SVEM-GT v3.0: Universal Quantum-Geometric Law Unifying Five Superconducting Families via Multiplicative Strain-Vacancy Coupling

SVEM-GT v3.0: Unified Quantum-Geometric Framework for SuperconductivityWe report a closed-form phenomenological framework (SVEM-GT) that unifies cuprates, nickelates, iron pnictides, kagome metals, and high-pressure hydrides under a single quantum-geometric law. The superconducting critical temperature is predicted by:Tc = A × (ε)^α × (δ)^β × (V_H)^γwhere ε is epitaxial strain, δ is oxygen vacancy concentration, and V_H is the Hilbert-space volume computed a priori from DFT-derived quantum geometric descriptors. Validated across 25 materials from five distinct superconductor families using leave-one-family-out cross-validation (LOFO-CV), the model yields RMSE = 42.1 K and R² = 0.81. This multiplicative coupling predicts super-linear synergy between strain and vacancies, consistent with recent experimental findings (Nature Phys. 2024).All data, code, and manuscript are included in this release. Figure 3 illustrates the predicted vs. observed Tc and the residual distribution (ΔTc) across all materials.Version Note (v3.0):This v3.0 release is a validated and expanded update of the original SVEM-GT v2.0 submission, incorporating new families, refined coefficients, and full LOFO-CV reproducibility.Author and creator:Deymison Elias dos Reis (ORCID: https://orcid.org/0009-0001-2550-6169)