Foundations of Field Dynamics (UEF): Core Substrate, Continuum Kinematics, Emergent Time, and Topological Solitons (Document #0)

Abstract: This work establishes the minimal, closed axiomatic foundation of the Unified Elastic Field (UEF) model, also formalized as Field Dynamics. Physical space is identified as a continuous, three-dimensional, quasi-incompressible elastic monolith (the Field Ocean) with reference unperturbed density $\rho_0 \approx 4.30 \times 10^{18}\text{ kg/m}^3$ and shear modulus $\mu_0 \approx 3.865 \times 10^{35}\text{ Pa}$. We demonstrate that physical time and thermodynamic entropy are emergent macroscopic manifestations of substrate shear relaxation, eliminating time as a fundamental geometric coordinate. Matter is shown to be non-foreign inclusions, but localized topological eigenmodes of the continuum: superluminal cavitation voids (baryons) and continuous vortex knots of the Hopf fibration (leptons). We introduce the foundational cosmogony of the Primordial Neutron Monolith, demonstrating how the decompression of a balanced $C_3$-symmetric tri-blade vortex lock resolves cosmological electroneutrality ($N_p \equiv N_{e^-}$), the neutron mass defect $\Delta m = 1.2933\text{ MeV}$, and the primordial $75\% / 25\%$ hydrogen-to-helium ratio. Furthermore, we provide first-principles continuum derivations of mass-energy equivalence $E = mc^2$, Newton's inertia $F = ma$ via hydrodynamic added mass ($M_{\text{add}}$), the pressure-gradient nature of gravity $\nabla P$, the exact aspect ratio invariant $\Lambda = \pi^2 + 1/6$, and a predictive derivation of the fine-structure constant $\alpha^{-1} \approx 137.21$. This paper serves as the root architectural framework for a dedicated series of specialized modular preprints.