return new_mapping, new_definitions


def _replace_refs(
    *,
    schema: dict[str, Any],
    old_name_to_new_name_map: dict[str, str],
) -> dict[str, Any]:
    new_schema = deepcopy(schema)
    for key, value in new_schema.items():
        if key == "$ref":
            value = schema["$ref"]
            if isinstance(value, str):
                ref_name = schema["$ref"].split("/")[-1]