TITLE: Have any complexity classes been shown to be equal or non equal in the past five years?
QUESTION [8 upvotes]: A prediction was made 5 years ago; "In the next five years, two classes in the Complexity Zoo as of 10 August 2011, will either be shown to be equal or shown to be unequal." http://predictionbook.com/predictions/2992
I am looking for information about progress in computational complexity theory in the past 5 years to resolve / answer this.

REPLY [3 votes]: In [1], the authors show (among a bunch of other things) that $TC^1 = AC^1[p_n]$ where $p_n$ is the $n^\text{th}$ prime and $n$ is the number of input bits to the circuit.
Depending on how strictly you read the original question, this may or may not be a satisfactory answer. First, the Complexity Zoo is quite good for what it is but is far from comprehensive: it includes a definition of $AC^1$ under its entry for $AC$ (via definitions of $AC^i$) but offers no such parallel definition for $TC^1$ despite it being a perfectly standard complexity class. Also, it has no entry for $AC^i[m]$ even though it's reasonably easy to infer from the surrounding context for $AC^i$ and $AC^0[m]$. Second, the classical view of $AC^i[m]$ is that the modulus is constant with respect to the size of the input; the definition given in the Complexity Zoo does not require this.  

Allender, Eric, Anna Gál, and Ian Mertz. "Dual VP classes." International Symposium on Mathematical Foundations of Computer Science. Springer Berlin Heidelberg, 2015.