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 that were reported before in successful application to separating organic from non-organic molecules and in the context of the study of selection and evolution. We 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 not explain selection or evolution beyond known and previously established connections, some of which are reviewed.

翻译：我们证明组装理论、路径复杂度、组装指数和组装数均被纳入算法复杂度（柯尔莫哥洛夫-所罗门诺夫-柴廷复杂度）的弱化版本范畴，其依赖基于统计压缩的近似方法，所得结果源于使用严格等价于LZ系列压缩算法（如ZIP、GZIP或JPEG等压缩算法中使用的算法）的方法。此类主流算法已被证明能经验性地复现组装理论先前在成功区分有机分子与非有机分子以及选择与进化研究中的报告结果。我们论证了组装理论与香农熵及统计压缩之间的关联性及完全等价性，并指出作为统计方法的组装理论与因果关系的脱节。我们证明，在缺乏逻辑一致性和经验证据的情况下，对分子进行传统统计压缩描述或构建其理论基础，并不能解释或量化生成过程（物理或生物过程）中的偏差，包括由选择和进化引起的偏差。我们认为，在基本论证中，组装理论作者混淆了物体的组装方式与因果方向性，并得出结论：组装理论未能超越已知且已确立的关联（其中部分已予评述）解释选择或进化。