The Plate–Projection Boundary in Newton–SCT Dynamics

Boundary reference notice (22 September 2026). This record is linked as boundary context for Paper A12, Dynamics of the Lambert W Newton Iteration: Basin Geometry, Routing Transitions, and Finite-Rank Period-Three Resonance (DOI: 10.5281/zenodo.21845665). Its allocation to A12 is limited to the boundary note described in the publication plan. This link does not declare this record superseded and does not extend A12 beyond its stated Newton-dynamics and finite-matrix scope. The original description below and deposited files are retained. Paper 35 in the "Geometry of the Critical Line" programme. The Cover Function C_α(z) = z − exp(−α/z) generates two mathematical arcs: an SCT geometric arc (Papers 0–10) and a Newton transport arc (Papers 20–34). This paper determines the boundary between shared structure and side-specific structure across these arcs. Three correspondences are proved from existing results: the arcs share a Level 1 constraint type (Theorem A, citing Paper 33) and a Level 2 decoupling type (Theorem B, citing Paper 34). The Newton side admits a Level 3 period-3 transport skeleton (Theorem C, citing RN6). A new proposition proves the separated σ-equation route to an SCT Level 3 skeleton is algebraically obstructed; five further critical-slice constructions are tested and all fail. Bridge 4 (lobe spacing) is reclassified: simple Lambert-root geometry is monotone in α and cannot generate the non-monotone spacing lifecycle, which is projection-born. The principal result is a three-layer classification, earned by the cumulative positive and negative evidence: a shared plate layer (Cover Function, Bridges 1–2), a partially shared reduction layer (typed cascades, Theorems A–C), and a side-specific projection layer (Newton Z₃, lobe spacing) that is not directly bridgeable. Forty-two falsified hypotheses constitute the evidence base.