Second **LANE** site from the archived triage (#3154), same additive
shape as #3160.
## The bug
`liveLineageChildFilter` is the lineage-integrity gate (VAL-DATA-010)
behind `deleteTask` and `archiveTask`: a parent with **live** children
is refused with `TaskHasLineageChildrenError`.
It excluded children in the `archived` column **by id**. So on a board
that renames that lane, an archived child still counted as live and the
parent could not be deleted — with an error naming a child the operator
had **already filed away**.
## The fix is permissive, and that is the correct direction
The gate exists to protect **live** children; an archived child is not
one. Resolving makes fewer rows block, which is what the gate always
meant.
I am flagging this explicitly because *"a conversion makes a delete gate
stop firing"* deserves a second look. The second look is that it was
firing on rows it was never meant to protect.
## LANE, not STATE
The two STATE sites in this inventory are marked at their own sites
(#3157) and must never be resolved — one of them deletes directories.
This one asks about the board.
## Wired at every caller, not left as an optional seam
`findLiveLineageChildrenImpl` (has `store`) and both
`archive-lifecycle-2.ts` gates resolve and pass it.
`hasLiveLineageChildren` takes the same parameter so the two readers
**cannot disagree** about which children are live — the half-conversion
shape this program keeps finding, and the reason #3129's earlier attempt
was reverted for leaving a seam unsupplied.
## Parity gate satisfied
Same reason as #3160: the conversion is **additive** — it keeps the
literal as the fallback, so no encoding's literal count moves and a
caller supplying no set gets byte-identical SQL.
## Measured
- 4 new cases; parity test still **2/2**, inventories unmoved.
- **MUTATION**: dropping the resolved branch fails the renamed case and
leaves the legacy **control**, the **fail-soft** case, and the
parent/project-scope **negative** green.
- lineage / archive / soft-delete / archived suites — **6 files / 19
tests pass**.
- `tsc --noEmit -p packages/core` clean; census `--strict`,
`check-sql-column-literals`, `check-fnxc-future-dates` clean.
## Census
**Unchanged** — the literal remains the fallback arm, by design.
Co-authored-by: Claude Opus 5 (1M context) <noreply@anthropic.com>
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