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\label{thm:no-knobs-principle}
Let $\Sector{D}, \Sector{A}, \Sector{B}, \Sector{C}$
denote the four primitive sectors
of the $4{+}1$ decomposition
(Chapter~\ref{ch:four-plus-one-decomposition}),
and let $\kappa(\Sector{i}, \Sector{j})$
be the coupling function of Definition~\ref{def:coupling-function}.
Then:
\begin{enumerate}
    \item[\textup{(i)}] \textbf{Determination.}
          Every sector coupling is determined by~$\iota_\tau$:
          \[
              \kappa(\Sector{i}, \Sector{j})
              \;=\;
              f_{ij}(\iota_\tau,\, M_d)
          \]
          for a specific rational function~$f_{ij}$
          and primorial depth~$d$
          depending only on the generator pair $(g_i, g_j)$.
    \item[\textup{(ii)}] \textbf{Completeness.}
          The No Knobs Ledger
          (Definition~\ref{def:coupling-ledger},
          Table~\ref{tab:no-knobs-ledger})
          is exhaustive:
          it contains all $10$ distinct couplings,
          and no coupling exists between primitive sectors
          that is not listed.
    \item[\textup{(iii)}] \textbf{Rigidity.}
          No deformation of the coupling functions exists
          within the framework.
          If $\kappa'$ is any alternative coupling assignment
          that is compatible with the Langlands$_0$ functor
          and the $4{+}1$ decomposition,
          then $\kappa' = \kappa$.
\end{enumerate}
In particular,
the framework has no free parameters.