New imaging research shows that brain activity differs in sleep-deprived and well-rested people. The study, in the May 21 issue of The Journal of Neuroscience, shows that individuals who are sleep-deprived experience periods of near-normal brain function, but these periods are interspersed with severe drops in attention and visual processing.

This seems a more plausible explanation than the typical "reduced cognitive ability" statement applied. I had sleep apnea for several years, undiagnosed, and did reasonably impressive cognitive things at the time. I guess I also had distraction or ambition trouble. Hyperconcentration, and then not so much. After treatment (CPAP, then surgery), cognitive function did not improve (not anywhere like my physical energy level did).