2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226013A semifinite spectral triple for an algebra canonically associated to canonical quantum gravity is constructed. The algebra is generated by based loops in a triangulation and its barycentric subdivisions. The underlying space can be seen as a gauge fixing of the unconstrained state space of Loop Quantum Gravity. This paper is the second of two papers on the subject.43 pages, 1 figureHigh Energy Physics - TheoryGeneral Relativity and Quantum CosmologyMathematical Physicstext