This is a follow up to this [question][1], and is related to this [question][2] of Shiva Kinali.

It seems that the proofs in these papers ([Allender][3], [Caussinus-McKenzie-Therien-Vollmer][4], [Koiran-Perifel][5]) use hierarchy theorems. I want to know if the proofs are "*pure*" diagonalization theorems, or if they use something more that usual diagonalization. So my question is 

> is there a reasonable relativization which puts permanent in uniform $\mathsf{TC^0}$?

Note that I am not sure how to define oracle access for uniform $\mathsf{TC^0}$, I know that finding the correct definition for small complexity classes is nontrivial. Another possibility is that permanent is not complete for $\mathsf{\#P}$ in the relativized universe, in which case I should use some complete problem for $\mathsf{\#P}$ in the relativized universe in place of it, and I think $\mathsf{\#P}$ should have a complete problem in any reasonable relativized universe.


  [1]: https://cstheory.stackexchange.com/questions/80/which-results-in-complexity-theory-make-essential-use-of-uniformity
  [2]: https://cstheory.stackexchange.com/questions/1388/proofs-barriers-and-p-vs-np
  [3]: http://ftp.cs.rutgers.edu/pub/allender/threshold.pdf
  [4]: http://www.iro.umontreal.ca/~mckenzie/camcthvo97.ps
  [5]: http://arxiv.org/abs/0902.1866