for z = κ and α = ( κ − d ) / 2 , κ ∈$_{R}$ ; (14) let us remark that scale invariance is achieved for any real number κ , thus (13) and (14) actually constitute a one-parameter family of scale transformations. This is, there is one degree of freedom in the critical exponents, or in other words, the scaling form is insensitive to the dynamic exponent. Contrarily, in a radial geometry the correlation, Eq. (11), is scale invariant only if κ = 1 /γ : this is the constraint imposed by the geometrical factor J . The Jacobian determinant J = sin( θ$_{1}$ ) d − $^{1}$sin( θ$_{2}$ ) d − 2 · · · sin( θ$_{d}$$_{−}$$_{1}$ ) for a d − dimensional interface, where θ$_{1}$, · · · , θ$_{d}$$_{−}$$_{1}$ is the set of polar angles, while it is of course independent of the azimuth angle θ$_{d}$ . So this constraint appears for d ≥ 2, but it is not present for d = 1. The reason is that the one-dimensional radial interface is topologically identical to the one-dimensional, topologically toroidal, interface which results from assuming periodic boundary conditions on the growing domain setting. In this case, the angle-like coordinate x , to which the azimuth angle is akin, may be either dimensional or dimensionless (this could be expressed by means of the dichotomy of Lagrangian/Eulerian coordinates similarly to the developments in [20]). On the other hand, the polar angles, ranging only π radians, cannot be associated to periodic coordinates which could have dimensions. This fixes the scaling z = 1 /γ . One can use the ambiguity of Eq. (12) to claim that z = ζ is a good dynamic exponent in this case, but that would be accepting that topology can modify the scaling. Also, the value of the auto-correlation exponent in this case suggests that z = 1 /γ is the good dynamic exponent [20]. In any case, it is now clear that there is no basis for claiming that correlation (10)-(12) is a consequence of scaling (2) in the present framework. This is because, although both forms are invariant to the transformation (13) for z = ζ (for linear equations like (3)), self-similar form (10)-(12) preserves scale invariance independently of the value of z (as specified in Eq. (14)). So this second form is much more general and the value z = ζ plays no special role in it (let us note again that the value z = 1 /γ plays a special role in the sense that it appears in the auto-correlation function [20]). Despite this ambiguity in the growing domain situation, it is clear that the radial correlation (11) is just invariant for { ˜ α$_{r}$, z$_{r}$ } , and the classical exponents { α$_{c}$, z$_{c}$ } play no role in this case. This can be seen by means of a direct application of transformation (13) to this correlation and substituting α and z for the two different alternatives. 9