What was already known
Lassak’s bound held for reduced polygons and follows for constant-width bodies; mixed curved-and-segment bodies remained unresolved.
AI involvement
GPT-5.5 Pro found the retained counterexample in a semi-directed search. Kominers set the problem and method and supplied the geometric proofs and exposition.
The model found the explicit counterexample itself inside a human-directed geometric search.
Importance
Gives a concrete counterexample to the general reduced-body area conjecture.
Limitations
The maximal area remains unknown. Exact rational enclosures support the numerical inequalities, while the full reducedness proof lacks a documented complete check by a named method.
Technical verification
The author gives exact rational certificates for curvature-density and area inequalities, but the source does not document who or what checked the full reducedness proof. Refine.ink's review has unspecified personnel and method, so no human or machine checking method is counted.
Human understanding
Kominers explains the quarter-disk blunting mechanism and the support-face/contact argument that makes the resulting body reduced.
Correction and publication history
Gives a concrete counterexample to the general reduced-body area conjecture.
Read this published revision