Riemann Lattice Framework for Superconductivity

This work introduces a unified geometric framework for superconductivity derived from the non-trivial zeros of the Riemann zeta function. By connecting the Stochastic Planck Time Hypothesis (SPTH) with lattice-scale wave functions, the model demonstrates that the critical line Re(s)=1/2 serves as the universal axis of stability. Applying this principle to orthogonal coordinates yields cubic lattices, while tetrahedral coordinates naturally produce diamond structures, reproducing known crystal geometries directly from number theory. Three material-specific equations—linking coherence lengths, anisotropy, and CuO2 layer count—predict Tc across diverse superconductors with remarkable accuracy, requiring only a single calibration constant. The framework explains anomalies such as Bi-2212 supermodulation and identifies multi-channel conduction pathways in MgB2, YBCO, and Hg-1223. Beyond superconductivity, the isotropic number encodes universal confinement physics, suggesting implications from atomic lattices to cosmic-scale structures. This elevates the Riemann Hypothesis from a mathematical conjecture to a physical inevitability, positioning the Riemann lattice as a fundamental law of nature.