new_field_mapping: dict[
        tuple[ModelField, Literal["validation", "serialization"]], JsonSchemaValue
    ] = {}
    for field_key, schema in field_mapping.items():
        new_schema = _replace_refs(
            schema=schema,
            old_name_to_new_name_map=old_name_to_new_name_map,
        )
        new_field_mapping[field_key] = new_schema

    new_definitions = {}