O5 dark-siren forecasts for modified GW propagation: background robustness of the posterior

Binary black hole mergers without electromagnetic counterparts are expected to dominate O5 gravitational-wave catalogs. Recent CHIMERA 2.0 forecasts typically fix m to a CMB-informed value and use spectroscopic hosts when available, but the corresponding sensitivity of the posterior has not been assessed for pure dark sirens on the public O5 mock catalog. We analyze 300 O5-sensitivity mock events without galaxy catalogs, varying m over [0.20,,0.35] (including Planck 0.315), and compare fixed-background inference with joint (H 0,, m,,) inference. The marginalized posterior is 0.9783 plus or minus 0.3548 and shows no change across this interval. Only GW luminosity distances enter the analysis, so the likelihood constrains, D L EM (H 0,, m); when m is changed, H 0 shifts to compensate and the marginal remains unchanged. Joint inference gives joint = 0.9550 plus or minus 0.3710, with rho 0.05 for the m -- and H 0 -- pairs, whereas rho H 0 m-0.4 and the H 0 median moves by 4.2, km,s-1,Mpc-1 over the adopted m range. Galaxy-catalog analyses on the same events at fixed m = 0.3 reach about 7.5% precision on, compared with plus or minus 36.3% here; the larger uncertainty is driven mainly by missing host redshifts. Sub-percent tests will therefore still require measured redshifts even if dark sirens dominate the detection rate.