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/api/chat/route.ts

@@ -0,0 +1,5 @@
+import { handleChatRequest } from "@/src/server/chat-handler";
+
+export async function POST(req: Request) {
+	return handleChatRequest(req);
+}

app/api/chats/[id]/route.ts

@@ -0,0 +1,8 @@
+import { getChat } from "@/src/store/chats";
+
+export async function GET(_req: Request, { params }: { params: Promise<{ id: string }> }) {
+	const { id } = await params;
+	const chat = getChat(id);
+	if (!chat) return Response.json({ error: "Not found" }, { status: 404 });
+	return Response.json(chat);
+}

app/api/chats/route.ts

@@ -0,0 +1,12 @@
+import { createChat, listChats, titleFromPrompt } from "@/src/store/chats";
+
+export async function GET() {
+	return Response.json({ chats: listChats() });
+}
+
+export async function POST(req: Request) {
+	const body = (await req.json().catch(() => ({}))) as { title?: unknown };
+	const title = typeof body.title === "string" ? body.title : "";
+	const chat = createChat(titleFromPrompt(title || "Untitled session"));
+	return Response.json({ id: chat.id, title: chat.title });
+}