{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:pavez-signe-length-control-spanning-subdivisions",
  "title": "Pavez-Signe's Length-Control Question for Spanning Subdivisions",
  "canonical_statement": "Pavez-Signe (2024) conjectured a Dirac-type condition for spanning $H$-subdivisions and asked whether the subdivision paths can additionally be required to have similar lengths; Lee (2025) resolved the existence conjecture in the stronger digraph setting. Answered affirmatively with epsilon-room: for every $\\varepsilon > 0$ there is $C_0$ such that every $n$-vertex digraph $D$ with $n \\ge C_0 h$ and minimum semi-degree $\\delta^0(D) \\ge (1/2+\\varepsilon)n$ contains a spanning $H$-subdivision whose path lengths differ by at most one, for every digraph $H$ with $h$ arcs and no isolated vertices.",
  "plain_summary": "VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "partial",
  "solution_events": [
    {
      "id": "vibemathed:pavez-signe-length-control-spanning-subdivisions:event",
      "problem_id": "vibemathed:pavez-signe-length-control-spanning-subdivisions",
      "type": "proved",
      "status": "partial",
      "occurred_at": "2026-08-14T00:00:00.000Z",
      "title": "Nearly balanced spanning subdivisions in dense digraphs",
      "summary": "VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
      "ai_contribution": "ai_assisted",
      "attempt_ids": [
        "vibemathed:pavez-signe-length-control-spanning-subdivisions:attempt"
      ],
      "method_family_ids": [
        "vibemathed:pavez-signe-length-control-spanning-subdivisions:method"
      ],
      "source_assertion_ids": [
        "vibemathed:pavez-signe-length-control-spanning-subdivisions:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:pavez-signe-length-control-spanning-subdivisions:attempt",
      "problem_id": "vibemathed:pavez-signe-length-control-spanning-subdivisions",
      "model": "ChatGPT 5.6",
      "provider": "OpenAI",
      "attempted_at": "2026-08-14T00:00:00.000Z",
      "human_collaborators": [
        "Zhilan Wang",
        "Shuo Wei",
        "Jin Yan"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The acknowledgement states the authors used ChatGPT 5.6 to assist in the development of the probabilistic partition argument in one named lemma, plus language polishing, with all arguments independently verified by the authors.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "Nearly balanced spanning subdivisions in dense digraphs",
          "url": "https://arxiv.org/abs/2608.14432",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Pavez-Signe's Length-Control Question for Spanning Subdivisions",
          "url": "https://vibemathed.com/problem/pavez-signe-length-control-spanning-subdivisions",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:pavez-signe-length-control-spanning-subdivisions:verification",
      "problem_id": "vibemathed:pavez-signe-length-control-spanning-subdivisions",
      "solution_event_id": "vibemathed:pavez-signe-length-control-spanning-subdivisions:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Checked by this site on 17 August 2026 against the paper's LaTeX (arXiv:2608.14432, Wang-Wei-Yan): the attribution chain (Pavez-Signe's conjecture and question, Lee's resolution of existence) is in the abstract, the answer carries an epsilon in the semi-degree threshold rather than the exact conjectured bound - hence Partial, and the paper's own closing question asks for the exact threshold - and the AI acknowledgement is verbatim as quoted. Not checked here; days old, no independent review.",
      "sources": [
        {
          "label": "VibeMathed: Pavez-Signe's Length-Control Question for Spanning Subdivisions",
          "url": "https://vibemathed.com/problem/pavez-signe-length-control-spanning-subdivisions",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "Nearly balanced spanning subdivisions in dense digraphs",
          "url": "https://arxiv.org/abs/2608.14432",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "Nearly balanced spanning subdivisions in dense digraphs",
      "url": "https://arxiv.org/abs/2608.14432",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Pavez-Signe's Length-Control Question for Spanning Subdivisions",
      "url": "https://vibemathed.com/problem/pavez-signe-length-control-spanning-subdivisions",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "expand",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:pavez-signe-length-control-spanning-subdivisions:signal:recent_partial_result",
      "problem_id": "vibemathed:pavez-signe-length-control-spanning-subdivisions",
      "kind": "recent_partial_result",
      "reason": "A source-reported partial result may support bounded expansion.",
      "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"
}