What is the primary use of the Geodesic Manifold skill?

It is designed for high-precision spatial calculations on spherical surfaces, such as calculating the shortest path between two points on Earth for flight or ship navigation.

How does the GF(3) trit assignment work?

It uses a ternary logic system (+1, 0, -1) to categorize tasks: +1 for generating paths, 0 for calculating transforms, and -1 for validating the optimality of the shortest path.

What mathematical models are included?

The skill covers the Haversine formula, Riemannian metric tensors, Christoffel symbols, spherical interpolation (Slerp), and manifold category theory concepts.

Does this skill support SQL databases?

Yes, it includes specific integration patterns for DuckDB using the spatial extension to perform geometric queries and manage geodesic route data.

Geodesic Manifold Geometry

Name: Geodesic Manifold Geometry
Author: plurigrid

byplurigrid

•

Data Science & ML

Calculates geodesic paths, spherical trigonometry, and Riemannian manifold metrics for complex navigation and spatial modeling.

This skill provides specialized mathematical capabilities for working with spherical geometry and Riemannian manifolds, specifically optimized for Earth-surface calculations. It enables Claude to compute high-precision great circle distances using the Haversine formula, generate interpolated waypoints for flight or shipping routes, and perform advanced differential geometry operations like calculating Christoffel symbols and metric tensors. By integrating with DuckDB Spatial and implementing GF(3) trit logic for path validation, it offers a robust framework for developers working on planetary-scale navigation, topological modeling, and quantum geography.

Key Features

01Riemannian metric tensor and Christoffel symbol computation for spherical surfaces

02Category theory modeling for manifold structures and fiber bundles

03Great Circle (Haversine) distance calculations for accurate Earth navigation

047 GitHub stars

05Geodesic waypoint generation with seed-based coloring and GF(3) validation

06DuckDB Spatial integration for SQL-based geographic data management

Use Cases

01Optimizing global flight paths and maritime shipping routes using great circle math

02Modeling physical or data phenomena on curved surfaces using differential geometry

03Building high-performance spatial databases for geographic information systems (GIS)

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi geodesic-manifold

For use in Claude.ai and ChatGPT

Download Skill