将Feature/XP.Common和Feature/XP.Hardware分支合并至Develop/XP.forHardwareAndCommon，完善XPapp注册和相关硬件类库通用类库功能。

XP.Common/Database/Helpers/PaginationHelper.cs

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+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+using XP.Common.Database.Models;
+
+namespace XP.Common.Database.Helpers
+{
+    /// <summary>
+    /// 分页计算辅助工具
+    /// </summary>
+    public static class PaginationHelper
+    {
+        /// <summary>
+        /// 计算分页偏移量（SQLite OFFSET）
+        /// </summary>
+        public static int CalculateOffset(PaginationRequest pagination)
+        {
+            if (pagination.PageIndex < 1) pagination.PageIndex = 1;
+            if (pagination.PageSize < 1) pagination.PageSize = 20;
+            return (pagination.PageIndex - 1) * pagination.PageSize;
+        }
+
+        /// <summary>
+        /// 验证并修正分页参数
+        /// </summary>
+        public static PaginationRequest ValidateAndFix(PaginationRequest pagination)
+        {
+            var fixedPagination = new PaginationRequest
+            {
+                PageIndex = pagination.PageIndex < 1 ? 1 : pagination.PageIndex,
+                PageSize = pagination.PageSize < 1 ? 20 : (pagination.PageSize > 1000 ? 1000 : pagination.PageSize),
+                OrderBy = pagination.OrderBy ?? string.Empty
+            };
+            return fixedPagination;
+        }
+    }
+}