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

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…