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/agent/teacher-agent.ts

@@ -0,0 +1,36 @@
+import * as fs from "node:fs";
+import { ToolLoopAgent, stepCountIs, type LanguageModel } from "ai";
+import { openrouter } from "@openrouter/ai-sdk-provider";
+import { PATHS } from "../../config.ts";
+import { teacherTools } from "./tools.ts";
+
+/**
+ * The teacher agent. Everything pi used to provide (agent loop, tool calling,
+ * streaming, multi-step) is these few lines now.
+ *
+ * The model is injectable so tests can pass a MockLanguageModelV4 and drive
+ * deterministic scripted lessons (see tests/chat-flow.test.ts).
+ */
+
+const DEFAULT_MODEL = process.env.LH_MODEL ?? "anthropic/claude-sonnet-4.5";
+
+const instructions = fs.readFileSync(PATHS.teacherPrompt, "utf-8");
+
+export function createTeacherAgent(model?: LanguageModel) {
+	return new ToolLoopAgent({
+		model:
+			model ??
+			openrouter(DEFAULT_MODEL, {
+				// Ask OpenRouter for reasoning tokens when the model supports them;
+				// they stream as reasoning parts into the UI's collapsible block.
+				reasoning: { enabled: true, effort: "medium" },
+			}),
+		instructions,
+		tools: teacherTools,
+		// Both tools are client-side (no execute) — a tool call ends the server
+		// turn automatically. stepCountIs is just the safety net.
+		stopWhen: stepCountIs(20),
+	});
+}
+
+export type TeacherAgent = ReturnType<typeof createTeacherAgent>;