Exact Reduction and a Machine-Verifiable First-Tower-Step Separation for USp(6)-Covariant Quantum Compression

This is the successor to the USp(4) result (doi:10.5281/zenodo.21694560) in the Satyalogos operational-integration program, extending it to the first nontrivial rank step of the symplectic tower, USp(6) = Sp(3). In the USp(6) = Sp(3) covariant compression model the carrier is W = V14 ⊕ V21 = sl(6) (dimension 35), encoded through a six-dimensional covariant memory M = V6 and decoded. Working entirely over the Gaussian rationals Q(i), we reduce the effective-channel physical- and PPT-positivity cones to seven Hermitian isotypic blocks by exact Gram-dual congruence, identify the correct 36-dimensional real metric-Hermitian outer span, certify a coherent lower witness by exact construction, and certify an outer-PPT upper bound by an exact rational sum-of-Hermitian-squares dual whose defining identity holds with zero residual. The result is the exact chain F*_effEB,V6 ≤ F*_outerPPT,36 ≤ 1/100 < 1/40 < 39587/1382976 ≤ F*_coh(Sp3), so a specific coherent covariant channel strictly outperforms every entanglement-breaking effective channel through the six-dimensional memory V6. Two standalone verifiers — one dependency-free (Python standard library only), one a full reconstruction — recheck the certificates with no optimizer and no floating point in the proof path; both return ALL PASS. Three registers are kept visibly separate: [T] exact theorem, [N] numerical diagnostic, [O] open/conditional. The exact optima, the tightness of the 1/100 bound, and any general Sp(n) or capacity interpretation remain open. The Sp(2) and Sp(3) objectives are analogous covariant functionals — shown distinct by an exact normalization-bridge computation — so the tower correspondence is structural rather than one identical functional carried up the tower. The attached bundle contains the manuscript, both verifiers, the exact-rational datasets, run scripts, and SHA-256 manifests for full reproducibility.