feat: Show resolving_conflict activity state on initiative cards

Add 'resolving_conflict' to InitiativeActivityState and detect active
conflict agents (name starts with conflict-) in deriveInitiativeActivity.
Conflict resolution takes priority over pending_review since the agent
is actively working.

- Add resolving_conflict to shared types and activity derivation
- Include conflict agents in listInitiatives agent filter (name + mode)
- Map resolving_conflict to urgent variant with pulse in InitiativeCard
- Add merge: prefix to INITIATIVE_LIST_RULES for merge event routing
- Add spawnConflictResolutionAgent to INVALIDATION_MAP
- Add getActiveConflictAgent to detail page agent: SSE invalidation

apps/web/src/components/InitiativeCard.tsx

@@ -32,11 +32,12 @@ export interface SerializedInitiative {
 
 function activityVisual(state: string): { label: string; variant: StatusVariant; pulse: boolean } {
   switch (state) {
-    case "executing":      return { label: "Executing",      variant: "active",  pulse: true };
-    case "pending_review": return { label: "Pending Review",  variant: "warning", pulse: true };
-    case "discussing":     return { label: "Discussing",      variant: "active",  pulse: true };
-    case "detailing":      return { label: "Detailing",       variant: "active",  pulse: true };
-    case "refining":       return { label: "Refining",        variant: "active",  pulse: true };
+    case "executing":          return { label: "Executing",          variant: "active",  pulse: true };
+    case "pending_review":     return { label: "Pending Review",     variant: "warning", pulse: true };
+    case "discussing":         return { label: "Discussing",         variant: "active",  pulse: true };
+    case "detailing":          return { label: "Detailing",          variant: "active",  pulse: true };
+    case "refining":           return { label: "Refining",           variant: "active",  pulse: true };
+    case "resolving_conflict": return { label: "Resolving Conflict", variant: "urgent",  pulse: true };
     case "ready":          return { label: "Ready",           variant: "active",  pulse: false };
     case "blocked":        return { label: "Blocked",         variant: "error",   pulse: false };
     case "complete":       return { label: "Complete",        variant: "success", pulse: false };

apps/web/src/components/StatusDot.tsx

@@ -45,6 +45,10 @@ export function mapEntityStatus(rawStatus: string): StatusVariant {
     case "medium":
       return "warning";
 
+    // Urgent / conflict resolution
+    case "resolving_conflict":
+      return "urgent";
+
     // Error / failed
     case "crashed":
     case "blocked":

apps/web/src/hooks/useLiveUpdates.ts

@@ -24,6 +24,7 @@ export const INITIATIVE_LIST_RULES: LiveUpdateRule[] = [
   { prefix: 'task:',       invalidate: ['listInitiatives'] },
   { prefix: 'phase:',      invalidate: ['listInitiatives'] },
   { prefix: 'agent:',      invalidate: ['listInitiatives'] },
+  { prefix: 'merge:',      invalidate: ['listInitiatives'] },
 ];
 
 export function useLiveUpdates(rules: LiveUpdateRule[]) {

apps/web/src/lib/invalidation.ts

@@ -44,6 +44,7 @@ const INVALIDATION_MAP: Partial<Record<MutationName, QueryName[]>> = {
   spawnArchitectDiscuss: ["listAgents"],
   spawnArchitectPlan: ["listAgents"],
   spawnArchitectDetail: ["listAgents", "listInitiativeTasks"],
+  spawnConflictResolutionAgent: ["listAgents", "listInitiatives", "getInitiative"],
 
   // --- Initiatives ---
   createInitiative: ["listInitiatives"],