https://en.wikipedia.org/wiki/Frank_Nelson_Cole
If you 'destroyed RSA' through better factorization, all you have to do is start publishing factors of RSA challenge numbers.
Matthew Green has a fun thread about other ways to approach this along with an interesting "real talk about factoring" sidebar by Nadia Heninger:
https://twitter.com/matthew_d_green/status/13669500931784990...
This isn't science, it's math. As the article mentions, there is an 862-bit RSA challenge that hasn't been factored yet. Factoring it should be possible on commodity hardware if the claims in the paper are true. So why not just do it? The test of success is simple: either you win the challenge or you don't.
Then why would I trust it? You don't need to write code, you need to write an example
As Linus Torvalds says: talk is cheap, show me the code
Academia is full of "paper scientists" that put out papers but produce nothing of value.
They are also full of postgraduate students as well that would be more than willing to work together and put a proof-of-concept code with the paper.