test: pin a neutral shell and nested agent shell in the Herdr control smoke test

docs/verification/runtime-backends.md

@@ -1705,7 +1705,7 @@ herdr pane process-info --pane w1:p1 --session "$LAB" | jq -c '.result.process_i
 ```
 
 Before the fix `fm_backend_agent_state herdr` read that second state as `alive`, so `bin/fm-control.sh <id> relaunch` and `bin/fm-spawn.sh --relaunch` were refused for as long as the registration lived, which is hours.
-The registration is still present after the wait, and Herdr's own `pane report-agent` leaves the same shape behind on any pane, which is what the lifecycle-control guard uses.
+The registration is still present after the wait, and a `pane report-agent` registration whose agent process exits under a nested shell leaves the same shape behind on any pane, which is what the lifecycle-control guard uses; with no nested shell, Herdr releases that registration within about a second.
 
 Two vendor facts the fix rests on, both read from the outputs above and from `fm_backend_herdr_pane_process_state`'s `pane process-info` parse:
 
@@ -1744,7 +1744,7 @@ ok - real herdr 0.9.0 + pi 0.85.1: a running registered pi classifies alive at p
 ok - real herdr 0.9.0 + pi 0.85.1: the registration left behind by a quit pi reads stale-agent and recovers as dead
 ```
 
-`tests/fm-control-herdr-smoke.test.sh` proves the same shape through the control plane with no harness launched (the two `stale` lines under "Agent lifecycle control" above): a registration over a real agent-named process reads `alive`, stopping that process makes the pane read `stale-agent` and recover as `dead` while `agent get` still reports the record, `exit` then reports `already-stopped`, and `--relaunch` reuses the same endpoint with the local copy intact.
+`tests/fm-control-herdr-smoke.test.sh` proves the same shape through the control plane with no harness launched (the two `stale` lines under "Agent lifecycle control" above): a registration over a real agent-named process running under a nested shell reads `alive`, stopping that process makes the pane read `stale-agent` and recover as `dead` while `agent get` still reports the record, `exit` then reports `already-stopped`, and `--relaunch` reuses the same endpoint with the local copy intact.
 `tests/fm-backend-herdr.test.sh` pins the logic portably with canned `process-info` bodies over real processes, driving the signals apart: the identical shell-only foreground reads `stale-agent` for a childless shell and `live` when an agent-named process is still a descendant of that shell, a `working`, `done`, or `blocked` record over a shell-only pane reads the same as `idle`, an unreadable process view reads `unknown` and refuses husk closing, a transient prompt helper beside the shell settles into `stale-agent` on the next shell-only sample while a foreground that never settles within the bound still reads `live`, and `busy_state` verifies a `working` record before reporting busy.
 `tests/fm-crew-state.test.sh` pins the recovery classifier: a stale registration over a shell-only pane reports agent gone rather than alive or unreachable, and a stale `working` record never reports the pane working.
 A stale-registration pane is never a husk: create, reclaim, presentation recovery, and session cleanup keep refusing it, and only recovery reuses it.

tests/fm-control-herdr-smoke.test.sh

@@ -83,6 +83,29 @@ $TASK_IDS
 EOF
 [ -n "$TAB_ID" ] && [ -n "$PANE_ID" ] || fail "create_task did not return tab/pane ids"
 
+# Herdr starts the pane in the developer's login shell, whose prompt is not this
+# test's to choose. A prompt drawn with an agent composer glyph - a `❯` prompt
+# is exactly claude's bare composer row - anywhere in the viewport makes the
+# final exit case read the composer as holding pending text instead of as
+# unproven. An rc-free bash with a shell-glyph prompt on a cleared screen draws
+# no recognized composer chrome, so every composer verdict below depends on this
+# test alone. `exec` keeps the pane's shell pid.
+BASH_BIN=$(command -v bash) || fail "bash not found"
+printf -v BASH_Q '%q' "$BASH_BIN"
+fm_backend_herdr_send_text_line "$SESSION:$PANE_ID" "exec env PS1='hsmoke\$ ' HISTFILE=/dev/null $BASH_Q --noprofile --norc" \
+  || fail "could not pin a neutral shell prompt in the task pane"
+fm_backend_herdr_send_text_line "$SESSION:$PANE_ID" "clear" \
+  || fail "could not clear the login shell's output from the task pane"
+neutral_screen_shown() {  # the viewport holds nothing but the neutral prompt
+  fm_backend_herdr_visible_capture "$SESSION:$PANE_ID" 2>/dev/null \
+    | awk 'NF { n++; last = $0 } END { exit(n == 1 && last ~ /^hsmoke\$ *$/ ? 0 : 1) }'
+}
+for _ in $(seq 1 50); do
+  ! neutral_screen_shown || break
+  sleep 0.1
+done
+neutral_screen_shown || fail "the task pane did not settle on a cleared neutral shell prompt"
+
 {
   echo "window=$SESSION:$PANE_ID"
   echo "endpoint_task_id=hsmoke"
@@ -233,6 +256,14 @@ start_agent_process() {
     || version_fail "a real agent-named foreground process reads '$(fm_backend_herdr_pane_process_state "$SESSION" "$PANE_ID")' rather than 'agent' through pane process-info"
 }
 
+# Herdr keeps a registration after its agent exits only when a nested
+# interactive shell sits under the pane's top shell (issue #4115); an agent that
+# exits straight back to the top shell is released within about a second, which
+# would race the stale-registration case below. So the agent runs under a
+# nested shell, the crew shape `treehouse get` leaves behind. It inherits the
+# neutral PS1 and HISTFILE from the top shell's environment.
+fm_backend_herdr_send_text_line "$SESSION:$PANE_ID" "$BASH_Q --noprofile --norc" \
+  || fail "could not start a nested shell in the task pane"
 start_agent_process
 herdr pane report-agent "$PANE_ID" --source fm-control-smoke --agent fm-control-smoke-agent \
   --state idle --session "$SESSION" >/dev/null 2>&1 \