Submit an academic paper to arXiv built over a patented idea We have our idea patented with the company we are working currently for. But, we have also been writing a paper draft on the theory and the mathematics behind the idea with practical results, plots, comments, and future directions. Can we submit the paper to arXiv linking it to the original patent? I am confused because arXiv is for open publishing but having the core idea patented doesn't, probably, allow open usage of the algorithm. Does it then contain the same academic value and worth putting on arXiv? Does arXiv allow such a thing at all? Thanks
To the best of my knowledge, arXiv has no rules against posting preprints that discuss patented material.  The only requirement is that you grant them a license in the copyright of the text you posted, so that they can distribute the article without having you sue them.  They have no such strict "open publishing" rules as you suggest.

However, in many jurisdictions, if you publish your invention (i.e. make it public in any way) before applying for the patent (or maybe before having it granted?), your patent can be invalidated.  Thus, you should consult with your patent attorney before publishing anything.