For theta>0, give a tuple weight exp(-theta times its weighted degree). Every tuple of weighted degree below p_t has weight at least exp(-theta p_t). Summing over nonnegative exponents gives the product over modes of 1/(1-exp(-theta w_Z)). Since each weight occurs at most 6M/D times, the logarithm of the tuple count is at most theta p_t+(6M/D) S, where S=sum_{j>=1} -ln(1-exp(-theta j)). The log-series identity -ln(1-z)=sum_{h>=1} z^h/h gives S=sum_{h>=1} 1/(h(exp(theta h)-1)). Using exp(x)-1>=x for positive x gives S<=sum_{h>=1} 1/h^2 divided by theta. That square-reciprocal sum is at most two: for h>=2, use 1/h^2<=1/(h-1)-1/h and telescope. Nonnegative terms justify the rearrangement.