Conjugation Equivariance and Transport Parity in the Newton Dynamics of C_α(z)

Paper 33 in the "Geometry of the Critical Line" programme. The Newton transport arc (Papers 20–32) established the exact empirical equality P_{C,-1} = P_{C,0} — equal bounce traffic through conjugate corridors — at every tested α, to machine precision. This paper derives the transport parity as a theorem. For real α, the Cover Function C_α(z) = z − exp(−α/z) is equivariant under complex conjugation: C_α(z̄) = C̄_α(z). The Newton map inherits this equivariance, which exchanges the basins of z_k and z_{-(k+1)}. Any conjugation-symmetric initial measure therefore produces equal bounce probabilities through conjugate corridor pairs. A precise structural correspondence with the SCT geometric framework (Papers 0–10)…