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

We 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: where is epitaxial strain, is oxygen vacancy concentration, and is the Hilbert-space volume computed a priori from DFT-derived quantum geometric descriptors. The model is validated across 25 materials from five distinct superconductor families using leave-one-family-out cross-validation (LOFO-CV), yielding RMSE = 42.1 K and . 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.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)本研究报道了一种闭形式唯象框架（SVEM-GT），该框架可将铜基超导体、镍基超导体、铁基磷族超导体、笼目金属与高压氢化物统一于单一量子几何定律之下。超导临界温度可通过下式预测： 其中 为外延应变， 为氧空位浓度， 为通过密度泛函理论（Density Functional Theory, DFT）衍生的量子几何描述符先验计算得到的希尔伯特空间体积。本模型采用留一族交叉验证（LOFO-CV）对来自5个不同超导体家族的25种材料进行了验证，最终得到均方根误差（Root Mean Square Error, RMSE）=42.1 K 以及 。该乘性耦合效应可预测应变与空位之间存在超线性协同作用，这与2024年发表于《自然·物理学》的最新实验结果相符。本发布包包含全部数据、代码与手稿。版本说明（v3.0）：本v3.0版本是对原始SVEM-GT v2.0提交版本的经验证并扩展的更新，新增了超导体家族、优化了模型系数，并实现了留一族交叉验证的完全可复现性。作者与制作者：Deymison Elias dos Reis（ORCID：https://orcid.org/0009-0001-2550-6169）