{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:polynomial-time-low-degree-conjecture",
  "title": "The Polynomial-Time Low-Degree Conjecture",
  "canonical_statement": "The low-degree conjecture predicts that when the low-degree advantage between a planted distribution and a uniform null distribution stays bounded, no polynomial-time algorithm can distinguish them. It is false. There is a planted distribution that agrees with the null through the relevant degree, is invariant under vertex relabeling, and is nevertheless distinguished in polynomial time by a rank argument.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "resolved",
  "solution_events": [
    {
      "id": "vibemathed:polynomial-time-low-degree-conjecture:event",
      "problem_id": "vibemathed:polynomial-time-low-degree-conjecture",
      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-07-22T00:00:00.000Z",
      "title": "arXiv:2607.20318 - The Polynomial-Time Low-Degree Conjecture is False",
      "summary": "the construction is probabilistic; an explicit uniformly samplable example remains open",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:polynomial-time-low-degree-conjecture:attempt"
      ],
      "method_family_ids": [
        "vibemathed:polynomial-time-low-degree-conjecture:method"
      ],
      "source_assertion_ids": [
        "vibemathed:polynomial-time-low-degree-conjecture:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:polynomial-time-low-degree-conjecture:attempt",
      "problem_id": "vibemathed:polynomial-time-low-degree-conjecture",
      "model": "ChatGPT 5.4, 5.5, 5.6",
      "provider": "OpenAI",
      "attempted_at": "2026-07-22T00:00:00.000Z",
      "human_collaborators": [
        "Songtao Mao"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The statement on AI use is specific in both directions. The author first put forward constructions from two-dimensional Reed-Muller-style codes and asked whether they could be made invariant under all vertex relabelings while keeping efficient decoding; the model's responses established that they could not, closing off that route. The rank argument that carries the paper was later developed with ChatGPT 5.6 after the author fed it ideas in the spirit of his Remark 2.5. The author independently checked, simplified and organized every proof.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv:2607.20318 - The Polynomial-Time Low-Degree Conjecture is False",
          "url": "https://arxiv.org/abs/2607.20318",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Polynomial-Time Low-Degree Conjecture",
          "url": "https://vibemathed.com/problem/polynomial-time-low-degree-conjecture",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:polynomial-time-low-degree-conjecture:verification",
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      "solution_event_id": "vibemathed:polynomial-time-low-degree-conjecture:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Single-author arXiv preprint; not yet peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: The Polynomial-Time Low-Degree Conjecture",
          "url": "https://vibemathed.com/problem/polynomial-time-low-degree-conjecture",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2607.20318 - The Polynomial-Time Low-Degree Conjecture is False",
          "url": "https://arxiv.org/abs/2607.20318",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv:2607.20318 - The Polynomial-Time Low-Degree Conjecture is False",
      "url": "https://arxiv.org/abs/2607.20318",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Polynomial-Time Low-Degree Conjecture",
      "url": "https://vibemathed.com/problem/polynomial-time-low-degree-conjecture",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:polynomial-time-low-degree-conjecture:signal:watch_only",
      "problem_id": "vibemathed:polynomial-time-low-degree-conjecture",
      "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"
}