Relational Access Symmetry in the Intrinsic Observability Framework

We introduce a relational extension of the Intrinsic Observability Framework (IOF), termed Relational Access Symmetry (RAS), in which the roles of observable and hidden subspaces are exchanged between distinct observational structures. While the previously introduced Access Transformation Symmetry (ATS) preserves observational statistics under redefinitions of subsystem decomposition, it does not alter the underlying observational standpoint. In contrast, RAS represents a transformation between observational structures themselves, under which what is accessible in one description becomes inaccessible in another, and vice versa. We formulate RAS as a relational exchange symmetry between observable and hidden subspaces, implemented via a unitary mapping between alternative tensor decompositions of the total Hilbert space. Unlike ATS, RAS does not require invariance of measurement outcomes; rather, it imposes a structural covariance under the exchange of observational roles. As a consequence, observable and hidden subspaces must be isomorphic, enforcing an intrinsic balance between accessible and inaccessible degrees of freedom. This result provides a new structural perspective on the hidden sector in quantum theory: instead of being arbitrary or merely residual, the hidden subspace acquires a constrained and structured character, determined by its relational equivalence to the observable subspace. RAS thus elevates the hidden sector from an unspecified complement to a symmetry-related counterpart, offering a refined structural understanding of observability within the IOF.