On the sharpness of Denjoy's theorem

Rohil Prasad

The retained AI-origin construction gives a C¹ circle diffeomorphism with irrational rotation number, a wandering interval and derivative modulus ω(t)=t log(1/t), the barrier case in Prasad’s Corollary 1.1.

Sources for this record

What was already known

Earlier examples reached moduli such as t log(1/t)^(1+ε), but the t log(1/t) barrier was open.

AI involvement AI-centered

GPT 5.6 Sol Ultra proposed the essential barrier-case construction. Rohil Prasad repaired, checked and rewrote the proof and discovered the broader theorem.

The barrier-case construction's essential ingredients originated in the model draft, while the final proof and general theorem required central human repairs and extension.

Importance Notable

Reaches the previously open logarithmic regularity barrier for Denjoy counterexamples.

Limitations

The model draft needed missing arguments and major human reformulation. Prasad supplied the completed proof and the broader theorem for every weaker-than-Lipschitz concave modulus; that extension is separately credited to him.

Technical verification Formal (human)

Prasad explicitly reports manually checking the authoritative final proof, including the AI-origin barrier construction after reconstruction. Claude's error search is not counted as a separate completed check.

Formal checking

Prasad explicitly reports manually checking the authoritative final proof, including the AI-origin barrier construction after reconstruction. Claude's error search is not counted as a separate completed check.

Checker
Rohil Prasad, paper author
Scope
Barrier-case Denjoy example at ω(t)=t log(1/t), within the final proof
Basis
Reported by the linked checker
Evidence source

Checking a formal statement does not establish that it matches the original problem.

Human understanding Full

Prasad reconstructed and explains the model-origin construction and the refined proof, including which generalization and lemma changes he supplied.

Correction and publication history