Preprint: Vitrum Cosmicum Vacui (VCV48) Model Validation with Gravitational Lenses.

This appendix documents the empirical validation of the Vitrum Cosmicum Vacui (VCV48) model, a theoretical framework that proposes a crystalline structure of Oh symmetry for the cosmic vacuum. In this model, matter and gravity emerge as viscoelastic responses of this lattice, whose vorticity coupling ξ(z) constitutes the core of gravitational lens mass predictions. The preliminary version of the model, based solely on ξ(z), showed a signicant spurious correlation between the predicted mass and the observed velocity dispersion (σ) in massive catalogs like DESI LRG. To eliminate this correlation, a prole compression function fcomp(σ, z; p) was introduced, which corrects the mass ratio based on the dynamic environment of each galaxy. The objective of this appendix is twofold. First, to document the calibration of the four free parameters of fcomp using the DESI LRG catalog as a training set. Second, to subject the calibrated model to a strict external validation using a double-blind methodology: the parameters, once optimized, are completely frozen and applied to independent datasets including strong gravitational lenses (Chen+ 2019), time-delay lenses (STRIDES), and galaxy clusters (eROSITA), without any readjustment. To ensure the precision and traceability of the calculations, a Rust Kernel has been implemented that encapsulates all the fundamental physical functions. This kernel calcu- lates the vorticity coupling ξ(z) and comoving distances using exclusively frozen constants derived from the Oh geometry, among them the Debye temperature ΘD = 35.77 K. This approach avoids the use of arbitrary or hardcoded constants, ensuring that every model prediction is traceable to fundamental physical parameters. The structure of this appendix reects the complete workow: parameter calibration (Section 1), external validation with three datasets (Section 2), local density dependence analysis (Section 3), implementation of an environmental phase transition model (Section 4), validation on strong lenses (Section 5) and time-delay lenses (Section 6), and an inde- pendent cross-validation of the Debye thermal correction using SDSS and DESI (Section 7).