Selected PR1094 precision: signed cancellation through unitary frames

[bitplane]

DONE — #1282

The unchanged selected PR1094 R480 programs have exact signed scalar/Horner maxima 131088 forward and 1154896 backward. The sufficient local envelopes are 18/21 bits instead of the retained positive recurrence's 52/68. Exact squared inequalities include partially stored real/imaginary components within the same 18/21 bits. Under the inherited global execution/precision hypotheses, replacing only the local term gives 397 → 350 sufficient bits. The production payload remains 512 and kappa is unchanged.

The written proof is a prefix norm corollary of the credited Lemma G conjugation theorem. Four exact boundary examples distinguish common frames, exact recipes, unitary labels and partial stores. At forward event 24223, scratch reaches 131088 although register rows peak at 131072, so coefficient work cannot be omitted.

Checks: 39386 scalar prefixes with sparse rational and dense integer engines; both 704-column endpoints and 960 wrapper unit rows; independent reverse functional plus whole-word primitive attainment of both peaks; 216 exact unitary-frame words, 2376 cuts and 57024 matrix entries; eight selected-word/bound controls. The entire unchanged original local driver passes both orientations and all 25 controls, with an identical regenerated receipt. Registered Python 3.12 and optimized Python 3.14 agree; six package/kernel tests include read-only relocation and source/receipt corruption.

Math commit: a7e3e61 on base dadfea6. Signed receipt: 17c82644f920abd7b9a776481efec1740f0ae75b99c53bf331e3e1442d328300. Source, exact predecessor heads and credit are in research/complex-signed-prefix-audit/.

No native/Clifford or full global cold replay, compiler/common-label/hosting realization, recursive-child internal precision, roundoff/tape/exact recovery, analytic transfer or new Lean proof is claimed. README/TASK give bounded formalization and production-admission follow-ups. The original larger bound is valid; this is no claimed acceptance defect. Claim released.

Original claim retained below:

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CLAIM

Question: Under exactly which common-frame and wrapper hypotheses can cancellations in signed scalar-prefix rows sharpen the physical Hilbert-space precision bound for the selected PR1094 R480 word? Does endpoint unitarity alone suffice? I will test that implication with exact counterexamples, then independently replay both unchanged source-bound scalar programs including coefficient-work prefixes.

Base: dadfea6. Selected PR1094: 0fc329d; parent PR1087: 589d1ce. OS assignment nonce 9e66acdf5b86cc4b02a0d212138d7b3e, adversarial-audit / uniform-transfer-audit, priority revision 2.

Method/domain: quantified unitary-frame transport lemma plus a minimal exact adverse instance; both archived forward/backward 704-column R480 programs, every scalar/Horner prefix and wrapper/frame boundary. No changed supplier word, paid profile, production payload or kappa claim. All-size physical realization and recursive child internals remain separate obligations.

Overlap: PR821 already gives the per-replica maximum-norm argument, so that initial idea is dropped. PR1184 accelerates the existing positive-envelope checker; PR734 changes coefficient circuits while preserving their envelopes; PR745 checks arbitrary private inputs and endpoints; PR1255 audits exact helper chart phases. This audit asks when signed-row cancellation survives the physical frame/normalization interface and checks the resulting unchanged-word prefix, rather than duplicating those results.

Expected artifact: research/complex-signed-prefix-audit/ with explicit hypotheses, source pins, exact independent replay and semantic controls, or a precise handoff if the implication fails.

Claim expires: 2026-10-13 23:25 UTC. Gareth Davidson (@bitplane), with substantial OpenAI Codex assistance. Claims are advisory.