recv: hoist RECV_BATCH_MAX into hive-sh4re, drop magic 5 in wake hint

hive-ag3nt/src/serve_common.rs

@@ -32,9 +32,9 @@ pub fn format_wake_prompt(
         String::new()
     } else {
         // Suggested batch size is clamped to the server-side recv cap
-        // (see `RECV_BATCH_MAX` in hive-c0re) so the hint never asks
-        // for more than one round-trip can deliver.
-        let batch = unread.min(5);
+        // so the hint never asks for more than one round-trip can
+        // deliver.
+        let batch = unread.min(u64::from(hive_sh4re::RECV_BATCH_MAX));
         format!(
             "\n\n({unread} more message(s) pending in your inbox — call `mcp__hyperhive__recv` \
              with `max: {batch}` to drain the next batch before acting. If the \

hive-c0re/src/socket_server.rs

@@ -149,13 +149,10 @@ async fn serve(stream: UnixStream, agent: String, coord: Arc<Coordinator>) -> Re
 /// positive `wait_seconds`.
 pub(crate) const RECV_LONG_POLL_MAX: std::time::Duration = std::time::Duration::from_mins(3);
 
-/// Server-side hard cap on `Recv.max`. Bounds the size of a single
-/// round-trip so a confused caller can't drain the entire inbox in
-/// one go and blow past wire-buffer sizes; everything above the cap
-/// silently clamps. 5 keeps individual turns small — a big backlog
-/// is drained over several recv calls instead of one giant pop
-/// (#2150).
-pub(crate) const RECV_BATCH_MAX: u32 = 5;
+/// Server-side hard cap on `Recv.max` — canonical value lives in
+/// `hive_sh4re::RECV_BATCH_MAX` so the harness's wake-prompt hint and
+/// this enforcement site can't drift apart (#2150).
+pub(crate) const RECV_BATCH_MAX: u32 = hive_sh4re::RECV_BATCH_MAX;
 
 pub(crate) fn recv_timeout(wait_seconds: Option<u64>) -> std::time::Duration {
     match wait_seconds {

hive-sh4re/src/lib.rs

@@ -7,6 +7,16 @@ pub mod paths;
 pub mod priv_proto;
 pub mod wire_time;
 
+/// Server-side hard cap on `Recv.max` (see `AgentRequest::Recv`). Bounds
+/// the size of a single round-trip so a confused caller can't drain the
+/// entire inbox in one go and blow past wire-buffer sizes; everything
+/// above the cap silently clamps. 5 keeps individual turns small — a big
+/// backlog is drained over several recv calls instead of one giant pop
+/// (#2150). Lives here so both the enforcing side (hive-c0re's
+/// socket_server) and the hinting side (hive-ag3nt's wake prompt + tool
+/// docs) reference one constant instead of a scattered magic value.
+pub const RECV_BATCH_MAX: u32 = 5;
+
 // -----------------------------------------------------------------------------
 // Host admin socket — /run/hyperhive/host.sock
 // -----------------------------------------------------------------------------