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/ui-message.ts

@@ -0,0 +1,19 @@
+import type { UIMessage } from "ai";
+import type { AskToolInput, QuizToolInput } from "./tools.ts";
+import type { QuestionAnswerData } from "../core/question-core.ts";
+
+/**
+ * The typed UI message for the teacher chat — gives the frontend typed tool
+ * parts ("tool-quiz" / "tool-ask_user_question" with typed input/output)
+ * without importing the server-side agent into the client bundle.
+ *
+ * Declared explicitly (not via InferUITools) because a client-side tool has
+ * no execute function, so its OUTPUT type lives only here: the structured
+ * answer record the client builds and sends via addToolOutput.
+ */
+export type TeacherUITools = {
+	quiz: { input: QuizToolInput; output: QuestionAnswerData };
+	ask_user_question: { input: AskToolInput; output: QuestionAnswerData };
+};
+
+export type TeacherUIMessage = UIMessage<unknown, never, TeacherUITools>;