Spec #136: finished becomes a Series fact, Lane gate rewritten on it (#157)

finished_at lands on series (0016 seeds it from the pre-flip finished
bookmarks, then flips those bookmarks to archived), the poll gate and
eligible count read the flag instead of a per-Reader vote, PUT rejects
the finished status like any unknown value, and the web UI drops the
Finished tab, badge and finish button. Novel merge rank is archived >
reading. Per-Reader disagreement (one Reader keeps a finished Series in
reading forever) is what the flag repairs; the cutover keeps polling
state unchanged for every Series.

backend/internal/api/handlers.go

@@ -73,14 +73,11 @@ func (h *Handler) Put(w http.ResponseWriter, r *http.Request) {
 	}
 
 	// An empty status is "no opinion" and Upsert keeps the stored bucket.
-	// Finishing a series is a web-UI decision, so the JSON API refuses it
-	// rather than trusting every client to leave it alone.
+	// Anything else outside the two lifecycle buckets is a client bug, not
+	// something to silently coerce — finished included, which is no longer a
+	// bucket at all (issue #157).
 	switch b.Status {
 	case "", store.StatusReading, store.StatusArchived:
-	case store.StatusFinished:
-		http.Error(w, "status "+store.StatusFinished+" can only be set from the web UI",
-			http.StatusBadRequest)
-		return
 	default:
 		http.Error(w, "invalid status", http.StatusBadRequest)
 		return