Paper CLXXXIV: Klein Ladder Pion-Muon Exit and Re-Entry as the Origin of the Lattice QCD Hadronic Vacuum Polarization Enhancement: Interpretation of BMW (2026)

The BMW Collaboration has published (Nature, April 22 2026) a hybrid lattice-QCD calculation of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment, obtaining aμ^LO-HVP = 715.1(3.4)×10 ¹ , bringing the Standard Model prediction into ⁻ ⁰ agreement with the Fermilab measurement at 0.5σ. We show that this result is a direct consequence of the Klein ladder pion-muon exit and re-entry mechanism of the one-octonion brane-bulk framework. In the framework, virtual pions in the HVP loop sit on the k=2 rung of the G₂ Klein ladder (short-root sector, H , λ=1). With probability f_bulk = 1−sinc²(Eν/2mπ) = 3.691%, ⁺ each pion exits the brane into the AdS₅ bulk and re-enters, via a two-amplitude Dirac comb process: exit sinc(Eν/2mπ) followed by re-entry sinc(Eν/2mπ) (the same amplitude, by AdS antisymmetry z→L²/z). The R-ratio dispersive method is blind to this transit because the e e ⁺ ⁻ detector measures only the brane surface (initial and final pion states), not the intermediate bulk excursion. The Euclidean lattice path integral naturally includes all bulk paths because the AdS radial direction is identified with Euclidean time. Correcting for BMW's hybrid approach (5% data- driven tail, missing f_bulk), the framework predicts aμ^HVP(hybrid) = 717.4×10 ¹ , agreeing with ⁻ ⁰ BMW at 0.68σ. Three falsifiable window-by-window 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.