A finite cover for coefficient positivity of stretched Littlewood–Richardson polynomials in the seven-row, size-thirty box

We give a finite cover argument for nonnegativity of the ordinary monomial coefficients of every stretched Littlewood–Richardson polynomial with partition lengths at most seven and outer size at most thirty. Explicit reductions leave 358,952 residual triples. The computational part consists of exact finite enumeration, local reduction checks and rational Ehrhart polynomial computations. The manuscript states the computational dependencies separately from the mathematical implication they establish. This 19-page preprint is publication edition 1.0.4. Code and complete computational evidence are available in the linked repository; the referenced evidence release is version 1.0.2. The result is restricted to the stated finite box and relies on the stated exact-software assumptions.