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/AGENTS.md

@@ -200,12 +200,16 @@ stored** and clients must adopt that response rather than their own payload.
 
 ### Lifecycle buckets — `status` on each bookmark
 
-`reading` | `archived` | `finished`, orthogonal to `favorite`. Archived and
-finished appear only in their own tab, never in All, Updated, Favourites or the
-recent strip. The poller keeps checking archived series and skips finished ones.
+`reading` | `archived`, orthogonal to `favorite`. Archived rows appear only
+in their own tab, never in All, Updated, Favourites or the recent strip. The
+poller keeps checking archived series; a finished Series (issue #157) is a
+`series.finished_at` fact the Lane gate reads, with every bookmark on it
+archived.
 
-- `finished` is settable only from the web UI; `PUT /bookmarks/{key}` rejects
-  it with 400.
+- `PUT /bookmarks/{key}` accepts only the two values; anything else —
+  `finished` included — is a plain 400, and the web UI's own status control
+  validates the same way. The 0016 migration is the only writer of the flag
+  today; the undo is writing 0.
 - **An empty incoming status means "keep the stored one"**, and it is resolved
   on the `VALUES` side of `Store.Upsert`, not in the conflict clause:
   `excluded.*` is the post-evaluation row, so a default applied there would