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.
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
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 / SN | mu | sigma mu | mB0 | sigma mB | M_B live | diagonal weight |
|---|
- Distance law
- Computing.
- Hubble law
- Computing.
- Residual fit
- Computing.
- Anchor shift
- Computing.
Uncertainties, free choices, approximations, and conventions
- Units: H0 is in km/s/Mpc. Distance moduli and stellar magnitude shifts are in mag. Host names follow the source tables.
- Published versus computed: the common-fit H0 values, uncertainties, intercepts, host moduli, supernova magnitudes, 0.994 ± 0.010 linearity slope, and 8.2 sigma rejection are published inputs. Row M_B values, diagonal weights, proxy means, tension values, regression, and anchor propagation are computed in this browser.
- Covariance: the row proxy assumes diagonal errors. It does not contain the full released Pantheon+ covariance or the simultaneous ladder fit. Shared supernovae, siblings, photometric calibration, NGC 4258, and analysis choices create correlations.
- Free choices: selected indicator, host sample, early endpoint, correlation coefficient, optional systematic floor, JAGB field, and any mean, median, or model estimator offset are user choices. The last three estimator offsets are deliberately not supplied with invented defaults.
- Cepheids: results depend on the geometric anchor, period-luminosity slope, metallicity correction, reddening law, filter transformation, phase sampling, crowding correction, and rejection convention.
- TRGB: results depend on age, metallicity, bandpass, color correction, field selection, edge detector, photometric pipeline, and sample completeness.
- JAGB: results depend on field, color cuts, incompleteness, luminosity-function shape, and choice among mode, mean, median, model, or a middle across variants.
- Supernovae: results depend on host selection, survey calibration, light-curve fitter, intrinsic scatter, peculiar-velocity treatment, Hubble-flow sample, and correlations among shared hosts.
- Early universe: Planck's 67.4 ± 0.5 is an inference under the base spatially flat six-parameter LambdaCDM model, not a direct late-universe measurement. The two DESI endpoints also require stated cosmological data combinations and priors.
- Tension convention: the displayed statistic is valid only for Gaussian endpoints with the correlation coefficient chosen above. It is not an analysis-independent verdict.
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
- Planck Collaboration, A&A 641 A6, DOI 10.1051/0004-6361/201833910. Peer-reviewed, published online 2020-09-11.
- Riess et al., ApJL 934 L7, DOI 10.3847/2041-8213/ac5c5b. Peer-reviewed, 2022. Published baseline: 73.04 ± 1.04 km/s/Mpc.
- Riess et al., ApJL 962 L17, DOI 10.3847/2041-8213/ad1ddd. Peer-reviewed, published online 2024-02-06.
- Riess et al., ApJ 977 120, DOI 10.3847/1538-4357/ad8c21. Peer-reviewed, published 2024-12-10. Published common three-method result: 72.6 ± 2.0 km/s/Mpc.
- Freedman et al., ApJ 985 203, DOI 10.3847/1538-4357/adce78. Peer-reviewed, published 2025-05-27.
- Li et al., ApJ 988 97, DOI 10.3847/1538-4357/addd0c. Peer-reviewed, published 2025-07-20.
- Riess et al., arXiv:2509.01667v1. Preprint submitted 2025-09-01; the checked record says ApJ submitted. Reported preprint values: 73.49 ± 0.93 and 73.18 ± 0.88 km/s/Mpc.
- DESI Collaboration, JCAP 2025 02 021, DOI 10.1088/1475-7516/2025/02/021. Peer-reviewed.
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/.