Vitrum Cosmicum Vacui (VCV48) Integrated Analysis of Cosmic Harmonics, Variation of Fundamental Constants and Phase Coherence.

We present an analysis of the VCV48 cosmic crystalline lattice model using 712, 472 LRG galaxies from the DESI catalog and 323, 474 galaxies from the SDSS DR7 catalog. Five observational pillars are investigated: (1) the variation of the ne-structure constant (∆α/α) as a function of the galactic halo velocity dispersion, (2) phase alignment by cosmic domains through rotations in the SO (3) group, (3) the correlation of the lattice phase transition with the Sloan Great Wall (SGW), (4) the derivation of the Finger-of-God Law for the lattice harmonics, and (5) the hemispheric asymmetry in the correlation function with respect to the CMB dipole and its dependence on halo vorticity. Calibrating the saturation parameter SATBOOST to 1. 5 (eective threshold ≈ 560 km/s) yields a dierential ∆ (∆α/α) = −2. 05 ± 0. 31 ppm between high- and low-mass regimes. Without this calibration (SATBOOST = 1. 0), the rst-principles prediction of −5. 34 ppm diers by 10. 7σ, marking the current agreement as a phe- nomenological t rather than an independent model verication. The complementary analyses reveal: a rotational phase transition of the lattice co- incident with the SGW at 324 Mpc (combined signicance ∼ 4. 5σ), a Finger-of-God compression of 0. 075 Mpc per harmonic, and maximum phase coherence (+2. 81σ) in very high vorticity halos (vdisp ≤ 500 km/s) in the SDSS sample. The derivation of SATBOOST from rst principles and the direct spectroscopic measurement of ∆α/α in individual galaxies constitute future tests of the model, together with the evalu- ation of harmonic 10 at low redshift where the VCV48 theoretical model places the BAO despite the fact that the lattice is almost completely degenerate in that regime.