The SE group, Cognitive Science, keeps deleting my account on the basis of an invalid identity. Supposing science was evidence-based, I asked what proof I needed to provide to support my identity and they did not respond but re-deleted the account. What's a guy to do?
Your account was deleted since it was created with the intention of avoiding a suspension.
This means you have one of two options:
If you know you did something that deserved a suspension, don't try to pretend you didn't - just gracefully accept the consequences and learn from it. You absolutely will not win that battle.
If, on the other hand, you know you did not do anything that deserved a suspension, you should clearly and calmly describe your situation and present your case on the cogsci meta. Do not lie, however, as it will only hurt your case. The moderators are not stupid. Bear in mind that mods deal with things like this on an every-day basis and know how to recognize certain behavior patterns.
Based on your suspicious and weirdly insistent injections of "must be some kind of glitch" into your comments there, and your attitude (e.g. "supposing science was evidence-based") here, as well as your unnecessarily defensive comments to Jan above, it seems to me that you know what you did and are trying a bit too hard to hide it. Obviously I have no information on the topic, but it generally pays in the long run to be open-minded and honest, and accept consequences gracefully.
Suspensions are handed out to address serious issues. You will find them in Suspension Reasons.
What you can do:
Try to remedy the original reason for which your account was suspended.
Don't try to circumvent the suspension by creating alternate accounts.
Ask on Meta (which you have already done earlier and now).
Use the Contact Us link at the bottom of the Cogsci.SE page to contact the community team. Describe the details along with the context of the situation, so that they will review your case.
Moderators tend not to explicitly search for users avoiding suspensions by using sock puppets. Those get discovered if the sock draws moderator attention for some reason, often because the sock exhibits the same problematic behaviour as the original account. At this point the moderator might discover evidence that the new user is the same person as a suspended user, which leads to a much quicker and harsher reaction. But even if there isn't enough evidence that the new user is a sock, continuing with problematic behaviour will inevitably end in a suspension.
Socks of suspended users are discovered due to their bad behaviour most of the time, and only after they draw attention the moderators validate their suspicion with additional data.