Stacked Proximate-Prime Quadratics and the Covering of Square Intervals

This is a continuation of Congruence Entropy and Prime-Rich Proximate-Prime Quadratics, which established that the prime density of a single proximate-prime polynomial (PPP) is governed almost entirely by its local congruence structure, summarized by the Bateman–Horn constant C_f (equivalently the congruence entropy E_f). Here we study the collective behavior of stacks of prime-rich monic PPPs under a covering objective: given the square intervals ("bands") B_k = [k², (k+1)²), how many curves must be stacked before the union of their prime values meets every band up to index M?