\documentclass[12pt]{article}
\usepackage{amsmath, amssymb}
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\usepackage{natbib}
\usepackage{geometry}
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\title{
FRCMFD WATCHDOG PAPER — Exploratory Null Test \\
\large A Null Test for Correlations Between Residual Rotation-Curve Parameters \\
and Large-Scale Velocity-Field Kinematics
}
\author{Derek Flegg}
\date{May 2026}
\begin{document}
\maketitle
\begin{abstract}
We present an exploratory null test for correlations between the residual
rotation-curve parameter $\Delta\gamma_{\rm resid}$ and large-scale kinematic
observables derived from the 2M++ reconstructed velocity field. Using a matched
sample of 80 SPARC galaxies, we test for associations with directional
alignment, shear tensor eigenvalues, and vorticity magnitude. All tests control
for distance-dependent structure in the reconstructed field. Raw correlations
show weak trends, but all partial correlations (conditioning on distance) are
consistent with zero. Bootstrap confidence intervals and permutation tests
confirm the robustness of these null results. Within the SPARC $\times$ 2M++
overlap sample, we find no statistically significant evidence for coupling
between $\Delta\gamma_{\rm resid}$ and the tested kinematic variables.
\end{abstract}
\section{Introduction}
\input{intro.tex}
\section{Data and Sample}
\input{data.tex}
\section{Methodology}
\input{methods.tex}
\section{Results}
\input{results.tex}
\section{Discussion}
\input{discussion.tex}
\section{Conclusion}
\input{conclusion.tex}
\section*{Data and Code Availability}
All data and code are archived in the FRCMFD locked repository.
\section*{Acknowledgments}
We thank the SPARC and 2M++ teams for publicly available data.
\bibliographystyle{apalike}
\bibliography{references}
\end{document}
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