DCRP49: PFET–Neumann Independence and Off-Central Rigidity

Building on the two pressure observables DCRP48 left behind — DCRP31's PFET and DCRP48's pressure-Neumann/mixed-Hessian response — and formally connecting for the first time to the cofactor/pressure-response coherence and vorticity-stress realizability frontier of X72 Round36, 37, and 41–43, this round tests whether the two pressure channels obey a universal algebraic coupling. The exact affine Euler solution u=S_0x, p=-½x^TS_0^2x serves as an explicit counterexample: its PFET current is identically zero while its pressure-Neumann flux is strictly positive, so no universal coupling theorem holds. Instead, combining DCRP48 with the X72 affine pressure-response defect E_p=H_P^0+C_S^0 yields an off-central pancake vorticity-density law whose damping coefficient agrees exactly with DCRP35, and shows that removing both replenishment sources simultaneously forces the response slope to equal exactly c=1/2. STOP-D49 establishes that off-central response cannot be sustained for free — it must be replenished either by inward turnover or by the X72 mixed-affine pressure defect — and when both are absent, the only survivor is the invisible central slope c=1/2, left to DCRP50 to substitute this value and test its compatibility with DCRP35, DCRP31, and X72 vorticity-stress realizability.