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Does a universal summation process recover the degree of a circle map from its Fourier moduli, that is, does $\sum_n \sigma_{n,\varepsilon} n |\hat f(n)|^2 \to \deg f$ hold for Holder maps below the threshold? No. For every $0 < \alpha < 1/3$ there is an $f \in C^{0,\alpha}(S^1;S^1)$ for which the sum fails to converge to $\deg f$, answering Open Problem 5.6 from Brezis's list of favourite open problems negatively for all $p > 3$. The endpoint $C^{0,1/3}$ is left unresolved.
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The disclosure states that ChatGPT generated preliminary drafts of the proofs in the manuscript. The author then verified each argument in detail, revised the proofs where necessary, checked the cited sources, determined the final formulation of all results, and takes sole responsibility for the content.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Single-author arXiv preprint; the construction combines degree-zero quotients of Blaschke factors with a Baire category argument. Not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
negative below the 1/3 threshold; the endpoint case is still open
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.