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 live regime, vanishing for tested k not divisible by 3 and remaining nonzero at multiples of 3. Third, graph-theoretic analysis of the thresholded transient graph reveals a nontrivial strongly connected core of period 3 with a perfect 3-class cyclic partition at every live alpha, shrinking and then disappearing at the routing floor. The note also documents key negative results: the phenomenon is not explained by local Jacobian structure, Lambert-branch angle geometry, naive path-length residue counts, or simple pocket-local support. The exact 120-degree phase alignment is fragile under random perturbation, while the three-fold multiplicity is robust under local ablation. The Newton-side structural mechanism is therefore resolved, while the corresponding SCT-side interpretation remains open.