A distance-ladder switchboard

Two Rulers That Will Not Agree

Swap three JWST distance indicators, change the supernova sample, and watch the inferred Hubble constant and its naive tension with Planck move. The instruments separate what is measured, what is model-dependent, and what remains disputed.

Evidence frozen 2026-07-29

Layer one · the first rulerChange the stars, keep the lane

The first instrument holds the Pantheon+ supernova lane and the NGC 4258 anchor convention fixed. Change only the stellar indicator. The large value is the peer-reviewed common-sample result. The second value is rebuilt here from the rounded Appendix A rows with diagonal errors, so its disagreement with the full fit remains visible.

Stellar distance indicator

Loading host coverage

Published common fit

Computing

km/s/Mpc, Riess et al. 2024

Live row proxy

Computing

rounded rows, diagonal-only weights

Naive Planck tension

Computing

independent Gaussian endpoints only

Loading the published table rows.

Computing the ladder equation.

The row proxy is not promoted to the paper's answer. Appendix A explicitly calls its row method an approximation to the simultaneous ladder fit. Rounded moduli, shared anchors, sibling supernovae, and released covariance terms cannot be recovered by pretending every row is independent. The four sample buttons carry the paper's own approximate sample expectations, which it states with the word about rather than as fitted pairs: 73.17, about 71.2, about 73.6 and about 72.9 km/s/Mpc. Only the merged 16 supernova entry has a published uncertainty in that table, plus or minus 2.1, and it is used here. The plus or minus shown on the two selection subsets is this page's own propagation, not a published pair, and it should be read as an indication of scale rather than as the paper's error bar. And one thing the displayed error bars leave out. The paper states twice, in the notes to Table 4 and Table A1, that its subsample uncertainties exclude the geometric distance error to the maser host NGC 4258, worth about 1.1 km/s/Mpc. Those truncated uncertainties are what the selection buttons carry, so every tension this instrument reports against the early-universe value is an upper bound on the real significance, not the significance itself. Adding the maser term in quadrature moves the two selection subsets from roughly 1.8 and 3.0 sigma down to roughly 1.6 and 2.7. The merged 16 supernova entry uses the paper's own section 3.3 pair, 72.9 plus or minus 2.1, which already includes that term.

Layer two · the sample-selection laboratoryKeep the candle, move the sample

A more serious objection is that changing the star is not the only choice. Hold HST Cepheids fixed and move only the selected supernova hosts. These are published expected values for the named selections, recombined live with whichever early-universe endpoint and covariance convention you choose.

HST Cepheids, published sample expectations

Preparing the sample comparison.

Live tension calculator

Computing

Preparing inputs

Do not compare only the central values. The CCHP and SH0ES lanes use different supernova samples, fitters, anchors, calibrator counts, and uncertainty models. The selector above isolates one published sample effect. It does not turn the full pipelines into interchangeable parts.

Further instrument · the suspect removedDraw the crowding trend

The five-host JWST comparison measured each Cepheid distance twice, once with HST and once with JWST. Toggle the specific distance-growing bias model that was proposed to bridge the high and low values. The browser fits the five published residuals itself.

JWST minus HST distance modulus

Fitting the published host residuals.

Computed here

Computing the weighted line.

Published test

Mean: -0.011 ± 0.032 mag. The specified distance-growing crowding model is rejected at 8.2 sigma.

The fitted line above is a transparent regression of five rounded table rows. The paper's 8.2 sigma result comes from its full model and error treatment. This page does not manufacture that significance from a five-point redraw.

Further instrument · the anchor movesMove one field in NGC 4258

JAGB 2.0 found that two NGC 4258 mode measurements differ by 0.11 ± 0.022 mag. Choose the inner field, the outer field, or their midpoint. Then choose the published middle-of-variants or mode result. Mean, median, and model are exposed as free offsets because the paper does not publish one unique H0 for each label.

NGC 4258 anchor field

Computing the anchor propagation.

Live propagated H0

Computing

Preparing the field convention

The check · rebuilt in this browser

The table below is filled from the selected Appendix A rows. Every absolute supernova magnitude is recomputed as M_B = m_B^0 - mu. The live proxy then takes an inverse-variance mean and applies the displayed Pantheon+ intercept.

host / SNmusigma mumB0sigma mBM_B livediagonal weight
Distance law
Computing.
Hubble law
Computing.
Residual fit
Computing.
Anchor shift
Computing.

Uncertainties, free choices, approximations, and conventions

What is still open

The tested distance-growing HST Cepheid crowding model is strongly disfavored. The remaining spread is not assigned to one cause. Stellar zero points and population effects, supernova calibration and sample choice, underestimated covariance, other systematics, the early-universe model, and new physics remain live possibilities. CCHP's published paper reports TRGB and JAGB results while its Cepheid analysis remains ongoing. JAGB has no demonstrated standardization for the observed field and luminosity-function variation. The September 2025 SH0ES result has since been peer-reviewed and published as Astrophysical Journal Letters 992 L34 (17 October 2025, DOI 10.3847/2041-8213/ae0ad6), carrying the same two values.

Primary sources and publication status

The CCHP erratum is real and published: Astrophysical Journal 993 252, DOI 10.3847/1538-4357/ae146d, 10 November 2025. It corrects the error bars of Figure B1 only. The supernova absolute-magnitude slope against distance modulus weakens from 0.08 plus or minus 0.02 to 0.03 plus or minus 0.02, and its significance falls from above 3 sigma to 1.6 sigma. The erratum states that the result is not used elsewhere in the analysis and does not affect the rest of the paper, so the 70.39 value stands.research/two-rulers-will-not-agree/.