Incremental Emergence in Multifractal Asymmetry Spaces: Stabilization, Volatility, and Structural Position

This repository contains the manuscript and fully reproducible analysis code for the paper“Incremental Emergence in Multifractal Asymmetry Spaces: Stabilization, Volatility, and Structural Position.” The study investigates how hierarchical position in Fractal Asymmetry Theory (FAT) space is dynamically realized as an ensemble of datasets is assembled incrementally, rather than treating emergence depth as a static, final-state property. Using a single archived Unified Temporal–Measurement Framework (UTMF v5.2) FULL_DETAILS JSON snapshot containing subset-level multifractal outputs, dataset-level FAT vectors are reconstructed deterministically in post-processing. No raw data are accessed and no UTMF reruns are performed. An incremental growth experiment is then carried out: datasets are added one-by-one in random order, with full hierarchical clustering recomputed after each insertion. For each dataset, trajectory-valued Emergence Depth ED₅₀(k), rank evolution, stabilization scale, volatility, and insertion-induced structural reorganization are measured across many randomized growth realizations. Across 500 growth runs (as reported in the paper), emergence trajectories converge robustly toward well-defined final values, revealing: a universal emergence depth growth curvature, a sharp phase transition in rank stabilization, strong asymmetry in structural influence during insertion, and distinct dynamical structural roles among datasets. These properties are summarized using the Structural Position Descriptor (SPD) and the derived Structural Anchoring Index (SAI), which jointly characterize both the final geometric position of a dataset in FAT space and the dynamical pathway by which that position is reached. The analysis demonstrates that emergence in FAT space is neither instantaneous nor arbitrary. Instead, hierarchical position is realized through constrained, reproducible trajectories governed by latent structural properties that become manifest only through interaction with the ensemble itself. Contents Manuscript PDF Reproducible Python analysis script(FAT_ED_incremental_emergence_growth_analysis.py) Metadata references to the archived UTMF v5.2 FULL_DETAILS JSON Reproducibility Analysis operates exclusively on archived UTMF v5.2 metadata Dataset-level FAT vectors and Emergence Depth are reconstructed deterministically Incremental growth experiments are stochastic by design All figures in the paper correspond to 500 growth realizations Re-running the analysis with the same JSON snapshot, random seed, and number of runs reproduces the reported results Using different numbers of runs yields statistically consistent but not numerically identical results No learning, optimization, or model fitting is applied. Related resources UTMF v5.2 metadata archive: DOI 10.5281/zenodo.18149263 Fractal Asymmetry Theory (FAT): An Empirical Asymmetry Kernel Observed Across Physical Domains Emergence Depth: A Hierarchical Coordinate in Multifractal Asymmetry Spaces Structural Memory in Emergent Systems: Trajectories Beyond Emergence Depth Emergence Is Confined: Empirical Limits on Post–Emergent Structure Related works and software This study is part of a series of fully reproducible investigations based on the Unified Temporal–Measurement Framework (UTMF), Fractal Asymmetry Theory (FAT), and Emergence Depth (ED). Core methodological components include: jedi_mfdfa: A minimal and robust implementation of Multifractal Detrended Fluctuation Analysis, embedded verbatim in all UTMF metadata archives(Software DOI: 10.5281/zenodo.17982899; Paper DOI: 10.5281/zenodo.17990463) UTMF-Core: A universal framework for multifractal measurement across heterogeneous physical time series(Software DOI: 10.5281/zenodo.17808853; Paper DOI: 10.5281/zenodo.17905073) UTMF v5.1: Cross-domain multifractal coherence analysis(Software DOI: 10.5281/zenodo.17926485; Paper DOI: 10.5281/zenodo.17927721) UTMF v5.2: Subset design and stability regimes in multifractal analysis(Software DOI: 10.5281/zenodo.18096777; Paper DOI: 10.5281/zenodo.18098538) Foundational structural analyses include: Fractal Asymmetry Theory (FAT): An Empirical Asymmetry Kernel Observed Across Physical Domains(DOI: 10.5281/zenodo.17993683) Emergence Depth: A Hierarchical Coordinate in Multifractal Asymmetry Spaces(DOI: 10.5281/zenodo.18124466) Structural Memory in Emergent Systems – Trajectories Beyond Emergence Depth(DOI: 10.5281/zenodo.18149464) Emergence Is Confined: Empirical Limits on Post–Emergent Structure(DOI: 10.5281/zenodo.18192204) All incremental emergence analyses reported here operate on the same archived UTMF v5.2 FULL_DETAILS metadata snapshot(DOI: 10.5281/zenodo.18149263), ensuring a shared empirical foundation across the series. License Manuscript: CC-BY 4.0 Code: MIT License