Navier-Stokes Unified Form — Simultaneous Binary/Trinary Stagger
Unified Form — Simultaneous Binary/Trinary Stagger
\[
\boxed{
\mathscr S_i=(B_i,\tau_i),
\qquad
B_i\in\{0,1\},
\qquad
\tau_i\in\{-1,0,+1\},
\qquad
\mathscr S_{i+1}=\mathscr S_i+1_{\mathrm{eff}}(i)
}
\]
\[
\boxed{
\mathcal L_i(z)
=
\phi^{-1/\phi}
\sqrt{F_nP_n2^n}\,(1+z)^n
+
1_{\mathrm{eff}}(i)e^{i\pi\Lambda_\phi(i)},
\qquad
\Omega_{n+1}=T(\Omega_n),
\qquad
T(x)=1+\frac1x,
\qquad
N(\Omega)\in\{-1,0,+1\}
}
\]
**C/D:**
\[
v_0=D_n(r)\hat r
\;\longrightarrow\;
(B_i,\tau_i)\ \text{simultaneous}
\;\longrightarrow\;
\phi^{3.5n}\to\infty
\;\longrightarrow\;
T=\phi^{-n_e}<\infty.
\]
**A/B:**
\[
N(v_0)\in\{-1,0,+1\}
\;\longrightarrow\;
(B_i,\tau_i)\ \text{simultaneous}
\;\longrightarrow\;
N(\Phi^{-1})\in\{-1,+1\}
\;\longrightarrow\;
\|\nabla u\|\le G_{\max}
\;\longrightarrow\;
\|u\|\ \text{bounded}.
\]
