# Proof Narrative: Local Cepheid-variable measurements of the Hubble constant exceed 72 km s⁻¹ Mpc⁻¹ while the 2018 Planck CMB inference yields a value below 68 km s⁻¹ Mpc⁻¹

## Verdict

**Verdict: PROVED (with unverified citations)**

Two independent methods of measuring how fast the universe is expanding give numbers that don't agree — and this proof confirms the gap is exactly as wide as claimed.

## What was claimed?

The claim is that two leading methods of measuring the Hubble constant — the rate at which the universe expands — give results that are not just different, but separated by a clear threshold. Specifically, the most comprehensive measurement using Cepheid variable stars (a well-established cosmic distance marker) comes in above 72 km/s/Mpc, while the inference drawn from the cosmic microwave background by the Planck satellite's 2018 data comes in below 68 km/s/Mpc. If both halves are true, that's a gap of at least 4 km/s/Mpc between two methods that, under our standard model of cosmology, should agree. This matters because it would mean either one or both methods has an unrecognized flaw — or our standard cosmological model is incomplete.

## What did we find?

The SH0ES team (Riess et al. 2022) measured the Hubble constant at 73.04 km/s/Mpc using Cepheid variables observed with the Hubble Space Telescope across 42 galaxies. This value comfortably exceeds the 72 km/s/Mpc threshold by about 1 km/s/Mpc. The measurement was drawn directly from the published paper on arXiv, and the same number appears in the peer-reviewed journal publication — both sources agree exactly.

The Planck Collaboration's 2018 result, derived from temperature fluctuations in the cosmic microwave background under the standard ΛCDM cosmological model, gives 67.4 km/s/Mpc. This sits 0.6 km/s/Mpc below the 68 threshold. Even at the upper edge of its stated uncertainty, the value reaches only 67.9 — still below 68. This result was confirmed through both the original arXiv paper and the ESA Planck Science Portal, which independently report the same number.

The gap between the two measurements is 5.64 km/s/Mpc. This is the quantity at the heart of the well-known "Hubble tension," a discrepancy that has persisted across multiple independent analyses and now exceeds 5 standard deviations in statistical significance.

Attempts to find counter-evidence came up empty. Lower Hubble constant values around 69.8 km/s/Mpc do exist, but they come from a different technique — the Tip of the Red Giant Branch method — not from Cepheid variables. The most comprehensive Cepheid-based measurements, including those from an independent team, still exceed 72. On the Planck side, extended cosmological models can push the inferred value slightly higher, but the claim refers specifically to the standard base-ΛCDM analysis, which is firmly at 67.4. More recently, observations from the James Webb Space Telescope independently surveyed over 1,000 Cepheid variables and confirmed the SH0ES result, ruling out a systematic error in the Hubble telescope measurements.

## What should you keep in mind?

Two of the four citations used in this proof could not be automatically verified — the IOPscience and arXiv pages for these papers returned content that the automated checker couldn't parse. In both cases, however, the same numerical values were confirmed through a second independent source that was successfully verified. No conclusion rests solely on an unverified citation.

The ESA Science Portal, one of the verified sources, is operated by the European Space Agency — the organization that ran the Planck mission — making it highly authoritative, even though it wasn't classified as such automatically.

This proof establishes that the specific numerical thresholds in the claim hold. It does not address whether either measurement is "correct," what causes the tension, or whether the standard cosmological model needs revision. The Hubble tension is an active area of research with no settled explanation.

## How was this verified?

This claim was evaluated by extracting central values from primary published sources, comparing them against the stated numerical thresholds, and cross-checking each value against an independent source. You can read [the structured proof report](proof.md) for a full summary of findings, examine [the full verification audit](proof_audit.md) for source-by-source citation details and adversarial checks, or [re-run the proof yourself](proof.py) to reproduce the result from scratch.