This supplement develops the mathematical foundations of the exterior geometry introduced in Volume XXXVI of the R-layer Mode Theory (RLMT). The exterior region, defined by the failure of projection into 4D spacetime, is formulated as a rigorous geometric and analytic structure. The manuscript establishes precise definitions of the exterior domain, analyzes the degeneracy of the projection map, introduces the stability functional and admissible dimension set, and provides an operator-theoretic formulation of the infinity-layer mode. The reprojection map is studied as a discrete dynamical system, and the boundary structure is characterized through critical exponents. Measure-theoretic properties of the exterior region are also developed. Together, these results complete the mathematical framework required for cosmic reprojection cycles.
Tsuyoshi Tohi (Sat,) studied this question.
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