# Protocol: Rendering Mathematical Notation

## 1. The Standard: Unicode

To ensure simplicity, performance, and a dependency-free codebase, all mathematical notation in this application **MUST** be written using standard **Unicode characters**.

### Rationale
Using Unicode for mathematical symbols (e.g., `p̂₁`, `√`, `Σ`) instead of a complex typesetting library like KaTeX or MathJax offers several advantages for this project:
-   **Simplicity:** Content is human-readable directly in the source code.
-   **No Dependencies:** The application does not need to load any external libraries, fonts, or stylesheets for math rendering. This improves load times and reduces potential points of failure.
-   **Performance:** Rendering is instantaneous as symbols are native text characters.

## 2. Implementation

All mathematical symbols should be entered directly into the strings within `src/data/slides.ts`.

-   **Correct:** `'The difference we observe is simply p̂₁ - p̂₂.'`
-   **Correct:** `{ type: 'formula', tex: 'SE(p̂₁ - p̂₂) = √((p₁(1-p₁)/n₁) + (p₂(1-p₂)/n₂))' }`

Basic HTML tags like `<strong>` and `<em>` can be used within text strings for emphasis. These will be rendered using `dangerouslySetInnerHTML`, which is considered safe as the content is developer-controlled and static.

## 3. Forbidden Practices

-   **Do not use TeX or LaTeX syntax** (e.g., `\hat{p}_1`, `\frac{}{}`).
-   **Do not add any math rendering libraries** like KaTeX or MathJax to the project.
-   **Do not use images for formulas.** All math must be text-based.