title: "A degree-three local-weight cap and an improved relevant-variable bound"
author: "Ricardo Pinho (ORCID 0009-0006-2744-2599)"
status: "Unrefereed preprint, 23 October 2026. No optimality claimed; exhaustive priority is not asserted."
repository: "https://github.com/rpinho/c44-certificate/tree/f3fb25dfb88de3da8b1a0b30f03fdb51b78ccef9"
tao_table_pr: "https://github.com/teorth/optimizationproblems/pull/258"
run_checkers_from_this_folder:
  - "python3.12 -B verify_c44_exact.py certificates/c44_candidate.json"
  - "python3.12 -B independent/verify_c44_fraction.py certificates/c44_candidate.json"
checker_provenance: "Both checkers were written separately by the same AI agent, without importing one another. No independent human review or proof-assistant formalization."
ai_use: "Analysis and proof drafting by AI agents under my direction; I reviewed the results at summary level. AI agents also prepared the certificate, checkers and publication materials."
third_party_data:
  files: ["sources/wellens-certificate.json", "sources/wellens-result.json"]
  origin: "Unchanged public data from BakeLab/Epi-results, mathematics/wellens, commit 97fa6a420f417458e11723c8bceb70f1529e447a"
  sha256_certificate: "ce66f1097a7284e9845113fa1dc39267932cc934fd23d9019ff13d3dcb39cf49"
  rights: "No explicit upstream license was located; these files retain their upstream rights."
licenses: "Paper CC BY 4.0. Original checker code and the new small C44 certificate: MIT (see the repository)."