We prove the full equivalence between Assembly Theory (AT) and Shannon Entropy via a method based upon the principles of statistical compression renamed `assembly index' that belongs to the LZ family of popular compression algorithms (ZIP, GZIP, JPEG). Such popular algorithms have been shown to empirically reproduce the results of AT, results that have also been reported before in successful applications to separating organic from non-organic molecules and in the context of the study of selection and evolution. We show that the assembly index value is equivalent to the size of a minimal context-free grammar. The statistical compressibility of such a method is bounded by Shannon Entropy and other equivalent traditional LZ compression schemes, such as LZ77, LZ78, or LZW. In addition, we demonstrate that AT, and the algorithms supporting its pathway complexity, assembly index, and assembly number, define compression schemes and methods that are subsumed into the theory of algorithmic (Kolmogorov-Solomonoff-Chaitin) complexity. Due to AT's current lack of logical consistency in defining causality for non-stochastic processes and the lack of empirical evidence that it outperforms other complexity measures found in the literature capable of explaining the same phenomena, we conclude that the assembly index and the assembly number do not lead to an explanation or quantification of biases in generative (physical or biological) processes, including those brought about by (abiotic or Darwinian) selection and evolution, that could not have been arrived at using Shannon Entropy or that have not been reported before using classical information theory or algorithmic complexity.

翻译：我们通过一种基于统计压缩原理（被重新命名为“装配指数”，属于ZIP、GZIP、JPEG等流行LZ系列压缩算法）的方法，证明了装配理论（AT）与香农熵之间的完全等价性。这些流行算法已被实证能够复现AT的结果——这些结果此前已在分离有机分子与非有机分子以及研究选择与进化的语境中被成功报道过。我们证明装配指数值等价于最小上下文无关文法的大小。该方法的统计可压缩性受限于香农熵以及其他等效的传统LZ压缩方案（如LZ77、LZ78或LZW）。此外，我们论证了AT及其支撑路径复杂度、装配指数和装配数的算法所定义的压缩方案与方法，均被纳入算法（Kolmogorov-Solomonoff-Chaitin）复杂度理论框架。由于AT目前在定义非随机过程因果性方面缺乏逻辑一致性，且缺乏实证证据表明其优于文献中能够解释相同现象的其他复杂度度量，我们得出结论：装配指数与装配数无法解释或量化生成性（物理或生物）过程中的偏差（包括由非生物或达尔文式选择与进化带来的偏差），而这些偏差既无法用香农熵推导，也无法用经典信息论或算法复杂度此前未报道的方式加以解释。