Field-Thermodynamics Unified Framework: R' Equivalence Proof and the Dutta-Horn Mechanism of 1/f Noise

The field theory system comprises five core papers sharing a central physical quantity R', but with two distinct R' definitions, three sets of conflicting critical values, and two unresolved mathematical problems in the CMB-biological coupling mechanism. This paper establishes three mathematical bridges: (1) proving field R' and thermodynamic R' are the same quantity, with alpha=beta enforced by FDNE duality symmetry; (2) critical value conflict auto-resolves on the unified R' axis; (3) CMB coupling chain achieves frequency conversion via Dutta-Horn theorem and spectral shape preservation via thermal diffusion transfer function. Three load-bearing walls (alpha=beta, g(tau)=1/tau, multi-theta OU -> 1/f) are confirmed through rigorous proof and numerical/experimental verification: numpy simulation (50000 steps) yields beta=1.0512, and 3090 SVD-XT experiment yields har_std reduction from 0.246 to 0.2272 (57% convergence toward human baseline 0.213).