Retained History and Leakage in Nonequilibrium Systems

This repository contains the manuscript source, generated figure, and minimal reproduction script for:

Retained History and Leakage in Nonequilibrium Systems:
A Four-Channel Audit Framework for Phase-Amplitude Correspondence

Author: Yoshida
Date: July 9, 2026

Overview

This manuscript proposes a four-channel audit framework for systems in which observable structure may depend on:

• phase phi
• coherent amplitude A
• retained history Gamma
• leakage or exported history J_out

The paper is a correspondence and audit framework, not a replacement for established physical, chemical, thermodynamic, quantum, or biological theories. Its main purpose is to clarify when a candidate retained-history coordinate should be treated as a testable variable rather than as a metaphor.

Repository Contents

.
├── README.md
├── retained_history_leakage_four_channel_audit_framework.tex
├── retained_history_leakage_four_channel_audit_framework.pdf
├── outputs/
│   ├── retained_history_leakage_audit_demo.png
│   └── retained_history_leakage_audit_demo.json
└── scripts/
    └── retained_history_leakage_audit_demo.py

Build Requirements

The manuscript was compiled with pdflatex via latexmk.

Required LaTeX packages:

• geometry
• amsmath
• amssymb
• amsthm
• bm
• graphicx
• array
• booktabs
• caption
• hyperref

The figure-generation script requires Python with:

• numpy
• matplotlib

Reproducing the Figure

From this directory, run:

python3 scripts/retained_history_leakage_audit_demo.py

This regenerates:

outputs/retained_history_leakage_audit_demo.png
outputs/retained_history_leakage_audit_demo.json

The numerical model is dimensionless and methodological. It illustrates the sign reversal between target-side leakage and observer-side data gain; it is not proposed as a universal microscopic measurement theory.

Compiling the Manuscript

From this directory, run:

latexmk -pdf -interaction=nonstopmode -halt-on-error retained_history_leakage_four_channel_audit_framework.tex

The expected output is:

retained_history_leakage_four_channel_audit_framework.pdf

The current source has no external \input{...} dependency. The only required figure file is:

outputs/retained_history_leakage_audit_demo.png

License

This repository is licensed under the following terms:

• Code: MIT License
• Manuscript and Figures: Creative Commons Attribution 4.0 International (CC BY 4.0)