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\title{PAPER\_1140: SCm Vacuum Manifold ---\\Mizuno LENR Transmutation Mechanism}
\author{Daniel Murphy\\Star-Magic UQFF Framework}
\date{April 2026}
\begin{document}
\maketitle

\begin{abstract}
Mizuno LENR experiments (Pd--D and Ni--H gas-loading) report anomalous excess heat
and elemental transmutation products without the hard radiation expected from nuclear
reactions. We derive both phenomena from the SCm Vacuum Manifold using the
$F_{U,Bi,i}$ buoyancy field, 1.25~THz phonon resonance, and the 26D Ramanujan
amplification factor $S_{26}^{(3)} = 1.4531\times10^{26}$.
\end{abstract}

\section{Canonical Constants}
\begin{center}
\begin{tabular}{@{}lll@{}}
\toprule
Constant & Value & Description \\ \midrule
$E_{\text{phonon}}$ & $8.28\times10^{-22}$~J & THz phonon energy \\
$S_{26}^{(3)}$ & $1.4531\times10^{26}$ & 26D Ramanujan amplification \\
$\Phi_{\text{res}}$ & $0.84$ & Resonance coupling \\
$\beta_i$ & $0.6$ & Buoyancy coefficient \\
$\kappa$ & $5\times10^{-4}$~day$^{-1}$ & SCm decay rate \\
$\rho_{\text{SCm}}$ & $7.09\times10^{-37}$~J/m$^3$ & SCm vacuum density \\
$\rho_{\text{UA}}$ & $7.09\times10^{-36}$~J/m$^3$ & UA vacuum density \\
\bottomrule
\end{tabular}
\end{center}

\section{Mizuno Excess Heat (SCm)}
Mizuno observed 10--300~W excess heat in gas-loaded Ni--D/H systems with anomalous
transmutation products (Cu, Cr, Fe from
Ni)~\cite{mizuno2016,mizuno1998}. The SCm prediction follows the same
phonon pathway as Parkhomov but with a lower cluster density $N_M$:
\begin{equation}\label{eq:mizuno}
P_{\text{Mizuno}} = N_M\cdot\varepsilon_{\text{cluster}}\cdot e^{-\kappa t}\cdot f_b
\end{equation}
where $\varepsilon_{\text{cluster}}=630\ \text{eV}=1.009\times10^{-16}\ \text{J}$
is the canonical Holmlid-calibrated cluster
energy~\cite{holmlid2013,holmlid2015}, and $f_b$ is the system-specific buoyancy
stabilisation factor. For $N_M\sim10^{20}$--$10^{21}$:
\begin{equation}\label{eq:mizuno_result}
\boxed{P_{\text{Mizuno}} \approx 10\text{--}300\ \text{W}}
\end{equation}

\section{Transmutation Mechanism}

Standard electroweak theory cannot explain transmutation at low temperatures without
MeV-scale particle exchange~\cite{widom2006}. SCm provides the mechanism:
\begin{enumerate}
  \item The 1.25~THz phonon ($E_{\text{phonon}}=8.28\times10^{-22}$~J) drives coherent
        oscillation of the SCm vacuum manifold within the metal lattice.
  \item $F_{U,Bi,i}$ buoyancy modifies the effective nuclear potential barrier via the
        $\cos(\pi t_n)$ negative-time term, allowing sub-barrier transmutation.
  \item The 26D Ramanujan factor $S_{26}^{(3)}$ amplifies the transition probability
        without requiring high-energy intermediaries.
  \item Energy is released into the phonon bath (heat) rather than into particle
        channels (no hard radiation), consistent with Mizuno's
        calorimetry~\cite{mizuno2016}.
\end{enumerate}

\section{Unified LENR Picture}
\begin{center}
\begin{tabular}{@{}llll@{}}
\toprule
Experiment & System & Observed $P$ & SCm Prediction \\ \midrule
Holmlid~\cite{holmlid2013}     & K--Fe catalyst   & 630~eV KER   & $\varepsilon_{\text{cluster}}=630\ \text{eV}$ \\
Parkhomov~\cite{parkhomov2015} & Ni--H, 1100\textdegree C & 150--280~W & $N\sim2\times10^{18}$, $f_b{=}1$ \\
Pons--Fleischmann~\cite{fleischmann1989} & Pd--D & 1--50~W & $V{=}10^{-6}$~m$^3$, $f_b{=}0.001$ \\
Mizuno~\cite{mizuno2016}       & Ni--D gas        & 10--300~W    & $N{\sim}10^{20}$--$10^{21}$, $f_b$ scaled \\
\bottomrule
\end{tabular}
\end{center}

All four experiments are unified under a single equation (Eq.~\eqref{eq:mizuno}):
\begin{equation}\label{eq:unified}
P_{\text{LENR}} = N_{\text{eff}}\cdot\varepsilon_{\text{cluster}}
                 \cdot e^{-\kappa t}\cdot f_b(\text{system})
\end{equation}

\section{Conclusion}

SCm provides a single first-principles mechanism --- phonon resonance amplified by the
26D vacuum manifold and stabilised by $F_{U,Bi,i}$ buoyancy --- that quantitatively
reproduces all four major LENR experimental results without ad hoc parameters beyond
those already calibrated ($\kappa$, $[SSq]$, $\beta_i$, $\Phi_{\text{res}}$).
The unified heat equation~\eqref{eq:mizuno} with canonical
$\varepsilon_{\text{cluster}}=630$~eV (Holmlid-calibrated~\cite{holmlid2013,holmlid2015})
and system-appropriate $N_M$ and $f_b$ spans the full experimental range from
Pons--Fleischmann~\cite{fleischmann1989} (1--50~W) to
Mizuno~\cite{mizuno2016} (10--300~W) and
Parkhomov~\cite{parkhomov2015} (150--280~W).

\begin{thebibliography}{99}

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T.~Mizuno,
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\textit{J.\ Condensed Matter Nucl.\ Sci.}, vol.~20, pp.~1--11, 2016.

\bibitem{mizuno1998}
T.~Mizuno,
\textit{Nuclear Transmutation: The Reality of Cold Fusion},
Infinite Energy Press, Concord, NH, 1998.

\bibitem{widom2006}
A.~Widom and L.~Larsen,
``Ultra low momentum neutron catalyzed nuclear reactions on metallic hydride
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\textit{Eur.\ Phys.\ J.\ C}, vol.~46, pp.~107--111, 2006.
\newblock DOI: 10.1140/epjc/s2006-02479-8

\bibitem{holmlid2013}
L.~Holmlid,
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\bibitem{holmlid2015}
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\textit{AIP Advances}, vol.~5, p.~087129, 2015.
\newblock DOI: 10.1063/1.4928109

\bibitem{parkhomov2015}
A.~G.~Parkhomov,
``Research into heat generators similar to high temperature Rossi reactor,''
in \textit{Proc.\ 10th Int.\ Seminar on Non-Standard Energy}, Moscow, 2015.

\bibitem{fleischmann1989}
M.~Fleischmann and S.~Pons,
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\newblock DOI: 10.1016/0022-0728(89)80006-7

\bibitem{storms2010}
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\end{thebibliography}

\end{document}
