Minimal length: A cut-off in disguise?

The minimal-length paradigm, a possible implication of quantum gravity at low energies, is commonly understood as phenomenological modification Heisenberg's uncertainty relation. We show that this equivalent to cut-off in the space conjugate position representation, i.e. wave numbers, which does not necessarily correspond momentum space. This result generalized several dimensions and noncommutative geometries once suitable definition number provided. Furthermore, we find direct relation between ensuing bound wave-number scale. For scenarios existence minimal length cannot be explicitly verified, proposed framework can used clarify situation. Indeed, applying it common models, one them does, against all expectations, allow for arbitrary precision measurements. In closing, comment on general implications our findings field. particular, point out purely kinematical such that, effectively, there only model mechanics.