Just adding a couple corrections:

> which sets a lower limit of about eight times the mass of the Sun.

While this is the lower limit for how massive a star must be to undergo a core collapse supernova, the remnant left behind is not the same mass as the entire star, but closer to the mass of the iron core, as the outer layers get ejected in the supernova explosion! Successful core collapse supernovae can explode and leave behind a ~1.4 solar mass neutron star. If the explosion is asymmetric, some of the mass can remain bound to the neutron star and fall back onto it. If enough fall back accretes, the neutron star will no longer have enough pressure support to be able to resist collapse into a black hole. Otherwise, sometimes the supernova fails, leading to direct collapse. With these two routes combined, core collapse supernova potentially make black holes 2 - 100 solar masses.

> the only confirmed mechanism for the creation of the black hole is the collapse of a massive star

Additionally, I think it's safe to say core collapse is not the only confirmed mechanism of black hole formation. There are two other generally accepted black hole formation routes, although they are much less frequent: Accretion induced collapse and neutron star mergers.

In x-ray binaries, material from a non-compact star can accrete onto a neutron star and cause accretion induced collapse, much like the fall back mechanism.

Additionally, neutron star mergers can create black holes of ~2 to 4 solar masses, if the combined remnant from the two of them exceeds the maximum mass of a neutron star.