Prove the completeness of generalized fishnet determinants as a Steinmann basis

Prove or disprove that the determinants N_\lambda^{(m)} of ladder integrals form a basis for all polynomials in ladder integrals that satisfy the Steinmann conditions.

Background

The paper introduces generalized fishnet determinants N_\lambda^{(m)} as determinants of ladder integrals indexed by partitions. These determinants automatically satisfy the relevant Steinmann double-discontinuity constraint and are identified, through a dual matrix-model representation, with expectation values of Schur polynomials.

The cited prior work proposed that these determinants span the entire space of Steinmann-compatible polynomials in ladder integrals. The present paper uses this conjecture as context and constructs ASD combinations within this class, but does not establish the conjectured completeness in full generality. The conclusion correspondingly describes the exhaustion of all ASD Steinmann combinations only conjecturally.