Stuck in an argument. I claim this is theoretically possible:
Provided you could build a type 1 Dyson Sphere, made from a supposed material that rivals the structural integrity of a white dwarf, i.e. is close to or bordering that of electron degeneracy pressure, used enough of it for the Dyson Sphere to have a mass massively exceeding the maximum amount of a white dwarf, 1.4+ solar masses the moment the last element was put in place, would the pressure as calculated between two halves of the sphere be able to reach and breach electron degeneracy pressure maximum at the seams?
EDIT, 2nd ed: Basically, could a theoretical object, made from a supposed as yet not invented exotic matter material (not degenerate matter per se, but close to the brink), not being a white dwarf, under given circumstances manage to only be held up by electron degeneracy pressure? And if so would adding mass cause it to collapse?
I understand that degenerate matter itself would never be available in that manner, hence "under very specific conditions."
Yes, I know this is asking you to put aside some normal rules of physics; in asking you to accept a material that does not currently exist, and realize that I perhaps overstep the rules of this page, but I don't know who else I could ask.
Also great thanks to those who have commented and answered thus far. You have all been great help.