How many amicus briefs will be filed in Baze?

My phone has been ringing of the hook with media eager to talk about the cert grant in Baze.   I am not at all surprised that a lot of folks (myself included) are trying to figure out exactly what to make of the cert grant and what the grant might mean for pending executions throughout the nation.

Amidst all the head-scratching, Orin Kerr here makes this nice point at The Volokh Conspiracy:

This case really calls out for amicus participation to give the Justices context: In particular, it really needs briefs by leading historians on the history and evolution of how executions were carried out over time in the United States and at common law.  What techniques were used in different historical periods, and why did they change? A really top-notch brief on the history of methods of execution would provide some very helpful context for the Justices.  Obviously it wouldn't decide the case for the seven nonoriginalist Justices, but it would be quite helpful background for all of them. I hope someone is inspired to write a careful and balanced brief on this issue; that person would truly be a "friend of the Court."

I concur with the value of scholars being friendly to the Court in this case, especially because I suspect that a lot of partisan advocates will be chiming in.  Specificially, I am pretty sure the SG and many states will be filing in support of Kentucky and many anti-death penalty groups will be filing in support of Baze.  Any non-partisan brief that is, in Orin's words, "careful and balanced" should get special attention from the Justices.