Missing Json root element

I am not sure I fully understand goals and scenarios - also please note that example support and in general customization and extensibility are more advanced in Swagger Core v2 (https://github.com/swagger-api/swagger-core/wiki/Swagger-2.X---Getting-started, supporting OpenAPI 3.0)  - however the example content is not dependent on any serialization preference on the server side, as it is dynamically built by swagger-ui (if an `example` field doesn't exist at Pet level) out of the defined schema.

The schema resolved by swagger-core from Pet Pojo is also not dependent on whatever Jackson mapper serialization options of the Pojo itself (there can be many mapper, each applying or not WRAP_ROOT_VALUE, e.g the one used by the REST framework of choice, the one in use by swagger-core, any other..).

It analyze the properties/members of the Pojo  and build a `Model` of it. This model (e.g. a `ModelImpl` object) is then serialized to JSON/YAML along with the whole resolved `Swagger` object to output the serialized resolved Swagger definition. 

If the expected JSON accepted (or returned) by your endpoints includes the`Pet` as a property within a "wrapper" (as with Jackson WRAP_ROOT_VALUE) this would need to be defined in the model used, you could for example define a wrapper class and add that as type of the ApiParam or ApiImplicitParam annotation, e.g.

public class PetWrapper{
    public Pet pet;
}

As mentioned above, a slightly more complicated alternative is providing an `example` value to the model, to obtain something like:

  Pet:
    type: "object"
    example: 
      pet:
        id: 0
        name: "mypet"
    properties:
      id:
        type: "integer"
        format: "int64"
      name:
        type: "string"

unfortunately there is no annotation in Swagger Core v1 allowing to define the example for root models, but you can provide your own along with a custom ModelResolver, e.g.:

    class CustomConverter extends ModelResolver {


        public CustomConverter(ObjectMapper mapper) {
            super(mapper);        }
            
        @Override
        public Model resolve(JavaType type, ModelConverterContext context, Iterator<ModelConverter> next) {
            Model model = super.resolve(type, context, next);
            BeanDescription beanDesc = _mapper.getSerializationConfig().introspect(type);
            final ExampleAnnotation ann = beanDesc.getClassAnnotations().get(ExampleAnnotation.class);
            if (ann != null && !StringUtils.isBlank(ann.value())) {
                try {
                    model.setExample(Json.mapper().readTree(ann.value()));
                } catch (JsonProcessingException e) {
                    e.printStackTrace();
                    return model;
                }
            }
            return model;
        }
    }

@Target({ElementType.TYPE})
@Retention(RetentionPolicy.RUNTIME)
@Inherited
public @interface ExampleAnnotation {
    String value() default "";
}

configuring it via service loader or in bootstrap code:

ModelConverters.getInstance().addConverter(new CustomConverter());

you would then be able to define the example for your pojo as you like:

@ExampleAnnotation("{\"Pet\": {\"id\" : 0, \"name\": "...."}}")
public class Pet {
    private long id;
    private Category category;
...
...