This work introduces an invariant-classified reactor architecture within the SEXA Unified Field Theory (SEXA UFT), extending Recursive Soil Bearing Architecture (RSBA) through the incorporation of symmetry-governed admissibility conditions defined by a high-order finite group constraint inspired by the Monster symmetry structure. Within this framework, exciternion tensor states are defined over a recursive state space and subjected to a group action G ⋅ Ξ ∈ S_Ξ where G denotes a finite sym