[jeremydiviney]

PR705 leaves nine fixed eight-call Clifford register words unclassified when equal group products have different accumulated Fourier ranks. This extends its determinant argument by choosing arbitrary Laurent path weights and requiring homogeneity only for coefficients forbidden by the endpoint. The resulting exact certificate excludes evolved-27 for every invertible choice of its four 3-by-3 scalar blocks, even without a shared final frame per input column.

The certificate has interior weights (1,0,1), (-1,-1,0), (0,0,0), row potentials (-1,0,0) and column potentials (0,1,1). Its scalar weighted determinant has degree zero, while every permitted determinant term has valuation at least one. PROOF.md gives the general argument over a formal group algebra, including why cancellation of forbidden coefficients is preserved.

Across all nine unresolved words, one global and 918 frame-specific certificates exclude 1,093 of 1,152 endpoint frame triples; 59 remain unclassified. Of the exclusions, 865 already follow from the elementary allowed-entry matching test. The weighted criterion adds 228 exclusions beyond that baseline. No exhaustive comparison against predecessor support/polynomial methods is claimed.

No new κ or positive eight-call primitive. This is a fixed-word obstruction and reusable search filter in the inherited formal projective Clifford model. It does not close the general m=3, W=3, s=8 problem, infer formal linear independence from concrete 8-by-8 matrices, or extend to arbitrary circuit representations. The eight other whole words remain unclassified here.

Validation:

• Standard-library replay reconstructs all nine unresolved cases from the unchanged 73-word source corpus and verifies 919 exact certificates. Independent dense Gaussian multiplication/conjugation and symbolic paths agree on all 2,187 full paths, group classes, ranks and frames.
• Three exact nine-call positive controls, 104 Laurent determinant controls, and mutations of cancellation homogeneity, valuation bounds, strict gaps and frame coverage pass.
• Isolated relocated replay takes about 0.7 seconds locally. Equivalent gzip recompression is accepted; altered source/payload pins, incomplete coverage, a repinned zero-gap certificate and optimized Python are rejected. validate.py reproduces these controls.
• Optional one-thread SciPy discovery regenerates all nine exclusion counts; its numerical outcomes are never trusted without exact rational verification. It is not needed for replay.
• make selected-record-check passes. No full make verify or selected supplier cold replay is claimed for this standalone addition.

Reproduce:

python3 -B -S research/weighted-path-valuations/verify.py
python3 -B -S research/weighted-path-valuations/validate.py

Expected: PASS_WEIGHTED_PATH_VALUATIONS and PASS_WEIGHTED_PATH_CLI_CONTROLS.

All changes are confined to research/weighted-path-valuations/. Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. Credits: littleBro's PR705 (eeb0cd605415a73b792915aaa9185000f293c84a) supplies the predecessor argument, unchanged corpus and screen.py; PR680 (c3a5b6b7afec35d259c29bc2d8bb8516e975ad31) supplies unchanged model.py and dense.py; eumemic's PR288 and the retained Swapnil Jain/upstream lineage supply the framework. All three source files and the corpus are byte-identical to the pinned PR705 head. NOTICE.md and ORIGINS.json retain attribution and exact pins.

Prepared by Jeremy Diviney with substantial OpenAI Codex assistance. Apache-2.0; no literature-priority claim, independent human peer review or proof-assistant verification is asserted. Pre-submission overlap checks included PR720's distinct abelian bit theorem and PR791's distinct idempotent endpoint audit, with current metadata refreshed through PR799.

[Mister-Meeseeks]

100-PR batch review at d7d83e0a9b98f95a4443d1060336be267ac3fd80.

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

Reviewed scope: Weighted Laurent path determinant certificate closes one literal word and additional frame assignments; remaining cases explicitly unclassified.

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.