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 HeshamFS/materials-simulation-skills --skill numerical-stabilitygit clone --depth 1 https://github.com/HeshamFS/materials-simulation-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/heshamfs/materials-simulation-skills/numerical-stability)<a href="https://agentmods.dev/skills/heshamfs/materials-simulation-skills/numerical-stability"><img src="https://agentmods.dev/badge/skills/heshamfs/materials-simulation-skills/numerical-stability/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/heshamfs/materials-simulation-skills/numerical-stability"><img src="https://agentmods.dev/badge/skills/heshamfs/materials-simulation-skills/numerical-stability.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 | $0.00092 | $0.03954 |
| Opus 5.5 | $0.00037 | $0.01582 |
| Sonnet 5.5 | $0.00018 | $0.00791 |
| Haiku 4.5 | $0.00009 | $0.00395 |
Grade A, and why
numerical-stability 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 2d 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 — 252 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Numerical Stability
Goal
Provide a repeatable checklist and script-driven checks to keep time-dependent simulations stable and defensible.
Requirements
- Python 3.10+
- NumPy (for matrix_condition.py and von_neumann_analyzer.py)
- See
scripts/requirements.txtfor dependencies
Inputs to Gather
| Input | Description | Example |
|---|---|---|
Grid spacing dx |
Spatial discretization | 0.01 m |
Time step dt |
Temporal discretization | 1e-4 s |
Velocity v |
Advection speed | 1.0 m/s |
Diffusivity D |
Thermal/mass diffusivity | 1e-5 m²/s |
Reaction rate k |
First-order rate constant | 100 s⁻¹ |
| Dimensions | 1D, 2D, or 3D | 2 |
| Scheme type | Explicit or implicit | explicit |
Decision Guidance
Choosing Explicit vs Implicit
Is the problem stiff (fast + slow dynamics)?
├── YES → Use implicit or IMEX scheme
│ └── Check conditioning with matrix_condition.py
└── NO → Is CFL/Fourier satisfied with reasonable dt?
├── YES → Use explicit scheme (cheaper per step)
└── NO → Consider implicit or reduce dt (grid refinement requires a coupled timestep reduction)
Stability Limit Quick Reference
| Physics | Number | Explicit Limit (1D) | Formula |
|---|---|---|---|
| Advection | CFL | C ≤ 1 | C = v·dt/dx |
| Diffusion | Fourier | Fo ≤ 0.5 | Fo = D·dt/dx² |
| Reaction | Reaction | R ≤ 1 | R = k·dt |
Multi-dimensional correction: For d dimensions, diffusion limit is Fo ≤ 1/(2d).
Script Outputs (JSON Fields)
| Script | Key Outputs |
|---|---|
scripts/cfl_checker.py |
metrics.cfl, metrics.fourier, recommended_dt, stable |
scripts/von_neumann_analyzer.py |
results.max_amplification, results.stable |
scripts/matrix_condition.py |
results.condition_number, results.is_symmetric |
scripts/stiffness_detector.py |
results.stiffness_ratio, results.real_part_stiffness_ratio, results.imag_dominated, results.stiff, results.recommendation, results.warning |
What ships with it
11 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.
- CHANGELOG.md 3.9 KB
- evals/evals.json 11 KB
- evals/files/fem_stiffness_spd.npy 20 KB
- references/common_pitfalls.md 6.3 KB
- references/scheme_catalog.md 5.2 KB
- references/stability_criteria.md 4.9 KB
- scripts/cfl_checker.py 11 KB runs code
- scripts/matrix_condition.py 5.6 KB runs code
- scripts/requirements.txt 12 B
- scripts/stiffness_detector.py 6.6 KB runs code
- scripts/von_neumann_analyzer.py 4.3 KB runs code
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.
- 2d ago Changed · +25 lines 72a3ee463edf
- 1mo ago First seen · 227 lines · 92 tokens per session scan A a5f9ed325f16
numerical-stability is a skill published in the GitHub repository HeshamFS/materials-simulation-skills (83 stars, last pushed 3d ago), licensed Apache-2.0. It adds 92 tokens to every session and 3,954 once invoked, about $0.0004 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 2026-08-30.
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