lukeprog linked above the Hsu paper that documents good correlation between different narrow human intelligence measurements. The author concludes that a general g factor is sufficient.

All humans have more or less the same cognitive hardware. The human brain is prestructured that specific areas normally have assigned specific functionality. In case of a lesion other parts of the brain can take over. If a brain is especially capable this covers all cranial regions. A single dimension measure for humans might suffice.

If a CPU has a higher clock frequency rating than another CPU of the identical series: the clock factor is the speedup factor for any CPU-centric algorithm.

An AI with NN pattern matching architecture will be similar slow and unreliable in mental arithmetics like us humans. Extend its architecture with a floating point coprocessor and its arithmetic capabilities will rise by magnitudes.

If you challenge an AI that is superintelligent in engineering but has low performance regarding this challenging requirement it will design a coprocessor for this task. Such coprocessors exist already: FPGA. Programming is highly complex but speedups of magnitudes reward all efforts. Once a coprocessor hardware configuration is in the world it can be shared and further improved by other engineering AIs.

To monitor AI intelligence development of extremly heterogeneous and dynamic architectures we need high dimensional intelligence metrics.