Outer Mutual Visibility on Discrete Tori: A Parity Defect and a Computer-Assisted Classification

This unrefereed preprint gives a computer-assisted classification of the outer mutual-visibility number of C_m Cartesian-product C_n for all integers 3 <= m <= n. The value is 2m, with a one-point defect on odd squares, apart from 24 listed small exceptions. For m,n >= 10 the proof is analytical; the remaining infinite families reduce to 39 finite cases. The definitions, fiber bound and known values 3x3=4 and 4x4=6 are explicitly credited. Eight scoped AI-review reports found no new mathematical gap. The final stage inherited 36 reported independent numerical values, whose source code and raw logs were not provided; the remaining three values have direct certificates. Substantial generative-AI assistance and AI cross-checking were used. No human peer review has occurred. References are PARTIAL and novelty and priority remain INCONCLUSIVE. The accompanying source archive contains the unchanged verification code and evidence. Historical HOLD labels in the sealed candidate describe its preparation stage; the author has subsequently authorized public distribution. Repository: https://github.com/yonezaemon1-hub/no44-outer-mutual-visibility-toriResearch inquiries: yonezaemon1+research@gmail.comCopyright (c) 2026 Ryutaro Yonezu. All rights reserved.