Problem detail · source-aware
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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 $\chi_f \varepsilon^2$.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
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.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
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.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.