What critical threshold must be reached for a collapsing cloud to initiate sustained stellar furnace activity?

The core temperature must become high enough to initiate thermonuclear reactions

A body collapsing purely under gravity, such as a brown dwarf, can achieve significant heat and density, but it cannot become a true star capable of sustained shining unless it crosses a specific physics threshold. This crucial threshold involves reaching an extreme core temperature and pressure sufficient to overcome the electrostatic repulsion between atomic nuclei. Only when this ignition point is met do thermonuclear reactions commence, converting matter into energy and establishing the perpetual energy source that defines a main-sequence star. Objects failing to reach this ignition point remain merely pre-main-sequence objects.