update template doc

app/src/content/chapters/demo/best-pratices.mdx

@@ -38,18 +38,6 @@ Favor **concise captions** and callouts that clarify what to look at and why it
   
 </div>
 
-### Use the right color
-
-A palette encodes **meaning** (categories, magnitudes, oppositions), preserves **readability** and **accessibility** (sufficient contrast, color‑vision safety), and ensures **perceptually smooth transitions**. The three families below illustrate when to use **categorical**, **sequential**, or **diverging** colors and how they evolve from the same **reference hue**.
-
-<div className="">
-  <HtmlEmbed src="palettes.html" />
-</div>
-
-<Sidenote>
-  You can choose a color from the palette to update palettes and copy them to your clipboard. It will be applied to the <a href="/" target="_blank">whole page</a>.
-</Sidenote>
-
 ### Use the right chart
 
 Picking the right visualization depends on your goal (compare values, show distribution, part-to-whole, trends, relationships, etc.). The Visual Vocabulary poster below provides a concise mapping from **analytical task** to **chart types**.

app/src/content/chapters/demo/greetings.mdx

@@ -12,4 +12,5 @@ import HfUser from '../../../components/HfUser.astro';
   <HfUser username="molbap" name="Pablo Montalvo-Leroux" />
   <HfUser username="lewtun" name="Lewis Tunstall" />
   <HfUser username="guipenedo" name="Guilherme Penedo" />
+  <HfUser username="fracapuano" name="Francesco Capuano" />
 </div>

app/src/content/chapters/demo/markdown.mdx

@@ -63,13 +63,17 @@ See also the complete [**Markdown documentation**](https://www.markdownguide.org
 
 ### Math
 
-KaTeX is used for math rendering. You can use **inline** notation `$...$` or **block** `$$...$$` notation. As an example, this is an **inline** math equation: $x^2 + y^2 = z^2$ and this is a **block**:
+**KaTeX** provides full LaTeX math support with two simple syntaxes:
+
+**Inline math** — Use `$...$` for equations within text: $x^2 + y^2 = z^2$
+
+**Block math** — Use `$$...$$` for centered equations:
 
 $$
 \mathrm{Attention}(Q,K,V)=\mathrm{softmax}\!\left(\frac{QK^\top}{\sqrt{d_k}}\right) V
 $$
 
-Aligned math equations are also supported. You can add IDs to equations using `\htmlId{my_id}` and then reference them with links like [this equation](#trajectory_definition).
+**Advanced features** — Aligned equations with IDs for cross-referencing:
 
 ```math
 \htmlId{trajectory_definition}{\begin{align}
@@ -80,6 +84,7 @@ Aligned math equations are also supported. You can add IDs to equations using `\
 \end{align}}
 ```
 
+You can reference equations with links like [this equation](#trajectory_definition).
 
 <Accordion title="Code example">
 ```mdx