Mathematical Foundations of Structured Space Theory (SST) — Supplement 1: Post-Release Extensions

A major extension of the Mathematical Foundations of Structured Space Theory (SST) This supplement marks the first substantial expansion of the mathematical SST program following the release of the main Mathematical Foundations paper. Its central advance is the proposal of a universal SST equation as a candidate underlying law for transport, reintegration, closure, and leakage across multiple physical regimes. While preserving the original lattice axioms and weak-field structure, the supplement advances SST in a more unified direction by connecting gravitational transport, matter structure, empirical isotope behavior, and localized pattern stability within a single conceptual framework. The work introduces:(1) a clarified transport interpretation consistent with weak-field relativistic recovery;(2) a matter–source correspondence expressed through the effective gravitational projection N_grav;(3) an isotope-level empirical reduction that reproduces measured mass data with high precision under fixed parameters;(4) a nonlinear closure–leakage formalism for stability and discrete pattern classes; and(5) the proposed universal SST equation as the candidate underlying law spanning weak-field, atomic, particle-like, and strong-field regimes.