{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:first-proof-q8-polyhedral-lagrangians",
  "title": "First Proof Question 8: Smoothing Polyhedral Lagrangians",
  "canonical_statement": "Question 8 of the First Proof experiment (Abouzaid et al.) asks whether a polyhedral Lagrangian surface with exactly four faces meeting at every vertex necessarily admits a Lagrangian smoothing. The research report assembles ChatGPT-suggested constructions into an affirmative argument for orientable surfaces in $(\\mathbb{R}^4, \\omega)$: smooth the edges, verify the vertex links are unknots with rot 0 and tb -1, and cap off with Lagrangian disks via Chartraine's results.",
  "plain_summary": "VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "candidate",
  "solution_events": [
    {
      "id": "vibemathed:first-proof-q8-polyhedral-lagrangians:event",
      "problem_id": "vibemathed:first-proof-q8-polyhedral-lagrangians",
      "type": "proved",
      "status": "candidate",
      "occurred_at": "2026-02-13T00:00:00.000Z",
      "title": "arXiv",
      "summary": "VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:first-proof-q8-polyhedral-lagrangians:attempt"
      ],
      "method_family_ids": [
        "vibemathed:first-proof-q8-polyhedral-lagrangians:method"
      ],
      "source_assertion_ids": [
        "vibemathed:first-proof-q8-polyhedral-lagrangians:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:first-proof-q8-polyhedral-lagrangians:attempt",
      "problem_id": "vibemathed:first-proof-q8-polyhedral-lagrangians",
      "model": "ChatGPT 5.2, Gemini Pro",
      "provider": "OpenAI, Google DeepMind",
      "attempted_at": "2026-02-13T00:00:00.000Z",
      "human_collaborators": [
        "Antonio Alfieri",
        "Connor Novak"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "A deliberate two-team methodology: Team A explored solutions with ChatGPT 5.2 and had to defend the generated material; Team B checked correctness with human reasoning plus Gemini Pro. The report even documents ChatGPT's initial wrong idea (a spurious obstruction), and a key citation the model gestured at was pinned down by the humans in review meetings.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2602.13519",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: First Proof Question 8: Smoothing Polyhedral Lagrangians",
          "url": "https://vibemathed.com/problem/first-proof-q8-polyhedral-lagrangians",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:first-proof-q8-polyhedral-lagrangians:verification",
      "problem_id": "vibemathed:first-proof-q8-polyhedral-lagrangians",
      "solution_event_id": "vibemathed:first-proof-q8-polyhedral-lagrangians:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "A self-described research report with an unusual format; the argument is assembled but no independent review has appeared, so it enters as a candidate.",
      "sources": [
        {
          "label": "VibeMathed: First Proof Question 8: Smoothing Polyhedral Lagrangians",
          "url": "https://vibemathed.com/problem/first-proof-q8-polyhedral-lagrangians",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2602.13519",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv",
      "url": "https://arxiv.org/abs/2602.13519",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: First Proof Question 8: Smoothing Polyhedral Lagrangians",
      "url": "https://vibemathed.com/problem/first-proof-q8-polyhedral-lagrangians",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:first-proof-q8-polyhedral-lagrangians:signal:verify_now",
      "problem_id": "vibemathed:first-proof-q8-polyhedral-lagrangians",
      "kind": "verify_now",
      "reason": "The source labels this result as a candidate; verification should precede reuse.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "uncertainties": [
    "The source status is candidate and must not be represented as solved.",
    "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"
}