{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:kozerenko-skochko-imbalance-conjecture",
  "title": "The Imbalance Conjecture",
  "canonical_statement": "The imbalance of an edge uv of a finite simple graph is the absolute difference of the degrees of u and v. Kozerenko and Skochko conjectured that the multiset of all edge imbalances is graphic - realizable as the degree sequence of some graph - whenever every edge has positive imbalance. Proved.",
  "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",
  "solution_events": [
    {
      "id": "vibemathed:kozerenko-skochko-imbalance-conjecture:event",
      "problem_id": "vibemathed:kozerenko-skochko-imbalance-conjecture",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-08-10T00:00:00.000Z",
      "title": "arXiv",
      "summary": "The key step is a lower bound on the truncated imbalance sum, which yields every Erdos-Gallai inequality for the sorted imbalance list; a parity computation finishes it.",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:kozerenko-skochko-imbalance-conjecture:attempt"
      ],
      "method_family_ids": [
        "vibemathed:kozerenko-skochko-imbalance-conjecture:method"
      ],
      "source_assertion_ids": [
        "vibemathed:kozerenko-skochko-imbalance-conjecture:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:kozerenko-skochko-imbalance-conjecture:attempt",
      "problem_id": "vibemathed:kozerenko-skochko-imbalance-conjecture",
      "model": "GPT-5.6 Sol Max",
      "provider": "OpenAI",
      "attempted_at": "2026-08-10T00:00:00.000Z",
      "human_collaborators": [
        "Yousof Yavari"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The generative-AI disclosure says the model was asked to solve the problem outright: \"The proof presented in this manuscript was generated using OpenAI's GPT-5.6 Sol with the max reasoning setting (\\\"GPT-5.6 Sol Max\\\") after Yousof Yavari prompted the model to solve the question addressed in this manuscript. Yousof Yavari subsequently revised and edited the proof, added further details, and clarified its exposition.\"",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Imbalance conjecture",
          "url": "https://en.wikipedia.org/wiki/Imbalance_conjecture",
          "kind": "wikipedia",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2608.09191",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Imbalance Conjecture",
          "url": "https://vibemathed.com/problem/kozerenko-skochko-imbalance-conjecture",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:kozerenko-skochko-imbalance-conjecture:verification",
      "problem_id": "vibemathed:kozerenko-skochko-imbalance-conjecture",
      "solution_event_id": "vibemathed:kozerenko-skochko-imbalance-conjecture:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "A preprint days old. The author credits Eric Hou with independently verifying the proof, which is a second reader rather than the kind of review that moves an entry up the ladder.",
      "sources": [
        {
          "label": "VibeMathed: The Imbalance Conjecture",
          "url": "https://vibemathed.com/problem/kozerenko-skochko-imbalance-conjecture",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2608.09191",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv",
      "url": "https://arxiv.org/abs/2608.09191",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Imbalance Conjecture",
      "url": "https://vibemathed.com/problem/kozerenko-skochko-imbalance-conjecture",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:kozerenko-skochko-imbalance-conjecture:signal:watch_only",
      "problem_id": "vibemathed:kozerenko-skochko-imbalance-conjecture",
      "kind": "watch_only",
      "reason": "Current public evidence does not meet the default replay threshold.",
      "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"
}