The question the controls address

Galaxy predictions depend on a reconstructed baryonic field, including stellar mass, gas and their spatial distributions. A residual between a predicted and observed speed can therefore respond to source assumptions as well as to the gravitational law. The controls ask whether changing the stellar source changes the normalization and residual ordering while the MQ response prescription is held fixed. [1] [4]

The numerical results below are reported in the current MQ galactic manuscript. This Brief checks their stated definitions and reproduces limited arithmetic from the printed summaries; it is not an independent catalog-level reanalysis. The external stellar-population and survey papers supply source information, not separate endorsements or independent replications of the MQ result. [1] [2] [3]

The fixed prediction and the input that changes

Let $\mathrm{𝑅}$ denote positive galactocentric radius in metres, ${\mathrm{𝑣}}_{\mathrm{New}}\left(\mathrm{𝑅}\right)$ the positive Newtonian circular speed calculated from the adopted baryonic source in metres per second, and ${\mathrm{𝑔}}_{\mathrm{bar}}\left(\mathrm{𝑅}\right)$ its positive acceleration in metres per square second. Equation (1a) defines the circular-speed representation of that source. These equation labels belong to this Brief. [1]

Let ${\mathrm{𝑣}}_{\mathrm{real}}\left(\mathrm{𝑅}\right)$ denote the predicted realized circular speed, and ${\mathrm{𝑎}}_{\mathrm{MQ}}$ the positive MQ acceleration scale in metres per square second. Equation (2b) is the unchanged local galactic law. The stellar substitution changes the Newtonian speed and baryonic acceleration entering it, while the scale and functional form remain fixed. [1]

In the WISE substitution, each catalog stellar mass is divided by its galaxy’s SPARC 3.6 micrometre luminosity to obtain an external stellar normalization. That normalization scales the existing unit-mass-to-light disk and bulge templates. The calculation retains the gas contribution, published distance and inclination, observed velocities and MQ scale. It does not optimize the stellar normalization against MQ residuals. [1]

This is a source recomputation, not simply adding stellar mass as another statistical predictor. It also does not independently rebuild the entire radial mass profile. The use of the SPARC light templates retains uncertainty in radial stellar-population gradients and in the disk–bulge decomposition. An integrated stellar mass can change the total normalization without uniquely determining where that mass lies.

Figure 1 distinguishes three analyses that use similar language but answer different questions.

Same-galaxy comparisons reveal the normalization shift

The fiducial source is the manuscript’s baseline SPARC stellar prescription; the alternative source uses the external WISE normalization. Table 1 compares them on identical galaxies within each row. Comparing a WISE overlap with a different full catalog would mix a source change with a sample change. The highest SPARC quality class is class 1; the final row also restricts inclination to 30–80 degrees. [1]

The normalization is a galaxy-level geometric MQ-to-observed velocity ratio, formed through logarithmic offsets. It is not the ratio of all pooled mean speeds, an arithmetic average of percentage residuals or a per-radius scatter measure. Unity denotes no geometric population offset under that particular statistic.

For the 60-galaxy controlled overlap, 1.0854 means a geometric predicted-to-observed normalization 8.54% above unity. The change relative to the fiducial value of 0.9915 is a different comparison: about 9.5%. Neither statement means that every radial prediction has that fractional error. The manuscript reports a 9.46% relative source shift from its underlying calculation.

Dividing the printed four-decimal ratios alone gives a 9.47% shift when rounded to two decimal places. The small difference is consistent with rounding at the precision of the printed summaries; the underlying outputs are needed for an exact reproduction. Table 2 preserves the manuscript’s reported relative shifts rather than implying that all of their digits can be regenerated from rounded ratios. No new uncertainty estimate is inferred from this difference.

Gas-rich controls reduce stellar-source leverage

The source then selects nested controls using quality, inclination and gas richness before examining MQ residuals. Gas richness is atomic hydrogen mass divided by 3.6 micrometre luminosity, with mass and luminosity expressed in solar units. The stated thresholds are at least 0.5 for the gas-rich subset and at least 1.0 for the stricter gas-dominated subset. These are operational selection cuts, not claims that a luminosity ratio is a universal gas fraction. [1]

The much smaller shifts in the gas-rich controls are consistent with lower leverage from stellar normalization. They do not prove that either stellar-mass prescription is uniquely correct. A large p-value is not proof of exact equality or a quantified upper bound on every possible source effect, particularly in an eight-galaxy subset. These nested selections also share galaxies and cannot be counted as independent confirmations.

Figure 2 plots the same reported ratios. The connectors show a change of source estimate, not uncertainty intervals, galaxy-by-galaxy trajectories or three independent observational populations.

Marginal trends and matched ordering answer different questions

A marginal trend compares residual normalization with characteristic observed velocity across the chosen sample. Under the WISE-source recomputation, the 111-galaxy overlap has a Pearson correlation of −0.1182 with a reported p-value of 0.2166. The 71 highest-quality galaxies reverse sign to +0.2140, with p-value 0.0732. In the 60 inclination-controlled galaxies, Pearson gives +0.2627 with p-value 0.0426, while Spearman gives +0.2176 with p-value 0.0950. The negative marginal trend is therefore source-sensitive; the last two statistics do not establish a uniformly robust monotonic relation. [1]

The matched test asks a conditional question at nearly equal stellar mass. Eligible pairs have a WISE stellar-mass difference no greater than 0.10 dex, an inclination difference no greater than 15 degrees and a separation in base-10 logarithmic mean observed speed of at least 0.10 dex. A dex is a base-10 logarithmic unit; 0.10 dex corresponds to a factor of about 1.26. A maximum-cardinality non-overlapping pairing gives ten pairs, with each galaxy used at most once. [1]

Residual-blind pairing means that the MQ residual is not used to optimize pair selection. It does not mean that the design uses no kinematic information: observed speed explicitly enters the velocity-separation criterion. The logarithmic residual itself contains observed speed through the predicted-to-observed ratio. These dependencies must be retained in interpreting a conditional association.

The paired offset is oriented from the lower-speed to the higher-speed member. It subtracts their logarithmic MQ-to-observed normalizations. Table 3 therefore reports a persistent negative conditional ordering, including after the external WISE masses have actually been propagated through the baryonic calculation. The fiducial matched diagnostic and the WISE-source recomputation must not be described as the same analysis.

As a reproducible interpretation of the reported mean WISE paired offset, raising ten to −0.12685 gives about 0.7467. This is the geometric higher-to-lower ratio of the two members’ MQ-to-observed normalizations. It is not a claim that the higher-speed galaxy’s absolute speed is smaller. No raw pair measurements or new uncertainty interval are inferred from this conversion.

The complementary 60-galaxy multivariate result retains a negative standardized conditional velocity coefficient of −0.1697, with HC3 robust standard error 0.0265 and a reported galaxy-bootstrap 95% interval from −0.2148 to −0.1175. The source also reports strong velocity–stellar-mass correlation, 0.9578, and variance inflation factors of 16.8 and 20.8 for those predictors. The regression remains sensitive to that collinearity. It is a conditional diagnostic, not a causal velocity correction to Equation (2b). [1]

What the results establish and leave unresolved

The source substitution demonstrates sensitivity to an independently supplied stellar normalization. Gas-rich controls identify a regime with much smaller sensitivity to that change. Matched and multivariate controls show that some conditional ordering persists. Taken together, these findings do not reduce to either a universal success or a conclusive rejection of the fixed law. They identify where stronger source information would be most discriminating. [1] [5]

Reported p-values concern specified statistical hypotheses and samples. They are not probabilities that MQ is correct, that an observational error caused a residual or that a particular stellar-mass model is true. Repeated matching tolerances reuse pairs, nested gas cuts reuse galaxies and source variants reuse rotation curves. Their significances cannot be multiplied as independent evidence.

Likewise, better normalization in a quality-selected subset does not establish that discrepancies elsewhere are merely data errors. Radial points share distance, inclination and source assumptions within each galaxy. A near-unity population normalization can coexist with substantial radial scatter. Both galaxy-level patterns and source covariance belong in a complete test.

The next source test is a resolved radial profile

The manuscript specifies a prospective calculation for DDO 50, DDO 216, IC 1613, NGC 1569 and NGC 3738. It proposes using the published radial stellar-population information of Zhang and collaborators with LITTLE THINGS gas and kinematic products. The distinction from an integrated WISE substitution is spatial: the stellar mass must be placed at each radius, not only assigned a new total normalization. [1] [6] [7]

Freeze the radial source, observational conversions, MQ scale and response law before examining the residuals. A substantial reduction of the existing discrepancies would help localize sensitivity to the source reconstruction. Persistent coherent residuals with a well-constrained source would place more direct pressure on the fixed law. The cited source treats this calculation as outstanding, rather than a completed confirming experiment.

Duey and collaborators’ stellar-population analysis is useful external input and carries its own population-model uncertainties. It is not a guarantee of exact masses or a complete resolution of radial source structure in the MQ implementation. A stronger test needs those uncertainties propagated rather than replacing a source estimate with a supposedly error-free alternative. [2]

Chronology and interview source requests

September 8, 2026 is the archive’s completed-source milestone, not a journal publication or verified original announcement date for these checks. This October 26, 2026 Brief uses later public revisions openly. It does not imply that every table or qualification was already present at the September milestone. [1]

For an interview, request the same-galaxy overlap lists, stellar-normalization recipe, fixed parameter file, all selection and matching rules, paired source predictions and residual definitions. Ask for radial source covariance and results on the difficult systems, not only a best-quality average. Finally, request a clear separation between completed sensitivity checks and the still-prospective resolved-profile calculation.