ops(scripts): dispatch, queue gating, heartbeat, quota probe

dispatch-turn.sh (headless turn launcher with TURN_MODEL routing),
queue-after.sh (serial gate chain + quota-wall guard), pmo-heartbeat.sh
(PMO wake loop), quota-probe-then-chain.sh (post-wall relaunch).

scripts/pmo-heartbeat.sh

@@ -0,0 +1,20 @@
+#!/usr/bin/env bash
+# pmo-heartbeat.sh — wake the PMO session while the overnight chain runs.
+# Self-terminates when inbox-work has no TASKs AND no semaphore slots are held.
+
+INBOX=/home/reachableceo/.coordinate/inbox-work
+SLOTS=/home/_crossfeed/metrics/active
+LOG=/home/reachableceo/.coordinate/logs/heartbeat.log
+INTERVAL=3600
+
+while true; do
+  pending=$(ls -1 "$INBOX"/TASK-*.md 2>/dev/null | wc -l)
+  active=$(ls -1 "$SLOTS"/*.pid 2>/dev/null | wc -l)
+  if [ "$pending" -eq 0 ] && [ "$active" -eq 0 ]; then
+    echo "$(date -Is) chain drained — heartbeat exiting" >> "$LOG"
+    exit 0
+  fi
+  screen -S RCEO-PMO -X stuff "hb: chain check — verify reports, archive, mirror redmine, redispatch flakes, dispatch next$(printf '\r')"
+  echo "$(date -Is) wake sent (pending=$pending active=$active)" >> "$LOG"
+  sleep "$INTERVAL"
+done