Quasiperiodic Control Temporal Boundary Stabilisation and Dynamical Topological Phases

Recent experimental demonstrations of quasiperiodic temporal control—most notably Fibonacci-driven pulse sequences—have revealed unexpectedly stable dynamical phases in quantum systems, including time-quasicrystalline behaviour and extended coherence lifetimes. This paper provides a theoretical interpretation of such phenomena within the ψ₀-OCM (Osborne Cosmological Model), where stability arises not from algorithmic error suppression but from boundary-conditioned stabilization of dynamical configurations. Within this framework, quasiperiodic driving is interpreted as a non-resonant constraint pattern that suppresses destabilizing modes by preventing phase closure across temporal boundaries. Temporal order emerges as a stabilised topological phase rather than a symmetry-broken state, with robustness governed by boundary compatibility rather than periodicity. The analysis reframes quasiperiodic control as a form of temporal boundary stabilization, offering a unifying explanation for time-quasicrystals, enhanced coherence, and dynamically protected phases without invoking exotic new matter. Implications are discussed for quantum control, non-equilibrium phases of matter, and the interpretation of time in non-algorithmic physical models.