PNT-normalized port envelope controlled by the logarithmic gap

Let $M$ be a regular relative mesh with $\delta>0$, $n>1$, nonzero cutoff $W$, and scale separation, so its canonical prime partition is defined. Fix a ratio $\rho>1$. Assume further $W\ge2$ and that $W$ exceeds the uniform reciprocal-prime-sum cutoff. Let $s\ge0$ and let $p$ be a canonical tangent prime. Write $A$ for the current ratio-cell lower endpoint, $Y$ for its exponent-band upper endpoint, $N_p(s)$ for the source port numerator envelope, and $C_M$ for the uniform reciprocal-sum constant. Let $D_p$ be the source PNT denominator for the current cell, and let $\ell(p)$ be its natural prime label. Then

This is the normalized pointwise traffic estimate used in distributed tangent budgets.