Regularity of Interspherical Central Projection: Formulation without Tangent Hyperplanes and Degeneracy at R=0

This paper proves that central projection defined directly between surfaces of concentric hyperspherical shells possesses none of the pathological properties of classical gnomonic projection via tangent hyperplanes. Specifically: (1) the interspherical map is a diffeomorphism for all R,R>0, regular and non-divergent over the full sphere (Theorem 1); (2) forward projection to R=0 is well-defined and smooth with no divergence — the only limitation is that the Jacobian degenerates to zero, making the inverse map undefined (Theorem 2); (3) the tan-theta divergence at the equator in gnomonic projection is intrinsic to the use of tangent hyperplanes and structurally absent from interspherical projection (Theorem 3). As a corollary, the R>0 constraint in the three-layer model [M1] is unnecessary; all claims hold for R>=0.