Where to publish supplementary math intensive material for magazine article
If the main idea of the mathematical evaluation can be explained in words, then the details may not be necessary to make public, as the motivated reader can certainly rederive them. 

If on the other hand the math is non-trivial, then it should be explained in a high level way, with appropriate references to the more advanced techniques used.

If the math is highly non-trivial, then that would be sufficient material for a publication in mathematics, and the full paper on the math may be posted on the arxiv.

And no, personally I wouldn't use researchgate. Researchgate is not a journal, and submissions there do not count as publications. The same applies to arxiv too, and if you have a paper-worthy mathematical result, it ought to be eventually submitted for publication.