this "the idea of triangles would still exist" statement looks very reasonable, but can we ever proove it? you can not remove ALL consciousness to verify. at least a bit consciousness must be in the system to do the experiment.
yes, it very much coincides with all of our understanding of reality, that abstract ideas like triangluarity is independent from any consciousness. at least any consciousness known or conceivable to us so far.
so my extension to this statement would be - admittedly supernaturally-sounding - that: Even if all sentient life in the universe died out tomorrow, the idea of triangles (and "triangluarity") would still exist, possibly because there is a consciousness above/beyond of the conceivable the universe to sustain their existence.
If so, then consciousness doesn't need to exist for information structures to exist.
"Within consciousness" doesn't belong here. Even if all sentient life in the universe died out tomorrow, the idea of triangles (and "triangluarity") would still exist.