Geometry-orchestrated objective reduction from a multiscale resonance chain: Polyatomic time crystals

Abstract

We develop a nonlinear-systems framework in which a multiscale resonance chain is represented as a finite polyatomic clock network with geometry-dependent synchronization. The model is motivated by soft condensed biological matter, with emphasis on microtubule-associated dielectric, aromatic, and cavity-like structures. Using a Sakaguchi–Kuramoto-type network, we introduce curvature concentration, host–guest nesting, and sectorized geometric phase as explicit control parameters that reshape coupling strengths and phase lags. The model outputs are geometry-dependent synchronization plateaus, bifurcation-like plateau displacement, anesthetic-induced de-locking trends, local sensitivity rankings, and a two-parameter perturbation phase diagram showing how anesthetic strength and cavity and dielectric detuning jointly reshape the locking boundary. We then project a normalized Diósi–Penrose self-energy proxy onto the same parameter space to obtain collapse-time contour maps linked to the underlying locking landscape. This coupling between nonlinear synchronization and collapse-model phenomenology yields experimentally testable predictions: discrete cross-scale resonance bands, geometry-induced shifts of locking plateaus, anesthetic-sensitive reduction of synchrony at π-rich sites, cavity and dielectric tuning of contour structure, and path-selective quantum-light readout. This manuscript presents a falsifiable model in which geometry, synchronization, and energy-density contrast generate measurable dynamical signatures in calibrated soft-matter resonance systems.