initial-value-problem
Existence and uniqueness of solutions to ODEs with initial conditions
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-initial-value-problem
Repository
Skill path: skills/initial-value-problem
Existence and uniqueness of solutions to ODEs with initial conditions
Open repositoryBest for
Primary workflow: Ship Full Stack.
Technical facets: Full Stack.
Target audience: everyone.
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 initial-value-problem into Claude Code, Codex CLI, Gemini CLI, or OpenCode workflows
- Review https://github.com/plurigrid/asi before adding initial-value-problem to shared team environments
- Use initial-value-problem for development workflows
Works across
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Sub-skills: 0.
Aggregator: No.
Original source / Raw SKILL.md
---
name: initial-value-problem
description: Existence and uniqueness of solutions to ODEs with initial conditions
version: 1.0.0
---
# Initial Value Problem
**Trit**: -1 (MINUS)
**Domain**: Dynamical Systems Theory
**Principle**: Existence and uniqueness of solutions to ODEs with initial conditions
## Overview
Initial Value Problem is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
## Mathematical Definition
```
INITIAL_VALUE_PROBLEM: 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
# Initial Value Problem 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**: initial-value-problem
**Type**: Dynamical Systems / Initial Value Problem
**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)
```