Poset reconstruction is the determination of a finite partially ordered set, up to order isomorphism, from its deck. The deck is the multiset of order isomorphism types of the induced partially ordered sets obtained by deleting one element at a time (Cintioli 2026).
Cintioli (2026) proved that every partially ordered set with at least four elements and width at most three is reconstructible from its deck. Here width is the maximum number of elements in an antichain. The theorem does not settle reconstruction for arbitrary width. Cintioli (2026) attributes discovery and development of the proof to ChatGPT, with adversarial review by Claude, and assumes responsibility for its correctness.
