moma 0.2.5

Moving Origin Modular Arithmetic (MOMA), a library for modeling complex systems
Documentation

MOMA: Moving Origin Modular Arithmetic

Crates.io Docs.rs License: MIT OR Apache-2.0 CI

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 = "0.1.9" # Replace with the latest version

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);
}

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:

at your option.