The Stochastic Computation System: A Parametrized Mathematical Framework for Binary,

This supplementary package accompanies the manuscript “The Stochastic Computation System: A Parametrized Mathematical Framework for Binary, Stochastic and Quantum-Compatible Two-Level Regimes”. The package provides supplementary theoretical notes, reproducible Colab/Python modelling code, generated numerical tables, figures and a reproducibility README. The supplementary material is organized into six sections: S1. Formal SCS coordinates and admissibility;S2. Effective sample size and correlated Bernoulli bitstreams;S3. Density-matrix coherence and physical admissibility;S4. Admissible SCS channels and noisy AND example;S5. Baseline comparison, benchmark scaling and finite-resource regime adequacy analysis;S6. Reproducibility information. The numerical studies illustrate the operational interpretation of the stochastic dispersion parameter σ through effective sample size, validate the density-matrix-compatible interpretation of the normalized coherence coordinate κ, verify weak admissibility conditions for deterministic and noisy SCS channels, and compare model-level error–resource behaviour across selected binary, stochastic and quantum-compatible benchmark regimes. The package also includes a finite-resource adequacy-map analysis based on the probability-domain error Δp. This analysis identifies parameter regions in which binary approximation, stochastic Bernoulli estimation or coherence-enhanced benchmark descriptions are adequate under explicitly prescribed tolerance and resource assumptions. These results are intended as model-level numerical illustrations and should not be interpreted as hardware measurements or experimental validation of a particular physical implementation. Included files:- SCS_Supplementary_Material.pdf- SCS_Supplementary_Material.docx- SCS_revision_supplementary_modeling.ipynb- SCS_revision_supplementary_modeling.py- SCS_supplementary_outputs.zip- README_SCS_supplementary.txt