No one verifies. There is only a problem if someone challenges. Anyone can challenge, but it’s usually done only in vicious rivalries.
In Michigan they do verify the signatures. They did when I lived there back in the ‘80’s and apparently they still do. In 2012 a GOP candidate was kicked off the ballot for invalid signatures.
I don’t know what it is with New York....maybe you’re telling me.
Or the party has big plans for you. BO won his first election by getting his opponents knocked off the ballot for bogus registrations. Then he won his Senate seat by getting a crony judge to release the sealed divorce records of Jack Ryan