structured-decomp

StructuredDecompositions.jl: Sheaves on tree decompositions for FPT algorithms.

Skill for Claude CodeCodex

Install

Getting it into your agent

One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.

agentmods
npx agentmods add skills/plurigrid/asi/structured-decomp
Any agent
npx skills add plurigrid/asi --skill structured-decomp
Clone the repo
git clone --depth 1 https://github.com/plurigrid/asi

Made for: Claude Code, Codex.

Per session 21 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 379 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. Scan, not verified.
Origin original No closer match found in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5 $0.00021 $0.00379
Opus 5 $0.00010 $0.00189
Sonnet 5 $0.00004 $0.00076
Haiku 4.5 $0.00002 $0.00038

Measured today against content hash 644cbf4fa759, method: parsed. Prices are Anthropic first-party input rates as of 2026-08-30, from the pricing page.

Security

Grade A, and why

structured-decomp scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured today.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

ies/music-topos/.agents/skills/structured-decomp/SKILL.md · 56 lines

What it actually says

Structured Decompositions Skill

Core Concepts

StrDecomp = Functor d: ∫G → C where:

  • ∫G = category of elements of shape graph
  • C = target category (Graph, FinSet, etc.)
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:

# 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
Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. today First seen · 56 lines · 21 tokens per session scan A 644cbf4fa759

Subscribe to this mod's changes

structured-decomp is a skill published in the GitHub repository plurigrid/asi (61 stars, last pushed 1mo ago), licensed MIT. It adds 21 tokens to every session and 379 once invoked, about $0.0001 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-09-01.

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