Random 3-SAT: What is the consensus experimental range of the threshold? The critical ratio of clauses to variables for random 3-SAT is more than 3 and less than 6, and seems to be commonly described as "around 4.2" or "around 4.25".  Mezard, Parisi, and Zecchina prove (in the physics sense) that the critical ratio is 4.256, whereas the first and third authors prove that it is 4.267.

What is the range of values that the critical ratio could possibly take?


The motivation for me asking this question is that if the ratio could be $2+\sqrt{5} \approx 4.236$, then the standard reduction of 3-SAT to NAE-3-SAT (transforming $m$ clauses and $n$ variables into $2m$ clauses and $m+n+1$ variables) gives a ratio of $\phi$, which seems unlikely but would be pretty cool.
In light of the Ding--Sly--Sun verification of the 1-step Replica Symmetry Breaking picture for kSAT (when k is large enough) I think experts would now be pretty surprised if the MPZ/MMZ-conjectured formula for the 3SAT satisfiability threshold (approximate value: 4.2667) is incorrect.