No Singularities in VEQF_ Mathematical Resilience Against Indefinite Compression and Non-Singular Cosmology

Singularities—in black holes or the Big Bang—represent unphysical infinities where physical laws break down, often signaling incomplete theories. In the Vacuum Energy Quanta Field (VEQF) framework, we demonstrate mathematically that such singularities are impossible due to inherent resilience against indefinite compression. Building on discrete lattice structure, Transactional Configuration Index (TCI) thresholds, and entropy-driven gradients, we prove density bounds and non-singular cosmological origins via supermassive black hole collisions. Expanded derivations show super-cubic binding energies cap collapse, while observational ties (e.g., JWST dust rings, galaxy dynamics) provide testable predictions. This work unifies non-singular cosmology with VEQF, resolving metaphysical inconsistencies in standard models and offering a pathway for empirical validation. For broader accessibility, we include intuitive explanations and comments on mainstream critiques.