In an author account linked from Google’s proof-review project, a proposed lower-bound argument depended on distinguishing two frequency patterns. The AI feedback exposed a calculation error: the relevant patterns were {1, 1} and {2}, not {1, 1} and {3}. At p = 1, the distinction the argument needed disappears.[2]
Why that one value breaks the step
The p-th frequency moment adds each non-zero frequency raised to the power p. For {1, 1}, the result is 1^p + 1^p = 2. For {2}, it is 2^p. Substituting p = 1 gives 2 in both cases. A method looking only at that moment cannot separate these two patterns at p = 1.
Reproducing the local calculation
| p | Moment of {1, 1} | Moment of {2} |
|---|---|---|
| 1 | 2 | 2 |
| 2 | 2 | 4 |
| 3 | 2 | 8 |
William Swartworth’s account says the authors corrected their analysis to cover all p. He also describes two mistaken AI objections, including a notation-parsing error. The useful outcome was therefore a specific repaired argument, not blanket acceptance of the review.[2]
What the broader pilot measured
Google offered optional pre-submission assistance for STOC 2026 using an advanced Gemini reasoning system. Its account, first published in December 2025 and subsequently updated, reports that more than 80% of submitted papers opted in. More than 100 people answered the survey; 97% found the feedback helpful and 97% said they would use it again. These are respondent assessments from the provider-run pilot, not proof-error detection rates.[1]
A mathematical reviewer can contribute at several scales. It may catch a typo, expose a missing assumption, or find a special case that invalidates a claimed general step. The p = 1 example belongs to the third category: the objection points to a value anyone can substitute and check.
From an objection to a repair
A useful critique identifies the statement, the condition under which it fails and the consequence for later steps. Here the condition is explicit and the calculation is short. The authors still have to inspect the reduction and repair the argument; the two-line calculation does not do that work for them.
That is a more concrete standard for proof-assistance output than how convincingly it sounds like peer review. Ask what a reader can check, what changes after the check, and whether the corrected argument still establishes the intended result.
Sources & further reading
- Gemini provides automated feedback for theoretical computer scientists at STOC 2026 Google Research · 15 Dec 2025 · Accessed 14 Oct 2026
- Example Reviews: author feedback from theoretical-computer-science papers David P. Woodruff, Carnegie Mellon University · Accessed 14 Oct 2026