What is an operad in the context of this skill?

An operad is a mathematical structure that models operations with multiple inputs and a single output, providing a rigorous framework for hierarchical substitution and composition.

How does the GF(3) triad integration work?

It utilizes a balanced ternary logic (-1, 0, +1) to ensure that combined operations maintain structural equilibrium and algebraic consistency within the system.

Can I use this for general software architecture?

Yes, while mathematically grounded, it is highly effective for designing any modular software system where components must be composed according to strict type or 'color' rules.

What is the 'Little Disks' operad used for?

In this skill, it models configuration spaces where objects cannot overlap, which is useful for 2D field theories, layout engines, and topological data analysis.

Operad Compose

Name: Operad Compose
Author: plurigrid

byplurigrid

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データサイエンスとML

Facilitates structured generation and composition of complex multi-input operations using colored operads and category theory principles.

概要

Operad Compose is a specialized Claude Code skill designed for modeling and executing structured substitution and composition patterns. Built on the mathematical framework of colored operads, it allows users to define, compose, and visualize complex operations across domains like generative music, topology, and concurrent logic. It is an essential tool for developers and researchers working on modular AI architectures, formal verification, and any system where compositional coherence and structural integrity are paramount.

主な機能

Automates verification of operadic associativity and unit properties
Supports GF(3) triadic logic for ensuring compositional coherence
Implements colored operadic substitution for n-ary operations
Visualizes operadic trees and complex structural mapping
2 GitHub stars
Integrates with Little Disks (E2) and May operad frameworks

ユースケース

Modeling concurrent systems and loop spaces in topological research
Generating modular musical structures via the Rubato Composer framework
Orchestrating AI skill compositions with guaranteed mathematical integrity

概要

主な機能

Automates verification of operadic associativity and unit properties
Supports GF(3) triadic logic for ensuring compositional coherence
Implements colored operadic substitution for n-ary operations
Visualizes operadic trees and complex structural mapping
2 GitHub stars
Integrates with Little Disks (E2) and May operad frameworks

ユースケース

Modeling concurrent systems and loop spaces in topological research
Generating modular musical structures via the Rubato Composer framework
Orchestrating AI skill compositions with guaranteed mathematical integrity