2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96158We study a geometry of the partition function which is defined in terms of a solution of the five-term relation. It is shown that the 3-dimensional hyperbolic structure or Euclidean AdS_3 naturally arises in the classical limit of this invariant. We discuss that the oriented ideal tetrahedron can be assigned to the partition function of string.16 pages, 4 figuresHigh Energy Physics - TheoryHyperbolicity of Partition Function and Quantum Gravitytext