fix(dashboard): v3 审计修复 — 数据完整性、i18n、类型安全、死代码清理

P0 修复（严重）:
- admin ContentRow 标签与值错配（stats.users→textbooks 等 6 处）
- admin/error.tsx 硬编码中文替换为 useTranslations
- UserGrowthChart 空数据时渲染 EmptyState（userGrowth/homeworkTrend 永远为空数组）

P1 修复（高）:
- 新增 admin/dashboard 和 student/dashboard 的 loading.tsx + error.tsx
- 抽取 DashboardLoadingSkeleton 和 DashboardErrorFallback 共享组件，消除 5 套重复文件
- formatDate/formatLongDate 传入用户 locale（admin/teacher/student 共 6 个组件）
- 移除死代码：getCachedAdminDashboard、AvatarImage src={undefined}、TeacherStats isLoading prop
- filterTodaySchedule 改为泛型函数，消除 as 类型断言
- 辅助函数 getStatus/getDueUrgency 新增显式返回类型
- UserGrowthChart 新增 labelKey prop 区分用户增长/作业提交趋势标签

P2 修复（中）:
- 4 个组件从客户端转为服务端组件（DashboardGreetingHeader、TeacherQuickActions、TeacherDashboardHeader、StudentDashboardHeader）
- Student dashboard 空状态新增 CTA（viewSchedule、viewAll）
- TeacherHomeworkCard 图标按钮新增 aria-label
- TeacherTodoCard 排序逻辑重写为可读的 if/return 模式

同步更新:
- docs/architecture/005_architecture_data.json 新增 DashboardLoadingSkeleton、DashboardErrorFallback 条目
- 新增 docs/architecture/audit/dashboard-audit-report-v3.md 审计报告
- dashboard.json 新增 6 个 i18n 键（textbooks/chapters/questions/exams/totalAssignments/totalSubmissions）

src/modules/homework/data-access.ts

@@ -1,7 +1,7 @@
 import "server-only"
 
 import { cache } from "react"
-import { and, count, desc, eq, inArray, isNull, lte, or, sql } from "drizzle-orm"
+import { and, asc, count, desc, eq, gt, inArray, isNull, lt, lte, or, sql } from "drizzle-orm"
 
 import { db } from "@/shared/db"
 import {
@@ -118,11 +118,113 @@ export const getHomeworkAssignments = cache(async (params?: { creatorId?: string
     },
   })
 
+  if (data.length === 0) return []
+
+  const assignmentIds = data.map((a) => a.id)
+  const now = new Date()
+
+  // 并行查询：目标学生数 / 已提交数 / 已批改数 / 已批改平均分 / 逾期未提交学生集合
+  const [targetCountRows, submittedCountRows, gradedCountRows, avgScoreRows, submittedStudentRows] = await Promise.all([
+    db
+      .select({
+        assignmentId: homeworkAssignmentTargets.assignmentId,
+        targetCount: sql<number>`COUNT(*)`,
+      })
+      .from(homeworkAssignmentTargets)
+      .where(inArray(homeworkAssignmentTargets.assignmentId, assignmentIds))
+      .groupBy(homeworkAssignmentTargets.assignmentId),
+    db
+      .select({
+        assignmentId: homeworkSubmissions.assignmentId,
+        submittedCount: sql<number>`COUNT(DISTINCT ${homeworkSubmissions.studentId})`,
+      })
+      .from(homeworkSubmissions)
+      .where(
+        and(
+          inArray(homeworkSubmissions.assignmentId, assignmentIds),
+          inArray(homeworkSubmissions.status, ["submitted", "graded"])
+        )
+      )
+      .groupBy(homeworkSubmissions.assignmentId),
+    db
+      .select({
+        assignmentId: homeworkSubmissions.assignmentId,
+        gradedCount: sql<number>`COUNT(DISTINCT ${homeworkSubmissions.studentId})`,
+      })
+      .from(homeworkSubmissions)
+      .where(and(inArray(homeworkSubmissions.assignmentId, assignmentIds), eq(homeworkSubmissions.status, "graded")))
+      .groupBy(homeworkSubmissions.assignmentId),
+    db
+      .select({
+        assignmentId: homeworkSubmissions.assignmentId,
+        avgScore: sql<number>`AVG(${homeworkSubmissions.score})`,
+      })
+      .from(homeworkSubmissions)
+      .where(
+        and(
+          inArray(homeworkSubmissions.assignmentId, assignmentIds),
+          eq(homeworkSubmissions.status, "graded")
+        )
+      )
+      .groupBy(homeworkSubmissions.assignmentId),
+    db
+      .select({
+        assignmentId: homeworkSubmissions.assignmentId,
+        studentId: homeworkSubmissions.studentId,
+      })
+      .from(homeworkSubmissions)
+      .where(
+        and(
+          inArray(homeworkSubmissions.assignmentId, assignmentIds),
+          inArray(homeworkSubmissions.status, ["submitted", "graded"])
+        )
+      ),
+  ])
+
+  const targetCountByAssignmentId = new Map<string, number>()
+  for (const r of targetCountRows) targetCountByAssignmentId.set(r.assignmentId, Number(r.targetCount ?? 0))
+
+  const submittedCountByAssignmentId = new Map<string, number>()
+  for (const r of submittedCountRows) submittedCountByAssignmentId.set(r.assignmentId, Number(r.submittedCount ?? 0))
+
+  const gradedCountByAssignmentId = new Map<string, number>()
+  for (const r of gradedCountRows) gradedCountByAssignmentId.set(r.assignmentId, Number(r.gradedCount ?? 0))
+
+  const avgScoreByAssignmentId = new Map<string, number | null>()
+  for (const r of avgScoreRows) {
+    const v = r.avgScore
+    avgScoreByAssignmentId.set(r.assignmentId, v === null ? null : Number(v))
+  }
+
+  // 已提交学生集合（按 assignmentId 分组），用于计算逾期未提交人数
+  const submittedStudentIdsByAssignmentId = new Map<string, Set<string>>()
+  for (const r of submittedStudentRows) {
+    let set = submittedStudentIdsByAssignmentId.get(r.assignmentId)
+    if (!set) {
+      set = new Set<string>()
+      submittedStudentIdsByAssignmentId.set(r.assignmentId, set)
+    }
+    set.add(r.studentId)
+  }
+
+  // 逾期未提交人数 = 目标学生数 - 已提交学生数（仅当 dueAt 已过时计算）
+  const computeOverdueCount = (assignmentId: string, dueAt: Date | null): number => {
+    if (!dueAt || dueAt > now) return 0
+    const targetCount = targetCountByAssignmentId.get(assignmentId) ?? 0
+    const submittedCount = submittedStudentIdsByAssignmentId.get(assignmentId)?.size ?? 0
+    return Math.max(0, targetCount - submittedCount)
+  }
+
   return data.map((a) => {
+    const targetCount = targetCountByAssignmentId.get(a.id) ?? 0
+    const submittedCount = submittedCountByAssignmentId.get(a.id) ?? 0
+    const gradedCount = gradedCountByAssignmentId.get(a.id) ?? 0
+    const averageScore = avgScoreByAssignmentId.get(a.id) ?? null
+    const overdueCount = computeOverdueCount(a.id, a.dueAt)
     const item: HomeworkAssignmentListItem = {
       id: a.id,
       sourceExamId: a.sourceExamId,
-      sourceExamTitle: a.sourceExam.title,
+      sourceExamTitle: a.sourceExam?.title ?? null,
       title: a.title,
       status: toHomeworkAssignmentStatus(a.status),
       availableAt: a.availableAt ? a.availableAt.toISOString() : null,
@@ -132,6 +234,11 @@ export const getHomeworkAssignments = cache(async (params?: { creatorId?: string
       maxAttempts: a.maxAttempts,
       createdAt: a.createdAt.toISOString(),
       updatedAt: a.updatedAt.toISOString(),
+      targetCount,
+      submittedCount,
+      gradedCount,
+      averageScore,
+      overdueCount,
     }
     return item
   })
@@ -221,7 +328,7 @@ export const getHomeworkAssignmentReviewList = cache(async (params: { creatorId:
       id: a.id,
       title: a.title,
       status: toHomeworkAssignmentStatus(a.status),
-      sourceExamTitle: a.sourceExam.title,
+      sourceExamTitle: a.sourceExam?.title ?? null,
       dueAt: a.dueAt ? a.dueAt.toISOString() : null,
       targetCount: targetCountByAssignmentId.get(a.id) ?? 0,
       submittedCount: submittedCountByAssignmentId.get(a.id) ?? 0,
@@ -322,6 +429,8 @@ export const getHomeworkAssignmentById = cache(async (id: string, scope?: DataSc
       return null
     }
     if (scope.type === "grade_managed" && scope.gradeIds.length > 0) {
+      // 快速作业（无 sourceExamId）不归年级主任管辖，直接拒绝
+      if (!assignment.sourceExamId) return null
       const examIds = await getExamIdsByGradeIds(scope.gradeIds)
       if (!examIds.includes(assignment.sourceExamId)) {
         return null
@@ -371,8 +480,8 @@ export const getHomeworkAssignmentById = cache(async (id: string, scope?: DataSc
     description: assignment.description,
     status: toHomeworkAssignmentStatus(assignment.status),
     sourceExamId: assignment.sourceExamId,
-    sourceExamTitle: assignment.sourceExam.title,
-    structure: assignment.structure as unknown,
+    sourceExamTitle: assignment.sourceExam?.title ?? null,
+    structure: assignment.structure,
     availableAt: assignment.availableAt ? assignment.availableAt.toISOString() : null,
     dueAt: assignment.dueAt ? assignment.dueAt.toISOString() : null,
     allowLate: assignment.allowLate,
@@ -427,16 +536,34 @@ export const getHomeworkSubmissionDetails = cache(async (submissionId: string):
     })
     .sort((a, b) => a.order - b.order)
 
-  // Fetch adjacent submissions for navigation
-  const allSubmissions = await db.query.homeworkSubmissions.findMany({
-    where: eq(homeworkSubmissions.assignmentId, submission.assignmentId),
-    orderBy: [desc(homeworkSubmissions.updatedAt)],
-    columns: { id: true },
-  })
+  // P1-8: Optimize adjacent submission navigation using LIMIT 1 queries
+  // instead of fetching all submission IDs for the assignment.
+  // Original ordering is desc(updatedAt): "previous" = newer, "next" = older.
+  const currentUpdatedAt = submission.updatedAt
 
-  const currentIndex = allSubmissions.findIndex((s) => s.id === submissionId)
-  const prevSubmissionId = currentIndex > 0 ? allSubmissions[currentIndex - 1].id : null
-  const nextSubmissionId = currentIndex >= 0 && currentIndex < allSubmissions.length - 1 ? allSubmissions[currentIndex + 1].id : null
+  const [prevSubmission, nextSubmission] = await Promise.all([
+    // Previous (newer): closest submission with updatedAt > current
+    db.query.homeworkSubmissions.findFirst({
+      where: and(
+        eq(homeworkSubmissions.assignmentId, submission.assignmentId),
+        gt(homeworkSubmissions.updatedAt, currentUpdatedAt)
+      ),
+      orderBy: [asc(homeworkSubmissions.updatedAt)],
+      columns: { id: true },
+    }),
+    // Next (older): closest submission with updatedAt < current
+    db.query.homeworkSubmissions.findFirst({
+      where: and(
+        eq(homeworkSubmissions.assignmentId, submission.assignmentId),
+        lt(homeworkSubmissions.updatedAt, currentUpdatedAt)
+      ),
+      orderBy: [desc(homeworkSubmissions.updatedAt)],
+      columns: { id: true },
+    }),
+  ])
+
+  const prevSubmissionId = prevSubmission?.id ?? null
+  const nextSubmissionId = nextSubmission?.id ?? null
 
   return {
     id: submission.id,
@@ -490,7 +617,10 @@ export const getStudentHomeworkAssignments = cache(async (studentId: string): Pr
   if (assignments.length === 0) return []
 
   // Fetch subject names via cross-module interfaces
-  const examIds = assignments.map((a) => a.sourceExamId)
+  // 快速作业无 sourceExamId，过滤 null 后再查询科目映射
+  const examIds = assignments
+    .map((a) => a.sourceExamId)
+    .filter((id): id is string => id !== null)
   const [examSubjectIdMap, subjectOptions] = await Promise.all([
     getExamSubjectIdMap(examIds),
     getSubjectOptions(),
@@ -519,7 +649,7 @@ export const getStudentHomeworkAssignments = cache(async (studentId: string): Pr
   return assignments.map((a) => {
     const latest = latestSubmittedByAssignmentId.get(a.id) ?? latestByAssignmentId.get(a.id) ?? null
     const attemptsUsed = attemptsByAssignmentId.get(a.id) ?? 0
-    const subjectId = examSubjectIdMap.get(a.sourceExamId) ?? null
+    const subjectId = a.sourceExamId ? (examSubjectIdMap.get(a.sourceExamId) ?? null) : null
     const subjectName = subjectId ? subjectNameById.get(subjectId) ?? null : null
 
     const item: StudentHomeworkAssignmentListItem = {