Structural Convergence of Graded Hilbert Spaces and Restricted Observables Across UV Geometries

We observe that realistic supergravity-based UV completions relevant for phenomenology converge on a common operational structure: a geometric involution induces a graded Hilbert space H= H+ ⊕H−, phenomenological access is restricted to A+ ⊂B(H+), and the operationally inaccessible complement H− constitutes a bulk-sized sector in each examined model class—not a small correction—making operational inaccessibility structurally unavoidable rather than fine-tuned. The operational consequences of this structure are exact and UV-detail-independent: accessible expectation values factor through ρ++, Π-dephasing is indistinguishable under A+, and when H+− ≠ 0 the A+-restricted evolution of ρ++(t) is effectively open. We anchor the convergence observation in Table 1 across Kaluza–Klein orbifolds, Hořava–Witten, heterotic orbifolds, brane models, and F-theory, and illustrate with an explicit benchmark extraction of an odd-channel proxy αodd. Chirality of the low-energy spectrum is treated correctly as conditional.