% Paper 039
% 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 039}
\newcommand{\papertitle}{Null Experiments for Laboratory Cogravity with Symmetry-Matched Moving Masses}
\newcommand{\papersubtitle}{A falsification-first protocol for rotating, translating, and modulated dense sources}
\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 designs laboratory cogravity experiments as null-bounding and artifact-classification studies. It gives a signal model with an effective amplitude $\beta_C$, explains why the strict Jefimenko-scale signal from ordinary rotors is far below near-term tabletop sensitivity, and defines a reversal-controlled run matrix for rotating and translating source masses. The deliverable is not a breakthrough claim; it is a signed likelihood over $\beta_C$, nuisance templates, and failed controls suitable for a JMP0X1B null ledger.
\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}
Laboratory cogravity claims are vulnerable because the expected signal from ordinary moving masses is extraordinarily small while mundane artifacts are plentiful. The problem is not to design a sensational experiment. The problem is to design a null protocol that would make any future claim legible: controls first, signal model first, bounds first.

This proposal treats the laboratory as a falsification and artifact-classification platform. A positive result is not expected. A useful negative result is expected if it improves upper bounds on effective cogravity amplification or eliminates a family of apparatus mistakes.

\section{Model}
Let $y(t)$ be a force, torque, phase, or acceleration readout. The proposed analysis model is
\begin{equation}
  y(t)=\beta_C S_C(t)+\sum_i \theta_i N_i(t)+\epsilon(t),
\end{equation}
where $S_C(t)$ is the cogravity signature exported by the solver, $\beta_C$ is an effective amplitude parameter, $N_i(t)$ are nuisance templates, and $\epsilon(t)$ is residual noise. In the strict Jefimenko normalization $\beta_C=1$. A laboratory search can instead report an upper bound on $|\beta_C|$ relative to the model.

For a rotor of angular momentum $L$ at distance $r$, the natural cogravity scale is
\begin{equation}
  K_{\rm lab}\sim \frac{G L}{2c^2r^3}.
\end{equation}
For $L=10^4\,\mathrm{kg\,m^2\,s^{-1}}$ and $r=1\,\mathrm m$, this is approximately $4\times10^{-24}\,\mathrm{s^{-1}}$. A detector moving at $1\,\mathrm{m\,s^{-1}}$ would therefore see an acceleration scale near $10^{-24}\,\mathrm{m\,s^{-2}}$. This is far below ordinary tabletop backgrounds.

The experimental goal is therefore not detection at $\beta_C=1$. The goal is to constrain large effective deviations, validate reversal methods, and publish artifact ledgers.

\section{Claims}
\begin{claim}[Symmetry matching is mandatory]
A cogravity laboratory protocol must include source reversal, counter-rotation, dummy-mass runs, detector reversal where possible, distance modulation, vibration monitors, magnetic monitors, thermal monitors, and blind analysis. Omitting these controls makes the result uninterpretable.
\end{claim}

\begin{claim}[Newtonian multipole leakage is the first enemy]
Moving masses create time-dependent Newtonian gradients through imperfect balancing, eccentricity, bearing motion, and building vibration. A cogravity channel is not credible until Newtonian multipoles have been measured, bounded, or cancelled below the claimed residual.
\end{claim}

\begin{claim}[Nulls should be published as likelihoods]
A null experiment should report a likelihood or posterior over $\beta_C$ and nuisance parameters, not a binary statement that nothing happened. The null result then becomes useful input for a Bayesian null ledger.
\end{claim}

\begin{claim}[The kill criterion is quantitative]
If nuisance templates explain the reversible channel with stable coefficients across blind runs, or if the inferred $\beta_C$ changes under apparatus relocation, the candidate signal is killed unless a new pre-registered mechanism predicts that behavior.
\end{claim}

\section{Evidence Plan}
A first experiment can use two symmetry-matched source modules: co-rotating, counter-rotating, and dummy-loaded states with equal mechanical power and matched thermal paths. The detector may be a torsion balance, accelerometer stack, atom-interferometer channel, or other precision inertial readout. The exact sensor is less important than the control schedule.

The minimum run matrix is
\begin{center}
\begin{tabular}{llll}
\toprule
Run class & source state & expected cogravity parity & primary nuisance \\
\midrule
A & rotor forward & $+$ & vibration, magnetic pickup \\
B & rotor reverse & $-$ & bearing asymmetry \\
C & counter-rotating pair & cancellation or selected gradient & motor heating \\
D & dummy inertia & 0 & thermal and acoustic \\
E & source displaced & distance scaling & floor coupling \\
F & blinded mixed order & model-defined & analyst bias \\
\bottomrule
\end{tabular}
\end{center}

The analysis should fit all runs simultaneously and report the posterior for $\beta_C$. A result is publishable even when the posterior is wide, provided the apparatus metadata and nuisance ledger are complete.

\section{JMP0X1B Implementation Surface}
This protocol can be encoded as a typed experiment plan:
\begin{verbatim}
record CogravityNullRun {
  source_state, reversal_id, detector_state,
  environmental_channels, blind_label, signature_digest
}
record BetaBound { beta_C_interval, nuisance_model, controls_passed }
fn analyze_null(runs, signature) -> BetaBound effects{Audit, Statistics}
\end{verbatim}
The result should feed NullLedger and the formal verification protocol for frontier physics experiments.

\section{Release and Review Plan}
Release the apparatus diagram, source mass ledger, motor state schedule, raw time series, environmental channels, blind labels after unblinding, solver signature, analysis code, and posterior over $\beta_C$. The paper should state explicitly that the expected $\beta_C=1$ signal is below near-term laboratory sensitivity unless the apparatus has an independently justified amplification mechanism.

\section{Open Questions}
\begin{itemize}
\item Which sensor class gives the best bound on large effective deviations from the Jefimenko normalization?
\item Can source modules be designed so Newtonian multipoles cancel while cogravity parity survives?
\item What environmental channels best predict false reversal-odd signals?
\item How should failed apparatus designs be published so later groups do not repeat them?
\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}
