Training is too expensive for the training data to be the preferred form for making modifications to the work. Given that, the weights themselves are the closest thing these things have to "source code".

And this is where the reproducibility argument falls apart: on what basis can we insist that the preferred form for modifying an LLM (the weights) must be reproducible to be open source but the preferred form for modifying a piece of regular software (the code) can be open sourced as is, with none of the processes used to produce the code?

No, I'm using the strict definition "capable of being reproduced", where reproduce means "to cause to exist again or anew". In and of itself the word doesn't comment on whether you're starting from source code or anything else, it just says that something must be able to be created again.

Yes, in the context of compilation this tends to refer to reproducible builds (which is a whole rabbit hole of its own), but here we're not dealing with two instances of compilation, so it's not appropriate to use the specialized meaning. We're dealing with two artifacts (a set of C files and a set of weights) that were each produced in different ways, and we're asking whether each one can be reproduced exclusively from data that was released alongside the artifact. The answer is that no, neither the source files or the weights can be reproduced given data that was released alongside them.

So my question remains: on what basis can we say that the weights are not open source but the C files are? Neither can be reproduced from data released alongside them, and both are the preferred form which the original authors would choose to make modifications to. What distinguishes them?