Can I claim authorship on work I wasn't personally involved in, that uses a framework I developed for my research?

Disclaimer: This is somewhat field-dependent. I'm answering based on what I believe to be the current situation in computer science / related fields.

1) Can you claim authorship given the way things have evolved? Probably not.

2) Would it have been a good idea for him to find a way to include you in the research collaboration so that you could get something out of your work? Yes.

The area of academia in which I work (*) is structured so as to value ideas over implementation. In practice, that means that it's not uncommon for people who write large amounts of code for a project to get little credit for it, which seems inherently unjust.

The way sensible people usually handle this is to make sure that people who do a lot of implementation work are given an opportunity to contribute scientifically over and above that - that allows them to justify their authorship in scientific terms, regardless of the fact that they also made significant non-scientific contributions to the overall project.

It's certainly possible to take advantage of implementers by not doing this, but people who do that tend to find themselves doing the implementation work themselves.

Bottom line: He should have had the common sense to include you in the scientific collaboration, and if he didn't have that common sense then his supervisor should have suggested it.

As an aside, I would view the situation somewhat differently if you already had a publication as a result of your work. In that case, you've already got the credit for working on the framework, and there's less of a moral obligation to include you in the new collaboration: instead, they can simply cite you. I'm certainly not of the view that writing a framework entitles you to be involved in every paper that is ever built on top of that framework - indeed, I've written frameworks that other people have continued to use for later research, and I wouldn't expect to be involved with the papers in question.

(*) As pointed out in the comments, this may not be the case in other fields.

Approaching this question from a psychological rather than legalistic perspective, I would argue similarly to vadim123 that the question you should ask is not "should I claim co-authorship?" When you feel a need to "claim" anything, you are putting yourself in an adversarial position relative to the student and other collaborators. This is likely to antagonize them and put them on the defensive with the perception that you are coming to stake a claim to a piece of property they have ownership of. Given the marginal nature of your claim, this zero-sum type of logic would mean that your chances of success would be very slim and you would run a substantial risk of hurting your reputation and/or souring your working relationship with the paper's authors and other colleagues.

On the other hand, it's important to keep in mind that this is not in fact a zero-sum situation. While I don't think you should be talking about "claiming" authorship, there is nothing to stop you from suggesting that you may become an author to the work by participating in its writing and including the framework you wrote as one of the topics discussed in the paper. The key is to do this in a diplomatic, sensitive way that appeals to the authors' self-interest and points out various ways in which it might very well be to their benefit to add you as a coauthor. It's also important that your offer makes it clear that you don't intend to force the issue and consider a decision not to include you as a coauthor to be a reasonable and legitimate one. Above all, avoid any use of accusatory, entitled-sounding or negatively charged words (such as "claim" or "deserve").

Here's an example (perhaps slightly exaggerated for dramatic effect) of how an email to the student bringing up the issue might work:*

*credit to @ff524 for the fictional - I assume - basket weaving research theme ;-)

Dear Joe,

I heard that you and [insert name of group/collaborators] are working on a paper on your new results about basket weaving. Congratulations, I'm glad something came out of that project. I hope you manage to publish it somewhere good.

I thought I'd run something by you in connection with that. As you know, I spent several months working quite hard on the Basketweaving Framework that you used in that analysis. While I don't necessarily think that that should entitle me to coauthorship in your paper (and if you don't want to offer me coauthorship, I understand and think that's completely reasonable), it did occur to me that if you were to offer to let me take part in writing the paper and become a coauthor you could get several benefits that might not have occurred to you:

First, we could add a section about the basket weaving framework itself, which I created. I don't know if you wanted to mention it, but the new content could improve the paper and make it appeal to a wider audience, and possibly be accepted to a more prestigious conference, etc.

Second, another way that I could help is that I am a really good writer and put a lot of work into each paper I write - you can look at my existing papers and see how polished they are, with great figures etc. - and I can assure you that I am willing to work very hard to ensure that this paper has the same level of polish that would help the quality of the work shine through. Did I mention that my most recent paper was accepted to the International Congress Of Basketweavers? ;-)

Third, I've found in my career so far that while having coauthors does dilute a bit the credit you get for papers you write, it does so much less than you might think, and this effect is usually greatly outweighed by the fact that a coauthor is essentially a free spokesperson working for you, who goes around giving talks about your joint work at various places, and who can often say nice things about you in those talks that you couldn't easily get away with saying about yourself. Maybe it's cynical of me to be thinking in this way, but that's just one of the quirks of academia and how it operates and it's just as well to be aware of it.

As I said I'm happy with whatever decision you and the group end up making, just thought you might want to think about this.

Authorship is much like right-of-way on the roads, in that it can be given but not taken. The answer to any question that begins with "Can I claim authorship" is no; instead one should ask "Should I receive authorship". Of course, both drivers and authors sometimes make mistakes (and can be criticized or punished for those mistakes), and sometimes people get hurt.

Such difficulties can be avoided by simply discussing, at the beginning of any research collaboration, what the possible authorship outcomes might be from the results. With an agreement in place, a potential he-said-she-said situation disappears, and a withheld coauthorship becomes a clear offense.

As the other answers and comments indicate, the specifics of the OP's situation is highly contextually dependent. OP should discuss how to proceed with senior members of his or her department, who will have more useful advice than strangers on the internet.