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Why Loom

Most notes are read-only: definition → theorem → proof, flowing past your eyes. You finish the page and remember nothing. Loom typesets the other layer too — the weave of your own understanding:

• 🧵 A page is cloth on a loom. Warp threads are the ideas in play (a left selvage rail). Knots are results that bind them (theorem boxes). Loose threads are your open questions. A warmth gauge records how well you actually grok each block.
• ✍️ Passive + active in one document. The exposition is written to be read; the high-value steps are left blank (\fillin), proofs ship as skeletons (\TODO), and the book's examples are restaged as "your turn" computations. The source is your answer key.
• 🎨 Dyed in real pigments. Indigo, madder, weld, iron-gall — historical textile and ink dyes no maths template uses. Headings incised in Optima, body and math in Libertinus, 中文 in Songti/楷体. Every cover carries a procedurally-woven emblem.
• 🤖 An AI skill that writes them for you. Point Claude at a chapter and the fill-in-notes skill produces a complete, compiling notebook in this style — organized around a spine, not transcribed.

Quickstart

git clone https://github.com/Polaris-Aeterna/loom-notes.git
cd loom-notes/template
latexmk -xelatex main.tex      # or: xelatex main.tex (twice)

Then write. A blank starter, doubling as a live cheat-sheet of every command, is in template/main.tex. Open the repo in VS Code and the bundled .vscode/settings.json builds with XeLaTeX on every save (LaTeX Workshop defaults to pdflatex, which fails here).

Requirements. XeLaTeX (TeX Live 2023+). Libertinus ships with TeX Live; Optima / Avenir Next / Songti / 楷体 are macOS system fonts. On other platforms, swap the three \newfontfamily lines in loom.cls for any display sans — everything else stays.

On Overleaf

The root loom.cls relies on macOS fonts, so two Overleaf-ready editions live under overleaf/ — both keep \documentclass{loom} and the full command set (set the compiler to XeLaTeX):

	font setup	upload?
overleaf/libertinus/	all-Libertinus + Noto CJK — body & math match the original	nothing to upload
overleaf/classico/	URW Classico (closest to the Optima look) — contributed by fn-gn	4 font files, you supply

Most people want overleaf/libertinus/: copy it into a project, compile, done.

The toolkit (all built into the class)

you want…	you write…
the woven cover	\loomcover{title}{sub}{author}{date}
a result / definition / example	theorem · definition · example (auto-styled knots)
the intuition voice	strand env, \whisper{…}, \keyword{…}
a blank to fill	\fillin[width]
a proof gap	\TODO{the missing step}
a do-it-yourself box	yourturn env + \workspace[n] ruled lines
how well you grok it	\warmth{0..5}
a margin recall prompt	\recall{question}
an open thread / a recurring object	\loose{…} · \warp{key} / \pick{key}

Full reference: skill/reference/loom-commands.md.

The AI skill

skill/ is a Claude skill that turns a textbook chapter, lecture, or paper into a finished Loom notebook: it finds the spine, drafts each section in the Loom grammar, engineers the gaps at the right density (~70% read / 30% fill), compiles, and verifies. See SKILL.md, and the hard-won XeLaTeX gotchas in reference/pitfalls.md.

Examples

The first four are original expositions of public-domain mathematics — one each from linear algebra, signals, information, and optimization — safe to learn from and to share.

	the spine
examples/svd/	the Singular Value Decomposition — "ask a matrix anything; read the answer off Σ"
examples/fourier-transform/	the Fourier transform — "Fourier is the eigenbasis of shift"
examples/entropy/	entropy — "the price of uncertainty: you can't pay less, you needn't pay more"
examples/gradient-descent/	gradient descent — "the rate is a tax on conditioning"
examples/concentration-of-measure/	concentration of measure — proof-skeleton style, organized "by engine"
examples/nonlinear-algebra/	nonlinear algebra, Ch. 1–2 — closely follows Michałek–Sturmfels (GSM 211); cite the book
examples/demo/	every visual feature on two pages

License & credits

Code (the loom.cls class and the skill): MIT — see LICENSE. Use it, fork it, re-dye it.

The example notebooks are study notes that restate results from their sources (cited inline). They're shared under fair-use for education; if you publish notes that closely track a copyrighted text, attribute clearly and prefer an original example. The mathematics belongs to its authors.

Woven by 北极甜虾 (Polaris), 2026. Type by Libertinus, Optima, Avenir Next. Dyes after indigo, madder, weld, and iron-gall.