What was already known
The 2025 IRIS paper posed the face-count inequality as a conjecture.
AI involvement
Claude agents found the counterexamples in John Erlbacher’s directed Demonstrandum campaign. Erlbacher audited its verification gates.
Claude agents supplied the witnesses under Erlbacher’s direction; individual-result autonomy is not documented.
Importance
Corrects a specific proposed inequality about faces of simple 3-polytopes.
Limitations
The witness refutes the printed real-valued bound. It does not refute an integer-rounded weakening, Barnette’s theorem or the paper’s other conjectures. The original OpenReview page could not be read directly; the conjecture wording follows the cited frozen transcription.
Technical verification
Independent Python and Rust exact checkers reportedly certify the five counterexamples to the printed inequality.
Independent checking
exact computation
- Checker
- Independent Python and Rust counterexample checkers, plus census re-derivation
- Scope
- The five 10-face counterexamples to printed IRIS Conjecture 6.1
- Basis
- Reported by the linked checker
Human understanding
No named person explains the individual construction; Few is the evidence default.
Correction and publication history
The five polytopes refute the printed real-valued face bound.
Read this published revision