Selected PR1094 residual charts: same projector versus exact phase

[bitplane]

DONE — PR #1255, final submitted head add1e2673ef000c097ec0fd70058e644af048d6b.

The selected construction passes the audit. Orthogonality and the active projector alone do not determine its exact normalized complex residual: an orthogonal rebase S preserves the product of C gates iff every row of S has weight 1 modulo 4. The four-axis I+J rebase preserves geometry and spectators but changes i/4 to -i/4; a six-axis nonpermutation rebase is a positive case. The phase-refinement principle is classical; this is its explicit source-bound application.

All 69,120 selected helper roles and 10,002 emitted 73-axis charts pass; 10,008 chart/width signatures give 5,348,224 exact kernel coefficient checks. The complete dimension1–6 census covers 23,817 orthogonal matrices. The pinned controller's isolated unchanged predicates reject the phase-changing chart and a wrong spectator route. Its C-only evaluator agrees on 512 input columns. This is not a reported production defect.

Registered Python 3.12 replay and a read-only isolated optimized Python 3.14 replay pass, including eight package tests. Mathematical receipt: 34f3fc87deac2e04323d140b490133f7ebe2788c66143c926b5e266126993269; source-predicate receipt: 0f1fc10c00dfbedeebc2c96353c18bdc2a7fff9a40abbd789397e21b395bf1cb.

The normalized local endpoint, full scalar/native/phase-wrapper replay, physical compiler/hosting, invoice/precision/tape and analytic transfer remain inherited. No new supplier, runtime or kappa claim. README/TASK give bounded follow-ups for a fully priced phase-preserving rebase and a formal proof. Predecessor and parallel work retain credit. Claim released.

Original claim retained below:

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CLAIM

Question: For the selected PR1094/T16 residual charts, do orthogonality, the active subspace and its projector determine the exact normalized complex residual? Audit the stronger ordered-axis/phase obligation, using a four-axis orthogonal rebase that keeps the active projector but can change the exact convolution kernel. This is a test of a weakened implication, not an allegation of a selected production bug.

Base: 49b3157. Selected PR1094 source: 0fc329d. Sources: the actual selected-replay archive, literal 69,120 owners, 10,002 emitted 73-axis charts, inherited C-gate semantics and controller audit. Do not use the historical evidence/local or evidence/global directories as current replay.

Method/domain: separately implemented exact Gaussian-integer convolution kernels, orthogonal binary basis rebases through dimension six, a quantified phase-refinement criterion, and a source-bound check of every selected helper route/active slice/spectator completion. Test an embedded four-axis same-projector rebase and compare its literal operator with the expected pending-axis product. If the current contract rejects it, record that protection. Stop at this finite source boundary and theorem; no native scalar replay, new supplier or kappa claim.

Nearest work: PR1209 checks selected pending-axis independence and chronological cuts but excludes spectator charts. PR1149 checks canonical-frame recursive rank. PR702/712 independently check historical local wrapper phases. This audits a physical orthogonal rebase of the normalized residual and distinguishes same-projector maps by their Z/4 weight refinement; it does not repeat those local wrapper identities.

Expected artifact: research/selected1094-chart-phase, proof/receipt and explicit rejection controls, one focused PR if the finding is confirmed. Card supplier-boundary-audit, refined scope; OS chooser seed08486e2f4cb05dd9e1b849fa4eff7033, priority revision2. About60 minutes total, final quarter for verification and handoff.

Claim expires: 2026-10-13T22:47:17.819161+00:00.

Gareth Davidson (@bitplane), with substantial OpenAI Codex assistance. Credit Rohan Arun, Jeremy Kothe, Hao Yan, Josie Elliston, the Clifford/normalization lineage and parallel auditors; classical quadratic-refinement facts carry no priority claim.