refactor: fold is_party_alive into party_conn_state

One liveness primitive instead of two. The PID argument was a vestige
(format-checked, never probed, since the kill -0 removal); dropping it
means a roster with a garbage SERVER_PID can no longer mask a live
socket in host/moderation/role resolution.

party

@@ -312,34 +312,6 @@ roster_list() {
 # Liveness
 # --------
 
-# Liveness check: the socket is a live tmux server we can speak the tmux
-# protocol to. `tmux -S list-clients` exits 0 only against a real tmux
-# server bound to that exact socket path, which simultaneously rules out
-# stale roster pointers (server gone), AF_UNIX impostors (a same-group
-# user planting a hand-rolled listener via `nc -lU`), and PID-reuse
-# leftovers, none of those answer the tmux handshake. Stronger than any
-# PID check, and it works regardless of who owns the server process.
-#
-# Earlier revisions also gated on `kill -0 $pid` as a cheap pre-filter.
-# That broke cross-user discovery on every non-Linux POSIX target: per
-# POSIX, kill(2) signal 0 may return EPERM when the caller lacks
-# send-permission, and illumos, all the BSDs, and macOS honor that.
-# Linux is the outlier that returns 0 for "exists, even if not
-# signalable," and Linux ABI environments (LX-branded zones) inherit
-# that behavior, which is why the bug hid in the test matrix until a
-# native illumos run surfaced it. The PID arg is kept in the function
-# signature for caller compatibility and as a numeric-validation guard,
-# but is no longer probed. Local var names are prefixed to avoid
-# clobbering caller-side `pid` / `sock` (POSIX sh has no real locals).
-is_party_alive() {
-    _pa_pid="$1"
-    _pa_sock="$2"
-    case "$_pa_pid" in
-        '' | *[!0-9]* ) return 1 ;;
-    esac
-    "$PARTY_TMUX" -S "$_pa_sock" list-clients >/dev/null 2>&1
-}
-
 # Classify the caller's relationship to a party socket. Prints exactly
 # one of:
 #   ok           : live tmux server, the caller is authorized.
@@ -360,6 +332,20 @@ is_party_alive() {
 #                  to a hidden party, never to a false "ok".
 #   dead         : nothing speaking the tmux protocol at that socket
 #                  (stale roster, killed server, AF_UNIX impostor).
+#
+# This probe is the ONLY liveness primitive. `tmux -S <sock>
+# list-clients` exits 0 only against a real tmux server bound to that
+# exact socket path, which rules out stale roster pointers, AF_UNIX
+# impostors (a same-group user planting a hand-rolled listener via
+# `nc -lU`), and PID-reuse leftovers in one shot. Earlier revisions had
+# a separate is_party_alive() that also format-checked the roster's
+# SERVER_PID, a vestige of a `kill -0` pre-filter that broke cross-user
+# discovery on every non-Linux POSIX target: per POSIX, kill(2) signal
+# 0 may return EPERM when the caller lacks send-permission, and
+# illumos, all the BSDs, and macOS honor that. Linux (and LX-branded
+# zones) return 0 for "exists, even if not signalable", which is why
+# the bug hid in the test matrix until a native illumos run surfaced
+# it. SERVER_PID stays in the roster as display-only metadata.
 party_conn_state() {
     _cs_err=$("$PARTY_TMUX" -S "$1" list-clients 2>&1 >/dev/null) \
         && _cs_rc=0 || _cs_rc=$?
@@ -712,8 +698,9 @@ EOF
     fi
     if [ -d "$party_dir" ] && [ -f "$rec" ]; then
         roster_read "$rec" 2>/dev/null || true
-        if is_party_alive "${RR_SERVER_PID:-}" "${RR_SOCKET:-}"; then
-            echo "party: '$name' is already running (pid $RR_SERVER_PID)" >&2
+        if [ -n "${RR_SOCKET:-}" ] \
+           && [ "$(party_conn_state "$RR_SOCKET")" != dead ]; then
+            echo "party: '$name' is already running" >&2
             exit 1
         fi
     fi
@@ -1078,7 +1065,7 @@ resolve_authoritative_party() {
         [ -L "$d" ] && continue
         [ -O "$d" ] || continue
         roster_read "$rec" || continue
-        is_party_alive "$RR_SERVER_PID" "$RR_SOCKET" || continue
+        [ "$(party_conn_state "$RR_SOCKET")" != dead ] || continue
         [ "$RR_HOST_USER" = "$USER" ] || continue
         [ -z "$target" ] || [ "$target" = "$RR_PARTY_NAME" ] || continue
         set -- "$@" "$rec"
@@ -1391,7 +1378,7 @@ EOF
         tmux_sock="${TMUX%%,*}"
         for rec in $(roster_list); do
             roster_read "$rec" || continue
-            is_party_alive "$RR_SERVER_PID" "$RR_SOCKET" || continue
+            [ "$(party_conn_state "$RR_SOCKET")" != dead ] || continue
             [ "$RR_SOCKET" = "$tmux_sock" ] || continue
             sock="$RR_SOCKET"; host_sess="$RR_PARTY_NAME"; break
         done
@@ -1399,7 +1386,7 @@ EOF
     if [ -z "$sock" ]; then
         for rec in $(roster_list); do
             roster_read "$rec" || continue
-            is_party_alive "$RR_SERVER_PID" "$RR_SOCKET" || continue
+            [ "$(party_conn_state "$RR_SOCKET")" != dead ] || continue
             "$PARTY_TMUX" -S "$RR_SOCKET" list-clients -F '#{client_user}' 2>/dev/null \
                 | grep -qx "$USER" || continue
             sock="$RR_SOCKET"; host_sess="$RR_PARTY_NAME"; break