This preprint studies the Rice-Mele chain at golden-ratio dimerization v/w = 1/phi. The specialization induces the Legendre parameter n = 4 phi^-3and gives the exact modular invariant j = 78608. The lower-band Zak phase is reduced to complete elliptic integrals and shown to be strictlymonotone in the staggered potential Delta, yielding a unique positive point DeltaR where the Zak phase equals the Mocanu-Rogers target 2 pi RM. The target phase is also rewritten using the Dirichlet L-value L (chi₅, 1) of Q (sqrt (5) ).
Sorin G. Mocanu (Mon,) studied this question.