Beating Substrate Theory (BST) is an experimental computational framework exploring the emergence of observable structures from a discrete oscillatory substrate.
This repository contains the reference numerical experiments developed within the BST research program, together with the supporting infrastructure required for reproducibility and further investigation.
The repository focuses on computational reconstruction and experimental exploration. Interpretative, theoretical, and correspondence studies are maintained separately from the framework itself.
experiments/ Numerical experiments and reconstruction studies
results/ Generated outputs and validation artefacts
scripts/ Reproduction and utility scripts
historical/ Historical research stages and precursor documents
The framework currently includes experiments investigating:
- Closure dynamics
- Latent projection and observable equivalence
- Reconstruction and generative memory
- Arbitration and branch selection
- Multi-resolution (Zeta) dynamics
- Emergent geometry
- Interaction and matter reconstruction
- Vacuum-wave backgrounds
- Structure formation
- Curvature and gravity-like emergence
- Robustness and falsifiability analyses
Experiments are organized progressively.
The repository includes foundational experiments (00–19), intermediate reconstruction studies (20–56), and higher-level reconstruction and synthesis experiments (57–71).
Not all experiments are executed by the default reproduction script.
Create a Python environment and install the required dependencies:
pip install -r requirements.txtIndividual experiments can be executed directly:
python experiments/01_closure/canonical_closure_law_test.pySome higher-level experiments are included for completeness and reproducibility purposes and may require substantial computation time.
A repository-wide reproduction utility is also provided:
python scripts/reproduce.pyThe default reproduction script currently executes the foundational experiment suite used for framework validation.
Additional experiments, including higher-level reconstruction studies and synthesis milestones, are available in the experiments/ directory and may be executed individually when required.
The historical/ directory contains archived research documents and intermediate development stages that contributed to the evolution of the BST framework.
These materials are preserved for transparency and traceability.
The primary purpose of this repository is reproducibility.
All scientific claims associated with BST should be evaluated through the experiments, generated outputs, validation procedures, and formal verification resources associated with the framework.
Numerical experiments, reconstruction studies, and independent formal verification are provided to facilitate transparent evaluation and replication of results.
In addition to the numerical experiments contained in this repository, a Lean 4 formalization of the BST theorem framework has been developed.
The purpose of the formalization is not to establish the physical validity of BST, but to verify that the formalized theorem chain follows rigorously from the adopted definitions and assumptions.
Current verification status:
- 27 verified Lean modules
- 0 compilation errors
- 0 warnings
- 0 sorry
- No additional axioms introduced
The Lean project provides an independent logical consistency check that complements the experimental and computational results contained in this repository.
The formalization currently covers major components of the BST framework, including reconstruction, closure dynamics, observable equivalence, arbitration, branch selection, emergent geometry, wave-cluster taxonomy, periodic attractors, matter taxonomy, topological selection, contact networks, and universality.
The Lean formalization is maintained separately from the experimental framework and may be consulted independently by reviewers interested in formal verification.
If you use this repository in academic work, please cite the project using the information provided in CITATION.cff.
This repository is distributed under the license provided in LICENSE.