TARS agent system
The construction was found by the TARS agent system (foundation model not disclosed); the proof was reconstructed and manually verified by the human authors.
Provider: unknown · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Stanley's Problem 4 on Differential Posets
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
For a differential poset $P$, must the weighted $2$-multichain series $M_{P,2}(q)$ be a rational multiple of $F_P(q)^2$, the square of its rank generating series?
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
What AI did
Verification boundary
A locally finite $1$-differential poset with nonrational quotient series over every characteristic-zero field; the construction yields continuum many such series. Author-verified arXiv preprint, not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Timeline
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arXiv:2607.24541 - A negative answer to Stanley's Problem 4 on differential posets
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Known method families
construction (source-reported)
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
- VibeMath has not independently verified the mathematical claim.
- AI-attempt independence and training-data exposure are unknown unless explicitly documented.
- VibeMath has not independently audited the mathematical statement, proof, or novelty claim.