Spectral-Band Universality in Phase-Modulated Information Rivalry Dynamics

Description We study externally driven Phase-Modulated Information Rivalry (PMIR) dynamics on networked systems and identify a previously uncharacterized form of spectral-band universality. Across multiple degree-matched graph topologies—including periodic lattices, random regular graphs, Watts–Strogatz networks, and stochastic block models—we show that macroscopic PMIR rivalry observables do not collapse under raw time or single-eigenvalue scaling. Instead, universality emerges when dynamics are projected onto contiguous Laplacian spectral bands and time is rescaled by the second Laplacian eigenvalue. Within each spectral band, rescaled rivalry response curves collapse across topologies and system sizes, while remaining distinct across bands. This behavior defines a mesoscopic universality structure: dynamics are topology-independent within bands but not globally scale-invariant. Crucially, this structure is predictive. Band-indexed affine models trained on a subset of topologies accurately predict the dynamics of held-out topologies, significantly reducing error relative to uncalibrated spectral scaling. Higher spectral bands exhibit the strongest predictive consistency, while low-band failures (e.g., ring lattices with vanishing spectral gap) delineate the boundary of the universality class rather than contradict it. These results establish an empirically validated universality class for driven network dynamics, governed by spectral structure rather than geometry or microscopic realization. The findings bridge features of diffusive spectral control and nonlinear mean-field behavior without requiring a continuum limit, thermodynamic limit, or equilibrium assumption, and suggest testable analogues in other Laplacian-driven physical and information-theoretic systems.