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 hamzabellouch/agent-skills --skill tensor-calculus-differential-formsgit clone --depth 1 https://github.com/hamzabellouch/agent-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/hamzabellouch/agent-skills/tensor-calculus-differential-forms)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/tensor-calculus-differential-forms"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/tensor-calculus-differential-forms/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/hamzabellouch/agent-skills/tensor-calculus-differential-forms"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/tensor-calculus-differential-forms.svg" alt="Reviewed on agentmods" width="80" height="20"></a>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 | $0.00037 | $0.00350 |
| Opus 5.5 | $0.00015 | $0.00140 |
| Sonnet 5.5 | $0.00007 | $0.00070 |
| Haiku 4.5 | $0.00004 | $0.00035 |
Grade A, and why
tensor-calculus-differential-forms 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 6d 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.
What it actually says
Tensor Calculus and Differential Forms
ID: math.tensor_calculus
Domain: Mathematics → Geometry
Difficulty: 5/5
Prerequisites
- math.vector_calculus
- math.linear_algebra
Core Concepts
- tensors
- index notation
- covariant/contravariant
- metric tensor
- connection
Key Equations
$$ T^{\mu\nu} = \Lambda^\mu_{\ \alpha}\Lambda^\nu_{\ \beta}T^{\alpha\beta} $$ $$ \Gamma^\lambda_{\mu\nu} = \tfrac12 g^{\lambda\sigma}(\partial_\mu g_{\sigma\nu} + \partial_\nu g_{\sigma\mu} - \partial_\sigma g_{\mu\nu}) $$
Methods
- Manipulate indices carefully
- Raise/lower with the metric
- Compute covariant derivatives
Typical Problem Types
- Stress-energy tensor
- Curvature computation
- Relativistic kinematics
Common Pitfalls
- Summing over the wrong pair of indices
- Mixing up upper/lower indices
Related Skills
- rel.general.geodesics
- rel.special.four_vectors
References
- Schutz Geometrical Methods
- Misner Thorne Wheeler Ch.3
What ships with it
1 file 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.
- 6d ago First seen · 57 lines · 37 tokens per session scan A 85a327ba07d7
tensor-calculus-differential-forms is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed 6d ago), licensed MIT. It adds 37 tokens to every session and 350 once invoked, about $0.0001 per session on Opus 5.5. 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 2026-10-10.
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