# 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

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## 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/$c^2$.

## Closures S653--S662

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

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

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

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

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

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

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

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

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

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

## Summary
\begin{tabular}{lllr}
\toprule
ID & Particle & Mass (GeV) & Error \midrule
S653 & W boson & 80.379 & **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
**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).