rowth of Cosmic Structure in the Sigma–Schmidt Duality: Consistent Constraints within the Sigma–Friedmann Framework

This work presents the first growth-of-structure constraints on the Sigma–Schmidt Duality (SSD), a dual-field cosmological framework in which a 1D extracting singularity and a 2D expanding singularity interact through a dynamical signal σ(t). Using the simplified Sigma–Friedmann signature functionF(a) = 1 + ε ln(a) + α (ln a)²,we numerically solve the general-relativistic growth equation and compute fσ₈(z) for direct comparison with real redshift-space distortion (RSD) data from 2dFGRS, SDSS LRG, BOSS CMASS, VIPERS and eBOSS (0.17 < z < 0.85). A two-dimensional grid search over (ε, α) shows that SSD remains fully consistent with current growth data, yielding a mild 0.4–0.7% suppression of fσ₈(z) relative to ΛCDM and a negligible Δχ² = –0.081. Combined with earlier SSD results – including DESI DR2 BAO improvements and the 1D Hawking-temperature correction – the analysis demonstrates that the Sigma–Schmidt Duality remains viable across independent cosmological probes. All computations were performed via explicit numerical integration (RK45), with no approximations beyond standard GR linear theory. Overall, this upload provides the full PDF of the paper “Growth of Cosmic Structure in the Sigma–Schmidt Duality” and establishes SSD as a coherent, testable and data-compatible cosmological framework.