Stanley's Rankwise Lower-Bound Conjecture for Differential Posets

Precise statement

Must every $r$-differential poset have at least as many elements in each rank as $Y^r$, the $r$-th Cartesian power of Young's lattice? For $r = 3$ the new construction has fourth-rank size $50$ against $51$ for $Y^3$.

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

TARS agent system

The counterexample was generated by the TARS agent system (underlying foundation model not disclosed) through autonomous mathematical search, then examined and independently verified by the human authors.

Provider: unknown · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

Explicit construction verified by the human authors and published as an arXiv preprint. Not yet peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-07-28

   arXiv:2607.22988 - An explicit counterexample to Stanley's rankwise lower-bound conjecture

   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.