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.
npx skills add curiositech/some_claude_skills --skill knot-theory-educatorgit clone --depth 1 https://github.com/curiositech/some_claude_skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/curiositech/some_claude_skills/knot-theory-educator)<a href="https://agentmods.dev/skills/curiositech/some_claude_skills/knot-theory-educator"><img src="https://agentmods.dev/badge/skills/curiositech/some_claude_skills/knot-theory-educator/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/curiositech/some_claude_skills/knot-theory-educator"><img src="https://agentmods.dev/badge/skills/curiositech/some_claude_skills/knot-theory-educator.svg" alt="Reviewed on agentmods" width="80" height="20"></a>- NVIDIA SkillSpector pass
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.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00096 | $0.02673 |
| Opus 5 | $0.00048 | $0.01337 |
| Sonnet 5 | $0.00019 | $0.00535 |
| Haiku 4.5 | $0.00010 | $0.00267 |
Grade A, and why
knot-theory-educator 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 7d ago.
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.
How it starts
The opening of the file, as written. The whole thing — 317 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Knot Theory Educator
Transform abstract braid theory and topological concepts into intuitive, visual, interactive learning experiences. This skill bridges the gap between formal mathematics and genuine understanding.
When to Use
✅ Use for:
- Creating visual explanations of braid generators (σ₁, σ₂, etc.)
- Building step-wise animations showing crossing sequences
- Designing explainer cards for mathematical terms
- Translating group theory concepts into physical intuition
- Creating interactive demonstrations of 2-strand vs 3-strand differences
- Illustrating why certain operations commute (or don't)
❌ NOT for:
- Pure computation of knot invariants (Jones polynomial, etc.)
- Academic research-level proofs
- General mathematics tutoring unrelated to braids/knots
- Software architecture decisions for visualization frameworks
Core Principle: The Physical-First Approach
Shibboleth: Experts explain braids through physical manipulation first, notation second.
Novice approach: "σ₁ is a generator of B₃ satisfying..."
Expert approach: "Imagine holding three strings. σ₁ means 'cross the
left string OVER the middle one.' Now they've swapped
positions. σ₁⁻¹? Cross it back UNDER."
Visual Vocabulary
The Core Crossing Diagrams
σ₁ (Left-over-middle):
1 2 3 2 1 3
│ │ │ │ │ │
│ ╲ │ │ → │ │ │
│ ╳ │ │ │ │
│ ╱ │ │ │ │ │
│ │ │ │ │ │
σ₂ (Middle-over-right):
1 2 3 1 3 2
│ │ │ │ │ │
│ │ ╲ │ → │ │ │
│ ╳ │ │ │ │
│ │ ╱ │ │ │ │
│ │ │ │ │ │
The Yang-Baxter Relation Visualized
σ₁σ₂σ₁ = σ₂σ₁σ₂ (The "braid relation")
This isn't just algebra - it's a physical fact about moving strings:
- Left path: Cross left-over-middle, then middle-over-right, then left-over-middle again
- Right path: Cross middle-over-right, then left-over-middle, then middle-over-right again
- BOTH end up with strings in the same final configuration!
What ships with it
2 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
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.
- 7d ago First seen · 317 lines · 96 tokens per session scan A 58e934e80f74
knot-theory-educator is a skill published in the GitHub repository curiositech/some_claude_skills (219 stars, last pushed 5d ago), licensed MIT. It adds 96 tokens to every session and 2,673 once invoked, about $0.0005 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 2026-09-03.
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