UI iteration 1: app shell + full LaTeX pipeline

Layout:
- Home = knowledge-graph placeholder (main view) with new-session input
  docked below; session list moved out of home into a hamburger drawer
- SessionDrawer: slide-over session navigation (backdrop/ESC close, active
  highlight, fetches /api/chats on open) on both home and chat headers
- Chat header loses the back button — the drawer is the navigation

Math (inline $ was silently not rendering):
- @streamdown/math defaults singleDollarTextMath:false — now
  createMathPlugin({ singleDollarTextMath: true }) in message + reasoning
- katex.min.css imported in layout (streamdown does not inject plugin
  styles; display math only looked right via browser MathML fallback)
- QuizCard/AnsweredCard route question/options/explanation through
  MessageResponse; user chat bubbles render markdown+math too
- Currency hazard: micromark-extension-math@3.1 lacks pandoc's
  closing-digit rule, so bare '$5 and $10' parses as math — defense is at
  the source: system prompt now instructs escaped \$5 / 'USD' for money

Hydration fix (React #418):
- QuizCard shuffled options with Math.random() — server/client orders
  diverged. shuffleOptions now takes an injectable RNG; QuizCard passes
  seededRandom(toolCallId) (mulberry32/FNV-1a in question-core). Same
  question → same stable order across reloads; still varies per question.

Tests: 53 pass (5 new math-rendering pins incl. fenced-vs-one-line $$
behavior and the escaped-currency contract). tsc + next build clean.
Verified live in browser: inline/display math in text + cards, drawer
open/navigate/active-highlight/ESC, no console errors, no font 404s.

components/ai-elements/message.tsx

@@ -14,7 +14,7 @@ import {
 import { cn } from "@/lib/utils";
 import { cjk } from "@streamdown/cjk";
 import { code } from "@streamdown/code";
-import { math } from "@streamdown/math";
+import { createMathPlugin } from "@streamdown/math";
 import { mermaid } from "@streamdown/mermaid";
 import type { UIMessage } from "ai";
 import { ChevronLeftIcon, ChevronRightIcon } from "lucide-react";
@@ -324,7 +324,14 @@ export type MessageResponseProps = ComponentProps<typeof Streamdown>;
 // Type-only version skew: @streamdown/code bundles shiki@3 types while
 // streamdown@2.5 expects shiki@4 types. Both work at runtime (each ships its
 // own highlighter); the cast papers over the .d.ts mismatch.
-const streamdownPlugins = { cjk, code, math, mermaid } as unknown as PluginConfig;
+// singleDollarTextMath: the teacher prompt instructs $...$ inline math (the
+// LLM-native convention); remark-math's default here is false.
+const streamdownPlugins = {
+  cjk,
+  code,
+  math: createMathPlugin({ singleDollarTextMath: true }),
+  mermaid,
+} as unknown as PluginConfig;
 
 export const MessageResponse = memo(
   ({ className, ...props }: MessageResponseProps) => (