The Hubble Tension Recounted Term by Term: An Error-Budget Audit of the Distance Ladder and the Early-Universe Inference

The local distance ladder measurement of the Hubble constant, H0 = 73.04 ± 1.04 km s-1 Mpc-1 (Riess et al. 2022), exceeds the value inferred from the cosmic microwave background under the standard cosmological model, H0 = 67.4 ± 0.5 km s-1 Mpc-1 (Planck Collaboration et al. 2020), by 5.64 km s-1 Mpc-1, or 7.72 per cent of the local value. This paper recounts the published uncertainty budget of the distance ladder, term by term, using the error budget published by the SH0ES team itself (Riess et al. 2022, Table 7), and computes a single diagnostic for each term: the shift, expressed as a multiple of that term's own quoted uncertainty, that the term would need to undergo, acting alone, to absorb the entire discrepancy. No single term in the published budget suffices at anywhere near its quoted size. The largest single contribution to the combined budget, the mean of the supernova calibrator sample at 0.9 per cent, would need to be displaced by 8.58 times its quoted uncertainty; the combined geometric-anchor term, at 0.7 per cent, would need 11.03 times; the Cepheid metallicity terms would need between 15.44 and 51.48 times, depending on the anchor; and the photometric zero-point term would need 77.22 times. Even under the most generous accounting, in which every rung term is displaced coherently in the same direction, each term must still move by 2.57 times its quoted uncertainty, and a uniform rescaling of the entire local error budget by a factor of 5.40 would be required to reduce the discrepancy to one standard deviation. The published Planck uncertainty, treated the same way, would need to be displaced by 11.28 times its quoted size. The arithmetic therefore excludes any explanation of the discrepancy in terms of a single known systematic effect at its published magnitude, and constrains multi-term explanations to require several large, same-direction excursions simultaneously. No new cosmology is proposed.