Finite Nonlinear Separations for Exact Four-Cycle Graph Codes
Year: 2026
Type: preprint
Abstract: This unrefereed preprint studies codes of labelled simple graphs in which the symmetric difference of two distinct codewords is forbidden to be exactly the edge set of one four-cycle. The condition concerns an exact four-cycle difference, rather than every difference containing a four-cycle. For every n >= 4, the largest linear code has cardinality 2^(binom(n,2) - ceil(log2(n))). The exact unrestricted optimum is 192 at n = 5, compared with the linear optimum 128, and 6144 at n = 6, compared with the linear optimum 4096. For n = 6, a finite Fourier-positive kernel gives the matching upper bound; a 96-word seed translated over 64 cosets attains it. The accompanying unchanged v1.4 evidence bundle contains the explicit witness, proof memo, standard-library Python verification scripts, saved verification results, and SHA-256 checksums. The pairwise verifier checks 18,871,296 unordered pairs and finds zero prohibited differences. Independent computational cross-checks have passed. These checks do not constitute formal peer review. To the best of the author's knowledge, these particular finite values and the all-n linear formula were not found in the literature examined. This is not a priority or first-discovery claim. Historical novelty remains INCONCLUSIVE. Information about earlier or overlapping work is welcome at the research contact below. The proof memo in the evidence bundle records a pre-audit stage and includes an outdated statement that external recomputation was pending. The authoritative v1.4 manuscript and publication gate record the completed independent computational cross-check. The original audited bundle is preserved unchanged. GitHub repository: https://github.com/yonezaemon1-hub/no26-exact-four-cycle-graph-codes Research Inquiries — Yonezu Research Lab Contact: [email protected]
Author: Yonezu, Ryutaro
Institution: Laboratory Krone
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221870327
Cites:
Cited by:
Related to: