The math behind Recent Average Credit (RAC)

Greetings fellow BOINCers and Gridcoin enthusiasts!

While working on a proposed version of the Gridcoin whitepaper, I got involved in trying to sort out exactly how Recent Average Credit (RAC) is calculated in the BOINC source code (the exact location in the source code is here). I was a bit confused at first. Since I'm actually a theoretical physicist by trade, I set out to make sense of RAC in my own terms. The explanation I came up with can be downloaded here.

I realize people have discussed RAC elsewhere (see links below), but I hope my explanations can shed some additional light. I know in particular this may be useful to the Gridcoin community. Since RAC translates directly into a researcher's magnitude, and thereby Gridcoin payouts, we want to make sure RAC is calculated in a way that, among other requirements, 1) accurately captures a researcher's average contributions on a project-by-project basis, and 2) is hard to unfairly manipulate to get more GRC. In the long run, one could ask whether RAC is even the best way of quantifying researcher contributions. At any rate, an understanding of how RAC works mathematically is important for making Gridcoin secure and fair.

Disclaimer: Physicists and mathematicians are notorious for making really dumb mistakes. I sincerely hope there are none in my write-up. Per the academic parlance, I at least hope my explanations are "correct in spirit." 

Finally, although I wrote the linked write-up myself, the basic scaffolding was taken from an early version of this document. In addition, a discussion similar to mine can be found here. The main differences are that my approach takes an alternative starting point, and is also more formal from a mathematical point of view. Lastly, there is some background information in this post. 

I welcome any thoughts/feedback. If you find any errors, feel free to point them out in the comments.