Vertical Non-Injectivity and the Stability of the Observable Rank: Closing the Unconditional Transfer cχ → δpair → β∗

O18 established the minimal fibre condition: Born-Infeld parity is the only global symmetry of SBI[χ], ensuring that each fibre of the non-injective projection Π is exactly \χ, -χ\. O22 proved the shell-alignment conjecture of O21, and O23 derived the threshold condition Σc(n₃) = 3 from the quaternionic maximality of the admissible neutral traceless sector. Together, these results show that the integer $3$ in Σc(n₃) = 3 is a property of ImΠ ∩ Nₜᵣₗ, not of the cardinality of the fibres. The condition of O18 is therefore stronger than necessary: the programme requires only that any symmetry of SBI acts vertically with respect to Π, 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 Ceff. As a corollary, the transfer chain\[c_χ \;\; δₚₐᵢᵣ \;\; β^* = {1}{δₚₐᵢᵣ + 1/2} ≈ 0.126\]is established unconditionally with respect to the fibre structure of Π. Non-injectivity may increase microscopic multiplicity, but cannot enlarge the admissible observable structure.