Could a sufficiently massive Dyson Sphere under very specific conditions depend solely on electron degeneracy pressure for structural integrity?

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.

• A Dyson sphere is really a Dyson spherical shell, and I'm struggling to understand what you mean in the context of a hollow shell of material. – J. Murray Dec 15 '18 at 6:05
• Simplest explanation: Assume the Dyson sphere is of a size and material that allows it to exist without buckling before the last large piece is added. Its total mass exceeds the Chandrasekhar limit of 1.4 solar masses by a solid amount once the last piece is added. If one calculate the gravitational pressure the entire sphere has on itself, which can be done by seeing it as two half spheres and where they connect as a seam, would the pressure at the seam be able to exceed electron degeneracy pressure maximum and cause gravitational collapse from reaching the Chandrasekhar limit? – GHolven Dec 15 '18 at 6:26
• Again ... the Chandresekhar limit is derived under the assumption that the system is a homogeneous sphere. It's totally out of context to refer to it while discussing a hollow spherical shell. – J. Murray Dec 15 '18 at 6:34
• Assume my command of the language simply isn't good enough then. To put it extremely simply: If the material making up the Dyson Sphere was capable of having sufficient density, could it theoretically end up only staying up due to electron degeneracy pressure, and if so would having it pass a certain amount of mass theoretically have it collapse from exceeding the limits of EDP? I have been using the wrong terminology. – GHolven Dec 15 '18 at 7:23
• How does your Dyson sphere material achieve a density near that of white dwarf matter without the huge pressure that a white dwarf's gravity supplies? Why do you even want it to have such high density? – PM 2Ring Dec 15 '18 at 8:20