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The review archive

Paper assessments.

Ratings summarize the strongest checked finding in the stated scope. They do not certify every result.

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18 papers

Authorship, mathematical field and scoped review findings
Paper	Authorship	Field	Rating
A product counterexample to the simplex maximum	Model	Geometry and dynamics	No substantive issue foundThe arguments covered by the dated panel report and recorded source checks.
A proof of the positive density conjecture for integer Apollonian circle packingsJean Bourgain, Elena Fuchs	Human	Number theory and arithmetic groups	Substantive proof defectThe intended uniform singular-series bound (author-copy Lemma 3.6) and the separate congruence-average/short-interval deduction.
A smooth nonquadratic entire affine maximal graph in dimension ten	Model	Geometry and dynamics	No substantive issue foundThe arguments covered by the dated panel report and recorded source checks.
A uniform influence bound for hypergraph properties	Model	Combinatorics and probability	No substantive issue foundThe arguments covered by the dated panel report and recorded source checks.
An explicit noncoordinate polynomial with affine three-space zero fibre	Model	Algebra and algebraic geometry	No substantive issue foundThe arguments covered by the dated panel report and recorded source checks.
An explicit power saving for the exact discrete Fourier transform	Model	Analysis and algorithms	No substantive issue foundThe arguments covered by the dated panel report and recorded source checks.
An uncertainty principle for cyclic groups of prime orderTerence Tao	Human	Analysis and algorithms	Typos onlyMain uncertainty theorem and its two applications in arXiv math/0308286v6.
Arithmeticity, superrigidity, and totally geodesic submanifoldsUri Bader, David Fisher, Nicholas Miller, Matthew Stover	Human	Geometry and dynamics	Substantive proof defectConfirmed defects in the supplied compatibility proof; proposed repairs and the full arithmeticity theorem remain under verification.
Effective version of Ratner's equidistribution theorem for SL(3,R)Lei Yang	Human	Geometry and dynamics	Headline claim refutedPublished Theorems 1.2–1.3 are refuted by a checked counterexample. The curve corollaries remain unresolved.
Generalization of Selberg’s 3/16 Theorem and Affine SieveJean Bourgain, Alex Gamburd, Peter Sarnak	Human	Number theory and arithmetic groups	Substantive proof defectFalse intermediate assertions and defective supplied proof passages, checked in their stated editions.
Generic thinness in finitely generated subgroups of SL_n(Z)Elena Fuchs, Igor Rivin	Human	Number theory and arithmetic groups	Substantive proof defectSubstantive defects and false local assertions are checked. The main generic-thinness statement and replacement proof remain unresolved.
Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutionsElena Fuchs, Chen Meiri, Peter Sarnak	Human	Number theory and arithmetic groups	Headline claim refutedThe claimed seven-family parameter classification is refuted. The thinness results have separate, partly unresolved outcomes.
On the Fourier-Walsh spectrum of the Moebius functionJean Bourgain	Human	Number theory and arithmetic groups	Substantive proof defectThe periodic Fourier approximation and local estimates (4.6)–(4.14).
On the Local-Global Conjecture for Integral Apollonian GasketsJean Bourgain, Alex Kontorovich	Human	Number theory and arithmetic groups	Substantive proof defectSpecified local assertions and supplied proofs in arXiv 1205.4416v2; the journal typesetting was not inspected.
Quadratic stabilization of the canonical Foulkes–Howe map	Model	Algebra and algebraic geometry	No substantive issue foundThe arguments covered by the dated panel report and recorded source checks.
The Quasi-Riemann Hypothesis	Model	Number theory and arithmetic groups	UnresolvedFocused checks and supplied full-text assessments; complete proof chain not verified.
Weakly mixing polygonal billiardsJon Chaika, Giovanni Forni	Human	Geometry and dynamics	Substantive proof defectSubstantive defects in the supplied proof are checked. Main weak-mixing statements remain unresolved; the full intended-range cyclic-cover counterexample is not certified here.
Étale covers with a prescribed exterior sheet	Model	Algebra and algebraic geometry	UnresolvedInternal construction checked relative to stated external inputs.