{
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  "source": "vibemath",
  "problem_id": "vibemathed:cvp-polynomial-hardness",
  "title": "Polynomial-Factor Hardness for the Closest Vector Problem",
  "canonical_statement": "Is the closest vector problem NP-hard to approximate within polynomial factors $n^c$? Yes for some $c > 0$: hardness of approximation reaches polynomial factors, with consequences for decoding and related lattice problems - a foundational question underpinning post-quantum cryptography where hardness had stalled at almost-polynomial factors since the late 1990s.",
  "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:cvp-polynomial-hardness:event",
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      "occurred_at": "2026-08-01T00:00:00.000Z",
      "title": "OpenAI: Ten advances in mathematics and theoretical computer science",
      "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_discovered",
      "attempt_ids": [
        "vibemathed:cvp-polynomial-hardness:attempt"
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      "provider": "OpenAI",
      "attempted_at": "2026-08-01T00:00:00.000Z",
      "human_collaborators": [],
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      "prompt_public": null,
      "outcome": "Generated by an internal version of OpenAI's Astra: per the announcement, the mathematical arguments were produced by the system (roughly 2,000 dollars of compute at Sol API rates across all ten results), humans prepared the manuscripts with the same model, and the model then formalized the argument in Lean. A narrated reasoning walkthrough is published for each result.",
      "failed_routes": [],
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        },
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          "kind": "transcript",
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        },
        {
          "label": "VibeMathed: Polynomial-Factor Hardness for the Closest Vector Problem",
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      "sources": [
        {
          "label": "VibeMathed: Polynomial-Factor Hardness for the Closest Vector Problem",
          "url": "https://vibemathed.com/problem/cvp-polynomial-hardness",
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      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Polynomial-Factor Hardness for the Closest Vector Problem",
      "url": "https://vibemathed.com/problem/cvp-polynomial-hardness",
      "kind": "source-assertion",
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  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:cvp-polynomial-hardness:signal:verify_now",
      "problem_id": "vibemathed:cvp-polynomial-hardness",
      "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"
}