The Sigma–Schmidt Duality (SSD)

This master paper consolidates the full structure of the Sigma–Schmidt Duality (SSD), a unified physical framework based on two complementary singularities: the expanding surface-like Sa and the extracting axial Se. Their asymmetric interaction generates the dimensionless order parameter σ(t), from which 1D, 2D, and 3D spatial structures naturally emerge.The paper presents the complete theoretical foundation, including the conservation equations, the σ-based field formulation, the effective Lagrangian with Φ = √(Se Sa), and the Sigma–Friedmann Bridge linking SSD to cosmological expansion.Observable predictions include deviations in BAO distances, oscillatory dark-energy evolution, spin correlations, and a 1D-corrected Hawking temperature derived from Sσ = h(A) S_BH. The framework is falsifiable through DESI, Euclid, LISA, and PBH evaporation signatures.This unified document serves as the primary reference for SSD and integrates previously fragmented releases into one coherent master work.