Quantum Mechanics as Tensor Mechanics of the Cosserat Continuum Field: Geometric Quantization and Empirical Validation of the Hydrogen Atom

**Preprint | Continuum Field Entropy Microscopic Validation Series** We present a deterministic, field-dynamic derivation of the Hydrogen atom using the Continuum Field Entropy (CFE) framework. By modeling the Primordial Field as a non-Newtonian Cosserat continuum, we replace abstract quantum probability and localized forces with topological geometry and thermodynamic drag. The proton is modeled as a 3-vortex Helmholtz resonance, generating a macroscopic tension landscape comprised of a 1/r tensional baseline superimposed with spherical standing waves (Bessel functions). The electron is defined as a single-axis Möbius twist of the antisymmetric tension tensor. Utilizing a non-Hermitian CFE Hamiltonian incorporating a thermodynamic dissipator (i₃₈ₒₒ²), we demonstrate that the interference of precisely three Bessel modes can be parameterized via a Soft-Lock Condition (Tₚ / r = 0) to organically map to Bohr’s quantized orbitals (r n²) without relying on arbitrary angular momentum postulates. Furthermore, we mathematically anchor the CFE limits of the modern (z 0) vacuum to derive Planck’s constant, the elementary charge, the electron mass, and the fine-structure constant (1/137) entirely from field elasticity. Finally, we computationally validate the CFE model by demonstrating that the topological yielding of the electron soliton (quantum jumps) mathematically reduces to the classical Rydberg formula, inheriting its 99. 999% accuracy against the empirical NIST wavelengths of the Hydrogen Lyman and Balmer series when accounting for reduced mass. The residual 0. 001\% variance corresponds exactly to the un-factorized O (²) spin-tension fine-structure coupling. **Project Integration: **This document is a standalone validation report. The underlying universal field equations, foundational axioms, and the complete multi-disciplinary validation framework can be found in the primary master manuscript (DOI: 10. 5281/zenodo. 20631794).