feat(protocol): deliver 'War Room' UI with Incursion Engine

We've transformed the Social-Dense Hub into a high-fidelity operational surface.
- BACKEND: Implemented Global Incursion Engine in agent-sessions.ts (N^2 overlap detection) and added the 60m 'Idle' state.
- API: Enriched the sessions payload with full metadata and active conflict arrays.
- HEADER: Delivered 4-state agent stations (Active/Stale/Evicted/Idle) with real-time 'time-ago' timers.
- FEED: Implemented the 'Fire Map' visuals:
  * Global Incursion Ticker: High-visibility alerts for agent collisions.
  * Local Conflict Badges: Pulsing pills on affected task cards.
- Refactored components for React-static compliance and strict TypeScript safety.

This commit completes the visibility track, allowing the human supervisor to monitor agent presence and friction in real-time.

OPERATIVE: silver-castle
SESSION: 2026-02-14-1430

src/lib/agent-sessions.ts

@@ -2,8 +2,9 @@ import type { ActivityEvent } from './activity';
 import type { BeadIssue } from './types';
 import { listAgents, deriveLiveness } from './agent-registry';
 import { inboxAgentMessages, type AgentMessage } from './agent-mail';
+import { statusAgentReservations, classifyOverlap } from './agent-reservations';
 
-export type AgentSessionState = 'active' | 'reviewing' | 'deciding' | 'needs_input' | 'completed' | 'stale' | 'evicted';
+export type AgentSessionState = 'active' | 'reviewing' | 'deciding' | 'needs_input' | 'completed' | 'stale' | 'evicted' | 'idle';
 
 export interface SessionTaskCard {
   id: string;
@@ -50,6 +51,49 @@ export async function getAgentLivenessMap(): Promise<Record<string, string>> {
   return map;
 }
 
+export interface Incursion {
+  scope: string;
+  agents: string[];
+  severity: 'exact' | 'partial';
+}
+
+/**
+ * Calculates global incursions by comparing all active reservations.
+ */
+export async function calculateIncursions(): Promise<Incursion[]> {
+  const statusResult = await statusAgentReservations({});
+  if (!statusResult.ok || !statusResult.data) return [];
+
+  const reservations = statusResult.data.reservations;
+  const incursions: Incursion[] = [];
+  const processedPairs = new Set<string>();
+
+  for (let i = 0; i < reservations.length; i++) {
+    for (let j = i + 1; j < reservations.length; j++) {
+      const resA = reservations[i];
+      const resB = reservations[j];
+
+      // Don't compare an agent against themselves
+      if (resA.agent_id === resB.agent_id) continue;
+
+      const overlap = classifyOverlap(resA.scope, resB.scope);
+      if (overlap !== 'disjoint') {
+        const key = [resA.agent_id, resB.agent_id].sort().join(':') + ':' + [resA.scope, resB.scope].sort().join('|');
+        if (processedPairs.has(key)) continue;
+        processedPairs.add(key);
+
+        incursions.push({
+          scope: overlap === 'exact' ? resA.scope : `${resA.scope} ↔ ${resB.scope}`,
+          agents: [resA.agent_id, resB.agent_id],
+          severity: overlap
+        });
+      }
+    }
+  }
+
+  return incursions;
+}
+
 /**
  * Gathers all relevant communication for all agents to build a summary for aggregation.
  */