What was already known
Stöhr’s nonnegative three-element maximum was known. Nathanson asked how permitting negative elements changes the extremal problem; the comparison was unresolved even for three-element bases.
AI involvement
Van Doorn and Monticone used Aristotle to discover and formally prove the original comparisons. Nathanson studied those arguments, used the conversational interface for clarification, developed the paper’s new proofs and wrote the manuscript.
The source explicitly calls Aristotle’s original comparison proofs autonomous. Nathanson’s subsequent new proofs and manuscript are human work.
Importance
Settles the comparison for this infinite family of small additive bases and supplies human-readable proofs building on an AI-discovered solution.
Limitations
The result concerns k=2, hence three-element sets, and positive integer h; it does not resolve the arbitrary-cardinality postage-stamp problem. The authors report Aristotle’s Lean verification, but this review did not obtain exact public formal statements or reproduce them. Human rewritten proofs are not a separate AI discovery or an outside checking receipt.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The manuscript reports that Aristotle’s original comparisons were formally verified in Lean. The exact original public formal statements and pinned proof artifact were not obtained, so statement fidelity and complete checking scope remain pending rather than being inferred from the tool’s name.
Human understanding
Named human researchers explain or reconstruct the scoped central mechanism in the cited paper/account; credit for that explanation is separate from technical checking. Van Doorn and Monticone used Aristotle to discover and formally prove the original comparisons. Nathanson studied those arguments, used the conversational interface for clarification, developed the paper’s new proofs and wrote the manuscript.
Correction and publication history
Primary statement, hypotheses, prior bounds, AI role and evidence scope reviewed on 16 October 2026 against every current catalog/update page and existing immutable revisions. New recent scoped contribution; ordinary notifying editor publication.
Read this published revision