(と〜) thinking that […] (with the next clause explaining that the truth is contrary to expectations)

to seem, to appear

in my opinion; I think; I guess; upon thought; upon reflection; upon contemplation / conceivably; presumably

as one wishes, in a way that one wants

(as と思われ) (2channel slang) Synonym of と思う (to omou)

continuative of the passive of 思う (omou); continuative of 思われる (omowareru)

a public announcement

to announce publicly

Kyūjitai form of 口実 (“excuse, pretext”)

a higher dimension, a higher order / high level; meta- / (mathematics) higher order; higher degree