Real-rootedness for the odd-entry 2-bridge-link family

Prove that the Q-polynomial of the 2-bridge link represented by a continued fraction with 2n+1 entries, all equal to 1, is r-stable for the relevant positive integers n, meaning that all of its nonzero zeros are real.

Background

The paper proves r-stability for the family of 2-bridge links K_n=[11⋯11] whose continued fraction has 2n entries, all equal to 1. The author then notes that the analogous family with 2n+1 entries equal to 1 has been checked for a few small values of n.

A complete proof for this odd-entry family is explicitly unavailable in the paper, leaving the extension of the established even-entry result as an unresolved problem.