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、组装指数与组装数均被纳入并构成算法（Kolmogorov-Solomonoff-Chaitin）复杂度的弱化版本，其基础依赖于基于统计压缩的近似方法。该理论所得结果源于使用与ZIP、GZIP或JPEG等压缩算法中严格等价的LZ系列压缩算法。已有实证表明，此类流行算法可复现组装理论此前在分离有机分子与非有机分子、以及选择与演化研究中的成功应用结果。我们证明组装理论与香农熵及统计压缩之间的关联性与完全等价性，并揭示其作为统计方法在因果性上的割裂。通过论证，我们指出：对分子进行传统统计压缩描述或构建其理论基础，若缺乏逻辑一致性与实证支撑，并不能解释或量化生成过程（包括物理或生物过程）中的偏差——尤其是选择与演化所引发的偏差。我们主张，组装理论作者在其基本论证中将物体可能组装的方式与因果方向性混为一谈，并得出结论：除某些已知且已确立的关联之外（其中部分关联已在此文评述），组装理论未能对选择或演化提供超越现有认知的解释。