I post this as a separate comment.
At this point, I am not capable with addressing the thing you pointed out - the way to block fake results in open network. From the very beginning, I don't want to make the system closed-network nor login required as I want people to join the calculation instantly. Technically, I think it is impossible to prevent reporting fake result as long as it is open network system - which means my design doesn't fit to seeking rigor.
If someone starts another project that handles calculations in better way, I would like to learn from it.
Your project is not bad. It's the way you've worded this post and your article that comes across as misleading and deceptive.
There's no definitive proof that a world record has been set. Nor that every individual block has been processed and reported honestly. What is known is that the system provides a mechanism for volunteers to submit counterexamples if they choose to. That's something.
It's possible for clients to act dishonestly and withhold counterexamples. There's an incentive to claim independent credit. So the clients have incentive to lie.
So your project doesn't ensure that every block has been verified, it allows honest participants to report findings. That's the reality and you should frame it that way in the post and article.