What kind of mathematical functions does this skill utilize?

It primarily uses the Möbius function for numerical inversion and contravariant functors for duality graph generation.

How does this skill integrate with the Sparsification Spine?

It targets Layer 5 (Inversion/Duality), providing the mathematical framework to fill the critical gap in mapping structures back to their origin seeds.

What is the primary purpose of the Möbius Color Duality skill?

It performs backward mapping to recover local structural seeds from global color distributions, effectively inverting the generation process in topological data structures.

Does it support ternary logic systems?

Yes, it includes specialized support for GF(3) ternary extensions via the TriadicColorInverter class.

Möbius Color Duality

Name: Möbius Color Duality
Author: plurigrid

byplurigrid

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Data Science & ML

Recovers local structural seeds from global color distributions using Möbius inversion and topological duality.

About

The Möbius Color Duality skill enables Claude to perform complex backward mapping within topological structures, specifically addressing the inversion gap in the Amp thread corpus. By implementing numerical Möbius inversion and GF(3) triadic color extensions, it allows the system to move from global aggregates back to local seeds. This is essential for workflows involving sparsification spines, ACSet ontologies, and contravariant functor structures where structural recovery and duality are required for complete system synthesis.

Key Features

Numerical Möbius inversion for high-fidelity color space recovery
GF(3) triadic color extension for ternary state management
Automated recovery of original seeds from complex global aggregates
Sparsification spine integration for Layer 5 inversion tasks
Duality graph generation using contravariant functor logic
2 GitHub stars

Use Cases

Closing the critical 1.6% inversion gap in topological corpus analysis
Mapping triadic color distributions to hierarchical ontologies
Inverting synthetic generation processes to identify underlying data seeds

About

Key Features

Numerical Möbius inversion for high-fidelity color space recovery
GF(3) triadic color extension for ternary state management
Automated recovery of original seeds from complex global aggregates
Sparsification spine integration for Layer 5 inversion tasks
Duality graph generation using contravariant functor logic
2 GitHub stars

Use Cases

Closing the critical 1.6% inversion gap in topological corpus analysis
Mapping triadic color distributions to hierarchical ontologies
Inverting synthetic generation processes to identify underlying data seeds