Quantum Region Connection Calculus for operator defined region relations

Quantum theory typically presupposes a fixed factorisation of the total Hilbert space into subsystems, or an equivalent fixed choice of commuting subalgebras. This convention hard-codes a classical notion of boundary between "System A" and "System B". Recent work has formalised subsystem ambiguity by defining partitions directly at the level of C*-subalgebras, including non-tensor-factor subsystems, and by studying representability and the role of centres. In parallel, work under the label "quantum mereology" studies how subsystems can emerge top-down from spectral structure or from changes of tensor product structure. The aim here is different. We define RCC-style region relations directly from unitary invariants of pairs of sharp region projectors, so that boundary indefiniteness is a relation-level observable rather than a chosen decomposition. A quantum mereotopology is developed in which "regions" are represented by projection operators and their topological relations are defined intrinsically, without background space and without a privileged tensor product structure. The central object is the commutator of region projectors, whose spectrum and operator norms quantify the extent to which a putative boundary is definite or indefinite. A quantum extension of region connection reasoning is proposed in which the commuting regime yields a classical Boolean core of region relations, while a noncommuting regime captures superposed and dynamically entangled partitions through an explicit interface sector. This yields a coordinate-free separability criterion expressed purely in terms of region relations, and it provides a framework in which boundary fuzziness becomes an observable notion tied to measurement compatibility.