MOMA: Moving Origin Modular Arithmetic

MOMA is a Rust framework for exploring number theory, cryptography, and bioinformatics through the lens of Moving Origin Modular Arithmetic.

The crate is designed for researchers and developers who are interested in a novel, relational framework for analyzing complex sequences.

The Core Idea: A Barycenter for Numbers

The inspiration for this crate comes from the concept of a barycenter in astrophysics. Just as the Earth and Moon orbit a common center of mass that is not the exact center of the Earth, MOMA treats modular arithmetic as a system where the "zero point" or "origin" is not fixed.

This origin shifts dynamically based on a contextual value—typically a prime number p—and the chosen OriginStrategy. This provides a novel relational framework for analyzing complex systems.

The original inspiration came from this NASA article: What Is a Barycenter?

Core Concepts

The MOMA framework is built on a few simple but powerful concepts:

• MomaRing: The primary object for all calculations. A ring is defined by a modulus and a chosen OriginStrategy.
• OriginStrategy: A trait that defines how the origin moves, making the framework highly extensible.
• Analysis Tools: A suite of modular tools for deeper analysis:
  • Number Theory: MassField, OriginDrift, CompositeInfluence, CompositeDampener, GoldbachProjector, Entropy, and ResonanceFinder.
  • Bioinformatics: BioSigAnalyzer, CodonTable, and Mutation for mapping numeric signatures to biological events.

Features

• Flexible Core: A powerful and extensible system based on the MomaRing and OriginStrategy trait.
• Advanced Analysis Tools: A suite of high-level structs for statistical, number-theoretic, and bioinformatics analysis.
• Cryptographic Primitives: Demonstrates how MOMA can be used to build components like a Key Derivation Function.
• Prime Number Utilities: A helper primes module for primality testing and prime generation.
• Pure Rust: Built with safe, idiomatic Rust.

Installation

Add MOMA to your Cargo.toml:

[dependencies]
moma = "0.3.6" # Replace with the latest version

or rather just run cargo add moma from the terminal

Exploring MOMA

MOMA is a toolkit for exploration across different domains.

Example 1: Finding "Resonance"

Use the ResonanceFinder to find primes where the MOMA signature is a multiple of another property of the prime, such as its number of prime factors (prime_factor_mass).

use moma::resonance::ResonanceFinder;
use moma::strategy;
use moma::primes;

// Find primes where the signature (using CompositeMass strategy)
// is divisible by the prime's factor mass.
let finder = ResonanceFinder::new(
    100,
    strategy::CompositeMass,
    primes::prime_factor_mass,
);

// Search for resonance events in the range 1 to 500.
let resonances = finder.find_in_range(1, 500);

println!("Found {} resonance events.", resonances.len());
for (prime, signature) in resonances {
    println!("  - Resonance at p={} with signature {}", prime, signature);
}

Example 2: Bioinformatics Signature Analysis

Use the BioSigAnalyzer to map MOMA signatures to simulated genetic mutations.

use moma::biosig::BioSigAnalyzer;
use moma::strategy;

let analyzer = BioSigAnalyzer::new(60, strategy::CompositeMass);
let dna_sequence = "AGCTGCGATCGTACGATCGATCGTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCT";

// Analyze the mutational effect of the signature derived from prime 13.
if let Some((signature, mutation)) = analyzer.analyze(13, dna_sequence) {
    println!("Signature for p=13 is {}", signature);
    println!("Resulting mutation type: {:?}", mutation.mutation_type);
}

More Examples

There are more examples in the GitHub repository including:-

• Cosmology - For the Astrophysicists
• BioInformatics - For Biologists
• Prime Gaps - For the number theorists
• Goldbach Projector - For Goldbach Conjecture theorists
• Origin Drift - to understand MOMA's drifting Origin
• Key Derivation Function (KDF) - For Cryptographers
• Mass Field - How to create a massfield for a specific range

Author

Neil Crago — experimental mathematician

Contributing

Contributions are welcome! If you have an idea for a new OriginStrategy, an analysis tool, or find a bug, please feel free to open an issue or submit a pull request.

License

This project is licensed under either of:

• Apache License, Version 2.0, (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option

Related Crates

This crate is part of a collection of crates by the same author: These include:-

• MOMA_simulation_engine
• Fractal_Algebra
• tma_engine
• factorial_engine
• fa_slow_ai
• coheron
• curvature