I understand the marketing hype around this, but Honda brands all of their engines with Honda and uses Honda specific parts with Honda replacement parts through Honda dealers. The Jailing-Honda relationship has nothing to do with your single cylinder 124cc engine. If you take the time to do more research you'll find this out and you are working off a link that has been circulating for some time. Additionally, when you take apart your engine, you'll see lifan and Jailing markings on the parts inside the cases. Honda doesn't have anything to do with the motor you own as it's made by Jailing and branded by a GPX. Jailing does partner with Honda on other things, but not single cylinder engines. Look at the markings on your cylinder. Here's your cylinder manufacturer for that engine:
http://www.cngongyu.com/doce/gsjj.htm
The importer no longer brands their "GPX" motors as being affiliated with Honda either, unless they haven't updated their webpage on that specific product.
Lastly, see attached picture of your stator plate behind the flywheel. Those are lifan parts.
In summary, the GPX has engine parts from Lifan, Jailing, Gongyu and a ton of other companies in China. It's still a decent motor, but in now way affiliated with Honda, Jailing-Honda or honda's quality control when they have parts manufactured for them in China.