TCV-ϕ III: primordial perturbations across the cohesive bounce and CLASS/CAMB bridge diagnostics

This third paper develops the primordial perturbation sector of the same TCV-ϕ effective field theory defined in Papers I and II. Its purpose is to formulate and benchmark a Mukhanov–Sasaki pipeline across a cohesive-bounce background, compute tabulated primordial spectra, and extract baseline observables such as nₛ, Aₛ, r, and ₛ in explicit benchmark regimes. The paper distinguishes carefully between EFT-derived ingredients and phenomenological closure ansätze used to complete the background and perturbative calculations. It also provides a reproducible bridge to CLASS/CAMB using exported primordial tables, intended as a consistency tool rather than a full likelihood-level analysis. In the benchmark presented here, the scalar sector yields As ~ 2. 1e-9, ns ~ 0. 9643, and alphaₛ ~ -1. 43e-3, while the reconstructed matter spectra from power-law and external-table modes remain nearly identical, validating the interface at the benchmark level.