{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:erdos-996",
  "title": "Erdős Problem #996",
  "canonical_statement": "Let $n_1<n_2<\\cdots$ be a lacunary sequence of integers and $f\\in L^2([0,1])$ with $n$th Fourier partial sum $f_n$. Is there an absolute constant $C>0$ such that if $\\| f-f_n\\|_2 \\ll (\\log\\log\\log n)^{-C}$ then $\\frac{1}{N}\\sum_{k\\leq N}f(\\{\\alpha n_k\\})\\to\\int_0^1 f$ for almost every $\\alpha$? A preprint answers this negatively via a dyadic spike-block counterexample.",
  "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:erdos-996:event",
      "problem_id": "vibemathed:erdos-996",
      "type": "disproved",
      "status": "candidate",
      "occurred_at": "2026-04-21T00:00:00.000Z",
      "title": "erdosproblems.com/996",
      "summary": "Answered negatively in a preprint that also settles the p=2 case of problem #995; erdosproblems.com still lists the problem open",
      "ai_contribution": "ai_assisted",
      "attempt_ids": [
        "vibemathed:erdos-996:attempt"
      ],
      "method_family_ids": [
        "vibemathed:erdos-996:method"
      ],
      "source_assertion_ids": [
        "vibemathed:erdos-996:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:erdos-996:attempt",
      "problem_id": "vibemathed:erdos-996",
      "model": "GPT-5.4 Pro",
      "provider": "OpenAI",
      "attempted_at": "2026-04-21T00:00:00.000Z",
      "human_collaborators": [
        "Boon Suan Ho"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "Per the paper's acknowledgements, GPT-5.4 Pro was used during development to explore proof strategies, test intermediate formulations and assist with exposition; all arguments were independently verified by the author, who takes full responsibility.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "arXiv preprint",
          "url": "https://arxiv.org/abs/2604.18535",
          "kind": "paper",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "erdosproblems.com/996",
          "url": "https://www.erdosproblems.com/996",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Erdős Problem #996",
          "url": "https://vibemathed.com/problem/erdos-996",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:erdos-996:verification",
      "problem_id": "vibemathed:erdos-996",
      "solution_event_id": "vibemathed:erdos-996:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "An arXiv preprint with no independent review yet; erdosproblems.com still lists the problem open.",
      "sources": [
        {
          "label": "VibeMathed: Erdős Problem #996",
          "url": "https://vibemathed.com/problem/erdos-996",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "erdosproblems.com/996",
          "url": "https://www.erdosproblems.com/996",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "erdosproblems.com/996",
      "url": "https://www.erdosproblems.com/996",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Erdős Problem #996",
      "url": "https://vibemathed.com/problem/erdos-996",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:erdos-996:signal:verify_now",
      "problem_id": "vibemathed:erdos-996",
      "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"
}