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 hwl668/Scientific-learning-skills- --skill fuzzy-understandinggit clone --depth 1 https://github.com/hwl668/Scientific-learning-skills-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.
[](https://agentmods.dev/skills/hwl668/scientific-learning-skills-/fuzzy-understanding)<a href="https://agentmods.dev/skills/hwl668/scientific-learning-skills-/fuzzy-understanding"><img src="https://agentmods.dev/badge/skills/hwl668/scientific-learning-skills-/fuzzy-understanding/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/hwl668/scientific-learning-skills-/fuzzy-understanding"><img src="https://agentmods.dev/badge/skills/hwl668/scientific-learning-skills-/fuzzy-understanding.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 | $0.01368 |
| Opus 5 | $0.00046 | $0.00684 |
| Sonnet 5 | $0.00018 | $0.00274 |
| Haiku 4.5 | $0.00009 | $0.00137 |
Grade A, and why
fuzzy-understanding 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
目标
诊断学习者在某个知识点上的具体卡点，针对性修复，而不是重新讲一遍。
适用场景
- 学过概念但说不清是什么
- 会背定义但不会用
- 做题时感觉"好像懂了又好像没懂"
- 公式会用但不知道为什么
Memory 系统
类型：分析记忆（不参与间隔复习）。
存储位置：memory/fuzzy-understanding/
存储内容：
- 常见卡点模式库：哪个知识点上哪类卡点最频繁（如"极限 ε-N 定义→符号不懂"高频）
- 有效诊断话术：哪些追问能最快速定位卡点类型
读/写规则：
- 写入：每次诊断结束后，记录卡点类型→知识点→修复策略的映射。
- 读取：下次遇到相似描述时，优先匹配已记录的卡点模式，加速诊断。
- 管理：说"清除 fuzzy-understanding 记忆"删除。
输入判断
先做快速诊断。让学习者回答：
- 用你自己的话说一下这个东西是什么？（检测理解深度）
- 你做到过相关的题吗？哪一步卡住了？（定位断裂点）
- 你觉得它和什么有联系？（检测知识网络）
诊断框架
判断学习者属于哪一类问题（可多选）：
| 类型 | 表现 | 修复策略 |
|---|---|---|
| 概念混淆 | 把 A 和 B 搞混 | 对比辨析，找核心差异 |
| 符号不懂 | 看到符号不知道含义 | 逐符号翻译，简化记号 |
| 推导断裂 | 知道结论但不知道中间怎么来的 | 补中间步骤，每次只补一步 |
| 前置知识缺失 | 因为某个前置概念导致整个听不懂 | 定位前置点，先补基础 |
| 只会背不会迁移 | 例题会做，换一个就不会 | 变式训练，抽核心方法 |
| 公式会用但不知道为什么 | 能套公式但说不清原理 | 从直觉到推导重建理解 |
执行流程
快速诊断 → 指出卡点 → 针对性修复 → 验证理解 → 变式测试
1. 快速诊断
根据学习者描述，用上述诊断框架判断卡点类型。
2. 指出卡点
明确告诉学习者："根据你的描述，你可能卡在 _______。"
3. 针对性修复
按诊断类型选择修复策略，只修卡住的部分。
4. 验证理解
让学习者用自己的话重新解释一遍，或用一道简单题验证。
5. 变式测试
给一道变了条件/场景的题，确认不是"刚好背对"。
输出格式
## 诊断结果
你可能的卡点：[具体描述]
## 修复
[针对性讲解，不是从头讲]
## 验证
[一道确认理解的题]
## 变式
[一道迁移题]
常见误区
| 常见错误 | 为什么错 | 正确理解 |
|---|---|---|
| "我感觉懂了就是真懂了" | 主观"懂感"不能区分表面理解和深层理解 | 只有能解决变式题才算真懂——换条件/场景后还能做对 |
| "模糊的地方跳过就行" | 知识是链式的，一个模糊点会级联放大 | 每个模糊点必须定位、修复、验证，不能跳过 |
| "多看看书就会了" | 反复阅读产生熟练错觉，不检测真实理解 | 主动回忆 + 自测 > 反复阅读（提取练习效应） |
反例：什么时候不要这样做
- 学习者完全零基础 → 用
zero-base-learning - 学习者理解清晰只是想深化 → 用
deepening-learning - 不要重新讲一遍整个概念——只修卡住的部分
- 不要跳过诊断直接给解释——那只是瞎猜
- 不要只说"你需要多练习"——说具体练什么、怎么练
测试样例
输入：我学了矩阵乘法，我会算 A×B，但我不知道我在算什么。老师说矩阵表示线性变换，但我不理解"变换"是什么意思。
期望输出方向：
- 诊断：卡在"线性变换"这个前置概念上的直觉理解（前置知识缺失 + 概念混淆）
- 指出卡点："你会算乘法但不知道矩阵在做什么——你缺的是对'线性变换'的直觉"
- 修复：用"平面上点的映射"来解释线性变换，2×2 矩阵把 (1,0) 和 (0,1) 映射到哪里
- 验证：给定一个矩阵 [2,0; 0,3]，说说它把正方形变成了什么
- 变式：把矩阵换成 [1,1; 0,1]，预测效果
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 · 120 lines · 92 tokens per session scan A 95db6330e0b9
fuzzy-understanding is a skill published in the GitHub repository hwl668/Scientific-learning-skills- (13 stars, last pushed 1mo ago), licensed MIT. It adds 92 tokens to every session and 1,368 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.
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