Two-rung ladder: H 0 from Tip of the Red Giant Branch and geometric anchors alone

We infer the Hubble constant H 0 from the 400 Extragalactic Distance Database hosts with a tip of the red giant branch (TRGB) distance, calibrated on the geometric anchors of the Large Magellanic Cloud and NGC 4258. We forward-model the tip magnitudes and host redshifts including magnitude-limited selection, sky exposure, and density-dependent galaxy bias, conditioning on each of the 80 Manticore-Local realisations of the local density and peculiar-velocity fields in turn. As most hosts lie at cz CMB 1000 km/s, where peculiar velocities are important, the inference is limited by the variance of these fields rather than by the TRGB calibration. For a fixed realisation, the redshift likelihood and density smoothing each move H 0 by less than 1 km/s/Mpc and a velocity monopole by 5.4 plus or minus 3.4 km/s/Mpc, whereas the field-to-field scatter in H 0 is 5.2 km/s/Mpc. Weighting the posteriors from each realisation equally gives H 0 = 68.4 plus or minus 5.9 km/s/Mpc, while weighting each by its Bayesian evidence gives 72.3 plus or minus 2.6 km/s/Mpc. The latter value is set by a single particularly high-evidence realisation, making it sensitive to the finite sampling of the reconstruction posterior. This ladder therefore cannot yet arbitrate the Hubble tension. Extending the TRGB data beyond the present 1000 km/s, together with improved reconstructions of the local Universe, would reduce the field-to-field scatter well below the 5.2 km/s/Mpc we find here.