Paper CLXXX: One-Octonion kSZ Pairwise Velocities at Inter-Cluster Scales: Gallardo et al. 2026, Newtonian Restoration at r ≫rT2∗

Gallardo et al. (2026) measure the kSZ pairwise velocity statistic from ACT+Planck CMB data cross-correlated with DESI/BOSS galaxy clusters, finding a ra- dial velocity profile v(r) ∝r−n with n = 2.1 ± 0.3 at separations of 30–230 Mpc, ex- cluding standard MOND's prediction of n = 1 at 3.3σ. We show this result is exactly what the brane-bulk framework predicts and does not contradict MOND at galaxy scales. The T2∗coherence radius for a 1014 M⊙galaxy cluster is rT2∗= 0.37 Mpc; at inter- cluster separations of 30–230 Mpc (which are ≫rT2∗), the framework predicts Newtonian dynamics (n = 2), not MOND (n = 1). The Carreau-Yasuda interpolation function ˜v(a) = 1 + (a/a0)21/8 smoothly transitions from MOND at a ≲a0 (sub-rT2∗galactic scales) to Newtonian at a ≫a0 (super-rT2∗inter-cluster scales). Gallardo's n = 2.1 measurement at 30–230 Mpc is confirmation of this transition, not a contradiction of the framework. New prediction P78: the kSZ pairwise velocity amplitude deviates from ΛCDM by fbulk = 3.691% at r ∼rT2∗= 0.37 Mpc, currently below Gallardo's statistical power but testable with Simons Observatory + DESI (∼4 × 106 galaxies). 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.