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

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 ρ₀ ≈ 4.30 × 10¹⁸ kg/m³ and shear modulus μ₀ ≈ 3.865 × 10³⁵ 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 C₃-symmetric tri-blade vortex lock resolves cosmological electroneutrality (Nₚ ≡ Ne⁻), the neutron mass defect Δ m = 1.2933 MeV, and the primordial $75% / 25%$ hydrogen-to-helium ratio. Furthermore, we provide first-principles continuum derivations of mass-energy equivalence E = mc², Newton's inertia $F = ma$ via hydrodynamic added mass (Madd), the pressure-gradient nature of gravity ∇ P, the exact aspect ratio invariant Λ = π² + 1/6, and a predictive derivation of the fine-structure constant α⁻¹ ≈ 137.21. This paper serves as the root architectural framework for a dedicated series of specialized modular preprints.