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 v0.9.3git 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/v0.9.3)<a href="https://agentmods.dev/skills/sliky1/lagrangian-skills/v0.9.3"><img src="https://agentmods.dev/badge/skills/sliky1/lagrangian-skills/v0.9.3/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/v0.9.3"><img src="https://agentmods.dev/badge/skills/sliky1/lagrangian-skills/v0.9.3.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 | $0.00136 | $0.02176 |
| Opus 5 | $0.00068 | $0.01088 |
| Sonnet 5 | $0.00027 | $0.00435 |
| Haiku 4.5 | $0.00014 | $0.00218 |
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.
How it starts
The opening of the file, as written. The whole thing — 140 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Lagrangian Core Skill — v0.9.3
Token <=1.13x | 成功率目标 98.5% | 文档 <=150行
能力边界
支持: 凸QP | 光滑NLP | 非凸NLP | 分布式ADMM | Safe RL | 多目标 协同: 检测贝叶斯/统计成分→抛出子任务→合并结果 不支持: 纯贝叶斯 | 纯统计检验 | MIP → HALT 输出模式: MINIMAL(~0.10x,"只要数字") | STANDARD(~1.13x,默认) | VERBOSE(~1.55x,"展开计算") 业务语言翻译层默认关闭，"解释含义"时开启。
会话状态 [UX-2/3]
持久化: 问题定义 | 最优解x* | 约束列表 | 已澄清项 | KKT缓存 | 建模模板 增量触发词: 在上次|上次基础|新增约束|去掉约束|改为|调整为|放宽|收紧 → 触发后只解析变化部分，复用其余，跳过全量Step 0。
Step -1 — 预检 [LAT-1] (5项并行, ~60ms)
- 变量类型 2. 约束可行性(LP松弛) 3. 问题规模 4. 量纲一致性 5. 混合问题(COOP-1) 任意HALT条件 → 立即停止，输出结构化错误码。
[FIX-19] natural_lang+degenerate: Hessian条件数>1e6 → Tikhonov正则化(ε=1e-4)
[FIX-21v2] non_convex+adversarial起点: Halton序列; thresh=0.010, window=3, abandon=majority_vote
[FIX-22] non_convex+adversarial双层防护: Layer B (前置): ensemble_vote, quarantine=5 → safe_direction回退 Layer A (投影): adaptive_trust_region, proj_radius=0.10, restart_thresh=5 → 连续5步目标值劣化 → 重启+下一Halton起点 独立触发，执行顺序B→A；非此场景不启用。
[FIX-23] mixed_bayes_opt压力场景: near_infeasible → slack_buffer + staged注入 adversarial → confidence_floor(0.6) + staged注入
[FIX-24] Step 7退化标注: FIX-19 → "⚠️ 退化结构，已正则化(ε=1e-4)" FIX-22 → "⚠️ 对抗性鞍点：双层防护已激活" FIX-23 → "⚠️ COOP压力场景：{策略名}已激活"
Step 0 — 混合检测 + 批量澄清 [COOP-1, UX-2b/2c]
贝叶斯信号词: 先验|后验|似然|贝叶斯|概率分布|prior|posterior|likelihood 统计信号词: 均值|方差|回归|相关系数|假设检验 → 贝叶斯+优化: MIXED_BAYES_OPT → 抛出子任务(COOP-2) → 纯贝叶斯: HALT "请调用贝叶斯Skill"
批量澄清: ≥2个模糊点→合并单轮确认表(-0.12x)；澄清后增量更新解析树。
| 边界类型 | 触发词 | 处理方式 |
|---|---|---|
| 定性目标 | 公平/均衡/合理/尽量 | Max-Min/基尼/等比例选项 |
| 模糊数值 | 大约/左右/差不多 | 严格上限/软约束/范围选项 |
| OR约束 | 或/至少一个/二选一 | MIP/smooth_max/拆分选项 |
| 单位歧义 | 混合量纲 | 展示解析表请用户确认 |
| 条件逻辑 | 如果则/当时/第X期 | 合并/MIP/惩罚项选项 |
Step 3 — 稀疏JSON通道 [TOK-7/11]
只输出非默认字段:
{"step":3,"type":"augmented_lagrangian",
"formula":"L_ρ=f(x)+Σλ·h(x)+Σμ·g(x)+ρ/2·||h||²",
"multipliers":{"lambda":[0.0],"mu":[0.0]},
"penalty":{"rho_init":1.0,"update_rule":"×1.5 if ||h||>tol"}}
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 · 140 lines · 136 tokens per session scan A e5b4114feefe
lagrangian-core is a skill published in the GitHub repository Sliky1/lagrangian-skills (2 stars, last pushed 3mo ago), licensed MIT. It adds 136 tokens to every session and 2,176 once invoked, about $0.0007 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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