🧶 Loom

Weave your understanding — a gorgeous XeLaTeX class for fill-in study notes

Notes you both read and fill: statements and intuition to take in, blanks and proof-skeletons to work out. Learn by active recall, on paper that looks like an illuminated manuscript.

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.

Singular Value Decomposition — a definition knot, the geometry, a Your turn	Fourier transform — the dictionary, the convolution theorem
Entropy — the information diagram, Gibbs' inequality	Gradient descent — the rate, and the cost of conditioning
Concentration of measure — theorem stated, proof left as a skeleton	Every device on one page (the demo)

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.

The toolkit (all built into the class)

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.

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.