We show that the effective quantum description reconstructed in Modal Triplet Theory must be formulated on a complex Hilbert space. Admissible basin outcomes induce an orthomodular lattice of propositions with infinite orthogonality, placing the theory within the scope of Solèr’s theorem. An admissibility-based formulation of local tomography excludes quaternionic Hilbert space, while phase-rich coherence requirements exclude real Hilbert space. The result is a rigidity theorem: complex Hilbert space is uniquely enforced by admissibility and locality.
Peter Nero (Wed,) studied this question.