The Sigma–Schmidt Duality: Effective Field Theory, Spiral Metric, and Observational Signatures

This work presents the first fully formulated version of the Sigma–Schmidt Duality as a two-scalar effective field theory with a unit-disk constraint, antisymmetric kinetic coupling, and a torsional Bianchi II spiral metric. The dual order parameter $\sigma(t) = S_e(t) S_a(t)$ naturally generates a geometric 2D→3D roll-up mechanism that produces angular momentum, dimensional friction, and a non-singular Big Bang front. A derived, non-polynomial deformation of the Friedmann equation is obtained from the EFT and tested against DESI DR2 BAO data using full covariance and Planck sound-horizon priors. The model achieves a statistically significant improvement of $\Delta\chi^2 = -7.43 \pm 0.8$ relative to $\Lambda$CDM (≈2.9σ). The Sigma–Schmidt Duality provides a falsifiable framework with geometric origin of expansion, angular momentum, and late-time acceleration, and predicts helical large-scale-structure signatures observable with Euclid and SKA.