A Universal Measurement Geometry for Multifractal Analysis: Empirical Coherence, Hierarchical Structure, and the Fractal Asymmetry Kernel

This archive accompanies the paper: A Universal Measurement Geometry for Multifractal Analysis:Empirical Coherence, Hierarchical Structure, and the Fractal Asymmetry Kernel and provides the complete, reproducible analysis substrate underlying all figures, tables, and quantitative claims reported therein. Overview The archive contains five files that together define a strictlymeasurement-level, fully deterministic post-processing pipeline based on asingle archived output of the Unified Temporal–Measurement Framework(UTMF v5.2). All analyses operate exclusively on archived multifractal metadata.No raw time-series data are accessed, and no multifractal computations arere-executed. The empirical foundation of this archive is the composite metadata file: UTMF_CAPSTONE_COMPOSITE_v1.jsonDOI: https://doi.org/10.5281/zenodo.18407143 This JSON archive constitutes the explicit boundary between measurement andanalysis in the UTMF programme. Files included in this archive 📄 1. Capstone paper (PDF) A Universal Measurement Geometry for Multifractal Analysis.pdf The complete manuscript synthesizing Papers P1–P12 of the UTMF / FAT / ED / FAKresearch programme.All figures and quantitative results in the paper are generated by the scriptsincluded in this archive, operating on the referenced composite JSON. 📄 2. Analysis and plotting script utmf_capstone_v1.0_analysis_and_plotcell.py A single, self-contained Python analysis cell that: loads the composite UTMF metadata JSON, reconstructs FAT vectors, FAK increments, and hierarchical relations, computes Emergence Depth (ED₅₀), post-emergent structure, confinement metrics, and generates all plots used in the capstone paper. The script performs no learning, optimization, or adaptive fitting.Random sampling (where used) is controlled by fixed seeds.Execution is fully deterministic given the same inputs. 📄 3. Derived incremental emergence data FAK_P9_incremental_collapse_utmf_20260122_014330UTC.csv A deterministically derived table containing normalized incremental emergencetrajectories used in the analysis of universal curvature and rank stabilization(Paper P9). This CSV is generated directly from the composite UTMF metadata and contains nomanually edited or externally sourced data. 📄 4. CSV derivation script utmf_capstone_derive_ed_fak_csvs.py A preprocessing script that: reads the composite UTMF metadata JSON, reconstructs dataset-level FAT vectors, computes Emergence Depth (ED₅₀), derives Fractal Asymmetry Kernel (FAK) increments, and writes all CSV files used by the main analysis script. This script defines the exact, auditable transformation from archivedmeasurement metadata to tabular analysis inputs. 📄 5. README README.md A concise guide describing the archive structure, file roles, execution order,and reproducibility guarantees. Measurement scope and reproducibility All results are empirical and measurement-level. No physical models, dynamical assumptions, or causal interpretations areencoded in the data or code. The Fractal Asymmetry Kernel (FAK) and Emergence Depth (ED) are derived solelyfrom observed multifractal outputs under a fixed UTMF v5.2 protocol. Given the same composite JSON and scripts, all figures and numbers arereproduced exactly. This archive therefore constitutes a complete, auditable, and reproduciblemeasurement reference for multifractal analysis under UTMF v5.2. This work constitutes a measurement-level empirical synthesis and does not propose physical models or dynamical mechanisms. Citation If you use this archive, please cite both: the Zenodo record itself, and the accompanying capstone paper included herein.