We investigate the ultraviolet behavior of four-dimensional Lorentzian covariant loop quantum gravity (LQG) and address the problem of infinite ambiguities relating to the triangulation dependence of spinfoam amplitudes. We consider the complete LQG amplitude that sums spinfoam amplitudes over two-complexes. By introducing spin-network stacks and their covariant extension, spinfoam stacks, the summation over complexes is partitioned into distinct families. We demonstrate that the theory exhibits a condensation phenomenon, where quantum geometry condenses to a dominant small-spin configuration. We identify a candidate fixed point controlling the ultraviolet (small-spin) regime of covariant LQG. At this fixed point, the complete LQG amplitude dynamically reduces to a topological theory at leading order, and the infinite ambiguities of triangulation dependence reduce to a finite set of boundary coefficients associated with a finite basis of three-dimensional boundary blocks. These results provide a definition for the continuum limit of spinfoam theory at the fundamental level.

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• Loop quantum gravity