Eventual simple negative roots for rank-four capacity-two partition truncations

Let m_1+...+m_q=n be an arbitrary partition into positive integers and let M(m) be the rank-four truncation of the direct sum of U_min(2,m_i),m_i. For every fixed 0 < alpha < 1/2, we prove there is an integer N_alpha, independent of the number of blocks and of the particular partition, such that whenever n >= N_alpha and max_i m_i <= alpha*n, the Ehrhart h-star polynomial of the base polytope has degree n-ceil(n/4) and all roots are distinct, real, and strictly negative. The number of blocks may grow with n, and blocks of sizes one and two are allowed. An exact inclusion-exclusion formula reduces the Ehrhart numerator to finitely many color levels. A binomial-tail kernel has positive real part after division by cosh(sqrt(t)); its even part therefore has infinitely many simple negative roots. A compactification of decreasing block masses, allowing dust, gives a threshold uniform over all partitions. Two moving endpoint regimes use a cancellation based on the sum of the block sizes, not the number of blocks. The threshold is not explicit. The result does not cover alpha=1/2, all small orders, other ranks or capacities, or arbitrary nonpaving matroids. Some members are uniform and paving. Weighted multi-hypersimplex and split-matroid frameworks and the Adiprasito--Zhang uniform-matroid result are prior work; no global-first claim is made. Status: internally reviewed preprint; external mathematical review and formal peer review pending. The archive includes accepted TeX/PDF, frozen Markdown, the exact 37-file supporting closure, checksums and reproduction instructions. Historical dependency labels are not public review claims.