Systematic Trends of Temporal Membrane Effects Based on History Retention in Galaxy Rotation Curves

Galaxy rotation curves have long been discussed as evidence for dark matter or modifications of gravitational dynamics.
In this work, we reexamine these systematic discrepancies within the framework of Temporal Membrane Theory (TMT), interpreting them not as new dynamical components or geodesic modifications, but as history-retained correction effects arising from gradients in reconstructed temporal structure.

In this study, the term history retention refers to a situation in which correction effects induced by the temporal membrane are not relaxed or re-adjusted during subsequent evolution, but are continuously preserved and reflected in the reconstructed observational rotation structure.
These effects appear only at the level of observational reconstruction and do not correspond to physical modifications of local time flow, particle dynamics, or geodesic motion.

Using existing galaxy rotation curve data, we analyze the systematic behavior of temporal membrane parameters without introducing any additional correction terms or free parameters.
The fitting procedure is performed independently for each galaxy, and no information about galaxy age, morphology, or distance is used during parameter estimation.

Our results show that temporal membrane effects do not exhibit a simple causal dependence on observational distance.
Instead, they are systematically organized according to how strongly temporal membrane correction effects have been retained over a galaxy’s evolutionary history, for which galaxy diameter serves as a practical proxy.

Furthermore, we demonstrate that apparent distance correlations disappear once galaxy size is controlled, while systematic trends remain with respect to history retention.
We also reinterpret the absence of spiral arm structures in massive galaxies not as a failure of arm formation mechanisms, but as a visibility limit imposed by temporal structure, where excessive temporal membrane gradients destroy azimuthal phase coherence in observational reconstruction.

Importantly, this work does not claim that galaxy rotation curves are generated as a structural necessity of temporal membrane effects.
Rotation structures are understood as the result of multiple contributing factors—baryonic distribution, formation history, environment, and interactions—within which temporal membrane effects appear as a conditionally retained, observationally reconstructed component.

This study provides an alternative organizational framework for galaxy rotation curves, repositioning the problem from dynamical modification to the structure of observational time reconstruction.
All summarized datasets used for post-analysis are provided as supplementary materials.