KaTeX math rendering ($...$ and $$...$$)

[SyNeto]

Goal

Render inline (`$...$`) and display (`$$...$$`) math expressions using KaTeX, fully offline, no CDN.

Why

Math notation in technical/academic Markdown is unreadable as raw `$` delimiters. KaTeX is the de-facto offline math renderer — fast, no MathJax-style DOM cost.

Proposed approach

• `npm install --save-dev katex` and bundle `katex.min.js` with esbuild into `vendor/`.
• Vendor the KaTeX CSS and fonts (`KaTeX_*.woff2`) into `vendor/katex/`.
• Declare the font files in `web_accessible_resources` of `manifest.json` so the CSS can resolve them via `chrome-extension://...` URLs.
• Either rewrite KaTeX CSS `url(...)` references at build time, or inject a runtime `<style>` block with URLs from `chrome.runtime.getURL()`. Decide based on which keeps the build simpler.
• Integrate as a marked extension that scans for `$` and `$$` delimiters and replaces matches with KaTeX-rendered HTML.

Constraints

• No CDN. Everything bundled locally. Fonts must NOT load from `cdnjs`, `unpkg`, or any external host.

Acceptance criteria

• `$E = mc^2$` renders inline math
• `$$\int_a^b f(x)dx$$` renders display math
• No network requests issued by KaTeX (verify in DevTools Network tab)
• Works on `file:///` pages
• No regression on docs without math