8 COS-C - Collapsing-Structure Cosmology: Discrete Spacetime, Discrete Friedmann Dynamics, Inflation, and Observable Links

Collapsing–Structure Cosmology (COS–C) is the cosmological application module of the Collapsing-Structure (COS) program. It develops an effective cosmological framework based on discrete shell dynamics, shell-to-shell collapse maps, background recursions, and perturbative protocols on quantized graph-shell configurations. The manuscript formulates a discrete Friedmann-like background description, including an effective scale-factor operator derived from shell volume, shellwise Hubble parameters, source-corrected continuity relations, and conditions for recovering FLRW/ΛCDM behavior as a continuum benchmark under stated regularity and correction-scaling assumptions. Inflation is modeled through rapid shell generation, with discrete e-folding, slow-roll parameters, horizon-crossing criteria, Bunch–Davies-like adiabatic initial states, and reheating parametrization. Scalar and tensor perturbation protocols define candidate links to CMB spectra and stochastic gravitational-wave backgrounds, including possible fine oscillations, mild off-diagonal covariance, non-Gaussianity diagnostics, quasi-line SGWB structures, polarization/chirality indicators, and tensor–scalar consistency corrections. These CMB and SGWB signatures are presented as testable candidate channels and falsification targets rather than completed data fits. The module also studies information-theoretic arrow-of-time diagnostics for collapse-induced CP/CPTP maps and describes numerical controls such as Wronskian-preserving integration, Floquet-stability checks, constraint-residual monitoring, posterior-predictive tests, and reproducibility requirements.