Contribution Review

Identify what the work actually adds. Keep correctness, novelty, significance, and external acceptance as separate questions.

Compare at theorem level

Read the manuscript's principal statements and the available proof status. Seek the closest existing theorem, not merely papers with similar titles. Use primary papers, author manuscripts, or authoritative mathematical references. If source access fails, state the exact unavailable comparison and continue with what can be established.

For each principal result compare:

• the old and new hypotheses and quantifiers;
• the conclusion, constants, domains, and parameter range;
• whether the mechanism is new, an extension, a specialization, or a reformulation;
• whether the result improves an unconditional bound or supplies a reusable construction;
• which dependency is still unproved.

A result can be correct without being original, original without solving the main problem, or useful without being a breakthrough. Absence of a search hit does not establish priority. Conversely, an old general mechanism does not settle the novelty of a specific stronger local or quantitative theorem.

Separate completed literature comparisons from outstanding priority questions. Do not present "not independently reviewed" as a proof gap. If correctness needs examination, route only that task to proof-audit.

Output

Lead with the strongest supported contribution and the precise remaining uncertainty. Give theorem-specific primary citations close to the comparison they support. If asked to rank discoveries, include only as many entries as satisfy the user's criterion; distinguish possible candidates from confirmed discoveries.

Assess length by what a reader needs to identify and reconstruct the contribution. Suggest a focused article when the central result is obscured by multiple exploratory routes, rather than treating page count as evidence of invalidity. Compare formalization and numerical certificates by what they establish, not by their presence alone.

For publication recommendations, hand the comparison to research-closeout. Do not publish, contact researchers, or submit material solely because a review recommends doing so.