Assembly Theory is an approximation to algorithmic complexity based on LZ compression that does not explain selection or evolution

We demonstrate that Assembly Theory (AT) is reliant on Shannon Entropy and a method based upon statistical compression that belongs to the LZ family of compression algorithms, family which comprises popular algorithms used in ZIP, GZIP, or JPEG. Such popular algorithms have been shown to empirically reproduce the results of AT that were reported before in successful applications to separating organic from non-organic molecules and in the context of the study of selection and evolution. In particular, the assembly index calculation method is an LZ compression scheme, even if used for classification or explanatory purposes. 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 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 made with Shannon Entropy or had not been reported before with algorithmic complexity.