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plurigrid/asi

semi-conjugacy

Surjective map intertwining two dynamical systems

First seen Jun 20, 2026

Installation

$ npx skills add plurigrid/asi --skill semi-conjugacy
View on skills.sh ↗ GitHub repository ↗

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More details

Agent compatibility

Declared targets from SKILL.md / docs. Unmarked agents are not listed — the skill may still install via the CLI.

Claude Code Not declared
Cursor Not declared
Codex Not declared
GitHub Copilot Not declared
Windsurf Not declared
Gemini CLI Not declared
Cline Not declared
OpenCode Not declared

Also listed on

Alternate registries and mirrors of this skill.

Repository health

Stars 62
License LICENSE
Default branch main
Open issues 3
Status Active

Package contents

Files included with this skill beyond the listing page.

  • skill md SKILL.md 2,074 B
  • docs SUMMARY.md 71 B

History

  1. First seen on skills.sh
  2. First recorded snapshot · 1 installs

SKILL.md

Semi-conjugacy

Trit: 1 (PLUS) Domain: Dynamical Systems Theory Principle: Surjective map intertwining two dynamical systems

Overview

Semi-conjugacy is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.

Mathematical Definition

SEMI-CONJUGACY: Phase space × Time → Phase space

Key Properties

  1. Local behavior: Analysis near equilibria and invariant sets
  2. Global structure: Long-term dynamics and limit sets
  3. Bifurcations: Parameter-dependent qualitative changes
  4. Stability: Robustness under perturbation

Integration with GF(3)

This skill participates in triadic composition:

  • Trit 1 (PLUS): Sources/generators
  • Conservation: Σ trits ≡ 0 (mod 3) across skill triplets

AlgebraicDynamics.jl Connection

using AlgebraicDynamics

# Semi-conjugacy as compositional dynamical system
# Implements oapply for resource-sharing machines

Related Skills

  • equilibrium (trit 0)
  • stability (trit +1)
  • bifurcation (trit +1)
  • attractor (trit +1)
  • lyapunov-function (trit -1)

Skill Name: semi-conjugacy Type: Dynamical Systems / Semi-conjugacy Trit: 1 (PLUS) GF(3): Conserved in triplet composition

Non-Backtracking Geodesic Qualification

Condition: μ(n) ≠ 0 (Möbius squarefree)

This skill is qualified for non-backtracking geodesic traversal:

  1. Prime Path: No state revisited in skill invocation chain
  2. Möbius Filter: Composite paths (backtracking) cancel via μ-inversion
  3. GF(3) Conservation: Trit sum ≡ 0 (mod 3) across skill triplets
  4. Spectral Gap: Ramanujan bound λ₂ ≤ 2√(k-1) for k-regular expansion
Geodesic Invariant:
  ∀ path P: backtrack(P) = ∅ ⟹ μ(|P|) ≠ 0
  
Möbius Inversion:
  f(n) = Σ_{d|n} g(d) ⟹ g(n) = Σ_{d|n} μ(n/d) f(d)