What was already known
Erdős conjectured that the supremum of such fiber exponents is one. Prior work of Baker–Harman reached a multiplicity exponent 0.7039, and Lichtman reached 0.7156 through smooth shifted-prime estimates (manuscript introduction, pp. 1–2).
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Attains the optimal power exponent for the largest fibers of Euler’s totient function and resolves Erdős’s conjecture.
Limitations
The theorem produces infinitely many n for each fixed epsilon; it does not say every n has such a large fiber. The stronger smooth shifted-prime input is separate.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, and prior-work review for non-notifying local inclusion.
Read this published revision