lucidia math

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lucidia math is part of the BlackRoad OS ecosystem — a sovereign, distributed operating system built on edge computing, local AI, and mesh networking by BlackRoad OS, Inc.

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Advanced mathematical engines: consciousness modeling, unified geometry, quantum finance, prime exploration.

pip install lucidia-math

What is this?

Lucidia Math provides specialized mathematical computation engines for AI research and scientific computing:

Forge - Mathematical Foundations

Module	Lines	Description
consciousness.py	650	Consciousness modeling and emergence patterns
unified_geometry.py	402	Unified geometric transformations
advanced_tools.py	356	Advanced mathematical utilities
main.py	209	CLI and orchestration
numbers.py	120	Number theory foundations
proofs.py	86	Automated proof assistance
fractals.py	51	Fractal generation
dimensions.py	41	Multi-dimensional analysis

Lab - Experimental Mathematics

Module	Lines	Description
unified_geometry_engine.py	492	Geometry computation engine
amundson_equations.py	284	Custom equation systems
iterative_math_build.py	198	Iterative mathematical construction
trinary_logic.py	111	Three-valued logic system
prime_explorer.py	108	Prime number exploration
quantum_finance.py	83	Quantum-inspired financial models
frameworks.py	80	Mathematical framework abstractions

Quick Start

from forge import consciousness, unified_geometry
from lab import prime_explorer, quantum_finance

# Consciousness modeling
state = consciousness.ConsciousnessState()
emergence = state.compute_emergence_pattern()

# Unified geometry
transform = unified_geometry.UnifiedTransform()
result = transform.apply_to_manifold(data)

# Prime exploration
primes = prime_explorer.explore_range(1, 10000)
patterns = prime_explorer.find_patterns(primes)

# Quantum finance
model = quantum_finance.QuantumPortfolio(assets)
optimal = model.optimize()

CLI Usage

# Run the math forge
lucidia-math

# Explore primes
lucidia-math primes --range 1:10000

# Generate fractals
lucidia-math fractals --type mandelbrot --depth 100

Architecture

lucidia-math/
├── forge/                  # Mathematical foundations
│   ├── consciousness.py    # Consciousness modeling (650 lines)
│   ├── unified_geometry.py # Geometric transformations (402 lines)
│   ├── advanced_tools.py   # Advanced utilities (356 lines)
│   ├── main.py             # CLI entry point
│   ├── numbers.py          # Number theory
│   ├── proofs.py           # Proof assistance
│   ├── fractals.py         # Fractal generation
│   └── dimensions.py       # Multi-dimensional analysis
├── lab/                    # Experimental mathematics
│   ├── unified_geometry_engine.py  # Geometry engine (492 lines)
│   ├── amundson_equations.py       # Custom equations (284 lines)
│   ├── iterative_math_build.py     # Iterative construction
│   ├── trinary_logic.py            # Three-valued logic
│   ├── prime_explorer.py           # Prime exploration
│   └── quantum_finance.py          # Quantum finance
└── pyproject.toml

Trinary Logic

The trinary_logic module implements a three-valued logic system:

from lab.trinary_logic import Trinary, TRUE, FALSE, UNKNOWN

# Three-valued operations
a = TRUE
b = UNKNOWN
c = a.and_(b)  # Returns UNKNOWN
d = a.or_(b)   # Returns TRUE

License

MIT - See LICENSE for details.

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Built by BlackRoad OS

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📜 License & Copyright

Copyright © 2026 BlackRoad OS, Inc. All Rights Reserved.

CEO: Alexa Amundson | PROPRIETARY AND CONFIDENTIAL

This software is NOT for commercial resale. Testing purposes only.

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See LICENSE for complete terms.