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Given the importance of the claim, we want to start by exposing the followingconsideration: this claim comes out more than a year after the article"Practical applications of Set Shaping Theory in Huffman coding" which reportsthe program that carried out an experiment of data compression in which thecoding limit NH0(S) of a single sequence was questioned. We waited so longbecause, before making a claim of this type, we wanted to be sure of theconsistency of the result. All this time the program has always been public;anyone could download it, modify it and independently obtain the reportedresults. In this period there have been many information theory experts whohave tested the program and agreed to help us, we thank these people for thetime dedicated to us and their precious advice. Given a sequence S of randomvariables i.i.d. with symbols belonging to an alphabet A; the parameter NH0(S)(the zero-order empirical entropy multiplied by the length of the sequence) isconsidered the average coding limit of the symbols of the sequence S through auniquely decipherable and instantaneous code. Our experiment that calls intoquestion this limit is the following: a sequence S is generated in a random anduniform way, the value NH0(S) is calculated, the sequence S is transformed intoa new sequence f(S), longer but with the symbols belonging to the samealphabet, finally we code f(S) using Huffman coding. By generating astatistically significant number of sequences we obtain that the average valueof the length of the encoded sequence f(S) is less than the average value ofNH0(S). In this way, a result is obtained which is incompatible with themeaning given to NH0(S).

Overcoming the compression limit of the individualsequence (zero order empirical entropy) using the Set Shaping Theory