DCRP50: Central-Response Affine NO-GO and the Three-Component Frontier

Building on DCRP49's central-response reduction c=B_q=1/2, and combining DCRP38's affine/non-affine strain-residual decomposition, DCRP41's fixed-plane zero-deformation tensor, and the affine pressure-response defect and vorticity-stress realizability frontier from X72 Round37 and 42–43, this round substitutes c=1/2 back into the flat scalar representation and proves that the mixed pressure Hessian ∇_hP_z automatically vanishes (two of the five mixed components of the X72 defect cancel identically), compressing the remaining defect exactly to three components. It further proves a central-rigidity theorem: a canonical affine pancake (S=A_pan) cannot coexist with nonzero planar vorticity — affine strain forces the vorticity to zero — constituting an explicit 'exact-affine NO-GO'. STOP-D50 establishes that this cofactor-invisible central response cannot realize a pointwise canonical affine pancake with nonzero vorticity: every active central survivor must carry non-affine strain, turnover/cancellation, a residual three-component pressure defect, or must solve the full nonlinear wave–pseudo-eikonal system, left to DCRP51 to analyze whether that system forces q to be affine.