Cultural hearth is the origin of a particular cultural trait. And it is also the area from which the culture of a group diffused. An example would be South Asia and northern Andes being the hearths of agriculture based on vegeatative propagation.
A cultural hearth is a place where a culture is born. There are seven primary culture hearths: Nile Valley Indus Valley Wei-Huang Valley Ganges Valley Mesopotamia Mesoamerica West Africa Andean America All of these places contributed to cultures which included martial arts of one form or another.