What was already known
Monical, Tokcan and Yong conjectured Ehrhart positivity for every Schubitope.
AI involvement
The authors report that GPT-5.6 Sol Pro found the retained counterexample on the first prompt after a 38-minute search. Humans chose the search target; ChatGPT also generated SageMath checking code. The identified Schubitope is the central AI-origin construction.
The paper attributes the concrete counterexample to GPT-5.6 Sol Pro, while the human authors directed the search and supplied the final mathematical exposition.
Importance
An explicit negative coefficient refutes the universal conjecture.
Limitations
This example does not classify which Schubitopes remain positive. Li and St. Dizier derived the counting formula and report exact SageMath checks of the displayed coefficient.
Technical verification
The paper reports a SageMath computation of the exact Ehrhart polynomial of its explicitly defined lattice polytope, including a strictly negative rational quadratic coefficient. Its counting derivation supplies a second way to frame the finite calculation.
Formal checking
Integer dynamic-programming lattice-point counts at t=0–13, exact rational interpolation of the degree-13 Ehrhart polynomial, and three holdout dilations
- Checker
- SageMath code reported by Li and St. Dizier
- Scope
- The specified Schubitope has Ehrhart coefficient [t²]=−687323/79200
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The human authors identify the polytope as a Minkowski sum of two hypersimplices and derive an explicit bounded-composition formula for its Ehrhart counts.
Correction and publication history
An explicit negative coefficient refutes the universal conjecture.
Read this published revision