Finish Phase 22: the half of Petal that works with the tunnel down

Grammar lite, the false-friend list, the daily invitation and the offline
miscollocations — the four remaining §5–§6 items, all client-side and all
alive on a box that cannot reach the model.

The offline collocations forced a schema change. `type` had been doubling
as the answer to "which engine found this" — `mechanics` meant offline —
and that stops being true the moment an offline rule proposes a
collocation. Migration 0013 adds `source` (llm | local) and every pass now
scopes its DELETE by engine; without it the coach silently wiped every
offline chunk on the page. Existing rows backfill by type, so a pre-0013
collocation row is claimed as the coach's, which it was: the offline list
did not exist yet.

The rule pack is hand-curated rather than mined, and the entries left out
are the point — `married with` is wrong until "married with children",
`arrive to` wants at or in depending on the noun. A pack running on every
keystroke must not correct correct writing.

Claude-Session: https://claude.ai/code/session_016y6gyuHkQXPiEuW8RGQyua

web/src/components/Companion/PetalCompanion.tsx

@@ -13,6 +13,11 @@ interface Props {
   editTick: number
   acceptTick: number
   text: string
+  // The open document is still empty — the one state the daily writing
+  // invitation is offered in.
+  blankPage: boolean
+  // Called when she takes the invitation up, with the English prompt.
+  onAcceptInvitation: (prompt: string) => void
 }
 
 // Emoji placeholder per mood, used for any mood a companion has no Lottie for.
@@ -30,17 +35,38 @@ const STORAGE_KEY = 'petal.companion'
 // useCompanion and shows a Mandarin-first speech bubble for cheers, tips, and
 // break reminders. Clicking the mascot opens a picker to switch companions
 // (the choice persists in localStorage).
-export function PetalCompanion({ wordCount, saveStatus, llmDown, editTick, acceptTick, text }: Props) {
+export function PetalCompanion({
+  wordCount,
+  saveStatus,
+  llmDown,
+  editTick,
+  acceptTick,
+  text,
+  blankPage,
+  onAcceptInvitation,
+}: Props) {
   const t = usePack()
-  const { mood, bubble, dismiss, holdBubble, releaseBubble } = useCompanion({
+  const {
+    mood,
+    bubble,
+    dismiss,
+    holdBubble,
+    releaseBubble,
+    acceptInvite,
+    declineInvite,
+    setInviteHandler,
+  } = useCompanion({
     wordCount,
     saveStatus,
     llmDown,
     editTick,
     acceptTick,
     text,
+    blankPage,
   })
 
+  useEffect(() => setInviteHandler(onAcceptInvitation), [setInviteHandler, onAcceptInvitation])
+
   const [companionId, setCompanionId] = useState<string>(
     () => readPref(STORAGE_KEY) || DEFAULT_COMPANION,
   )
@@ -179,6 +205,36 @@ export function PetalCompanion({ wordCount, saveStatus, llmDown, editTick, accep
           >
             {bubble.en}
           </p>
+
+          {/* The daily invitation's two answers. "Not today" is a real button
+              sitting level with the other one, not a small grey escape — a no
+              that has to be hunted for isn't much of a no. */}
+          {bubble.invite && (
+            <div className="mt-3 flex flex-wrap items-center gap-2">
+              <button
+                type="button"
+                onClick={(e) => {
+                  e.stopPropagation()
+                  acceptInvite(bubble.invite!.prompt)
+                }}
+                className="rounded-full px-3.5 py-1.5 text-sm font-bold"
+                style={{ background: 'var(--color-accent)', color: 'var(--color-plum)' }}
+              >
+                {t.companion.inviteAccept}
+              </button>
+              <button
+                type="button"
+                onClick={(e) => {
+                  e.stopPropagation()
+                  declineInvite()
+                }}
+                className="rounded-full px-3.5 py-1.5 text-sm font-semibold"
+                style={{ background: 'var(--color-surface-alt)', color: 'var(--color-plum)' }}
+              >
+                {t.companion.inviteDecline}
+              </button>
+            </div>
+          )}
         </div>
       )}