Exact Cut Thinness, Parity Obstructions, and Attainment Gaps in Complete Bipartite Graphs
Year: 2026
Type: preprint
Abstract: Research No.57 — limited-scope preprint v1.0. Ryutaro Yonezu — Independent Researcher. We study exact combinatorial cut thinness of complete bipartite graphs with fixed left size: an even/odd finite-attainment dichotomy, first odd attainment thresholds, exact small-left-size values, K5/K7/K9 attainment spectra and the K7 non-star threshold 189. The K5 n=62 correction and twelve K9 nonattainment cases are preserved. This is not a formula for every K(k,n). Independent AI mathematical audit: PASS within the author-reported audited scope. Windows PowerShell 5.1 reproduction: PASS based on the author-provided 2026-11-06 19:37 JST log. The publication assistant inspected that log and reran the two unchanged Python checkers on Linux; it did not independently execute them on Windows. Raw Windows logs and machine-identifying information are excluded. Novelty INCONCLUSIVE. References PARTIAL. Not human peer-reviewed. All rights reserved. Existing thinness definitions and prior upper bounds are credited in the manuscript. No originality or world-first claim is made. Google Scholar/OpenAlex indexing is not checked. v0.9 mathematics, constants, witness tables, code and evidence are frozen. v1.0 changes only version and research/audit/publication status text and adds publication documentation. GitHub repository: https://github.com/yonezaemon1-hub/no57-exact-cut-thinness-bipartite-graphsGitHub Release: https://github.com/yonezaemon1-hub/no57-exact-cut-thinness-bipartite-graphs/releases/tag/v1.0 SHA256 PDF: 7b3e22d67726a1ecf17257e5b9fd8bf2e6047d0b1805c44af67afde26e9d2461SHA256 ZIP: b87967a709f193626f275eb5f1382a9fee356bb085bfb93a4db4cfa8af1c46ab
Author: Yonezu, Ryutaro
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225386269