The L log L Fourier-convergence conjecture

What OpenAI claims

Proves that the ordinary symmetric Fourier partial sums of every complex-valued function in L log L(𝕋) converge almost everywhere along the full sequence. This resolves the classical sufficiency conjecture at the L log L scale. (Lean)

Paper

1. Almost-everywhere Fourier convergence in L log L

   23 September 2026 · Preprint, not peer reviewed · PDF

   We prove that the ordinary symmetric Fourier partial sums of every complex-valued function in L log L on the circle converge almost everywhere to the function along the full sequence. This establishes the classical L log L sufficiency conjecture.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.