# Syntax

This page documents the core markdown and linking syntax used throughout the vault.  
The goal is readability, consistency, and dense interconnection between notes.

Good notes are usually:

 - short
 - heavily linked
 - structurally consistent
 - easy to scan
 - easy to expand later

---

## Text Formatting

Text emphasis should be used sparingly. Over-formatting makes notes harder to scan.

### Bold

Use double asterisks for strong emphasis.

```md
**important concept**
```

Example:

**important concept**

### Italic

Use single asterisks for softer emphasis, terminology, or tone.

```md
*foreign phrase*
```

Example:

*foreign phrase*

### Inline Code

Inline code is useful for commands, identifiers, filenames, functions, variables, and technical terminology.

```md
Use `printf()` to write to stdout.
```

Example:

Use `printf()` to write to stdout.

---

## Headers

Headers define hierarchy and improve navigation.

Use shallow hierarchies whenever possible. Deep nesting usually indicates that a note should be split into multiple pages instead.

```md
# Main page title
## Section
### Subsection
#### Detail
```

A page should normally contain only a single `#` title at the top.

---

## Internal Links

Internal links are the foundation of the vault.

Instead of organizing information through folders alone, pages should reference related concepts directly. This creates a graph structure rather than a strict tree structure.

### Standard Link

```md
[[syntax]]
```

This creates a direct link to another page.

### Aliased Link

```md
[[syntax|Markdown syntax]]
```

Aliases improve readability while preserving stable page names internally.

Internal links are usually preferable to repeating information.

---

## External Links

Use standard markdown links for websites and external resources.

```md
[youtube](https://www.youtube.com/)
```

Example:

[youtube](https://www.youtube.com/)

External links should generally complement notes rather than replace them.

---

## Lists

Lists are useful for sequencing, categorization, and compact information density.

### Ordered Lists

Use ordered lists when sequence matters.

```md
1. First item
2. Second item
3. Third item
```

Example:

1. First item
2. Second item
3. Third item

### Unordered Lists

Use unordered lists for grouped concepts where order is irrelevant.

```md
- First item
- Second item
- Third item
```

Example:

- First item
- Second item
- Third item

---

## LaTeX

LaTeX is used for mathematics, statistics, finance, physics, and formal notation.

### Inline Equations

```md
$E = mc^2$
```

Example:

$E = mc^2$

### Block Equations

Block equations improve readability for larger expressions.

```md
$$
\frac{\partial V}{\partial t} +
\frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} +
rS\frac{\partial V}{\partial S} - rV = 0
$$
```

Example:

$$
\frac{\partial V}{\partial t} +
\frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} +
rS\frac{\partial V}{\partial S} - rV = 0
$$

---

## Code Blocks

Use fenced code blocks for multiline code snippets.

Language identifiers enable syntax highlighting.

```c
#include <stdio.h>

int main() {
    printf("Hello world!\n");
    return 0;
}
```