POCD Appendix D: Explicit 12\times 12 CRT Block Operator Construction and a Reproducible Spectral-Compression Demonstration

Appendix D provides: · A fully explicit CRT permutation P (so the factorization can be checked line-by-line). · Explicit S_{12}, explicit S_3,S_4, and the identity P^\top S_{12}P=S_3\otimes S_4. · An explicit dissipative generator L_0=-\gamma(2I-S_{12}-S_{12}^\ast) with closed-form eigenvalues. · An explicit cross-block coupler L_1=K_3\otimes Q_4. · Concrete projectors \Pi_H^{(3)},\Pi_L^{(3)} and a measurable compression indicator C(t). · A theorem guaranteeing first-order block interaction, and a sufficient condition framework for net block compression on finite windows. This makes the CRT spectral compression concept reproducible in a literal 12\times12 matrix laboratory.