End-to-end perturbation architecture for a nonsingular cyclic cosmology: regular bounce transfer, quantum gauge response, and observational inference

We develop the perturbative and computational architecture required to propagate scalar fluctuationsthrough the nonsingular high-density branch of the frozen cyclic cosmology introduced in thepreceding work. The theory contains one canonical propagating scalar, a nondynamical cuscutonsector generating the finite-density bounce, and a hypercharge/Maxwell field coupled axially tothe scalar. Working in a formulation that never divides by the Hubble parameter, we show thatthe local scalar constraint block remains nonsingular at the high-density H = 0 crossing, derivea positive reduced scalar kinetic coefficient there, and obtain a finite positive fixed-k principalgradient coefficient. We construct a Hamiltonian/differential-algebraic transfer formulation for thephysical phase-space variable (ζ,Πζ) and formulate the produced gauge-field response as a causalWard-consistent quantum influence kernel rather than as an arbitrary local fluid. We further specifythe transfer to a tabulated primordial spectrum, the CLASS/Cobaya inference interface, structuralpriorhierarchy, Bayesian-evidence protocol, and a hash-based reproducibility layer. The exact finalhistorical gauge normalization and unequal-time archive used in the frozen high-density benchmarkare not present in the persisted source material, and a direct reconstruction does not reproducethe complete archived state. We therefore do not claim a regenerated final primordial spectrumor Bayesian evidence in this work; instead, we isolate the exact local perturbative closure and thecomplete end-to-end framework required for a future verified high-density transfer calculation.