APPLIED TRIGONOTOPOLOGY: DEFINING A FOUR-DIMENSIONAL FUNCTION TO COLLAPSE THE SPACE BETWEEN DISTANT POINTS

ABSTRACT This article introduces a novel theoretical framework in which spatial connection is governed by non-temporal resonance rather than chronological causality. Based on the concept of trigonotelary geometry, we propose a harmonic field function that connects distant spatial points through a fourth-dimensional entanglement parameter, Θ. The function T(P, Θ) defines spatial relationships based on phase alignment and structural resonance, allowing for ontological simultaneity — a condition in which distinct positions share identical functional states. Unlike conventional space time metrics, this model implies instantaneous transitions between resonant nodes, independent of trajectory or elapsed time. We derive the mathematical properties of the trigonotelary function and demonstrate its implications for topology, causality, and system complexity. This approach opens new possibilities for understanding non-locality in physics and historical processes. The resulting formulation challenges traditional models of spatial continuity, replacing geometric proximity with harmonic identity. KEYWORDS: Ontology of time, Entropy, Functional identity, Topology, Spacetime.