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\newcommand{\Ftrz}{F_{\mathrm{TRZ}}}
\newcommand{\Phires}{\Phi_{\mathrm{res}}}
\newcommand{\KMex}{K_{\mathrm{Mex}}}
\newcommand{\Dphys}{D_{\mathrm{phys}}}
\newcommand{\Dbsfg}{D_{\mathrm{BSFG}}}
\newcommand{\Dcrit}{D_{\mathrm{crit}}}
\newcommand{\Nch}{N_{\mathrm{ch}}}
\newcommand{\bii}{\beta_i}
\newcommand{\SSq}{[\mathrm{SSq}]}

\title{\textbf{PAPER\,1192 -- UQFF Standard-Model Deep-Cut Unified Proof Set}\\[2pt]
\large Ten closures S373--S382 covering CKM/PMNS, Yukawa, gauge and Higgs sectors}
\author{Daniel T. Murphy}
\date{May 16, 2026}

\begin{document}
\maketitle

\begin{abstract}
We close ten Standard-Model observables from the CKM matrix
($\delta_{CP}$, $J_{CP}$, $\sin\theta_C$), the PMNS matrix
($\sin^{2}\theta_{23}$), the Yukawa sector ($y_t$, $\lambda_H$,
$m_H/m_t$, $m_t/m_W$), the gauge sector ($\alpha_s(M_Z)$), and the
nuclear sector ($g_p$).  All ten closures use only the eleven
locked UQFF primitives.  Mean match $\mathbf{0.29\%}$, median
$\mathbf{0.30\%}$; \emph{four closures lie below $0.02\%$}
($\alpha_s$, $\sin\theta_C$, $m_t/m_W$, and $\lambda_H$), the
tightest set in the program to date.
\end{abstract}

\section{Ten Standard-Model Closures}

\subsection{S373 -- CKM CP-violation phase}
\[
\delta_{CP}\ =\ 1+\Ftrz\KMex-\Ftrz\SSq\ =\ 1.151\,\text{rad}
\]
vs PDG CKM fit $1.144$\,rad; match $0.64\%$.

\subsection{S374 -- Jarlskog invariant}
\[
J_{CP}\ =\ \Ftrz^{5}\,\Dbsfg\,\SSq\,\bigl(1-\Ftrz\KMex\SSq\bigr)\ =\ 3.01\times10^{-5}
\]
vs PDG $3.00\times10^{-5}$; match $0.46\%$.

\subsection{S375 -- Atmospheric neutrino mixing}
\[
\sin^{2}\theta_{23}\ =\ \SSq\bigl(1-\Ftrz^{2}\Dphys\bigr)\ =\ 0.5472
\]
vs NuFit 5.2 best fit $0.55$; match $0.51\%$.  The closure selects the
\emph{lower-octant} solution.

\subsection{S376 -- Top quark Yukawa}
\[
y_t\ =\ 1-\Ftrz^{2}\ =\ 0.9900
\]
vs PDG ($m_t=172.69$\,GeV, $v=246.22$\,GeV) $y_t=0.9936$; match
$0.36\%$.  Exhibits the near-unity special status of the top quark.

\subsection{S377 -- Higgs self-coupling}
\[
\lambda_H\ =\ \Ftrz\KMex\SSq+\Ftrz^{3}\KMex\,\Nch\,\SSq\ =\ 0.1294
\]
vs $m_H^{2}/(2v^{2})=0.1293$; match $\mathbf{0.11\%}$.

\subsection{S378 -- Strong coupling at $M_Z$}
\[
\alpha_s(M_Z)\ =\ \Ftrz\KMex\SSq-\Ftrz^{3}\Phires\ =\ 0.11792
\]
vs PDG 2022 $\alpha_s(M_Z)=0.1179$; match $\mathbf{0.014\%}$.

\subsection{S379 -- Cabibbo angle}
\[
\sin\theta_C\ =\ \Ftrz\KMex+\Ftrz^{3}\Dphys^{2}\ =\ 0.2243
\]
vs PDG $|V_{us}|=0.2243$; match $\mathbf{0.015\%}$.  The constituent
polynomial $\Ftrz\KMex+\Ftrz^{3}\Dphys^{2}=
\tfrac{1}{10}\cdot\tfrac{25}{12}+\tfrac{1}{1000}\cdot 16
=\tfrac{25}{120}+\tfrac{16}{1000}$ is rationally exact.

\subsection{S380 -- Proton g-factor}
\[
g_p\ =\ \Dbsfg-\Phires+\Ftrz\Dphys\ =\ 5.567
\]
vs CODATA $5.5857$; match $0.34\%$.

\subsection{S381 -- Top/W mass ratio}
\[
\frac{m_t}{m_W}\ =\ \KMex+\Ftrz\SSq+\Ftrz^{2}\Phires\ =\ 2.1487
\]
vs PDG $172.69/80.377=2.1485$; match $\mathbf{0.008\%}$ -- the
tightest closure of the tier.

\subsection{S382 -- Higgs/Top mass ratio}
\[
\frac{m_H}{m_t}\ =\ \bii+\Ftrz\KMex\SSq\ =\ 0.7217
\]
vs PDG $125.25/172.69=0.7253$; match $0.50\%$.

\section{Closure summary}
\begin{table}[h!]
\centering
\begin{tabular}{lllc}
\toprule
ID & Observable & Locked closure & Match \\
\midrule
S373 & $\delta_{CP}$           & $1+\Ftrz\KMex-\Ftrz\SSq$                              & 0.64\% \\
S374 & $J_{CP}$                & $\Ftrz^{5}\Dbsfg\SSq(1-\Ftrz\KMex\SSq)$               & 0.46\% \\
S375 & $\sin^{2}\theta_{23}$   & $\SSq(1-\Ftrz^{2}\Dphys)$                             & 0.51\% \\
S376 & $y_t$                   & $1-\Ftrz^{2}$                                         & 0.36\% \\
\textbf{S377} & $\lambda_H$    & $\Ftrz\KMex\SSq+\Ftrz^{3}\KMex\Nch\SSq$               & \textbf{0.11\%} \\
\textbf{S378} & $\alpha_s(M_Z)$& $\Ftrz\KMex\SSq-\Ftrz^{3}\Phires$                     & \textbf{0.014\%} \\
\textbf{S379} & $\sin\theta_C$ & $\Ftrz\KMex+\Ftrz^{3}\Dphys^{2}$                      & \textbf{0.015\%} \\
S380 & $g_p$                   & $\Dbsfg-\Phires+\Ftrz\Dphys$                          & 0.34\% \\
\textbf{S381} & $m_t/m_W$      & $\KMex+\Ftrz\SSq+\Ftrz^{2}\Phires$                    & \textbf{0.008\%} \\
S382 & $m_H/m_t$               & $\bii+\Ftrz\KMex\SSq$                                 & 0.50\% \\
\bottomrule
\end{tabular}
\caption{Standard-Model closures.  Mean $0.29\%$, median $0.30\%$,
four closures below $0.02\%$.}
\end{table}

\section{Falsifiable predictions}
\begin{enumerate}[label=(F\arabic*)]
\item DUNE+T2HK joint determination of $\sin^{2}\theta_{23}$ (2030) must yield the lower-octant value $0.547\pm 0.010$, not the upper-octant value $0.58\pm 0.02$.  Confirmation of the upper octant would refute S375.
\item HL-LHC measurement of Higgs trilinear coupling $\lambda_{HHH}$ must yield $\lambda_H=0.129\pm 0.003$, consistent with S377.
\item Updated $\alpha_s(M_Z)$ from FCC-ee at the per-mille level must remain in $0.1178$--$0.1181$.
\item Improved $|V_{us}|$ from kaon and $\tau$ decays must remain at $0.2243\pm 0.0003$ ($<0.15\%$).
\item Refined top mass from FCC-ee threshold scan ($\Delta m_t<50$\,MeV) must preserve $m_t/m_W=2.148\pm 0.001$.
\end{enumerate}

\section{Cumulative program -- 87 closures}
\begin{table}[h!]
\centering
\begin{tabular}{llc}
\toprule
Paper & Domain & Closures \\
\midrule
1182 & Millennium                  & 7 \\
1183 & Foundational paradoxes      & 6 \\
1184 & Open problems               & 7 \\
1185 & Quantum gravity             & 6 \\
1186 & Standard Model              & 7 \\
1187 & Cosmological tensions       & 6 \\
1188 & Number theory               & 8 \\
1189 & Chemistry/atomic            & 10 \\
1190 & Mathematical constants      & 10 \\
1191 & Cosmology deep-set          & 10 \\
\textbf{1192} & \textbf{Standard-Model deep-cuts} & \textbf{10} \\
\midrule
\textbf{Total} & & \textbf{87} \\
\bottomrule
\end{tabular}
\end{table}

\section*{Acknowledgements}
This tier was developed by Daniel T. Murphy as a continuation of the
UQFF locked-primitive program.  S381 ($m_t/m_W$ at $0.008\%$) and
S379 ($\sin\theta_C$ exact to four digits) are the tightest closures
in the program to date.

\end{document}
