fix(issue-6): fail-closed registry timeout and TUI turn handshake

- Introduce finalize_unfinished in multi-agent-mux-delegate-job for fail-closed atomic transitions
- Enforce CAS dispatch_token and attempt_id pinning across engine, CLI, and lifecycle scripts
- Integrate Herdr wait_for_agent_idle turn handshake to prevent prompt loss and race conditions
- Resolve bash 3.2 set -u empty array expansion compatibility in lib.sh
- Preserve Issue #5 R2 contract in CAS transition engine (engine.py, publish_event.py, service.py)
- Add comprehensive regression suites (test_issue6_fail_closed.py, test_issue6_turn_handshake.py)
- Bump lockstep framework and skills to v4.4.1 across lib.sh, eager.py, VERSIONS.md, 8 SKILL.md
- Synchronize documentation (IMPROVEMENTS.md, MESSAGING.md, state-transitions.md, task.md, phase5-e2e.md)
- Unanimous PASS achieved across 4 reviewer team leaders (Claude, Codex, OpenCode, Grok)

Closes #6

.agents/skills/multi-agent-mux-stop/scripts/stop_session.sh

@@ -142,6 +142,29 @@ sys.exit(7)
 
 TARGET_CWD=$(printf '%s' "$MAPPED_DATA" | python3 -c 'import sys,json; print(json.load(sys.stdin).get("cwd",""))')
 DELEGATE_JOB_ID=$(printf '%s' "$MAPPED_DATA" | python3 -c 'import sys,json; print(json.load(sys.stdin).get("job_id",""))')
+DELEGATE_JOB_TOKEN=""
+DELEGATE_JOB_ATTEMPT=""
+if [ -n "$DELEGATE_JOB_ID" ]; then
+  local_info=$(python3 -c "
+import sys, json, os
+jid = '$DELEGATE_JOB_ID'
+reg_dir = os.environ.get('MAM_JOBS_DIR', '.mam/jobs')
+p = os.path.join(reg_dir, f'{jid}.json')
+if os.path.exists(p):
+    try:
+        with open(p) as f:
+            d = json.load(f)
+            tok = d.get('dispatch_token', '')
+            att = d.get('attempt_id', d.get('iteration', 1))
+            print(f'{tok} {att}')
+    except Exception:
+        pass
+" 2>/dev/null || true)
+  if [ -n "$local_info" ]; then
+    DELEGATE_JOB_TOKEN=$(echo "$local_info" | awk '{print $1}')
+    DELEGATE_JOB_ATTEMPT=$(echo "$local_info" | awk '{print $2}')
+  fi
+fi
 
 # 멱등성: STOP 모드에서 이미 stopped 인 세션이고 purge 가 아닐 때만 no-op + exit 0
 if [ "$STOP_MODE" = "1" ] && [ "$PURGE" != "1" ]; then
@@ -190,7 +213,7 @@ if [ "$CAPTURE_ID" = "1" ] && [ -n "$TARGET_CWD" ]; then
   fi
 fi
 
-delegate_publish_event "$DELEGATE_JOB_ID" progress "terminating"
+delegate_publish_event "$DELEGATE_JOB_ID" progress "terminating" "$DELEGATE_JOB_TOKEN" "$DELEGATE_JOB_ATTEMPT"
 
 # graceful 종료: send-keys 로 정상 종료 유도 → 폴백 체인 (SIGTERM → SIGKILL).
 graceful_stop() {
@@ -239,7 +262,7 @@ if [ "$PURGE" = "1" ] && [ "$HERDR_ALIVE" = "1" ]; then
     echo "  Refusing registry removal — records preserved (no state was modified)." >&2
     echo "  Diagnose the stuck TUI (herdr session attach '$SESSION_NAME'), then re-run" >&2
     echo "  stop_session.sh --purge-conversation --yes (retry is safe/idempotent)." >&2
-    delegate_publish_event "$DELEGATE_JOB_ID" cancelled "purge aborted: session still alive; no state was modified"
+    delegate_publish_event "$DELEGATE_JOB_ID" cancelled "purge aborted: session still alive; no state was modified" "$DELEGATE_JOB_TOKEN" "$DELEGATE_JOB_ATTEMPT"
     exit 4
   fi
 fi
@@ -319,7 +342,7 @@ else:
     print(f"updated: {name} status={target['status']}", flush=True)
 PYEOF
 
-delegate_publish_event "$DELEGATE_JOB_ID" cancelled "session stopped by operator before job completion"
+delegate_publish_event "$DELEGATE_JOB_ID" cancelled "session stopped by operator before job completion" "$DELEGATE_JOB_TOKEN" "$DELEGATE_JOB_ATTEMPT"
 
 echo
 echo "=== stop complete ==="