Cubic augmentation of a two-moment model: an exact finite absorption theorem and its limits

We study adjoining a half-bandwidth signed cubic trace and a spectral count ladder to a bandwidth-one trace/Frobenius model motivated by zeta-zero certificates. In a finite circle model with mass N = 64, flat windows, and explicit budget centers, we prove exact absorption over the full atom-only class: the augmented and baseline optima agree for both the distinct-count and simple-fraction objectives. Three explicitly specified integer-marked grid columns attain the lower bounds. Their mixing weights are defined algebraically, and an Arb certificate proves all strict feasibility and inertia inequalities. The witness satisfies the ladder at every positive threshold, not just on a finite threshold grid. We also give the exact conjugate-pair spectrum, the isolated-block cubic identity, grid Parseval, and the sharp conditional spectral-capacity constant 2 sqrt(2). The result is a finite model theorem, not an unconditional statement about zeta zeros. Version 2 corrects an infeasible witness, a cubic-tolerance mismatch, and an incorrect rationality claim in version 1. Global absorption in the pair-containing or pinned classes remains unproved; equality on a searched column dictionary and heuristic pricing do not establish it.