Disjointness of local knowledge under open-ended evolution

Prove that, in open-ended evolutionary systems, the contextual knowledge possible sets of different individuals are at least partially disjoint at any given time and across time; that is, establish that observers generally inhabit different known-worlds such that their contextual knowledge possible (the set of states they consider possible under their current theory and decision procedure) is non-coincident.

Background

The framework develops local, observer-specific knowledge rooted in individual theories and known-worlds that evolve through continual novelty. Because open-ended evolution induces different encounters with theory-breaking predicates and necessitates idiosyncratic theory revision, individual knowledge partitions become incomplete and heterogeneous.

This conjecture formalizes the claim that knowledge fragmentation is endemic in open-ended systems, undermining the standard assumptions of common knowledge and shared partitions that underpin traditional epistemology and many equilibrium results.