Relay-Exit Throat Width and Local Corridor Accessibility Across the Routing Transition

Paper 26 in the "Geometry of the Critical Line" programme. Papers 22–25 localised a routing transition near α ≈ 0.48 in the Newton dynamics of C_α(z) = z − exp(−α/z), but the geometric mechanism remained unresolved. This paper tests whether the transition is accompanied by a coarse geometric event or by a more localised change in escape-channel accessibility. A whole-window audit finds no critical-point event, no significant motion of the nearest critical point toward the relay boundary, and no visible basin-boundary catastrophe. Along fixed relay-exit transects in u-space, the bounce fraction reaches a local minimum near the routing floor, and the k=0 and k=−1 corridor throat widths narrow by approximately…