Covariant Multi-Higgs Transduction, Relativistic Dirac-Sommerfeld Elliptic Wavepackets, and Emergent Gravitonic Stress-Energy Coupling

We establish a covariant, mathematically self-consistent field-theoretic framework—the extended TN Model—that redefines elementary fermion rest mass as a dynamical, ergodic equilibrium process rather than a static scalar postulate. Within a Z3-aligned Three-Higgs-Doublet Model (3HDM) characterized by three neutral vacuum expectation values (Φ0,1, Φ0,2, Φ0,3), bound Dirac fermions act as non-linear quantum transducers governed by aˆ sesquilinear spinor-current Lorentz functional Γ[𝜓, 𝑔𝜇𝜈] (𝑥) on the Sobolev space 𝑊1,4(M). We prove that relativistic elliptic Dirac-Sommerfeld wavepackets (0 < 𝑒 < 1) play the central dynamical role: whereas circular states (𝑒 = 0) yield a stationary kinematic invariant indistinguishable from a static mass parameter, eccentric states generate periodic periapsis transduction peaks regularized by the quantum Compton scale 𝜆𝐶 and 𝐿4 gradient coercivity. Over macroscopic intervals Δ𝑡 ≫ 𝑇, the Fourier zero-mode projection locks in macroscopic inertial stability. Through a unified Einstein-Hilbert metric variation, we prove that the reversible periapsis-apoapsis mass-energy excursion feeds a covariant Bohm-Dirac quantum-potential stress tensor D𝜇𝜈 (|𝜓|2, 𝜁), identically satisfying the contracted Bianchi identities ∇^𝜇 𝐺𝜇𝜈 = 0. In the two-fermion sector, we demonstrate via Hardy-Sobolev coercivity that this apoapsis gradient tension, combined with the odd-parity nodal structure 𝜓↑↑(0) = 0, generates a strictly bounded, collapse-free attractive potential well that binds equal-spin (𝑆 = 1) triplet Cooper pairs against Coulomb repulsion. Finally, we derive an exact gravito-kinematic coupling tensor predicting an eccentricity-amplified frequency L shift Δ𝜈 ∝ 𝛾^3 •ℎ 𝑖𝑗𝑣 𝑖𝑣𝑗 in atomic spontaneous emission under passing gravitational waves, establishing four quantitative, falsifiable experimental protocols.