New Supplement 2 Published — Mathematical Foundations of SST: General-Relativistic Recovery via Regge Calculus
Supplement 2 DOI: 10.5281/zenodo.19376061
Supplement 1 DOI: 10.5281/zenodo.19141923
Main Mathematical Foundations paper DOI: 10.5281/zenodo.19080507
A new supplement to Mathematical Foundations of Structured Space Theory (SST) is now available on Zenodo.
This work closes a key open problem in the framework: the absence of a dynamical gravitational field equation. By establishing a Regge-calculus realization of the SST lattice, the supplement provides the missing equation and shows that SST equilibrium corresponds to Regge stationarity.
In the weak-field regime, the resulting equations reduce to the Poisson equation and are variationally equivalent to the linearized Einstein field equations. In the continuum limit, the Regge formulation converges to general relativity, recovering the Schwarzschild, Kerr, and Friedmann sectors within the SST framework.
This closes the main gravitational gap in SST and establishes the gravitational sector as formally complete at the framework and continuum-limit level.
Major achievements of SST (current state)
With Supplement 2, the SST framework now includes:
- Recovery of General Relativity
Through Regge-calculus realization, SST reproduces the Einstein field equations in the continuum limit and recovers Schwarzschild, Kerr, and Friedmann solutions. - Unified lattice-based description of space and fields
Space is modeled as a discrete graviton lattice with propagation governed by invariant relations (e.g., gF · d = c). - Electromagnetism as transverse lattice modes
EM behavior emerges from transverse ripple modes with Maxwell-consistent structure. - Emergent time and gravitational redshift
Time arises from lattice reintegration rates, with gravitational time dilation derived from lattice gradients. - Atomic mass and isotope structure (Supplement 1)
A lattice-based formulation connects structure to atomic mass through a reduced-parameter relation across isotopes. - Particle ontology via UPF
Particles are described as stable pattern-states on the lattice, extending SST into particle, atomic, and radiative regimes.
Together, these results move SST toward a more unified description of physical phenomena across gravitational, electromagnetic, and atomic domains, within a single underlying framework.
Still more work remains — but this marks a major step forward.
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