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…