Previously, we proved that any implementation of the concept of `copy number' underlying a hypothesis related to selection and evolution called Assembly Theory (AT) and its metric assembly index (Ai) claimed to unify biology and physics, is not fundamentally or methodologically different from Entropy-based algorithms like ZIP compression. Here we respond to new arguments that defend AT by showing some Ai's divergence from LZW for some specific provided examples. Here we show that the weak empirical correlation between Ai and LZW reported as evidence in favour of AT is based on incomplete and misleading experiments. When the experiments are completed and its behaviour is studied, fast asymptotic convergence to LZW compression and Shannon entropy is exhibited, in accordance with the mathematical proof previously offered, which remains undisputed. This contribution completes the theoretical and empirical demonstration that any variation of the copy-number concept underlying AT, which involves counting the number of repetitions in an object, such as a molecule, to arrive at a measure of life, is equivalent to popular statistical compression and Shannon entropy. We show that the authors' argument that the intractability of AT separates Ai from standard compression does not withstand basic scrutiny and that their empirical results separating organic from inorganic compounds have not only been previously reported, avoiding claims of grand unification between physics and biology, but are mostly driven by molecular length -- which the authors did not control for. This makes AT unsuitable and redundant, especially when applied to their own experimental data, on which we have proven that both Shannon entropy and LZ compression deliver equal or better results without the extra steps and the additional assembly jargon.

翻译：先前我们证明，任何基于"拷贝数"概念实现的选择与演化相关假说——即声称统一生物学与物理学的装配理论（AT）及其度量指标装配指数（Ai）——在本质上或方法论上与基于熵的算法（如ZIP压缩）并无区别。本文针对近期为AT辩护的新论点作出回应，该论点通过特定示例展示Ai与LZW算法的差异。我们指出，被引作AT证据的Ai与LZW之间微弱经验相关性，其实源于不完整且具有误导性的实验。当实验被完善并系统研究其行为时，Ai会快速渐近收敛于LZW压缩与香农熵，这与先前提出的数学证明完全一致，且该证明至今未被质疑。本研究成果从理论与实证层面完整论证：AT所依赖的拷贝数概念的任何变体（即通过统计对象如分子中的重复次数来量化生命特征）均等价于经典统计压缩与香农熵。我们表明，作者关于AT计算复杂性使Ai区别于标准压缩的论点经不起基本检验，且其区分有机与无机化合物的实证结果不仅早有报道（并未宣称实现物理与生物的大统一），而且主要受分子长度驱动——而作者未对此变量进行控制。这使得AT尤其在其自身实验数据上显得既不适用又冗余，因为我们已证明香农熵与LZ压缩在无需额外步骤和复杂装配术语的情况下，能取得同等或更优的结果。