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This paper introduces a Thermodynamic Unified Field Theory (UFT) where prime-enforced symmetry constraints emerge from helical recoils in photrino dynamics, unifying phase behaviors and transport phenomena through a covariant fugacity-Hessian equation. By deriving the viscous stress tensor from entropy maximization without pa-rameters, the framework resolves Navier-Stokes limitations (e.g., infinite speeds, non-Fourier transport) and reproduces empirical phase diagrams for substances like he-lium, water, and neon via prime-locked gears. We demonstrate how primes arise from triad indivisibility, leading to rational direction cosines that enforce shell uniformity and curvature floors. Applications to catalysis, superfluidity, and non-equilibrium systems highlight UFT's potential as a parameter-free TOE candidate, with time and gravity as emergent distortions in the flux sea.