We show that many-body dynamical localization (MBDL) in the kicked Lieb-Liniger model Yang et al. , PRL 136, 123402 (2026) is the exact many-body analog of balanced steady-state free precession (bSSFP) in magnetic resonance imaging, with the Gudermannian function gd (x) = arctan (sinh (x) ) serving as the canonical mathematical bridge between the flat-space (brane) and hyperbolic-space (AdS₅ bulk) descriptions. Three identifications are established with full mathematical rigour and zero free parameters. (i) The on-site Lorentzian distribution of Vᴵ = tan (φᴵ) in the mapped lattice model is the exact analog of the off-resonance Lorentzian in bSSFP: both arise from the theorem that tan (Uniform−π/2, π/2) is Cauchy-distributed, and in bulk coordinates arcsinh (Vᴵ) has the Gudermannian as its cumulative distribution function. (ii) The algebraic hopping tail Wᴵᴵ' q λ in flat momentum space is exactly exponential in AdS hyperbolic ∼ ⁻ coordinates (q = sinh (ρ) ) with rate λ, via q λ = sinh λ (ρ) ≈ 2λ exp (−λρ). (iii) The tail crossover λ = 4 ⁻ ⁻ → 3 as interaction strength increases corresponds exactly to the G₂ permutohedron eigenvalue transition k = 6 → k = 4, revealing hidden G₂ structure in the Lieb-Liniger model. The crossover scale γ 1 is reproduced geometrically at gd (ρcross) = π/4, giving qcross = sinh (log (1+√2) ) = 1 ∼ exactly without any free parameter. Additionally, the Gudermannian saturation gd (x) → π/2 as x → ∞ naturally encodes the MOND acceleration saturation at the sump T2* coherence radius. Three falsifiable predictions are stated. 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.
Bharathi Jagadeesan (Tue,) studied this question.