A Topos–Bicategorical Framework for Consciousness-Centered Relational Quantum Dynamics (RQD)

We introduce a novel mathematical framework for Relational Quantum Dynamics (RQD) that unifies topos theory, bicategorical structures, and Hilbert-space enrichment to rigorously capture observer-dependent quantum phenomena within a consciousness-centered ontology. By taking R as the category of relational contexts, we construct the topos of presheaves [R_op, Set], in which propositions are assigned context-dependent truth values. Leveraging the sheaf–theoretic approach to contextuality, we show that cohomological obstructions in this topos precisely account for the absence of global sections—formally encoding the inherent contextuality of quantum measurements. To model multi- observer interactions, we develop a bicategorical structure where observers are represented as 1-morphisms and awareness updates as 2-morphisms, thereby ensuring reciprocity and consistency in relational information exchange. Furthermore, by enriching RR over the category of Hilbert spaces, we demonstrate that the resulting structure forms a dagger compact category, recovering standard quantum mechanics as a special degenerate case. Finally, we cast the many–observer paradigm in terms of an indexed (fibered) category of Hilbert spaces, analogous to a principal bundle over measurement contexts, thereby formalizing the splitting of reality into multiple, context–dependent perspectives. This framework provides a robust, formal basis for understanding quantum states as emergent relational constructs, where truth is inherently perspectival and no absolute observer–independent reality exists.