Explicit Z9 Tessellation of the Bifurcation Two-Sphere in the PTRH Framework: Sector Decomposition, Equivariance, and Closure of Gap G1
Abstract
Closes Gap G1 of PTRH Paper 11 by constructing the explicit Z9-equivariant tessellation of the bifurcation two-sphere Sigma cong S^2. Three results are established at [V]: (1) the Z9-invariant prismatic metric induces a Z9 isometry of Sigma by rotation by 2pi/9; (2) nine wedge domains D_n tile S^2 with covering, disjointness, equivariance, and equal area 4pi/9; (3) the F-crystal eigenspace M_n is paired with D_n via torsion-phase matching, yielding a Z9-equivariant bijection. Gap G1 is upgraded from [O] to [V].
Fields of Study & Subjects
Nonlinear Waves and Solitons
Black Holes and Theoretical Physics
High-pressure geophysics and materials
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 23 May 2026
- Document type
- Preprint