Emergent Geometry, Quantization, and Cosmological Dynamics from a Single Nonlinear Field 2.0

The ψ Framework 2. 0 presents an extended formulation of a unified geometric theory based on a single nonlinear field ψ describing the tension and coherent organization of an underlying physical manifold. In this framework, spacetime is not fundamental but emerges collectively from the relaxation dynamics of coherent geometric structures. updated formulation introduces two central concepts: coherent streak dynamics and geometric hysteresis. Physical entities are interpreted as stable or propagating coherent configurations of manifold tension, while irreversible large-scale behavior emerges from hysteretic relaxation of geometric coherence. arises naturally from geometric stability conditions rather than external quantum postulates. Stable compactified modes generate leptonic resonances, while neutrinos emerge as extended phase-propagation modes. In the weak-field regime, the framework recovers an emergent Schrödinger dynamics with an effective Planck constant and Coulomb interaction derived from ψ-field deformations. is reinterpreted as a gradient of coherent phase relaxation rather than a fundamental force or primary spacetime curvature. On cosmological scales, the observed Hubble relation, cosmological redshift, and time dilation emerge from cumulative geometric relaxation of propagating coherent streaks, without requiring dark energy, dark matter, or fundamental metric expansion. ψ Framework 2. 0 therefore proposes a unified non-metric geometric ontology in which microphysics, gravitation, quantum behavior, and cosmological dynamics emerge coherently from the same nonlinear manifold dynamics.