Sorry, but it is fine and correct as I read it.
About the closest any research has come to supporting [this theory]
= the research that is closest to supporting [this theory]
= research has noit confirmed [this theory], but the one about to be mentioned is closest to doing so
[the tiredness theory]
is
[the research does this]
"about the closest to" a cupcake is a muffin
these things are similar and one is the most similar of all things considered
to confirm
[that research confirms]
that adults yawn more often on weekdays than at weekends,
and [also confirms] that school children yawn more frequently in their first year at primary school than they do in kindergarten.
Any help?
NTN: no thanks necessary, but more comment/questions, ok.