What was already known
Aaronson's 2008/2009 quantum-oracle separation ruled out perfect QMA completeness by black-box methods, without a quantitative bound. Jeffery and Witteveen had shown that black-box amplification reaches doubly-exponentially-close completeness. The first Aaronson–Witteveen preprint used GPT-5's rational-function step to prove this was optimal; Phillip Harris later supplied a simpler determinant argument for the published version.
AI involvement
The first preprint explicitly credits GPT-5-Thinking with the rational trace and rational-growth approach, a pivotal step within a human-designed theorem proof. The later determinant replacement is credited to Phillip Harris.
The first preprint explicitly credits GPT-5-Thinking with r(z)=tr[(I−P(z))⁻¹] and the complex rational-growth approach. Aaronson and Witteveen designed the problem and completed the argument; Harris supplied the later replacement.
Importance
The model-suggested function enabled one version of the quantitative completeness proof. The current published theorem rests on Harris's replacement, so the AI contribution is an alternative historical proof idea rather than the current theorem's proof.
Limitations
The AI-origin step concerns the completeness barrier only. Aaronson and Witteveen set the question, adapted an earlier quantum oracle, and supplied the rest of the argument; the soundness barrier is not attributed to GPT-5. The published Quantum version replaces the rational trace with Harris's determinant, and journal publication therefore does not directly check the superseded AI argument. No separate completed human or machine check of that original argument was located.
Technical verification
The AI-origin rational approach appears as a complete argument in the first preprint, but no completed rigorous human or machine check of that superseded approach is documented. Journal publication checks the revised determinant proof, not this selected step.
Human understanding
Aaronson and Witteveen explain how the rational trace separates yes- and no-instance behavior and how the growth bound yields the completeness limit.
Correction and publication history
Primary-version comparison isolates a documented AI-origin proof idea from the later human replacement.
Read this published revision