Math RefereeWhat the review labels mean.
Separate the written proof, a proposed repair and the headline results.
Colors summarize the stated review scope. They do not certify an entire theorem, measure an author, or rank human and model-generated mathematics. Each panel page explains its disposition and remaining obligations.
Green: no substantive defect was found in the audited argument. Read the scope and imported-input qualifications; this is not a guarantee of correctness.
Green with a correction label: localized typographical errors have checked corrections that preserve the main argument. Tao’s comparison paper is in this category; its main results are supported after two typo corrections, while a separate attributed extension remains outside the audit.
Amber: a substantive local defect has an explicit replacement that was separately checked. Bourgain’s approximation is in this category. The repaired local estimates hold under the stated assumptions; his full headline results remain unresolved in this review because other proof obligations are open.
Red: a substantive defect remains without a checked repair in the reviewed scope. This describes the supplied argument. A false theorem requires its own counterexample or refutation; an unsuccessful repair search does not prove irreparability.
Neutral: important proof steps, external-reference hypotheses or review coverage remain unresolved. Unverified means neither correct nor disproved. Resource failures provide no mathematical verdict.
Ratings in the paper table.
The table distinguishes the strongest substantiated finding in the stated scope from unfinished review coverage. It does not call a paper perfect, and a defective argument does not refute its conclusion. The linked panel report states exactly which claims were checked.
- No substantive issue found: no substantive defect was found within the audited scope; external inputs and coverage qualifications remain.
- Typos only: checked typographical corrections preserve the audited argument.
- Substantive proof defect: a serious local proof problem was established. A repair may be checked, proposed or still missing; the panel report distinguishes these outcomes.
- Headline claim refuted: an explicitly named central stated claim has a checked refutation. This need not refute every other theorem in the paper. The Fuchs–Meiri–Sarnak entry concerns its parameter classification; thinness claims have separate outcomes.
- Unresolved: no more definite curated classification has been established; this includes missing external checks and incomplete assessments.
Open the classification table ↗
Read three outcomes separately.
Original proof: what the supplied text establishes. Replacement proof: whether a proposed correction has been checked, and at what scope. Headline results: what follows after those checks and which dependencies remain.
Agreement between models is evidence to inspect, not a formal certificate. Reports distinguish AI assessments, source adjudication, exact computations, formal verification and pending human grades.