@Corvo My point is that you can't have been a Gen-three synth Pre-war. Which kind of screws with the whole implanted memories thing considering the Vault-tec rep remembers you post-war.

Personally i dont think your a synth, since not only you have clear memories of before the war, being a solider in the army, or being a lawyer, and the robots over in that one navel ship quest recognize you and say that you where apart of the army at one point.
And on top of that you see your wife or husband in the cryo pod and also see Shawn being kidnapped with Shawn having very vivid memories about that day if you bring that up to him, so they either put up a lot of trouble not only putting you in that cryo pod, but also making a fake baby a fake wife and a whole elaborate plan to making you think the institute took your child but if Shawn wanted you to become his replacement then why ? but ill get back to that, and also would you think Kellogg would have it somewhere in his memory banks of a plan of putting a synth in one of the cryo-pods and setting up a huge act on making him or her think that there son was kidnapped and there significant other being shot But that doesn't show when you get inside his brain and if so for what ? and going back to the replacement thing, why dont Shawn just make you the perfect replacement without any other outside influences judging your actions before meeting him? that doesnt make any sense m'kay
And why would Shawn give you the opportunity to take control of the institute when he says that the current model of synths are very unstable and is still being tested, so i dont think the SS is a synth but i do like how that quest brings up the thought that you might be, cant really disprove nore prove it since you cannot loot your dead body.

I dont think the player character is a snyth, as Proudnoob said, you have clear memories before the war and robots recognise you. I think in the DLC, they are just messing with a game mechanic of the player makes the character and doesnt know too much about them

Philosophically, the existence of the external objects cannot be proven. Think about it, without eyes, can you prove to yourself that a beacon locates hundred meters away from your original eye sight. Iphone for a blind man is a music player and a normal phone(not the graphical smartphone). For a deaf man, Iphone is not a phone because you can't hear the voice from the otherside. Without all the senses of perception, we cannot perceive anything thus no existence can be proven. The existence of the external object was built upon your sense.

...enter the matrix

If one is synth...all are synth; the difference is some are aware that they are synth, while others cling to the notion that they are not...neither of which matters because the scenario of bombs falling never happened...all of humanity is living their life as a coppertop battery while their mind is occupied inside a convincing scenario of being a savior to a barren wasteland in boston. Why else is it possible to die and reload or choose different diffculties when you create a new "life"...oh shit is it possible that I'm a battery and Fallout is the simulation...Wait the fuck a second where is the guy asking if i want the blue pill?

No.... I don't think the main character is a synth, why would father wan't to replace his own father/mother? Also, the main character remembers the Silver Shroud in the Silver Shroud quest, and if I remember correctly some other things.
Another thing is Synths don't need the basic human needs like food and water, so survival mode sorta proves that the SS isn't a synth.

The FO4 protag is definetly human. Thats all there is to say.