BCT Appendix JH: The Hopfion Interior — Topology of the BCT Interior Condensate and the Octet-Hopfion Condensate

This appendix identifies the natural topology of the interior condensate Ψ₂ inside each BCT Planck-scale sphere. The unique topologically non-trivial ground state is a hopfion — a field configuration classified by the Hopf invariant H∈ℤ, the generator of π₃(S²)=ℤ. The ground-state configuration is named the Octet-Hopfion Condensate (OHC), reflecting the octahedral-tetrahedral BCT void geometry and the Hopf-fibration internal topology. Six results are established: (1) topological quantisation — discrete energy levels from integer Hopf winding; (2) half-integer spin from the SU(2)→SO(3) double cover; (3) each BCT sphere with OHC Hopf charge H=n corresponds to a Penrose twistor of helicity n/2; (4) three fermion…