%
\label{prop:functor-collapse}
The functor category $[E_3^{\op}, E_3]$
contains no objects of genuinely new structural type.
Every presheaf $F : E_3^{\op} \to E_3$
is classified by the four ABCD coordinates
inherited from the coherence kernel.
Therefore:
\[
    [E_3^{\op}, E_3] \;\subseteq\; E_3.
\]

[Proof sketch]
An object $F \in [E_3^{\op}, E_3]$
is a functor whose values and morphisms
live in~$E_3$.
The structural type of~$F$ is determined by:
\begin{enumerate}
    \item the type of its values
          (objects of $E_3$, classified by the ABCD chart),
    \item the type of its action on morphisms
          (enriched morphisms of $E_3$,
          classified by the split-complex bipolar structure).
\end{enumerate}
For $F$ to have a structural type
not already present in~$E_3$,
it would need a coordinate component
not expressible as a function
of $(A, B, C, D)$.
Such a component would require a fifth orbit channel.

By the Ontic Closure Theorem (I.T01)
and the Ladder Saturation Theorem (I.T02),
no fifth orbit channel exists.
The Pentation Non-Injectivity Lemma (I.L01)
provides the concrete obstruction:
any attempt to define a fifth canonical coordinate
fails because pentation lacks
the injectivity scaffold needed
for type distinction.

Therefore $F$ is classified by the existing coordinates,
and $[E_3^{\op}, E_3] \subseteq E_3$.