What are the dependencies for using this skill?

This skill requires Lean 4 and Mathlib4 v4.14.0 to perform full type-checking and proof verification.

Which mathematical domains are covered by this skill?

The skill covers Spectral Gaps, CRDT eventual consistency, CIEDE2000 color harmony, Pontryagin duality, and p-adic matching.

What is the primary purpose of the lean4-music-topos skill?

It provides a suite of machine-checked Lean 4 proofs for complex theorems spanning music theory, color science, distributed systems, and category theory.

Can I integrate these proofs into my existing software?

Yes, the skill supports Lean-to-Haskell and Lean-to-Wasm extraction, allowing you to use verified logic within production environments.

Does this skill help with AI and Machine Learning?

Yes, it includes formal proofs for preference learning convergence, neural network loss function bounds, and adversarial robustness certificates.

Lean 4 Music Topos Verification

Name: Lean 4 Music Topos Verification
Author: plurigrid

byplurigrid

•

Security & Testing

Formalizes and verifies complex mathematical theorems across music theory, color harmony, and distributed systems using Lean 4.

The lean4-music-topos skill provides a rigorous framework for the formal verification of Music Topos theorems, bridging high-level mathematical theory with practical software correctness. It includes over 14 specialized modules that provide machine-checked proofs for diverse domains, including spectral gap analysis in Blume-Capel models, eventual consistency in CRDTs, and perceptual color metrics using CIEDE2000. This skill is ideal for developers and researchers who need to validate the underlying logic of multi-agent systems, optimization algorithms, and categorical isomorphisms with absolute mathematical certainty.

Key Features

01Perceptual color space verification using CIEDE2000 metrics and p-adic matching logic.

02Proven correctness for Conflict-Free Replicated Data Types (CRDT) ensuring distributed consensus.

03Cross-domain proof orchestration with extraction capabilities to Haskell and WebAssembly.

04Formal guarantees for neural network preference learning and optimization convergence.

058 GitHub stars

06Comprehensive formalization of the Spectral Gap Theorem (λ₂ = 1/4) and mixing times.

Use Cases

01Proving convergence rates and adversarial robustness for AI preference learning models.

02Validating perceptual consistency and harmonic spacing in advanced color design software.

03Verifying the mathematical integrity of distributed consensus and synchronization algorithms.

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi lean4-music-topos

For use in Claude.ai and ChatGPT

Download Skill