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 \[Q_5 = Q_4 × \{0,1\},\] 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 \[4 × 2 = 8.\] 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: \[D = boundary cells, = fibre channels,|Q_5| = global state space.\] Accordingly, the denominator of the mirror-to-baryonic ratio decomposes as \[32 = global Q_5 state count,\] \[8 = tesseract boundary-cell normalization,\] \[25 = dual-fibre channel normalization.\] Combined with Theorems 106–109, every factor in \[ρMB=3840 · 9/32 · 8 · 25·160/161=864/161=5.366459627…\] 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 \[ρMB={Eₘᵢᵣᵣₒᵣ}{Ebaryonic}.\] 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.