Identify the relationship between the higher Links–Gould invariant and the V2-polynomial

Determine whether the V2-polynomial coincides with the higher Links–Gould invariant $LG^{(1)}$.

Background

The paper discusses higher Links–Gould invariants LG(n)LG^{(n)}, noting that the Murasugi-sum multiplicativity theorem proved for the ordinary Links–Gould invariant does not extend to these higher invariants. In this context, the authors refer to the V2-polynomial and state that its conjectural identification with LG(1)LG^{(1)} remains an unresolved claim.

References

This can be seen from simple computations, e.g. Hopf links have $q$-monic $LG{(1)}$, but that's not the case for the trefoil and figure eight (see e.g. for the $V_2$-polynomial which conjecturally coincides with $LG{(1)}$).

— The top coefficient of the Links-Gould invariant is Murasugi-sum multiplicative  (2610.09354 - Anghel et al., 7 Oct 2026) in Section 1, Introduction