Paper CXI · One-Octonion Brane-Bulk Framework · Prediction P187 The Proton Charge Radius from Fano 4:3 Node Geometry and the Genesis Tilt

The proton charge radius puzzle — the decade-long discrepancy between electron-scattering and muonic-hydrogen measurements — converges in 2026 to r = 0. 8406 ± 0. 0015 fm from hydrogen 2s– ₚ 6p spectroscopy. We show that the One-Octonion Brane-Bulk Framework predicts this value from first principles with zero free parameters: r = 4ħ/ (m c) × 1 − sin² (θ₆䃒) /7 = 0. 840636 fm ₚ ₚ where ħ/ (m c) = 0. 210309 fm is the reduced Compton wavelength of the proton and θ₆䃒 = 4. 054° is ₚ the Genesis tilt derived from Fano plane geometry in Paper I. The predicted value agrees with the 2026 measurement to 0. 004% (0. 02σ). The formula has two geometric origins: the factor 4 arises from the Fano 4: 3 node asymmetry (the 4 nodes complementary to the 3 quark color nodes set the confinement boundary) ; the correction 1 − sin² (θ₆䃒) /7 arises because the Genesis tilt displaces the color sectors slightly from their ideal Fano positions, requiring additional confinement energy distributed across all 7 Fano nodes. This prediction connects three independently established quantities: the proton charge radius (spectroscopy), the Compton wavelength (mass measurement), and the Genesis tilt (baryogenesis, Paper I). The framework further predicts that as proton radius measurements improve by a factor of 2. 5× in precision, the tilt correction sin² (θ₆䃒) /7 = 0. 0714% will become directly measurable, providing an independent determination of θ₆䃒 from atomic physics alone. 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.