A Period-3 Transient Core in the Newton Transfer Operator of C_alpha(z) = z - exp(-alpha/z)

Research Note 6 in the "Geometry of the Critical Line" programme. This note reports the structural identification of the transient mechanism underlying the Newton-side Z3 phenomenon observed in the Ulam-Galerkin transfer operator for the Newton map of the Cover Function C_alpha(z) = z - exp(-alpha/z). Using the absorbing Markov chain partition Q = [T R; 0 I], the note shows that the relevant eigenvalues live in the transient block T, not in the absorbing pocket where the leading eigenvector concentrates. Three main results are established. First, the transient block contains a tower of coupled Z3 triplets across the live stagnation band. Second, the trace sequence Tr(T^k) exhibits an exact mod-3 pulsar in the…