fix(ai-formats): accept Claude context_management in responses conversion

crates/aether-ai-formats/src/formats/registry.rs

@@ -486,6 +486,7 @@ fn standard_request_root_field_is_audited(source: FormatId, key: &str) -> bool {
             key,
             "cache_control"
                 | "container"
+                | "context_management"
                 | "inference_geo"
                 | "max_tokens"
                 | "messages"
@@ -858,7 +859,12 @@ fn request_extension_key_is_cross_format_safe(
                 | "prompt_cache_key"
                 | "prompt_cache_retention"
                 | "verbosity",
-        ) | (FormatId::ClaudeMessages, _, "claude", "output_config")
+        ) | (
+            FormatId::ClaudeMessages,
+            _,
+            "claude",
+            "context_management" | "output_config",
+        )
             | (
                 FormatId::ClaudeMessages,
                 FormatId::OpenAiChat | FormatId::GeminiGenerateContent,
@@ -2517,6 +2523,25 @@ mod tests {
         assert_eq!(converted["input"][0]["content"][0]["type"], "input_text");
     }
 
+    #[test]
+    fn claude_request_to_responses_accepts_context_management() {
+        let body = json!({
+            "model": "claude-sonnet",
+            "messages": [{"role": "user", "content": "hello"}],
+            "max_tokens": 128,
+            "context_management": {
+                "edits": [{"type": "clear_tool_uses_20250919"}]
+            }
+        });
+
+        let converted = convert_request_pure("claude:messages", "openai:responses", &body)
+            .expect("context_management is audited for Claude cross-format requests")
+            .value;
+
+        assert_eq!(converted["model"], "claude-sonnet");
+        assert!(converted.get("context_management").is_none());
+    }
+
     #[test]
     fn pure_request_conversion_does_not_apply_model_or_stream_edits() {
         let body = json!({