Per my knowledge and learning, I would say that the inner core is solid. This was so because of the high temperature (magma) that cycles around it causing different kinds of metals to compress as one. Also, it should be a solid in order to maintain the balance of the Earth. I think, the heaviness of the inner core of the Earth is well-proportioned to that of the moon's heaviness that is why we experienced perfect gravity.
The inner core is made up of solid materials,iron in particular
the mass of the ather layers keep it in its phase