Understanding Entanglement Through the Lens of Quantifiable Algebraic Structures: Application to Bird Navigation

We propose a unified mathematical meta-framework for long-distance navigation in birds, based on a bundle-theoretic representation of multisensory integration within evolving combinatorial structures. Various information streams–uch as magnetic, celestial, olfactory, and landmark cues–are modeled as typed fibers over a time-varying simplicial base, which is reconstructed from behavioral trajectories and neural co-activity. In this framework, integration is framed as a global consistency problem: coherent system-level representations occur when there are globally compatible assignments across overlapping local contexts. This is equivalent to finding global sections of an evolving bundle. The tension between local and global perspectives is formalized in quantum theory through the concept of contextuality, which expresses the impossibility of a single, non-contextual global assignment that is consistent with all local marginals. In Bell-type scenarios, this aligns with operational non-locality and device-independent signatures of entanglement. We demonstrate that the same constraint semantics provide a precise mathematical connection between canonical contextuality models and biological cue integration, treating contextuality as a calculus for diagnosing and localizing incompatibilities in distributed representations. Our theory introduces two computable topological observables: critical simplices and interface loops. Critical simplices identify discrete remapping pivots where the structural scaffold must be reconfigured to restore consistency, while interface loops detect transient conflict cycles at the boundaries between different information streams. Together, these observables form a diagnostic “compass” that integrates cues onto a common scaffold, localizes incompatible overlaps, and predicts when spatial representations need to be remapped. We validate our framework using standard quantum contextuality scenarios, including Bell’s theorem and KCBS, successfully recovering established contextuality classifications through bundle obstructions and loop signatures. We then apply this framework to an anatomy-aware model of avian navigation, in which entanglement-capable cryptochrome/radical-pair dynamics serve as a microscopic source of non-classical correlations, without assuming that macroscopic entanglement occurs across neural circuits. In this model, microscopic non-classicality influences adaptive functions by leaving persistent, computable contextual footprints within the evolving biological scaffold, providing testable signatures at the level of remapping events and context-dependent cue integration.