Coherence as a Control Variable in Multiscale Biological Regulation: Analytical Foundations of the Bounded Phase Coherence Principle

In prior work, the Bounded Phase Coherence Principle was proposed as a unifying hypothesis explaining inverted-U stability relationships across physiological domains. This manuscript provides an analytical foundation for that proposal by reframing bounded phase coherence as a dynamical control principle in multiscale biological regulation. Using an Ott–Antonsen mean-field reduction of noisy Kuramoto–Sakaguchi ensembles, we derive closed low-dimensional dynamics for coherence order parameters and connect local recovery rates to Jacobian eigenstructure. A windowed stability functional is introduced that combines recovery, metastability penalties, and complexity rewards, demonstrating how a bounded intermediate operating window of coherence can arise within the synchronized regime, distinct from classical criticality at the synchronization threshold. A simulation-based calibration protocol is outlined, allowing the preferred coherence window to be estimated empirically rather than assumed as a universal setpoint. Version: PreprintRelated work: Expands the theoretical framework introduced in “Bounded Phase Coherence Maximizes Stability in Living Systems” (Zenodo record 18235945).