The approximate uniform sampling conjecture for gaps in survival intervals

Let $p_k$ be a prime, let $\mathcal{G}(p_k^{\#})$ be the corresponding Eratosthenes-sieve cycle, and let $\Delta H(p_k)=[p_k^2,p_{k+1}^2]$ be its interval of survival. The population of a gap is its number of occurrences in the relevant interval or cycle. Approximate uniform sampling conjecture. For large enough primes, the populations of the gaps within $\Delta H(p_k)$ are approximately uniformly sampled from their populations in $\mathcal{G}(p_k^{\#})$. This narrower conjecture is presented as sufficient for the paper's estimates of surviving sieve gaps; no resolution is given in the source.