Math RefereeOfficial journal comparison — 21 October 2026
Supplied PDF: Annals of Mathematics 203 (2026), 695–735, 41 pages,
DOI 10.4007/annals.2026.203.3.1. User supplied the file; it was found at
math-referee: (the filename includes a trailing colon).
SHA-256: 27e5811e95e9ef31a35e64ee54131dca3cf92e08e92e8071a4307f9de1414265.
This is a targeted independent comparison of the published passages with the frozen arXiv v2 source, not an assertion of complete edition identity. It supersedes the launch-time note that the journal PDF was unavailable. The initial native requests remain frozen against v2 and have not been resubmitted.
| Passage | Journal page | PDF page | Directly checked content |
|---|---|---|---|
| Definition 4.1 | 708 | 14 | Lipschitz control is defined after parallel transport; this definition does not impose a bound on ordinary section norm. |
| Corollary 5.2 | 715 | 21 | Hypothesis (d) uses maximum distance to integral cohomology, equal to gamma; (A) gives the logarithmic time interval; (C) requires multiplicative growth of that distance. The displayed section range is still the ambient bundle. |
| Proposition 5.1 proof after (21) | 718 | 24 | The preceding growth argument is applied to the section after subtracting the parallel integral section. |
| Theorem 1.3 proof | 726–728 | 32–34 | The proof projects to the positive-exponent part, iterates Corollary 5.2 explicitly on p. 727 and uses the resulting lattice-distance bound in the eigenvalue contradiction. |
Text was extracted from all 41 pages. Typeset formulas on PDF pages 21 and 24 were also rendered and visually inspected. The decisive hypothesis is distance to the integer lattice, not small ordinary Hodge norm; no additional small-norm condition was found in the compared statement. All three numerical bounds (d), (A), (C) and the integral-subtraction step agree in substance with the v2 source.
This comparison confirms the location and persistence of the contested statements. It does not by itself verify the proposed cyclic-cover counterexample's complete bundle and recurrence hypotheses, refute the main weak-mixing theorem, or supply a repair. Those mathematical questions remain separate from the edition comparison and native panel assessments.
Additional supporting archive items are identified in the original report. View the manuscript hashes and repository snapshot.