\section{Boundary of the theorem}
\label{sec:scope-boundary}

The theorem constructs one fully marked geometric pentagon and its literal
weight-zero Walker lift.  The remaining limitations distinguish that result
from uniqueness, higher coherence, and downstream quantum comparisons.

\subsection{Existence, not choice independence}

The quantifier is
\[
 \text{for every supplied protected sector, there exists one coordinated
 system}.
 \tag{15.1}\label{eq:existence-boundary}
\]
There is no uniqueness assertion.  The proof does not compare two arbitrary
coordinated systems, and therefore does not imply independence of arbitrary
bands, disk charts, endpoint gauges, collar widths, or representatives of
the proved local slide class.  Equal endpoint chart-system values also do not
identify their labelled incidences.

\subsection{No higher or global conclusion}

The five-edge relation is one pentagon in one supplied three-handle sector.
Nothing here constructs a simultaneous family of such pentagons or verifies
relations among pentagons.  Consequently, the theorem does not by itself
establish higher coherence, coherence for an arbitrary sequence of
handleslides, stabilization invariance, or global Heegaard invariance.

Similarly, the Walker conclusion is the literal equality of the two
weight-zero route products in the stated convention.  The proof uses only
the forward multiplication law.  It contains no converse, injectivity, or
pair-determination claim, and it does not pass to a projective quotient or
forget the weights.

The theorem is therefore not a TQFT-functoriality theorem and makes no claim
about WRT invariants, Habiro completions, or \(\widehat Z\).  Such conclusions
would require additional comparison and global-coherence input not supplied
here.

\subsection{The downstream comparison remains separate}

An operator-level pentagon built from these geometric representatives also
requires a compatible comparison between a reduced skein module and the
fixed-level TQFT state space.  This is the input denoted
\(\mathrm{COMP\mbox{-}Q}\) in the comparison formulation.  Its construction
is separate from the geometric theorem proved here.  The present result
supplies the complete-marked geometric relation to be transported; it makes
no stronger functorial conclusion.

\subsection{Geometric output}

The reusable output is the relative route equality, together with the
complete marking, common Lagrangian, and zero Walker weights that make it
literal.