Localized Exit-Pocket Z₃ Resonance and Its Collapse at the Routing Floor

Research Note 4 in the "Geometry of the Critical Line" programme. This research note documents a localized transient resonance in the Ulam-Galerkin spectrum of the Newton map associated with the Cover Function C_α(z) = z - exp(-α/z). In the pre-floor regime, the dominant nontrivial transient structure appears as a Z₃ triplet: three eigenvalues of equal magnitude with phases 0°, +120°, and -120°. Eigenvector extraction shows that all three modes localize in the same exit-neighbourhood pocket rather than across multiple spatial zones. Near the routing floor, the magnitude of this triplet collapses by roughly two orders of magnitude without spatial relocation. At α = 1.0, the dominant transient structure shifts to a different pocket in the deep relay and exhibits Z₂ rather than Z₃ symmetry. The note also records three falsified mechanisms. First, relative to the one-step corridor split at Im(u) = 0, the off-diagonal norm of Q_α is zero for all sampled real α values, so cross-corridor leakage is not the relevant observable in the real-α regime. Second, no period-3 orbit was found in the 200×200 upper-half-plane search at α = 0.42, and the only refined candidate at α = 0.52 has multiplier scale incompatible with the observed |λ₃|. Third, the data do not support a three-zone transport-cycle interpretation: the triplet modes share the same spatial support rather than occupying separate radial bands. This note is an empirical checkpoint within the Newton transport arc. It does not claim a microscopic mechanism for the Z₃ phase structure, a connection to the SCT spectral factorization or Bridge 3, an explanation of the partial recovery at α = 0.52, or resolution independence beyond the tested construction. The λ₁ = λ₂ = 1 contamination persists in the current Ulam-Galerkin operator, so the analysis is carried out on λ₃ onward as the operative transient diagnostic.