Spacetime Topological Emergent Micro-Solitons (STEMS): A Non-Linear Geometric Framework for Quantum Foundations and the Einstein-EPR Program

We establish the complete mathematical and physical architecture of Spacetime Topological Emergent Micro-Solitons (STEMS), an analytical framework deriving fermionic quantum matter, elementary charge quantization, and non-local correlations directly from non-linear teleparallel spacetime geometry. We demonstrate that John Wheeler’s classical geon program and Riemannian metric solitons fail fundamentally due to the Lichnerowicz theorem and Derrick’s scaling instability. By reformulating gravitational dynamics within the Teleparallel Equivalent of General Relativity (TEGR) augmented by higher-order completely antisymmetric axial Weitzenböck torsion invariants (T_axial = (A_μ A^μ)²), we prove that non-linear geometric pressure counteracts spatial contraction, guaranteeing the rigorous mathematical existence of stable, localized, singularity-free three-dimensional triad solitons without external matter fields. Charge quantization is derived strictly off-shell as an integer topological winding number governed by the third homotopy group π₃(SO(3)) ≅ π₃(S³) ≅ ℤ, establishing that elementary electric charge (q = Q · e₀) is the topological degree of an anholonomic spatial frame twist. Fermionic spin-1/2 kinematics and the Pauli Exclusion Principle are derived from purely bosonic frame configurations via Finkelstein-Rubinstein configuration-space topology (π₁(C_Q=odd) ≅ ℤ₂) and an explicit five-dimensional Wess-Zumino-Witten topological action with quantized level k = 1. On the sub-Planckian computational stencil (l_sub-P ≤ 10⁻⁵⁴ m), a discrete Dirac-Kähler mapping demonstrates that inhomogeneous differential forms on cell complexes decouple into four-component Dirac spinors in the continuum limit, precluding Nielsen-Ninomiya fermion doubling. Through the Execution-Budget Formulation (EBF), relativistic kinematics (E² = p²c² + m₀²c⁴) is derived as an exact computational resource partitioning between spatial hopping and internal topological recurrence. Particle rest mass is shown to be an ab-initio stationary eigenvalue balancing non-linear torsion tension against electrostatic repulsion, resolving the 42-order-of-magnitude hierarchy gap between bare substrate clock rates and observed particle scales via topological duty-cycle dilution. Finally, the framework realizes the ER=EPR correspondence as invariant micro-torsion wormhole filaments on deterministic relational networks, reproducing continuous singlet correlations (E(a, b) = -cos θ_ab) and algebraically saturating the Tsirelson bound (2√2) under local-deterministic dynamics, while preserving strict macroscopic causality through a step-by-step algebraic proof of the No-Signaling theorem. Quantitative, falsifiable empirical benchmarks are provided across multi-TeV lepton scattering, cosmic string tensions (Gμ ≤ 10⁻¹⁷), and cosmological high-ℓ CMB power deficits (~ -2.4%).