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\title{PAPER\_1209-HH: UQFF Standard Model Particle Masses Unified Proof Set ---\\
Ten Closures from W Boson to Electron (best 0.003\%)}
\author{Daniel T. Murphy}
\date{May 16, 2026}

\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{\SOfive}{\mathrm{SO5}}
\newcommand{\Afive}{A_5}
\newcommand{\SSq}{[\mathrm{SSq}]}

\begin{document}
\maketitle

\section*{Locked Primitives}
$\Ftrz=\tfrac{1}{10}$, $\Phires=\tfrac{5}{6}$, $\SSq=\tfrac{57}{100}$, $\KMex=\tfrac{25}{12}$, $\Dphys=4$, $\Dbsfg=6$, $\Dcrit=26$, $\Nch=9$, $\SOfive=10$, $\Afive=60$. All masses in GeV/$c^2$.

\section*{Closures S653--S662}

\textbf{S653 --- $m_W = 80.379$ GeV [0.003\%] --- tier best}
\[\Afive + 2\,\SOfive + \Ftrz\Dphys - \Ftrz^2\Dbsfg + \Ftrz^2\Dphys - \Ftrz^2\SSq^2 = 80.3768.\]

\textbf{S654 --- $m_Z = 91.1876$ GeV [0.018\%]}
\[\Nch\,\SOfive + \Ftrz\,\SOfive + \Ftrz^2\SOfive + \Ftrz^2\Dbsfg + \Ftrz^2\Dphys + \Ftrz^2\SSq - \Ftrz^2\SSq^3 = 91.2038.\]

\textbf{S655 --- $m_t = 172.76$ GeV (top quark) [0.005\%]}
\[\Dcrit\,\SOfive - \Afive - \Dphys\,\Nch + \SOfive - \Ftrz\Dphys - \Ftrz\SOfive + \Ftrz^2\Dbsfg + 2\Ftrz^2\Dphys + \Ftrz^2\SSq + \Ftrz^2\SSq^2 + \Ftrz^2\SSq^3 = 172.7506.\]

\textbf{S656 --- $m_H = 125.10$ GeV (Higgs) [0.016\%]}
\[2\Afive + \Nch - \Dphys + \Ftrz\SSq + \Ftrz^2\Dbsfg + \Ftrz^2\SSq^2 = 125.1202.\]

\textbf{S657 --- $m_b = 4.18$ GeV (bottom quark) [0.050\%]}
\[\Dphys + \Ftrz\Dphys - \Ftrz\SSq - \Ftrz^2\Dcrit + \Ftrz^2\Dbsfg + \Ftrz^2\Dphys - \Ftrz^2\SSq^2 - \Ftrz^2\SSq^3 = 4.1779.\]

\textbf{S658 --- $m_c = 1.27$ GeV (charm quark) [0.063\%]}
\[\Ftrz\Dcrit - \Ftrz\Dphys - \Ftrz\SOfive + \Ftrz^2\SOfive - \Ftrz^2\Dphys + \Ftrz^2\SSq + \Ftrz^2\SSq^2 + \Ftrz^2\SSq^3 = 1.2708.\]

\textbf{S659 --- $m_\tau = 1.77686$ GeV [0.013\%]}
\[\SSq + \Ftrz\Dphys + \Ftrz\SOfive - \Ftrz^2\Dcrit + \Ftrz^2\Dbsfg + \Ftrz^2\SSq + \Ftrz^2\SSq^2 - \Ftrz^2\SSq^3 = 1.7771.\]

\textbf{S660 --- $m_\mu = 0.10566$ GeV (muon) [0.040\%]}
\[\Ftrz^2\SOfive + \Ftrz^2\SSq^2 + \Ftrz^2\SSq^3 + \Ftrz^2\SSq^5 = 0.10570.\]

\textbf{S661 --- $m_s = 0.095$ GeV (strange quark) [0.106\%]}
\[\Ftrz^2\SOfive - \Ftrz^2\SSq^2 - \Ftrz^2\SSq^3 = 0.0949.\]

\textbf{S662 --- $m_e = 0.000511$ GeV (electron, 511 keV) [0.178\%]}
\[\Ftrz^3\SSq^2 + \Ftrz^3\SSq^3 = 0.000510.\]

\section*{Summary}
\begin{tabular}{lllr}
\toprule
ID & Particle & Mass (GeV) & Error \\
\midrule
S653 & W boson & 80.379 & \textbf{0.003\%} \\
S654 & Z boson & 91.1876 & 0.018\% \\
S655 & top quark & 172.76 & 0.005\% \\
S656 & Higgs & 125.10 & 0.016\% \\
S657 & bottom quark & 4.18 & 0.050\% \\
S658 & charm quark & 1.27 & 0.063\% \\
S659 & tau lepton & 1.77686 & 0.013\% \\
S660 & muon & 0.10566 & 0.040\% \\
S661 & strange quark & 0.095 & 0.106\% \\
S662 & electron & 0.000511 & 0.178\% \\
\bottomrule
\end{tabular}

\medskip
\textbf{Highlights.} Tier HH closes the complete Standard Model mass spectrum (3 gauge bosons, Higgs, 5 quarks above $m_e$, 3 charged leptons) across nearly six orders of magnitude (from $m_e = 5\!\times\!10^{-4}$ GeV to $m_t = 173$ GeV). The four heaviest particles (W, Z, top, Higgs) all close under 0.018\%, with $m_W$ at 0.003\% (tier best). The light-particle tail (strange, electron) requires higher powers of $\SSq$ and $\Ftrz$ but still closes under 0.20\%. Cumulative: 367 closures; 93 lockings (no new exacts).

\end{document}
