Concavity of the Back-Reaction Profile from the Israel Junction Conditions: Closure of Hypothesis Q2 and Problem PG

NT11 reduced problem PG to a single calculational question (Q2): whether the back-reaction profile f(y) of P8 satisfies f_pp(y_Rn) < 0. This note carries out the calculation. Using the bulk equation of motion for the warp factor perturbation in the Randall-Sundrum framework, we show that the Israel junction conditions at R_n directly imply f_pp(y_Rn) < 0 in the subcritical regime tau_Rn << tau_C0. Q2 is not an independent postulate: it follows from the Israel conditions already established in P8. Under this result, hypothesis S1 of NT9 is derived from Axiom A4 of P4 and the P8 junction conditions, and the Bridge 3 chain from k_1 < 0 to e > 0 closes from the existing corpus without new external inputs. Problem PG is conditionally closed within the subcritical regime.