feat: auto-create Integration phase for multi-leaf initiatives

When an initiative has multiple end phases (leaf nodes with no
dependents), queueAllPhases now auto-creates an Integration phase
that depends on all of them. This catches cross-phase incompatibilities
(type mismatches, conflicting exports, broken tests) before review.

apps/server/trpc/routers/phase-dispatch.ts

@@ -4,10 +4,35 @@
 
 import { TRPCError } from '@trpc/server';
 import { z } from 'zod';
-import type { Task } from '../../db/schema.js';
+import type { Phase, Task } from '../../db/schema.js';
 import type { ProcedureBuilder } from '../trpc.js';
 import { requirePhaseDispatchManager, requirePhaseRepository, requireTaskRepository } from './_helpers.js';
 
+const INTEGRATION_PHASE_NAME = 'Integration';
+
+const INTEGRATION_TASK_DESCRIPTION = `Verify that all phase branches integrate correctly after merging into the initiative branch.
+
+Steps:
+1. Build the project — fix any compilation errors
+2. Run the full test suite — fix any failing tests
+3. Run type checking and linting — fix any errors
+4. Review cross-phase imports and shared interfaces for compatibility
+5. Smoke test key user flows affected by the merged changes
+
+Only fix integration issues (type mismatches, conflicting exports, broken tests). Do not refactor or improve existing code.`;
+
+/**
+ * Find phase IDs that have no dependents (no other phase depends on them).
+ * These are the "end" / "leaf" phases in the dependency graph.
+ */
+function findEndPhaseIds(
+  phases: Phase[],
+  edges: Array<{ phaseId: string; dependsOnPhaseId: string }>,
+): string[] {
+  const dependedOn = new Set(edges.map((e) => e.dependsOnPhaseId));
+  return phases.filter((p) => !dependedOn.has(p.id)).map((p) => p.id);
+}
+
 export function phaseDispatchProcedures(publicProcedure: ProcedureBuilder) {
   return {
     queuePhase: publicProcedure
@@ -23,7 +48,40 @@ export function phaseDispatchProcedures(publicProcedure: ProcedureBuilder) {
       .mutation(async ({ ctx, input }) => {
         const phaseDispatchManager = requirePhaseDispatchManager(ctx);
         const phaseRepo = requirePhaseRepository(ctx);
-        const phases = await phaseRepo.findByInitiativeId(input.initiativeId);
+        const taskRepo = requireTaskRepository(ctx);
+
+        let phases = await phaseRepo.findByInitiativeId(input.initiativeId);
+        const edges = await phaseRepo.findDependenciesByInitiativeId(input.initiativeId);
+
+        // Auto-create Integration phase if multiple end phases exist
+        const existingIntegration = phases.find((p) => p.name === INTEGRATION_PHASE_NAME);
+        if (!existingIntegration) {
+          const endPhaseIds = findEndPhaseIds(phases, edges);
+          if (endPhaseIds.length > 1) {
+            const integrationPhase = await phaseRepo.create({
+              initiativeId: input.initiativeId,
+              name: INTEGRATION_PHASE_NAME,
+              status: 'approved',
+            });
+
+            for (const endPhaseId of endPhaseIds) {
+              await phaseRepo.createDependency(integrationPhase.id, endPhaseId);
+            }
+
+            await taskRepo.create({
+              phaseId: integrationPhase.id,
+              initiativeId: input.initiativeId,
+              name: 'Verify integration',
+              description: INTEGRATION_TASK_DESCRIPTION,
+              category: 'verify',
+              status: 'pending',
+            });
+
+            // Re-fetch so the new phase gets queued in the loop below
+            phases = await phaseRepo.findByInitiativeId(input.initiativeId);
+          }
+        }
+
         let queued = 0;
         for (const phase of phases) {
           if (phase.status === 'approved') {