Reproducibility materials for Mean-Preserving Thinning and Response Information in Causal Sets

Abstract

Reproducibility materials for “Mean-Preserving Thinning and Response Information in Causal Sets” by Yutong Bai. This software package accompanies a study of retarded scalar propagation on causal sets, distinguishing exact mean-response consistency under coordinated thinning from the reconstruction of realization-dependent responses. It provides computational checks for the finite-poset thinning identities, controlled stochastic response formulas, and count-aware reconstruction results developed in the manuscript and its Supplemental Material. The archive contains:• Python scripts for interval-moment and covariance identities, source-response checks, and deterministic source–detector quadrature;• exact finite-poset and symbolic Poisson-moment tests for thinning, conditional prediction, and total-count and cell-count information;• six reference quadrature datasets for the smooth-source, finite-detector example;• installation instructions, numerical methods and parameters, a unified validation command, citation metadata, and file-integrity checksums. The README identifies the model parameters and commands needed to reproduce all six reference configurations. The calculations use Python, NumPy, and SymPy and require no external datasets or random seeds. The unified runner performs the symbolic and finite checks together with a low-resolution detector calculation; the full reference quadrature runs are available separately through the documented commands. These materials support reproducibility but are not formal proof certificates. The detector results are obtained by deterministic quadrature, not Poisson Monte Carlo. Reported refinement differences are empirical convergence checks rather than rigorous error bounds, and the reconstruction-risk predictions are not independently simulated losses. Development logs, correspondence, manuscript drafts, and duplicate intermediate outputs are excluded.