What was already known
Pandey conjectured that I(GP(n,k),x) is real-rooted exactly when k is even, for n≥2k+1.
AI involvement
Claude agents proposed the counterexamples and checkers. John Erlbacher directed the campaign, audited its verification gates and accepts responsibility; individual-result autonomy is not documented.
The release credits AI agents with proposing retained constructions or proofs and Erlbacher with directing the campaign; AI-centered is the supported individual-result level.
Importance
Small exact counterexamples correct both directions of a recent graph conjecture.
Limitations
The release reports exact Sturm and independent brute-force checks of these finite graphs. The scan of 3≤n≤14 is additional evidence, not a classification of all parameters.
Technical verification
An exact independence-polynomial/Sturm checker and independent Rust brute force reportedly certify both counterexample directions, including admissible parameters.
Formal checking
exact computation
- Checker
- check_pandey_parity.py exact Sturm checker and bf_gp.rs Rust brute force
- Scope
- GP(9,2), GP(7,3) and GP(3,1) against Pandey Conjecture 4.1
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Human direction and gate auditing are documented, but no named person explains the central reasoning of this individual AI result. Few is the evidence default, not a finding of inability to understand it.
Correction and publication history
Small exact counterexamples correct both directions of a recent graph conjecture.
Read this published revision