What was already known
The threshold was known to be necessary, but its sufficiency was conjectured. Earlier explicit non-five-voter examples were much larger.
AI involvement
Chindelevitch and Harutyunyan credit Claude with the co-backing idea and enumeration implementation. They selected the problem, verified Section 7 and wrote the final argument.
Claude is explicitly credited with the co-backing idea central to the Paley(43) non-inducibility proof; the broader research and final paper remain human-led.
Importance
Gives a small explicit counterexample to the conjectured five-voter criterion.
Limitations
This assesses Section 7’s Paley(43) result, not the paper’s other tournament claims or three-voter Kemeny hardness. The exact certificate and author verification are source-reported.
Technical verification
The authors explicitly report human verification of Section 7. Its finite non-inducibility screen and maximum acyclic-subgraph count are presented as exact, reproducible computational certificates with rational arithmetic, while the combinatorial reduction is supplied in the paper. These checks are source-reported.
Formal checking
Orbit subset dynamic programming and end-to-end finite shell-and-screen enumeration with exact LP/ILP certificates; source-reported.
- Checker
- The paper's reproducibility scripts and exact arithmetic verifier, as reported by Chindelevitch and Harutyunyan
- Scope
- Paley(43) has maximum acyclic subgraph size 543 and no five-voter inducing profile after the Section 7 reduction
- Basis
- Reported by the linked checker
Explicit Section 7 human verification recorded in the paper's AI-use table, with the mathematical proof and verification ledger; source-reported.
- Checker
- Leonid Chindelevitch and Ararat Harutyunyan, the human authors
- Scope
- Theorem 7.1, including the co-backing reduction and Paley(43) five-voter conclusion
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The human authors explain how co-backing, tight slack and the finite screen rule out five voters for Paley(43), despite Claude's role in originating the idea.
Correction and publication history
Gives a small explicit counterexample to the conjectured five-voter criterion.
Read this published revision