Regular Minimal Spheres in Two-Time Spherically Symmetric Vacuum Spacetimes: Local Initial-Data Classification of Throats and Null Screen Optics

Unreviewed preprint. The primary manuscript is in English. A corresponding Japanese companion with the same version number, theorem numbering, equation numbering, and references is included. Manuscript version v0.13, dated 8 October 2026.We study static diagonal Ricci-flat metrics with p time directions and spherical dimension q greater than one. We prove a necessary and sufficient local initial-data condition for a regular nondegenerate minimal sphere, including propagation of the vacuum constraint. Within this ansatz, one time warp factor does not allow such a sphere, whereas two or more allow local solutions. For p=2 and q=3, all throat initial data are matched to a branch of the known multitemporal Tangherlini family. The curvature singularity and finite proper distance to the singular end are established results; we connect them to the initial-data classification and check the finite radial null affine length. For p=2 and arbitrary q greater than one, the throat constraint implies that the corresponding sphere is nonstationary in the dimensionally reduced Einstein frame, making its consistency with known no-go results explicit. We also compute the optical tensor of affine radial null congruences. The screen has one timelike direction, and spherical area flare-out coexists with a decreasing full-screen expansion under the vacuum Raychaudhuri equation. Our contribution is restricted to the explicit initial-data classification, its correspondence with known solutions, and the optical and conformal-frame comparisons. We do not claim a new exact solution or a regular two-ended traversable wormhole.This manuscript concerns a specified static, diagonal, spherically symmetric vacuum ansatz. It does not establish the empirical validity of a general six-dimensional bulk theory. Detailed prior-art comparison and extensions beyond the proved parameter ranges remain open, as stated in the manuscript.