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.

src/server/chat-handler.ts

@@ -0,0 +1,42 @@
+import { createAgentUIStreamResponse, type UIMessage } from "ai";
+import { createTeacherAgent, type TeacherAgent } from "../agent/teacher-agent.ts";
+import { getChat, saveMessages } from "../store/chats.ts";
+
+/**
+ * One chat turn: run the teacher agent over the client's message list and
+ * stream the UI message stream back. Framework-free (plain Request/Response)
+ * so tests can drive it directly with a scripted mock model — the Next route
+ * handler in app/api/chat is a one-line wrapper.
+ *
+ * The client owns the message list between turns (useChat); the server
+ * persists the canonical state (client messages + agent response) onFinish.
+ */
+export async function handleChatRequest(req: Request, agent?: TeacherAgent): Promise<Response> {
+	let body: { chatId?: unknown; messages?: unknown };
+	try {
+		body = await req.json();
+	} catch {
+		return Response.json({ error: "Invalid JSON body" }, { status: 400 });
+	}
+	const chatId = typeof body.chatId === "string" ? body.chatId : "";
+	if (!chatId || !getChat(chatId)) {
+		return Response.json({ error: "Unknown chat" }, { status: 404 });
+	}
+	if (!Array.isArray(body.messages)) {
+		return Response.json({ error: "messages must be an array" }, { status: 400 });
+	}
+
+	return createAgentUIStreamResponse({
+		agent: agent ?? createTeacherAgent(),
+		uiMessages: body.messages as UIMessage[],
+		onFinish: ({ messages, isAborted }) => {
+			// Persist even when aborted: the partial transcript (including any
+			// pending question part) is what makes resume work.
+			try {
+				saveMessages(chatId, messages as UIMessage[]);
+			} catch (err) {
+				console.error(`[chat ${chatId}] persist failed:`, err, { isAborted });
+			}
+		},
+	});
+}