Losing heat by radiation since millions of years ago, can the mantle be just that, cooled slag on top of a molten core ?

Define what you mean be 'slag'.  Is cooled lava 'slag'?  Is granite slag?  Is basalt slag?

45 minutes ago, Externet said:

Losing heat by radiation since millions of years ago, can the mantle be just that, cooled slag on top of a molten core ?

It is not clear to me what you mean by "slag". How does calling it that add to understanding?

Slag is extraneous material, separated from the desired metal in the process of ore smelting, which is a chemical reduction, generally from oxides. So far as I know, it is not thought that a chemical reduction from oxides is how the metallic core of the Earth came to form. The evidence from meteorites seems to me to suggest that iron and nickel exist in space debris already in elemental form.

Edited September 13, 20214 yr by exchemist

51 minutes ago, Externet said:

Losing heat by radiation since millions of years ago, can the mantle be just that, cooled slag on top of a molten core ?

If you're asking if the earth was to a large degree molten in its remote past, and the crust solidified as it cooled, the answer is yes.

https://en.wikipedia.org/wiki/History_of_Earth