VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
An asymptotic formula for $p(k)$, the limiting probability that a random permutation has an invariant set of size $k$: it is asymptotically $k^{-\delta}(1+o(1))$ times a smooth positive function, sharpening a line of estimates running through Łuczak-Pyber and Eberhard-Ford-Green.
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.
What AI did
GPT o4-mini, ChatGPT Pro 5.4
The authors "originally discovered that g was almost constant via the use of GPT o4-mini. Upon being asked to prove this fact, the model suggested the broad strategy" (initially miscomputing an integral, then completing the evaluation after being pointed at Mellin transforms). A separate argument in the paper is ChatGPT Pro 5.4's, shortened and checked by the authors, kept because it was cleaner than their own.
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
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.