Computational number theory · open methods & data
Experiments you can rerun.
Compare candidate-selection methods, inspect exact prime-pair counts, and check the data behind a result. ProofX publishes small, reproducible experiments in Goldbach and Collatz, with a separate Lean layer for finite certificates.
Published experiment / GB-001
Bounded comparisonDoes structural selection find sparse Goldbach partitions?
Three policies. The same finite domain and candidate budget. A complete reference dataset makes the outcome inspectable, including when a baseline performs better.
- Domain
- Even integers 4–10,000
- Policies
- Directed, uniform, sequential
- Budget
- 64 unique candidates per run
- Repetitions
- Seeds 0, 1, 2
Read the protocol, compare results, and download every row →
Start with a reproducible comparison
After installing the Python toolkit, run:
python -m codebase.cli benchmark goldbach --max-n 10000 --budget 64 --seeds 0 1 2 --output-dir results/my-comparison
python -m codebase.cli benchmark verify results/my-comparisonThe first command writes the reference, candidate ledgers, hashes, and environment metadata. The second recounts every reference value with independent trial-division primality. Use a new output directory for each experiment.
Choose a research tool
| Workflow | Use it for | Status |
|---|---|---|
| Goldbach comparison | Compare selection policies against a complete bounded reference. | Protocol, data, independent recount |
| Collatz inspector | Inspect trajectories and run directed searches through the CLI. | Experimental ranking; no baseline study yet |
| Search ledger viewer | Explore exported candidate features locally in your browser. | Exploration tool |
| Lean certificates | Kernel-check specific Collatz trajectories and Goldbach witnesses. | Finite statements only |
| Riemann diagnostics | Inspect numerical zero spacing and coefficient calculations. | Experimental; no off-line zero search |
Help test a method
The next useful contributions are independent reproductions, alternative baselines, held-out size intervals, and counterexamples to implementation assumptions. Include the command, environment, manifest, and a minimal failing case.
ProofX is maintained by Mohammed Alkindi. Its experiments do not prove an open conjecture. Germinal is a separate vendored project.