Teach it back: the AI becomes the curious student

A new mode where the user explains a topic in their own words and the AI
plays a curious classmate: short reactions, exactly one follow-up question
at a time, never "correct"/"wrong", never lecturing, and everything it knows
comes from the user's own decks and notes.

- Entry points: a sidebar row next to Exam mode and a "Teach it back" action
  in every deck's menu (which prefills the topic and scope).
- Start screen: deck or typed topic, friendly/skeptical student, the same
  context and model chips as Chat (/teach?deck=<id> pre-selects the deck).
- Session: the student prompt is a mode of the existing /api/chat route, so
  model resolution, allowlists, rate limits and the streaming client are the
  same code; the personality lives in lib/prompts.ts (TEACH_*). The deck's
  cards travel as a numbered checklist and the student is told to ask about
  the ideas that were skipped; it must say so rather than guess when the
  notes cover nothing. One constant (TEACH_MAX_EXCHANGES = 10) ends the
  session, or the Finish button does.
- Recap: a teach_summary call (JSON, one repair retry) yields well / gaps
  with card references / next steps; each gap links to the card it means.
  "Add missed cards to review" schedules those activities due now; "Turn
  gaps into cards" generates one flashcard per gap from the deck's notes and
  shows an editable review list before saving.
- Sessions are chat conversations with a mode:"teach" marker + session
  record: same IndexedDB history, backup and sync, filtered out of the Chat
  screens; the recent list reopens a recap or continues a session.
- Reused pieces: MessageRow, Composer (now optional attach/scope chips and a
  mic), Markdown/KaTeX, AiDisclaimer, ContextPicker/ModelPicker, plus a
  shared useChatModels hook and useKeyboardInset extracted from Chat.
- Dictation: Web Speech API recognition (lib/speech-input.ts); the mic only
  renders where the browser supports it, and dictated phrases land in the
  draft.
- All strings in en + cs. teach-test: 44 checks (API prompts and guards,
  both entry points, the session, recap actions, history, exchange limit,
  360/390px layouts, mic on/off). Version 0.8.1, SW v103.

lib/history.ts

@@ -226,6 +226,53 @@ export function recordAnswer(input: AnswerInput, at = Date.now()): void {
 }
 
 /** Used by backup import and sync pulls. */
+/**
+ * Puts specific cards on the review schedule, due right now — Teach it back's
+ * "add the missed cards to review". A card that was already scheduled keeps
+ * its ease and lapse count; only the due date is pulled forward. Returns how
+ * many cards were scheduled.
+ */
+export function scheduleForReview(deckId: string, activityIds: string[], at = Date.now()): number {
+  const changed: SrsRecord[] = [];
+  for (const activityId of activityIds) {
+    const key = `${deckId}:${activityId}`;
+    const previous = schedules.get(key);
+    changed.push({
+      key,
+      deckId,
+      activityId,
+      ease: previous?.ease ?? 2.5,
+      reps: previous?.reps ?? 0,
+      intervalDays: 0,
+      lapses: previous?.lapses ?? 0,
+      dueAt: at,
+      lastAt: at,
+      lastCorrect: previous?.lastCorrect ?? false,
+    });
+  }
+  if (changed.length === 0) return 0;
+
+  schedules = new Map(schedules);
+  for (const schedule of changed) schedules.set(schedule.key, schedule);
+  notify();
+  markSyncDirty();
+
+  void (async () => {
+    try {
+      await ensureLearningHydrated();
+      await withDb("readwrite", (db) => {
+        const transaction = db.transaction(SRS, "readwrite");
+        const store = transaction.objectStore(SRS);
+        for (const schedule of changed) store.put(schedule);
+      });
+    } catch (error) {
+      console.warn("[freezmo] could not schedule the review cards", error);
+    }
+  })();
+
+  return changed.length;
+}
+
 export async function replaceLearning(nextAnswers: AnswerRecord[], nextSrs: SrsRecord[]): Promise<void> {
   const sorted = [...nextAnswers].sort((a, b) => b.at - a.at).slice(0, MAX_ANSWERS);
   answers = sorted;