We know that Dooku paid the Pyke syndicate to kill Sifo-Dyas sometime during the chancellorship of Finis Valorum. We know that because Valorum personally sent Sifo-Dyas to negotiate with the Pykes.
We also know that Darth Maul was bisected and went missing in last days of Valorum's rule, during the Naboo crisis.
Since Jedi do not kill fellow Jedi, this raises the question: did Dooku fall to the Dark Side and become the apprentice of Sidious before Maul was bisected?
P.S. In S06E10 of Clone Wars it is revealed that Dooku used his Sith name (Tyranus) to introduce himself to the Pyke syndicate when he contracted for the murder of Syfo-Dias. Since an apprentice usually gets his name from his master when he joins the Sith, this leaves even less chance that Dooku was not a Sith at that time.
To further complicate the matter, in Legends Sidious killed his master Plagueis on the night when he become chancellor, thus implying we had four Sith (instead of two) roaming about at some point in time.