core: lan_peer example — verify agent serverless sync without clipboard contention

A controllable LAN peer (dead server, doesn't touch the OS clipboard) used to
prove the desktop agent syncs over LAN alone. Confirmed both directions on macOS
with the server unreachable: pbcopy → agent → peer, and peer → agent → pasteboard.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

core/examples/lan_peer.rs

@@ -0,0 +1,32 @@
+//! A controllable LAN peer for verifying the agent's serverless sync, without a
+//! second clipboard-touching process. Dead server → only the LAN transport can
+//! move data.
+//!   cargo run --example lan_peer -- <room> <text-to-send>
+//! Prints `RECV <text>` for anything received; sends <text-to-send> once after
+//! discovery settles.
+
+use std::time::Duration;
+
+use tethercore::{Engine, Message, MessageHandler};
+
+struct Printer;
+impl MessageHandler for Printer {
+    fn on_message(&self, msg: Message) {
+        println!("RECV {}", msg.text);
+    }
+    fn on_status(&self, _connected: bool) {}
+}
+
+fn main() {
+    let room = std::env::args().nth(1).unwrap_or_else(|| "lan-verify".into());
+    let send = std::env::args().nth(2);
+    // High `from` so it accepts the agent's dial (lower id dials).
+    let e = Engine::new("http://127.0.0.1:1".into(), room, "zzz-peer".into(), "peer".into());
+    e.start(Box::new(Printer));
+
+    std::thread::sleep(Duration::from_secs(6)); // let mDNS discover + TCP connect
+    if let Some(s) = send {
+        e.send(s);
+    }
+    std::thread::sleep(Duration::from_secs(8));
+}