\label{prop:three-reading-equivalence-e1}
The $\Elayer{1}$ Mutual Determination instance $(B_1, S_1, I_1)$ admits exactly three non-trivial sector-restricted readings, corresponding to the three Millennium Problems at~$\Elayer{1}$:
\begin{center}
\begin{tabular}{lllll}
\toprule
\textbf{Reading} & \textbf{Sector} & \textbf{Boundary ($B$)} & \textbf{Interior ($I$)} & \textbf{Spectral ($S$)} \\
\midrule
NS & All five & $\tau$-admissible & Stabilized & Defect \\
 & sectors & fluid data & $\omega$-germ & contractivity \\
 & & (Def.~\ref{def:tau-admissible-fluid-data}) & (Thm.~\ref{thm:positive-regularity}) & $\Delta \to 0$ \\
\addlinespace
YM & C-sector & $\tau$-admissible & Spectral gap & NF discreteness \\
 & (strong) & gauge data & $\Gamma^*_s > 0$ & $|\operatorname{NF}| \leq \operatorname{Prim}(k)$ \\
 & & (Def.~\ref{def:tau-admissible-gauge-data}) & (Thm.~\ref{thm:yang-mills-gap-theorem}) & \\
\addlinespace
Hodge & $B/C$ & $\sigma$-fixed & NF-addressable & Balanced \\
 & balanced & characters & in all sectors & $\chi_+/\chi_-$ \\
 & & (Def.~\ref{def:sigma-fixed-character}) & (Thm.~\ref{thm:nf-addressability}) & equilibrium \\
\bottomrule
\end{tabular}
\end{center}
The three readings exhaust the non-trivial sector projections of $(B_1, S_1, I_1)$:
\begin{enumerate}
\item[(i)] \textbf{NS} reads the full five-sector data and asks for global regularity---smooth gluing across all sectors.
\item[(ii)] \textbf{YM} reads the C-sector restriction and asks for discrete granularity---a spectral gap in the strong channel.
\item[(iii)] \textbf{Hodge} reads the $B/C$-balanced sublattice and asks for addressability---spectral visibility of all balanced characters.
\end{enumerate}
No fourth non-trivial reading exists: the $A$-sector (weak) and $D$-sector (gravity) are structurally symmetric to the $B$- and $C$-sectors at~$\Elayer{1}$ and do not generate independent Millennium-Problem-level consequences.