FAQ: Is the linking number (ΔLk) or the superhelical density (σ) that results from the DNA Gyrase (E.coli) (NEB #M7636) reaction fixed or random?

The resulting linking number is neither random nor fixed. There is a distribution of molecules of differing numbers of twists, based around a mean number. This value can vary based on factors, such as pH, temperature, ionic strength, sequence, length, cruciform formation, etc.