# Verification report ## Accepted result Theorem 1.1 proves inertia (N-1,1,0) and the positive-eigenvalue lower bound 1 - (cos(pi/m)-1/2) Delta under the displayed local and degree hypotheses. The uniform degree caps are 3 at m=5 and 2 at finite m>=6. Proposition 3.1 gives the full paired-part spectrum and shows that the next integer degree fails. The nonstar four-part examples satisfy all hypotheses. These are complete statements, not pending proof candidates. Corollary 1.2 invokes Theorem 1.1 of Blasco-Garcia, Cumplido, Holt, Morris-Wright and Rees. The absence of the two forbidden triples is proved explicitly. Complexity is in word length for each fixed presentation, not uniformly in a variable binary-encoded Coxeter matrix. ## Self audit The audit checks the perturbation sign, the codimension-one form bound, strictness excluding zero eigenvalues, all possible part-size cases in the negative-direction proof, and every invariant subspace in the sharpness spectrum. The two-negative obstruction still has the cited word algorithm. It is not a counterexample to an AIM conjecture. The local neighbor condition is essential: omitting it allows the positive-definite D4 star. Three vertices are excluded, in particular the positive-definite H3 triple. Properties of the displayed standard diagrams do not establish intrinsic properties of all alternative presentations or pairwise nonisomorphism of the abstract groups. ## Exact finite checks Rational-pair arithmetic in Q(sqrt(5)) is used throughout. All 1190 admissible small diagrams have the expected inertia. Across the 2120 tested cross-edge subsets for integer partitions of four and five vertices, local admissibility agrees with forbidden-triple avoidance. Eight paired-part sharpness instances pass exact inertia tests and 104 eigenvector identities. Three nonstar four-part examples and the D4 control also pass. Normal and optimized Python outputs are identical. The portable program and reports are in reproducibility/. These are finite regressions. The arbitrary-rank theorem is justified by the written proof, not by extrapolation from those tests. No numerical eigensolver, Artin word-algorithm implementation or proof assistant was used. ## Source scope and attribution The exact AIM entry asks for further finite-label Lorentzian examples. The construction contributes a specified family, not an exhaustive classification or a solution of the general Artin word problem. It also does not answer the more restrictive historical small-type question, which permits only exponents 2 and 3. Our examples use exponents at least 5. The multipartite spectral identity is classical and proved directly here; Delorme is cited for the background spectra. The Artin algorithm is prior work, publicly available since December 2024. The inherited weighted-star calculation is not presented as a new algorithm. A bounded search found no exact statement of this sharp assembly but does not establish priority. ## Artifact checks The standalone English source compiled successfully with the desktop compiler and the export compiler. All five PDF pages were visually inspected; no clipping, broken references or visible formula defects were found. The author line contains Alper Ferudun alone, with Mercury Software GmbH and contact details in a footnote. AI assistance is disclosed in ordinary prose, not a separate AI section. Package hashes and portable checker receipts accompany the source archive. Assessment: originating-researcher self-audit. Independent review: not performed. Formal verification: not performed. Absolute priority: not certified. The broad frozen source remains PARTIAL_RESULT.