The equality case for the improved positive-writhe inequality

Let the assumptions of Lemma~(c) hold, and consider the inequality in Remark~. Equality conjecture. Under these assumptions, the inequality is an equality. This proposed equality would provide the formula for $w_\tau(\zeta_2)$ needed to rule out more generally sequences of cylinders converging to buildings as in case (iii) of Proposition~(c) with arbitrary $d_2$.