An external population, with a specific source chain

LITTLE THINGS abbreviates Local Irregulars That Trace Luminosity Extremes, The H I Nearby Galaxy Survey. It centers on Very Large Array neutral-hydrogen observations of nearby dwarfs. Oh and collaborators supplied a 26-galaxy rotation-curve and mass-model study; O’Brien and collaborators later published alternative-gravity analyses and figures for 25 systems. The MQ calculation reuses these observational products for a separate comparison. None of those source studies is an MQ replication. [2] [3] [4]

The MQ preprint reports that sample availability and provenance exclusions were fixed before inspecting MQ residuals. Table 1 accounts for the reduction from the 26-galaxy source study to 15 non-SPARC galaxies. This reported residual-blind screening is distinct from demonstrating a public preregistration or an independently executed prospective trial. [1]

No exclusion is attributed here to a poor MQ residual. The selection does constrain the population to systems with the required source information. The result therefore concerns this 15-galaxy subset, not every LITTLE THINGS galaxy or a statistically complete census of dwarf galaxies. [1]

Recovering the baryonic source rather than inheriting a fitted curve

Observed circular-velocity markers and plotted vertical uncertainties were digitized separately from paired conformal-gravity and MOND panels. The source reports a median absolute difference of 0.15 km/s between the two extractions. This checks extraction consistency; it is not the full velocity uncertainty, an independent observation or a second galaxy sample. [1] [3]

The plotted Newtonian component is not used unchanged as the decisive baryonic input because the alternative-gravity analysis fitted stellar disk masses. The MQ reconstruction evaluates that fitted Freeman-disk contribution from the published mass and scale length, removes it in quadrature from the plotted Newtonian component, and recovers the represented gas contribution. It then builds the stellar term using Oh and collaborators’ SED-based stellar masses. SED means spectral energy distribution. [1] [2] [3]

The resulting source remains a reconstruction. Recovering gas from plotted components and replacing stellar normalization does not turn the inputs into direct force measurements. Distances, inclination, disk geometry, gas distribution, stellar radial templates, pressure support and noncircular motions can affect the source or the inferred circular-speed target. Their provenance and covariance remain necessary. [1]

The fixed local gravitational law

Let $\mathrm{𝑅}$ denote galactocentric radius in metres, ${\mathrm{𝑣}}_{\mathrm{New}}\left(\mathrm{𝑅}\right)$ the positive Newtonian circular speed of the reconstructed baryonic source in metres per second, and ${\mathrm{𝑔}}_{\mathrm{bar}}\left(\mathrm{𝑅}\right)$ the corresponding positive baryonic acceleration in metres per second squared. Equation (1a) is the circular-kinematic conversion. Brief equation labels are distinct from those of the source. [1]

Let ${\mathrm{𝑎}}_{\mathrm{MQ}}$ denote the MQ characteristic acceleration scale in metres per second squared and $\mathrm{𝜒}\left(\mathrm{𝑅}\right)$ the dimensionless realization depth. Equation (2b) defines that depth. The reported sample statistics use the original frozen nominal scale 1.20040492178 × 10⁻¹⁰ m s⁻², with no per-galaxy adjustment. [1]

Let $\mathrm{𝑃}\left(\mathrm{𝑅}\right)$ denote the dimensionless realized fraction. Its subdivision-consistent exponential form is Equation (3c), within the stated MQ construction. [1]

Let ${\mathrm{𝑔}}_{\mathrm{real}}\left(\mathrm{𝑅}\right)$ be the realized radial acceleration and ${\mathrm{𝑣}}_{\mathrm{real}}\left(\mathrm{𝑅}\right)$ its positive circular speed, with the same units as their baryonic counterparts. Equations (4d) and (5e) state the source-to-response conversion for positive baryonic acceleration and scale. [1]

The same law is applied across the selected galaxies. No galaxy-specific MQ acceleration, halo component or interpolation parameter is fitted to their observed velocities. This does not make the full astrophysical analysis parameter-free. The externally adopted baryonic and kinematic reconstructions contain assumptions and uncertainties. [1]

The current gravity overview reports a slightly revised shared-input acceleration calibration and explicitly keeps the published galaxy statistics under their original nominal value. It does not claim those catalog statistics were rerun. The cosmological normalization is a shared model dependency, so a separate population is not independent of every upstream theoretical input. [5]

What the reported normalization statistic means

The source reports 288 radial comparisons in 15 galaxies. Its galaxy-weighted mean logarithmic predicted-to-observed normalization is −0.00407 dex. In this statistic, logarithmic ratios are summarized within galaxies and the galaxy summaries receive equal weight in the population mean. A galaxy with more digitized radii therefore does not acquire population weight merely by contributing more points. [1]

Exponentiating the rounded mean with base ten gives 0.99067225, consistent with the reported geometric ratio 0.9907. That central ratio is 0.93% below unity. This arithmetic interpretation is not a 0.93% uncertainty or a one-percent accuracy guarantee for every curve.

For the interval, galaxies are resampling blocks. Resampling a galaxy carries its radial comparisons together, rather than pretending the 288 points are independent draws. The reported 95% interval is 0.868–1.130. It spans offsets from unity of −13.2% to +13.0%. It must not be relabeled as a one-standard-deviation error or an uncertainty assigned to each radial speed. [1]

Figure 1 plots the reported ratio and interval directly. It does not reconstruct a bootstrap distribution, which would require the underlying galaxy summaries and resampling procedure.

The high zero-offset probability does not establish equivalence within a prespecified narrow tolerance. Nor can pooled RMS, signed bias and geometric normalization be substituted for each other. Positive and negative radial errors can offset in a signed mean while absolute scatter remains substantial. Digitization and reconstructed-source uncertainty preclude treating the reported comparison as a precision pointwise likelihood. [1]

Source substitution and the next resolved-profile test

The current public source reports a galaxy-weighted ratio of 0.9655 when Oh and collaborators’ alternative kinematic stellar masses replace the primary SED masses. The fixed MQ law is unchanged. Compared with 0.9907, that is a -2.544% change in the aggregate ratio, calculated from the rounded values. It is not a uniform velocity correction at all radii. [1]

Table 3 separates that aggregate change from the source’s gas-dominated and stellar-important group summaries. The percentage conversions use base-ten exponentiation of the displayed mean logarithmic shifts. They illustrate the source sensitivity without recreating the galaxy catalog.

These source substitutions show that baryonic reconstruction can materially change normalization where stars are dynamically important. They do not identify every residual as a source error. Changing an integrated stellar mass rescales a radial template; it does not replace that template with an independently measured resolved stellar profile. [1]

The proposed next source test targets DDO50, DDO216, IC1613, NGC1569 and NGC3738, selected by stellar importance rather than favorable MQ residuals. The source identifies published resolved stellar profiles and LITTLE THINGS gas and kinematic products as inputs for that test. Those profiles must be adopted before residual inspection while keeping the MQ scale and law fixed. This resolved-profile analysis remains prospective in the cited account. [1]

Figure 2 separates the reconstructed source from the external observed velocities. It shows the protocol reported for this comparison, not new radio observations or a completed resolved-profile follow-up.

Velocity ordering, limited power and the evidence boundary

The source reports no significant correlation between galaxy-mean logarithmic normalization and logarithmic characteristic velocity: Pearson coefficient −0.282 with p = 0.308. Controlling stellar mass and inclination gives −0.257 with p = 0.355. These are source-reported exploratory population diagnostics, not independent confirmations of the mean result. [1]

The small matched-pair tests are underpowered. The primary stellar-mass tolerance yields only two non-overlapping pairs; relaxing it yields three or four. Failure to reproduce the stable ordering reported in SPARC does not establish velocity independence or prove that SPARC’s residual structure is purely observational. A larger, controlled population and resolved sources would strengthen that distinction. [1]

Independence here primarily means an out-of-SPARC target population and no MQ scale fitting to these velocity residuals. The analysis still shares its theoretical law and cosmological normalization with other MQ galaxy tests, and source and target information can share observational assumptions. The calculation was performed within the MQ program; the cited survey teams did not conduct a separate replication. [1] [5]

Rotation-curve consistency in this subset does not settle lensing, merging clusters or cosmological dark-matter requirements. The relevant result is a fixed-law population-normalization comparison with substantial individual scatter and source limitations. The displayed-value conversions in this Brief were checked, but the 288-point analysis and bootstrap were not independently rerun. [1] [7]

Chronology, access and reporting requests

September 27, 2026 is the archive review snapshot, distinct from the September 8 completed-source milestone and later revisions. Neither is assigned as a journal publication or original discovery date. This Brief was prepared October 26, 2026.

The preprint identifies public observational sources and says derived numerical products needed to reproduce the analysis are available from the author on reasonable request. A reproducibility request should include the full retained galaxy list, digitized paired-panel extractions, fitted-component removal, rebuilt stellar profiles, covariance assumptions, bootstrap implementation and galaxy-level residuals. The original observational papers remain the sources for their own measured and modeled products. [1]