Endpoint collision budget from effective list density

Let $n>0$, $K,h,H\in\mathbb N$ and $d>0$. Each request $r$ has distinct prime endpoint labels $s_r,t_r\le H$ and a positive natural lower-cardinality bound $m_r$. Assume $H\le n$, $H^2\le n$, and $dn\le m_r a$ for each endpoint $a$ of $r$. If $N$ is the source's broad upper endpoint at $(n,K,h)$ and $P_N$ is its ordered-pair endpoint budget, then

This gives explicit disjoint-label and shared-label coefficients for collision control.