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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{\SSq}{[\mathrm{SSq}]}

\title{\textbf{PAPER\,1193 -- UQFF Astrophysics Unified Proof Set}\\[2pt]
\large Ten closures S383--S392 spanning compact objects, black-hole geometry, stellar structure}
\author{Daniel T. Murphy}
\date{May 16, 2026}

\begin{document}
\maketitle

\begin{abstract}
We close ten astrophysical observables -- including the Chandrasekhar
mass, the TOV maximum neutron-star mass, the Schwarzschild photon
sphere and ISCO, the Bekenstein-Hawking entropy coefficient, the
white-dwarf radius-mass scaling exponent, the self-gravity coefficient
$3/5$, the Salpeter IMF slope, neutron-star compactness, and the
solar Schwarzschild ratio -- using only the eleven locked UQFF
primitives.  \textbf{Four closures are exact}: $M_{\text{Ch}}=
1.44\,M_\odot$, $r_{\text{ISCO}}=6M$, the WD exponent $-1/3$, and the
gravitational-binding coefficient $3/5$.  All ten closures match
observation to better than $0.7\%$.
\end{abstract}

\section{Ten Astrophysical Closures}

\subsection{S383 -- Chandrasekhar mass}
\[
M_{\text{Ch}}\ =\ \Ftrz\,\Dphys^{2}\,(1-\Ftrz)\ =\ \tfrac{1}{10}\cdot 16\cdot\tfrac{9}{10}\ =\ 1.44\,M_\odot
\]
vs textbook ($\mu_e=2$) $1.44\,M_\odot$; \textbf{exact}.

\subsection{S384 -- TOV maximum neutron-star mass}
\[
M_{\text{TOV}}\ =\ \KMex+\Ftrz\SSq+\Ftrz^{2}\SSq(\Dphys-\Phires)\ =\ 2.158\,M_\odot
\]
vs GW170817 + PSR J0740 multimessenger $2.16\,M_\odot$; match
$0.075\%$.

\subsection{S385 -- Schwarzschild photon sphere}
\[
\frac{r_{\text{ph}}}{M}\ =\ \KMex+\Phires+\Ftrz\ =\ 3.017
\]
vs GR exact $3$; match $0.56\%$.

\subsection{S386 -- Schwarzschild ISCO (primitive identification)}
\[
\frac{r_{\text{ISCO}}}{M}\ =\ \Dbsfg\ =\ 6
\]
\textbf{exact}.  The closure formally identifies the locked primitive
$\Dbsfg$ with the Schwarzschild innermost stable circular orbit factor.

\subsection{S387 -- Bekenstein-Hawking entropy coefficient}
\[
\frac{S_{\text{BH}}}{A}\ =\ \Ftrz\KMex+\Ftrz^{2}\Dphys\ =\ 0.2483
\]
vs Bekenstein-Hawking $\tfrac{1}{4}=0.25$; match $0.67\%$.

\subsection{S388 -- White-dwarf radius-mass scaling exponent}
\[
\text{WD exp}\ =\ -\Phires\Ftrz\Dphys\ =\ -\tfrac{5}{6}\cdot\tfrac{1}{10}\cdot 4\ =\ -\tfrac{1}{3}
\]
vs polytrope $n=3/2$ exponent $-1/3$; \textbf{exact}.

\subsection{S389 -- Gravitational binding-energy coefficient}
\[
U_{\text{grav}}\ \text{coeff}\ =\ \SSq+\Ftrz^{2}(\Dphys-1)\ =\ 0.57+0.01\cdot 3\ =\ 0.60
\]
vs uniform-sphere coefficient $\tfrac{3}{5}=0.6$; \textbf{exact}.

\subsection{S390 -- Salpeter initial-mass-function slope}
\[
\alpha_{\text{Salpeter}}\ =\ \KMex+\Phires-\Ftrz\Dbsfg+\Ftrz^{2}(\Dphys-\Phires)\ =\ 2.348
\]
vs Salpeter (1955) $\alpha=2.35$; match $0.071\%$.

\subsection{S391 -- Canonical neutron-star compactness}
\[
\frac{GM}{Rc^{2}}\ =\ \KMex\Ftrz+\Ftrz^{3}\Dphys\SSq\ =\ 0.211
\]
vs canonical NS ($1.4\,M_\odot$, $R=10$ km) $0.21$; match $0.29\%$.

\subsection{S392 -- Solar Schwarzschild ratio}
\[
\frac{R_s}{R_\odot}\ =\ \Ftrz^{6}\,\Dphys\,(1+\Ftrz\SSq)\ =\ 4.228\times10^{-6}
\]
vs $(2.95\,\text{km}/6.96\times10^{5}\,\text{km})=4.24\times10^{-6}$;
match $0.28\%$.

\section{Closure summary}
\begin{table}[h!]
\centering
\begin{tabular}{lllc}
\toprule
ID & Observable & Locked closure & Match \\
\midrule
\textbf{S383} & $M_{\text{Ch}}$        & $\Ftrz\Dphys^{2}(1-\Ftrz)$                       & \textbf{exact} \\
S384 & $M_{\text{TOV}}$               & $\KMex+\Ftrz\SSq+\Ftrz^{2}\SSq(\Dphys-\Phires)$  & 0.075\% \\
S385 & $r_{\text{ph}}/M$              & $\KMex+\Phires+\Ftrz$                            & 0.56\% \\
\textbf{S386} & $r_{\text{ISCO}}/M$    & $\Dbsfg$                                         & \textbf{exact} \\
S387 & $S_{\text{BH}}/A$               & $\Ftrz\KMex+\Ftrz^{2}\Dphys$                     & 0.67\% \\
\textbf{S388} & WD exponent           & $-\Phires\Ftrz\Dphys=-1/3$                       & \textbf{exact} \\
\textbf{S389} & $U_{\text{grav}}$ coeff & $\SSq+\Ftrz^{2}(\Dphys-1)=3/5$                  & \textbf{exact} \\
S390 & $\alpha_{\text{Salpeter}}$      & $\KMex+\Phires-\Ftrz\Dbsfg+\Ftrz^{2}(\Dphys-\Phires)$ & 0.071\% \\
S391 & NS compactness                  & $\KMex\Ftrz+\Ftrz^{3}\Dphys\SSq$                & 0.29\% \\
S392 & $R_s/R_\odot$                   & $\Ftrz^{6}\Dphys(1+\Ftrz\SSq)$                  & 0.28\% \\
\bottomrule
\end{tabular}
\caption{Four exact closures (rational identities); six numerical
closures all below $0.7\%$.}
\end{table}

\section{Falsifiable predictions}
\begin{enumerate}[label=(F\arabic*)]
\item NICER + LIGO-Virgo Run 5 (2027--2030) determination of $M_{\text{TOV}}$ must yield $2.16\pm 0.04\,M_\odot$ -- a value $>2.20\,M_\odot$ would refute S384.
\item Event Horizon Telescope next-generation imaging of Sgr A* and M87* must confirm $r_{\text{ph}}=3M$ ($r_{\text{shadow}}=3\sqrt{3}M$) within $1\%$; deviation would refute S385.
\item Updated NS X-ray pulse profile compactness (NICER PSR J0030, J0740, J0437) must remain in $0.20$--$0.22$ for canonical mass, supporting S391.
\item JWST-resolved stellar IMF in low-metallicity environments must remain consistent with Salpeter slope $2.35\pm 0.05$ above $\sim 1\,M_\odot$; substantial departure would refute S390.
\item Refined parallax of Sirius B by Gaia DR5 (2026) constraining the WD $M$-$R$ relation must remain compatible with $R\propto M^{-1/3}$ (S388).
\end{enumerate}

\section{Cumulative program -- 97 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 \\
1192 & SM deep-cuts                & 10 \\
\textbf{1193} & \textbf{Astrophysics}       & \textbf{10} \\
\midrule
\textbf{Total} & & \textbf{97} \\
\bottomrule
\end{tabular}
\end{table}

\section*{Acknowledgements}
This tier was developed by Daniel T. Murphy as a continuation of the
UQFF locked-primitive program.  The identification
$r_{\text{ISCO}}/M=\Dbsfg$ promotes $\Dbsfg$ from a numerical
primitive to a geometric identity in Schwarzschild spacetime; the
exact closures $M_{\text{Ch}}=1.44\,M_\odot$ and WD-exponent $-1/3$
exhibit how locked rational primitives recover textbook
results without fitting.

\end{document}
