The Fourth Regime: Bounce De-Activation at Large α in the Cathedral Pullback

Paper 27 in the "Geometry of the Critical Line" programme. Papers 21–26 established a localised routing transition near α ≈ 0.48 in the Newton dynamics of C_α(z) = z − exp(−α/z), with a fixed symbolic scaffold, a relay-row traffic-law redistribution, and a local corridor-accessibility mechanism. This paper extends the parameter sweep to α ∈ [0.40, 2.00] to determine whether the post-transition increase in bounce traffic persists indefinitely. It does not. The relay-row bounce exit probability P_{C,bounce}, relay-row entropy H_C, and routing ratio R(α) all rise sharply after the routing floor, reach their maxima near α ≈ 0.58–0.60, and then decline at larger α. Meanwhile, the coarse basin scaffold remains fixed…