How to make your small ideas into a research paper?
One of my biggest regrets is not writing down small ideas. There were waiting for a better time. But usually this time never came - either because I didn't find a good way to expand on the project, or because new projects left little time.

In There are no projects like side projects (which I wrote after finishing my PhD) there is:


  If you have a great project, do moonlight. Don’t wait for better times, because they won’t come. Maybe you overstate the need of money, institutional support or social confirmation?


Depending on the project, it can be a small draft (e.g. with a theorem and some comments on possible approaches to prove it) or a GitHub repository with code and some description.

Once something is shared, there are two main benefits:


you can talk about it / send it to your colleagues,
you made some progress, even if it is a small step, it's strictly more than nothing. 


Occasionally, during the writing phase you may:


see how to expand on it,
or realise that actually you already did a lot,
or discover that it is flawed (e.g. your proof is trivial or incorrect).


Additionally, if a few years later someone ask you - you will be able to recover it quickly, along with its core content (formulae, citations, etc).
Sharing means that you can share it with your future self.

Is it just a one-page LaTeX note? Just write it.