Boundary-Dimensional Normalization

Theorem 110 derives the boundary-dimensional normalization factor \(D=8\) appearing in the mirror-to-baryonic ratio established in Theorems 105 and 109. Rather than treating \(D\) as a ledger parameter, the theorem derives it directly from the coordinate decomposition

\[
Q_5 = Q_4 \times \{0,1\},
\]

where the Penteract consists of two coupled tesseract layers. Fixing one \(Q_4\) layer, its boundary is obtained by fixing an additional coordinate. Since there are four free coordinates and two boundary choices for each coordinate, the number of cubic boundary cells is

\[
4 \times 2 = 8.
\]

Therefore,

\[
D = 8.
\]

The theorem further proves that \(D=8\) is independent of both the fibre normalization \(F=25\) and the global state-space count \(|Q_5|=32\). These quantities count distinct geometric structures:

\[
D = \text{boundary cells},
\qquad
F = \text{fibre channels},
\qquad
|Q_5| = \text{global state space}.
\]

Accordingly, the denominator of the mirror-to-baryonic ratio decomposes as

\[
32 = \text{global }Q_5\text{ state count},
\]

\[
8 = \text{tesseract boundary-cell normalization},
\]

\[
25 = \text{dual-fibre channel normalization}.
\]

Combined with Theorems 106–109, every factor in

\[
\rho_{MB}
=
\frac{3840 \cdot 9}{32 \cdot 8 \cdot 25}
\cdot
\frac{160}{161}
=
\frac{864}{161}
=
5.366459627\ldots
\]

now carries an explicit structural derivation. The theorem, therefore, closes the arithmetic theorem-ledger for the mirror-to-baryonic ratio. The remaining conditionality is no longer associated with factor provenance, but with the physical interpretation of

\[
\rho_{MB}
=
\frac{E_{\mathrm{mirror}}}{E_{\mathrm{baryonic}}}.
\]

At the structural level, the derivation of \(D=8\) follows directly from the \(Q_5\) coordinate architecture and completes the factor-origin program initiated in Theorem 105.