fix(issue-18): bind the heartbeat timer to the agent process; scope started to the attempt; ignore re-sent finished dispatches

Review round 1 (claude NOT PASS) corrections:
- B2: the timer now watches a process - `--watch-pid`, or by default the
  nearest agent-CLI ancestor of the publishing command - and stops within
  one period once it is gone, so a crashed agent stops heartbeating and is
  closed after K x N; a remote runner watches itself. Documented as process
  liveness (an alive-but-stuck agent keeps heartbeating).
- R1: `_wait_started` accepts an events.log `started` only when it carries
  the current dispatch token (loop jobs share one events.log).
- R2: the remote runner ignores a re-sent dispatch of an attempt that
  already reached its terminal.
- R3: registry.md EOF blank line (git diff --check clean).
- R4: the ack error states the effective budget when the wall clock cut it.
- P3: stop_timer verifies the pidfile pid is this job's timer before
  signalling; a retained state message keeps its own seq watermark so it
  can never make the monotonic guard drop its own event.
- MULTI_AGENT_RULES.md timeout section updated for the contract.
- tests: agent-process death stops the timer, recycled-pid safety,
  attempt-scoped started, re-sent dispatch; acceptance 3 now kills the
  agent process instead of the timer. Help captures refreshed
  (--watch-pid). The wrapper can be sourced with
  MAM_DELEGATE_JOB_NO_MAIN=1 for helper-level tests.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01VCgu9Fa9iT7TbJUSzdq4Ff

.agents/skills/multi-agent-mux-delegate-job/multi-agent-mux-delegate-job

@@ -604,6 +604,11 @@ _wait_started() {
   wall=$(( ${START_TIME:-$(date +%s)} + ${TIMEOUT:-3600} ))
   [ "$deadline" -gt "$wall" ] && deadline=$wall
   local ev_log="$REGISTRY_DIR/$job_id.events.log"
+  # A loop job keeps one events.log across iterations: only a `started` that
+  # carries THIS attempt's dispatch token counts (review R1).
+  local started_re='"event": *"started"'
+  [ -n "${_disp_tok:-}" ] && started_re='"event": *"started".*"dispatch_token": *"'"$_disp_tok"'"'
+  local budget=$(( deadline - $(date +%s) ))
   while :; do
     st="$(_disk_status "$job_id")"
     if [ -n "$st" ] && [ "$st" != "pending" ]; then
@@ -612,7 +617,7 @@ _wait_started() {
     fi
     # publish_event records `started` here before its wire publish and before
     # the status sync, so a slow broker cannot delay the acknowledgement.
-    if [ -f "$ev_log" ] && grep -Eq '"event": *"started"' "$ev_log" 2>/dev/null; then
+    if [ -f "$ev_log" ] && grep -Eq "$started_re" "$ev_log" 2>/dev/null; then
       echo "inject: job $job_id recorded 'started' in events.log; treating the prompt as delivered and continuing." >&2
       return 0
     fi
@@ -620,7 +625,10 @@ _wait_started() {
       echo "inject: subscriber received started for job $job_id; treating the prompt as delivered and continuing." >&2
       return 0
     fi
-    [ "$(date +%s)" -ge "$deadline" ] && return 1
+    if [ "$(date +%s)" -ge "$deadline" ]; then
+      ACK_WAITED_S="$budget"
+      return 1
+    fi
     sleep 1
   done
 }
@@ -951,7 +959,7 @@ inject_agent() {
   local ack_s="${MAM_INJECT_ACK_GRACE_S:-$ACK_TIMEOUT}"
   if ! _wait_started "$job_id" "$ack_s" "${4:-}"; then
     trap - EXIT
-    echo "ERROR: 프롬프트 주입 실패 — 세션 '$sess': no 'started' within ${ack_s}s (ack timeout); not re-injecting" >&2
+    echo "ERROR: 프롬프트 주입 실패 — 세션 '$sess': no 'started' within ${ACK_WAITED_S:-$ack_s}s (ack timeout ${ack_s}s, bounded by the wall clock); not re-injecting" >&2
     return 1
   fi
 
@@ -976,7 +984,7 @@ remote_dispatch() {
   fi
   local ack_s="${MAM_INJECT_ACK_GRACE_S:-$ACK_TIMEOUT}"
   if ! _wait_started "$job_id" "$ack_s" "$sub_log"; then
-    echo "ERROR: remote session '$sess' published no 'started' within ${ack_s}s (ack timeout); not re-dispatching" >&2
+    echo "ERROR: remote session '$sess' published no 'started' within ${ACK_WAITED_S:-$ack_s}s (ack timeout ${ack_s}s, bounded by the wall clock); not re-dispatching" >&2
     return 1
   fi
   echo "작업이 원격 세션 '$sess'에 전달되었습니다."
@@ -1069,4 +1077,7 @@ main() {
   esac
 }
 
-main "$@"
+# Tests source this file to exercise single helpers (MAM_DELEGATE_JOB_NO_MAIN=1).
+if [ "${MAM_DELEGATE_JOB_NO_MAIN:-0}" != "1" ]; then
+  main "$@"
+fi

.agents/skills/multi-agent-mux-delegate-job/registry.md

@@ -205,4 +205,3 @@ $PY scripts/registry.py logs --list              # every job, live status
 | `transport` | `herdr` (pane injection) or `remote` (signed retained dispatch over the broker) | `herdr` |
 
 `<registry>/<job>.heartbeat.pid` / `.heartbeat.log` belong to the running heartbeat timer; a terminal publish removes the pidfile.
-