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Thank you @eumemic. This contribution is now recorded on main in the scoped reconciliation review and contributor credits. Contribution: Three-stage cover with general Clifford phases. Review and limits: Exact-head CI evidence for finite construction; uniform phase/compiler contracts remain assumptions, not consequences of geometry alone. 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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κ = 3.32205398986e-4 = 166102699493/500000000000000.
κ ≈ 332205398986/10¹⁵ > 2⁻¹².
Under PR130's retained three-stage cover and analytic/tape interfaces, this finite conditional witness supports T(n) = O(n(log n)^(1−κ)). It improves PR130's pinned
6a9970aclaim3.146011e-4by 5.59575%. The new claim uses our independently replayed physical operation frames and compensated scratch reuse as the complex local supplier for icekylinx's three-stage Cayley architecture. The PR130 bit supplier is unchanged.The complex word changes frames at 19,323 physical operation occurrences and reuses 2,108 dead slots at compensated births. Every birth subtracts the exact old response of the donor's actual current value. The complete source/workspace word is reversed in its actual chronology, restoring each surviving physical slot for arbitrary dirty inputs. Exact rational readout coefficients are split into bounded same-frame shears; all additional shears remain charged.
PR130's three cover stages use the forward word, complete reflected inverse, and forward word on separate invocation banks. Our nondegenerate frames are a special case of its arbitrary-subspace Clifford theorem. The fixed source lines and output hyperplanes remain unchanged, so the cover's exact interstage frame equalities, signed three-shear interchange and paid rank-zero endpoint/Pauli adapters continue to apply.
The profile removes exactly the obsolete two-stage data bridges, rank-one endpoint copies and auxiliary exteriors from the already audited local ledger, then divides the remaining multiplicities by the two-stage invocation count. It retains every local source/target move, internal transition and copied center. Three copies of this local inventory are combined with the actual per-stage exteriors of width 70 − 24 + dim σ. The source inventory is over physical slots: reused recipients have no separate stream or exterior. Independent accounting verifies the full histogram, nonnegative integral counts and
70×83839 − 5866338 = 2392.The full orthogonal group is still included:
|O(70,2)|has 2,415 bits, and the actual total role stock has 2,431 bits. Its factor cancels only in the normalized moment. The scalar/router reserve uses the full physical global stock and retains the 28,705 virtual roles for readout/compiler work. The per-invocation scalar guard 55,062,438,637,392 exceeds both the independent conservative guard 14,907,958,248 and its expanded literal count 12,160,614. The full finite router, exact odd-denominator grid, semantic guard and external row reserve remain paid. The row coefficient is 68,505, with degree 160,000.The unchanged weighted local-ring bit cover retains its complete
32m²rare-class fallback charge, stopped ordinary saving 3731649599/10¹³, uniform batching, weighted children and restored borrowed rows. It has slack at the new complex saving. Exact final assembly verifies all 47 strict constraints, seven margins, the next complex enclosure grid point and the next κ assembly grid point.Validation at current head
3acf2f9: The complete package verifier passes: fresh physical compiler and reuse pairs, independent literal reflection and dirty cleanup, scalar accounting, finite geometry regeneration, exact cover assembly, all 16 package controls, and unchanged source hashes. PR130's completemake three-stage-cover-verifyalso passes, leaving all 1,578 baseline files byte-identical. Independent checks reproduce the cover histogram and rational moment. The finite geometry audit covers every binary subspace through dimension four, including degenerate cases, and all 2,024 actual dimension-24 port seams. All 45 current-head CI checks pass, including the dedicated full verifier on Python 3.11, 3.13 and 3.14.The package binds the existing complex compiler, physical source inventory, full reflected scalar/frame ledger, finite geometry audit and exact certificate. Verification regenerates artifacts in a temporary copy and rejects disabled assertions, altered charges and missing physical records. The finite group is specified mathematically rather than enumerated. PR130's exact Clifford phases, group construction, uniform q-adic batching, weighted local-ring compiler and borrowed-row proofs are explicit dependencies, along with inherited normal-form, precision, analytic, prime, routing, recovery and fixed-tape interfaces. This is a conditional finite witness, not a practical runtime or unconditional theorem claim.
Credit: icekylinx with OpenAI GPT-6 Astra/Codex assistance for PR130's three-stage Cayley covers, generalized Clifford theorem, weighted local-ring compiler, rare-class fallback, internal rows and exact framework, and the PR104/115 lineage; James Chang / jamesyc with OpenAI assistance for PR124's compensated birth-cut reuse; eumemic with Anthropic Claude assistance for PR117's scalar DAG; Avi Eisenberg / ikeboy for the physical compiler; Zhihao Chen / jacklightChen and Swapnil Jain for the retained physical bit word; an664 for PR128's completed-core context; Rohan Arun, Aurel Prosz, RaD and all inherited contributors. Concurrent physical-frame work in PR125/126 remains credited. Our physical-frame optimizer, this local-word composition and independent checks were prepared for eumemic with OpenAI Codex assistance. All adopted licenses and source-specific disclosures are preserved.