Expansion by Assumption: GWTC-4.0's Hubble Constant and the Price of the Fiducial Mass Spectrum

Gravitational-wave standard sirens are advertised — correctly, in principle — as cosmology's cleanest new instrument: the waveform measures a merging binary's luminosity distance directly, with no distance ladder and no calibration chain. What the waveform does not measure is redshift. The LVK collaboration's GWTC-4.0 cosmology analysis (142 of the catalog's 218 sources, through the end of observing run O4a) obtains its redshifts statistically — from features in the compact-object mass spectrum, and from candidate host galaxies in the GLADE+ catalog — and returns H₀ = 75.4 ⁺¹²·⁸₋₉.₁ km/s/Mpc together with a modified-propagation parameter Ξ₀ = 1.4 ⁺¹·⁰₋₀·₄, where Ξ₀ = 1 is general relativity. This paper censuses the analysis's assumed steps and prices its two headline numbers. The H₀ error bar is 29% wide — its 68% interval, 21.9 km/s/Mpc across, is 3.9 times wider than the entire Planck–SH0ES gap (5.6 km/s/Mpc) the instrument is meant to arbitrate, and it contains both camps and all the space between them. The central value is conditional in a way the headline does not print: the abstract's own words make the estimate "assuming our fiducial model for the source-frame mass distribution" — the redshifts of most sources are read off mass-spectrum features whose source-frame positions are assumed, so the expansion rate is extracted jointly with, and partly from, the population model it presumes. And Ξ₀'s median sits 40% above general relativity's value, with GR resting exactly at the lower edge of the 68% interval — a posture that is neither a detection of modified propagation nor a confirmation of GR, and is quoted in the wild as whichever the quoter prefers. None of this is misconduct; it is the honest state of a young instrument. What my census objects to is only the quoting. Grade: MEASURED DISTANCES, ASSUMED REDSHIFTS — THE EXPANSION RATE IS PRICED AS CONDITIONAL. This paper stands outside my work on the vacuum catastrophe; it draws nothing from that work and repairs nothing in it.