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/ui/button-group.tsx

@@ -0,0 +1,83 @@
+import { cva, type VariantProps } from "class-variance-authority"
+import { Slot } from "radix-ui"
+
+import { cn } from "@/lib/utils"
+import { Separator } from "@/components/ui/separator"
+
+const buttonGroupVariants = cva(
+  "flex w-fit items-stretch has-[>[data-slot=button-group]]:gap-2 [&>*]:focus-visible:relative [&>*]:focus-visible:z-10 has-[select[aria-hidden=true]:last-child]:[&>[data-slot=select-trigger]:last-of-type]:rounded-r-md [&>[data-slot=select-trigger]:not([class*='w-'])]:w-fit [&>input]:flex-1",
+  {
+    variants: {
+      orientation: {
+        horizontal:
+          "[&>*:not(:first-child)]:rounded-l-none [&>*:not(:first-child)]:border-l-0 [&>*:not(:last-child)]:rounded-r-none",
+        vertical:
+          "flex-col [&>*:not(:first-child)]:rounded-t-none [&>*:not(:first-child)]:border-t-0 [&>*:not(:last-child)]:rounded-b-none",
+      },
+    },
+    defaultVariants: {
+      orientation: "horizontal",
+    },
+  }
+)
+
+function ButtonGroup({
+  className,
+  orientation,
+  ...props
+}: React.ComponentProps<"div"> & VariantProps<typeof buttonGroupVariants>) {
+  return (
+    <div
+      role="group"
+      data-slot="button-group"
+      data-orientation={orientation}
+      className={cn(buttonGroupVariants({ orientation }), className)}
+      {...props}
+    />
+  )
+}
+
+function ButtonGroupText({
+  className,
+  asChild = false,
+  ...props
+}: React.ComponentProps<"div"> & {
+  asChild?: boolean
+}) {
+  const Comp = asChild ? Slot.Root : "div"
+
+  return (
+    <Comp
+      className={cn(
+        "flex items-center gap-2 rounded-md border bg-muted px-4 text-sm font-medium shadow-xs [&_svg]:pointer-events-none [&_svg:not([class*='size-'])]:size-4",
+        className
+      )}
+      {...props}
+    />
+  )
+}
+
+function ButtonGroupSeparator({
+  className,
+  orientation = "vertical",
+  ...props
+}: React.ComponentProps<typeof Separator>) {
+  return (
+    <Separator
+      data-slot="button-group-separator"
+      orientation={orientation}
+      className={cn(
+        "relative m-0! self-stretch bg-input data-[orientation=vertical]:h-auto",
+        className
+      )}
+      {...props}
+    />
+  )
+}
+
+export {
+  ButtonGroup,
+  ButtonGroupSeparator,
+  ButtonGroupText,
+  buttonGroupVariants,
+}