Prime Obstructions to Integral Smith Forms of Schur Matrices

What is this paper trying to establish?

Do general Schur-function matrices always admit integral Smith forms after stabilization?

The central idea.

Constructs an infinite family of Schur-related matrices whose entry ideals are nonprincipal over the integral Laurent ring. The obstruction persists under identity stabilization and targets the general Schur-function clause of Kuperberg’s conjecture.

What changes if the method holds?

The proposed infinite family would falsify the broad Schur-function clause while leaving unrelated rectangular or specialized clauses untouched.

Where scrutiny should concentrate.

The paper identifies the following points as the highest-value targets for independent review.

1. 01
   The exact two-generator ideal calculation over integers rather than rational coefficients.
2. 02
   Preservation of the nonprincipal determinantal ideal under every identity stabilization.
3. 03
   The stable-equivalence transfer and the precise general Schur clause, excluding unrelated rectangular cases.