What was already known
The Clemens–Schmid invariant-cycle theorem gave the analogous rational statement; the integral degree-one case was open. A human author had already found an unpublished proof when QED received the problem, and later published that separate proof; an integral degree-two analogue was shown false.
AI involvement
A domain expert supplied the problem statement. QED generated a proof without further mathematical input; Yilong Zhang verified and explained it. A different human proof had already been found independently.
The QED report says the expert gave the problem with no further mathematical input and the system independently generated a different proof.
Importance
Provides an independent proof route for an integral degree-one invariant-cycle theorem.
Limitations
A human researcher had independently found an unpublished proof before the QED run and later published it. That proof is separate from QED’s argument; degree two has a counterexample.
Technical verification
The report and project README explicitly say Yilong Zhang independently verified the resulting proof of the degree-one integral invariant-cycle statement. This is a source-reported complete human check, not one reproduced here.
Formal checking
The report and project README explicitly say Yilong Zhang independently verified the resulting proof of the degree-one integral invariant-cycle statement. This is a source-reported complete human check, not one reproduced here.
- Checker
- Yilong Zhang, algebraic geometer and coauthor of the separate human proof
- Scope
- Surjectivity of H^1(X,Z) to H^1(X_t,Z)^T under the stated simple-normal-crossing degeneration assumptions
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The expert identifies and explains the proof's residue interpretation and reduction to Picard–Lefschetz theory.
Correction and publication history
QED generated a distinct proof from a problem-only prompt; Yilong Zhang verified and explained it.
Read this published revision