content

name	content
description	For writing or reviewing content for Lemma — applies the manifesto bar, the arc structure (hook → widget → numbered arc → pin → exercises → glossary), the Term backlink rule, and two-doors discipline. Use when planning a new module or application, drafting prose, or reviewing a draft for ship-readiness.

Content

Lemma is a textbook built backwards: application before abstraction, real question first, math second. This skill is for getting content past the bar.

The bar (the only one)

Does this make a curious learner understand something they could not understand before?

• Yes → it ships
• No → it doesn't, however polished

If a page is well-written but the reader walks away knowing the same thing they already knew, the page failed. Beautiful prose that restates understanding is worse than rough prose that creates it.

Page structure (the arc)

Every application page follows this skeleton:

1. Hook — a real-world question that the math is needed to answer ("What annual rate turns $41 into $1B in 16 years?"). One vivid paragraph. No math yet — the math has to be missed before it's introduced.
2. Widget — an interactive thing that makes the question tangible. The reader must be able to push values around and watch what happens.
3. Arc — numbered sections (1, 2, 3 …), each building on the previous. The numbering is not decorative; it gives readers a way to talk about the page ("the proof in §2") and forces a single load-bearing idea per section.
4. Pin — a boxed conclusion that crystallizes the whole page in 1–3 sentences. Memorable. Short. The thing the reader will quote later.
5. Exercises — 5–7 problems with reveal-able solutions. Cover this mix:
   • read the graph — uses the widget, no formula
   • compute by hand / no calculator — forces understanding, not lookup
   • write the equation — translation from English to math
   • the evil one — catches a likely misconception or breaks an approximation in a way the reader will remember
6. Glossary — page-scoped, auto-populated from <Term> usage on the page. Don't list everything — only what was actually used.

Module pages (e.g. the logarithm) follow the same shape but the hook is the identity that does all the work, and the arc shows it consumed by applications.

No knowledge gaps

Audience: post-secondary, 18+, smart, technical. Decision rule:

Would a smart 18-year-old developer need help here?

If yes, backlink it. Wrap the term in <Term id="…">…</Term> so it gets a glossary entry and the hover-counterpart treatment.

Backlink:

• Domain-specific things: float32, log_softmax, SPY, CAGR, slide-rule
• Anything you'd otherwise gloss with "(see Wikipedia)"
• Library functions and concepts that aren't universally known

Don't backlink:

• High-school basics: function, variable, multiplication, derivative
• General programming literacy: for loop, array, string

The baseline is post-secondary, not zero. Backlinking everything is as bad as backlinking nothing — both signal "I don't know who I'm writing for."

Two doors

• General mode: prose only. Accessible to anyone meeting the baseline, even if they never write code.
• Code mode: prose + Python snippets that complete the prose. The code is itself a teaching surface — function names and return values reinforce the equation. Don't duplicate the prose in comments.

When code mode is off, the page must still answer every question on its own.

Bilingual at the term level

• Every prose page has en + ko sources
• Every <Term id="x"> has src/data/glossary/x/en.md and …/ko.md
• Korean is not a translation of English. Both should read native — the same insight in two voices.

For Korean register and translation triage, switch to the translate skill.

Math notation

All math goes inside $...$ (inline) or $$...$$ (block) using KaTeX-renderable LaTeX. The build is strict — incompatible math fails CI.

• $x^2 + y^2 = r^2$, not <Formula>...</Formula> (retired) or Unicode (x²)
• Function names backslashed: \cos\theta, \log_2 x, \sqrt{x}, \frac{a}{b}
• Currency in prose escapes: \$100. Korean labels in math wrap: \text{달}
• KaTeX subset reference: https://katex.org/docs/supported.html

Full rule and gotchas in CONTRIBUTING.md § Math notation in prose.

Committee pattern (review)

For any non-trivial new page, spawn parallel subagents with different lenses (use the Agent tool with Explore for read-only review, or general-purpose for review + edits):

• Manifesto auditor — does the page pass the bar? Where exactly does the reader gain the new understanding? Quote the sentence.
• Beginner's eye — where would a smart 18-year-old stumble? Is every unfamiliar term backlinked? Is the hook actually a hook, or just a header?
• Mathematician's eye — are the equations right? Is notation consistent across the page (log vs ln, e^x vs exp(x))? Are any approximations stated (Stirling, Rule of 72) and any of their break-points called out?
• Copy editor — is any sentence load-bearing without earning its weight? Cut prose that restates the previous sentence. Cut hedges.
• Korean reader — is the ko.* prose native, or English-shaped? (Hand to the translate skill if so.)

Synthesize their feedback into a single revision pass. Don't merge advice mechanically — pick the right intervention.

Anti-patterns

• The textbook voice. "We will now consider…", "Let us define…". Cut.
• Front-loading definitions. A term defined before the reader needs it is a term forgotten. Define on demand, in the prose, with <Term>.
• Decorative interactivity. A widget that doesn't change the reader's understanding when they push it is dead weight. If the widget can be replaced by a static screenshot, replace it.
• Symmetric exercises. Six "compute X" problems is one problem six times. The mix exists for a reason.
• Polished filler. A page that reads beautifully and teaches nothing is the worst failure mode. Every paragraph must be doing work.