Hexagonal Phase Cosmology: A Dynamical Extension of World Consistency Theory(v3)

We introduce a cosmological framework termed Hexagonal Phase Cosmology, developed as a dynamical extension of World Consistency Theory. In this approach the vacuum of the universe is modeled by six interacting scalar phase fields forming a discrete hexagonal phase lattice that governs the large-scale evolution of spacetime. The phase variables evolve under a periodic potential with multiple degenerate minima, producing a resonance structure in the vacuum configuration space. The corresponding field equations are derived within a modified gravitational framework incorporating mimetic gravity and Born–Infeld curvature corrections. In a homogeneous Friedmann–Lemaˆıtre–Robertson– Walker cosmological background the phase lattice contributes an effective vacuum sector whose energy density influences the expansion dynamics of the universe. The coupled phase dynamics exhibits a global Lyapunov attractor that drives the system toward progressive phase synchronization over extremely long cosmological timescales. The discrete phase structure generates a finite configuration space containing N = 66 = 46656 resonance states. Using the present Hubble expansion rate as the characteristic phase rotation scale, the complete cosmic resonance cycle is estimated to be Tcycle ≈ 4.3 × 1015 years. At the terminal alignment state the vacuum potential approaches its global minimum, potentially halting cosmic expansion and triggering a nonsingular cosmological bounce regulated by Born–Infeld curvature dynamics. The phase lattice naturally produces an effective vacuum energy component capable of mimicking dark-energy behavior, while small oscillations of the phase variables may generate dark-matter-like excitations. Possible observational implications include modifications to the late-time expansion history and the presence of an ultra–low-frequency stochastic gravitational-wave background. Hexagonal Phase Cosmology therefore provides a geometric realization of global consistency prin ciples in cosmology and offers a novel framework for cyclic cosmic evolution driven by vacuum phase