Multiplicative expression for the coefficient in fermionic 3-3 relation

Recently, a family of fermionic relations were discovered corresponding to Pachner move 3-3 and parameterized by complex-valued 2-cocycles, where the weight of a pentachoron (4-simplex) is a Grassmann-Gaussian exponent. Here, the proportionality coefficient between Berezin integrals in the l.h.s. and r.h.s. of such relations is written in a form multiplicative over simplices.