Experimental Testbed for Relational Coherence Theory: A BEC-Based Toy Universe

It is noted that the Relational Ontology Framework (ROF) and Relational Coherence Theory (RCT) https://doi.org/10.5281/zenodo.16423366 provide the basis of the proposal of a laboratory-scale embodiment by BoseEinstein Condensate (BEC) acting as an analogue of the Primordial Relational Field (PRF). We prove that, in a Penrose type of coherence-driven phase transition, by reducing the 8D octonionic manifold to a 3D quantum system for adapt to actually technologies, crossings through the manifold of quantum universes can be simulated. Current quantum technologies allow the experiment to explore the main predictions of RCT: topological vortices as analogues of dark matter, emission in the 702 nm photon range (phenomenon of a consciousness threshold), and the emergence of geometry. Strict mathematical scaffolds connect the complete ROF/RCT framework with this "toy model universe" which is practically accessible. We deliberately reduce the 8D octonionic manifold to a 3D system with algebra to leverage existing quantum technologies, preserving the core phenomenology of ROF/RCT.