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.svg" alt="Measured on agentmods" 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 | $0.03636 |
| Opus 5 | $0.00046 | $0.01818 |
| Sonnet 5 | $0.00018 | $0.00727 |
| Haiku 4.5 | $0.00009 | $0.00364 |
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 8d 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 — 227 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 dx
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 3.7 KB
- evals/evals.json 5.8 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 7.4 KB runs code
- scripts/matrix_condition.py 4.6 KB runs code
- scripts/requirements.txt 12 B
- scripts/stiffness_detector.py 5.8 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.
- 8d 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 (66 stars, last pushed 2mo ago), licensed Apache-2.0. It adds 92 tokens to every session and 3,636 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 2026-08-30.
Other skills, from other repositories
search-math-results
Find program-conditioned math results, constructions, examples, counterexamples, analogies, and background references. Use when the current active program needs repair, mutation, analogy, a program shift, or carefully gated obstruction search.
check-referenced-statements
Validate externally referenced theorems by querying arXiv theorem search first and Codex's built-in web search second. Use when a markdown proof cites statements from external papers.
verify-sequential-statements
Verify a markdown proof in the order it is written. Use when the task is to check local correctness, theorem applicability, and reasoning gaps statement by statement through a paper-style proof.
construct-counterexamples
Construct candidate counterexamples to test a proposed conjecture, lemma, or intermediate claim by keeping the assumptions true while making the claimed conclusion fail. Use when a proposed conjecture/claim feels fragile or unproved, or when you are stuck in reasoning and want to see where the assumptions take effect…
construct-toy-examples
Generate and analyze simpler examples that satisfy both the assumptions and the conclusion of a theorem statement or subgoal. Use when you are stuck in reasoning and need simpler examples to regain traction, or when you want to see where the assumptions take effect and gain intuition.
obtain-immediate-conclusions
Derive immediate mathematical consequences from a theorem statement or subgoal. Use when starting a new problem, branch, or subgoal, or when cheap progress or a cleaner reformulation is needed before deeper proof search.