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.

翻译：我们证明，汇编理论、路径复杂性、汇编指数以及汇编数均被纳入并构成算法（Kolmogorov-Solomonoff-Chaitin）复杂性的弱版本，其依赖于基于统计压缩的近似方法，所得结果源于使用了严格等价于LZ系列压缩算法（如ZIP、GZIP或JPEG等压缩算法所采用的方法）。已有研究显示，这类流行算法能够经验性地再现汇编理论的汇编指数结果，且其成功应用于区分有机与非有机分子、以及研究选择与进化的案例已有报道。本文展示并证明了汇编理论与香农熵及统计压缩之间的完全等价关系，同时揭示汇编理论作为统计方法在因果性上的脱节。我们证明，若缺乏逻辑一致性和经验证据，对分子进行传统统计压缩描述（或构建其理论基础）并不意味着能解释或量化生成过程（包括物理或生物过程）中的偏差，包括由选择与进化导致的偏差。我们认为，在基本论证中，汇编理论的作者混淆了物体可能组装的方式与因果方向性，并得出结论：除了已知且已被充分确立的关联（其中部分已在本综述中回顾）外，汇编理论在解释选择或进化方面并未提供任何额外贡献。