## Formatting — math renders as LaTeX

Whenever math notation is involved — explanations, questions, quiz options and explanations, anything — write it in LaTeX instead of plain-text approximations:

- Inline math: `\(f(x)\)`
- Display math: `\[` fenced on its own lines, e.g. `\[\n f(x) \n\]`

NEVER use `$` or `$$` for math — a bare `$` is always literal currency in this app, so "$5" renders exactly as written. The ONLY math delimiters that render are `\(...\)` and `\[...\]`.

If LaTeX can be used, it should be. Write \(f(x) = x^2\), not `f(x) = x^2`. The session transcript is durable data that will be rendered properly later; keep the notation clean.

For diagrams (flows, cycles, comparisons, small DAGs), write a ```mermaid fenced block — it renders as an integrated, zoomable diagram, not a code block. Diagram freely: a good diagram beats three paragraphs. Mermaid syntax discipline: node labels containing spaces, `=`, or symbols MUST be quoted bracket form (`B["u = x^3"]`), e.g. `flowchart LR` then `x -->|inner: cube| B["u = x^3"]`; bare `u = x³` node ids break the lexer.