Cosmological Beginnings and Ends in the ψ Field in the Framework of the NSk Energy–Spectral Anchor

The aim of this work is to formulate the notions of a beginning and an end of the Universe purely in the language of the probability field ψ and of the NSk energy–spectral anchor on a class of manifolds of bounded geometry. The starting point is the postulate of the Universe as a global ψ field and the published NSk–Anchor module (version V3), which for the operator H = ħ c sqrt(-Δ_g) on manifolds from the class Geo defines the anchoring function F(Γ_eff) and the anchoring scale l0. Based on this formalism we define a ψ–Anchor genesis event as the first moment at which there exists a global shell of the ψ field with probability density approximately equal to 1, satisfying the anchor equation F(Γ_eff) = ρ. We also introduce classes of anchor ends of the world as situations in which the anchor equation ceases to have solutions or the NSk spectral assumptions break down, as well as a simple class of “silent ends”, in which structures disappear while the anchor remains valid. The work is purely kinematic in character: we describe conditions for existence and a classification of ψ–Anchor states, rather than their dynamics or the mechanism of the origin of the Universe.