{
  "schemaVersion": "1.2",
  "slug": "txgraffiti-c3-resolution",
  "title": "TxGraffiti Conjecture 15/3 resolution: a certificate-backed candidate counterexample",
  "shortTitle": "TxGraffiti Conjecture 15/3 resolution",
  "url": "https://evidencepress.org/releases/txgraffiti-c3-resolution/",
  "oneLine": "A connected cubic graph on 50 vertices has minimum maximal matching number 15 but independent domination number 16, giving a bounded candidate counterexample to the stated regular-graph inequality.",
  "abstract": "This unrefereed candidate release presents a connected cubic graph G on 50 vertices with mu*(G)=15 < 16=i(G), where mu* is the minimum cardinality of a maximal matching and i(G) is the independent domination number. It also develops an exact formula-graph identity based on bilateral deficiency and a conditional order threshold for cubic graphs with a dominating induced matching. The graph and certificate are public and replayable, but the exact release has not been independently rerun, independently reimplemented, formally verified, or conventionally peer reviewed.",
  "datePublished": "2026-08-08",
  "dateModified": "2026-08-08",
  "version": "4.0.0-rc1",
  "doi": "10.5281/zenodo.21852504",
  "doiUrl": "https://doi.org/10.5281/zenodo.21852504",
  "conceptDoi": "10.5281/zenodo.21852503",
  "pdfUrl": "https://github.com/ipitchford/txgraffiti-conjecture3-resolution/releases/download/v4.0.0-rc1/MANUSCRIPT.pdf",
  "altPdfUrl": "https://raw.githubusercontent.com/ipitchford/txgraffiti-conjecture3-resolution/v4.0.0-rc1/MANUSCRIPT.pdf",
  "zenodoUrl": "https://zenodo.org/records/21852504",
  "repoUrl": "https://github.com/ipitchford/txgraffiti-conjecture3-resolution",
  "releaseUrl": "https://github.com/ipitchford/txgraffiti-conjecture3-resolution/releases/tag/v4.0.0-rc1",
  "markdownUrl": "https://evidencepress.org/releases/txgraffiti-c3-resolution/index.md",
  "bibtexUrl": "https://evidencepress.org/releases/txgraffiti-c3-resolution/cite.bib",
  "audioUrl": "https://evidencepress.org/assets/audio/txgraffiti-c3-resolution.mp3",
  "imageUrl": "https://evidencepress.org/assets/og/txgraffiti-c3-resolution.png",
  "coverArtUrl": "https://evidencepress.org/assets/art/txgraffiti-c3-resolution.svg",
  "media": [
    {
      "type": "audio",
      "url": "https://evidencepress.org/assets/audio/txgraffiti-c3-resolution.mp3",
      "name": "Audio briefing — TxGraffiti Conjecture 15/3 resolution",
      "description": "AI-generated voice summary of the candidate result and its assurance boundary.",
      "transcriptUrl": "https://evidencepress.org/assets/audio/txgraffiti-c3-resolution.txt"
    }
  ],
  "authors": [
    "Release contributors"
  ],
  "license": "CC0-1.0",
  "status": "unrefereed-candidate",
  "verification": {
    "peerReviewed": false,
    "independentlyReproduced": false,
    "formallyVerified": false,
    "internallyReplayed": true,
    "detail": "Unrefereed candidate certificate-backed result. The theorem-critical deterministic checks pass in the recorded environment, from a clean extracted copy, in the pinned core container, and in GitHub Actions. The exact release has not been independently rerun, independently reimplemented, formally verified, or conventionally peer reviewed. The release does not claim unrestricted order-50 minimality among all cubic or regular graphs, uniqueness, first discovery, or secured novelty priority. The conditional threshold theorem depends on the cited external 20-clause theorem; the public predecessor graph and exact release lineage are recorded in PROVENANCE.md."
  },
  "assurance": [
    {
      "dimension": "availability",
      "label": "Availability and archiving",
      "question": "Is the evidence package publicly retrievable from an archive under a persistent identifier?",
      "state": "passed",
      "evidenceUrl": "https://zenodo.org/records/21852504",
      "note": "Exact archive deposited under version DOI 10.5281/zenodo.21852504; public record reports the release version and ZIP checksum."
    },
    {
      "dimension": "internalReplay",
      "label": "Internal replay",
      "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?",
      "state": "passed",
      "note": "Core replay passed from an extracted package in normal and optimized Python, with the pinned core container also built and replayed by the publisher.",
      "evidenceUrl": "https://github.com/ipitchford/txgraffiti-conjecture3-resolution/actions/runs/31263798738"
    },
    {
      "dimension": "independentRerun",
      "label": "Independent rerun",
      "question": "Has someone else run the supplied implementation and obtained the stated result?",
      "state": "not-assessed",
      "note": "No unaffiliated exact-v4 rerun has been reported."
    },
    {
      "dimension": "independentReimplementation",
      "label": "Independent reimplementation",
      "question": "Has someone else reached the result from an independent implementation?",
      "state": "not-assessed",
      "note": "No unaffiliated independent implementation of the exact release has been reported."
    },
    {
      "dimension": "formalVerification",
      "label": "Formal verification",
      "question": "Is a formalised statement machine-checked, and over which trusted base?",
      "state": "not-assessed",
      "note": "The release contains proof objects and deterministic checkers but no end-to-end formalization of the graph-theoretic claim."
    },
    {
      "dimension": "specialistReview",
      "label": "Specialist review",
      "question": "Has a domain specialist assessed the argument?",
      "state": "not-assessed",
      "note": "The supplied review and predecessor receipt are scoped to their exact historical objects; no external specialist review of this exact release is claimed."
    },
    {
      "dimension": "editorialPeerReview",
      "label": "Editorial peer review",
      "question": "Has a journal or venue run peer review to a decision?",
      "state": "not-assessed",
      "note": "No conventional venue peer review has occurred."
    },
    {
      "dimension": "dataEnvironmentReproducibility",
      "label": "Data and environment reproducibility",
      "question": "Are data and computational environment pinned well enough to rebuild?",
      "state": "passed",
      "evidenceUrl": "https://github.com/ipitchford/txgraffiti-conjecture3-resolution/blob/main/REPLAY_CONTAINER_2026-08-08.md",
      "note": "The core container base and image digest, replay commands and manifest checks are recorded; the optional MILP audit remains unrun on Apple silicon because its lockfile pins x86_64 wheels."
    }
  ],
  "provenance": {
    "aiGenerated": true,
    "aiAssisted": true,
    "generatedBy": [
      "Release contributors"
    ],
    "humanRole": "Research objective, supplied candidate package, mediation and publication authorization; the scholarly creator is cited as Release contributors.",
    "disclosure": "The release package records AI-assisted mathematical synthesis, verification, exposition and editorial integration. Producer-side replay and model agreement are not independent verification; the package's provenance and assurance files are authoritative for scope."
  },
  "problem": {
    "name": "TxGraffiti Conjecture 15/3: independent domination versus minimum maximal matching in regular graphs",
    "url": "https://github.com/djma/TxGraffiti-conjecture3-counterexample"
  },
  "corrections": [],
  "keywords": [
    "graph theory",
    "cubic graphs",
    "independent domination",
    "maximal matching",
    "TxGraffiti Conjecture",
    "certificate-backed mathematics",
    "proof-tree certificate",
    "reproducible research",
    "AI-generated mathematics",
    "unrefereed candidate"
  ],
  "keyResults": [
    "A connected cubic graph on 50 vertices satisfies mu*(G)=15<16=i(G), refuting the stated inequality for regular graphs.",
    "An exact formula-graph identity expresses independent domination through minimum bilateral deficiency under the stated hypotheses.",
    "Conditional on the cited 20-clause theorem, the release gives an order threshold within the subclass of cubic graphs with a dominating induced matching.",
    "The graph, explicit witnesses, proof-tree certificate, source code and deterministic replay commands are archived together."
  ],
  "reviews": [],
  "evidencePackage": "The DOI archive contains the manuscript and evidence supplement, the canonical graph in JSON, graph6 and edge-list encodings, explicit witnesses, a compressed proof-tree certificate, exact enumeration checks, source code, a pinned container definition, SHA-256 manifests, machine-readable claim and assurance records, provenance, sources and review-response documents. The publisher also replayed the core container on Apple silicon and the repository CI replay passes. These are scoped producer-side and publisher-side checks, not external theorem verification.",
  "openProblems": [
    "Independently rerun the exact v4 archive, beginning with the dependency-free core verifier and proof-tree checker.",
    "Provide an independent reimplementation of the 50-vertex graph checks and the bilateral-deficiency identity.",
    "Audit the semantic bridge from the graph-theoretic statement to the certificate and the conditional 20-clause input.",
    "Search the literature broadly for the exact identity and the TxGraffiti inequality under alternate terminology, and update attribution if antecedents are found.",
    "Determine whether order 50 is globally minimal among all cubic or regular counterexamples; the release does not claim that it is.",
    "Formalize the exact identity and the restricted threshold in a proof assistant."
  ],
  "relatedWorks": []
}