  In 2018, Kashaev introduced a square matrix indexed by the regions of a link
diagram, and conjectured that it provides a novel way of computing the
Levine-Tristram signature and Alexander polynomial of the corresponding
oriented link. In this article, we show that for the classical signature (i.e.
the Levine-Tristram signature at -1), this conjecture follows from the seminal
work of Gordon-Litherland. We also relate Kashaev's matrix to Kauffman's
"Formal Knot Theory" model of the Alexander polynomial. As a consequence, we
establish the Alexander polynomial and classical signature parts of the
conjecture for arbitrary links, as well as the full conjecture for definite
knots.
