feat: gate writer sections on a % teach: block (SP025)
Rewrite references/pedagogy.md around recite-vs-teach: reader model,
coverage density (sections_in is cite permission, not a to-do list),
intuition-before-formula three-beat, and paper-jump filling.
Every notes/sections/sec-*.tex must now answer gap / takeaway / jump /
omit above the first \section. lint.py checks presence only (it cannot
judge honesty); files opening with "% generated by" are exempt.
- scripts/lint.py: SP025 + is_writer_section / teach_gaps helpers
- tests/no-teach-block/: fixture with takeaway only, wired into test.sh
- examples/*: all 14 writer sections get real teach blocks
- SKILL.md, references/{agents,antipatterns,checklist}.md, DESIGN.md,
assets/notes-template.tex: route writers and consistency agent
through pedagogy.md
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# Pedagogy
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Reuse `youtube-render-pdf` teaching order: motive → idea → mechanism → evidence → takeaway.
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Job: teach the argument thread. The paper is the source of claims, not
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the outline of the notes.
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Paper-side changes:
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Section order is still motive → idea → mechanism → evidence → takeaway.
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That order is not a license to recap the PDF in a new sequence.
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- Cite `§` / `Eq.(n)` / Figure / Table / page, not timestamps.
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- Front page is a bibliography card, not a PDF cover screenshot.
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- Math is `\[` or `align`, never `$$`.
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- Formula three-beat: Chinese motive, display math, flat symbol list.
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- `quotebox` for a short quotation with a source; no long PDF paste.
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- End major sections with `\subsection{本章小结}`; end the notes with `\section{总结与延伸}`.
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- Figures stay outside boxes.
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## Recite vs teach
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Locked first/last titles: 「这篇论文在问什么」…「总结与延伸」, then appendix 符号表 / 推导链一览 / 图表清单.
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The default failure is a **closed-book failure**: a colleague who has
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not read this paper still cannot use the core claim, because the notes
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assume everything the paper assumes.
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| | Recite | Teach |
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|---|---|---|
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| Starts from | the paper's next subsection | what the reader still lacks |
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| Formula | "本节给出 Eq.(n)" then symbols | a world without the formula, then the formula |
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| Gap | whatever the paper already wrote | the jump the paper did not write |
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| Stops when | every cited paragraph is covered | the takeaway is usable |
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Reader model: a competent colleague in the ambient field, textbook
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level. They have **not** read this paper, do not know its notation, and
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will not reconstruct skipped algebra. Do not reteach the ambient
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textbook (softmax, SGD, …) unless a core claim hangs on a twist.
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If deleting the PDF would make the section unreadable as a lecture, it
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was a recap.
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## Before each section
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At the top of every writer `sec-XX.tex` (not `symbols.tex` / generated
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appendix), answer these four lines **before** the `\section`:
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```tex
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% teach:
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% gap: <读者此刻还缺什么，不是论文小节标题>
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% takeaway: <离开本节必须带走的一句>
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% jump: <论文跳过、读者会卡住的那一步；没有则 none>
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% omit: <论文这里有、本讲义故意不写的>
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```
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- `gap` — entering deficit, in the reader's words.
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- `takeaway` — one sentence. This is also the `本章小结`.
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- `jump` — the missing why / scale / naive alternative / extreme case.
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- `omit` — ceremony you will not import "for completeness".
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Do not start the body until all four are filled. `lint.py` enforces the
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four keys on every `notes/sections/sec-*.tex` as **`SP025`** (presence
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only — it cannot judge whether the answers are honest).
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## Coverage density
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`coverage.sections_in` is **cite permission**, not a to-do list.
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`ledger_ids` on the outline row are the teaching budget.
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- Outline: fewer lecture rows than paper subsections. Merge until each
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row has **one** takeaway. A row per paper `\subsection` is too dense.
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- Writer: teach this row's ids. A paper paragraph that is not required
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for a `status: core` claim stays out.
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- Supporting claims: in only if they unblock a core claim.
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- Dropped claims: never.
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Default skip (paper ceremony):
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- "the rest of this paper is organized as follows"
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- related-work tour (keep the 2–3 contrasts that **define the gap**)
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- contribution bullets that restate the abstract
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- dataset / hyperparameter / hardware laundry lists, unless a core
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empirical claim hangs on a specific number
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- every ablation, every appendix proof, every lemma not on an
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`expand: true` derivation
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- notation paragraphs that only duplicate the symbol appendix
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## Intuition before formulas
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Display math is a three-beat that must not be split:
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1. **Intuition in Chinese, with the formula still off-stage.** Use at
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least one of: analogy, contrast with the naive move, extreme case
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(0 / 1 / ∞), or tiny numbers. 「下面给出公式」/「本节引入 Eq.(n)」
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is not a motive.
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2. `\[` or `align` / `aligned`. Never `$$`.
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3. Flat symbol list: one item per symbol — 符号 — 含义 — 定义处.
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The section that owns the core mechanism then puts **one**
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`importantbox{如果你只记一件事}` with the takeaway sentence. At most
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one such box per major section. `本章小结` restates that sentence; it
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is not a new inventory.
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Pick one intuition tool, not all four. A running numeric example is
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allowed when scale or cancellation is the point; it is not mandatory.
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## Paper jumps
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Papers skip the why, the scale, and the obvious alternative. Before
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mechanism, name the stall and fill it:
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- Why this form, not the naive one?
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- What happens at 0 / 1 / ∞, or if the term is dropped?
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- Which quantity is a count vs a rate vs a scale?
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- Where does the gradient / information / mass actually flow?
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Fill in prose or `warningbox`. If the paper is silent and you would
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have to invent a result, say it is silent — do not fabricate.
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## Boxes and citations
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| box | payload |
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|---|---|
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| `importantbox` | walk-away: core claim, mechanism, 「如果你只记一件事」 |
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| `knowledgebox` | not the main thread: prerequisite, analogy, running example |
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| `warningbox` | naive-vs-correct, hidden assumption, paper-is-silent |
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| `quotebox` | short quotation + `§` / `Eq.(n)` in the title; ≲ 8 lines; no PDF paste |
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Routine exposition stays in prose. Figures stay outside every box.
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Cite `§` / `Eq.(n)` / Figure / Table / page, not timestamps. No
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`[cite]` placeholders. `\spsource{...}` at the point of use.
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Front page is a bibliography card (title, authors, year, venue, arXiv),
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not a PDF-cover screenshot. Default language is Chinese.
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End every major section with `\subsection{本章小结}`. End the notes
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with `\section{总结与延伸}` (limitations + compressed takeaways +
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open questions).
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Locked first/last titles: 「这篇论文在问什么」…「总结与延伸」, then
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appendix 符号表 / 推导链一览 / 图表清单. Outline may add or drop
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middle sections; it may not rename or drop the lock.
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Suggested skeleton (same lock as `assets/notes-template.tex`):
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```tex
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\section{这篇论文在问什么} % questions[] + motive
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\section{主张与贡献} % claims[status=core]，\splabel{C*}
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\section{预备：定义、假设、符号} % D* / A* / 符号摘要；不是论文 §2 巡游
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% --- outline-chosen mechanism sections ---
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\section{实验与证据} % only E* that isolate a core claim
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\section{总结与延伸}
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```
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## Antipatterns
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Each pair is the same lecture beat. Left recites; right teaches.
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### 1. Paper order, new wording
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```tex
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% recite
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本文第 3 节提出 scaled dot-product attention。
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作者将 $Q$、$K$ 做点积，除以 $\sqrt{d_k}$，再 softmax 乘 $V$。
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```
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```tex
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% teach
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% gap: 还以为「对齐再加权」就完了，不知道维数一涨会出什么事
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读者已经会「用相似度加权」。先看极端情况：$d_k$ 很大时，
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点积方差跟着涨，softmax 进饱和，梯度没了。
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除以 $\sqrt{d_k}$ 不是新算子，是把方差按回 1。
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```
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### 2. Formula with no off-stage intuition
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```tex
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% recite
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本节引入如下公式：
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\[
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\mathrm{Attention}(Q,K,V)=\mathrm{softmax}(QK^{\top}/\sqrt{d_k})V.
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\]
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\begin{itemize}
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\item $Q$ — query
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\item $K$ — key
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\item $d_k$ — key 维
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\end{itemize}
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```
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```tex
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% teach
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两个随机向量的点积有多尖，随维数走。不先压方差，后面的 softmax 是死的。
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\[
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\mathrm{Attention}(Q,K,V)=\mathrm{softmax}(QK^{\top}/\sqrt{d_k})V.
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\]
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\begin{itemize}
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\item $Q,K,V$ — query / key / value
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\item $d_k$ — key 维（shape parameter；缩放跟它走）
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\end{itemize}
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\begin{importantbox}{如果你只记一件事}
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$\sqrt{d_k}$ 是改写，不是新注意力。
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\end{importantbox}
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```
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### 3. Paper jump left as 「如式所示」
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```tex
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% recite
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如 Eq.(3) 所示，取 $A=d/H_{\mathrm{act}}$。
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```
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```tex
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% teach
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% jump: 论文直接写下 A，没说为什么不是 1/N
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走得越宽，越要把输出缩小，否则残差被宽隐层撑爆。
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所以是 $A=d/H_{\mathrm{act}}$：宽 $4096$ 时 $A=1/4$，宽 $1024$ 时 $A=1$。
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不是 $1/N$——专家总数还没进这把尺子。
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```
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### 4. Ceremony imported for completeness
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```tex
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% recite
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文献三条线：…（半页 related work）
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数据集为 ImageNet / CIFAR / …，硬件为 8$\times$A100，超参见表 7。
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```
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```tex
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% teach
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% omit: related-work 巡游、数据集表、硬件
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现成方法把问题当静态参数；缺的是带延迟和互馈的那一截。
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经验数字只在它能隔离这个机制时才进正文。
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```
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### 5. One lecture row per paper paragraph
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```tex
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% recite
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\subsection{Lemma 2}
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\subsection{Lemma 3}
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\subsection{Ablation on dropout}
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\subsection{Ablation on warmup}
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```
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```tex
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% teach
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% omit: 不在 DER1 上的 lemma；不能隔离 C1 的 ablation
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只展开 DER1 用到的那一步。Ablation 只留「去掉这项，C1 是否还成立」。
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```
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