What was already known
King, Gosset, Kothari and Babbush proposed the universal fractional-colouring bound as Conjecture 13 in their 2025 shadow-tomography work. Their efficient protocol also assumed efficient fractional-colouring sampling.
AI involvement
The paper credits GPT Sol 5.6 with deriving both main theorems. The human authors selected the research context, verified the results and explained them; prompt-level autonomy is not documented.
Both central counterexample theorems are expressly attributed to the model; no evidence establishes independence beyond the authors’ task framing.
Importance
Disproves a specific proposed bound for Pauli shadow tomography and supplies a broader graph-based criterion for counterexamples.
Limitations
The result concerns this fractional-colouring bound; it does not rule out other tomography algorithms. The three authors report verifying the results and explain both constructions. No separate external or machine check of the general criterion is documented.
Technical verification
The three authors explicitly report verifying all results, including the assessed Theorems A and B. This is a source-reported complete human check; no machine check of the general theorem is documented.
Human understanding
The authors explain the explicit seed and product amplification in §3 and §5, and the beta threshold argument in §6.
Correction and publication history
One paper-level claim reconciled across two source pointers; original AI attribution, author verification and prior conjecture reviewed.
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