The equality of regulator formulas for Gauss fibrations when a equals b

Let $f$ be a hypergeometric fibration of Gauss type, and let $\xi$ be an element whose regulator pairing with the homology cycle $\gamma_1$ is described by Theorem. The parameters $a$ and $b$ are those occurring in the fibration.

Gauss regulator equality conjecture. The first equality in Theorem is valid even when $a=b$.

The theorem establishes the formula under the hypothesis $a\ne b$; this conjecture asserts its extension to the remaining case.