feat: live-sync heartbeat commits machine-written paths

The checkout IS the deployment and symlinks make live state (memories,
auto-learned skills, agent config, desktop settings) dirty tracked files
continuously; no commit law covered machine churn, so it accumulated
unpushed for weeks — one disk held the only copy of ~61 managed skills,
a settings fix stayed local-only, and dirty trees refused merges.

scripts/live-sync.sh (systemd user timer, ~15 min) commits ONLY the
allowlisted machine/desktop-live tiers with hooks armed, merges
origin/main, pushes, and reaps wt/* worktrees older than 7 days. Task
dirt outside the allowlist is never staged; conflicts abort and alert
via ntfy; branch guard refuses off main; never --no-verify, never force.
Black-box contract pinned by tests/live-sync.bats (9 tests, suite 36/36).

Refs #11

dotfiles/systemd-user/.config/systemd/user/live-sync.service

@@ -0,0 +1,12 @@
+[Unit]
+Description=command-center live-sync heartbeat (commits machine-written paths)
+Documentation=file://%h/.omp/omp-docs/tools/live-sync.md
+
+[Service]
+# One-shot heartbeat: commit allowlisted live paths, merge trunk, push, reap
+# stale wt/* worktrees. Self-healing by design — a failed fetch/merge alerts
+# via ntfy and simply retries on the next tick; nothing to restart.
+Type=oneshot
+Nice=19
+IOSchedulingClass=idle
+ExecStart=%h/.omp/scripts/live-sync.sh

dotfiles/systemd-user/.config/systemd/user/live-sync.timer

@@ -0,0 +1,11 @@
+[Unit]
+Description=command-center live-sync heartbeat every 15 minutes
+
+[Timer]
+OnBootSec=5min
+OnUnitActiveSec=15min
+RandomizedDelaySec=3min
+Persistent=true
+
+[Install]
+WantedBy=timers.target