The epicyclic frequency κepi of stellar orbits in a galactic disk — the frequency of small radial oscillations around circular orbits — is shown to be the square root of the amplitude of the single brane degree of freedom that remains free after the Onsager vortex formation phase locks six angular modes into the flat 6, 3 hexagonal geometry of the pre-genesis brane. In the One-Octonion Framework, the pre-genesis brane is a flat 6, 3 hexagonal lattice (Baker-Campbell-Hausdorff zeroth/first order, Paper CCIX). During galaxy formation, the brane settles into this geometry through an Onsager-phase vortex ordering process: the seven Fano vortices organize into the hexagonal lattice, locking six angular (tangential) modes corresponding to the six nearest-neighbor bond directions at 0, 60, 120, 180, 240, 300. The single remaining free mode is the radial breathing amplitude (e7 direction, highest weight of G2). Because the six locked modes are tangential, they contribute zero radial restoring force. The only restoring force on the free radial mode is the Coriolis force in the rotating sump frame: κ2 epi = Afree = 2Ω2, giving κepi = √ 2 Ωexactly — the standard result for a flat rotation curve galaxy. This is verified at the solar circle to 2. 8% (Oort constant measurement). The 1 result extends the framework's sump mechanics (Papers I, XXIV, LXII) with a new geometric origin for the Oort constants A and B from the 6, 3 Onsager phase transition. 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.
Bharathi Jagadeesan (Tue,) studied this question.
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