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/store/chats.ts

@@ -0,0 +1,87 @@
+import * as fs from "node:fs";
+import * as path from "node:path";
+import type { UIMessage } from "ai";
+import { PATHS } from "../../config.ts";
+
+/**
+ * Chat store — one JSON file per chat in data/chats/.
+ *
+ * The stored messages are full AI SDK UIMessages (parts included). This is
+ * the canonical session record: a pending quiz is a tool part in
+ * `input-available` state, which is exactly what makes resume-mid-question
+ * free. The extraction pipeline (src/extract) will read these later; old pi
+ * sessions (data/sessions) remain bootstrap input only.
+ */
+
+export interface ChatRecord {
+	id: string;
+	title: string;
+	createdAt: string;
+	updatedAt: string;
+	messages: UIMessage[];
+}
+
+export interface ChatSummary {
+	id: string;
+	title: string;
+	createdAt: string;
+	updatedAt: string;
+	messageCount: number;
+}
+
+function chatFile(id: string): string {
+	if (!/^[A-Za-z0-9_-]+$/.test(id)) throw new Error(`Invalid chat id: ${id}`);
+	return path.join(PATHS.chats, `${id}.json`);
+}
+
+export function createChat(title: string): ChatRecord {
+	const now = new Date().toISOString();
+	const record: ChatRecord = {
+		id: `chat_${Date.now().toString(36)}_${crypto.randomUUID().slice(0, 8)}`,
+		title: title.trim() || "Untitled session",
+		createdAt: now,
+		updatedAt: now,
+		messages: [],
+	};
+	fs.mkdirSync(PATHS.chats, { recursive: true });
+	fs.writeFileSync(chatFile(record.id), JSON.stringify(record, null, "\t"), "utf-8");
+	return record;
+}
+
+export function getChat(id: string): ChatRecord | null {
+	try {
+		return JSON.parse(fs.readFileSync(chatFile(id), "utf-8")) as ChatRecord;
+	} catch {
+		return null;
+	}
+}
+
+export function listChats(): ChatSummary[] {
+	try {
+		fs.mkdirSync(PATHS.chats, { recursive: true });
+		return fs
+			.readdirSync(PATHS.chats)
+			.filter((f) => f.endsWith(".json"))
+			.map((f) => getChat(f.slice(0, -5)))
+			.filter((r): r is ChatRecord => r !== null)
+			.map(({ messages, ...summary }) => ({ ...summary, messageCount: messages.length }))
+			.sort((a, b) => b.updatedAt.localeCompare(a.updatedAt));
+	} catch {
+		return [];
+	}
+}
+
+/** Persist the full message list (client state + new response) after a turn. */
+export function saveMessages(id: string, messages: UIMessage[]): void {
+	const record = getChat(id);
+	if (!record) throw new Error(`Chat not found: ${id}`);
+	record.messages = messages;
+	record.updatedAt = new Date().toISOString();
+	fs.writeFileSync(chatFile(id), JSON.stringify(record, null, "\t"), "utf-8");
+}
+
+/** Derive a short title from the first user message. */
+export function titleFromPrompt(prompt: string): string {
+	const oneLine = prompt.replace(/\s+/g, " ").trim();
+	return oneLine.length > 72 ? `${oneLine.slice(0, 72)}…` : oneLine;
+}