What is a 3-MATCH gadget?

It is a mathematical structure that enforces local constraints (color matching) to solve 3-SAT problems by mapping them to colored subgraph isomorphism instances.

Can this skill be used for software optimization?

Yes, it applies 3-MATCH principles to inline caching for type-stable path selection, which can provide massive speedups in dynamic dispatch environments like Julia.

What is GF(3) conservation?

GF(3) conservation ensures that the sum of 'trits' (-1, 0, 1) in a gadget triad always equals zero modulo 3, maintaining compositional coherence across the graph.

How does Möbius filtering work in this skill?

It uses the Möbius function to filter out backtracking paths (composites) in a sequence, ensuring only prime, non-backtracking geodesics are processed.

Three-Match 3-SAT Gadget

Name: Three-Match 3-SAT Gadget
Author: plurigrid

byplurigrid

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Data Science & ML

Reduces 3-SAT problems to colored subgraph isomorphism using local geodesic constraints and GF(3) conservation.

About

The Three-Match skill provides a rigorous mathematical framework for reducing 3-SAT problems to colored subgraph isomorphism through specialized gadgets. By leveraging non-backtracking geodesics, Möbius inversion filtering, and GF(3) conservation, it ensures global correctness through local constraint satisfaction. This skill is ideal for researchers and developers working in graph theory, algebraic logic, and high-performance computing optimizations, such as type-stable path caching in Julia systems.

Key Features

2 GitHub stars
Automated 3-adic valuation checks for local constraints
GF(3) conservation verification (sum ≡ 0 mod 3)
Non-backtracking geodesic path generation with Möbius filtering
Correct-by-construction inline caching for type-stable paths
3-SAT to colored subgraph isomorphism reduction gadgets

Use Cases

Optimizing high-performance path traversal via zero-cost type-stable caching
Transforming complex boolean satisfiability problems into graph isomorphism instances
Implementing non-backtracking prime paths for topological computing research

About

Key Features

2 GitHub stars
Automated 3-adic valuation checks for local constraints
GF(3) conservation verification (sum ≡ 0 mod 3)
Non-backtracking geodesic path generation with Möbius filtering
Correct-by-construction inline caching for type-stable paths
3-SAT to colored subgraph isomorphism reduction gadgets

Use Cases

Optimizing high-performance path traversal via zero-cost type-stable caching
Transforming complex boolean satisfiability problems into graph isomorphism instances
Implementing non-backtracking prime paths for topological computing research