An explicit quadruple ratio

In his celebrated proof of Zagier's polylogarithm conjecture
for weight 3 Goncharov introduced a "triple ratio", a projective
invariant akin to the classical cross-ratio. He has also conjectured
the existence of "higher ratios" that should play an important role
for Zagier's conjecture in higher weights. Recently, Goncharov and
Rudenko proved the weight 4 case of Zagier's conjecture with a
somewhat indirect method where they avoided the need to define a
corresponding "quadruple ratio". We propose an explicit candidate for
such "quadruple ratio" and as a by-product we get an explicit formula
for the Borel regulator of K_7 in terms of the tetralogarithm function
(joint work with S. Charlton and H. Gangl).