DCRP48: Pressure-Driven Response Slope and Mixed-Hessian Telescoping

Building on the response slope c=B_q that DCRP47 derived from the constitutive relation w=B(q,s)-2a(s)z, together with its divergence equation and the [0,1] response window, this round first corrects it. It proves that DCRP47's current J_c is actually ∂_z(∇·V)=0 — merely a differentiated restatement of the constitutive relation under incompressibility, not an independent equation. The genuinely new dynamics comes from the vertical self-similar Euler momentum equation D_sc=-P_{zq}: the mixed pressure Hessian must be parallel to ∇_hq and is the sole driver of response-slope evolution. This yields a pressure-Poisson source identity, and shows that a zero mixed-pressure offset, together with DSS scaling and q=0 continuity, forces the response slope to be constant. STOP-D48 establishes that the response window is governed not by an independent compatibility equation but by the pressure Hessian: leaving [0,1] requires a finite pressure-Neumann flux, while staying inside it requires obeying a bounded telescoping budget, left to DCRP49 to compare this pressure-Neumann gap against DCRP31's PFET gap on the same annulus.