fix(functions): server-authoritative, mode-aware, deterministic daily question

Replace pickRandomQuestionId (empty pool → unresolvable q_default_daily fallback)
with pickDailyQuestionId(date): computes today's weekday mode (mirrors the client
DailyModeResolver.DOW_DEFAULTS, FROZEN) and deterministically indexes the free
daily pool by epochDay % poolSize — the SAME question the free client would pick,
now assigned server-side.

Fixes two things at the root:
- The daily 'questions' pool was empty, so every couple got q_default_daily, which
  the client can't resolve → each device fell back to its own local selection
  (the DQ-MISMATCH-001 class; the client half was pinned to the free pool in C1).
- Partners in different time zones computed different device-local weekdays and got
  different questions; a single server-assigned id makes both devices identical.

Firestore 'questions' seeded with the 75 free daily_fun_mc weekday questions (ids
match the client asset DB so getQuestionById resolves them). Pool fetched once and
filtered in memory — no composite index needed.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

functions/src/questions/assignDailyQuestion.ts

@@ -23,9 +23,9 @@ export const assignDailyQuestion = functions.pubsub
     const today = cstDateString()
     const nextDay = nextCstDateString()
 
-    const questionId = await pickRandomQuestionId()
+    const questionId = await pickDailyQuestionId(today)
     if (!questionId) {
-      console.error('[assignDailyQuestion] no active questions available')
+      console.error('[assignDailyQuestion] questions pool not seeded — skipping assignment')
       return
     }
 
@@ -109,7 +109,7 @@ export const assignDailyQuestionCallable = functions.https.onCall(async (data: R
   if (date !== today) {
     throw new functions.https.HttpsError('invalid-argument', 'Daily question can only be assigned for today.')
   }
-  const questionId = await pickRandomQuestionId()
+  const questionId = await pickDailyQuestionId(today)
   if (!questionId) {
     throw new functions.https.HttpsError('internal', 'No active questions available.')
   }
@@ -150,22 +150,53 @@ export const assignDailyQuestionCallable = functions.https.onCall(async (data: R
  * so the app still functions during rollout. In production, keep the local
  * Room database and Firestore pool in sync through the existing seed flow.
  */
-async function pickRandomQuestionId(): Promise<string | null> {
+// Weekday → daily mode tag. FROZEN to mirror the client's DailyModeResolver.DOW_DEFAULTS
+// (app/.../domain/DailyModeResolver.kt); JS getUTCDay(): 0=Sun … 6=Sat.
+const WEEKDAY_MODE_TAGS: Record<number, string> = {
+  0: 'mode_tiny_date_night',   // Sunday — Slow Burn Sunday
+  1: 'mode_soft_monday',       // Monday — Mood Check Monday
+  2: 'mode_snack_mission',     // Tuesday — Tiny Win Tuesday
+  3: 'mode_no_phone_moment',   // Wednesday — Real One Wednesday
+  4: 'mode_laugh_reset',       // Thursday — Laugh It Off Thursday
+  5: 'mode_flirty_friday',     // Friday — Flirty Friday
+  6: 'mode_weekend_side_quest',// Saturday — Side Quest Saturday
+}
+
+/** Days since epoch for a YYYY-MM-DD Chicago date — mirrors LocalDate.toEpochDay() the client
+ *  uses for its deterministic daily offset, so server and client land on the same question. */
+function epochDayOf(dateStr: string): number {
+  const [y, m, d] = dateStr.split('-').map(Number)
+  return Math.floor(Date.UTC(y, m - 1, d) / 86_400_000)
+}
+
+/**
+ * Deterministically pick the SAME daily question the free client would compute for [dateStr]:
+ * today's weekday mode, ordered by id, indexed by epochDay % poolSize. Making this SERVER-side and
+ * authoritative also fixes partners in different time zones getting different questions (the client
+ * falls back to device-local weekday only when there is no server assignment). Returns null if the
+ * questions pool is unseeded so the caller can no-op rather than write an unresolvable id.
+ */
+async function pickDailyQuestionId(dateStr: string): Promise<string | null> {
   const db = admin.firestore()
+  // The whole free daily pool is tiny (~75 rows); fetch once and filter in memory to avoid a
+  // composite index on (active, isPremium, modeTag).
   const snapshot = await db
     .collection('questions')
     .where('active', '==', true)
     .where('isPremium', '==', false)
     .get()
+  if (snapshot.empty) return null
 
-  if (snapshot.empty) {
-    // Rollout fallback: keep the feature working until the questions pool is seeded.
-    return 'q_default_daily'
-  }
-
-  const docs = snapshot.docs
-  const chosen = docs[Math.floor(Math.random() * docs.length)]
-  return chosen.id
+  const weekday = new Date(`${dateStr}T12:00:00Z`).getUTCDay()
+  const modeTag = WEEKDAY_MODE_TAGS[weekday]
+  const inMode = snapshot.docs
+    .filter((d) => d.get('modeTag') === modeTag)
+    .sort((a, b) => (a.id < b.id ? -1 : a.id > b.id ? 1 : 0))
+  const pool = inMode.length > 0
+    ? inMode
+    : snapshot.docs.slice().sort((a, b) => (a.id < b.id ? -1 : a.id > b.id ? 1 : 0)) // wildcard/empty-mode fallback
+  const offset = ((epochDayOf(dateStr) % pool.length) + pool.length) % pool.length
+  return pool[offset].id
 }
 
 /**