As far as most should be concerned, CSW is not satoshi.
If you want to be exact, CSW is almost certainly not satoshi. There is a chance CSW is a master troll, perhaps even a master baiter.
In a useful system of beliefs, we have reality and we have fiction: true and false. Something is true if it is not false, and vice versa. The determination of which category is defined purely by the rules of which the system operates, be they axioms or derived thereof.
To further designate truthfulness, there is a concept called 'burden of proof'. Some may choose to use the null hypothesis to exemplify a similar point.
We will begin with our baseline point:
P1 - An individual claiming that they are satoshi without evidence is not satoshi.
If P1 is not true, then any individual claiming they are satoshi is satoshi. This is an undesirable outcome, thus P1 is true. If you wish to continue with P1 as false, then allow me to offer an alternative to the next point: P2 - I am satoshi. This presents a burden of proof. After all, believing others' words as if they were reality would be a quick path to doom.
P2 - A message signed with satoshi's keys verifies ownership of the keys and satoshi's cryptographic identity.
P3 - Craig Steven Wright has not signed a message with any of satoshi's keys, Bitcoin-based or not.
P4 - Craig Steven Wright has faked a signed message, claiming to be satoshi.
P5 - Craig Steven Wright has not shifted the burden of proof and has insufficient evidence to prove ownership (partial or full) of the satoshi name.
I could go on but we already have 40 pages of the thread. Feel free to jam anything against P5. The other points are surely sound to even B:SV supporters.