blackroad-operating-system/packs/research-lab

BlackRoad OS Research Lab Pack

Mathematical research, quantum computing experiments, and computational proof systems for the BlackRoad OS ecosystem.

Overview

The Research Lab pack provides a unified home for all mathematical and computational research within BlackRoad OS. It parallels and integrates with the blackboxprogramming/blackroad-prism-console math modules.

Structure

research-lab/
├── math/                      # Mathematical modules
│   ├── hilbert_core.py        # Hilbert space symbolic reasoning
│   ├── collatz/               # Collatz conjecture verification
│   ├── linmath/               # Linear mathematics (C library)
│   ├── lucidia_math_forge/    # Symbolic proof engine
│   └── lucidia_math_lab/      # Experimental mathematics
├── quantum/                   # Quantum computing
│   ├── lucidia_quantum/       # Quantum core
│   └── quantum_engine/        # Circuit simulation
├── experiments/               # Research experiments
│   └── br_math/               # Mathematical experiments
├── docs/                      # Documentation
├── pack.yaml                  # Pack manifest
└── README.md                  # This file

Modules

Hilbert Core (hilbert_core.py)

Quantum-inspired symbolic reasoning using density matrices and projectors.

from hilbert_core import pure_state, truth_degree, projector_from_basis

# Create a pure state
psi = pure_state([1, 0, 0])

# Measure truth degree
P = projector_from_basis([[1], [0], [0]])
degree = truth_degree(psi, P)  # Returns 1.0

Collatz Verification (collatz/)

Distributed Collatz conjecture verification system.

# Start orchestrator
python -m collatz.orchestrator --start 1 --end 1000000000 --db ./campaign.sqlite

# Run workers on devices
python -m collatz.worker --db ./campaign.sqlite

Lucidia Math Forge (lucidia_math_forge/)

Symbolic proof engine with contradiction detection.

• proofs.py - Lightweight symbolic proof engine
• operators.py - Mathematical operators
• numbers.py - Number theory
• fractals.py - Fractal generation
• dimensions.py - Dimensional analysis

Lucidia Math Lab (lucidia_math_lab/)

Interactive mathematical exploration.

• prime_explorer.py - Prime analysis with Ulam spirals
• trinary_logic.py - Ternary logic systems
• quantum_finance.py - Quantum-inspired financial math
• iterative_math_build.py - Iterative construction

Linear Math (linmath/)

C header library for vectors, matrices, and transformations.

#include "linmath.h"

vec3 v = {1.0f, 2.0f, 3.0f};
mat4x4 m;
mat4x4_identity(m);
mat4x4_rotate_Z(m, m, 0.5f);

Research Areas

Area	Description	Modules
Number Theory	Primes, Collatz, Riemann	collatz, prime_explorer
Proof Systems	Symbolic proofs, contradictions	lucidia_math_forge, hilbert_core
Quantum Computing	Circuits, simulation	lucidia_quantum, quantum_engine
Computational Geometry	Linear algebra, transforms	linmath, hilbert_core
Logic Systems	Trinary, fuzzy, non-classical	lucidia_math_lab

Integration

With QLM Lab

# The pack integrates with /qlm_lab
from qlm_lab import api as qlm
from packs.research_lab.math import hilbert_core

With Agent System

Research agents from the agent registry can interact with these modules:

• agent.lucidia.core - Core Lucidia intelligence
• agent.lucidia.math - Mathematical operations
• agent.research.assistant - Research coordination

Source Repositories

This pack parallels content from:

• blackboxprogramming/blackroad-prism-console (source)
• BlackRoad-OS/blackroad-os-prism-console (target)

Maintained sync ensures mathematical research is available across the ecosystem.

Contributing

1. Add new experiments to experiments/
2. Extend math modules in math/
3. Update pack.yaml with new modules
4. Run verification tests before committing

License

Apache 2.0 - See LICENSE file