diff --git a/package-debian.sh b/package-debian.sh
index 0d459e84..c8e2448c 100644
--- a/package-debian.sh
+++ b/package-debian.sh
@@ -676,6 +676,15 @@ EOF
   find "$stage/opt/v2rayN" -type f -exec chmod 0644 {} +
   [[ -f "$stage/opt/v2rayN/v2rayN" ]] && chmod 0755 "$stage/opt/v2rayN/v2rayN" || true
 
+  # Core binaries must be executable before installation: ordinary users cannot
+  # chmod the root-owned files installed by dpkg.
+  local core
+  for core in xray/xray sing_box/sing-box mihomo/mihomo; do
+    if [[ -f "$stage/opt/v2rayN/bin/$core" ]]; then
+      chmod 0755 "$stage/opt/v2rayN/bin/$core"
+    fi
+  done
+
   deb_out="$OUTPUT_DIR/v2rayn_${VERSION}_${deb_arch}.deb"
   dpkg-deb --root-owner-group --build "$stage" "$deb_out"
 
diff --git a/v2rayN/ServiceLib.Tests/Common/UnixFileModeTests.cs b/v2rayN/ServiceLib.Tests/Common/UnixFileModeTests.cs
new file mode 100644
index 00000000..ac268078
--- /dev/null
+++ b/v2rayN/ServiceLib.Tests/Common/UnixFileModeTests.cs
@@ -0,0 +1,42 @@
+namespace ServiceLib.Tests.Common;
+
+public class UnixFileModeTests
+{
+    [Test]
+    public async Task AlreadyExecutableSystemBinary_ShouldNotRequireOwnership()
+    {
+        if (OperatingSystem.IsWindows())
+        {
+            return;
+        }
+
+        // /bin/sh is executable but owned by root on the Unix CI runners.
+        // A regular user must not need chmod permission just to launch it.
+        var mode = File.GetUnixFileMode("/bin/sh");
+        await Utils.SetUnixFileMode("/bin/sh").Should().BeTrue();
+        await File.GetUnixFileMode("/bin/sh").Should().BeEqualTo(mode);
+    }
+
+    [Test]
+    public async Task NonExecutableOwnedFile_ShouldGainExecuteBitsWithoutLosingOtherPermissions()
+    {
+        if (OperatingSystem.IsWindows())
+        {
+            return;
+        }
+
+        var path = Path.GetTempFileName();
+        try
+        {
+            var mode = UnixFileMode.UserRead | UnixFileMode.UserWrite | UnixFileMode.GroupRead;
+            File.SetUnixFileMode(path, mode);
+
+            await Utils.SetUnixFileMode(path).Should().BeTrue();
+            await File.GetUnixFileMode(path).Should().BeEqualTo(mode | UnixFileMode.UserExecute | UnixFileMode.GroupExecute | UnixFileMode.OtherExecute);
+        }
+        finally
+        {
+            File.Delete(path);
+        }
+    }
+}
diff --git a/v2rayN/ServiceLib.Tests/Services/SpeedtestServiceBatchTests.cs b/v2rayN/ServiceLib.Tests/Services/SpeedtestServiceBatchTests.cs
new file mode 100644
index 00000000..b5cdef19
--- /dev/null
+++ b/v2rayN/ServiceLib.Tests/Services/SpeedtestServiceBatchTests.cs
@@ -0,0 +1,59 @@
+namespace ServiceLib.Tests.Services;
+
+public class SpeedtestServiceBatchTests
+{
+    [Test]
+    [Arguments(0)]
+    [Arguments(1000)]
+    public async Task EmptySelection_ShouldReturnNoBatches(int pageSize)
+    {
+        await GetBatches([], pageSize).Count.Should().BeEqualTo(0);
+    }
+
+    [Test]
+    [Arguments(0)]
+    [Arguments(-1)]
+    public async Task NonPositivePageSize_ShouldKeepEveryEligibleProfile(int pageSize)
+    {
+        var profiles = CreateProfiles();
+        var batches = GetBatches(profiles, pageSize);
+
+        await batches.Count.Should().BeEqualTo(profiles.Count);
+        await batches.SelectMany(batch => batch).Count().Should().BeEqualTo(profiles.Count);
+        foreach (var profile in profiles)
+        {
+            await batches.SelectMany(batch => batch).Count(item => ReferenceEquals(item, profile)).Should().BeEqualTo(1);
+        }
+    }
+
+    [Test]
+    public async Task NormalBatches_ShouldRespectPageSizeAndKeepCoreTypesSeparate()
+    {
+        var profiles = CreateProfiles();
+        var batches = GetBatches(profiles, 2);
+
+        await batches.Count.Should().BeEqualTo(3);
+        await batches.SelectMany(batch => batch).Count().Should().BeEqualTo(profiles.Count);
+        foreach (var batch in batches)
+        {
+            await (batch.Count > 0 && batch.Count <= 2).Should().BeTrue();
+            await batch.Select(item => item.CoreType).Distinct().Count().Should().BeEqualTo(1);
+        }
+    }
+
+    private static List<ServerTestItem> CreateProfiles() =>
+    [
+        new() { CoreType = ECoreType.Xray },
+        new() { CoreType = ECoreType.Xray },
+        new() { CoreType = ECoreType.Xray },
+        new() { CoreType = ECoreType.sing_box },
+        new() { CoreType = ECoreType.sing_box }
+    ];
+
+    private static List<List<ServerTestItem>> GetBatches(List<ServerTestItem> profiles, int pageSize)
+    {
+        var service = new SpeedtestService(new Config { SpeedTestItem = new() }, _ => Task.CompletedTask);
+        var method = typeof(SpeedtestService).GetMethod("GetTestBatchItem", BindingFlags.Instance | BindingFlags.NonPublic)!;
+        return (List<List<ServerTestItem>>)method.Invoke(service, [profiles, pageSize])!;
+    }
+}
diff --git a/v2rayN/ServiceLib/Common/Utils.cs b/v2rayN/ServiceLib/Common/Utils.cs
index f1613782..393c4fe7 100644
--- a/v2rayN/ServiceLib/Common/Utils.cs
+++ b/v2rayN/ServiceLib/Common/Utils.cs
@@ -1441,7 +1441,11 @@ public class Utils
             if (File.Exists(fileName))
             {
                 var currentMode = File.GetUnixFileMode(fileName);
-                File.SetUnixFileMode(fileName, currentMode | UnixFileMode.UserExecute | UnixFileMode.GroupExecute | UnixFileMode.OtherExecute);
+                var executableMode = currentMode | UnixFileMode.UserExecute | UnixFileMode.GroupExecute | UnixFileMode.OtherExecute;
+                if (currentMode != executableMode)
+                {
+                    File.SetUnixFileMode(fileName, executableMode);
+                }
                 return true;
             }
         }
diff --git a/v2rayN/ServiceLib/Services/SpeedtestService.cs b/v2rayN/ServiceLib/Services/SpeedtestService.cs
index c1a7de38..a5155589 100644
--- a/v2rayN/ServiceLib/Services/SpeedtestService.cs
+++ b/v2rayN/ServiceLib/Services/SpeedtestService.cs
@@ -587,6 +587,12 @@ public class SpeedtestService(Config config, Func<SpeedTestResult, Task> updateF
     private List<List<ServerTestItem>> GetTestBatchItem(List<ServerTestItem> lstSelected, int pageSize)
     {
         List<List<ServerTestItem>> lstTest = [];
+        if (lstSelected.Count == 0)
+        {
+            return lstTest;
+        }
+
+        pageSize = Math.Max(pageSize, 1);
         var lst1 = lstSelected.Where(t => t.CoreType == ECoreType.Xray).ToList();
         var lst2 = lstSelected.Where(t => t.CoreType == ECoreType.sing_box).ToList();
 
diff --git a/v2rayN/ServiceLib/ViewModels/StatusBarViewModel.cs b/v2rayN/ServiceLib/ViewModels/StatusBarViewModel.cs
index 5cfe417f..91895e3f 100644
--- a/v2rayN/ServiceLib/ViewModels/StatusBarViewModel.cs
+++ b/v2rayN/ServiceLib/ViewModels/StatusBarViewModel.cs
@@ -219,7 +219,8 @@ public partial class StatusBarViewModel : MyReactiveObject
         await ConfigHandler.InitBuiltinRouting(_config);
         await RefreshRoutingsMenu();
         await InboundDisplayStatus();
-        await ChangeSystemProxyAsync(_config.SystemProxyItem.SysProxyType, true);
+        // The view refreshes its icon on initialization; interaction handlers are not registered yet.
+        await ChangeSystemProxyAsync(_config.SystemProxyItem.SysProxyType, false);
 
         BlRouting = true;
     }