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Gaps between clusters of semiprimes shrink unconditionally to $\exp((\pi+\varepsilon)\sqrt{\rho})$ via an exact variational solution to Sono's sieve.
Neither $p-1$ nor $p+1$ dominates the other's largest prime factor: both $P^+(p+1) > P^+(p-1)$ and its reverse hold unconditionally for a positive proportion of primes.