Observable-Rank Stability under Vertical Non-Injectivity: Closing the Fibre-Structure Conditionality in the Born–Infeld-to-Cascade Chain

O18 established the minimal fibre condition: Born–Infeld parity is the only global symmetry of ${S_{\mathrm{BI}}}[\chi]$, ensuring that each fibre of the non-injective projection $\Pi$ is exactly $\{\chi, -\chi\}$. O22 proved the shell-alignment conjecture of O21, and O23 derived the threshold condition $\Sigma_c(n_3) = 3$ from the quaternionic maximality of the admissible neutral traceless sector. Together, these results show that the integer $3$ in $\Sigma_c(n_3) = 3$ is a property of $\operatorname{Im}\Pi \cap {\mathcal{N}_{\mathrm{trl}}}$, not of the cardinality of the fibres. The condition of O18 is therefore stronger than necessary: the programme requires only that any symmetry of ${S_{\mathrm{BI}}}$ acts vertically with respect to $\Pi$, i.e.\ does not enlarge the real rank of the admissible neutral traceless sector. The present paper proves this verticality condition directly from Born–Infeld admissibility and the quaternionic maximality established in O23, without requiring a classification of $\mathcal{C}_{\mathrm{eff}}$. As a corollary, the fibre-structure conditionality in the ${c_{\mathrm{BI}}} \to {\delta_{\mathrm{pair}}}$ segment is closed: its observable rank is independent of fibre cardinality. This does not establish the separate ${\delta_{\mathrm{pair}}} \to {\beta^*}$ capacity-to-rate step, for which no native Heisenberg growth carrier is defined in the corpus. Non-injectivity may increase microscopic multiplicity, but cannot enlarge the admissible observable structure.