Deconstructing Emergent Signatures in the Detrended Mertens Function: A Methodological Evaluation

This work presents a methodological evaluation of commonly reported dynamical signatures in the detrended Mertens function, [ S(x)={M(x)}{√x}. ] Using a hierarchy of increasingly constrained null models, the study re-examines three widely discussed quantities: the Memory Collapse Ratio (MCR), Random Phase Surrogate (RPS) response, and the Higuchi Fractal Dimension. The results show that these signatures can be explained by cumulative integration, marginal step statistics, and deterministic square-free structure without requiring additional nonlinear dynamical mechanisms. The proposed framework emphasizes the importance of hierarchy-matched null models when interpreting feature-space statistics of arithmetic sequences. This repository contains the complete manuscript (PDF) together with the bibliographic information required for citation.