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.

components/home.tsx

@@ -0,0 +1,78 @@
+"use client";
+
+import { useState } from "react";
+import { useRouter } from "next/navigation";
+import { Button } from "@/components/ui/button";
+import { Input } from "@/components/ui/input";
+import type { ChatSummary } from "@/src/store/chats";
+
+export function Home({ chats }: { chats: ChatSummary[] }) {
+	const router = useRouter();
+	const [topic, setTopic] = useState("");
+	const [busy, setBusy] = useState(false);
+
+	const start = async () => {
+		const t = topic.trim();
+		if (!t || busy) return;
+		setBusy(true);
+		try {
+			const res = await fetch("/api/chats", {
+				method: "POST",
+				headers: { "Content-Type": "application/json" },
+				body: JSON.stringify({ title: t }),
+			});
+			const { id } = (await res.json()) as { id: string };
+			router.push(`/chat/${id}?prompt=${encodeURIComponent(t)}`);
+		} catch {
+			setBusy(false);
+		}
+	};
+
+	return (
+		<main className="mx-auto flex min-h-dvh w-full max-w-2xl flex-col px-4 py-10">
+			<h1 className="mb-1 text-2xl font-semibold">Learning Harness</h1>
+			<p className="mb-8 text-sm text-muted-foreground">
+				A teacher with a memory. Start a session on anything you want to understand.
+			</p>
+
+			<form
+				className="mb-10 flex gap-2"
+				onSubmit={(e) => {
+					e.preventDefault();
+					void start();
+				}}
+			>
+				<Input
+					value={topic}
+					onChange={(e) => setTopic(e.target.value)}
+					placeholder="What do you want to learn?"
+					autoFocus
+				/>
+				<Button type="submit" disabled={!topic.trim() || busy}>
+					{busy ? "Starting…" : "Start"}
+				</Button>
+			</form>
+
+			<h2 className="mb-3 text-sm font-medium uppercase tracking-wide text-muted-foreground">Sessions</h2>
+			{chats.length === 0 ? (
+				<p className="text-sm text-muted-foreground">No sessions yet.</p>
+			) : (
+				<div className="flex flex-col gap-2">
+					{chats.map((c) => (
+						<button
+							key={c.id}
+							type="button"
+							onClick={() => router.push(`/chat/${c.id}`)}
+							className="rounded-lg border px-4 py-3 text-left transition-colors hover:bg-accent"
+						>
+							<div className="truncate font-medium">{c.title}</div>
+							<div className="text-xs text-muted-foreground">
+								{c.messageCount} messages · {new Date(c.updatedAt).toLocaleString()}
+							</div>
+						</button>
+					))}
+				</div>
+			)}
+		</main>
+	);
+}