Entropy-Scalar Relation: From Thermodynamic Attractors to CMB Observables in Cyclic Cosmology

We derive the mapping from the thermodynamic attractor (Paper IV) to observable CMB parameters: the scalar spectral index n_s, tensor-to-scalar ratio r, tensor tilt n_t, and non-Gaussianity parameters f_NL and g_NL. The key result is the consistency relation n_t · τ_relax = −1, which is independent of the details of the bounce mechanism and depends only on the attractor thermodynamics. This relation constitutes the framework's "smoking gun" — a prediction that is qualitatively distinct from both single-field inflation (n_t = −r/8) and standard ekpyrotic models (n_t ≈ 0).Part V of VII.