The Fractal Asymmetry Kernel (FAK): A Universal Statistical Geometry Observed Across Multifractal Measurements

This archive accompanies the paper: The Fractal Asymmetry Kernel (FAK):A Universal Statistical Geometry Observed Across Multifractal Measurements Scientific context This paper introduces the Fractal Asymmetry Kernel (FAK):a domain-independent empirical kernel governing local asymmetry updates inmultifractal measurement spaces. FAK is defined as the pooled statistical distribution of normalizedsubset-to-subset fractal-dimension updates derived from theUnified Temporal–Measurement Framework (UTMF).Where earlier work focused on hierarchical embedding, emergence timing, orstructural ordering, this study isolates the measurement-level update geometryof multifractal asymmetry itself. The kernel is constructed entirely in post-processing from archived UTMF outputs.No raw data are accessed, and no UTMF computations are rerun. Although the incremental ensemble construction protocol was originally developedfor Emergence Depth (ED) analysis, it is used here solely as an observationalscaffold to generate large numbers of comparable local asymmetry update events.No claims of temporal dynamics, causality, learning, or evolution are introduced. Empirical scope and findings Using a heterogeneous ensemble of 114 datasets(81 empirical and 33 synthetic), spanning: gravitational-wave strain data, cosmological maps, large-scale structure surveys, particle physics event streams, pulsar timing residuals, atomic spectra, astrometric catalogues, quantum random number generators, the paper demonstrates that: normalized asymmetry updates collapse onto a single, symmetric,heavy-tailed distribution across all domains; the kernel exhibits a near-Gaussian core with systematic,reproducible non-Gaussian tails; kernel structure is robust under dataset reordering, subset shuffling,reversal, duplication, and synthetic augmentation; independence diagnostics show weak, bounded dependence without long-rangememory or directional dynamics; kernel structure is decoupled from Emergence Depth, hierarchical position,and stabilization timing. Together, these results establish the Fractal Asymmetry Kernel as ameasurement-level empirical constraint on how multifractal asymmetry islocally realized under a fixed estimation protocol. No generative, causal, or physical interpretation is imposed.All conclusions are strictly empirical. Contents of this archive This Zenodo release contains: the final PDF of the paper“The Fractal Asymmetry Kernel (FAK): A Universal Statistical Geometry ObservedAcross Multifractal Measurements”; a paper-grade Python analysis cell that generates all 11 figuresreported in the paper directly from archived metadata and the accompanying CSV; a CSV file containing per-dataset Fractal Asymmetry Kernel structuraldescriptors, including final ED50 position, rank stabilization timing,volatility measures, and insertion-impact statistics; the exact Python cell used to generate this CSV, implementing thestandard incremental growth experiment and exporting the resulting metrics; a README.md describing execution, data dependencies, and reproducibility. The CSV filename encodes the timestamp of the source JSON snapshot, providingexplicit verification of the metadata–analysis linkage. Data dependency All analyses rely on the following archived metadata snapshot: UTMF v5.2 FULL_DETAILS metadata archiveFilename: FULL_DETAILS_utmf_v5.2_20260112_011327 UTC.jsonDOI: https://doi.org/10.5281/zenodo.18226887 This JSON file contains complete subset-level multifractal outputs for alldatasets processed under an identical UTMF v5.2 configuration. All Fractal Asymmetry Kernel quantities—including normalized asymmetry updates,increment distributions, conditional kernels, stress tests, and per-datasetstructural descriptors—are reconstructed deterministically in post-processingfrom this archive. The included CSV is a derived artifact produced exclusively from this snapshotusing the provided CSV-generator cell. Scope and reuse This release documents a fully reproducible, data-driven characterizationof the Fractal Asymmetry Kernel. It is intended as a reference for: empirical studies of multifractal asymmetry update geometry; cross-domain comparison of multifractal measurements; methodological analysis of subset-based multifractal estimation; future quantitative characterization of kernel structure(e.g. tail indices, higher-order moments, and parametric approximations). The archive does not include: raw experimental measurements; UTMF execution code; the FULL_DETAILS metadata itself (archived and cited separately). Relation to prior and subsequent work This paper builds on: Fractal Asymmetry Theory (FAT), the Unified Temporal–Measurement Framework (UTMF v5.2), earlier Emergence Depth (ED) studies. It is analytically distinct from work on hierarchical emergence,post-emergent trajectories, or structural memory. Quantitative parametrization of the Fractal Asymmetry Kernel(e.g. tail indices, kurtosis, goodness-of-fit testing) is deferred to dedicatedfollow-up studies. All upstream software, metadata archives, and datasets are archived independentlyand cited explicitly in the paper.