The six active sectors of \(M_\infty\), the particles that live in each, and the inactive band that the chain skips. Click a sector — in the panel or the scene.
Each sector is an infinite, flat, macroscopic space; the geometry label (\(\mathbb{CP}^1\), \(S^3\), …) names the local symmetry of that sector's potential minimum, not a compact shape. The tower orders them by sector dimension \(d\). The greyed rungs are \(d=7,8,9\) — supercritical but unreached by the coupling chain, so no active geometry forms there.