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 zero-base-learninggit 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-/zero-base-learning)<a href="https://agentmods.dev/skills/hwl668/scientific-learning-skills-/zero-base-learning"><img src="https://agentmods.dev/badge/skills/hwl668/scientific-learning-skills-/zero-base-learning.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 | $0.00069 | $0.02039 |
| Opus 5 | $0.00034 | $0.01019 |
| Sonnet 5 | $0.00014 | $0.00408 |
| Haiku 4.5 | $0.00007 | $0.00204 |
Grade A, and why
zero-base-learning 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 — 197 lines — stays where its author put it; the contents beside it link to each section on GitHub.
目标
让零基础学习者在最短时间内建立对一个知识点的直觉理解和基本应用能力。
适用场景
- 第一次接触某个概念（如极限、矩阵、导数、熵）
- 没有相关前置知识
- 之前看了教材但完全读不懂
- 能说出名词但完全不知道是什么意思
Memory 系统
类型：分析记忆（不参与间隔复习）。
存储位置：memory/zero-base-learning/
存储内容：
- 哪些直觉类比在哪些知识点上效果好（如"趋近墙壁"解释极限效果好）
- 哪些例题被反复要求重复讲解（说明这个例题特别有效或特别容易卡住）
读/写规则：
- 写入：每次解释结束后，如果使用的直觉类比收到了用户"懂了"的确认，自动记录该类比 → 知识点映射。
- 读取：下次讲解同类知识点时，优先参考已记录的类比模式。
- 管理：说"清除 zero-base-learning 记忆"删除。
输入判断
必须做，不可跳过。 即使学习者说"我完全不懂"，也要追问至少 2 个问题，避免误判。
第一层：区分"真零基础"和"隐藏的前置缺失"
- 你之前听说过这个概念吗？在哪里听说的？（判断有没有模糊印象）
- 让你猜一下这个东西在干什么，你会怎么猜？（判断直觉基础）
- 你有没有学过 [相关前置知识]？（判断是否因为前置缺失导致听不懂）
第二层：校准回答起点
根据回答，选择不同起点：
| 回答特征 | 起点选择 |
|---|---|
| "完全没听说过，也猜不出来" | 从问题背景 + 生活直觉开始 |
| "听说过但说不清楚，好像和 X 有关" | 从生活直觉开始，用他的 X 印象做桥梁 |
| "大概知道但一看到符号就懵" | 可能是符号恐惧而非零基础，考虑转 fuzzy-understanding |
| "之前学过 [前置知识] 但没学好" | 先用 1 句话补前置知识，再开始 |
第三层：校准知识版本
不同阶段需要不同的定义深度。例如：
- 问"什么是极限"，如果是高中生 → 用数列极限 + 直觉，不引入 ε-δ
- 问"什么是极限"，如果是大一数学系 → 需要 ε-N 正式定义但逐句翻译
执行流程
输入判断 → 问题背景 → 生活/图像直觉 → 最小概念 → 正式定义 → 最小例题 → 常见误区 → 自测问题
注意：这里的"输入判断"不是可选的——是执行流程的第一步。
1. 输入判断
见上方"输入判断"章节。
2. 问题背景
先讲这个概念是为了解决什么问题而发明的。不要从定义开始。
例子：
- 导数是"我需要知道函数在某点变化的快慢"
- 极限是"我需要严格描述'趋近'这个动作"
3. 直觉解释
用生活或图像类比。先给直觉，再给定义。
例子：
- 极限 = 你走向一堵墙，每一步走剩下距离的一半。你永远在靠近，但数学上我们说你"趋近于"那堵墙。
- 导数 = 车速表。你在某个瞬间的速度，就是你位置曲线在这一点的切线斜率。
4. 最小概念
给出最核心的概念骨架，用一句话说清楚。这句话要让学习者可以直接用来回答"X 是什么"。
5. 正式定义
给出严格的数学/形式化定义，但必须：
- 先给出完整定义
- 然后用逐句翻译的方式解释每个符号/术语在说什么
- 不要假设学习者能自己读懂符号
6. 最小例题
一个最简单、数字最干净、能跑通的例子。手把手过一遍，每一步解释为什么。
例题选取原则：
- 数字尽量简单（避免分数、根号干扰理解）
- 只涉及当前概念，不引入新概念
- 能展示定义中的每个关键条件
7. 常见误区
必须包含。 这是本次优化新增的强制环节。
输出这个点上 2-3 个最常见的错误，格式为：
| 常见错误 | 为什么错 | 正确理解 |
|----------|---------|---------|
| 错误 1 | 原因 | 正解 |
至少覆盖以下类型中的 2 种：
- 概念混淆（把这个概念和另一个搞混）
- 条件遗漏（忘记定义中的某个前提条件）
- 直觉陷阱（直觉上说得通但数学上不对的情况）
8. 自测问题
提供 2-3 个递进难度的问题：
- 第 1 题：基础理解题（能直接用定义回答）
- 第 2 题：简单应用题（用最小例题的方法解）
- 第 3 题：概念边界题（测试是否落入常见误区）
附带答案提示（折叠或简要说明）。
输出格式
## 诊断
[基于输入判断的 1 句话定位，如"你应该是第一次接触这个概念，我们从零开始"]
## 它要解决什么问题
[1-2 句话，建立动机]
## 直觉理解
[生活类比 / 图像直觉]
## 核心概念
[一句话说清]
## 正式定义
[定义 + 逐部分翻译]
## 最小例题
[最简单可跑通的例子，分步骤]
## 常见误区
| 常见错误 | 为什么错 | 正确理解 |
|----------|---------|---------|
| ... | ... | ... |
## 自测题
1. [基础题]
2. [应用题]
3. [陷阱题]
## 答案提示
[简要答案]
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 · 197 lines · 69 tokens per session scan A 151737702349
zero-base-learning is a skill published in the GitHub repository hwl668/Scientific-learning-skills- (13 stars, last pushed 1mo ago), licensed MIT. It adds 69 tokens to every session and 2,039 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 2026-08-30.
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