984/10^14, and conditional kappa = 1715630240171/(2*10^16), 7.278% above PR109. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
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Thank you @rohanarun. This contribution is now recorded on main in the scoped reconciliation review and contributor credits. Contribution: Cyclic strips on both axes and positive matchings. Review and limits: Exact-head CI evidence; actual matchings and envelope bounds are distinct checks. 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: |
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fb550b9b1a3c60cc419701e530494ed754d08cefin 2409.831 seconds, completed 2026-10-09T00:45:01.380047+00:00:make -j1 verify(78 isolated test modules and 20 historical patch checks), both producer regenerations, exact assembly and six adversarial controls. All 39 research-head GitHub checks passed; no source drift. Seeresearch/cyclic-strips-both-axes/validation.jsonfor evidence hashes.Live comparison: PR #110 appeared during submission and reports κ = 8.58478×10⁻⁵, about 0.07728% above this candidate. This PR therefore makes no current-record claim. Its cyclic-strip construction may be compatible with #110's deferred readouts, but that combination has not been verified.
Under all of PR104's inherited and newly proposed interfaces (as used by #107–#109), T(n)=O(n(log n)^(1−κ)) with κ = 1715630240171/(2·10^16) = 8.578151200855×10⁻⁵, 7.278% above #109 (7.9961717358×10⁻⁵), 7.384% above #108, 9.999% above #107.
Idea. Both axes of #104 compute leave-one-out strip sums with s_j = A_{j−1}+B_{j+1}. We replace them with cyclic interval strips (#62's construction from the frame-compiler lineage): build every cyclic interval I(a,m)=I(a,m−1)+v_{a+m−1}; s_j is the complementary interval. Every interval has a later consumer with a containing cover, so the unchanged carrier matchers join far more additions.
PairedExclusionCircuit.block's strip layout (cyclic, carry last), loaded privately; positive labels recomputed by the unchanged labeler; positive matching = envelope matching.((i^1) in (a,b), i).Checks:
research/cyclic-strips-both-axes/verify.pyregenerates both rows from source with every exact support/center/scatter/frame assertion and the unchanged matchers; certifies the stopped coarse moment (rejects COARSE+10⁻¹³), the strict complex moment (rejects b+10⁻¹⁴), all 47 constraints and 7 margins (rejects κ+10⁻¹⁷).test_controls.pyrejects the #104 bit row, the #108 complex row, unpaid cleanup, omitted loss and an unpaid role on the mathematics alone (certificate comparison disabled), and accepts the selected rows. 336 source pins.Scope: finite conditional witness; #104's opposite-bank factorization, stopped streaming and odd-denominator grid interfaces remain written proof dependencies. No optimality/runtime claim.
Credit: icekylinx (#104), Avi Eisenberg (#62 intervals, #53), Rohan Gupta / gupt1156 (#55 dual-suffix strips), #107–#109, and all predecessors in #104's NOTICE/SOURCES. Prepared by Rohan Arun with Anthropic Claude assistance.
Independent local verification of
fb550b9b1a3c60cc419701e530494ed754d08cefalso passed: both producer rows regenerated, exact assembly and three next-grid checks passed, and all six adversarial controls passed. Full repository verification is now complete; see the committed receipt.