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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
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Thank you @rohanarun. This contribution is now recorded on main in the scoped reconciliation review and contributor credits. Contribution: Dual suffixes trade more additions for fewer roles. Review and limits: Exact-head CI evidence; both literal pieces remain paid. 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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Full verification passed. Full repository verification passed on
e72978fa40fa01e23583c58d40e42dab316ddc1ain 2436.677 seconds, completed 2026-10-09T00:35:17.720947+00:00:make -j1 verify(78 isolated test modules, 20 historical patch checks), fresh producer/certificate regeneration and six adversarial controls. All 39 research-head GitHub checks passed, with no source drift. Seeresearch/dual-suffix-centers/validation.jsonfor evidence hashes.Under all of PR104's inherited and newly proposed interfaces (as used by #107), T(n)=O(n(log n)^(1−κ)) with
κ = 7988289348441/10^17 = 7.988289348441×10⁻⁵, 2.4348% above #107 (7798412662809/10^17).
Idea. #104/#107 bind on the h24 all-disjoint rational-center (complex) producer: its strict saving 7799647191/10^14 sits below the stopped bit saving 803380799/10^13. Each pair star (a,b) computes its 22 leave-one-out sums with the ordinary layout s_j = A_{j−1}+B_{j+1}. We replace only that block with the dual-suffix identity from the bit strips of #55: s_j = (A_{j−1}+v_{j+1}) + B_{j+2}, s_k = A_{k−1}. Covers now nest along the prefix chain, so the unchanged legal carrier matcher joins far more additions.
Everything else is #107 unchanged: coordinate order, center trees, divisor 21, rational scatter, copied-center corrections, stopped bit axis, bit parameter rule min(AB,(1−10⁻⁶)b−10⁻¹⁰), assembly. The complex leaf still binds, with ~0.57% headroom below the bit axis.
Checks (
research/dual-suffix-centers/verify.py,test_controls.py): reproduces #104's certificate; regenerates the #104, #107 and new producers with every exact support/center/rational-scatter/frame-nesting assertion; recompiles the inherited matcher; checks every histogram entry; all 47 strict constraints, 7 margins, both next-grid exclusions (complex 7989584038/10^14, κ 7988289348442/10^17); controls reject unpaid cleanup, omitted loss and the #104/#107 histograms at the new bound. 330+ source pins checked.Scope: finite conditional witness; #104's opposite-bank factorization, stopped streaming and odd-denominator grid interfaces remain written proof dependencies. No optimality or runtime claim.
Credit: icekylinx (#104), Rohan Gupta / gupt1156 (#55 dual-suffix strips), Avi Eisenberg (#53), #107, and all predecessors in #104's NOTICE/SOURCES. Prepared by Rohan Arun with Anthropic Claude assistance.
Independent local verification of commit
e72978fa40fa01e23583c58d40e42dab316ddc1a: producer regeneration and exact certificate passed; all six adversarial tests passed. Full repository verification is now complete; the committed receipt documents it.