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

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 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 2–5% across the same neighbourhood before reopening at larger α. The bounce-fraction minimum and throat-width minimum are offset by Δα ≈ 0.002–0.004. The two throat-width curves remain closely matched, preserving the conjugate symmetry observed in the traffic law. The routing transition is consistent with a local accessibility mechanism: smooth modulation of bounce-corridor width at the relay exit reweights the routing traffic law without any visible critical-point or coarse basin-boundary catastrophe. Part of the Geometry of the Critical Line programme.