{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:fractional-colouring-pauli-shadow-tomography",
  "title": "The Fractional Colouring Conjecture for Triply Efficient Pauli Shadow Tomography",
  "canonical_statement": "Conjecture 13 of King, Gosset, Kothari and Babbush asserts that for the set $B_\\varepsilon(\\rho)$ of Pauli observables with expectation value at least $\\varepsilon$ in magnitude, the fractional chromatic number of the induced anticommutation graph is $O(\\varepsilon^{-2})$; it would give a triply efficient Pauli shadow tomography algorithm. False: there are states and observables for which no finite constant bounds $\\chi_f \\varepsilon^2$.",
  "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:fractional-colouring-pauli-shadow-tomography:event",
      "problem_id": "vibemathed:fractional-colouring-pauli-shadow-tomography",
      "type": "disproved",
      "status": "candidate",
      "occurred_at": "2026-08-20T00:00:00.000Z",
      "title": "Counterexamples to the fractional coloring conjecture for triply efficient shadow tomography",
      "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_co_developed",
      "attempt_ids": [
        "vibemathed:fractional-colouring-pauli-shadow-tomography:attempt"
      ],
      "method_family_ids": [
        "vibemathed:fractional-colouring-pauli-shadow-tomography:method"
      ],
      "source_assertion_ids": [
        "vibemathed:fractional-colouring-pauli-shadow-tomography:assertion"
      ]
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  ],
  "attempts": [
    {
      "id": "vibemathed:fractional-colouring-pauli-shadow-tomography:attempt",
      "problem_id": "vibemathed:fractional-colouring-pauli-shadow-tomography",
      "model": "GPT Sol 5.6",
      "provider": "OpenAI",
      "attempted_at": "2026-08-20T00:00:00.000Z",
      "human_collaborators": [
        "Jędrzej Stempin",
        "Santiago Llorens",
        "Felix Huber"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The arXiv comments field reads \"Found with GPT Sol 5.6\", and the paper's AI statement says the model was used to derive the main results, Theorem A and Theorem B. The construction amplifies fractional chromatic numbers, beta numbers and expectation values through lexicographic graph products.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "Counterexamples to the fractional coloring conjecture for triply efficient shadow tomography",
          "url": "https://arxiv.org/abs/2608.20113",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Fractional Colouring Conjecture for Triply Efficient Pauli Shadow Tomography",
          "url": "https://vibemathed.com/problem/fractional-colouring-pauli-shadow-tomography",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:fractional-colouring-pauli-shadow-tomography:verification",
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      "solution_event_id": "vibemathed:fractional-colouring-pauli-shadow-tomography: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:2608.20113v1, 14pp): the refuted statement is Conjecture 13 of King, Gosset, Kothari and Babbush in PRX Quantum 6, 010336 (2025), and the AI statement is as quoted. The constructions were not checked here. Days-old preprint, no independent review.",
      "sources": [
        {
          "label": "VibeMathed: The Fractional Colouring Conjecture for Triply Efficient Pauli Shadow Tomography",
          "url": "https://vibemathed.com/problem/fractional-colouring-pauli-shadow-tomography",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "Counterexamples to the fractional coloring conjecture for triply efficient shadow tomography",
          "url": "https://arxiv.org/abs/2608.20113",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "Counterexamples to the fractional coloring conjecture for triply efficient shadow tomography",
      "url": "https://arxiv.org/abs/2608.20113",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Fractional Colouring Conjecture for Triply Efficient Pauli Shadow Tomography",
      "url": "https://vibemathed.com/problem/fractional-colouring-pauli-shadow-tomography",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:fractional-colouring-pauli-shadow-tomography:signal:verify_now",
      "problem_id": "vibemathed:fractional-colouring-pauli-shadow-tomography",
      "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"
}