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 Sliky1/lagrangian-skills --skill v0.1.0git clone --depth 1 https://github.com/Sliky1/lagrangian-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/sliky1/lagrangian-skills/v0.1.0)<a href="https://agentmods.dev/skills/sliky1/lagrangian-skills/v0.1.0"><img src="https://agentmods.dev/badge/skills/sliky1/lagrangian-skills/v0.1.0/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/sliky1/lagrangian-skills/v0.1.0"><img src="https://agentmods.dev/badge/skills/sliky1/lagrangian-skills/v0.1.0.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 | $0.00056 | $0.00441 |
| Opus 5 | $0.00028 | $0.00220 |
| Sonnet 5 | $0.00011 | $0.00088 |
| Haiku 4.5 | $0.00006 | $0.00044 |
Grade A, and why
lagrangian-core 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 11d 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
Lagrangian Core Skill — v0.1.0
能力边界
支持: 凸QP | 光滑NLP | 基础非凸NLP 不支持: 分布式 | Safe RL | 多目标 | 贝叶斯混合
核心方法: 增广拉格朗日法 (ALM)
目标: min f(x) s.t. h(x)=0, g(x)≤0
L_ρ = f(x) + Σλ·h(x) + Σμ·g(x) + ρ/2·||h||²
求解步骤:
- 初始化 x₀, λ₀, μ₀, ρ₀=1.0
- 内层: min_x L_ρ(x, λ, μ) → x*
- 更新乘子: λ ← λ + ρ·h(x*), μ ← max(0, μ + ρ·g(x*))
- 更新惩罚: ρ ← 1.5ρ if ||h||>tol
- 收敛判断: ||h(x*)||<1e-6 且 ||∇L||<1e-6
KKT条件验证
∇f + Σλ∇h + Σμ∇g = 0 h(x*) = 0, g(x*) ≤ 0 μ ≥ 0, μ·g(x*) = 0
失败处理
输出: 错误类型 + 一行说明
输出格式
最优解 x* → 目标值 f(x*) → KKT残差 → 约束状态
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.
- 11d ago First seen · 41 lines · 56 tokens per session scan A 16c72ac7982b
lagrangian-core is a skill published in the GitHub repository Sliky1/lagrangian-skills (2 stars, last pushed 3mo ago), licensed MIT. It adds 56 tokens to every session and 441 once invoked, about $0.0003 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 2026-08-31.
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