The document discusses Boolean satisfiability (SAT) problems and whether they exhibit genuine phase transitions. It summarizes that while 2-SAT has a proven discontinuous phase transition, the conjectured transition for 3-SAT at α ≈ 4.2 has not been proven. A toy model is presented showing that 3-SAT may not display a real phase transition but only a threshold phenomenon induced by statistics. The model supports investigating quantitative parameters like number of solutions instead of just existence of a solution. The document questions whether k-SAT problems truly exhibit phase transitions or if usage of the term needs clarification.