Structural Memory in Emergent Systems: Trajectories Beyond Emergence Depth

This archive accompanies the paper: Structural Memory in Emergent Systems: Trajectories Beyond Emergence Depth The paper investigates how emergent systems are structurally organized after their point of emergence, using hierarchical geometry derived fromFractal Asymmetry Theory (FAT) representations. Scientific context Emergence Depth (ED) was previously introduced as a scalar, hierarchy-derivedcoordinate that marks the linkage height at which a dataset becomesstructurally unavoidable within a population embedded in FAT space.While ED₅₀ captures *when* a dataset emerges, it does not describe *how*structural organization continues beyond that point. This work extends the Emergence Depth framework by introducingpost-emergent structural trajectory metrics derived directly from thehierarchical dendrogram topology:- the number of hierarchical merge steps after emergence;- the cumulative linkage height accumulated along the post-emergent path. Together, these quantities characterize the structural memory of a dataset:the amount of hierarchical organization that remains accessible after emergence. Empirical findings Using a heterogeneous ensemble of 108 datasets(78 empirical and 30 synthetic), the paper shows that:- Emergence Depth is strongly negatively correlated with post-emergent structural trajectory length;- datasets that emerge early tend to occupy deep, highly structured regions of FAT space;- datasets that emerge late typically undergo minimal subsequent hierarchical integration;- datasets with similar ED₅₀ values can nevertheless follow markedly different post-emergent structural trajectories. These patterns are observed consistently across physical domains and persistwhen synthetic datasets are removed, indicating that they arise from thegeometry of FAT space rather than domain-specific effects. No generative, causal, or temporal assumptions are introduced.All results are strictly empirical and derived from archived multifractaloutputs. Contents of this archive This Zenodo release contains:- the final PDF of the paper;- the exact Python analysis cell used to generate all figures and quantitative results reported in the paper.- a README.md The analysis code operates exclusively on archived UTMF v5.2 metadata anddoes not rerun the UTMF pipeline or access any raw data. Data dependency All analyses rely on a single archived metadata snapshot: - UTMF v5.2 FULL_DETAILS metadata archive DOI: https://doi.org/10.5281/zenodo.18149263 This JSON file contains subset-level multifractal outputs for 108 datasets,processed through the identical UTMF v5.2 pipeline configuration.Dataset-level FAT vectors and Emergence Depth values are reconstructeddeterministically in post-processing. Scope and reuse This release documents a reproducible, data-driven extension of the EmergenceDepth framework.It is intended as a reference for:- hierarchical analysis in multifractal asymmetry spaces;- comparative studies of emergent structure across heterogeneous systems;- methodological reuse of Emergence Depth and post-emergent trajectory metrics. The archive does not include raw measurements, UTMF execution code, or theFULL_DETAILS metadata itself, which are archived and cited separately. This paper builds on:- Fractal Asymmetry Theory (FAT),- the Emergence Depth (ED) framework,- and the UTMF v5.x measurement pipeline. All upstream software and datasets are archived independently and citedexplicitly in the paper.