{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:kauers-zeilberger-conjectures-2a-2b",
  "title": "Conjectures 2a and 2b of Kauers and Zeilberger",
  "canonical_statement": "Conjectures 2a and 2b of Kauers and Zeilberger, on the asymptotics of a family of restricted lattice walks. Both are obtained from a local limit theorem for excursions of Markov-modulated random walks in cones.",
  "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:kauers-zeilberger-conjectures-2a-2b:event",
      "problem_id": "vibemathed:kauers-zeilberger-conjectures-2a-2b",
      "type": "proved",
      "status": "candidate",
      "occurred_at": "2026-08-11T00:00:00.000Z",
      "title": "Solutions to Five Challenge Problems in Enumerative and Algorithmic Combinatorics",
      "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:kauers-zeilberger-conjectures-2a-2b:attempt"
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      "id": "vibemathed:kauers-zeilberger-conjectures-2a-2b:attempt",
      "problem_id": "vibemathed:kauers-zeilberger-conjectures-2a-2b",
      "model": "Claude",
      "provider": "Anthropic",
      "attempted_at": "2026-08-11T00:00:00.000Z",
      "human_collaborators": [
        "Jaideep Sai Padhi"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The paper's division of labour, in its own words: the model \"generated the mathematical ideas, the proofs, and the verification code\", while the author \"selected the problems and determined when a line of attack should be abandoned; executed all computations, on hardware the system could not access; designed and enforced the verification protocol\". It adds that neither role was passive: the system did not merely formalise ideas supplied to it, and the author did not merely execute instructions.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "Solutions to Five Challenge Problems in Enumerative and Algorithmic Combinatorics",
          "url": "https://arxiv.org/abs/2608.11290",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Conjectures 2a and 2b of Kauers and Zeilberger",
          "url": "https://vibemathed.com/problem/kauers-zeilberger-conjectures-2a-2b",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
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  "verifications": [
    {
      "id": "vibemathed:kauers-zeilberger-conjectures-2a-2b:verification",
      "problem_id": "vibemathed:kauers-zeilberger-conjectures-2a-2b",
      "solution_event_id": "vibemathed:kauers-zeilberger-conjectures-2a-2b: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 21 August 2026 against the paper (arXiv:2608.11290v2): the division of labour is verbatim as quoted, all five challenges are reported fully solved, and two further problems are reported only partial and are NOT entered here. The paper states a four-principle verification protocol that distinguishes proved, machine-verified and supported claims, and ships code and verification scripts. Those scripts were not re-run here. Days-old preprint, no independent review.",
      "sources": [
        {
          "label": "VibeMathed: Conjectures 2a and 2b of Kauers and Zeilberger",
          "url": "https://vibemathed.com/problem/kauers-zeilberger-conjectures-2a-2b",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
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          "label": "Solutions to Five Challenge Problems in Enumerative and Algorithmic Combinatorics",
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          "kind": "primary-mathematical-source",
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  "sources": [
    {
      "label": "Solutions to Five Challenge Problems in Enumerative and Algorithmic Combinatorics",
      "url": "https://arxiv.org/abs/2608.11290",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Conjectures 2a and 2b of Kauers and Zeilberger",
      "url": "https://vibemathed.com/problem/kauers-zeilberger-conjectures-2a-2b",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
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  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:kauers-zeilberger-conjectures-2a-2b:signal:verify_now",
      "problem_id": "vibemathed:kauers-zeilberger-conjectures-2a-2b",
      "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"
}