Limiting random SAT thresholds, sharp variance and computability

For random k-SAT with independent uniformly signed proper clauses sampled with replacement, proves finite positive limiting thresholds and hitting-time variance $\Theta_k(n)$ for every fixed k ≥ 3, and computability of the 3-SAT threshold. We credit Gaia Carenini with priority for resolving the threshold-existence conjecture in her concurrent [ECCC TR26-229](https://eccc.weizmann.ac.il/report/2026/229/), made public October 5, 2026; this family supplies another proof and the sharper variance and computability results.