The Fibre Obstruction for Assembly Theory: An AI-Generated, Machine-Checked Counterexample to Exact Quantification by Assembly Index and Copy Number

Assembly Theory proposes that assembly index and copy number can quantify the degree of selection or causation embodied in an observed ensemble. This paper tests the exact probabilistic interpretation of that claim. We present an infinite family of counterexamples under an undirected recursive-reuse process described in Assembly Theory’s published dynamics. The paired ensembles have identical assembly indices, identical copy numbers, identical assembly-index/copy-number profiles, and exactly the same calculated Assembly value. Nevertheless, their probabilities under the no-selection process differ by (2^n), where (n) is the copy number of the repeated object. The resulting information deficit is unbounded. The underlying obstruction is that assembly index records only the length of a shortest construction pathway, whereas the probability of producing an object depends on all available construction pathways. Assembly index plus copy number therefore discards information required to exactly quantify full-ensemble null surprisal or the minimum information-theoretic constraint needed to produce the ensemble. The result does not invalidate one-sided threshold detection or every possible definition of selection. It establishes a precise limitation on interpreting Assembly as an exact measure of selection-as-null-constraint. This work was produced through an AI-directed research experiment involving OpenAI’s Sol 5.6 and Anthropic’s Claude Opus 5 and Claude Fable 5. The research director selected the target claim and made the models available, but did not provide the mathematical reasoning or research workflow. ChatGPT independently designed the adversarial multi-model process, including hostile refereeing, independent reconstruction, correction tracking, and machine-checkable verification. The accompanying reproducibility bundle contains exact rational-arithmetic enumerators, 29 passing assertions, cryptographic hashes, the complete correction history, and external referee reports.