invariant-measure
Measure preserved by the flow
Packaged view
This page reorganizes the original catalog entry around fit, installability, and workflow context first. The original raw source lives below.
Install command
npx @skill-hub/cli install plurigrid-asi-invariant-measure
Repository
Best for
Primary workflow: Ship Full Stack.
Technical facets: Full Stack.
Target audience: Theoretical mathematicians or researchers specializing in advanced dynamical systems theory who are already deeply familiar with concepts like invariant measures, GF(3) algebra, and Möbius inversion..
License: Unknown.
Original source
Catalog source: SkillHub Club.
Repository owner: plurigrid.
This is still a mirrored public skill entry. Review the repository before installing into production workflows.
What it helps with
- Install invariant-measure into Claude Code, Codex CLI, Gemini CLI, or OpenCode workflows
- Review https://github.com/plurigrid/asi before adding invariant-measure to shared team environments
- Use invariant-measure for development workflows
Works across
Favorites: 0.
Sub-skills: 0.
Aggregator: No.
Original source / Raw SKILL.md
---
name: invariant-measure
description: Measure preserved by the flow
version: 1.0.0
---
# Invariant Measure
**Trit**: -1 (MINUS)
**Domain**: Dynamical Systems Theory
**Principle**: Measure preserved by the flow
## Overview
Invariant Measure is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
## Mathematical Definition
```
INVARIANT_MEASURE: 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** (MINUS): Sinks/absorbers
- **Conservation**: Σ trits ≡ 0 (mod 3) across skill triplets
## AlgebraicDynamics.jl Connection
```julia
using AlgebraicDynamics
# Invariant Measure 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**: invariant-measure
**Type**: Dynamical Systems / Invariant Measure
**Trit**: -1 (MINUS)
**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)
```