v3: AI SDK pivot — pi removed, Next.js 16 + AI SDK 7 + AI Elements teacher app

The teaching agent no longer runs on pi. Stack:
- ToolLoopAgent (ai@7) + OpenRouter (OPENROUTER_API_KEY), model via LH_MODEL,
  default anthropic/claude-sonnet-4.5 with reasoning tokens
- quiz/ask_user_question = client-side tools (no server execute): the call
  lands as a typed tool part in input-available state; the card grades via
  src/core/question-core.ts; addToolOutput sends the verdict; the teacher's
  reaction continues the same assistant message
- resume-mid-quiz is free: the pending tool part persists in the transcript
- persistence: one JSON per chat (data/chats/), full UIMessage transcripts,
  saved onFinish (also on abort)
- UI: AI Elements (owned copy-paste components, pruned to the five in use)
  + button-based QuizCard/AnsweredCard (ask answers never graded)
- pi fully removed: TUI, extensions, Fastify+WS server, bridge, custom
  protocol all deleted (recoverable from git history)
- tests: question-core units carry over; chat-flow integration drives
  handleChatRequest with MockLanguageModelV4 (48 tests, zero tokens);
  render smoke tests guard the cards (renderToStaticMarkup)

Carried over unchanged: teacher system prompt, question-core, schema/
ledger/derive/extract pipeline, data model.

app/chat/[id]/page.tsx

@@ -0,0 +1,26 @@
+import { notFound } from "next/navigation";
+import { Chat } from "@/components/chat";
+import { getChat } from "@/src/store/chats";
+import type { TeacherUIMessage } from "@/src/agent/ui-message";
+
+export const dynamic = "force-dynamic";
+
+export default async function ChatPage({
+	params,
+	searchParams,
+}: {
+	params: Promise<{ id: string }>;
+	searchParams: Promise<{ prompt?: string }>;
+}) {
+	const [{ id }, { prompt }] = await Promise.all([params, searchParams]);
+	const chat = getChat(id);
+	if (!chat) notFound();
+	return (
+		<Chat
+			chatId={chat.id}
+			title={chat.title}
+			initialMessages={chat.messages as TeacherUIMessage[]}
+			initialPrompt={prompt}
+		/>
+	);
+}