{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:erdos-671",
  "title": "Erdős Problem #671",
  "canonical_statement": "For triangular arrays of nodes $a_i^n\\in[-1,1]$ let $\\mathcal{L}^nf$ be the Lagrange interpolation polynomials of a continuous $f$, with fundamental polynomials $p_i^n$. Is there a choice of nodes such that for every continuous $f$ there is some $x$ where $\\limsup_n \\sum_i\\lvert p_{i}^n(x)\\rvert=\\infty$ and yet $\\mathcal{L}^nf(x) \\to f(x)$? Is there a choice with $\\limsup_n \\sum_i\\lvert p_{i}^n(x)\\rvert=\\infty$ for every $x$, yet for every continuous $f$ some $x$ has $\\mathcal{L}^nf(x)\\to f(x)$? Both questions are claimed resolved in the affirmative.",
  "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-671:event",
      "problem_id": "vibemathed:erdos-671",
      "type": "proved",
      "status": "candidate",
      "occurred_at": "2026-06-22T00:00:00.000Z",
      "title": "erdosproblems.com/671",
      "summary": "Both parts claimed answered affirmatively, with a Lean formalization; two proof claims are filed on erdosproblems.com but the problem is still listed open",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:erdos-671:attempt"
      ],
      "method_family_ids": [
        "vibemathed:erdos-671:method"
      ],
      "source_assertion_ids": [
        "vibemathed:erdos-671:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:erdos-671:attempt",
      "problem_id": "vibemathed:erdos-671",
      "model": "GPT-5.5 Pro, Codex",
      "provider": "OpenAI",
      "attempted_at": "2026-06-22T00:00:00.000Z",
      "human_collaborators": [
        "Liam Price"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "GPT Pro produced the affirmative resolutions of both questions and Codex the Lean formalization; the humans directed the models with a writing-style prompt and cleaned up terminology, a workflow the site's owner singled out as unusually readable for AI-assisted papers.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Write-up",
          "url": "https://www.overleaf.com/read/gqmfrhsprtqm#59ac11",
          "kind": "paper",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "erdosproblems.com/671",
          "url": "https://www.erdosproblems.com/671",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Erdős Problem #671",
          "url": "https://vibemathed.com/problem/erdos-671",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:erdos-671:verification",
      "problem_id": "vibemathed:erdos-671",
      "solution_event_id": "vibemathed:erdos-671:event",
      "level": "lean_verified_statement_audited",
      "mathematical_correctness": "supported",
      "statement_fidelity": "audited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "The argument comes with a Codex-produced Lean formalization checkable online; no independent audit of statement fidelity, and erdosproblems.com still lists the problem open with the claims filed.",
      "sources": [
        {
          "label": "VibeMathed: Erdős Problem #671",
          "url": "https://vibemathed.com/problem/erdos-671",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "erdosproblems.com/671",
          "url": "https://www.erdosproblems.com/671",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "erdosproblems.com/671",
      "url": "https://www.erdosproblems.com/671",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Erdős Problem #671",
      "url": "https://vibemathed.com/problem/erdos-671",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:erdos-671:signal:verify_now",
      "problem_id": "vibemathed:erdos-671",
      "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"
}