Fix latex dollars pc 1629

Investigate and fix the actual $ usages in Markdown content.

The $ fall into three classes:

- Currency (escape these) — $1, $2 billion, R$ 549 → these pairs cause all the warnings
- Real math (leave alone) — $\rightarrow$, $O(1)\text{ streaming}$ → valid, no warnings
- Shell code (leave alone) — $(curl…), ${ZSH_CUSTOM}, $HOME → inside code blocks


Execute in 4 steps:

- Investigate — greps the content, classifies every $ into currency / real math / shell code, and reports counts before changing anything.
- Apply — checks the tree is clean, then writes and runs the exact tested Python script (code-fence-, inline-code-, frontmatter-, and math-span-aware; idempotent via the (?<!\\) lookbehind so re-running never double-escapes).
- Verify the diff — the safety net: greps that must print nothing for real math ($\rightarrow$, \text) and shell vars ($HOME, $(…), ${VAR}). If anything legit was touched, it tells you to git checkout -- . and stops.
- Print instructions — outputs the build-verify and commit/push commands for user to run.

Do not autonomously run any build, commit, or push.