Mathematical Foundations of Structured Space Theory (SST), Version 2

Mathematical Foundations of Structured Space Theory (SST) presents the consolidated axiomatic and mathematical reference for the SST/UPF framework. SST is a geometric–gravitonic framework in which physical constants, field equations, and selected particle, nuclear, cosmological, macroscopic, and materials-sector results are derived from a structured graviton lattice modeled by a vertex-transitive tetrahedral–octahedral/FCC geometry. The framework is characterized by the lattice variables graviton density, graviton frequency, lattice spacing, ripple tension, phase compatibility, and closure behavior, with the primary geometric invariants z = 12 and |F| = 4. Starting from the propagation identities E1–E3 and the FCC lattice structure, the manuscript derives the speed of light c, Planck’s constant h, Newton’s gravitational constant G, vacuum response coefficients, the Planck scale, and the weak-field gravitational gradient laws. Maxwell-form equations emerge from the transverse vector mode of the lattice equations of motion, with c = 1/√(ε₀μ₀) recovered as an internal consistency condition. Lorentz invariance is recovered in the continuum limit from isotropic wave propagation enforced by the Oh point-group symmetry of the cuboctahedral coordination shell, with leading lattice anisotropy first appearing only at fourth order. Weak-field general-relativistic behavior is recovered through the E7–E8 potential-form solutions and is extended through a Regge-calculus construction that connects the FCC simplicial complex to the Einstein equations in the continuum limit. Version 2 is a consolidation and alignment update. It supersedes Mathematical Foundations Version 1 and Supplements 1–4 as the current mathematical reference for the framework. The revision integrates the prior supplement material into a single manuscript, updates the R1–R51 result inventory, clarifies the status tags for exact, derived, worked, and calibrated results, and aligns the derivations with the latest versions of Structured Space Theory (SST) and the Unified Pattern Framework (UPF). The manuscript includes derivations and validation summaries for p6 pattern closure, particle masses, lepton and quark sector relations, mixing angles, gauge-sector quantities, neutron drip-line structure, nuclear binding and mass-bridge behavior, cosmological ratios, Schumann resonance corrections, and a superconductivity channel criterion. It distinguishes formal derivations from worked realizations, validation-facing summaries, provisional observations, and open structural items. This record also includes companion validation appendices, machine-readable CSV validation datasets derived from AME2020 and NUBASE2020, and a verification package containing tools/code intended to support independent reproduction of the validation calculations. The upload is provided for transparency, reproducibility, and independent review of the stated SST/UPF derivations and empirical checks. This manuscript is a preprint and has not been peer reviewed. Related worksStructured Space Theory (SST) — latest-version record DOI: 10.5281/zenodo.17154635Unified Pattern Framework (UPF) — latest-version record DOI: 10.5281/zenodo.17900824Empirical Validation of Structured Space Theory (SST) — latest-version record DOI: 10.5281/zenodo.17400680 LicenseCC BY-NC-ND 4.0