Mathematical Formalisms

Mathematical work by Jared D. Dunahay AEO Trivector LLC, Bedford, NH

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This repository is the public companion to mathematical papers and formalisms by Jared D. Dunahay. Each paper lives in its own self-contained subdirectory under papers/, with the manuscript source, verification code, unit tests, and a deterministic reproduction script.

Papers

Year	Title	Status	Code	arXiv	DOI
2026	A Canonical Non-Commutative Deformation of $\mathbb{T}^8$ Indexed by $\mathrm{Cl}(3,0)$: Spectrum, Pfaffian, and a Pythagorean Spectral Identity	Submitted	papers/2026-noncommutative-t8-clifford/	(pending)	10.5281/zenodo.20031520

Each paper directory contains a self-contained README with the theorem-claim-test traceability map, installation, and reproduction instructions.

Quick verification

To verify all computational claims across all papers in this repository:

git clone https://github.com/Orion-sextant/Mathematical-Formalisms.git
cd Mathematical-Formalisms
make verify

make verify installs each paper's package and runs its test suite. Continuous integration runs the same workflow on every commit.

What "verifies" means here

The unit tests in this repository verify the finite algebraic computations stated in the corresponding papers. They check that the canonical data, closed-form identities, and spectral computations reported in print are reproduced exactly (to numerical precision) by independent symbolic and numerical implementations.

The tests do not prove the underlying theorems. The proofs are in the papers; the code reproduces the load-bearing computations on which the proofs rest.

Structure

Mathematical-Formalisms/
│
├── README.md                              # This file
├── LICENSE                                # MIT (code) + CC BY 4.0 (papers)
├── CITATION.cff                           # Repository-wide citation metadata
├── Makefile                               # Top-level orchestration
├── pyproject.toml                         # Repository-wide dev tooling
├── .gitignore
├── .github/workflows/verify.yml           # CI: install + test every paper
│
└── papers/
    └── YYYY-paper-slug/
        ├── README.md                      # Paper-specific verification map
        ├── paper/
        │   ├── main.tex                   # LaTeX source
        │   ├── main.bbl                   # Bibliography (kept for arXiv)
        │   ├── refs.bib
        │   └── figures/
        ├── src/                           # Implementation
        ├── tests/                         # Pytest suite
        ├── examples/
        │   └── reproduce_paper_claims.py  # Single deterministic script
        └── pyproject.toml                 # Paper-specific package

Citation

Each paper has its own preferred citation; please cite the relevant paper directly. Software citations are accumulated under a single Zenodo DOI for this repository at each tagged release. See CITATION.cff and individual paper subdirectories for details.

License

• Code (src/, tests/, examples/): MIT License
• Papers and prose documentation (papers/*/paper/, READMEs): Creative Commons Attribution 4.0 International (CC BY 4.0)

See LICENSE for full text.

Author

Jared D. Dunahay AEO Trivector LLC, Bedford, NH ORCID: 0009-0004-5735-2872

Archival

Tagged releases are archived on Zenodo, which automatically deposits each release into the Software Heritage Archive. Each release carries both a citable DOI and a persistent SWHID for long-term source preservation.

Identifier	Type	Points to
10.5281/zenodo.20031519	Concept DOI	All versions of this repository
10.5281/zenodo.20031520	Version DOI	v1.0.0 specifically

When citing this software, prefer the concept DOI, which always resolves to the latest version. When citing a specific snapshot used to reproduce results, use the corresponding version DOI.