Cosmochrony – Simulation code

Simulation algorithms and numerical experiments supporting the Cosmochrony framework, with a focus on χ-field relaxation dynamics and the technical material referenced in the paper appendix (Numerical Methods / Simulation Algorithms).

Status: research code / evolving. The goal is clarity and reproducibility rather than production-grade APIs.

What this repository contains

This repository hosts:

• Numerical implementations of finite-dimensional approximations of χ-field relaxation dynamics.
• Thematic numerical experiments, organized by scientific axis (spectral analysis, geometry, appendix sweeps).
• Executable scripts used to generate figures, tables, and validation results referenced in the manuscript.

Conceptually, the simulations are meant as computational probes of the Cosmochrony dynamics: they do not introduce additional physical postulates (no fundamental lattice or graph assumption), but rely on auxiliary discretizations or bases for numerical stability and diagnostics.

Repository structure

The repository is organized by scientific role, not as a Python package:

simulation/
├── README.md
├── LICENSE
├── CITATION.cff
├── requirements.txt
│
├── scripts/        # Explicit entry points (what to run)
│   ├── main.py
│   ├── toy_cosmochrony_1d.py
│   ├── toy_cosmochrony_1d_a.py
│   ├── chi_relaxation_validation.py
│   ├── critical_tests_cosmochrony.py
│   ├── collect_D4_csv.py
│   ├── galaxy_rotcurve.py
│   ├── galaxy_rotcurves_3panel.py
│   ├── plot_cmb_lowell_planck_vs_cosmochrony.py
│   └── cmb_lowell_tests_corr_rescale.py
│
├── spectral/       # Spectral / Laplacian diagnostics (eigenmodes, ratios, convergence)
│   ├── lap_ratio.py
│   ├── spectral_ratio.py
│   ├── convergence_8_3.py
│   ├── eigenmodes.py
│   ├── spectral_test.py
│   └── make_spectral_fig.py
│
├── geometry/       # S³, Hopf fiberbase, weighted Laplacians, stiffness / curvature
│   ├── compare_mc_vs_weighted_laplacian_hopf_*.py
│   ├── compare_mc_vs_weighted_laplacian_s3.py
│   ├── weighted_laplacian_s3_bias.py
│   ├── weighted_measure_laplacian_s3_fiberbase.py
│   ├── weighted_laplacian_s3_fiberbase_db.py
│   ├── s3_relaxation_bias_ratio.py
│   ├── curvature_derivation.py
│   ├── stiffness_derivation.py
│   ├── stiffness_integration.py
│   └── stiffness_ratio.py
│
├── appendix_D4/    # Appendix D4 numerical sweeps and aggregated results
│   ├── summary_D4_all.csv
│   └── sweeps/
│
├── data/           # Input data (Planck CMB, galaxy rotation curves)
│   ├── Planck/
│   └── Rotmod_LTG/
│
├── figures/        # Final figures referenced in the manuscript
└── output/         # Optional: transient/generated outputs (typically gitignored)

Relation to the Cosmochrony paper

These simulations support the numerical and technical appendices of the Cosmochrony manuscript, in particular:

• discretized and coarse-grained relaxation flows,
• stability of localized (soliton-like) configurations,
• spectral / Laplacian diagnostics (e.g. convergence and ratio tests),
• Appendix D4 sweeps and saturation analyses,
• comparative studies (CMB low-ℓ, galaxy rotation curves).

If you are reading the paper, see the appendix section Simulation Algorithms for χ-Field Dynamics and related technical supplements.

• Paper / main project: https://github.com/Cosmochrony
• Website (if applicable): https://cosmochrony.org

Quickstart

1) Create a virtual environment

python -m venv .venv
source .venv/bin/activate   # macOS / Linux
# .venv\Scripts\activate    # Windows
python -m pip install -U pip

2) Install dependencies

pip install -r requirements.txt

3) Run a simulation script

This repository is script-driven. Typical usage:

python scripts/<script>.py
python scripts/<script>.py --help
python spectral/<script>.py
python geometry/<script>.py

Examples:

python scripts/main.py
python spectral/convergence_8_3.py
python scripts/galaxy_rotcurves_3panel.py
python scripts/plot_cmb_lowell_planck_vs_cosmochrony.py

Reproducing results

This section provides minimal, concrete recipes to reproduce representative numerical results used in the Cosmochrony manuscript.
All commands assume that the virtual environment is activated and dependencies installed.

---

1) Appendix D4 — χ-field relaxation sweeps and saturation diagnostics

Appendix D4 relies on parameter sweeps whose aggregated results are stored under appendix_D4/.

To regenerate or aggregate sweep summaries:

python scripts/collect_D4_csv.py

This script scans the sweep result directories and produces consolidated CSV summaries (e.g. summary_D4_all.csv), used to generate the figures in Appendix D4.

Precomputed sweep outputs and figures are available under:

appendix_D4/sweeps/

2) Spectral diagnostics — convergence and ratio tests

Key spectral diagnostics (including convergence and characteristic ratios) are implemented in the spectral/ directory.

Typical runs:

python spectral/convergence_8_3.py
python spectral/spectral_ratio.py
python spectral/lap_ratio.py

To generate the corresponding spectral figures:

python spectral/make_spectral_fig.py

These scripts probe eigenmode structure, convergence behavior, and robustness of the spectral ratios discussed in the manuscript.

3) CMB low-ℓ comparison (Planck vs Cosmochrony)

Low-ℓ CMB comparisons use publicly available Planck Release 3 data included under data/Planck/.

To generate the comparison plots:

python scripts/plot_cmb_lowell_planck_vs_cosmochrony.py

Additional rescaling / correction tests:

python scripts/cmb_lowell_tests_corr_rescale.py

Generated figures include:

• cmb_lowell_planck_lcdm_cosmochrony.pdf
• related diagnostic PDFs in the repository root or figures/.

4) Galaxy rotation curves

Galaxy rotation curve data (LTG sample) are provided under data/Rotmod_LTG/.

To reproduce the multi-panel rotation curve comparison:

python scripts/galaxy_rotcurves_3panel.py

This generates:

• galaxy_rotcurves_3panel.pdf

Notes on reproducibility

• Scripts are intended to be self-contained and explicit, rather than hidden behind a unified pipeline.
• Many scripts generate figures directly as PDF/PNG for traceability with the manuscript.
• When randomness is involved, scripts either fix or report the random seed.
• Large parameter sweeps are precomputed and versioned for transparency.

Scope and intent

These simulations are numerical probes, not a standalone simulation framework. Their purpose is to:

• validate internal consistency,
• explore stability and convergence regimes,
• support figures and tables in the Cosmochrony manuscript.

They should be read in conjunction with the corresponding theoretical sections of the paper.

How to cite

If you use this code in academic work, please cite the Cosmochrony paper. A CITATION.cff is provided to standardize citations. (preferred citation points to the Zenodo DOI of the manuscript).

Contributing / contact

Issues and pull requests are welcome, especially for:

• improving reproducibility (CLI options, configuration files),
• documentation and “how to reproduce figure X from the paper” recipes,
• numerical robustness and clarity of the experiments.

License

This repository is released under the Creative Commons Attribution 4.0 International License (CC BY 4.0).