Extension of the Field Dynamics Conjecture: Hydrodynamic Perturbations, Cosmic Web Formation, Galactic Core Halos, and SPH Formalism in a Riemann-Cartan Spacetime

We present a comprehensive, step-by-step mathematical development extending the FieldDynamics Conjecture within the Seashell-Universe Model. Operating under a static backgroundmetric governed by Einstein-Cartan-Sciama-Kibble (ECSK) gravity, we reinterpretingthe dark sector as pure geometric manifestations of spacetime torsion and contorsiongradients. We derive the hydrodynamic perturbation equations, establish the modified Jeanslength threshold, formulate the localized cosmic birefringence signatures within cosmic webfilaments, construct the algorithmic architecture for an N-body/SPH simulation, and analyticallysolve the flat-core density profile that naturally reproduces galactic rotation curves.