We demonstrate that Assembly Theory, pathway complexity, the assembly index, and the assembly number are subsumed and constitute a weak version of algorithmic (Kolmogorov-Solomonoff-Chaitin) complexity reliant on an approximation method based upon statistical compression, their results obtained due to the use of methods strictly equivalent to the LZ family of compression algorithms used in compressing algorithms such as ZIP, GZIP, or JPEG. Such popular algorithms have been shown to empirically reproduce the results of AT's assembly index and their use had already been reported in successful application to separating organic from non-organic molecules, and the study of selection and evolution. Here we exhibit and prove the connections and full equivalence of Assembly Theory to Shannon Entropy and statistical compression, and AT's disconnection as a statistical approach from causality. We demonstrate that formulating a traditional statistically compressed description of molecules, or the theory underlying it, does not imply an explanation or quantification of biases in generative (physical or biological) processes, including those brought about by selection and evolution, when lacking in logical consistency and empirical evidence. We argue that in their basic arguments, the authors of AT conflate how objects may assemble with causal directionality, and conclude that Assembly Theory does nothing to explain selection or evolution beyond known and previously established connections, some of which are reviewed here, based on sounder theory and better experimental evidence.

翻译：我们证明，Assembly Theory、路径复杂性、组装指数及组装数量均被包含于算法复杂性（Kolmogorov-Solomonoff-Chaitin理论）的弱版本中，该版本依赖基于统计压缩的近似方法，其结论源于严格等价于ZIP、GZIP或JPEG等压缩算法所采用的LZ系列压缩算法。此类通用算法已被实证可复现AT的组装指数结果，并已成功应用于有机分子与非有机分子的区分以及选择与进化研究。本文揭示并证明Assembly Theory与香农熵及统计压缩之间的完整等价关系，同时指出AT作为统计方法在因果性方面的缺失。我们证明，当缺乏逻辑一致性与实证证据时，对分子进行传统统计压缩描述或其理论基础，并不能解释或量化生成过程（物理或生物过程）中的偏向性，包括由选择与进化引发的偏向。我们认为，AT作者在基本论证中混淆了物体组装方式与因果方向性，并得出结论：Assembly Theory在解释选择或进化方面并未超越已有且更早建立的关联性（本文基于更严谨的理论与更充分的实验证据回顾了部分关联）。