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We reassess the problem of separability of the kinematic Hilbert space inloop quantum gravity under a new mathematical point of view. We use theformalism of frames, a tool used in signal analysis, in order to remove theredundancy of the moduli structures in high valence graphs, without resortingto set extension of diffeomorphism group. For this, we introduce a localredundancy which encodes the concentration of frame vectors on the tangentspaces $T_pM$ around points of intersections $p$ of smooth loops $\alpha$ in$\mathbb{R}^{3}$.

Moduli Structures, Separability of the Kinematic Hilbert Space and Frames in Loop Quantum Gravity