Standard Sirens: Where the Gravitational-Wave Measurement Stands and How Many Events Arbitration Takes

Gravitational-wave standard sirens measure luminosity distance absolutely, from the waveform itself, with no ladder and no ruler — the only proposed arbitration of the Hubble tension whose systematics share nothing with either side. This paper computes where that arbitration currently stands and what it will take to complete. The single bright siren, GW170817, gives H0 = 70 (+12/−8) km/s/Mpc, or 70.3 ± 5.2 with the radio jet's inclination constraint added; both values sit within 0.6 sigma of Planck and of SH0ES simultaneously, arbitrating nothing yet. The event-count roadmap is then computed exactly: distinguishing the two contending values (a fractional separation of 8.43 percent) at three sigma requires about 29 events with 15-percent distances, or 51 with 20-percent distances; reaching a total precision of 2 percent requires 57 events at 15 percent per event, 25 at 10 percent, or 13 at 7 percent; and a 1 percent determination requires 225, 100, or 50 events in the same cases. A floor that no event count removes is quantified: host-galaxy peculiar velocities of 200 km/s contribute a fractional error of 6.7 percent at redshift 0.01, falling to 1 percent only beyond redshift 0.067, so the arbitration sample must be drawn from beyond the local velocity field's reach or carry modelled velocity corrections. Against the bounced-cosmology frame and every other party to the dispute, the sirens' verdict is the same: the method is unbiased by construction and currently outnumbered; the roadmap above states, in events, exactly how outnumbered. This study is computed from published values; it is not a measurement.