Lohmiller & Slotine (Proc. R. Soc. A 482:20250413, 2026) propose a classical contracting-flow construction on the eikonal phase S(x,t) which they argue recovers quantum-wave evolution. Vattay (Comment, arXiv:2605.02621) correctly observes that the construction reproduces only the Hamilton-Jacobi + continuity sector of the Madelung-Bohm decomposition: it cannot generate the quantum potential Q = −ℏ²∇²√ρ/(2m√ρ), without which the recovered evolution is the classical limit of the Schrödinger equation, not the equation itself. We resolve this debate within the One-Octonion Brane-Bulk (OOB) framework. In OOB, the classical sector is the brane-localised f_bulk → 0 limit. Q arises as the back-reaction of brane-bulk transit components of the wavefunction on the brane density profile, with characteristic length the particle Compton scale ℓ_C = ℏ/(mc) and characteristic weight the transit probability f_bulk(E) = 1 − sinc²(E/2m_π). An order-of-magnitude estimate recovers the Madelung-Bohm form |Q| ≈ (ℏ²/2m)·|∇²√ρ|/√ρ structurally. The Gudermannian Class-III bridge (CCLII) supplies the smooth classical ↔ quantum interpolation via the same f_III = 1 − 4/π² blend used in the neutrino-sector chain. The Lohmiller-Slotine theorem is exact at f_bulk = 0; Vattay's missing piece is exactly the contribution identified here. Five predictions span atomic (null OOB at E ≪ m_π) to GeV (0.98 coherence loss in transparent media, tying to CCLVII). Honest scope: structural argument, not rigorous Schrödinger re-derivation; the O(1) coefficient is not pinned without further assumptions. Companion to CCLVII (same f_bulk(E) wavelength-asymmetry channel).Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.