{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:planar-four-terminal-dgg",
  "title": "Four-Terminal Planar Case of the Dinitz-Garg-Goemans Cost Conjecture",
  "canonical_statement": "Does the Dinitz-Garg-Goemans cost-preserving unsplittable-flow rounding conjecture survive on acyclic planar instances with only four terminals? An explicit instance answers no: every cost-nonincreasing unsplittable routing has upper overload at least $335$ while the maximum demand is $294$.",
  "plain_summary": "VibeMathed reports this item as open. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "open",
  "solution_events": [
    {
      "id": "vibemathed:planar-four-terminal-dgg:event",
      "problem_id": "vibemathed:planar-four-terminal-dgg",
      "type": "disproved",
      "status": "open",
      "occurred_at": "2026-07-23T00:00:00.000Z",
      "title": "Public research disclosure v0.1.0 (GitHub release)",
      "summary": "restricted planar four-terminal case",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:planar-four-terminal-dgg:attempt"
      ],
      "method_family_ids": [
        "vibemathed:planar-four-terminal-dgg:method"
      ],
      "source_assertion_ids": [
        "vibemathed:planar-four-terminal-dgg:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:planar-four-terminal-dgg:attempt",
      "problem_id": "vibemathed:planar-four-terminal-dgg",
      "model": "GPT-5.6 Pro",
      "provider": "OpenAI",
      "attempted_at": "2026-07-23T00:00:00.000Z",
      "human_collaborators": [
        "Matthew Protti"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "GPT-5.6 Pro carried out much of the construction search, symbolic derivation, proof development, exact-verifier development, adversarial critique and manuscript preparation. The human author selected and framed the problem, directed the investigation, caught a cost-normalization error, required exact and adversarial checks, set the claim scope and approved the release. A later Codex session independently re-encoded the key graph, finite and symbolic checks and ran deterministic stress and release checks.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Manuscript (PDF)",
          "url": "https://github.com/matthewprotti/planar-ssuf-four-terminal-bound/releases/download/v0.1.0/ssuf_four_terminal_note_v5.pdf",
          "kind": "paper",
          "license": null
        },
        {
          "label": "Exact verification suite (verify_all.py)",
          "url": "https://github.com/matthewprotti/planar-ssuf-four-terminal-bound/blob/v0.1.0/scripts/verify_all.py",
          "kind": "code",
          "license": null
        },
        {
          "label": "AI-use and provenance note",
          "url": "https://github.com/matthewprotti/planar-ssuf-four-terminal-bound/blob/v0.1.0/AI_USE_AND_PROVENANCE.md",
          "kind": "transcript",
          "license": null
        },
        {
          "label": "The general conjecture, disproved a day earlier",
          "url": "https://vibemathed.com/problem/dinitz-garg-goemans-unsplittable-flow",
          "kind": "other",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "Public research disclosure v0.1.0 (GitHub release)",
          "url": "https://github.com/matthewprotti/planar-ssuf-four-terminal-bound/releases/tag/v0.1.0",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Four-Terminal Planar Case of the Dinitz-Garg-Goemans Cost Conjecture",
          "url": "https://vibemathed.com/problem/planar-four-terminal-dgg",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:planar-four-terminal-dgg:verification",
      "problem_id": "vibemathed:planar-four-terminal-dgg",
      "solution_event_id": "vibemathed:planar-four-terminal-dgg:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "The immutable v0.1.0 public disclosure ships a manuscript, exact data, an exhaustive verifier over all 16 routings and all 13 arcs, mutation tests, deterministic hashes and a separate AI-assisted computational cross-check. The attained certificate is $335/294$; the package also proves the limiting lower bound $(299 - 41sqrt{41})/32$, with sharpness only in the stated fixed-topology, equal-full-cost, two-cheap-choice model. Released 2026-07-23, one day after the first public disproof of the general conjecture, and developed independently of it.",
      "sources": [
        {
          "label": "VibeMathed: Four-Terminal Planar Case of the Dinitz-Garg-Goemans Cost Conjecture",
          "url": "https://vibemathed.com/problem/planar-four-terminal-dgg",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "Public research disclosure v0.1.0 (GitHub release)",
          "url": "https://github.com/matthewprotti/planar-ssuf-four-terminal-bound/releases/tag/v0.1.0",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "Public research disclosure v0.1.0 (GitHub release)",
      "url": "https://github.com/matthewprotti/planar-ssuf-four-terminal-bound/releases/tag/v0.1.0",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Four-Terminal Planar Case of the Dinitz-Garg-Goemans Cost Conjecture",
      "url": "https://vibemathed.com/problem/planar-four-terminal-dgg",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:planar-four-terminal-dgg:signal:watch_only",
      "problem_id": "vibemathed:planar-four-terminal-dgg",
      "kind": "watch_only",
      "reason": "Current public evidence does not meet the default replay threshold.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "uncertainties": [
    "VibeMath has not independently verified the mathematical claim.",
    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
    "VibeMath has not independently audited the mathematical statement, proof, or novelty claim."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}