How does the involution principle work?

It follows the mathematical rule ι ∘ ι = id. This means applying the transformation once moves the system to an 'inverted' or 'other' perspective, while applying it a second time returns the system exactly to its original state.

What is 'unworlding' in this context?

Unworlding is the process of extracting the underlying frame-invariant structure from an interaction, allowing the core pattern to be applied across different contexts regardless of the specific evaluation frame or observer.

What is GF(3) conservation?

GF(3) conservation is a mathematical constraint used to ensure that in a triadic system—such as three agents or three primary colors—the sum of the states remains balanced, facilitating a stable Nash equilibrium.

How does this skill use Perceptual Control Theory (PCT)?

The skill implements hierarchical control where each level (from intensity to program) controls its own perception rather than its output, minimizing the error between the reference state and the observed state.

Unworlding Involution Dynamics

Name: Unworlding Involution Dynamics
Author: plurigrid

byplurigrid

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数据科学与机器学习

Extracts frame-invariant patterns and self-inverse derivation structures from interaction dynamics using GF(3) conservation.

Unworlding Involution is a specialized skill designed to identify and implement frame-invariant structures within complex interaction systems. By applying the mathematical principle of involution (ι ∘ ι = id), it allows for the extraction of a 'self-structure' that remains constant regardless of the observer's perspective. This skill is particularly useful for modeling best-response dynamics in multi-agent systems, ensuring structural harmony through GF(3) conservation, and implementing Perceptual Control Theory (PCT) where systems minimize the error between their internal perceptions and external reference states.

主要功能

01Nash equilibrium modeling for multi-agent systems

027 GitHub stars

03Frame-invariant pattern extraction (Unworlding)

04GF(3) conserved best-response dynamics

05Hierarchical Perceptual Control Theory (PCT) implementation

06Self-inverse derivation logic (ι ∘ ι = id)

使用场景

01Creating mathematically balanced triadic color systems and UI themes

02Designing self-stabilizing multi-agent communication protocols

03Modeling equilibrium states in decentralized game theory environments

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi unworlding-involution

For use in Claude.ai and ChatGPT

Download Skill