The minimum path-order threshold for burning eight-path forests

Abstract

Verification entry point: proof-and-verification-guide-release.md. Download the core ZIP, the seven ordinary layer ZIPs, all eight m27 parts and all ten m28 parts, and both assembly tools. Run node assemble-m27.js and node assemble-m28.js, then extract the core and all nine layer ZIPs into one directory and run verify_bundle.js. Both assembly tools check part hashes and reconstructed ZIP hashes. Original certificate and verifier bytes are unchanged. This record contains the preprint The minimum path-order threshold for burning eight-path forests, by Jiarui Wang (Liaoning University, China), and its computational supplement. The manuscript presents a computer-assisted upper bound L8 ≤ 68 for the minimum sufficient path order of eight-path forests. Combining it with the published lower bound of Tan and Teh gives the claimed equality L8 = 68. The new claim concerns the upper bound, not discovery of the lower bound or classification of all deficient eight-path forests. The supplement contains 64,804,301 exact odd-integer partition certificates for nine finite domains, a separately written Node.js verifier using only its standard library, a hash manifest, and existing exhaustive verification reports. The manuscript supplies the reduction, induction and arbitrary-order arguments. Checking this corpus does not require the search programs that generated the witnesses. Status: preprint, not externally peer reviewed or formally verified. AI agents were used extensively for mathematical development, code generation and checking, and manuscript preparation. The human author set the project's objective and approved the eight-path-forest research direction; made continuation and resource-allocation decisions; approved the evidence standard that timeouts and unfinished searches remain unresolved rather than count as negative results; requested repair of failed verification tooling and additional, separately implemented checks of the computational evidence and proofs; required documentation of identified limitations before manuscript preparation; and approved the public deposit and licenses. The author has reviewed and verified the mathematical arguments and critically revised the description of the research contributions. The computational certificates were checked by separately implemented programs. The author takes responsibility for the manuscript and its claims. No external human mathematical review has been obtained. Separate programs are not represented as independent human reviewers. Literature and priority: the literature review remains incomplete, with access limitations and unread sources documented in the manuscript. No confirmed global-priority claim is made. The deposit documents the content made publicly available in this version; it does not certify correctness or novelty. Files and licenses: the 8-page manuscript PDF, LaTeX source ZIP, certificate/verifier archives, and verification guide are included together. The manuscript, certificate data and prose documentation are CC BY 4.0; supplied executable source code is MIT. See LICENSES.md in the supplement for file-level scope. Superseded preparation guides: proof-and-verification-guide.md, proof-and-verification-guide-v1.md and proof-and-verification-guide-final.md describe earlier packaging attempts. They are retained for transparency; use only proof-and-verification-guide-release.md for this published file layout. Author-contribution clarification: the statement above reflects the author's confirmation on 1 October 2026 of completed personal verification and provides a fuller account of the human research decisions. The archived v1 PDF retains its original wording; this metadata clarification does not replace its files.