Modular-Flow Foundations of Entropy-Response Gravity: Consolidation and Primordial-Spectrum Applications

Paper XIV of the Entropy-Response Gravity (Bipartite KMS Gravity) programme (combined consolidation paper, incorporating the primordial-spectrum applications of the former Paper XV). Shows that the programme's results across regimes are corollaries of a single algebraic statement about modular flow on the Rindler-de Sitter product state, and derives the primordial-spectrum observables (n_s, r, alpha_s, f_NL) and the e-fold count N_e explicitly from the bipartite-vacuum correlators. First Zenodo deposit (v1). Two corrections applied before deposit: (1) the e-fold convention is corrected to the dimensionless N_total = ln(L_dS/ell_P) = 140.29 (the earlier ln[c/(a0 ell_P)] = 122.59 carries units s/m and is unit-system dependent), giving N_e = 75.39 and n_s = 1 - 2/N_e = 0.9735, reported openly with its +2.0 sigma tension against Planck 2018 (the earlier 0.9653's closer agreement was partly an artefact of the unit-dependent normalisation); (2) the a0 result is stated as the dimensionless ratio a0/(cH0) = 1/sqrt(4 pi^2 - 1), with the scale set by the input H0. r = 0, alpha_s = -2/N_e^2, f_NL = 0.