Decompression Kinetics of the Primordial Neutron: Motion Without Time, Toroidal Snap-Through Barrier, Resolution of the Beam-Bottle Puzzle, and Weak Sector Acoustics (Paper 4)

AbstractThis paper presents a deterministic theory of nucleonic weak sector processes formulated within the continuum mechanics of an underlying elastic substrate (Field Dynamics, Document #0). Abstract gauge postulates of quantum field theory—such as the hypothetical intermediate vector boson W- (80.4 GeV), fundamental point neutrinos with artificial mass hierarchies, and the geometric time coordinate t—are completely eliminated. We demonstrate that: (1) Ontology of Time and Motion as Retarded Rotation: A continuous four-dimensional time coordinate t does not exist in nature. Physical time is an emergent discrete cycle counter tracking internal soliton rotations with baseline cavity frequency \nu_0 = v_p / (2\pi R_p) \approx 6.72 \times 10^{22} s^{-1}. Translational motion through the absolute Field Ocean at velocity v redistributes the medium's capacity into translation, lowering the intrinsic cycle frequency: \nu(v) = \nu_0 \sqrt{1 - v^2/c^2}. The twin paradox is resolved without relativistic kinematic symmetry. (2) One Soliton in Two Pressure Phases and \mu_n/\mu_p = -2/3 Invariant: The proton and neutron represent two pressure-dependent phase states of the same three-blade cavitation soliton: the low-pressure proton [uud] (2 inflows \to 1 outflow) and the high-pressure neutron [udd] (1 inflow \to 2 outflows). Direct substitution into circulation invariants strictly reproduces the ratio \mu_n/\mu_p = -2/3 (\mu_n \approx -1.8633 \mu_N, 2.6% agreement with CODATA) without SU(6) symmetry, while ambient decompression explains the primordial 75% H to 25% He-4 ratio. (3) Origin of the 879 s Timescale and Snap-Through Barrier: The free neutron is stabilized against instantaneous decay by an elastic toroidal snap-through buckling barrier S_E^{(0)} = 6\Lambda_0 - 3\alpha_p \approx 59.3106, setting the primordial baseline \tau_{cosmos} \approx 855.1 s matching Big Bang Nucleosynthesis (BBN) requirements (850–860 s). (4) Resolution of the Beam-Bottle Puzzle: The 4\sigma discrepancy is resolved across a three-step regime ladder with rigorous classification of proven theorems versus motivated estimates: Cosmos baseline (855.1 s) \to Terrestrial bottle rest with reactive medium impedance \tau_{bottle} \approx 878.8 s (0.05% from UCN experiments) \to NIST beam drift in a 4.6 T solenoid field \tau_{beam} \approx 888.1 s (0.04% from NIST data). (5) Geometric Axial Form Factor g_A = 4/\pi: Derived as g_A = 4/\pi \approx 1.27324 (0.17% from experiment) from circumscribed shear cell packing and spherical twist averaging. (6) Acoustic Nature of Neutrinos and Parametric L \to T+T Decay: Neutrinos are identified as solitary longitudinal acoustic decompression pulses (L-modes). In dense stellar cores, they propagate at c_L \approx 1.355 c (accounting for the 3-hour head start in SN1987A), converting via stimulated Brillouin scattering into bound transverse shear waves (v = c) upon entering vacuum, complying with IceCube limits (|v-c|/c < 2.5 \times 10^{-12}).