structured-decomp

StructuredDecompositions.jl: Sheaves on tree decompositions for FPT algorithms

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byplurigrid

View on GitHub Installation ↓

Best use case

structured-decomp is best used when you need a repeatable AI agent workflow instead of a one-off prompt.

StructuredDecompositions.jl: Sheaves on tree decompositions for FPT algorithms

Teams using structured-decomp should expect a more consistent output, faster repeated execution, less prompt rewriting.

When to use this skill

You want a reusable workflow that can be run more than once with consistent structure.

When not to use this skill

You only need a quick one-off answer and do not need a reusable workflow.
You cannot install or maintain the underlying files, dependencies, or repository context.

Installation

Claude Code / Cursor / Codex

$curl -o ~/.claude/skills/structured-decomp/SKILL.md --create-dirs "https://raw.githubusercontent.com/plurigrid/asi/main/ies/music-topos/.agents/skills/structured-decomp/SKILL.md"

Manual Installation

Download SKILL.md from GitHub
Place it in .claude/skills/structured-decomp/SKILL.md inside your project
Restart your AI agent — it will auto-discover the skill

How structured-decomp Compares

Feature / Agent	structured-decomp	Standard Approach
Platform Support	Not specified	Limited / Varies
Context Awareness	High	Baseline
Installation Complexity	Unknown	N/A

Frequently Asked Questions

What does this skill do?

StructuredDecompositions.jl: Sheaves on tree decompositions for FPT algorithms

Where can I find the source code?

You can find the source code on GitHub using the link provided at the top of the page.

SKILL.md Source

# Structured Decompositions Skill

## Core Concepts

**StrDecomp** = Functor `d: ∫G → C` where:
- ∫G = category of elements of shape graph
- C = target category (Graph, FinSet, etc.)

```julia
using StructuredDecompositions

# Create decomposition from graph
d = StrDecomp(graph)

# Access components
bags(d)           # Local substructures
adhesions(d)      # Overlaps
adhesionSpans(d)  # Span morphisms
```

## The 𝐃 Functor

Lifts decision problems to decomposition space:
```julia
# Define problem as functor
k_coloring(G) = homomorphisms(G, K_k)

# Lift and solve
solution = 𝐃(k_coloring, decomp, CoDecomposition)
(answer, _) = decide_sheaf_tree_shape(k_coloring, decomp)
```

## FPT Complexity

Runtime: O(f(width) × n) where width = max adhesion size

## GF(3) Triads

```
dmd-spectral (-1) ⊗ structured-decomp (0) ⊗ koopman-generator (+1) = 0 ✓
sheaf-cohomology (-1) ⊗ structured-decomp (0) ⊗ colimit-reconstruct (+1) = 0 ✓
```

## References

- Bumpus et al. arXiv:2207.06091
- algebraicjulia.github.io/StructuredDecompositions.jl

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