I have a theory that I cannot test myself. A group that doesn't know me has the proprietary data needed to test it, and I think they could test it fairly easily (hours to weeks of work, I think). I plan to reach out and pitch my theory to them. My only contributions are the hypothesis and an argument for why it's plausible, and so worth checking out. Is it appropriate to discuss academic authorship off-the-bat in a situation like this?
It is not only appropriate, but essential to discuss authorship when you propose a collaboration. Pre-agreeing authorship arrangements will solve any number of problems down the track with any collaboration.
However, it is a bit tricky in this situation becuase once you've explained your idea, I guess they can say "no", and then go off and do it anyway (not that that would be very nice).
Yes, I think it is appropriate. But authorship also is not set in stone at the beginning of a collaboration -- it is contingent upon doing the work. One way to phrase it would be like "I have an idea related to XX that I think can be tested using data that you've gathered. I would like to perform an analysis and write up a paper. I would be honored if you would collaborate with me on this paper if you would agree provide the data and check that I am interpreting it correctly. Please let me know if you would like to discuss this collaboration."
- You would do the analysis and write the paper -- being first author.
- They would be collaborators.
- I also lays out expectations for each groups -- they could look at your proposal and conclude that it might only be a few days work (that's simply to transfer the data, explain it, review your analysis, and review the manuscript you write).
- They could steal your idea, but only after you two have had a kick-off meeting to discuss the ideas. Don't send the hypothesis in an email, and definitely not the analysis plan. Make sure they get it from direct discussions from you (ideally with at least a couple of people from their group, so that nobody on the team can claim to have come up with the idea). Maybe you could share the hypothesis in a phone call, but any description of the analysis should be to a few people. Ideally you already have the software written and maybe have some simulated dataset to go with it -- stuff they could not replicate easily. At least in my field, I wouldn't be too worried about someone stealing my ideas -- people have their own ideas and existing commitments; writing a paper is always at least a few weeks of work.
Aside from that, one way to claim the idea may be pre-registration.