Assembly Theory (AT) and its central measure, the assembly index (Ai), represent an invaluable opportunity to address some of the most persistent and widespread conflations and misconceptions about computability and complexity theory in science. The AT defence embodies several common concurrent misconceptions that pile on each other: the belief that Turing machines impose artefactual constraints, the mischaracterisation of Kolmogorov complexity as inapplicable, and the claims around Ai as different from Shannon entropy or compression algorithms. Here we show that the new arguments advanced by the AT group in their defence, are based on misleading and incomplete experiments that, when completed, show the extent of the correlations and overlapping with popular statistical compression algorithms, conforming with the mathematical equivalence to Shannon entropy previously mathematically proved and reported, which remains undisputed. Through theoretical and empirical analysis, we show that Ai does not offer a path towards fundamental novel causal or informational insights beyond what existing statistical frameworks already offer. Rather than offering a unifying theory of life as the AT authors suggest, we argue that AT obfuscates the field and provides a cautionary example of how the accumulation of conceptual mistakes can lead to a misleading theory. Finally, we show that Ai is a particular limited case of another complexity metric based on algorithmic (Kolmogorov) complexity, consisting of decomposing an object into its causal blocks that goes beyond, and outperforms, AT.

翻译：组装理论（AT）及其核心度量指标——组装指数（Ai），为解决科学中关于可计算性与复杂性理论最顽固且普遍的混淆与误解提供了宝贵契机。AT的辩护体现了多个相互叠加的常见并发误解：认为图灵机施加了人为约束、对柯尔莫哥洛夫复杂性不适用性的错误描述，以及声称Ai与香农熵或压缩算法存在本质差异。本文通过理论与实证分析表明，AT团队在其辩护中提出的新论点基于不完整且具有误导性的实验；当实验完善后，可揭示其与主流统计压缩算法的高度相关性与重叠性，这与先前已数学证明且无争议的、AT与香农熵的数学等价性一致。我们证明Ai并未提供超越现有统计框架的新型因果或信息洞察路径。与AT作者所声称的‘生命统一理论’相反，我们认为AT混淆了该领域的研究方向，并警示了概念错误的积累如何导致误导性理论的形成。最后，我们证明Ai是基于算法（柯尔莫哥洛夫）复杂性的另一种复杂度度量的特定受限案例，该方法通过将对象分解为因果模块，在性能与广度上均超越了AT。