What makes the proposed test discriminating

A present-epoch radial acceleration relation describes a response at the epoch where its inputs and normalization are evaluated. MQ proposes an additional age dependence. Once that relation is fixed, it prescribes how the same baryonic field would be realized at a different cosmic age. Testing that prescription is more restrictive than allowing a fresh phenomenological acceleration scale to be fitted in every redshift bin. [1] [6]

This does not distinguish MQ automatically from every model of dark matter or modified gravity. Competing predictions must be specified for the same observable and source assumptions. The immediate target is the prescribed age dependence, rather than the broad claim that every kind of earlier galaxy should rotate faster than every nearby galaxy.

The inverse-age scaling and its domain

Let ${\mathrm{𝐴}}_{\mathrm{𝑈}}$ denote the positive System Frame cosmic age at the epoch being tested and ${\mathrm{𝐴}}_{\mathrm{𝑈}\mathrm{,}\mathrm{0}}$ its present-epoch value, both in the same time units. This is realized elapsed cosmic time, not an SI-equivalent pre-referenceable quantum-epoch scale. Let ${\mathrm{𝑎}}_{\mathrm{MQ}}$ denote the characteristic MQ acceleration scale in metres per square second. Equation (1a) is its age dependence with the other source premises fixed. Equation labels here belong to this Brief. [1]

The source derives this scaling through the Internal Frame local expansion-rate realization used in the galactic normalization. The observational redshift conversion uses the System Frame expansion history. These rates have different roles in the construction and must not be exchanged simply because both are reported with inverse-time units. [1]

At half the present age, Equation (1a) doubles the characteristic acceleration scale; at one quarter, it multiplies the scale by four. That is a scaling of this galactic prescription, not a new laboratory measurement of a varying Newton constant. Physical use requires a defined positive realized age. Extrapolating the formula toward zero does not establish a realized epoch with a clock at zero age.

The baryonic source and predicted circular speed

Let $\mathrm{𝑅}$ be positive galactocentric radius in metres, ${\mathrm{𝑣}}_{\mathrm{New}}\left(\mathrm{𝑅}\right)$ the Newtonian circular speed from the adopted baryonic source in metres per second, and ${\mathrm{𝑔}}_{\mathrm{bar}}\left(\mathrm{𝑅}\right)$ the corresponding positive baryonic acceleration in metres per square second. It is the Newtonian speed squared divided by radius. Let ${\mathrm{𝑣}}_{\mathrm{real}}(\mathrm{𝑅},{\mathrm{𝐴}}_{\mathrm{𝑈}})$ denote the predicted realized circular speed at that radius and cosmic age. Equation (2b) applies the same local response law using the age-dependent scale. [1]

The fixed-source comparison holds the physical stellar and gas distributions, radius and Newtonian baryonic field unchanged while varying only the age argument. Decreasing the age increases the scale, reduces the realization fraction in the denominator and increases the predicted speed. The speed change depends on the baryonic acceleration; it is not equal to the scale change.

Figure 1 separates the controlled mathematical comparison from the evolving-source observational problem.

The exact fixed-source velocity ratio

Dividing Equation (2b) by the same prediction at the present age cancels the common Newtonian source speed. Equation (3c) therefore compares two ages at the same radius and baryonic field, using the positive circular-speed branch. It is an algebraic consequence of the fixed law, not an additional empirical result. [1]

The largest fractional response occurs at low baryonic acceleration relative to the relevant scales. Regions that remain high in acceleration relative to the age-adjusted scale approach the Newtonian response and have a smaller fractional age effect. The dependence is continuous, so a single universal percentage shift for an entire survey would discard information in the prediction.

A reproducible age-only example

Table 1 uses dimensionless age fractions so that no redshift conversion is hidden in the arithmetic. Both columns hold the baryonic source fixed. The first sets its acceleration to one tenth of the present-epoch scale; the second sets it equal to that scale. The table changes the age, not the source acceleration or its normalization to the present scale.

At half the present age, the scale is exactly doubled in this example. The predicted speed rises by 16.320% in the lower-acceleration column and 11.667% in the other column. These are calculated fractional changes, not observed galaxy offsets or uncertainty intervals. Figure 2 shows the same response across the displayed positive-age range.

Redshift requires an additional cosmological prescription

Redshift measures a change in the cosmological scale factor; it is not itself a cosmic-age reading. The source obtains age at a given redshift by subtracting lookback time from the present-age normalization. The lookback integral uses the reciprocal of the product of one plus redshift and the prescribed System Frame expansion rate. The integration extends from redshift zero to the target redshift, with units handled consistently. [1]

This coordinate conversion is conditional on the adopted expansion history. It does not derive that history from the galaxy data. A prospective test must specify the history, present-age normalization, relevant covariances and treatment of alternative allowed histories before examining velocity residuals. If the adopted history makes the target age nonpositive or lies outside the realization domain, the local law is not thereby licensed for a physical zero-age extrapolation.

The current source quotes an MQ present-age normalization of 13.7943(39) billion years, obtained by inserting the measured Fixsen CMB temperature into its cosmological construction. Parentheses indicate 0.0039 billion years in the final displayed digits of the quoted conditional uncertainty. This is not an independent observational determination of cosmic age, and that narrow input error does not quantify uncertainty in the absolute temporal normalization, source reconstruction or missing observational covariance. [1] [5]

Table 2 preserves the manuscript’s rounded redshift benchmark. It adopts that present-age normalization and a Planck 2018 flat late-time expansion benchmark. These are source-reported conditional example values, distinct from the independently reproduced age-fraction calculations of Table 1. They are not fits to galaxy data and are not universal predictions under every possible redshift-to-age history. [1] [4]

Both velocity columns keep the physical baryonic acceleration fixed relative to the present-epoch scale. They do not renormalize that source to the changing scale at each redshift. The rounded ages and ratios do not provide enough information to reconstruct the entire cosmological integration or a complete uncertainty budget. The underlying expansion prescription and numerical implementation should accompany a test.

Why intermediate-redshift surveys are useful, but are not already the test

RC100 supplies resolved hydrogen-alpha or carbon-monoxide rotation curves for 100 massive star-forming disks across redshifts about 0.6–2.5. Its published analysis uses beam-convolved dynamical models that include pressure support and dark halos. Those fitted halo decompositions cannot simply be relabeled as independent baryonic inputs to an MQ prediction. [2]

The KROSS analysis supplies spatially resolved hydrogen-alpha kinematic information for star-forming galaxies around redshift 0.9. Together, these studies show that the required observations are accessible in a useful epoch range. They do not report a completed frozen-parameter MQ age-dependence test. A consistent source reconstruction and observational forward model would still be required. [3]

The proposed interval, roughly redshifts 0.5–1.5, is a compromise between a larger predicted effect and the practical quality of resolved disk measurements. Higher-redshift examples may be exploratory, but a velocity gradient in one luminous compact source does not uniquely establish a circular-speed field or test the fixed-source relation.

What a prospective test must freeze and propagate

Before residual inspection, fix the sample and exclusion rules, age relation, cosmological history, source reconstruction, MQ normalization and likelihood or residual statistic. Stellar and gas inputs must be constrained without tuning them to eliminate the MQ residual. Preserve the radial range and match galaxies by independently reconstructed acceleration and relevant structure, rather than merely by luminosity or redshift. [1] [7]

A physical forward model must connect circular speed to observed line-of-sight velocity fields. Pressure support, inclination, spatial resolution and beam smearing can affect that conversion, while mergers, outflows and noncircular motions can invalidate a simple disk interpretation. Their treatment should be specified before selecting apparently successful examples.

Propagate shared uncertainties in distance, stellar normalization, gas conversion, source geometry and the age mapping. Radial points in one galaxy share inputs, and galaxies may share cosmological calibration. A galaxy-level or hierarchical analysis should retain those dependencies. Several redshift bins with overlapping assumptions are not automatically independent confirmations.

What would challenge the prediction, and what it would not settle

A statistically secure absence of the prescribed shift in suitably matched systems with independently constrained sources would challenge the stated age dependence of the galactic law. The analysis should publish its sensitivity to source and cosmological choices so that a null result is distinguishable from an uninformative measurement. Allowing a new MQ normalization in each bin would remove much of the test’s discriminating power. [1]

Conversely, an observed shift must be compared with competing physical and observational explanations. It would not, by itself, establish every upstream realization premise or complete a theory of galaxy formation. Assembly, cooling, feedback, mergers and the surrounding cosmology must be evolved to predict the abundance, luminosity and maturity of early galaxies. The source’s fixed-source curve does not calculate those quantities.

Chronology and source requests

The supplied archive entry uses September 27, 2026 as a research-review milestone. The underlying manuscript separately records a September 8 completed-source milestone and includes later revisions. Neither date is used here as a verified discovery, announcement or journal publication date. This Brief was prepared October 26, 2026, and retains the present source’s normalization limits. [1]

For an interview, request the timestamped age-dependent prediction, the exact expansion-history file, the present-age input chain, the sample and source rules, and executable predictions before residual inspection. Ask which parts of the observational forward model were validated independently and whether the dedicated test has actually been run. These questions keep a prospective discriminator separate from a claimed detection.