Universal Binary Affinity Framework: Binary Balance Law, Universal Mathematical Law, Reverse Universal Affinity Law, and Cross-System Validation

This work presents a unified binary-affinity framework built from a normalized two-state exponential family. For a binary variable z in {+1,-1} with weights exp(theta z), the normalized expectation X is exactly tanh(theta), and the inverse affinity is uniquely theta=atanh(X)=1/2 ln[(1+X)/(1-X)] for -1 pi. The pi limit is standard central-binomial asymptotics and is not claimed as a new physical derivation of pi. Physical checks are classified by evidential type. Published thermal spin-polarization data at 3.35 T are compared with the independent physical affinity theta=mu B/(k_B T), showing agreement at the precision of the published rounded values. The exact one-dimensional Ising relation =tanh(beta J) and a 2026 magnetic-tunnel-junction probabilistic Ising machine provide additional physical realizations of the same tanh structure. Finally, the 2026 photonic quantum-switch dataset is reanalyzed: the Bell-like causal witness is reconstructed as 1.808954375, while six pre-specified spacelike-marginal affinity diagnostics are statistically consistent with zero, with maximum |z| about 1.51. This demonstrates why strong correlation must not be automatically reinterpreted as a generic affinity or causal influence. The paper concludes with a claim hierarchy, prior-art boundary, multidimensional symmetric extension, and requirements for any future claim of universal physical validity.