Experimental Confirmation of Spontaneous Coherence Condensation in an Octonionic Language Model Bose-Einstein condensate (BEC) analog

The Relational Ontology Framework (ROF) proposes that reality emerges froma non-associative Primordial Relational Field valued in the octonions. A centralprediction is that any octonion-based system, when driven to minimise ontologicalfriction and maximise coherence, will spontaneously condense into a high-coherence,low-friction state a “baryonic node” in the field. We test this prediction us-ing an octonion-valued transformer language model (ROF-LLM) trained on theWikiText-103 corpus with additional loss terms that directly implement the ROFdynamics. A real-valued control model of identical capacity fails to exhibit thecondensation.We then extend the study to a Bose-Einstein condensate (BEC) analog, intro-ducing an order parameter α = max(0, 1 − (Cn/0.85)2) that collapses to zero whenthe coherence exceeds a critical threshold. The model spontaneously enters a con-densed state (α = 0) after ≈ 3600 steps, with final Cn = 0.90 and LM loss 1.05.The phenomenon is reproducible over five random seeds (mean condensation step3700 ± 80) and is insensitive to the exact threshold value. Ablation experimentsdemonstrate that both the coherence-promoting and friction-penalising loss termsare individually necessary.These results provide the first computational evidence that the octonionic ar-chitecture defines a unique attractor not accessible to standard neural networks,confirming the core mathematical claims of the Relational Ontology Framework.The additional BEC analysis shows that the condensation is a robust phase tran-sition, independent of the specific implementation of the BEC mechanism.