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\title{\Large Paper 015\\[0.6em]\textbf{Screened Scalar Readout in Electrostatic Energy Geometries}\\[0.3em]\large Range-dependent null predictions for radion-style projection models}
\author{JMP0X1B Research Group}
\date{Working paper draft / June 13, 2026}
\begin{document}
\maketitle
\begin{abstract}
Weak-field radion electrogravity turns electrostatic energy density into a scalar-source term and then asks whether gravity-like readout is constrained by null experiments. This paper extends that model to screened scalar responses. A scalar may be short-range, material-screened, geometry-screened, or environment-screened. Each case changes which capacitor dimensions and dielectric boundaries dominate the predicted residual. The output is a null-test map over scalar range, screening length, and geometry scale.
\end{abstract}

\noindent\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}
A scalar sourced by electrostatic energy density can look trivial if its range is either much shorter or much longer than the device. Existing weak-field bounds are useful, but experimental design needs range-specific observables. The problem is to decide which apparatus scales and material substitutions constrain which scalar regimes.

\section{Model}
We introduce a scalar s with source u\_E, mass m\_s, material coupling q(x), and optional screening term S(s,rho\_m). The linear regime yields a Green-function convolution; the nonlinear screened regime is treated by conservative envelopes. Scale pairs and dielectric swaps are the key controls.


\[
  (\nabla^2-m_s^2)s = -\alpha_E q(\mathbf{x})u_E(\mathbf{x}) - S(s,\rho_m),
  \qquad u_E=\frac{\epsilon E^2}{2}.
\]
\[
  F_s \sim \gamma_s c^2 \int_B \rho_B(\mathbf{x})\nabla s(\mathbf{x})\,d^3x,
  \qquad
  \Lambda=\{\lambda_s,\lambda_{\mathrm{screen}},L_{\mathrm{device}},L_{\mathrm{edge}}\}.
\]


\section{Claims}
\begin{enumerate}
\item \textbf{Claim 1.} Scalar projection searches should report exclusion as a surface over range and screening assumptions.
\item \textbf{Claim 2.} A single device scale cannot rule out both edge-local and device-scale scalar regimes.
\item \textbf{Claim 3.} Dielectric swaps are as important as voltage scans because material weighting can imitate or suppress scalar sourcing.
\item \textbf{Claim 4.} Symmetric thrust nulls do not eliminate local scalar energy-density gradients; they constrain only the net readout channel.
\end{enumerate}

\section{Evidence Plan}
The first study solves the linear scalar equation on canonical capacitor geometries and reports scale-pair ratios. The second defines conservative screened envelopes without claiming a microscopic theory. The third proposes experiments at room temperature, cryogenic temperature, and varied dielectric composition to test whether bounds are material-sensitive.

\section{JMP0X1B Implementation Surface}
A JMP0X1B simulation package should track units, geometry scale, material priors, mesh digests, and solver tolerances. The implementation can emit a range-screening exclusion grid suitable for the Bayesian null ledger.

\subsection*{Illustrative JMP0X1B-style contract}
\begin{verbatim}
record ScalarRun { geometry: GeometryDigest, lambda_s: Length, screen: ScreenModel, material_map: MaterialMap, voltage: Volt }
fn solve_scalar(run: ScalarRun) -> ScalarBound effects{FEM, Units, Deterministic, Audit}
\end{verbatim}


\section{Release And Review Plan}
Release canonical mesh geometries, parameter sweeps, exclusion grids, and a reviewer checklist requiring every claim to specify range, screening model, and material assumptions.

\section{Open Questions}
\begin{itemize}
\item Which scalar range is most constrained by existing UHV balances?
\item Can cryogenic dielectric behavior reduce nuisance thermal channels enough to improve scalar bounds?
\item How should nonlinear screening be bounded without adding arbitrary parameters?
\item What is the cleanest geometry for separating edge gradients from volume energy density?
\end{itemize}

\section{Conclusion}
Range and screening turn scalar readout from a vague electrogravity idea into a structured null program. The paper emphasizes exclusion surfaces, not positive claims.

\section*{References}
\begin{thebibliography}{99}
\bibitem{jmp005} JMP0X1B Research Group. \emph{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{jmp007} JMP0X1B Research Group. \emph{Ultra-High-Vacuum Null Tests of Electrostatic Projection Couplings with Symmetry-Matched Capacitors}. Working paper, 2026. \url{https://research.jmp0x1b.com/papers/uhv-electrostatic-null-tests.html}
\bibitem{jmp008} JMP0X1B Research Group. \emph{Finite-Element Discrimination of Boundary-Flux, Scalar, and Conventional Artifact Forces in Asymmetric Capacitors}. Working paper, 2026. \url{https://research.jmp0x1b.com/papers/fem-capacitor-force-discrimination.html}
\bibitem{kaluza} T. Kaluza. Zum Unit\"atsproblem in der Physik. \emph{Sitzungsberichte der Preussischen Akademie der Wissenschaften}, 966--972, 1921.
\bibitem{klein} O. Klein. Quantentheorie und f\"unfdimensionale Relativit\"atstheorie. \emph{Zeitschrift f\"ur Physik}, 37:895--906, 1926.
\bibitem{overduin} J. M. Overduin and P. S. Wesson. Kaluza-Klein gravity. \emph{Physics Reports}, 283(5--6):303--380, 1997.
\end{thebibliography}

\end{document}
