Foundational Research

Where math meets machine

BlackRoad Labs explores quantum computing, simulation theory, gematria computation, and experimental mathematics. 94 sections of foundational theory. 1,012 verified equations.

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Publications
Research papers
Original research in computational theory, quantum simulation, and mathematical foundations.
01
The Trivial Zero: A Computational Proof That Reality Is Self-Referential
SHA-256 hash chains as evidence of computational reality. Connects Gödel incompleteness, Riemann zeta functions, DNA encoding, and operating system ontology across 94 sections with 1,012 verified equations.
Simulation TheoryGödelRiemann94 Sections
Feb 2026
02
Quantum Framework: State-Vector Circuit Simulation
Dense complex NumPy state-vector simulator implementing Hadamard, Pauli-X/Y/Z, CNOT gates with projective measurement and state collapse. Includes VQE, QAOA, Grover's, and QFT algorithm implementations.
Quantum ComputingVQEGrover's
Jan 2026
03
Unsolved Problem Compendium
Computational approaches to 10 landmark unsolved problems: Riemann Hypothesis, P vs NP, Navier-Stokes existence and smoothness, Birch and Swinnerton-Dyer conjecture, and six others. Each with numerical experiments.
P vs NPNavier-StokesNumber Theory
Dec 2025
04
Gematria Computation Engine
Numerical encoding system mapping alphabetic characters to mathematical values. 156,675 FTS5 index entries across 228 SQLite databases powering pattern recognition and cross-reference analysis.
GematriaFTS5Pattern Analysis
2025
Disciplines
Focus areas
Six research domains spanning pure mathematics, quantum computing, and computational philosophy.

Quantum Simulation

State-vector circuit simulator with Bell states, entanglement, and projective measurement. Real quantum algorithm implementations.

VQE · QAOA · Grover's · QFT

Simulation Theory

Computational evidence for self-referential reality. Hash chains, Gödel encoding, and operating system ontology as proof framework.

94 sections · 1,012 equations

Gematria Computation

Algorithmic number-letter mapping with FTS5 full-text search across 228 databases. Pattern recognition at scale.

156,675 indexed entries

Number Theory

Riemann zeta function analysis, prime distribution, and computational approaches to the Riemann Hypothesis.

Riemann · Primes · Zeta zeros

Emergence Research

Experimental trinary logic and emergence simulations. Investigating how complex behavior arises from simple computational rules.

Trinary · Cellular automata

Computational Philosophy

Formal proofs connecting Gödel incompleteness, Lorenz attractors, Mandelbrot sets, and DNA encoding to computational substrates.

Gödel · Lorenz · Mandelbrot
History
Research timeline
Major milestones from the founding of the research program to present.
February 2026
The Trivial Zero published
94-section paper connecting SHA-256 hash chains, Gödel incompleteness, Riemann zeta, and DNA encoding into a unified computational proof of self-referential reality.
January 2026
Quantum Framework v1.0
State-vector simulator with VQE, QAOA, Grover's, and QFT implementations. Full pytest suite. Open-sourced on GitHub.
December 2025
Unsolved problem compendium
Computational approaches to 10 landmark unsolved problems including P vs NP, Riemann Hypothesis, and Navier-Stokes. Numerical experiments for each.
2025
Gematria engine reaches 156K entries
FTS5 full-text search index across 228 SQLite databases. Pattern recognition and cross-reference analysis at scale.
2024
BlackRoad Labs founded
Research division established within BlackRoad OS Inc. Initial focus: computational philosophy, gematria systems, and mathematical foundations.
Tools
Research stack
Open-source tools and frameworks powering our research.
Python
NumPy
SQLite / FTS5
Ollama
Hailo-8
pytest
Raspberry Pi 5

Explore the source

All research code is open-source. Clone the repos, run the simulations, verify the proofs.

View on GitHub
Related
Go deeper
6 AI Agents
52 TOPS Hailo-8
228 SQLite Databases
Simulation Engine
Education Platform
Compute Fleet