What was already known
Stanley posed the rational-factor question in 1988; Young’s lattice satisfies it. Earlier reflection and crown constructions supplied differential-poset families but not this nonrational quotient.
AI involvement
The TARS agent autonomously found the central counterexample. Xinan Dai reconstructed and checked the proof, reviewed the literature and wrote the paper.
The original paper explicitly says the TARS system found the counterexample during autonomous mathematical search; later human reconstruction is credited separately.
Importance
Gives a counterexample to Stanley’s named differential-poset question.
Limitations
The model is credited with finding the counterexample, while the origin of the coefficient-separation argument is not isolated. Dai reports reconstructing and manually verifying the result.
Technical verification
Dai reports manual verification of all mathematical results in the final argument. This is a source-reported completed human proof check; the paper says finite computations do not enter the theorem.
Formal checking
Manual verification after proof reconstruction
- Checker
- Xinan Dai
- Scope
- The differential-poset counterexample and nonrationality result for k=2
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Dai's reconstructed proof explains how crown choices change a quotient coefficient and how the resulting family defeats every rational series.
Correction and publication history
Gives a counterexample to Stanley’s named differential-poset question.
Read this published revision