What does GF(3) conservation mean in this context?

GF(3) conservation ensures that the sum of values (trits) in a gadget equals zero modulo 3, which acts as a mathematical check to maintain algebraic balance and correctness across the subgraph.

What is the primary purpose of the Three-Match skill?

It reduces 3-SAT problems to 3-coloring constraints using topological gadgets, allowing Claude to solve complex logic problems by ensuring global correctness through local validation.

How does Möbius filtering improve logic processing?

It uses a back-and-forth cancellation mechanism based on the Möbius function to filter out backtracking and composite paths, ensuring only prime, non-repeating geodesics are processed.

What is a non-backtracking geodesic?

It is a path through a graph or color space where no state is revisited, modeled after prime paths in number theory where the Möbius product is non-zero.

Three-Match 3-SAT Solver

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

byplurigrid

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Data Science & ML

Reduces 3-SAT problems to colored subgraph isomorphism using non-backtracking geodesics and Möbius filtering.

About

The Three-Match skill implements a rigorous mathematical framework for solving Boolean satisfiability (3-SAT) through topological reduction. By leveraging colored subgraph isomorphism, GF(3) conservation, and Möbius inversion, it ensures that local constraints satisfy global correctness by construction. This skill is highly specialized for developers and researchers working with complex graph-based logic, prime path geodesics, and non-backtracking algorithms where computational correctness must be algebraically guaranteed.

Key Features

2 GitHub stars
Möbius inversion filtering to eliminate backtracking and composite states
3-SAT reduction to 3-coloring via specialized ThreeMatch gadgets
Non-backtracking geodesic generation to ensure prime pathing
GF(3) modular conservation for automated verification of local constraints
3-adic valuation analysis for color matching at specific depths

Use Cases

Generating prime, non-backtracking paths for state machines and network routing
Verifying complex Boolean logic through topological graph reduction
Implementing self-correcting logic gadgets in decentralized computing environments

About

Key Features

2 GitHub stars
Möbius inversion filtering to eliminate backtracking and composite states
3-SAT reduction to 3-coloring via specialized ThreeMatch gadgets
Non-backtracking geodesic generation to ensure prime pathing
GF(3) modular conservation for automated verification of local constraints
3-adic valuation analysis for color matching at specific depths

Use Cases

Generating prime, non-backtracking paths for state machines and network routing
Verifying complex Boolean logic through topological graph reduction
Implementing self-correcting logic gadgets in decentralized computing environments