Given the importance of the claim, we want to start by exposing the following consideration: this claim comes out more than a year after the article "Practical applications of Set Shaping Theory in Huffman coding" which reports the program that carried out an experiment of data compression in which the coding limit NH0(S) of a single sequence was questioned. We waited so long because, before making a claim of this type, we wanted to be sure of the consistency of the result. All this time the program has always been public; anyone could download it, modify it and independently obtain the reported results. In this period there have been many information theory experts who have tested the program and agreed to help us, we thank these people for the time dedicated to us and their precious advice. Given a sequence S of random variables 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) is considered the average coding limit of the symbols of the sequence S through a uniquely decipherable and instantaneous code. Our experiment that calls into question this limit is the following: a sequence S is generated in a random and uniform way, the value NH0(S) is calculated, the sequence S is transformed into a new sequence f(S), longer but with the symbols belonging to the same alphabet, finally we code f(S) using Huffman coding. By generating a statistically significant number of sequences we obtain that the average value of the length of the encoded sequence f(S) is less than the average value of NH0(S). In this way, a result is obtained which is incompatible with the meaning given to NH0(S).

翻译：鉴于该观点的重要性，我们首先提出以下考量：这一观点发表于《集合整形理论在霍夫曼编码中的实际应用》一文（该文报告了质疑单序列编码极限NH₀(S)的数据压缩实验程序）一年多之后。我们等待如此之久，是因为在提出此类观点前需要确保结果的一致性。在此期间，该程序始终公开可访问，任何人都可下载、修改并独立复现所报告的结果。在此期间，多位信息论专家测试了该程序并慷慨提供协助，我们谨此感谢他们付出的时间与宝贵建议。给定由独立同分布随机变量构成的序列S（符号取自字母表A），参数NH₀(S)（零阶经验熵乘以序列长度）被视为通过唯一可译瞬时码对序列S符号进行编码的平均编码极限。我们质疑该极限的实验如下：随机均匀生成序列S，计算NH₀(S)值，将S转换为新序列f(S)（长度增长但符号仍属同一字母表），最后采用霍夫曼编码对f(S)进行编码。通过生成统计显著数量的序列，我们得到编码后序列f(S)的平均长度小于NH₀(S)的平均值。这一结果与NH₀(S)的传统意义不相容。