Volume IVb is the second of two parts of Volume IV of the programme Thermodynamics of Arithmetic Action. It collects TAA Lemmas 66-85; the companion Volume IVa contains Lemmas 48-65. The parts form one volume, split only because of the archive's 5 MB file limit. Volumes I-III (ai.viXra:2610.0045v2, 2610.0054, 2610.0052) recast the Riemann Hypothesis (RH) as the absence of negative-norm ("ghost") directions for the Weil form. Here we test modular forms and Eisenstein anomalies, hyperbolic geometry, 3D gravity, Farey fractions and codes, and isolate the obstruction. The ghost count kappa, the negative index of a Weil-type form, recurs throughout; for a Weil polynomial it equals the number of negative directions of the Rosati trace form, a classical fact we restate and check exhaustively for 13135 genus-2 polynomials. We prove a no-go theorem for positivity built from scaling-commuting multipliers. We show numerically that the Davenport-Heilbronn ghost is visible at finite Connes cutoff, with primes n <= 41. Closed geodesics on Bianchi orbifolds see only Euler-product channels, not the off-line zeros of Epstein zeta functions. Over function fields, the BSD count in a Mordell-Weil lattice is one Frobenius eigenvalue, tied to RH through the algebraicity of Frobenius. Certified computations show that extremal weight enumerators of self-dual codes satisfy Duursma's RH in stated ranges. A statement at the start lists exactly what is claimed across both parts, and where. Formalization and computations were AI-assisted, and this is disclosed. RH is NOT proved: no chapter supplies the missing positivity for zeta. What is missing is a global operator whose spectrum is the zeros, with a positive form from a global ample class.