Does it support the 6-functor formalism?

Yes, it implements and verifies the 6-functor formalism (f*, f_*, f!, f^!, tensor, Hom) and ensures the projection formula holds.

What is the difference between liquid and solid modules in this skill?

Liquid modules handle p-liquid norms for analytic structures, while solid modules provide completion via double-dual for more rigid algebraic structures.

What is the Scholze-Clausen condensed mathematics framework?

It is a modern mathematical approach that replaces topological spaces with 'condensed sets' to ensure that algebraic operations like tensor products behave well with topology.

How does this skill assist in BCI development?

It provides the topological and algebraic foundation required for 'chemputer' modeling and Brain-Computer Interface logic using GF(3) triads and ergodic coordinators.

Condensed Mathematics Framework

Name: Condensed Mathematics Framework
Author: plurigrid

byplurigrid

•

Data Science & ML

Unifies topology and algebra using the Scholze-Clausen framework to model condensed sets and liquid vector spaces.

The Condensed Mathematics skill brings the advanced mathematical theories of Peter Scholze and Dustin Clausen to Claude, providing a formal framework for bridging the gap between topology and algebra. By implementing condensed sets as sheaves on compact Hausdorff spaces, this skill enables precise modeling of liquid vector spaces, solid modules, and the 6-functor formalism. It is particularly useful for researchers and developers working on high-level AI architectures, Brain-Computer Interfaces (BCI), and complex algebraic geometry where traditional topological spaces fail to provide exactness in tensor products.

Key Features

01Support for analytic ring structures including discrete, liquid, and solid types

02Condensed set implementation using sheaves on profinite probes

03Liquid and solid vector space modeling with verified p-liquid norms

047 GitHub stars

05Verified Kunneth exactness for condensed abelian groups

06Full 6-functor formalism support including projection formulas

Use Cases

01Verifying complex sheaf conditions and tensor products in condensed categories

02Modeling Brain-Computer Interface logic using topological 'chemputer' principles

03Formalizing topological-algebraic interactions in advanced AI research

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi condensed-mathematics

For use in Claude.ai and ChatGPT

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