Global validity of Litherland’s quandle cocycle/Alexander module conjectures

Establish whether the two conjectures proposed by Richard Litherland in his 2002 work on quadratic quandles—that quandle cocycle invariants of a specific form are determined by the Alexander module—hold for all knots, extending beyond the cases of torus links and 2-bridge knots where they were proved.

Background

In his 2002 paper on quadratic quandles and link invariants, Richard Litherland proposed conjectures asserting that certain quandle cocycle invariants are determined by the Alexander module of the knot or link. He established these conjectures for specific families (torus links and 2-bridge knots). The open question asks whether these conjectures are valid for all knots, which would unify quandle cocycle invariants with Alexander module data across knot types.