How does it ensure the reliability of state transitions?

It uses Narya type theory to verify bridge types and observational equality, ensuring that every 'hop' from one conceptual state to another is logically sound and follows the triangle inequality.

What is the primary purpose of the Glass Hopping skill?

It provides a formal mathematical framework for Claude to navigate and connect different conceptual 'worlds' or domains using directed relations and type-verified transitions.

What is the role of GF(3) in this skill?

GF(3) conservation acts as a triadic balancing mechanism, assigning roles (Validator, Coordinator, Generator) to ensure that conceptual moves are balanced and logically conserved.

Does this skill integrate with other plurigrid tools?

Yes, it is designed to interleave with related skills like glass-bead-game, world-hopping, and ordered-locale to provide a comprehensive topological approach to AI reasoning.

Glass Hopping Navigation

Name: Glass Hopping Navigation
Author: plurigrid

byplurigrid

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Data Science & ML

Navigates complex conceptual possibility spaces using type-theoretic bridge transitions and ordered locale structures.

Glass Hopping is a sophisticated synthesis of conceptual mapping and state-space navigation designed for Claude. By treating glass beads as open sets within an ordered locale and world hops as directed bridge types, it provides a formal framework for transitioning between different domains—such as mathematics, music, and philosophy—while maintaining triadic balance (GF(3)). It utilizes Narya type theory to verify that every transition respects observational equality and the triangle inequality, providing a rigorous yet creative path through multi-dimensional concept spaces for researchers and advanced system designers.

Key Features

01GF(3) Triadic Conservation: Ensures logical balance between validator, coordinator, and generator roles.

02Ordered Locale Navigation: Uses directed (≪) relations to structure transitions between conceptual worlds.

032 GitHub stars

04Glass Bead Synthesis: Maps domain-specific concepts as opens in a complete Heyting algebra for conceptual meet/join operations.

05Narya-Verified Bridges: Formally checks every hop for type safety and observational equality using bridge types.

06Path Optimization: Automatically enforces the triangle inequality to minimize bridge chain lengths and ensure navigation elegance.

Use Cases

01Formal verification of conceptual shifts between disparate academic or technical domains.

02Managing multi-agent state transitions in complex simulation environments using sheaf theory.

03Automating structured knowledge synthesis and discovery via category theory and formal logic.

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi glass-hopping

For use in Claude.ai and ChatGPT

Download Skill