docs(shared): the cutover date is the gate, the flag refines it

docs/shared-expenses-design.md

@@ -13,7 +13,15 @@ recorded under [What was rejected](#what-was-rejected).
 ## The one rule
 
 **Spend and owed are different questions asked of the same table, and the line
-between them is `transaction_splits.settled`.**
+between them is the cutover date, refined by `transaction_splits.settled`.**
+
+`ACTIVE_OBLIGATION` is `ts.settled = false AND t.transaction_date >=
+'2026-01-09'`. Nothing before the cutover can be owed, because carryover
+transaction 2348 already carries the entire pre-cutover balance as one figure —
+so a split on an older transaction describes only *how an expense was shared*.
+That is what makes splitting history safe, and it is why the flag is a
+refinement rather than the guard: any delete-and-recreate write path resets a
+boolean, and one did.
 
 |  | Counts settled splits? | Why |
 |---|---|---|