"For accumulating 20 hours of held-breath underwater swimming within 3 weeks from start to finish– 10 or more points I.Q. gain; better span of attention; better span of awareness; better awareness of the interrelatedness of things and of ideas and/or perceptions; finding yourself way better at winning arguments or disputes!"
That's the kind of inference that allows these claims to proliferate.
This article makes a lot of claims about I.Q. scores before and after holding breath (specifically underwater, for some reason), but there are no links to studies, no mention of who or how many people participated, etc.
Not defending the overall claim, but there's a plausible reason why being underwater matters: the mammalian diving reflex. Holding your breath on land is not the same.
"For accumulating 20 hours of held-breath underwater swimming within 3 weeks from start to finish– 10 or more points I.Q. gain; better span of attention; better span of awareness; better awareness of the interrelatedness of things and of ideas and/or perceptions; finding yourself way better at winning arguments or disputes!"
It should go without saying this is nonsense.