What is the upper mass limit for a core remnant to form a stable neutron star?

Roughly 3 solar masses

The fate of the stellar remnant hinges critically on the mass remaining in the collapsed core immediately following the supernova explosion. If the leftover core mass surpasses the upper threshold, generally cited as being around 3 solar masses, the force of gravity becomes insurmountable. Nothing known within the framework of physics is capable of resisting this immense gravitational crush once this limit is breached. Consequently, the core continues its relentless collapse, leading not to a neutron star supported by internal pressure, but to the formation of a black hole. This demarcation point is crucial because it separates objects stabilized by quantum mechanical forces (neutron degeneracy pressure) from those that succumb entirely to gravitational collapse.