This release accompanies the paper Fractal Entropy as a Constrained Trajectory:Spectral, Dynamical, and Structural Geometry under Subset Actualization This paper presents an empirical investigation of how operational fractal entropymeasures respond locally to admissible changes in measurement configuration.Rather than treating entropy as a static dataset-level quantity, the study reframesentropy variation as a constrained trajectory in a fixed measurement space inducedsolely by subset actualization. Rather than proposing new entropy definitions, dynamical models, or theoreticalinterpretations, the paper addresses a complementary descriptive question to thepreceding studies in this series: How does fractal entropy move under admissible measurement variation, and is thismotion free, diffusive, or geometrically constrained? Dataset ensemble and scope The analysis uses a composite ensemble of 123 empirical datasets drawn fromdiverse physical measurement domains and comprising 11,475 valid subsetrealizations. All datasets are processed identically using the Unified Temporal–MeasurementFramework (UTMF v5.2).No synthetic or surrogate datasets are included in the analysis presented in thispaper.The role of synthetic controls has been resolved in prior work and is not revisitedhere. All results are derived exclusively from a single archived composite metadatasnapshot containing complete subset-level multifractal outputs.No raw experimental data are accessed, and no multifractal spectra are recomputed. Entropy representation and measurement geometry The analysis focuses on two complementary operational entropy proxies deriveddirectly from multifractal measurement outputs: • spectral area entropy• spectral curvature entropy Together, these quantities define a two-dimensional empirical entropy space withinthe established Fractal Asymmetry Kernel (FAK) measurement geometry. Entropy variation is examined strictly at the measurement level.Entropy displacements are constructed as geometric steps between consecutiveadmissible subset realizations.No temporal ordering, dynamical interpretation, generative model, orinformation-theoretic entropy formalism is invoked. Entropy trajectories and local displacement statistics For each dataset, admissible subset realizations are deterministically ordered andinterpreted as an entropy trajectory in entropy space.From these trajectories, the paper analyzes: • trajectory confinement and global geometry• local entropy step magnitudes• directional organization of entropy displacements• cumulative entropy-space exploration per dataset• mean local entropy displacement as a dataset-level descriptor These quantities characterize how entropy responds locally and cumulatively tosubset actualization, independent of entropy magnitude or stability alone. Principal empirical findings The analysis establishes several robust empirical results: Constrained entropy motionAcross all empirical datasets, entropy trajectories are confined to a narrow,diagonally aligned manifold in entropy space.Entropy does not diffuse freely under subset variation but moves alonggeometrically constrained paths shared across domains. Incremental, non-diffusive variationLocal entropy displacements are predominantly small, with rare but admissible largesteps.The resulting step-magnitude distribution is heavy-tailed but bounded, indicatingincremental reconfiguration rather than random wandering. Directional anisotropyEntropy displacement directions are strongly anisotropic and bimodally distributed.Purely one-dimensional entropy changes are suppressed, revealing coupled variationbetween spectral area and curvature entropy components. Dataset-level heterogeneity within global boundsCumulative entropy-space exploration varies substantially across datasets.However, when normalized by step count, mean local entropy displacement exhibitsremarkable uniformity, indicating a shared local metric within entropy space despitedataset-specific responsiveness. Relation to prior work This paper extends the empirical program of Papers 1, 2 and 3 of the Fractal Entropy-serie. Earlier studies established empirical bounds, stability regimes, and domain-dependentcollapse behavior of fractal entropy measures.The present work complements those results by characterizing the geometry and motionof entropy under admissible measurement variation. Within the trajectory framework, entropy stability corresponds to confinement withinregions of reduced local displacement rather than convergence to a fixed value.Residual variability is therefore interpreted as structured motion rather than noise. Scope and interpretation All analyses are conducted strictly within FAK space and interpreted asmeasurement-level geometry. No assumptions are made regarding:• temporal dynamics• causality• optimization principles• thermodynamic entropy• evolutionary or generative mechanisms Entropy trajectories are not dynamical trajectories.They encode admissible geometric response to measurement variation only. What this paper actually does This paper does not introduce a new entropy theory, propose entropy laws, or claimuniversality of entropy dynamics. Instead, it empirically demonstrates that fractal entropy variation is: • geometrically constrained• directionally organized• path-dependent• dataset-specific but globally bounded By reframing entropy as a constrained trajectory rather than a static scalar, thepaper clarifies how entropy can be meaningfully compared across datasets and domainsunder a fixed measurement protocol. This archive contains • the full paper in PDF format• a self-contained Python analysis script reproducing all figures and results• a README describing scope, usage, and reproducibility All results are fully reproducible from a single archived UTMF v5.2 compositemetadata snapshot.No raw experimental data are included, and no multifractal computations are re-run. Citation If you use this archive, please cite both: • the Zenodo record itself, and• the accompanying paper included herein.