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/hover-card.tsx

@@ -0,0 +1,44 @@
+"use client"
+
+import * as React from "react"
+import { HoverCard as HoverCardPrimitive } from "radix-ui"
+
+import { cn } from "@/lib/utils"
+
+function HoverCard({
+  ...props
+}: React.ComponentProps<typeof HoverCardPrimitive.Root>) {
+  return <HoverCardPrimitive.Root data-slot="hover-card" {...props} />
+}
+
+function HoverCardTrigger({
+  ...props
+}: React.ComponentProps<typeof HoverCardPrimitive.Trigger>) {
+  return (
+    <HoverCardPrimitive.Trigger data-slot="hover-card-trigger" {...props} />
+  )
+}
+
+function HoverCardContent({
+  className,
+  align = "center",
+  sideOffset = 4,
+  ...props
+}: React.ComponentProps<typeof HoverCardPrimitive.Content>) {
+  return (
+    <HoverCardPrimitive.Portal data-slot="hover-card-portal">
+      <HoverCardPrimitive.Content
+        data-slot="hover-card-content"
+        align={align}
+        sideOffset={sideOffset}
+        className={cn(
+          "z-50 w-64 origin-(--radix-hover-card-content-transform-origin) rounded-md border bg-popover p-4 text-popover-foreground shadow-md outline-hidden data-[side=bottom]:slide-in-from-top-2 data-[side=left]:slide-in-from-right-2 data-[side=right]:slide-in-from-left-2 data-[side=top]:slide-in-from-bottom-2 data-[state=closed]:animate-out data-[state=closed]:fade-out-0 data-[state=closed]:zoom-out-95 data-[state=open]:animate-in data-[state=open]:fade-in-0 data-[state=open]:zoom-in-95",
+          className
+        )}
+        {...props}
+      />
+    </HoverCardPrimitive.Portal>
+  )
+}
+
+export { HoverCard, HoverCardTrigger, HoverCardContent }