Functorial Fission: A Categorical Formulation of Nuclear Fission Energy

A rigorous mathematical and categorical treatment of nuclear fission energy, combining classical nuclear physics with category theory and typed functional programming.

Overview

This repository contains an arXiv-style paper presenting a novel functorial formulation of nuclear fission physics. While the underlying physics (mass-energy equivalence, binding energy, chain reactions) is well-established, this work provides a structural reformulation using:

• Category Theory: Nuclei as objects in a monoidal category, fission as morphisms, binding energy as a functor
• Type Theory: Haskell implementations encoding physical invariants at the type level
• Coalgebraic Semantics: Neutron branching modeled as coalgebras capturing chain reaction dynamics

Repository Structure

functorial-fission/
├── latex/                 # LaTeX source files
│   └── main.tex          # Main paper source
├── code/                  # Haskell implementation
│   └── src/
│       └── FunctorialFission.hs
├── pdf/                   # Compiled PDF output
├── docs/                  # GitHub Pages site
└── README.md

Key Contributions

1. Categorical Framework: Nuclear states form a symmetric monoidal category with fission as structure-preserving morphisms
2. Binding Energy Functor: A functor B: Nucl → Energy mapping nuclear configurations to their binding energies
3. Conservation as Natural Transformations: Charge, baryon number, and energy conservation emerge as natural transformations
4. Coalgebraic Chain Reactions: Neutron multiplication modeled as coalgebras over the branching functor

Building

LaTeX Paper

cd latex
pdflatex main.tex
bibtex main
pdflatex main.tex
pdflatex main.tex

Haskell Code

cd code
cabal build

Citation

If you use this work, please cite:

@article{long2025functorial,
  title={A Functorial Formulation of Nuclear Fission: Mass-Energy Equivalence,
         Binding Energy, and Chain-Reaction Dynamics in a Categorical Framework},
  author={Long, Matthew},
  journal={arXiv preprint},
  year={2025}
}

License

MIT License - See LICENSE file for details.

Author

Matthew Long Research in categorical physics, typed functional programming, and formal methods.