What was already known
Stanley proposed a coefficientwise lower bound by Yʳ. Earlier rank-growth and rank-gap theorems did not imply that proposed comparison.
AI involvement
The paper says TARS autonomously generated the counterexample. Xinan Dai, Wenhao Deng, Yingdong Shi, Tailin Wu and Yuchen Yang examined and independently verified it.
The source explicitly says the TARS agent system autonomously generated the retained counterexample before human examination.
Importance
Refutes Stanley’s rankwise lower-bound proposal for every r≥3.
Limitations
The result leaves r=1 and r=2 open. The authors report independent examination and verification of the construction; no separate checking report or TARS search transcript is supplied.
Technical verification
The named human authors report independent verification of the counterexample, and the paper gives the finite incidence replacement and infinite reflection extension. No machine proof check is documented. The reported completed human review supports Formal, without claiming independent reproduction here.
Independent checking
Independent human examination and verification of the TARS construction
- Checker
- Xinan Dai, Wenhao Deng, Yingdong Shi, Tailin Wu and Yuchen Yang, human authors
- Scope
- The rank-four counterexample and its extension to infinite r-differential posets for r≥3
- Basis
- Reported by the linked checker
Human understanding
The human authors examined the construction and present its point-and-pair incidence invariant, explicit block replacement and reflection extension, explaining the mechanism of the assessed rank-four failure.
Correction and publication history
Refutes Stanley’s rankwise lower-bound proposal for every r≥3.
Read this published revision