QMNF

Quantum Modular Numerical Framework

28 formally verified innovations. From integer primacy to unlimited depth.

15 months. Solo research. 24/24 theorems verified.
#23 New

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.

Generation 6 Lean4 Coq View Proof →
#24 New

Bootstrap-Free FHE

Symmetric mode with zero bootstrapping required.

Shared-key homomorphic encryption without refresh operations. Enables unlimited depth in symmetric settings.

Generation 6 Lean4 View Proofs →
#25 New

Real-Time FHE

Sub-millisecond homomorphic operations for live computation.

Core operations complete in under 1ms. Enables real-time encrypted analytics and streaming computation.

Generation 6 Lean4 View Benchmarks →
Latest Feb 2026

Clockwork Bootstrap

Unlimited depth via ultra-efficient bootstrapping.

Enables public-key mode with unlimited computational depth. Automatic refresh mechanism maintains noise budget indefinitely.

Generation 6 In Development Learn More →
#22

RayRam

Ray-RAM architecture for parallel homomorphic computation.

Distributed memory architecture enabling parallel homomorphic operations across multiple cores.

Generation 5 Lean4
#21

MANA

MANA framework - security architecture.

Comprehensive security framework for homomorphic encryption systems with formal threat modeling.

Generation 5 Lean4
#20

GSO

Generalized Sigma Orbit for noise management.

Advanced noise tracking and management system for maintaining noise budgets.

Generation 5 Lean4
#19

Time Crystal

Time crystal computations for deterministic scheduling.

Deterministic timing mechanisms ensuring consistent performance across platforms.

Generation 5 Lean4
#18

WASSAN

WASSAN security proofs for post-quantum resistance.

Formal security proofs demonstrating resistance to quantum attacks.

Generation 5 Lean4 View Proofs →
#17

Grover Swarm

Grover swarm optimization for parameter search.

Quantum-inspired optimization for finding optimal parameters.

Generation 5 Lean4
#16 Breakthrough

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.

Generation 4 Lean4
#15

PLMG Rails

Prime Ladder Mixed Gear system for tier expansion.

Systematic approach to expanding computational capacity through prime moduli.

Generation 4 Lean4
#14

Binary GCD

Binary GCD algorithm - exact without division.

Efficient greatest common divisor computation using only shifts and subtractions.

Generation 4 Lean4
#13

MQ-ReLU

Modular Quantized ReLU for integer neural networks.

Activation function enabling neural networks with zero floating-point operations.

Generation 4 Lean4 Coq
#12

Cyclotomic Phase

Cyclotomic phase computation for RLWE.

Phase calculations for ring learning with errors cryptography.

Generation 4 Lean4
#11

Integer NN

Integer-only neural networks - zero float operations.

Complete neural network implementation using only integer arithmetic for exact computation.

Generation 3 Lean4
Gen 3

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.

Generation 3 Lean4
Gen 3

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.

Generation 3 Lean4
Gen 3

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.

Generation 3 Lean4 Coq
#10

Persistent Montgomery

Persistent Montgomery multiplication for modular arithmetic.

Efficient modular multiplication with persistent state across operations.

Generation 3 Lean4 Coq
#09

Mobius Int

Mobius function integration for number-theoretic transforms.

Number-theoretic transformations using Mobius function properties.

Generation 3 Lean4
#08

Pade Engine

Pade approximation engine for transcendental functions.

Rational approximations of transcendental functions using integer arithmetic.

Generation 3 Lean4
#07

Shadow Entropy

CRT shadow entropy harvesting. NIST-compliant randomness.

Harvesting cryptographic randomness from division remainders. Passes all 15 NIST statistical tests.

Generation 2 Lean4 Coq Learn More →
#06

CRTBigInt

Dual-modulus CRT for ±2^126 range at 120ns performance.

Two-prime Chinese Remainder Theorem providing massive range with near-native speed.

Generation 2 Lean4 Coq
#05

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.

Generation 2 Lean4 Coq View Proofs →
#02

QMNF Core

Quantum-Modular Numerical Framework foundations.

Integer primacy axioms. Zero floating-point mandate. Deterministic computation across all platforms.

Generation 1 Lean4 Coq
NIST

AHOP Security

Augmented Homomorphic Orbit Problem - NIST Category 5.

256-bit security (AES-256 equivalent). Exceeds ML-KEM-1024 requirements.

Generation 1 Lean4 View Proofs →
CRT

CRT Foundations

Chinese Remainder Theorem formal verification.

Complete formal verification of CRT bijectivity, reconstruction, and modular arithmetic properties.

Generation 1 Lean4 Coq
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