fix: include judgeConfiguration in CompletionConfigDefault.ToLdValue()

LdAiCompletionConfigDefault.ToLdValue() was not serializing the
judgeConfiguration property, unlike LdAiAgentConfigDefault which did.
This meant the judge config was lost when the default round-tripped
through JsonVariation as an LdValue fallback.

Adds conditional serialization matching the agent default pattern and
a test that verifies the round-trip.

Co-Authored-By: mmccarthy@launchdarkly.com <mmccarthy@launchdarkly.com>

Author: devin-ai-integration[bot]

pkgs/sdk/server-ai/src/Config/LdAiCompletionConfigDefault.cs

@@ -173,7 +173,7 @@ internal LdValue ToLdValue()
             ["mode"] = LdValue.Of(LdAiCompletionConfig.Mode)
         };
 
-        return LdValue.ObjectFrom(new Dictionary<string, LdValue>
+        var root = new Dictionary<string, LdValue>
         {
             { "_ldMeta", LdValue.ObjectFrom(metaFields) },
             { "messages", LdValue.ArrayFrom(Messages.Select(m => LdValue.ObjectFrom(new Dictionary<string, LdValue>
@@ -191,7 +191,23 @@ internal LdValue ToLdValue()
             {
                 { "name", LdValue.Of(Provider.Name) }
             }) }
-        });
+        };
+
+        if (JudgeConfiguration != null)
+        {
+            root["judgeConfiguration"] = LdValue.ObjectFrom(new Dictionary<string, LdValue>
+            {
+                { "judges", LdValue.ArrayFrom(JudgeConfiguration.Judges.Select(j =>
+                    LdValue.ObjectFrom(new Dictionary<string, LdValue>
+                    {
+                        { "key", LdValue.Of(j.Key) },
+                        { "samplingRate", LdValue.Of(j.SamplingRate) }
+                    })))
+                }
+            });
+        }
+
+        return LdValue.ObjectFrom(root);
     }
 
     /// <summary>

pkgs/sdk/server-ai/test/LdAiClientTest.cs

@@ -875,4 +875,35 @@ public void CompletionConfigDefaultJudgeConfigurationSurvivesBuildFromDefault()
         Assert.Equal("coherence", result.JudgeConfiguration.Judges[0].Key);
         Assert.Equal(0.3, result.JudgeConfiguration.Judges[0].SamplingRate);
     }
+
+    [Fact]
+    public void CompletionConfigDefaultToLdValueIncludesJudgeConfiguration()
+    {
+        var mockClient = new Mock<ILaunchDarklyClient>();
+        var mockLogger = new Mock<ILogger>();
+
+        // Return the default LdValue directly so it round-trips through BuildCompletionConfig.
+        mockClient.Setup(x =>
+            x.JsonVariation("foo", It.IsAny<Context>(), It.IsAny<LdValue>()))
+            .Returns((string _, Context _, LdValue dv) => dv);
+        mockClient.Setup(x => x.GetLogger()).Returns(mockLogger.Object);
+
+        var judgeConfig = new LdAiConfigTypes.JudgeConfiguration(
+            new List<LdAiConfigTypes.JudgeConfiguration.Judge>
+            {
+                new LdAiConfigTypes.JudgeConfiguration.Judge("accuracy", 0.9)
+            });
+
+        var defaultConfig = LdAiCompletionConfigDefault.New()
+            .SetJudgeConfiguration(judgeConfig)
+            .Build();
+
+        var client = new LdAiClient(mockClient.Object);
+        var result = client.CompletionConfig("foo", Context.New(ContextKind.Default, "key"), defaultConfig);
+
+        Assert.NotNull(result.JudgeConfiguration);
+        Assert.Single(result.JudgeConfiguration.Judges);
+        Assert.Equal("accuracy", result.JudgeConfiguration.Judges[0].Key);
+        Assert.Equal(0.9, result.JudgeConfiguration.Judges[0].SamplingRate);
+    }
 }