Measure-Weighted Decomposition at the Relay Exit: Orbit Redistribution and Corridor Geometry in 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 29 in the "Geometry of the Critical Line" programme. The Jacobian of the Newton map at the relay exit is uniformly expanding and perfectly conformal, with condition number 1.00 across all alpha values, which rules out a local derivative-level mechanism for the routing transition in the map C-alpha of z equals z minus exp of negative alpha over z. This paper treats the relay exit, defined by real part of u equal to 1.5, as a measured Poincaré-style section, records the first outward crossing of each convergent orbit, and decomposes the bounce overlap into orbit-measure and corridor-geometry contributions using frozen-reference controls. The result is a mixed mechanism: both orbit redistribution and corridor-geometry shift contribute, and neither one alone reproduces the full transition. A reference-sensitivity analysis using reference alpha values 0.42, 0.481, 0.50, and 0.60 confirms that orbit-measure redistribution is the stronger contributor at every reference tested, although the absolute explanatory power remains limited in the core transition neighborhood. The routing transition is therefore best understood as a spread-overlap phenomenon at the relay exit within a uniformly expanding, conformal field.