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Abstract We present a new correspondence between a d-dimensional dynamical system and a family of higher-order derivative $$(d+1)$$ (d+1) -dimensional systems. This new scale-holographic relation is built by the explicit introduction of a dimensionful constant which determines the size of the additional dimension. Scale holography is particularly useful for studying non-local theories, since the equivalent dual system on the higher dimensional manifold can be made to be local, as we illustrate with the specific examples of the p-adic string theory and the free particle.