What was already known
Umans and Wang proposed short low-height n-divisor progressions as a stronger sufficient arithmetic-progression form of their conjectural program. The higher-rank Strong Divisor Conjecture is distinct.
AI involvement
Xinjie He and Amit Sahai say a Codex run using gpt-5.6-sol discovered the proof and initial write-up. They reviewed, verified and revised it.
The disclosure assigns discovery and initial proof to Codex, while named humans reviewed and wrote the final article; full autonomy beyond task setting is not documented.
Importance
Refutes a named arithmetic-progression version of the Umans–Wang divisor conjecture with a quantitative lower bound.
Limitations
The higher-rank Strong Divisor Conjecture is a separate question and is not refuted.
Technical verification
The two authors explicitly report subsequent human verification of the complete proof; no machine formalization is claimed.
Formal checking
Reviewed and verified the proof and citations, then revised the exposition
- Checker
- Xinjie He and Amit Sahai
- Scope
- Theorem 1.1 AP lower bound and Corollary 1.2 exponent exclusion
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the fixed prime band, semiprime incidence reduction and bounded-degree linear-space estimate.
Correction and publication history
Refutes a named arithmetic-progression version of the Umans–Wang divisor conjecture with a quantitative lower bound.
Read this published revision