The Transverse Decoupling Correspondence: Real Coefficients, Seven Failed Coordinate Maps, and the Algebraic Backbone of Bridge 2

Paper 34 in the "Geometry of the Critical Line" programme. Paper 33 proved that the transport parity P_C,-(k+1) = P_C,k follows from conjugation equivariance of the Cover Function C_α(z) = z - e^(-α/z) for real α. Research Note 3 proved that the transverse velocity V_y = Im(Φ’_α(u)) at any vertical section in u-space is α-independent. Paper 5 proved that the derivative coupling coefficient A(σ) in the separated σ-equation on M^5_SCT vanishes if and only if σ = 1/2. This paper identifies a precise structural correspondence between the Newton-side and SCT-side decoupling results. Both are consistent with a shared algebraic backbone: the cover constraint Φ + e^(iπ - α/Φ) = 0 reduces via Euler’s identity e^(iπ) =…