We present a covariant, completely positive and thermodynamically consistent refinement of the universal equation within the CUCE/Spinoza/Hilbert framework, denoted CUP-?*. The formulation unifies Tomonaga–Schwinger evolution on Cauchy hypersurfaces with a modular Gorini–Kossakowski–Lindblad Sudarshan (GKLS) generator that obeys detailed balance in the GNS metric with respect to a unified thermodynamic target ?*. We prove (i) foliation independence under local commutation, (ii) complete positivity of the finite-step propagator, (iii) existence of a global Lyapunov functional ensuring the second law, (iv) primitivity with a unique attractor ?*, and (v) local conservation via consistent coupling to the Einstein–Langevin equation with conserved stochastic sources. We further outline falsifiable predictions with quantitative protocols in superconducting circuits and optomechanics.