This is an interesting paper. Certainly we must expect some relic footprints from the primeval codes could be detected in the present standard genetic code. However, not only the renormalization group approach could suggest that most current prokaryotes may still contain relics of the primeval RNA World. As the authors suggest: “in coding sequences there is a 3-base periodicity in the nucleotide sequences as reflected by all possible correlations of single bases, duplets and triplets [49,42,61], the FDD of triplets [62], the autocorrelation function [63,59] or by the mutual information function of single bases [64]”. In particular, it is well known 3-base periodicity is detected in protein coding genomes regions by means of the application of Discrete Fourier Transform (DTF) as a peak at frequencies 1/3 (or 2/3). It could very interesting to apply the DFT to the three different genomes generated: Genomes having only RNY triplets, Genomes with only RNY, NYR and YRN triplets and Genomes with only RNY, RNR, and YNY triplets, i.e., it could be very interesting to verify if the 3-periodicity is also detected in the putative ancient genomes using DTF.
A weak point of the paper resides in assuming that a shift in the reading frames probably occurred, in particular, frame-shift reading mistranslations in the 2nd and 3rd reading frames. Thus, in order to evolve from the primordial sequence (or genetic code) of the type …RNYRNYRNY… to the present genomes (or standard genetic code) the last two mutational events should have taken place in the evolutionary history of life, every of which has a very low occurrence probability. The energetic and informational costs of these events are too high. It could be the reason why Francis Crick was opposed to this idea.