convergence-study

convergence-study is a skill for Claude Code from beita6969/ScienceClaw. It costs 25 tokens per session (1,141 once invoked), scanned A, original, MIT.

A numerical study that checks whether computed results approach a stable value as the mesh or time step becomes finer. It uses Richardson extrapolation to estimate the limiting value and the Grid Convergence Index to estimate remaining numerical error.

In plain words
What is it for?
Use it to compare solutions across spatial grids or time steps, estimate a refined result, calculate observed convergence orders and GCI, and produce a convergence assessment.
Why use it?
It helps show whether a simulation result is becoming trustworthy with refinement instead of relying on one grid or time step. The reported observed order and error estimates reveal whether convergence matches expectations.

Skill for Claude Code

Written for Claude Code: allowed-tools in frontmatter.

Good fit Use it to compare solutions across spatial grids or time steps, estimate a refined result, calculate observed convergence orders and GCI, and produce a convergence assessment.

Compare 6 skills from other repositories ↓
Install with agentmods
npx agentmods add skills/beita6969/scienceclaw/convergence-study
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.

Any agent
npx skills add beita6969/ScienceClaw --skill convergence-study
Clone the repo
git clone --depth 1 https://github.com/beita6969/ScienceClaw

Made for: Claude Code.

Wrote 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.

agentmods badge for convergence-study

README.md
[![agentmods](https://agentmods.dev/badge/skills/beita6969/scienceclaw/convergence-study.svg)](https://agentmods.dev/skills/beita6969/scienceclaw/convergence-study)
Your own site
<a href="https://agentmods.dev/skills/beita6969/scienceclaw/convergence-study"><img src="https://agentmods.dev/badge/skills/beita6969/scienceclaw/convergence-study.svg" alt="Measured on agentmods" height="20"></a>
Per session 25 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 1,141 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe. Third-party audits
  • NVIDIA SkillSpector pass 7 Sept 2026
How audits are shown
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 5.1 $0.00025 $0.01141
Opus 5 $0.00013 $0.00571
Sonnet 5 $0.00005 $0.00228
Haiku 4.5 $0.00003 $0.00114

Measured 8d ago against content hash b8990cc53427, method: parsed. Prices are Anthropic first-party input rates as of 2026-09-08, from the pricing page.

Security

Grade A, and why

convergence-study 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.

The scan reads SKILL.md. This mod also ships 4 executable files (scripts/dt_refinement.py, scripts/gci_calculator.py, scripts/h_refinement.py, …), listed below but not scanned — reading those needs a real analyzer, not pattern matching.

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.

skills/convergence-study/SKILL.md · 99 lines

How it starts

The opening of the file, as written. The whole thing — 99 lines — stays where its author put it; the contents beside it link to each section on GitHub.

Convergence Study

Goal

Provide script-driven convergence analysis for verifying that numerical solutions converge at the expected rate as the mesh or timestep is refined.

Requirements

  • Python 3.8+
  • NumPy (not required; scripts use only math stdlib)

Inputs to Gather

Input Description Example
Grid spacings Sequence of mesh sizes (coarse to fine) 0.4,0.2,0.1,0.05
Timestep sizes Sequence of dt values 0.04,0.02,0.01
Solution values QoI at each refinement level 1.16,1.04,1.01,1.0025
Expected order Formal order of the numerical scheme 2.0
Safety factor GCI safety factor (1.25 default) 1.25

Script Outputs (JSON Fields)

Script Key Outputs
scripts/h_refinement.py results.observed_orders, results.mean_order, results.richardson_extrapolated_value, results.convergence_assessment
scripts/dt_refinement.py Same as h_refinement but for temporal convergence
scripts/richardson_extrapolation.py results.extrapolated_value, results.error_estimate, results.observed_order
scripts/gci_calculator.py results.observed_order, results.gci_fine, results.gci_coarse, results.asymptotic_ratio, results.in_asymptotic_range

Workflow

  1. Run grid/timestep refinement study with at least 3 levels
  2. Compute observed convergence order with h_refinement.py or dt_refinement.py
  3. Compare observed order to expected order of the scheme
  4. Estimate discretization error via Richardson extrapolation
  5. Report GCI for formal solution verification using gci_calculator.py
  6. Document convergence results and any anomalies

Decision Guidance

Do you have 3+ refinement levels?
+-- YES --> Run h_refinement.py or dt_refinement.py
|           +-- Observed order matches expected? --> Solution verified
|           +-- Order too low? --> Check: pre-asymptotic, coding error, insufficient resolution
|           +-- Order too high? --> Check: superconvergence or cancellation effects
+-- NO (only 2 levels) --> Use richardson_extrapolation.py with assumed order
                           (less reliable without order verification)

Read the full file on GitHub · 99 lines

Files

What ships with it

6 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.

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. 8d ago First seen · 99 lines · 25 tokens per session scan A b8990cc53427

Subscribe to this mod's changes

convergence-study is a skill published in the GitHub repository beita6969/ScienceClaw (895 stars, last pushed 3mo ago), licensed MIT. It adds 25 tokens to every session and 1,141 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 2026-08-30.

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