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<p>Assembly Theory (AT) and its central measure, the assembly index (Ai), provide an opportunity to clarify persistent issues at the interface of computability, compression, and complexity in science. Presented as a novel measure of molecular complexity and as an explanation for selection and evolution, AT can instead be analysed and reproduced using established results from classical information theory, statistical compression, and algorithmic complexity. We show that the latest defence of AT relies on experiments that are incomplete as controls and do not establish the separation between Ai and standard compression-based measures. When extended and compared against established baselines, these experiments reveal substantial overlap in both concept and method with dictionary-based statistical compression algorithms, consistent with our previous formal proof that Ai is mathematically equivalent to the Shannon entropy rate through dictionary-based compression, a result that remains unchallenged. Through theoretical and empirical analysis, we show that Ai offers no new causal or informational insight beyond what existing statistical indices already offer. Rather than establishing the broad explanatory role claimed for AT, the evidence currently supports a more limited interpretation of Assembly Theory as a restricted version of a statistical-compression approach and related measure. We also show that Ai is a special case of an earlier and stronger metric grounded in algorithmic complexity, based on decomposing objects into causal blocks. Finally, we identify multiple technical problems in AT’s computational time-complexity arguments.</p>

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Assembly theory collapses to dictionary compression and is rendered redundant by common statistical algorithms

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月4日

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  • Luan Ozelim,
  • Abicumaran Uthamacumaran,
  • Felipe S. Abrahão,
  • Santiago Hernández-Orozco,
  • Narsis A. Kiani,
  • Jesper Tegnér,
  • Francisco Hernández-Quiroz,
  • Hector Zenil

摘要

Assembly Theory (AT) and its central measure, the assembly index (Ai), provide an opportunity to clarify persistent issues at the interface of computability, compression, and complexity in science. Presented as a novel measure of molecular complexity and as an explanation for selection and evolution, AT can instead be analysed and reproduced using established results from classical information theory, statistical compression, and algorithmic complexity. We show that the latest defence of AT relies on experiments that are incomplete as controls and do not establish the separation between Ai and standard compression-based measures. When extended and compared against established baselines, these experiments reveal substantial overlap in both concept and method with dictionary-based statistical compression algorithms, consistent with our previous formal proof that Ai is mathematically equivalent to the Shannon entropy rate through dictionary-based compression, a result that remains unchallenged. Through theoretical and empirical analysis, we show that Ai offers no new causal or informational insight beyond what existing statistical indices already offer. Rather than establishing the broad explanatory role claimed for AT, the evidence currently supports a more limited interpretation of Assembly Theory as a restricted version of a statistical-compression approach and related measure. We also show that Ai is a special case of an earlier and stronger metric grounded in algorithmic complexity, based on decomposing objects into causal blocks. Finally, we identify multiple technical problems in AT’s computational time-complexity arguments.