Publication identity and chronology

The article is Jody A. Geiger’s Resolving the Hubble tension 68.261 and 73.510 km s⁻¹ Mpc⁻¹, AIP Advances 15, 075134, DOI 10.1063/5.0269029. It is open access under CC BY 4.0. Its author affiliation is the Informativity Institute in Chicago. Table 1 records the publisher’s dates, also shown in Figure 1. These identify editorial events, not the first discovery of every component relation. [1]

The title asserts a resolution; the reporting question is what was calculated and what was independently tested. Journal publication establishes a citable scientific proposal. It does not convert the author’s physical interpretation into a finding of the SPT-3G or distance-ladder collaborations.

The physical problem and the proposed contribution

The Hubble tension concerns differing estimates of the present expansion rate from different observational and modeling chains. A cosmic microwave background analysis fits radiation power spectra within a cosmological model. A Cepheid-calibrated supernova ladder constructs distances and luminosity calibrations in the nearby universe. These are not direct observations of two independently evolving universes. [7] [8]

MQ proposes that the procedures correspond to different mapping normalizations of one underlying expansion account. Its Internal Frame is the discrete count-configuration domain. Its System Frame is the observable relational realization, connected to that domain through the Frames mapping. The hypothesis associates the lower calculated rate with CMB inference and the upper rate with the Cepheid ladder. The observational collaborations did not independently identify those frame assignments. [2] [3]

The central issue is therefore not whether one can write down two numbers. It is whether an observable-level model derives the proposed assignments and reproduces the radiation and distance-ladder data with their calibration dependencies. A geometric factor appearing in a calculation does not by itself establish that observational transfer. [2] [4]

Exact rate relations in current notation

Let ${\mathrm{𝐴}}_{\mathrm{𝑈}}$ denote the realized universe age in seconds, ${\mathrm{𝜃}}_{\mathrm{𝑠}\mathrm{𝑖}}$ the dimensionless MQ invariant coefficient and $\mathrm{\pi }$ the dimensionless circle constant. Let ${\mathrm{𝐻}}_{\mathrm{sys}}$ and ${\mathrm{𝐻}}_{\mathrm{int}}$ be the physical realized comparison rates labeled for the System Frame and Internal Frame, respectively. Equations (1a) and (2b) give inverse-second rates, before conversion to astronomical units. [2]

These formulas express the published rate construction using the current dimensionally explicit convention. The dimensionless coefficient is not identified with its momentum or angular realization. Both rates above are physical realized quantities; labeling one for the Internal Frame does not place an SI clock frequency in the primitive count domain. The lettered labels are local to this Brief. [2]

Adding the two definitions gives Equation (3c). The midpoint returns the inverse-age baseline exactly before rounding. The midpoint, two endpoints and their separation are dependent quantities, not additional independent observations.

Changing the common age changes both rates together. Their ratio cancels that common age factor, while retaining dependence on the invariant coefficient. A joint comparison must propagate shared inputs and covariance rather than multiply two agreement claims as though they came from independent theoretical predictions. [2] [4]

Reconstructing the historical displayed values

A reproducible rounded-input illustration uses an age of 13.794 billion Julian years, historical coefficient 3.26239030392 and the paper’s rounded megaparsec conversion of 3.08567758 × 10¹⁹ kilometres. One Julian year is exactly 31,557,600 seconds. The age becomes 435,305,534,400,000,000 seconds. These are stated reconstruction inputs, not a claim to recover every digit of the original calculation file. [9]

Take the inverse age, apply the two dimensionless multipliers in Equations (1a) and (2b), then multiply each inverse-second rate by the number of kilometres in one megaparsec. This expresses the same rates in km s⁻¹ Mpc⁻¹. Table 2 gives the results. The additional worked digits document arithmetic, not experimental accuracy.

The rounded-input calculation reproduces all three historical displayed rates. Averaging the two three-decimal published endpoints gives 70.8855 rather than the printed 70.885 baseline. The 0.0005 final-digit difference comes from recombining separately rounded numbers. It does not establish an additional physical offset.

The inverse-age relation is part of the model prescription. In general cosmology, universe age depends on the expansion history; spatial flatness alone does not require the current expansion rate to equal inverse age. A physical assessment must specify that history and its relation to observables rather than treat the baseline as a universal consequence of flat geometry. [6]

The historical observational comparison

Table 3 preserves the selected comparison entries printed in the article’s Table I. The SPT-3G value is the model-conditioned inference from its 2018 temperature and polarization dataset. Pantheon+ reports results for several cosmological models and combinations; the asymmetric ladder entry below is specifically the one reproduced in Geiger’s historical table, not a universal summary of every SH0ES result. [7] [8]

Figure 2 shows those central values with the quoted observational intervals. The ladder uncertainty remains asymmetric. No error bar has been invented for the historical model values, and no joint significance is computed. The central ladder residual is +0.110, slightly larger than a literal 0.1 threshold; the historical abstract’s blanket less-than-0.1 wording should not replace the printed-value arithmetic.

Later revisions belong to their own versions

Table 4 separates the publication from the current revised preprint. In the current notation, parentheses on 68.259(19) and 73.508(20) mean one-standard input-propagated uncertainties of 0.019 and 0.020 in the final rate units. The propagation is conditional on the MQ normalization and excludes unquantified model discrepancy. Those uncertainties cannot be attached retroactively to the old three-decimal values. [2]

The current source reconstructs the age from measured CMB temperature and other adopted inputs under a fixed temporal-normalization premise. The age is derived within that chain rather than an additional independent age measurement. The premise remains unverified; its model discrepancy is not captured by the small propagated uncertainties. Later CMB combinations can disagree more strongly with the lower branch than the selected historical comparison did. [2] [5]

What a stronger evaluation would establish

A full test should specify how the proposed realization acts on the CMB observables and the distance-ladder calibration chain, propagate the common theoretical inputs and relevant observational covariance, and compare the resulting likelihoods across relevant data. Recovering a selected compressed expansion-rate estimate is a useful consistency check but does not establish the physical origin of the observational discrepancy. [2] [4] [7] [8]

A journalist can distinguish three claims. The article was published, its stated rounded-input rate calculation can be reconstructed, and its proposed frame interpretation remains subject to empirical assessment. The first two do not logically establish the third. Neither a close residual nor editorial acceptance is a probability that the interpretation is correct.

Source requests should identify the published version, any later correction or calibration change, the age-normalization assumptions, the shared-input covariance and the observable-level prediction. Later results should be reported with their own dates and datasets. This Brief does not refit survey likelihoods or certify a demonstrated resolution.

July 22, 2025 is the verified publication date. This Brief was prepared October 27, 2026. Current terminology clarifies the account without claiming that every later definition, uncertainty qualification or observational test appeared in the original article.