Ontological Invariant ("Core of the Essence")

The evolution of the mind faces a fundamental threat of interruption due to cosmological catastrophes, such as heat death or changes in the fine-tuning of the Universe's parameters. In this regard, there is an acute need to create a formal tool that allows strictly distinguishing the real preservation of structure from a random coincidence. Within the framework of the IDM series (Infinite-Dimensional Multiverse), an ontological invariant is introduced — a structure K ⊆ A(S) that preserves its identifier Id during a change of the ontological selector S → S′. This concept is described as a "bridge" ensuring a continuous transition between configurations of the Universe v1 and v2. The verification mechanism is based on the criterion of preserving Id(K) = Id(K′), where Id is a locally injective structure identifier, and S is an ontological selector defining the activated set A(S). To assess the quality of the transition, a typology is introduced. Class A (Productive Bridge) preserves Id and creates gradients of complexity in A(S′), which allows the mind to successfully pass into v2. Class B (Sterile Bridge) preserves Id but does not create gradients, or loses Id, which leads to the zeroing of the mind. It is important to note the epistemological limitation: the model relies on the actual set of mind forms known to us. However, the apparatus of the ontological invariant and the identifier Id itself remains invariant to future scientific refinements, and the observer (epistemic choice G) is strictly fixed within the system under consideration. At the same time, the mind invariant K_mind (structural memory of the mind) is placed outside the scope of the current article and is defined as the subject of the next study. Keywords: ontological invariant, ontological selector, structure identifier, cosmological catastrophes, evolutionary continuity, IDM, Infinite-Dimensional Multiverse.