Relay-Bounce Routing Transition in the Cathedral Pullback Near α ≈ 0.48

Scoped supersession notice (22 September 2026). This record is part of the source research consolidated in Paper A12, Dynamics of the Lambert W Newton Iteration: Basin Geometry, Routing Transitions, and Finite-Rank Period-Three Resonance (DOI: 10.5281/zenodo.21845665). For the Newton-dynamics, routing, conjugation-parity, and finite-rank period-three results stated in that article, it supersedes the corresponding earlier programme presentation and is the current consolidated reference. Supersession is limited to that scope; other results, programme interpretations, and open problems in this record are not thereby replaced or resolved. In particular, the finite-matrix results do not assert a continuum resonance. The original description below and deposited files are retained for provenance. Paper 23 in the "Geometry of the Critical Line" programme. This paper reports a fine-scale α-sweep (55 values, Δα ≈ 0.0012) of the Cathedral window in the inverted Newton dynamics of C_α(z) = z − exp(−α/z). Near α ≈ 0.48, the data reveal a localized routing transition in the relay junction. Below α ≈ 0.481, hesitation orbits are concentrated on simple direct-convergence paths. Above this value, dynamical traffic is rapidly reweighted into pre-existing relay-bounce channels, with the dominant bounce word (C,−1,C) nearly tripling over Δα ≈ 0.02. The transition is a redistribution over an existing symbolic scaffold, not the birth of new orbit families. The result is robust under variation of the slow-orbit threshold, relay cutoff, symbolic coding scheme, and iteration cap (500 vs 2000). Part of the Geometry of the Critical Line programme.