9 COS-NUM - Collapsing-Structure Numerical Environment: Computational Toolkit, Quantized Graph Simulations, and CMB/SGWB Data-Driven Pipelines

COS-NUM is the Python-based numerical environment of the COS program, a cosmological framework built on collapsing-structure, quantized graph geometry (developed in the COS-S, COS-QF, COS-QSF, COS-QD, COS-SM, COS-SUSY, COS-GUT and COS-C modules). COS-NUM implements the internal COS models based on quantized shell–filament graphs together with CMB and SGWB data-processing pipelines in a common, reproducible and archivable computational framework. The code provides:– a numerical representation of COS graphs and associated discrete operators, implemented with sparse-matrix and spectral methods;– internal COS-graph simulations (eigenvalue spectra, diffusion and topological descriptors);– three data-driven pipelines: a CMB anomaly analysis (COS–Planck), a mutual-information-based CMB arrow-of-time analysis, and a stochastic gravitational-wave background (SGWB) COS+astrophysical model-fitting pipeline. A dedicated section investigates runtime scaling, memory usage and numerical convergence, and defines reference simulations and tiers of reproducibility. The code structure, public API and configuration files are documented in the accompanying paper and appendices, making COS-NUM the numerical backbone of the COS program and providing a transparent, reproducible and extensible pathway from model-theoretic constructions to concrete CMB/SGWB results.