[8] COS-C - Collapsing-Structure Cosmology: Discrete spacetime, discrete Friedmann dynamics, inflation, and observational signatures

Collapsing–Structure Cosmology (COS–C) is the cosmology module of the COS program, where spacetime is modeled as a discrete, quantized sequence of graph shells. The cosmic background is evolved by a discrete Friedmann recursion along shell-to-shell collapse maps. Within this framework we formalize inflation as rapid shell generation, introduce discrete slow–roll parameters, fix a Bunch–Davies–analog initial state and discrete horizon-crossing criteria, and include a reheating parametrization. From the normalization of primordial scalar and tensor modes we obtain predictions for the CMB power spectra and for the stochastic gravitational-wave background (SGWB). Discrete mode space yields testable signatures: (i) low-amplitude, quasi-periodic fine oscillations and mild off-diagonal covariance in TT, TE, EE with moderate non-Gaussianity; (ii) a comb-like quasi-line pattern in the SGWB across PTA/LISA/LVK bands, possibly chiral; (iii) a small discrete correction to the tensor–scalar consistency relation. We also outline a hybrid fitting pipeline that convolves the discrete primordial spectrum with standard Boltzmann codes. The arrow of time is tied to information-theoretic monotones of collapse-induced CPTP maps. Numerically we use a symplectic (Wronskian-preserving) integrator with Floquet-stability checks and constraint-residual control. In the continuum limit the framework reproduces ΛCDM, while discrete corrections are directly testable with current and near-future data.