In[]:=
Starting 5D geometric optimization over 36 states (13 Families)...
Fitted Universal Tension Sqrt[sigma] = 0.416622 GeV
Physical Light Mass m_u = 0.135708 GeV
Physical Strange Mass m_s = 0.219181 GeV
Physical Charm Mass m_c = 1.60364 GeV
Physical Bottom Mass m_b = 5.07134 GeV
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RMS of δϕ/(2π) = 0.378
RMS of J - α(M^2) = 0.187
RMS of (M_exp/M_theor - 1) [No Pion] = 0.077
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=== COPY THE LATEX CODE BELOW ===
\begin{table}[htpb]\scriptsize\centering\renewcommand{\arraystretch}{1.1}\setlength{\tabcolsep}{4pt}\begin{tabular}{lcccc | lcccc}\hline\hlineState & $J$ & $M_{\rm th}$ (GeV) & $M_{\rm exp}$ (GeV) & & State & $J$ & $M_{\rm th}$ (GeV) & $M_{\rm exp}$ (GeV) \\\hline\multicolumn{4}{c}{\textbf{Light Pseudoscalars ($\pi$, $q=0$)}} & & \multicolumn{4}{c}{\textbf{Light Vectors ($\rho$, $q=-1$)}} \\\hline$\pi$ & 0 & 0.271 & 0.140 & & $\rho$ & 1 & 0.878 & 0.775 \\$b_1$ & 1 & 1.168 & 1.229 & & $a_2$ & 2 & 1.394 & 1.318 \\$\pi_2$ & 2 & 1.586 & 1.671 & & $\rho_3$ & 3 & 1.756 & 1.689 \\ & & & & & $a_4$ & 4 & 2.052 & 1.967 \\ & & & & & $\rho_5$ & 5 & 2.308 & 2.330 \\\hline\multicolumn{4}{c}{\textbf{Strange Pseudoscalars ($K$, $q=0$)}} & & \multicolumn{4}{c}{\textbf{Strange Vectors ($K^*$, $q=-1$)}} \\\hline$K$ & 0 & 0.355 & 0.494 & & $K^*$ & 1 & 0.928 & 0.892 \\$K_1$ & 1 & 1.212 & 1.272 & & $K^*_2$ & 2 & 1.435 & 1.430 \\$K_2$ & 2 & 1.624 & 1.580 & & $K^*_3$ & 3 & 1.792 & 1.780 \\ & & & & & $K^*_4$ & 4 & 2.085 & 2.045 \\ & & & & & $K^*_5$ & 5 & 2.340 & 2.380 \\\hline\multicolumn{4}{c}{\textbf{Charm Pseudoscalars ($D$, $q=0$)}} & & \multicolumn{4}{c}{\textbf{Charm Vectors ($D^*$, $q=-1$)}} \\\hline$D$ & 0 & 1.739 & 1.865 & & $D^*$ & 1 & 2.118 & 2.008 \\$D_1$ & 1 & 2.331 & 2.422 & & $D^*_2$ & 2 & 2.506 & 2.463 \\$D_2$ & 2 & 2.660 & 2.747 & & $D^*_3$ & 3 & 2.799 & 2.763 \\\hline\multicolumn{4}{c}{\textbf{Charm-Strange ($D_s$, $q=0$)}} & & \multicolumn{4}{c}{\textbf{Charm-Strange Vectors ($D_s^*$, $q=-1$)}} \\\hline$D_s$ & 0 & 1.823 & 1.968 & & $D_s^*$ & 1 & 2.196 & 2.112 \\$D_{s1}$ & 1 & 2.407 & 2.460 & & $D_{s2}^*$ & 2 & 2.580 & 2.569 \\ & & & & & $D_{s3}^*$ & 3 & 2.869 & 2.860 \\\hline\multicolumn{4}{c}{\textbf{Bottom Pseudoscalars ($B$, $q=0$)}} & & \multicolumn{4}{c}{\textbf{Bottom Vectors ($B^*$, $q=-1$)}} \\\hline$B$ & 0 & 5.207 & 5.279 & & $B^*$ & 1 & 5.475 & 5.325 \\$B_1$ & 1 & 5.630 & 5.726 & & $B_2^*$ & 2 & 5.760 & 5.739 \\\hline\multicolumn{4}{c}{\textbf{Bottom-Strange ($B_s$, $q=0$)}} & & \multicolumn{4}{c}{\textbf{Bottom-Strange Vectors ($B_s^*$, $q=-1$)}} \\\hline$B_s$ & 0 & 5.291 & 5.367 & & $B_s^*$ & 1 & 5.557 & 5.415 \\$B_{s1}$ & 1 & 5.711 & 5.829 & & $B_{s2}^*$ & 2 & 5.840 & 5.840 \\\hline\multicolumn{4}{c}{\textbf{Charm-Bottom ($B_c$, $q=0$)}} & & \multicolumn{4}{c}{} \\\hline$B_c$ & 0 & 6.675 & 6.275 & & & & & \\\hline\hline\end{tabular}\caption{The theoretical twistor string masses versus the experimental PDG meson masses. All theoretical values are generated from a single global $\sum (\Delta S)^2 = 0$ optimization over 36 states spanning 13 meson families, extracting exactly 5 fundamental physical parameters: a universal planar tension $\sqrt{\sigma} \approx 417$ MeV, and four dynamically generated constituent boundary masses $m_u \approx 136$ MeV, $m_s \approx 219$ MeV, $m_c \approx 1.60$ GeV, and $m_b \approx 5.07$ GeV. The asymmetric heavy trajectories use the arithmetic mean of the respective constituent boundary masses. Therefore, the $D_s, B_s, B_c$ families are parameter-free geometric predictions. The pion falls below the string's mass threshold ($2m_u \approx 271$ MeV) due to explicit chiral symmetry breaking.}\label{tab:MassSpectrum}\end{table}
