Reproducibility Package for "Accumulation-Controlled Finite-Time Reduction in Irreversible Open Dynamics"

Description This repository provides the reproducibility package accompanying the manuscript: “Accumulation-Controlled Finite-Time Reduction in Irreversible Open Dynamics.” DOI: https://doi.org/10.5281/zenodo.18621639 The package contains all figure-generation scripts and supporting material required to reproduce the numerical illustrations presented in the main text and Supplemental Material (SM). Scope The code implements the accumulation-controlled reduction framework described in the manuscript. The central result is a finite-time certification criterion for reduced-order descriptions in irreversible open systems. Effective reduction to a single ordering coordinate is certified when the accumulated relaxation A_CW = ∫_CW Δ_L(t) dt is sufficiently large over a finite convergence window (CW), where Δ_L(t) is an operationally defined effective Liouvillian decay rate. The repository includes numerical illustrations of: Finite-time contraction controlled by A_CW Diagnostic filtering between locking and failure regimes Hierarchy breakdown Generator drift breakdown Short-memory breakdown Phase-diagram visualization of pass–fail regions The models are minimal illustrative systems designed to demonstrate the operational diagnostics. They are not intended as UV-complete physical models. Contents Main-text figures: Fig.1_CWTheorem.py Fig.2_toymodel_cw.py Fig.3_toymodel_cw_failure.py Supplemental figures: Fig.S1_hierarchy_failure.py Fig.S2_drift_failure.py Fig.S3_short_memory_failure.py Fig.S4_two_fast_modes.py Fig.S5_PhaseDiagram.py Additional files: README.md (execution instructions) requirements.txt (Python dependencies) Supplemental Material (PDF) Reproducibility All scripts are self-contained and generate publication-ready figures (black-and-white, APS-compatible layout). The numerical routines are intentionally minimal to emphasize diagnostic clarity and finite-time control bounds of the form: exp(−A_CW) + O(ε_M + ε_ad + r_gap^−1). Relationship to Other Work This repository is independent of the earlier PRD diagnostic package and contains code specific to the accumulation-controlled reduction framework presented in the present manuscript. Citation If you use this code or reproduce figures from this package, please cite: Cheolmin Kim,“Accumulation-Controlled Finite-Time Reduction in Irreversible Open Dynamics,”Zenodo (2026), DOI: https://doi.org/10.5281/zenodo.18621639 If the associated journal article is published, please cite the journal version in addition to this repository.