feat(#1990): surface pending recv() message count in get_loose_ends

docs/conventions.md

@@ -223,6 +223,18 @@ Per-variant fields:
 - `Reminder { id, owner, message, due_at, age_seconds }` —
   `due_at` is the absolute unix timestamp the scheduler is
   targeting; clients compute time-until-fire as `due_at - now`.
+- `PendingMessages { count }` — undelivered inbox messages the
+  agent still owes itself a `recv` for. Informational + not
+  cancellable (drain with `recv`); only emitted when `count > 0`,
+  and surfaced first in the agent-flavour list as the most
+  actionable signal. Counted host-side from the broker
+  (`count_pending`), so it reflects what's genuinely still queued —
+  the wake-message that drove the current turn is already delivered
+  and not counted.
+- `UnreadMatrix { rooms, summary }` — unread matrix notifications.
+  Informational + not cancellable (clear with `mark_read`). Unlike
+  the others this is injected by the in-container harness, not
+  hive-c0re, because the matrix daemon lives inside the agent.
 
 `age_seconds` saturates at zero on any clock anomaly (back-step,
 unsynchronised wall clock, etc.) so the bulleted list never

frontend/packages/agent/src/app.js

@@ -891,6 +891,12 @@ window.marked = marked;
           el('span', { class: 'inbox-ts' }, 'scheduled ' + fmtAge(t.age_seconds || 0) + ' ago'),
           el('div', { class: 'inbox-body' }, t.message || ''),
         );
+      } else if (t.kind === 'pending_messages') {
+        li.append(
+          el('span', { class: 'inbox-from' }, '✉ inbox'), ' ',
+          el('span', { class: 'inbox-sep' }, (t.count || 0) + ' pending message(s)'), ' ',
+          el('span', { class: 'inbox-ts' }, 'drain with recv'),
+        );
       } else {
         li.append(el('span', { class: 'inbox-body' }, JSON.stringify(t)));
       }

hive-ag3nt/src/mcp.rs

@@ -298,6 +298,12 @@ fn render_loose_ends(loose_ends: &[hive_sh4re::LooseEnd]) -> String {
                     "- reminder #{id} ({owner}, scheduled {age_seconds}s ago, due_at={due_at}): {message}"
                 );
             }
+            hive_sh4re::LooseEnd::PendingMessages { count } => {
+                let _ = writeln!(
+                    out,
+                    "- {count} pending inbox message(s) — drain with recv (recv(max: {count}) to batch)"
+                );
+            }
             hive_sh4re::LooseEnd::UnreadMatrix { rooms, summary } => {
                 let _ = write!(out, "- unread matrix messages in {rooms} room(s)");
                 if summary.is_empty() {

hive-c0re/src/loose_ends.rs

@@ -35,6 +35,17 @@ use crate::coordinator::Coordinator;
 pub fn for_agent(coord: &Coordinator, agent: &str) -> Result<Vec<LooseEnd>> {
     let now = now_unix();
     let mut out = Vec::new();
+    // Undelivered inbox messages this agent still owes itself a `recv`
+    // for. Surfaced first (most actionable) and only when non-zero so a
+    // clean inbox doesn't add noise. The wake-message that drove the
+    // current turn is already delivered, so this counts only what's
+    // genuinely still queued.
+    let pending_messages = coord.broker.count_pending(agent)?;
+    if pending_messages > 0 {
+        out.push(LooseEnd::PendingMessages {
+            count: pending_messages,
+        });
+    }
     // Show each pending approval to the agent that submitted it. The
     // submitter column is NULL for rows predating it; those count as
     // the root agent's.

hive-sh4re/src/lib.rs

@@ -386,6 +386,15 @@ pub enum LooseEnd {
         due_at: i64,
         age_seconds: u64,
     },
+    /// Undelivered inbox messages waiting to be `recv`'d by this agent.
+    /// Not cancellable — drain them with `recv`. Surfaced so an agent
+    /// doing a between-turns `get_loose_ends` sweep sees it still owes
+    /// itself a `recv` without having to poll the inbox separately. Only
+    /// emitted when `count > 0`.
+    PendingMessages {
+        /// Number of undelivered messages queued for this agent.
+        count: u64,
+    },
     /// Unread matrix notifications in one or more rooms. Not cancellable —
     /// use `mark_read` via the matrix MCP to clear. Injected by the
     /// in-container harness (not hive-c0re) because the matrix daemon