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(θG₂)/7] = 0.840636 fm ₚ ₚ where ħ/(m c) = 0.210309 fm is the reduced Compton wavelength of the proton and θG₂ = 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(θG₂)/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(θG₂)/7 = 0.0714% will become directly measurable, providing an independent determination of θG₂ 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.