What was already known
The L log L endpoint sufficiency for ordinary Fourier partial sums was a classical conjecture; the manuscript notes prior maximal and weighted endpoint estimates without the full stated convergence conclusion.
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
Settles a classical endpoint question in Fourier analysis.
Limitations
The result is for the circle, ordinary symmetric partial sums, and full-sequence almost-everywhere convergence.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note states the full L log L almost-everywhere convergence theorem for symmetric Fourier sums.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every complex-valued function on the circle with finite integral of |f| log(2+|f|), its ordinary symmetric Fourier partial sums converge almost everywhere to f along the full sequence.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
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, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision