{
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  "problem_id": "vibemathed:umans-wang-divisor-conjecture",
  "title": "The Umans-Wang Arithmetic-Progression Divisor Conjecture",
  "canonical_statement": "An $n$-divisor set contains a multiple of every integer from 1 to $n$. Umans and Wang proposed, as the arithmetic-progression form of their Strong $(\\alpha,\\beta)$-Divisor Conjecture, that such a progression exists with few terms of bounded magnitude, which would imply faster algorithms for polynomial and integer factorization. Refuted unconditionally, including its exponent-level relaxation.",
  "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",
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    {
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      "occurred_at": "2026-08-07T00:00:00.000Z",
      "title": "arXiv",
      "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.",
      "ai_contribution": "ai_discovered",
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        "vibemathed:umans-wang-divisor-conjecture:attempt"
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      "provider": "OpenAI",
      "attempted_at": "2026-08-07T00:00:00.000Z",
      "human_collaborators": [
        "Xinjie He",
        "Amit Sahai"
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      "prompt_public": null,
      "outcome": "\"The proof was discovered in an OpenAI Codex run using the gpt-5.6-sol model with reasoning effort set to ultra. Codex also produced the initial write-up. Subsequent human review verified the proof, reviewed the citations, and revised the exposition.\" The authors note the prompting strategy borrowed from the UCLA Moonshot Harness project.",
      "failed_routes": [],
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      "sources": [
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          "label": "arXiv",
          "url": "https://arxiv.org/abs/2608.06681",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Umans-Wang Arithmetic-Progression Divisor Conjecture",
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          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
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      "independence": "unknown"
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      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "A preprint days old with no independent review. The paper states the argument is self-contained, needs no computer-assisted calculation and no access to the model transcript, with the prime number theorem as its only analytic input, so it is checkable on its own terms.",
      "sources": [
        {
          "label": "VibeMathed: The Umans-Wang Arithmetic-Progression Divisor Conjecture",
          "url": "https://vibemathed.com/problem/umans-wang-divisor-conjecture",
          "kind": "source-assertion",
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          "label": "arXiv",
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      "url": "https://arxiv.org/abs/2608.06681",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Umans-Wang Arithmetic-Progression Divisor Conjecture",
      "url": "https://vibemathed.com/problem/umans-wang-divisor-conjecture",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
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    {
      "id": "vibemathed:umans-wang-divisor-conjecture:signal:watch_only",
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      "generated_at": "2026-09-13T16:28:40.178Z"
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  "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"
}