This proof aims to generalize the concept past just the 1 & 2 manifold cases. It's not super-gigantic, but it does generalize and does add (some) rigour that was absent in previous papers.
One of the ideas I'm still sort of struggling with is whether or not I can call the resultant manifolds as manifolds, considering the fact that the n-Super Sphere isn't technically, itself, a manifold if we're taking all of the components to be extant at the same time. This is to say: If components Ci, Sq', and As (for example) all exist as part of the same structure, it's not technically a manifold. But each individual component (for example As) is a manifold, and (again, for example) {As\{CP_{As}}} union {CP_{ci}} should also be a manifold.
Anyway, here's the proof (or, at least, the attempt at a proof).