Multi-Scale Fractal Transduction and Phase-Locking in Mesoporous Silicate Qudit Matrices under Macroscopic Schumann Cavity Coupling: Analytical Formulation and Numerical Audit

This report formulates a 64-node mesoporous forsterite (Mg₂SiO₄) array with fractal dimension D_f = 2.34 and integrates the tight-binding dynamics of the graph Laplacian raised to β = D_f/3 = 0.78. A separate telegrapher order α = D_f/2 = 1.17 is stated and is not integrated. The continuum order of the graph power is 2β = 1.56. The 7.8 Hz term is an imposed external drive and is not an eigenvalue derived from the silicate. The largest absolute row sum of the fractional Laplacian is 9.132×10⁻¹⁵. Under the declared scales t_0 = 1, v_0 = 0.20, and θ = 0.02, the time-averaged core probability is 0.248917 and the drive-frequency amplification factor is 1.030002. Net core-probability loss, with oscillatory round trips excluded, is 1.275274 zJ/s. The Landauer comparison rate is 17.467036 zJ/s. The comparison fails. The PowerShell wrapper and the Python integration script are printed in the appendix.