Paper CLX: One-Octonion The G₂-Brane as a Physical Realization of the Soliton Resolution Conjecture: Focal Zones as Solitons, Blowup as Mass Formation, and the

Frank Merle (IHES) received the 2026 Breakthrough Prize in Mathematics for proving key cases of the Soliton Resolution Conjecture (SRC): any solution to a nonlinear partial differential equation, however chaotic at finite times, asymptotically decomposes into a finite number of solitons — localized, shape- preserving structures — plus outgoing radiation. We demonstrate that the One-Octonion Brane-Bulk Framework is a physical realization of the SRC on a G₂-symmetric AdS₅/AdS₄ brane, with four exact identifications: (1) focal zones (standing waves in brane current) are the solitons; (2) mass formation is the blowup singularity; (3) Merle's theorem that friction cannot prevent blowup corresponds to the framework result that T2* dephasing (dissipation) cannot prevent focal zone formation; and (4) the baryogenesis asymmetry δM/M ≈ 6×10 ¹ is the soliton survival fraction — the ratio of solitons that escape H /H ⁻ ⁰ ⁺ ⁻ annihilation after brane nucleation — with surviving density nbaryon (δM/M)² × nKibble. The G₂ ∝ geometry enriches the flat-spacetime SRC in three ways: the 14 generators of G₂ = Aut( ¸) quantize the ℝ soliton species; the Ursa Major twist τ = arccos(1/√7) breaks the H /H symmetry to produce δM/M; and ⁺ ⁻ the κ=−1 transition (Paper CXXIX) sets the long-range soliton interaction as the MOND acceleration scale a₀ = cH₀/2π. The Planck-length brane elements (vortex core radius rcore = ℓ_P, minimum circulation Γ₁ = h/m_P) are the quantum of soliton — the simplest element of the G₂ soliton decomposition. We present the framework brane equations in the form of Merle's NLS/Navier-Stokes analogy, identify the super- critical regime with the G₂ nonlinearity at sub-Planck scales, and discuss the connection to topological solitons (primordial G₂ vortices, Paper CLVII). 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.