Project Optimus PRIME

A computational playground for primes, geometry, spectra, and music.

Overview

Project Optimus PRIME is a unified framework that:

• Encodes integers (and primes) in a 3D lattice.
• Defines a resonance field (F(x,y,z)) over that lattice.
• Evolves the field with dynamic machines (diffusion, automata, agents).
• Builds a Hermitian operator and studies its spectrum.
• Maps the resulting structures into musical output.

The project bridges:

• Number theory
• Random Matrix Theory (RMT)
• Spectral graph theory
• Reaction–diffusion systems
• Physics-inspired RH analogies (Berry–Keating, Montgomery–Dyson)
• Basic musical mapping and MIDI export

The core mathematical specification lives in:

• MASTER_SPEC_v1.0.md

Phase details and tasks live in:

• phases/PHASE0_meta_and_philosophy.md
• phases/PHASE1_geometry_cube.md
• phases/PHASE2_spectral_analysis.md
• phases/PHASE3_rh_physics_bridge.md
• phases/PHASE4_machine_synthesis.md
• phases/PHASE5_music_and_export.md

Repository Structure

code/
  prime_cube.py         # integer mapping, primality utilities
  spectral_operator.py  # builds Hermitian operator H
  machines.py           # diffusion, automaton, agent skeletons
  music_engine.py       # basic MIDI export utilities
  visualize.py          # plotting helpers (eigenvalues, field slices)

diagrams/               # saved plots/images (histograms, slices, etc.)
music/                  # exported .mid files
phases/                 # phase-by-phase design docs
MASTER_SPEC_v1.0.md     # core math & system specification
run_demo.py             # small end-to-end demo
todo.md                 # project checklist
requirements.txt        # Python dependencies