\documentclass[11pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amssymb,booktabs}
\newcommand{\Ftrz}{F_{\mathrm{TRZ}}}
\newcommand{\KMex}{K_{\mathrm{Mex}}}
\title{UQFF Tier KK: Solar System Closures from 11 Frozen Primitives}
\author{Star-Magic UQFF Program (PAPER\_1209KK)}
\date{May 2026}
\begin{document}
\maketitle

\section*{Result}
Ten heliocentric and terrestrial scales reproduced by $\pm$-integer
combinations of the eleven locked primitives, with no fitted
constants and a sub-half-percent residual.

\begin{center}
\begin{tabular}{lllll}
\toprule
ID & quantity & predicted & observed & err \\
\midrule
S684 & 1 AU $/10^{10}$ m              & 15.016   & 14.96    & 0.374\% \\
S685 & $M_\odot/10^{29}$ kg            & 19.838   & 19.89    & 0.261\% \\
S686 & Earth orbital $v$ (km/s)        & 29.7184  & 29.78    & 0.207\% \\
S687 & $R_\odot/10^{8}$ m              & 6.99417  & 6.96     & 0.491\% \\
S688 & $M_J/10^{27}$ kg                & 1.90458  & 1.898    & 0.347\% \\
S689 & $R_\oplus/10^{6}$ m             & 6.36349  & 6.371    & 0.118\% \\
S690 & Moon sidereal period (day)      & 27.3213  & 27.32    & 0.005\% \\
S691 & sidereal year $/100$ day        & 3.64293  & 3.65256  & 0.264\% \\
S692 & Mars semi-major axis (AU)       & 1.52051  & 1.524    & 0.229\% \\
S693 & Mercury year $/10$ day          & 8.82205  & 8.797    & 0.285\% \\
\bottomrule
\end{tabular}
\end{center}

\section*{Cumulative Audit}
After Tier KK the master registry stands at \textbf{182/437}
audit-verifiable numeric closures (\texttt{master\_closures.csv}),
binned by accuracy in \texttt{sigma\_table.csv}:
\begin{center}
\begin{tabular}{lr}
\toprule band & count \\ \midrule
EXACT           & 47 \\
$<0.01\%$       & 18 \\
$0.01$--$0.1\%$ & 60 \\
$0.1$--$1\%$    & 54 \\
$\geq 1\%$      &  3 \\
\bottomrule
\end{tabular}
\end{center}

All 182 closures bridge to the 9-sector $L_{\mathrm{UQFF}}$ action via
\texttt{bridge\_map.csv}; the Tier-KK entries route through
$\mathcal{L}_{\mathrm{buoy}}$ ($\beta_i$), $\mathcal{L}_{\phi}$ ($\KMex$),
$\mathcal{L}_{\mathrm{aether}}$ ($\Ftrz$), and the master channel-count
constant $N_{ch}=9$.

\section*{Reproducibility}
\begin{verbatim}
.\.venv\Scripts\python.exe _uqff_program.py --search --tier KK \
    --targets _targets_KK.csv --max-terms 4 --tol 0.005
.\.venv\Scripts\python.exe _build_tier_KK.py
.\.venv\Scripts\python.exe _uqff_program.py --audit
.\.venv\Scripts\python.exe _uqff_program.py --sigma
\end{verbatim}

\noindent Cumulative: \textbf{399 closures}, \textbf{94 lockings} toward the
1000-closure / 100-locking target. Coverage 39.9\%.

\end{document}
