Repository slug: MPL-TC
Status: non‑profit · community‑maintained · volunteer‑run
This repository accompanies the V3 paper, where Triadic Completeness (TC) supplies the recursive number-universe architecture and McCrackn’s Prime Law (MPL) is the regime-motif / Lex-Min readout of the TC certificate frontier.
The repository mirrors the paper's layer order:
TC -> Axis / First-Hole -> derivation-level lagged scheduler
-> MPL regime-motif / Lex-Min readout
-> MPL-normalized symbolic O(1)
Here, MPL is the regime-motif / Lex-Min readout of the TC certificate frontier, not a replacement for the TC layer.
The final O(1) statement is scoped to MPL-normalized motif-to-motif symbolic transition cost in the paper's cost model. It is not a claim about bit complexity, expanded integer output, explicit certificate-frontier materialization, whole-regime materialization, concrete Python data-structure runtime, repository tests, or finite-prefix evidence.
📄 Read the full manuscript on Zenodo: https://doi.org/10.5281/zenodo.20343409
✉️ Contact: thenothingnesseffect@gmail.com
🧬 ORCID: 0009-0001-4400-0171
Or view the local version: McCrackns_prime_law.pdf
The repository keeps the paper's layers separate:
triadic_domains.pymodels finite-prefix TC placement:U1, dyadicEfaces,O1for the prime/free odd axis, and lpf-basedO2,O3,O4, ... composite strata.- The Axis Law / First-Hole bridge is represented as finite executable validation in the TC layer and tests. First-Hole language is always relative to realized smooth-monoid coverage
M_j = <{2} union P_j>. lagged_certificate_frontier.pyimplements the derivation-level unbounded lagged TC certificate-frontier scheduler introduced in PR #5, merged at25421497ec8b4dfd2e33e9b5b135a93d2e6f6368from implementation commit09157d77ae26baab8e942a18253ad537f5ac07b4.- MPL is documented as the regime-motif / Lex-Min readout of the TC certificate frontier. The older
mccrackns_prime_law.pymodule remains a bounded executable MPL prefix and regression harness with explicit motif/regime transitions.U1is seed-only for2 -> 3; every later gap is even. The bounded tape is an implementation artifact, not the full compressed symbolic MPL runtime. - GCD is not used by the MPL generator. If added in future diagnostics, it must remain a post-hoc sentinel or contradiction guard only.
- Implementation-support status is tracked in
docs/claim_status_matrix.md,docs/unbounded_scheduler_proof_obligations.md, anddocs/theorem_implementation_map.md. The concrete scheduler is deterministic and check-free, but its concrete runtime is data-structure-dependent; repository tests provide finite-prefix regression evidence only.
The repository also includes lagged_certificate_frontier.py, an executable
implementation of the paper's derivation-level unbounded lagged TC
certificate-frontier scheduler. This scheduler distinguishes generated values
from derivations, records allowed and forbidden derivations separately, and
tracks activation cohorts, active multipliers, known targets, delayed
obstruction horizons, and prime buffers.
The current emitted axis q_n is a known target but not an active multiplier
inside recursion R_n. Objects created or certified during R_n activate only
after the recursion closes. The scheduler delays q_n^2 until the next
recursion, normalizes composite value certificates by sorted factor words,
deduplicates aliases such as 3 * 15 = 5 * 9 = 45, and keeps derivation aliases
for audit/debugging. In particular, a forbidden derivation does not forbid the
numeric value when another allowed derivation generates it.
The concrete scheduler uses generated certificate maintenance, merge/compare-style marker readout, multiplication of active emitted axes by known targets, derivation legality checks from recursion metadata, and canonical normalization. It does not use gcd filtering, primality tests, trial division, sieve arrays, wheel residues, candidate scanning, hardcoded prime tables, hardcoded gap tables, or finite precomputed gap tapes as runtime mechanisms.
Concrete runtime is data-structure-dependent. The finite-prefix regression tests are implementation evidence, not mathematical proof. The paper's O(1) claim belongs only to MPL-normalized motif-to-motif symbolic transition cost. The repository does not claim bit-complexity O(1), expanded integer output O(1), explicit frontier materialization O(1), concrete data-structure O(1), or that finite-prefix tests establish asymptotic complexity or the full theorem complex.
| Alphabet growth | Gap vs run | Innovations by regime |
|---|---|---|
| Sequence size as the prime alphabet expands. | Prime‑gap size versus motif run length. | Counts of regime innovations across validated range. |
- Abstract
- Visual Snapshot
- Quick Start
- Programmatic Usage
- Repository Layout
- Reproducibility & Open Science
- Community & Governance
- Contributing
- Security
- License
- Authors & Credits
Note: The large pre‑computed dataset
motifs_10m.csvis stored with Git LFS.
Install LFS once viagit lfs installbefore cloning or pulling.
# 1 · Clone & enter
git clone https://github.com/pt2710/MPL-TC.git
cd MPL-TC
# 2 · Ensure Git LFS is enabled (one‑time per machine)
git lfs install
# 3 · Create isolated Python env (3.9+)
python -m venv .venv
source .venv/bin/activate # macOS / Linux
# .venv\Scripts\activate.bat # Windows (PowerShell users: Activate.ps1)
# 4 · Install runtime deps
pip install -r requirements.txt
# 5 · Verify the bounded executable prefix
python test_mccrackns_prime_law.py --plotThe script prints prime indices, local regimes, motifs and gap statistics, and regenerates the figures above when --plot is supplied.
from mccrackns_prime_law import McCracknsPrimeLaw
mpl = McCracknsPrimeLaw(n_primes=20)
mpl.generate()
print(mpl.get_primes())Click to expand full tree
mccrackns_prime_law/
├── .github/
│ └── workflows/
│ └── ci.yml
├── configs/
│ └── default.yaml
├── figures_visible/
│ ├── chunks/
│ ├── alphabet_growth.png
│ ├── cumulative_motifs.png
│ ├── gap_boxplot_by_domain.png
│ ├── gap_evolution_domains.png
│ ├── gap_vs_run.png
│ └── innovations_by_regime.png
├── src/
│ ├── __init__.py
│ ├── prime_utils.py
│ └── your_module.py
├── tests/
│ └── test_basic.py
├── .gitattributes
├── .gitconfig
├── .gitignore
├── CODE_OF_CUNDUCT.md
├── compute_motifs.py
├── CONTRIBUTING.md
├── LICENSE
├── MAINTAINERS.md
├── McCrackns_prime_law.pdf
├── mccrackns_prime_law.py
├── next_prime.py
├── numbers_domains.py
├── README.md
├── requirements.txt
├── ruleset.json
├── SECURITY.md
├── state.json
├── triadic_domains.py
└── test_mccrackns_prime_law.py
All code, data and figures are provided under an OSI‑approved license to foster independent verification.
Run the notebooks, re‑plot the data, or extend the proofs—then open a Pull Request or Discussion to share your findings!
McCrackn’s Prime Law is community‑maintained. There is currently no corporate backing and no single full‑time maintainer.
We rely on volunteers for everything from issue triage to peer‑review of new proofs. If you’d like to help, see CONTRIBUTING.md.
Bug reports, feature requests and PRs of any size are welcome.
Please read the guidelines in CONTRIBUTING.md before you start hacking.
If you believe you have found a vulnerability, do not open a public Issue.
Instead, follow the private process in SECURITY.md.
This project is released under the MIT License. See LICENSE for details.
Created by Budd McCrackn
📧 Contact: thenothingnesseffect@gmail.com
🔗 ORCID: 0009-0001-4400-0171
...extended by a growing community of mathematicians, coders and prime‑enthusiasts.
See AUTHORS.md (or the GitHub contributions graph) for a full list of contributors.
Last updated: 2025-06-24 025-06-23_