AJ Conjecture for the family of double twist knots K(p,p)

Prove the AJ Conjecture for the family of double twist knots K(p,p), namely, show that the non-commutative A-polynomial annihilates the colored Jones polynomial for each K(p,p).

Background

The AJ Conjecture connects quantum topology (colored Jones polynomials) with classical geometry (A-polynomials). It has been established for most 2-bridge knots, but the subfamily of symmetric double twist knots K(p,p) remains unresolved.

The authors highlight this gap to motivate their triangulation-based approach to deformation varieties and A-polynomials for double twist knots.