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4 Discussion

[5.4.1] The idea underlying the construction of the counterexample can be generalized. [5.4.2] The freedom in the choice of the input functions \psi(t) and \lambda(\mathbf{r}) allows to construct a wide variety of continuum limits. [5.4.3] This shows that the claims in [3, 4, 5, 6, 7, 8] are too general.

[5.5.1] In summary the counterexample shows that a power law tail in the waiting time density is not sufficient to guarantee the emergence of the propagator of fractional diffusion in the continuum limit.