The mechanical layer of the Earth that is solid rock and moves least is the inner core.

Here's why:

* Solid Rock: The inner core is primarily made of iron and nickel, which are in a solid state due to immense pressure.

* Least Movement: While the inner core does have some movement due to the Earth's rotation, it is significantly less mobile than the outer core and the mantle. The inner core's movement is primarily a slow rotation, not the convection currents that drive plate tectonics in the mantle.

Let me know if you have any other questions!