You can use the "dropping a hash" method (patio11 has used this). As you progress your work, you publish a hash of it using a service trusted by everyone to correctly identify the researchers and timestamp their hashes.

If someone publishes the paper, you can then publish the files that resulted with the dropped hash and therefore prove you had certain progress of the work at a certain time.

4d merkle trees etched on a proton or something

Yes you can provably document your progress, but it doesn't solve the problem that someone else may have published overlapping ideas earlier and you can't prove that you didn't read what they published.

I was mostly thinking in the case of overlapping research as mentioned in the parent comment, not independent research years after the publication (where indeed it sounds impossible to prove you didn't read it).

Basically, if you could show that you had already made significant progress before the publication date, then you might be granted the patent as well.

a use for blockchain at last?