\label{thm:global-cartesian-gluing}
Let $\{U_x\}_{x \in \tau^1}$ be the family of local Hartogs bulk projections, with transition maps $\phi_{xy}$ constrained by the eight structural forces of Chapter~74.  Then:
\begin{enumerate}
\item\emph{(Existence.)}
The local bulks glue into a three-dimensional space
$M_{\tau^3} = \operatornamewithlimits{colim}_{x \in \tau^1} U_x$,
the colimit taken in the category of split-complex-enriched spaces over the primorial tower.

\item\emph{(Uniqueness.)}
The Coherent Force renders the cocycle data rigid: any two gluings compatible with all eight forces are canonically isomorphic.

\item\emph{(Simple connectivity.)}
The Spatial Force ensures $\pi_1(M_{\tau^3}) = 0$.

\item\emph{(Spectral purity.)}
The Harmonic Force ensures the global $\chi_+/\chi_-$ decomposition is pure: no off-diagonal leakage between sectors.

\item\emph{(Smoothness.)}
The Regular Force ensures all transition maps are diffeomorphisms.

\item\emph{(Discrete ground state.)}
The Discrete Force ensures a positive spectral gap: the first excited mode above the vacuum has energy bounded below.

\item\emph{(Legibility.)}
The Legible Force ensures cohomological data is NF-addressable: every $\sigma$-fixed cohomology class corresponds to an algebraic cycle.

\item\emph{(Codability.)}
The Codable Force ensures arithmetic data is finitely generated: discrete rational points label the patch structure.
\end{enumerate}