Research audit: exact phase criterion for selected PR1094 residual charts

[bitplane]

Change and mathematical scope

An orthogonal rebase can preserve the active projector, every spectator axis, support and amplitude magnitudes while changing the selected supplier's exact complex residual. Add research/selected1094-chart-phase/, a source-bound adversarial audit of this implication. The selected construction passes, and its existing stronger chart binding rejects the demonstrated mutant. No production defect or new κ is claimed.

For orthonormal active columns U and V=US with S orthogonal over F2, the products of the inherited C_q=((1+i)I+(1-i)X_q)/2 gates agree exactly iff every row of S has weight 1 modulo 4. The proof derives the phase character for every dimension. The four-axis I+J rebase is the smallest bad case: i/4 becomes -i/4 at one displacement while the diagonal stays -1/4. A six-axis nonpermutation rebase supplies a positive case. The quadratic-refinement principle is classical; the scoped application and executable evidence are the contribution.

Task and overlap

Card supplier-boundary-audit, refined to normalized physical residual charts and exact phase. Random chooser nonce 08486e2f4cb05dd9e1b849fa4eff7033, priority revision 2. Scoped claim: #1237. Experimental base 49b3157d1d89adcef16df8be98445451672be5ba; submission base dadfea6e8a78ff6ba901705f87532a71c6f5bbb8, with scientific inputs unchanged.

Selected PR1094 source 0fc329d0bec93ca7cd288eaea1295172e8789810, parent PR1087 589d1cedf5ef5f231182f4ec86408616311a8af0. The inputs are the actual selected replay archive and literal owners, not historical copied evidence directories. SOURCE/TASK metadata pins all inputs and the original task.

PR1209 (d1ba263139ceb6eb811628b7560a3f87f3c9652e) audits pending-axis independence and chronology, excluding spectator charts. PR1149 (f66dd4019d67a9660921bc204532306b47f4196e) audits canonical-frame rank. PR702/712 audit historical local wrapper phases. This contribution checks the normalized residual's physical active-basis phase refinement and current emitted-chart binding; it does not replace those distinct checks. Exact parallel heads and credit are in NOTICE.md.

The final 21:05 UTC overlap snapshot covers all 844 open PRs through #1247, nine Discussion threads/comments and 324 local records, with complete pagination and no refresh warnings. Declared literal-search coverage is recorded; no matching investigation was found. Historical PR407 is a separate entrance-frame construction. This is not a novelty certificate.

Validation

python3 -I -O -B research/selected1094-chart-phase/verify.py
python3 -I -O -B research/selected1094-chart-phase/production_check.py
python3 -I -O -B research/selected1094-chart-phase/test_package.py
python3.12 scripts/research_package.py --package research/selected1094-chart-phase

All 69,120 roles /144 calls /10,002 emitted charts pass. The check covers 53,300,658 Gram entries and all 10,008 (chart,width) signatures. Literal physical convolution, an independent subset formula and chart transport agree on 5,348,224 coefficients in both signs. All 23,817 orthogonal matrices in dimensions 1–6 pass the exact criterion over 2,996,852 coefficient comparisons. Six semantic controls and eight package tests cover operator columns, spectator fibers, enumeration completeness, and actual optimized source/container/receipt corruption.

Separately, unchanged source orthobasis/audit function ASTs and the chart-table assertion pass their original input and reject two mutations. The verbatim source C-only evaluator matches 512 complete input columns. This is an isolated source-predicate replay, not the top-level admission driver. The mathematical verifier imports no predecessor executable code.

Complete registered Python 3.12 replay and a read-only relocated Python 3.14 replay pass with identical mathematical and production receipts. Mathematical receipt: 34f3fc87deac2e04323d140b490133f7ebe2788c66143c926b5e266126993269. The selected-record check and metadata/Git pins also pass. Exact commands, limits and corrected harness issues are in VALIDATION.md. Hosted PR CI is reported separately.

The normalized local endpoint is inherited. Full scalar/native/phase-wrapper replay, cost/precision/tape invoices, all-size compiler, physical cover realization, analytic transfer and the multiplication theorem remain outside scope. No faster algorithm or improved paid profile is claimed.

Credit

Gareth Davidson (@bitplane), with substantial OpenAI Codex assistance; no subagents or independent human review. Credit Rohan Arun, Jeremy Kothe, Hao Yan, Josie Elliston, Douglas Colkitt, the Clifford/normalization lineage, and the parallel auditors named above. Apache-2.0; frozen inputs and attribution are preserved.

Open next questions

README/TASK describe two bounded follow-ups: test one phase-preserving six-axis rebase on a selected width-seven role with its complete physical cost, and formalize the universal phase criterion against exact C-gate semantics. Current literal route admission and the physical compiler remain explicit blockers; no improvement is implied by those suggestions.

[Mister-Meeseeks]

100-PR batch review at add1e2673ef000c097ec0fd70058e644af048d6b.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Exact Z/4 weight criterion for phase-preserving orthogonal rebase, all10002 emitted selected charts and source-predicate controls; inherited local normalization and full admission remain separate.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.