Applied Trigonotopology: Defining a Four-Dimensional Function to Collapse the Space between Distant Points

This article proposes a theoretical and mathematical model based on the Trigonotelary Function (TT) to describe the instantaneous transport of matter between two spatially distant points, without time as an explicit variable. The model suggests that spatial separation can be ontologically collapsed through topological equivalence modulated by structural frequencies and phases. The methodology integrates concepts from complex systems theory, graph theory, topology, Perelman’s geometric entropy, Cantor sets, Bell’s theorem, and the Poincaré conjecture. The TT function is formalized as a multidimensional harmonic vector field governed by the entanglement parameter θ. Theoretical results demonstrate that, under critical phase conditions, two distinct points can become functionally equivalent, enabling simultaneous manifestation without physical displacement. This functional equivalence finds conceptual support in analogies with quantum entanglement, neural synchronization, and resonance patterns. The study concludes by proposing a shift from metric-based space-time ontology to a functional mesh of resonance and topological equivalence, with implications for cosmology, fundamental physics, and historical theory.