% Paper 037
% JMP0X1B Research working paper draft
% Generated for research.jmp0x1b.com
\documentclass[11pt]{article}
\usepackage[letterpaper,margin=1in]{geometry}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{booktabs,array}
\usepackage{hyperref}
\usepackage{fancyhdr}
\usepackage{lastpage}
\hypersetup{colorlinks=true,linkcolor=black,citecolor=black,urlcolor=black}
\setlength{\parindent}{0pt}
\setlength{\parskip}{0.65em}
\setlength{\headheight}{14pt}
\emergencystretch=3em
\sloppy

\newcommand{\paperid}{Paper 037}
\newcommand{\papertitle}{Cogravitational Induction and Moving-Mass Observables}
\newcommand{\papersubtitle}{Rotation, translation, and time-dependent mass-current signatures in a Jefimenko-compatible field model}
\newcommand{\paperdate}{June 14, 2026}
\newcommand{\gfield}{\mathbf{g}}
\newcommand{\kfield}{\mathbf{K}}
\newcommand{\J}{\mathbf{J}}
\newcommand{\A}{\mathbf{A}}
\newcommand{\R}{\mathbf{R}}
\newcommand{\x}{\mathbf{x}}
\newcommand{\xp}{\mathbf{x}'}
\newcommand{\vvec}{\mathbf{v}}
\newcommand{\dd}{\,\mathrm{d}}
\newcommand{\tr}{t_{\mathrm r}}
\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}
\newcommand{\order}{\mathcal{O}}
\newtheorem{claim}{Claim}
\newtheorem{proposal}{Proposal}
\newtheorem{definition}{Definition}

\pagestyle{fancy}
\fancyhf{}
\lhead{JMP0X1B Research}
\rhead{Working paper draft}
\cfoot{\thepage\ of \pageref{LastPage}}

\begin{document}

\begin{center}
{\Large \textbf{\paperid}}\\[0.5em]
{\LARGE \textbf{\papertitle}}\\[0.35em]
{\large \papersubtitle}\\[0.8em]
JMP0X1B Research Group\\
Working paper draft / \paperdate
\end{center}

\begin{abstract}
This proposal develops a moving-mass observable catalogue for Jefimenko-style gravity/cogravity. It derives leading expressions for translating point masses and rotating compact sources, classifies the sign behavior of candidate signals under reversal controls, and identifies induction-style loop observables from the equation curl g equals minus the time derivative of K. The paper emphasizes scale honesty: laboratory cogravity from ordinary rotors is expected to be extremely small, so near-term value comes from null discipline, artifact separation, and bridges to geophysical and astrophysical tests.
\end{abstract}

\textbf{Status.} Draft manuscript for review and revision. This paper is not an empirical claim of new physics or field-ready technology. It is a structured proposal, theory note, protocol, or application architecture intended to be auditable, falsifiable, and publishable with source.

\tableofcontents
\newpage


\section{Problem}
The gravity/cogravity equations imply velocity-dependent fields from moving mass. The obvious temptation is to jump from that observation to propulsion or anomalous force claims. This paper takes the opposite route: build a catalogue of moving-mass signatures, parity rules, and scale estimates before any claim is allowed.

The target is a proposal paper that answers three questions. What cogravity field is produced by translating, rotating, and accelerating mass currents? Which observables change sign under source reversal? Which effects are already too small for direct laboratory detection but still useful as null-test templates?

\section{Model}
For a compact source, the cogravity field is
\begin{equation}
\kfield(\x,t)=-\frac{G}{c^2}\int\left(\frac{[\J]}{R^3}+\frac{[\partial_t\J]}{cR^2}\right)\times\R\,\dd^3x'.
\end{equation}
For a point source of mass $M$ with velocity $\vvec_s$ and acceleration $\mathbf a_s$, the leading retarded expression is
\begin{equation}
\kfield_s(\x,t)=-\frac{GM}{c^2}\left(\frac{[\vvec_s]\times\R}{R^3}+\frac{[\mathbf a_s]\times\R}{cR^2}\right),
\end{equation}
with all source quantities evaluated at $t-R/c$.

A test body with velocity $\vvec_t$ receives the velocity-dependent acceleration
\begin{equation}
  \mathbf a_C=\vvec_t\times\kfield_s.
\end{equation}
The sign is odd under reversal of the source velocity and odd under reversal of the detector velocity.

For a localized steady current, define the mass-current dipole
\begin{equation}
  \mathbf m_G=\frac{1}{2}\int \xp\times\J(\xp)\dd^3x'.
\end{equation}
The far-field cogravity is
\begin{equation}
  \kfield(\x)\simeq -\frac{G}{c^2r^3}\left(3\hat{\mathbf r}(\mathbf m_G\cdot\hat{\mathbf r})-\mathbf m_G\right).
\end{equation}
For a rigid rotor about a principal axis, $\mathbf m_G=\mathbf L/2$, where $\mathbf L$ is angular momentum. This gives the scale
\begin{equation}
  |\kfield|\sim \frac{G L}{2c^2r^3}.
\end{equation}
A laboratory rotor with $L\sim10^4\,\mathrm{kg\,m^2\,s^{-1}}$ at $r\sim1\,\mathrm m$ gives $|\kfield|\sim 4\times10^{-24}\,\mathrm{s^{-1}}$. Earth gives a near-surface dipole scale of order $10^{-14}\,\mathrm{s^{-1}}$. These scales set expectations before instrumentation is discussed.

\section{Claims}
\begin{claim}[Moving-mass observables are parity objects]
Every proposed cogravity observable should be classified by its sign under source reversal, detector reversal, spatial inversion, and time reversal. Without this parity ledger, cogravity signals are easily confused with vibration, thermal drift, magnetic pickup, or Newtonian multipole leakage.
\end{claim}

\begin{claim}[Cogravitational induction is a loop observable]
Equation $\nabla\times\gfield=-\partial_t\kfield$ implies
\begin{equation}
\oint_C \gfield\cdot\dd\boldsymbol\ell=-\frac{\dd}{\dd t}\int_S \kfield\cdot\dd\mathbf S.
\end{equation}
Time-varying mass currents should therefore be modeled as induction problems, not merely as instantaneous force calculations.
\end{claim}

\begin{claim}[Laboratory rotating-mass signals are expected to be tiny]
Near-term tabletop searches should not be presented as likely discoveries. Their honest role is to develop reversal discipline, artifact ledgers, and upper-bound machinery that can be reused in stronger astrophysical or geophysical contexts.
\end{claim}

\begin{claim}[Astrophysical checks are part of the same catalogue]
Frame-dragging, translational gravimagnetism, and binary timing are not optional background. They are high-leverage comparisons for any Jefimenko-compatible moving-mass model.
\end{claim}

\section{Evidence Plan}
The paper should publish a source catalogue with analytic and numerical entries:
\begin{enumerate}
\item uniformly translating point mass;
\item counter-translating mass pair with zero net momentum;
\item rigid rotating sphere;
\item thin ring and counter-rotating ring pair;
\item accelerated mass-current pulse;
\item binary point-mass toy model.
\end{enumerate}
Each entry should provide $\rho$, $\J$, the continuity residual, leading $\gfield$ and $\kfield$, parity signatures, and estimated magnitude.

A compact parity table should be part of the release:
\begin{center}
\begin{tabular}{llll}
\toprule
Control & $\gfield_N$ & $\kfield$ & common artifact \\
\midrule
source velocity reversal & even & odd & motor magnetic pickup odd/even mixed \\
detector velocity reversal & even & force odd & readout phase error odd \\
source mass swap & scales with mass & scales with mass current & vibration may not scale \\
co- vs counter-rotation & Newtonian similar & cogravity changes & bearing heating changes \\
\bottomrule
\end{tabular}
\end{center}

\section{JMP0X1B Implementation Surface}
A cogravity signature catalogue can be represented as source records with reversible controls:
\begin{verbatim}
record MovingMassSignature {
  source_family, rho, J, controls,
  predicted_g, predicted_K, parity, magnitude, artifacts
}
fn compare_controls(sig, run_pair) -> ResidualLedger
\end{verbatim}
The catalogue feeds the finite-element solver, the laboratory protocol, and the observational-bounds paper.

\section{Release and Review Plan}
Release a PDF, LaTeX source, analytic notebooks, and machine-readable signature records. Review should reject any entry that does not specify source support, continuity, retarded-time convention, reversal parity, and ordinary Newtonian multipole background.

\section{Open Questions}
\begin{itemize}
\item Which moving-mass geometries maximize cogravity parity while cancelling Newtonian multipoles?
\item Can atom interferometers provide useful bounds, or do seismic and Newtonian gradients dominate completely?
\item Which astrophysical observables are cleanest for translational mass-current effects?
\item Is there a useful reduced-order model for time-dependent cogravitational induction?
\end{itemize}


\section{Conclusion}
This paper turns one part of the gravity/cogravity idea into a named, reviewable work package. Its value does not depend on treating the framework as established physics. The value is the disciplined reduction of a speculative field analogy into equations, invariants, bounds, null tests, and release artifacts that can be audited and either extended or killed.

\section*{References}
\addcontentsline{toc}{section}{References}

\begin{thebibliography}{99}
\bibitem{jefimenko2000}
O. D. Jefimenko. \emph{Causality, Electromagnetic Induction, and Gravitation: A Different Approach to the Theory of Electromagnetic and Gravitational Fields}. Electret Scientific, 2nd ed., 2000.

\bibitem{jefimenko2006}
O. D. Jefimenko. \emph{Gravitation and Cogravitation: Developing Newton's Theory of Gravitation to its Physical and Mathematical Conclusion}. Electret Scientific, 2006.

\bibitem{heaviside1893}
O. Heaviside. A gravitational and electromagnetic analogy. \emph{The Electrician}, 31:281--282 and 359, 1893.

\bibitem{ruggiero2021}
M. L. Ruggiero. A note on the gravitoelectromagnetic analogy. arXiv:2111.09008, 2021.

\bibitem{kopeikin2005}
S. M. Kopeikin and E. B. Fomalont. Gravimagnetism, causality, and aberration of gravity in the gravitational light-ray deflection experiments. arXiv:gr-qc/0510077, 2005.

\bibitem{everitt2011}
C. W. F. Everitt et al. Gravity Probe B: Final results of a space experiment to test general relativity. \emph{Physical Review Letters}, 106:221101, 2011. arXiv:1105.3456.

\bibitem{jmp001}
JMP0X1B Research Group. Twelve Five-Dimensional Projection Models for Maxwell-Compatible Electromagnetism. Working paper, 2026. \url{https://research.jmp0x1b.com/papers/twelve-5d-projection-electromagnetism.html}

\bibitem{jmp005}
JMP0X1B Research Group. Weak-Field Radion Electrogravity from Maxwell-Compatible Five-Dimensional Projections. Working paper, 2026. \url{https://research.jmp0x1b.com/papers/weak-field-radion-electrogravity.html}

\bibitem{jmp017}
JMP0X1B Research Group. Conservation-First Stress-Energy Audits for Closed Electromagnetic Devices. Working paper, 2026. \url{https://research.jmp0x1b.com/papers/conservation-first-stress-energy-audits.html}

\bibitem{jmp023}
JMP0X1B Research Group. A Research Program for Maxwell-Compatible Projection Electromagnetism. Working paper, 2026. \url{https://research.jmp0x1b.com/papers/a-research-program-for-maxwell-compatible-projection-electromagnetism.html}
\end{thebibliography}


\end{document}
