DCRP43: Poincaré Scalar Transfer and Material Nonrecurrence

Building on DCRP42's canonical rank-two pancake branch G=0 and its scalar transport equation, and heeding DCRP32→34's warning that the raw self-similar-coordinate blow-up factor can be absorbed by same-parent re-root rescaling, this round avoids prematurely declaring a contradiction. It proves the exact one-period Poincaré flow-map transfer law, an existence theorem for a finite positive-scalar-weighted material turnover carrier, and a pointwise nonrecurrence theorem for nonzero scalar material labels under the Euler periodic gauge, establishing that Euler identity and material identity are distinct. The conclusion states explicitly that this is not a claim of physical contradiction; whether it amounts to a genuine same-parent obstruction is left to the next round's quotient-correct re-root-rescaling audit of q, r, ∇_hq, and |r|^p dy.