Can this skill be used for standard vector calculus?

Yes, it generalizes standard vector calculus—including gradient, curl, and divergence—into the universal language of differential forms using the exterior derivative.

What are signal manifolds in this context?

Signal manifolds are geometric representations of high-dimensional time-series or sensor data, such as BCI signals, where topological features represent underlying system states and dynamics.

How does it verify mathematical correctness?

The skill computationally verifies the fundamental de Rham property where the square of the exterior derivative is zero (d^2 = 0), ensuring the integrity of the cohomology chain.

Is this compatible with other topological analysis tools?

Yes, it is designed to integrate with persistent homology and spectral methods, forming a complete analytical framework for topological chemputing and manifold learning.

de Rham Cohomology for Signal Manifolds

Name: de Rham Cohomology for Signal Manifolds
Author: plurigrid

byplurigrid

•

Data Science & ML

Implements differential forms and exterior calculus on signal manifolds to bridge differential geometry and topological data analysis.

This skill provides a robust computational framework for the de Rham complex, allowing Claude to manipulate k-forms, compute exterior derivatives, and apply Hodge star operators to complex signal data. By leveraging Hodge decomposition and the Hodge-Laplacian, it identifies harmonic representatives and classifies cohomology classes within high-dimensional manifolds. It is specifically designed for advanced signal processing applications, such as Brain-Computer Interface (BCI) orchestration, where the underlying topological structure of data provides critical insights into system behavior and stability.

Key Features

017 GitHub stars

02Calculate the Hodge-Laplacian for manifold-based signal decomposition and curvature analysis

03Verify the fundamental property of the de Rham complex (d^2 = 0) with computational precision

04Compute exterior derivatives and wedge products for antisymmetric k-form manipulation

05Classify cohomology types including closed, exact, and harmonic form identification

06Apply Hodge star operators and metric duality for advanced harmonic analysis

Use Cases

01Analyzing high-dimensional BCI signal curvature and topological field strength

02Implementing signal/noise separation through Hodge decomposition and relative homology

03Identifying topological invariants and Betti numbers in complex sensor data manifolds

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi derham-cohomology

For use in Claude.ai and ChatGPT

Download Skill