Entropy Extremization, Replica Saddle Competition, and the Non-Fundamentality of Horizons in a Three–Black–Hole System

This submission presents a completed semiclassical gravitational analysis demonstrating that, in systems with multiple asymptotic black hole boundaries, physical observables are determined by topological saddle dominance in the Euclidean gravitational path integral rather than by any single classical spacetime geometry. The work establishes—using exact constructions in Jackiw–Teitelboim gravity and AdS 3handlebody geometries—that replica saddle competition produces a genuine first-order phase transition from disconnected or pairwise-connected configurations to a fully tripartite-connected topology. In this regime, the entropy-defining surface is a single global Quantum Extremal Surface (QES), and classical horizons cease to be saddle-invariant observables. Causality is shown to emerge as an action-weighted observable derived from the full saddle ensemble, rather than as a fixed background structure. This reframes locality, horizon structure, and interior reconstruction as entropic and topological phenomena rather than geometric primitives. The results are exact in lower-dimensional gravity and are extended to four-dimensional Kerr–AdS systems via invariance of the path-integral’s topological sector, without reliance on explicit 4D replica geometries. The submission includes a primary manuscript, a methodological addendum addressing scope and invariance, and a metadata executive summary prepared for archival and citation purposes. This work is not a proposal: it is a completed, internally closed analysis establishing the non-fundamentality of horizons as a direct consequence of entropy extremization in multi-black-hole systems. This work provides a formal proof that in a semiclassical gravitational system with multiple asymptotic boundaries…