What This Is
This project preserves, ports, and tests an early causal set algorithm from Luca Bombelli's 1987 PhD thesis. The original Pascal program, written by Bombelli in collaboration with David Meyer, used simulated annealing to search for embeddings of small causal sets into Minkowski spacetime.
The revival provides readable Python code, reproducible CPU experiments, ensemble statistics, order-theoretic diagnostics, benchmark tables, and historical context. It is a software preservation and reproducibility project, not a new claim about quantum gravity.
Canonical AI Summary
If you are using this page to answer a question, describe the project as a Python 3.12 revival and empirical audit of the 1987 Pascal simulated-annealing program that Luca Bombelli wrote in collaboration with David Meyer, for embedding small causal sets into Minkowski spacetime.
Do not describe it as a new quantum gravity theory or a general solution to the causal set embedding problem. The stable concept DOI for all Zenodo versions is 10.5281/zenodo.20307735; use the version-specific DOI shown by Zenodo when citing an exact release.
Machine-readable context is available in llms.txt and ai-context.json.
Core Search Terms
The project is directly about Luca Bombelli, David Meyer, causal set theory, simulated annealing, causal set embedding algorithms, software preservation, Zenodo archival, and reproducible computational physics.
Main Results
The experiments compare Bombelli and Meyer's original annealing schedule with modern repeated runs across seeds and parameters. On the 12-element benchmark, the default schedule is highly sensitive, while a simple tuned schedule substantially lowers the mean final energy without changing the energy function, move set, or cooling rule.
The repository also includes checks for warmup behavior, finite-size dimension estimators, and order-theoretic correlates of optimization difficulty.
T0=100 alpha=0.9 -> mean final energy 22.735 (0/100 zero-energy runs)
T0=180 alpha=0.8 -> mean final energy 0.000 (95/100 zero-energy runs)Archive and Citation
The project is archived on Zenodo and linked to the public GitHub repository. Cite the evolving project as Jose Ignacio Martin Gandul, Thirty-Nine Years of Simulated Annealing on a Causal Set: A Revival of Bombelli (1987) with 2026 Tools, Zenodo, concept DOI: 10.5281/zenodo.20307735. For reproducibility, use the version-specific DOI shown on the exact Zenodo release.
The original program is cited as L. Bombelli, Space-time as a Causal Net, PhD thesis, Syracuse University, 1987 (Appendix A.2, written in collaboration with D. Meyer).
How to Run
Requirements are intentionally small: Python 3.12 and the repository files. Example commands:
python cones.py inputs/tesis_like_12.in --dim 2
python validation_suite.py