fix(gateway): 3분 리셋 턴 간격을 허용한다

Ref의 실제 서버 계약인 120의 양의 약수 전체를 RESET, profile 기본값, 실행 중 설정에 일관되게 적용한다. 3분 DB seed와 Gateway API, 실제 Chromium 회귀 검증을 추가한다.

app/gateway-api/src/adminRouter.ts

@@ -49,7 +49,6 @@ const zServerAction = z.enum([
     'SHUTDOWN',
 ]);
 
-const TURN_TERM_MINUTES = [1, 2, 5, 10, 20, 30, 60, 120] as const;
 const AUTORUN_USER_OPTIONS = ['develop', 'warp', 'recruit', 'recruit_high', 'train', 'battle', 'chief'] as const;
 
 const ADMIN_ROLE_PREFIX = 'admin.';
@@ -430,7 +429,9 @@ const zInstallAutorun = z.object({
     options: z.array(z.enum(AUTORUN_USER_OPTIONS)),
 });
 
-const isAllowedTurnTerm = (value: number): boolean => TURN_TERM_MINUTES.some((term) => term === value);
+// Ref aligns a 12-month game year inside a 24-hour wall-clock day. That makes
+// every positive divisor of 120 valid, including 3 and 8 minutes.
+const isAllowedTurnTerm = (value: number): boolean => Number.isInteger(value) && value > 0 && 120 % value === 0;
 
 const zRuntimeSettings = z
     .object({
@@ -438,7 +439,7 @@ const zRuntimeSettings = z
             .number()
             .int()
             .refine((value) => isAllowedTurnTerm(value), {
-                message: 'turnTermMinutes must divide 120.',
+                message: '턴 시간은 120의 약수여야 합니다.',
             })
             .optional(),
         blockGeneralCreate: z.union([z.literal(0), z.literal(1), z.literal(2)]).optional(),
@@ -464,7 +465,7 @@ const zInstallOptions = z.object({
         .number()
         .int()
         .refine((value) => isAllowedTurnTerm(value), {
-            message: 'turnTermMinutes must divide 120.',
+            message: '턴 시간은 120의 약수여야 합니다.',
         }),
     sync: z.boolean(),
     fiction: z.number().int().min(0).max(1),

app/gateway-api/test/adminOperations.test.ts

@@ -825,7 +825,7 @@ describe('admin operation API', () => {
             { adminRoles: ['admin.profiles.settings:che:2'], firstUserIsAdmin: false }
         );
         const resetDefaults = {
-            turnTermMinutes: 10,
+            turnTermMinutes: 3,
             sync: true,
             fiction: 1 as const,
             extend: true,
@@ -853,6 +853,44 @@ describe('admin operation API', () => {
         ).rejects.toBeDefined();
     });
 
+    it('queues a three-minute reset because it is a valid divisor of 120', async () => {
+        const harness = await buildCaller(async (input) => ({
+            id: '66666666-6666-4666-8666-666666666666',
+            profileName: input.profileName,
+            type: 'RESET',
+            status: 'QUEUED',
+            sourceMode: input.sourceMode,
+            sourceRef: input.sourceRef,
+            payload: input.payload ?? {},
+            requestedBy: input.requestedBy,
+            createdAt: '2026-08-21T00:00:00.000Z',
+            updatedAt: '2026-08-21T00:00:00.000Z',
+        }));
+
+        await harness.caller.admin.operations.requestReset({
+            profileName: 'che:2',
+            sourceMode: 'COMMIT',
+            sourceRef: 'HEAD',
+            install: {
+                scenarioId: 1010,
+                turnTermMinutes: 3,
+                sync: true,
+                fiction: 1,
+                extend: true,
+                blockGeneralCreate: 0,
+                npcMode: 0,
+                showImgLevel: 3,
+                tournamentTrig: true,
+                joinMode: 'full',
+            },
+        });
+
+        expect(harness.createdInputs[0]).toMatchObject({
+            type: 'RESET',
+            payload: { install: { turnTermMinutes: 3 } },
+        });
+    });
+
     it('stores event season zero as the next season number', async () => {
         const harness = await buildCaller(
             async () => {