Clockwork Prime
Prime moduli emerge like clockwork via Bertrand's Postulate.
Eliminates coprimality checks. Tier expansion is deterministic. Uses Garner's algorithm as generalized K-Elimination.
Bootstrap-Free FHE
Symmetric mode with zero bootstrapping required.
Shared-key homomorphic encryption without refresh operations. Enables unlimited depth in symmetric settings.
Real-Time FHE
Sub-millisecond homomorphic operations for live computation.
Core operations complete in under 1ms. Enables real-time encrypted analytics and streaming computation.
Clockwork Bootstrap
Unlimited depth via ultra-efficient bootstrapping.
Enables public-key mode with unlimited computational depth. Automatic refresh mechanism maintains noise budget indefinitely.
RayRam
Ray-RAM architecture for parallel homomorphic computation.
Distributed memory architecture enabling parallel homomorphic operations across multiple cores.
MANA
MANA framework - security architecture.
Comprehensive security framework for homomorphic encryption systems with formal threat modeling.
GSO
Generalized Sigma Orbit for noise management.
Advanced noise tracking and management system for maintaining noise budgets.
Time Crystal
Time crystal computations for deterministic scheduling.
Deterministic timing mechanisms ensuring consistent performance across platforms.
WASSAN
WASSAN security proofs for post-quantum resistance.
Formal security proofs demonstrating resistance to quantum attacks.
Grover Swarm
Grover swarm optimization for parameter search.
Quantum-inspired optimization for finding optimal parameters.
Dual Codex Gear Manifold
The seed that unlocked unlimited depth through Clockwork Prime.
Dual-tier adaptive precision architecture with gear-based modular expansion. The foundational structure that enabled Bertrand's Postulate application for deterministic prime selection.
PLMG Rails
Prime Ladder Mixed Gear system for tier expansion.
Systematic approach to expanding computational capacity through prime moduli.
Binary GCD
Binary GCD algorithm - exact without division.
Efficient greatest common divisor computation using only shifts and subtractions.
MQ-ReLU
Modular Quantized ReLU for integer neural networks.
Activation function enabling neural networks with zero floating-point operations.
Cyclotomic Phase
Cyclotomic phase computation for RLWE.
Phase calculations for ring learning with errors cryptography.
Integer NN
Integer-only neural networks - zero float operations.
Complete neural network implementation using only integer arithmetic for exact computation.
RNS-Net
Residue Number System Neural Networks for exact deep learning.
Neural networks operating in RNS space. Weights and activations live in residue channels, enabling massively parallel exact training without gradient quantization noise.
One-Shot Learning
Single-example learning via exact gradient computation.
Integer neural networks enable perfect gradient preservation, allowing network updates from single training examples without accumulated error.
NextGen Rational
Advanced rational arithmetic with automatic simplification.
Enhanced p/q arithmetic with GCD-based reduction, supporting arbitrary precision numerators and denominators. Foundation for transcendental approximations.
Persistent Montgomery
Persistent Montgomery multiplication for modular arithmetic.
Efficient modular multiplication with persistent state across operations.
Mobius Int
Mobius function integration for number-theoretic transforms.
Number-theoretic transformations using Mobius function properties.
Pade Engine
Pade approximation engine for transcendental functions.
Rational approximations of transcendental functions using integer arithmetic.
Shadow Entropy
CRT shadow entropy harvesting. NIST-compliant randomness.
Harvesting cryptographic randomness from division remainders. Passes all 15 NIST statistical tests.
CRTBigInt
Dual-modulus CRT for ±2^126 range at 120ns performance.
Two-prime Chinese Remainder Theorem providing massive range with near-native speed.
K-Elimination
Exact RNS quotient recovery via single modular multiplication.
Foundational innovation. Computes exact quotient k = floor(X/M) in O(1) per channel. 27 Lean4 theorems verified.
QMNF Core
Quantum-Modular Numerical Framework foundations.
Integer primacy axioms. Zero floating-point mandate. Deterministic computation across all platforms.
AHOP Security
Augmented Homomorphic Orbit Problem - NIST Category 5.
256-bit security (AES-256 equivalent). Exceeds ML-KEM-1024 requirements.
CRT Foundations
Chinese Remainder Theorem formal verification.
Complete formal verification of CRT bijectivity, reconstruction, and modular arithmetic properties.