feat(issue-33): the job budget travels and the two clocks carry different labels

- wrapper: TIMEOUT falls back to MAM_JOB_TIMEOUT_S (--timeout > env > 3600);
  an invalid value warns and keeps 3600.
- loop: --job-timeout <sec> (run_loop.sh passes it on; refused in the legacy
  shell loop). The runner always hands the wrapper --timeout, so the budget
  the wrapper registers is the one its wait caps come from.
- runner: wait_for_job and the MAM_CHILD_WAIT_S default are budget + 300 s
  (MAM_WAIT_GRACE_S), today's 3900 with no option; an explicit
  MAM_CHILD_WAIT_S still wins.
- subscriber: the wall-clock budget returns 4 (RC_WALL_CLOCK), silence keeps
  2 (RC_NO_EVENT). The wrapper maps both to caller rc 2 and labels the close
  from the rc: wall_clock_timeout vs deadline_timeout; the disk-heartbeat
  grace that ends on the deadline is the wall clock too.
- registry close accepts wall_clock_timeout (engine: -> error); the remote
  runner's deadline and command-timeout details lead with wall_clock_timeout;
  the sub-job table files it CLOSED-UNCONFIRMED (first token, colon stripped).

Test expectations changed only where the contract changed: the loop's
contract_args now starts with --timeout, the subscriber's exit-code docstring
names rc 2/4, and the registry --help capture lists the new close kind.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

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

@@ -111,7 +111,7 @@ usage() {
 multi-agent-mux-delegate-job <command> [options]
 
   submit  --agent <name> (--prompt <text> | --prompt-file <path>) [--workdir <dir>] [--agent-session <label>]
-          [--timeout <sec>] [--idle-timeout <sec>] [--validate <script>]
+          [--timeout <sec> (default: $MAM_JOB_TIMEOUT_S or 3600)] [--idle-timeout <sec>] [--validate <script>]
           [--heartbeat <sec>] [--heartbeat-misses <count>] [--ack-timeout <sec>]
           [--registry-dir <dir>] [--dry-run] [--role <role_name>]
           [--type <direct|loop|discuss>] [--reviewer <reviewer_agent>]
@@ -140,6 +140,14 @@ EOF
 # ---- arg parsing helpers --------------------------------------------------
 AGENT="claude-code"; PROMPT=""; PROMPT_FILE=""; WORKDIR="$(pwd)"; AGENT_SESSION="herdr:claude"
 TIMEOUT=3600; IDLE_TIMEOUT=""; VALIDATE=""; DRY_RUN=0
+# Issue #33: the job budget falls back to $MAM_JOB_TIMEOUT_S (--timeout > env > 3600).
+if [[ -n "${MAM_JOB_TIMEOUT_S:-}" ]]; then
+  if [[ "$MAM_JOB_TIMEOUT_S" =~ ^[0-9]+$ && "$MAM_JOB_TIMEOUT_S" -gt 0 ]]; then
+    TIMEOUT="$MAM_JOB_TIMEOUT_S"
+  else
+    echo "WARNING: MAM_JOB_TIMEOUT_S=$MAM_JOB_TIMEOUT_S ignored (not a positive integer); using 3600" >&2
+  fi
+fi
 # Issue #18 liveness contract (N / K / T). An unset --idle-timeout derives K x N.
 HEARTBEAT_SEC="${MAM_HEARTBEAT_SEC:-30}"; HEARTBEAT_MISSES="${MAM_HEARTBEAT_MISSES:-4}"; ACK_TIMEOUT="${MAM_ACK_TIMEOUT_S:-180}"
 JOB_ID=""; REGISTRY_DIR="$REGISTRY_DIR_DEFAULT"; DELEGATE_ROLE="Worker"
@@ -803,7 +811,7 @@ _rc_for() {
 }
 
 finalize_unfinished() {
-  local job_id="$1" job_status="$2" sub_rc="$3" phase="${4:-}"
+  local job_id="$1" job_status="$2" sub_rc="$3" phase="${4:-}" FINALIZE_CLOCK=""
   if [ "${MAM_DELEGATE_FAIL_CLOSED:-1}" = "0" ]; then
     return 0
   fi
@@ -885,9 +893,16 @@ finalize_unfinished() {
       [ "$left" -le 0 ] && break
       sleep 1
     done
+    [ "$(date +%s)" -ge "$deadline" ] && FINALIZE_CLOCK="wall"
   fi
 
+  # Issue #33: the subscriber's rc says which clock ran out (4 wall clock,
+  # 2 no event); the disk-heartbeat grace above that ends on the deadline is
+  # the wall clock too. bash only carries the label.
+  local clock="${FINALIZE_CLOCK:-idle}"
+  [ "$sub_rc" = "4" ] && clock="wall"
   local close_req="deadline_timeout"
+  [ "$clock" = "wall" ] && [ "$phase" != "inject" ] && close_req="wall_clock_timeout"
   local detail=""
   if [ "$phase" = "preflight" ] || [ "$phase" = "idle_wait" ]; then
     close_req="cancelled"
@@ -896,6 +911,7 @@ finalize_unfinished() {
     [ "$phase" = "preflight" ] && [ -n "${PREFLIGHT_REASON:-}" ] && detail="$PREFLIGHT_REASON"
   fi
 
+  [ "$close_req" != "cancelled" ] && echo "finalize: $job_id closed by $([ "$clock" = "wall" ] && echo wall_clock || echo no_event) clock (budget ${TIMEOUT}s / idle ${IDLE_TIMEOUT}s)" >&2
   local close_args=(--job "$job_id" --request "$close_req")
   [ -n "$detail" ] && close_args+=(--detail "$detail")
   [ -n "${_disp_tok:-}" ] && close_args+=(--expect-dispatch-token "$_disp_tok")
@@ -925,7 +941,7 @@ finalize_unfinished() {
     if [ "$close_req" = "cancelled" ]; then
       "$PY" "$SCRIPT_DIR/scripts/publish_event.py" --registry-dir "$REGISTRY_DIR" --job "$job_id" --event cancelled --detail "$detail" ${disp_arg[@]+"${disp_arg[@]}"} 2>/dev/null || true
     elif [ "$sub_rc" -ne 1 ] || [ "$phase" = "inject" ]; then
-      local err_detail="deadline_timeout"
+      local err_detail="$close_req"
       [ "$phase" = "inject" ] && err_detail="agent_blocked"
       "$PY" "$SCRIPT_DIR/scripts/publish_event.py" --registry-dir "$REGISTRY_DIR" --job "$job_id" --event error --detail "$err_detail" ${disp_arg[@]+"${disp_arg[@]}"} 2>/dev/null || true
     fi