The Ontological Selector S: Formalization of the Concept and Its Difference from Epistemic Choice

The article eliminates the ambiguity in the use of the concept G in the MBM series. Previously, G denoted both the scale of observation (level of detail) and the selector of the set of elements of reality. Now two independent concepts are introduced: G (epistemic choice, scale) and S (ontological selector). It is shown that a change of G does not change the active set A(S) and, consequently, does not generate new universes. It is merely a change of description. A change of S, by contrast, changes the active set A(S), which signifies a transition to another universe. A formal apparatus for S is proposed. The space of configurations 𝕊 is the set of all possible values of the selector. Its structure (finite, countable, continuous) remains an open question. The projection operator P(S): Ω → U(S) singles out the activated set from the complete set Ω. Its idempotence and injectivity are assumed. The activated set A(S) is introduced, along with the condition for the existence of a stable universe: the set must be closed to maintain isolated space-time on a scale of 50–100 billion years. Rules for changing configurations S → S' are formulated. It is noted that the transition is reversible, unlike the irreversible branching in the many-worlds interpretation. However, reversibility is a property of the formal structure, not a practical possibility for an observer. The connection of S with topology T(S) and metric is discussed. The connection with EFOS (elements of reality are projections of EFOS at a given S) and the metrics of the series (SQ, HII, IIC) is established. Open questions are formulated: the nature of the space 𝕊, the existence of a "base" value of S (our Universe), criteria for distinguishing S and G, rules of transition, connection with topology and quantum measurements, possible empirical manifestations of a change of S. The formalization of S eliminates terminological confusion and sets the direction for further research.