From Integer Primacy to Unlimited-Depth FHE
November 2024 to February 2026. A complete reimagining of computational foundations, culminating in unlimited-depth homomorphic encryption.
Foundations: Integer Primacy
The journey began with a fundamental question: What if we built computation on integers, not floating-point approximations?
QMNF Core (#02)
Quantum-Modular Numerical Framework foundations. Integer primacy axioms established.
View Innovation →CRT Foundations
Chinese Remainder Theorem formal verification. The mathematical bedrock.
View Proofs →AHOP Security
Augmented Homomorphic Orbit Problem. NIST Category 5 compliance foundations.
View Proofs →Core Innovations: Exact Arithmetic
The breakthroughs that made exact computation practical at scale.
K-Elimination (#05)
Exact RNS quotient recovery via single modular multiplication. The 70-year-old division bottleneck solved. 27 Lean4 theorems verified.
View Innovation →CRTBigInt (#06)
Dual-modulus CRT for ±2^126 range at 120ns performance. Weaponized wraparound architecture.
View Innovation →Shadow Entropy (#07)
CRT shadow entropy harvesting. NIST-compliant randomness from division remainders.
Learn More →Mathematical Engines: Transcendentals & Networks
Extending exact arithmetic to transcendental functions and neural networks.
Pade Engine (#08)
Pade approximation engine for transcendental functions. Exact beyond polynomials.
View Innovation →Persistent Montgomery (#10)
Persistent Montgomery multiplication for modular arithmetic optimization.
View Innovation →Integer NN (#11)
Integer-only neural networks. Zero float operations. Exact gradients.
View Innovation →RNS-Net
Residue Number System Neural Networks. Weights and activations operate in residue channels for massively parallel exact training.
View Innovation →One-Shot Learning
Single-example learning enabled by perfect gradient preservation in integer arithmetic.
View Innovation →NextGen Rational
Advanced p/q arithmetic with GCD-based reduction. Foundation for transcendental approximations.
View Innovation →Advanced Systems: Scalability & Parallelism
Building systems that scale from embedded devices to cloud infrastructure.
Cyclotomic Phase (#12)
Cyclotomic phase computation for RLWE (Ring Learning With Errors).
View Innovation →MQ-ReLU (#13)
Modular Quantized ReLU for integer neural networks. Exact nonlinearity.
View Innovation →Binary GCD (#14)
Binary GCD algorithm. Exact greatest common divisor without division.
View Innovation →PLMG Rails (#15)
Prime Ladder Mixed Gear system for tier expansion. Adaptive scaling.
View Innovation →Dual Codex Gear Manifold (#16)
The seed that unlocked unlimited depth. Dual-tier adaptive precision with gear-based modular expansion. Enabled the Clockwork Prime breakthrough.
View Innovation →Foundations: Post-Quantum Security
Building towards practical homomorphic encryption.
Grover Swarm (#17)
Grover swarm optimization for parameter search. Quantum-inspired classical algorithms.
View Innovation →Unlimited Depth: The Breakthrough
The culmination of 15 months of solo research. Unlimited computational depth achieved.
Clockwork Prime (#23)
Prime moduli emerge like clockwork via Bertrand's Postulate. Eliminates coprimality checks. Deterministic tier expansion.
View Innovation →Clockwork Bootstrap
Ultra-efficient bootstrap mechanism. Enables unlimited depth. 46 automatic refreshes in 100 operations. The breakthrough that changes everything.
Learn More →Bootstrap-Free FHE (#24)
Symmetric mode with zero bootstrapping required. Original vision realized.
View Innovation →Real-Time FHE (#25)
Sub-millisecond homomorphic operations for live computation. Production-ready performance.
View Innovation →The Impact
From Theory to Production
15 months transformed fundamental mathematical research into a production-ready system with real-world applications.
Formally Verified
24 out of 24 theorems verified in Coq and Lean4. Every innovation built on proven mathematical foundations.
Unlimited Depth Achieved
The computational depth ceiling has been eliminated. Homomorphic encryption is now practical for deep circuits and complex analytics.