One-Octonion Brane-Bulk Framework — Paper CCCX: The Earliest Bar Lands on the Brane-Bulk Radius — GN20 at z=4.055 Confirms rT2*(M,z) and Prefers Baryons Over Dark Matter

The One-Octonion Brane-Bulk (OOB) framework assigns to every self-gravitating system a structural radius rT2*(M,z) = sqrt(G M / a0) * H0/H(z), the radius at which the Newtonian field falls to the sump acceleration a0 = cH0/2pi, redshifted by the cosmic expansion factor (register entries P18/P34). It is parameter-free, and the mass that enters it is the BARYONIC mass: OOB has no particle dark matter, so the only source is stars and gas. The Milky Way anchor fixes the convention - M_MW = 7e10 Msun is the Galaxy's baryonic (stars+gas) mass, not its ~1e12 Msun virial mass, and reproduces rT2*(MW) = 9.68 kpc at z=0. Applying the same relation to GN20, the dusty star-forming galaxy in GOODS-North at z=4.055 in which JWST/MIRI imaging has resolved a stellar bar (arXiv:2605.15273, 2026), the baryonic mass M*+M_gas = (1.0+/-0.6)+(2.9+/-0.4) = 3.9+/-0.7 x 1e11 Msun gives rT2* = 3.55+/-0.33 kpc, against a deprojected bar radius (semi-major axis) of 3.5+/-0.1 kpc - a match to 1.5% (0.15 sigma). The galaxy's dynamical mass, 5.4+/-2.4 x 1e11 Msun, would push the prediction to 4.18 kpc (+19%, 0.73 sigma). Since f_baryon = 0.7+/-0.3, the ~30% 'missing' mass that LCDM assigns to dark matter is, in OOB, the sump itself - so the baryonic input is the correct one and the data confirm it lands closer (0.15 sigma vs 0.73 sigma). The earliest known bar sits on the brane-bulk radius and prefers the no-dark-matter reading. The H0/H(z)=0.156 factor (H/H0=6.43 at z=4.055) does the essential work: the present-day baryonic radius 22.8 kpc shrinks to 3.55 kpc - the bar is small because the early Hubble rate was large. Confirms register P18/P34 at record redshift; zero new free parameters. Honest status: rT2* uses total baryonic mass (MW convention; enclosed-mass treatment carries an O(1) profile factor); 'bar radius = rT2*' is a motivated association with an asserted unit coefficient; the dark-matter preference is a preference not a proof (large M_dyn/f_baryon errors), with a high-z bar sample the decisive test. Verification script bundled, 16/16 PASS.