feat(udt-011): register TimeProvider.System in AddApplication DI

tests/SIGCM2.Application.Tests/Common/AddApplicationDependencyInjectionTests.cs

@@ -0,0 +1,30 @@
+using FluentAssertions;
+using Microsoft.Extensions.DependencyInjection;
+using SIGCM2.Application;
+
+namespace SIGCM2.Application.Tests.Common;
+
+/// <summary>
+/// UDT-011 T300.20.2 — DI registration smoke tests for AddApplication.
+/// Pure unit: no DB, no HTTP — just verifies the service container.
+/// </summary>
+public sealed class AddApplicationDependencyInjectionTests
+{
+    /// <summary>
+    /// [REQ-BE-CLOCK-004] TimeProvider.System must be registered as singleton
+    /// so all command handlers can inject it without a concrete coupling.
+    /// </summary>
+    [Fact]
+    public void AddApplication_Registers_TimeProvider_System()
+    {
+        var services = new ServiceCollection();
+        // AddApplication requires some infrastructure; provide minimal stubs
+        // by only testing the DI graph without building the full host.
+        services.AddApplication();
+        using var provider = services.BuildServiceProvider();
+
+        var timeProvider = provider.GetRequiredService<TimeProvider>();
+
+        timeProvider.Should().BeSameAs(TimeProvider.System);
+    }
+}