No, Daniel is not on the SSDI. But the son by 2nd wife appears to be. Only... SSDI birth year and census birth year are not perfectly aligned. And please forgive me, but I am less concerned at the moment with proving the Gibbs line than I am with finding and verifying male Abernathys for our DNA surname project.
I would naturally accept whatever information you have on Daniel's Abernathy children, of course.But the V in Josie's name may (or may not) have stood for Velma: Daniel Alexander Abernathy's younger brother Charles Oscar Abernathy had a daughter named Velma on the 1920 & 1930 Jackson County OK census, who may have been named after her. So portions of this Abernathy branch did continue at least until the 30's. Beyond that, I don't know. Yet.