Mathematical Formalization of Necessitated Update Activity (NUA) within the Kearon Conditional Unlocking Field (CUF)

This preprint introduces Necessitated Update Activity (NUA) as the sole ontological primitive of the Kearon Conditional Unlocking Field (CUF), a necessity-only framework in which all physical and abstract phenomena are derived from recursive update activity under constraint. Within this framework, stabilization, propagation, and retention are treated as constraint-shaped regimes of the same underlying activity rather than distinct substances or forces. Classical concepts such as light, matter, gravity, energy, and time are reclassified as emergent modes of NUA. The work also formalizes conditional unlocking events, including desorption, defined as the loss of retention when constraint intensity falls below viability thresholds. Desorption is shown to be a transition from a bound stabilization regime to a freely updating propagation regime, without invoking forces, energies, or observer-dependent mechanisms. All definitions are provided in a fully mathematical form, with explicit falsification conditions, and without importing particles, fields, spacetime, or collapse postulates.