Local C3 Rigidity of Symmetric Nonlinear Star-Triangle Equivalence

Research Note No.38, unrefereed, AI-assisted preprint v1.1. Ryutaro Yonezu, Yonezu Research Lab. First published 24 October 2026; audit-status follow-up 25 October 2026. For a three-terminal star with three identical odd C3 current-voltage characteristics f normalized by f'(0)=1, exact local realization by a triangle with three identical edge functions determines the germ of f from its cubic coefficient. No regularity of the triangle function is assumed. The local converse covers positive, zero and negative cubic coefficients and gives the fifth-order obstruction d=33c^2/20. The explicit star-triangle family and its existence are established prior art. The later received package-audit report gives MODEL/DOMAIN, B-prime PROOF, COMPUTATION and SOURCE PROVENANCE PASS, with KNOWN FAMILY ESTABLISHED. The reviewer reports check_hashes.py 27/27 PASS and a full verify.py rerun on Linux/Python 3.13.17, with all five result groups exactly matching the frozen evidence: polynomial/rational checks, formal series, numerical tests, negative controls and 80-digit checks. This includes 578 rational substitutions and 621 voltage triples. This supersedes the earlier PDF-only review's missing-code limitation. The reviewer also checked the cited BKS/BMS correspondence. Additional reviewer mpmath, general-parameter and BMS-log scripts/logs have not been supplied. Windows execution, human peer review and formal proof-assistant verification are not claimed. The reviewer correctly notes that the constant comparison assert F(0) != F(33,20) is vacuous; it is not counted as verification of the fifth-order obstruction. That result is supported by the analytic proof and computed formal coefficients. The original programs, PDF and companion ZIP are preserved unchanged. The PDF identity question is resolved. Fresh GitHub and Zenodo downloads both match the canonical 345028-byte ZIP PDF, SHA256 d43d8ecac798a7fbc9e4485378bb43c83eacad4a797842e48785f2ff23496854. The previously supplied standalone attachment is 394417 bytes, SHA256 3ca41d1ce6192006aa58e040fd97ac80b3adff93a2760fad565d708a452b2bc3, and contains Content Credentials/C2PA associated data. Extracted text and all six corresponding 100-dpi page renderings match. Gabrielli-Harris publisher full text was obtained and the relevant Section 7 citation checked author-side. REFERENCES remains PARTIAL and NOVELTY remains INCONCLUSIVE; no priority claim is made. This scoped comparison does not certify historical non-overlap. The unchanged attached ZIP contains LaTeX, offline standard-library Python verification programs, numerical limits, frozen evidence and original provenance/review materials. The later package-audit report and PDF/reference follow-up are available in the GitHub publication folder:https://github.com/yonezaemon1-hub/no38-local-c3-star-triangle-rigidity/tree/main/publication All rights reserved. Research inquiries and earlier overlapping work: yonezaemon1+research@gmail.com.Repository: https://github.com/yonezaemon1-hub/no38-local-c3-star-triangle-rigidity