The audit concerns the role of a result

Appendix E of the current galactic preprint classifies quantitative claims by their inputs, targets and evidentiary interpretation. It is authored within the MQ research program. Calling it an audit does not establish an external review, reproduce every underlying dataset or turn manuscript assertions into independently validated findings. [1]

A derivation establishes a consequence of stated premises. Empirical work asks whether that consequence describes measured quantities under appropriate source and error models. These are different achievements. More equations can make a framework more explicit and testable, but equation counts do not measure the probability that its physical premises are correct.

Table 1 gives the principal classification used by the source. Prospective versus retrospective timing is a separate label that can qualify a target comparison. These categories are not a ranked score, and the audit supplies no conversion from them to a global significance. [1]

Three different meanings of independence

Target independence means that the particular observable being tested did not determine the prediction. Statistical independence concerns the joint dependence of errors, inputs and data across results. Independent replication adds a separate execution of the analysis or experiment. A calculation can satisfy the first description without satisfying the other two. [1]

For example, two astrophysical tests can use different galaxies while sharing the same MQ acceleration normalization and cosmic-age input. A stellar-source substitution can supply new mass information while retaining the original rotation-curve target. Those distinctions matter even when all numerical work is correct. Figure 1 shows selected pathways rather than claiming to reconstruct the full dependency graph. [1] [3]

Calibration, temperature closure and expansion comparisons

The fine-structure measurement used to determine an MQ coefficient cannot also serve as an independent validation of that coefficient. Recovering the calibration through a subsequent realization chain is a useful closure test. The same caution applies when an exact SI input or a CODATA identity already contains a constant that a later numerical calculation recovers. [1] [3] [4]

The CMB temperature case requires an explicit input direction. In the historical route classified by Appendix E, MQ count geometry and an adopted Planck-derived age generate a temperature comparison. That age is informed substantially by CMB anisotropy data, so the source calls the result cross-scale closure rather than independent CMB confirmation. A radiation-density value derived from the same temperature is not an extra independent test. [1]

Other current MQ calculations run the input direction from a measured CMB temperature to a conditional cosmic-age normalization. The two routes must retain their own source versions and inputs. An age derived from the same temperature cannot be fed back and counted as a second measurement of that temperature. Small propagated input errors also do not quantify unmodeled physical discrepancy. [1] [4]

The two frame-resolved Hubble values share a common MQ scalar, age normalization and mapping construction. The assignment to observational regimes was retrospective. Appendix E therefore treats their agreements as internal closure, while the public prediction discussion identifies conditions that a future comparison could challenge. Neither wording supplies two statistically independent discoveries. [1] [2]

Likewise, MQ referenceability-domain fractions and standard cosmological density fractions have different physical definitions. Their numerical proximity is a correspondence benchmark. A dynamical cosmological calculation is required before those numbers could establish equivalence of the observables. [1]

What the galaxy examples demonstrate

Table 2 preserves selected source-reported results. Their numerical scales are intentionally different. RMS speed discrepancy, geometric normalization and a confidence interval answer different questions and are not a common scoring unit. [1]

The principal Milky Way calculation uses the McMillan baryonic source with its halo force excluded and Eilers velocities as a separate target. From the more precise printed RMS values 69.0279 and 8.8965 km/s, subtracting their ratio from unity gives a reduction of 87.112%. That is an effect-size statement about this baseline, not percentage accuracy or a ranking against every dark-matter model. [1]

The same prediction is formally rejected under the adopted observational diagonal alone. Adding the specified conditional McMillan normalization covariance changes the generalized result to a right-tail probability of 0.400. This is a concrete example of evidence depending on the uncertainty model. The full Eilers point-to-point covariance and complete McMillan posterior were not jointly propagated in that calculation. [1]

The SPARC high-quality subset is nested within its 175-galaxy catalog. It does not provide a second independent catalog, and its geometric ratio of 1.0042 does not guarantee that every radial speed is accurate to 0.42%. The empirical radial acceleration functional form also predates the MQ analysis. The claimed test concerns the fixed MQ normalization and proposed derivation under the adopted sources. [1] [10] [11]

The LITTLE THINGS central geometric ratio is 0.93% below unity, but the reported 95% galaxy-block interval spans −13.2% to +13.0% relative to unity. A near-unity center and a broad interval can coexist. Resampling galaxies keeps their radial points together; treating 288 radii as 288 independent galaxies would misstate the uncertainty. The external survey papers are sources of observations, not independent MQ replications. [1] [12]

A worked distinction between a fixed target and a fitted gap

The public gravitational-constant analysis combines mature BIPM and NIST mode comparisons with the stated covariance and campaign assumptions. It reports a common free-minus-servo separation of 60.994 ± 26.930 parts per million, where the uncertainty is one standard uncertainty. MQ’s fixed servo-normalized target is 34.9284 parts per million. The mode interpretation is MQ’s retrospective assignment, not an experimental endorsement by NIST. [6] [7] [13]

A compact Gaussian reconstruction illustrates the statistical questions. Hold that quoted standard uncertainty fixed, calculate the squared residual at each candidate mean, and exponentiate the negative residual square divided by twice the variance. Normalize the resulting likelihood to one at the freely fitted center. This uses the rounded common-gap summary; it does not rerun the paired-measurement covariance synthesis.

The reconstructed fixed-target-to-zero likelihood ratio rounds to 8.14, consistent with the source’s 8.14-to-1 comparison. Allowing the common gap to be fitted freely raises the raw likelihood by only 1.60 relative to the fixed MQ target. These are distinct comparisons. The free model has an added fitted parameter, and any information-criterion or Bayesian comparison must account for its assumptions and complexity. [6]

Table 3 and Figure 2 use the same reconstruction. The curve is a likelihood over candidate common gaps, not a posterior probability distribution, a new experimental sample or a distribution of the exact MQ prediction.

The source reports that allowing an additional heterogeneity contribution reduces the fixed-MQ-to-zero likelihood ratio to about 5.4. That sensitivity is material. A nonzero mode separation can also arise from apparatus effects, and a broad likelihood compatible with 34.9284 ppm does not uniquely identify MQ as its cause. The fitted maximum is not located at that exact target. [6] [7]

Statistical quantities cannot be exchanged as scores

Table 4 gives a practical interpretation guide. It is consistent with the American Statistical Association’s distinction between a test probability, effect size and the probability that a hypothesis is true. Each statistical method still requires its own sampling, covariance or model assumptions. [8]

An agreement described as a number of standard uncertainties is not automatically a discovery statistic. In particular, an older transformed Hubble concordance score cannot be multiplied by a laboratory likelihood ratio or a galaxy probability to create a portfolio-wide significance. They have different null hypotheses and dependency structures. [1] [2]

Chronology, open tests and a defensible synthesis

The dates must specify what was fixed. Pre-existing MQ numerical gravitational values are distinct from the later assignment of particular torsion-balance operating modes. Likewise, no galaxy-specific MQ parameter fitting does not establish that a study was publicly preregistered or conducted blind. A dated protocol should record the target, source construction, numerical prediction, uncertainty model and exclusion rules before target inspection. [1] [6] [9]

The proposed intermediate-redshift age-dependence test remains prospective in the cited source. Existing observations and an exact conditional law do not make it a completed comparison. Full lensing, cluster-merger and cosmological-spectrum calculations are also separate requirements. A limited spherical lens benchmark or an action-level mathematical closure cannot be counted as a successful nonlinear cluster simulation or a jointly fitted set of cosmological spectra. [1] [2]

Combining evidence is possible in principle, but requires a specified joint model. It must identify shared calibration variables, overlapping targets, source systematics, cross-covariance, fitted parameters and selection or retrospective choices. Hypotheses must be defined for the statistic being combined. Bayesian odds further require priors and explicit alternatives. Simply multiplying published probabilities or treating every concordance as a new independent trial does not meet those requirements. [1] [2]

September 27, 2026 remains the archive’s source-audit snapshot. The cited galactic manuscript separately records a September 8 completed-source milestone and later revisions. Neither is assigned here as a new experimental discovery or a verified publication date for this audit. This Brief was prepared October 26, 2026.

For reporting, request the dated source version, exact calibration inputs, target-data overlap, covariance matrices, residual definitions and the fit or likelihood implementation. Ask for all material residuals and sensitivity results, including unfavorable ones. This Brief reproduces summary arithmetic and the scalar likelihood illustration; it does not regenerate the galaxy catalogs, paired-mode covariance synthesis or a joint MQ evidence analysis.