Trilogía de la navegavilidad

This preprint presents version 3.0 of the Trilogía de la navegabilidad, a formal ontology of existence grounded in complete lattices, structural invariants, and monotone dynamics. Existence is defined as positive navigability within a viable region closed under infima; identity is characterized as a trajectory of minimal invariants; capacity denotes the ability of a system to modify its own structural space; and derivation captures compatible ruptures that generate new lattices and new identities. The text establishes general results on viability closure, minimal guaranteed navigability, irreversibility of boundary crossing, and existential collapse. It also formulates a conjecture on the existence and local uniqueness of derived spaces under saturation conditions. The work integrates philosophical intuition with mathematical rigor, offering a unified framework for persistence, transformation, fragility, and metamorphosis in physical, informational, and hybrid systems.