Foundations of Field Dynamics (UEF) — Paper 1: Quantum Reduction, Soliton Topology, and Cosserat Continuum Dynamics: Deterministic Derivation of Wave Mechanics, Spinor Fields, and Quantization Invariants

Abstract This paper presents a deterministic geometric reconstruction of wave mechanics and spinor fields from the continuum mechanics of an underlying elastic substrate. Space is identified as a quasi-incompressible micropolar Cosserat continuum with reference density ρ0 ≈ 4.30 × 1018 kg/m3 , shear modulus µ0 ≈ 3.865 × 1035 Pa, and transverse propagation velocity c = p µ0/ρ0 ≈ 2.998×108 m/s. We demonstrate that: (1) The electron mass me and the mass ratio mp/me ≈ 1822.4 (0.75% divergence relative to CODATA 1836.15) are reconstructed from the topological cleavage of the primordial C3-symmetric tri-blade neutron at volume ratio Vp/Ve = 2 + αp ≈ 2.3023 and detachment velocity vsever = 3c/Λ ≈ 0.2989 c (αe ≈ 239.3), relaxing to equilibrium core speed ve ≈ 0.197 c. (2) The electron core radius is nuclear-sized (Rcore ≈ 3 4Rp), while the macroscopic envelope is dynamically stabilized at Re = λ¯C by the centrifugal wave momentum barrier L = ¯h, halting Derrick collapse. (3) The Schrödinger equation emerges without quantum postulates from Madelung hydrodynamics, where Bohm’s potential QBohm = − ¯ 2 h m 2 e ∇ 2 R R is identical to Korteweg capillary-gradient stresses with coefficient κ = ¯ h 2 4 m 2 e ρ . (4) The 4-component Dirac bispinor is reduced from the six mechanical degrees of freedom of the Cosserat continuum constrained by two solenoidal incompressibility conditions (6 − 2 = 4). (5) The Landé factor g = 2 is proven as the kinematic ratio between the orbital wave momentum (L = ¯h) and the topological Hopf linking spin (S = ¯h/2).