Boundary Moduli II: Sporadic Isotropy Groupoids after Monster-Theta Enhancement: A Two-Paper Companion to Local Symmetry Refinement after Koizumi Descent

This paper is intended to be read as Part II of a two-paper sequence on exceptional symmetry for Clifford-Koizumi boundary moduli. Part I, [T. Matsuhisa. Boundary Moduli I:. Monster--Theta Enhancement of Boundary Moduli: Arithmetic Rigidity and Local Symmetry Refinement after Koizumi Descent, 2026. ⟨hal-05694716⟩ ], isolated a rigid Monster-Theta chart inside the local visible-dark theory, showed that a Leech-rigid and Griess-enhanced visible theta sector canonically selects a parity-refined saturated subgroupoid, and identified Monster isotropy on a rigid one-object component under a deliberately strong strictness hypothesis. The present paper retains that logical posture but generalises its structural spine. We define strict G-enhancements for prescribed exceptional finite groups G, prove a general isotropy-reduction theorem, establish a componentwise isotropy theorem on rigid one-object charts, and isolate a criterion for equivalence with the one-object groupoid BG. In this way, Part I becomes the prototype chart, whereas Part II formulates the componentwise exceptional-groupoid framework in which the Monster is no longer the terminus of the story but the first distinguished component. Every definition, proposition, and theorem is bracketed by a model example and a Counter-example. Sketch proofs are retained in the main text, whereas complete proofs and the necessary preliminaries are placed in the appendices.