The backward headline: X ≃ₜ S² ⇒ genus X = 0 (CC-sphere-topology, design §4)

Unit: sphere-topology (docs/design/sphere-topology.md §4). Assembles the topological fact (SimplyConnectedP1.lean: any space homeomorphic to OnePoint ℂ, in particular to the challenge sphere, is simply connected) with the analytic fact (GlobalPrimitive.lean: a simply connected compact Riemann surface has genus 0) into the exact backward-headline signature consumed by genus-zero-headline.

Main declaration: RS.SphereTopology.genus_eq_zero_of_homeo_sphere.

theorem RS.SphereTopology.genus_eq_zero_of_homeo_sphere {X : Type u_1} [TopologicalSpace X] [T2Space X] [CompactSpace X] [ConnectedSpace X] [ChartedSpace ℂ X] [IsManifold (modelWithCornersSelf ℂ ℂ) ⊤ X] (h : Nonempty (X ≃ₜ ↑(Metric.sphere 0 1))) : genus X = 0

The backward headline half (consumed by genus-zero-headline alongside Riemann–Roch's forward half). Only X's TOPOLOGY is used to get SimplyConnectedSpace X; genus X = 0 then uses X's OWN complex structure via GlobalPrimitive.lean — consistent, since Form1 X/ genus X are defined from X's own atlas, not from the sphere's.