diff --git a/jsonschema/schema.go b/jsonschema/schema.go
index 1d60de12..0b4764d6 100644
--- a/jsonschema/schema.go
+++ b/jsonschema/schema.go
@@ -204,6 +204,7 @@ func (s *Schema) MarshalJSON() ([]byte, error) {
 	if err := s.basicChecks(); err != nil {
 		return nil, err
 	}
+
 	// Marshal either Type or Types as "type".
 	var typ any
 	switch {
@@ -219,7 +220,19 @@ func (s *Schema) MarshalJSON() ([]byte, error) {
 		Type:                 typ,
 		schemaWithoutMethods: (*schemaWithoutMethods)(s),
 	}
-	return marshalStructWithMap(&ms, "Extra")
+	bs, err := marshalStructWithMap(&ms, "Extra")
+	if err != nil {
+		return nil, err
+	}
+	// Marshal {} as true and {"not": {}} as false.
+	// It is wasteful to do this here instead of earlier, but much easier.
+	switch {
+	case bytes.Equal(bs, []byte(`{}`)):
+		bs = []byte("true")
+	case bytes.Equal(bs, []byte(`{"not":true}`)):
+		bs = []byte("false")
+	}
+	return bs, nil
 }
 
 func (s *Schema) UnmarshalJSON(data []byte) error {
diff --git a/jsonschema/schema_test.go b/jsonschema/schema_test.go
index 4b6df511..19f6c6c7 100644
--- a/jsonschema/schema_test.go
+++ b/jsonschema/schema_test.go
@@ -54,9 +54,9 @@ func TestJSONRoundTrip(t *testing.T) {
 	for _, tt := range []struct {
 		in, want string
 	}{
-		{`true`, `{}`}, // boolean schemas become object schemas
-		{`false`, `{"not":{}}`},
-		{`{"type":"", "enum":null}`, `{}`}, // empty fields are omitted
+		{`true`, `true`},
+		{`false`, `false`},
+		{`{"type":"", "enum":null}`, `true`}, // empty fields are omitted
 		{`{"minimum":1}`, `{"minimum":1}`},
 		{`{"minimum":1.0}`, `{"minimum":1}`},     // floating-point integers lose their fractional part
 		{`{"minLength":1.0}`, `{"minLength":1}`}, // some floats are unmarshaled into ints, but you can't tell
diff --git a/mcp/testdata/conformance/server/tools.txtar b/mcp/testdata/conformance/server/tools.txtar
index b4068d1c..01fdb266 100644
--- a/mcp/testdata/conformance/server/tools.txtar
+++ b/mcp/testdata/conformance/server/tools.txtar
@@ -59,9 +59,7 @@ greet
 							"type": "string"
 						}
 					},
-					"additionalProperties": {
-						"not": {}
-					}
+					"additionalProperties": false
 				},
 				"name": "greet"
 			}