sphereComponent

This module builds the algebraic bridge from a compact 3D cubical region's Betti triple $(b_0,b_1,b_2)$ to the genus of its regular-neighborhood boundary. After Phase 25 found nonmanifold edges on the raw cubical surface, Phase 26 switched to the desingularized readout: the boundary of a regular neighborhood of ${q>0}$.

A corrected boundary component is one connected piece of that boundary after edge pairing and local vertex-link collapse. The carrier records only an integer Euler characteristic. Classically a 2-sphere has $\chi=2$, so the sphere component is the corresponding constant on that carrier.

The module status is partial through Phase 44 and conditional at Phase 47: arithmetic and numeric certificates are proved; the embedded digital-cubical collapse and homeomorphism to the geometric regular-neighborhood boundary remain open.

One-line definition: inhabit the corrected-component structure by setting the Euler field to the integer 2. No lemmas or tactics.

Supplies the spherical summands in the Phase-34 corrected component assemblies. Downstream, the horizon-annulus handle list is one torus plus one sphere, and the dyadic-sponge list is one genus-125 component plus 52 spheres. Those lists feed the algebraic half of the component-assembly bridge: with canonical component count and Euler half-sum, total genus is forced to $b_1$.

That bridge is what the cosmogenesis foam-interface desingularized script consumes. It does not close the geometric realization or homeomorphism theorems still marked open in the module doc; it only pins the Euler data of spherical pieces in the combinatorial certificates.