What is Möbius filtering in this context?

Möbius filtering is used to eliminate backtracking paths (composites) from a sequence, keeping only the 'prime' geodesic paths for valid logical transitions.

Why does this skill use non-backtracking geodesics?

Non-backtracking geodesics, or prime paths, prevent state revisiting in computation, ensuring that each step in the reduction is distinct and squarefree.

How is GF(3) conservation applied?

It acts as a local checksum where the sum of trits in a gadget must equal zero modulo 3, ensuring the local logic remains consistent with the global 3-SAT problem.

What is a 3-MATCH gadget?

A 3-MATCH gadget is a local constraint enforcement mechanism that uses color-matching and 3-adic valuation to map logical variables to graph nodes.

Three-Match SAT Solver Gadgets

Name: Three-Match SAT Solver Gadgets
Author: plurigrid

byplurigrid

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データサイエンスとML

Implements 3-SAT reductions via colored subgraph isomorphism and non-backtracking geodesics for topological computing.

The Three-Match skill provides a sophisticated framework for reducing 3-SAT problems to colored subgraph isomorphisms using specialized topological gadgets. By leveraging non-backtracking geodesics, Möbius inversion filtering, and GF(3) conservation, it ensures that satisfying local constraints guarantees global correctness. This tool is specifically designed for developers and researchers working within the 'topological chemputer' architecture, providing a robust mathematical foundation for complex logical reductions through graph theory and prime path analysis.

主な機能

01Enforces GF(3) conservation for local constraint verification

027 GitHub stars

03Applies Möbius inversion filtering to cancel out composite backtracking paths

04Provides seed-chained gadget sequences for complex problem modeling

05Reduces 3-SAT problems to 3-coloring and colored subgraph isomorphisms

06Generates non-backtracking geodesics to ensure unique state paths

ユースケース

01Algorithmic research into prime paths and Ramanujan spectral gaps

02Transforming logical constraint satisfaction problems into topological graph structures

03Formal verification of complex systems using colored subgraph isomorphism

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi three-match

For use in Claude.ai and ChatGPT

Download Skill