What is fixed, and what is being tested

The specific MQ claim is that a common galactic acceleration scale can be specified from non-galactic inputs before the galaxy velocities used for comparison are evaluated. The law then operates on an externally reconstructed Newtonian baryonic source. The claim concerns the provenance and use of a parameter, rather than the elimination of all astrophysical source modeling. [1] [2]

Here the System Frame is the realized observable description; the Internal Frame is the discrete count-configuration domain. The Frames mapping connects the two. These are MQ interpretive definitions. Their appearance in a rate label does not mean an astronomical measurement has independently identified either frame. [1]

The corrected relation and a public version difference

Let ${\mathrm{𝑎}}_{\mathrm{MQ}}$ denote the MQ galactic acceleration scale in metres per second squared, ${\mathrm{𝐻}}_{\mathrm{sys}}$ the System Frame dimensionful expansion rate in inverse seconds, $\mathrm{𝑐}$ the defined speed of light in metres per second, and ${\mathrm{𝜃}}_{\mathrm{𝑠}\mathrm{𝑖}}$ the dimensionless invariant MQ coefficient. Equation (1a) is the corrected relation used by the current public gravity overview. The Brief’s line labels are distinct from those of the source papers. [1]

The complementary Internal Frame rate is ${\mathrm{𝐻}}_{\mathrm{int}}$. It has a separate role in the frame-resolved expansion construction. The long galactic preprint inspected October 26, 2026 still names that branch in its Section 4.2 and Appendix D. The current overview explicitly uses the System Frame branch and states that the complementary branch is not the input to Equation (1a). This Brief follows the latter correction rather than silently treating the versions as identical. [1] [2]

The branch-label correction retains the source’s frozen nominal scale and the originally reported galaxy calculations. It should not be implemented by inserting the larger quoted complementary rate into the corrected relation. The later calibration discussed below is a separate recalculation from shared inputs. Table 1 keeps those operations and numerical versions distinct. [1] [2]

Units, age dependence and a reproducible central example

Let ${\mathrm{𝐴}}_{\mathrm{𝑈}}$ be the System Frame universe age in seconds and $\mathrm{\pi }$ the dimensionless circle constant. Equation (2b) gives the current age-to-rate relation in SI units. A rate quoted in kilometres per second per megaparsec must be converted to inverse seconds before it is used with SI light speed in Equation (1a). The dimensionless scalar expansion and the dimensionful rate are not interchangeable. [1]

The later overview reconstructs the age from the measured CMB monopole temperature 2.72548 ± 0.00057 K and the shared 2022 calibration, with the preprint’s epoch normalization held fixed. It reports 13.7943(38) billion Julian years. The age is derived, rather than a second independent measured input. The absolute temporal normalization remains an unverified premise; neither the measured temperature nor unit conversion establishes it. [1] [7]

For a central-value arithmetic check, adopt the coefficient 3.26239030504 and age 13.794339221862558 billion Julian years. One Julian year is exactly 31,557,600 seconds, and the speed of light is exactly 299,792,458 metres per second. Equation (2b) gives $2.212122057\times {10}^{-18}$ inverse seconds; Equation (1a) then gives $1.200368948\times {10}^{-10}$ metres per second squared, rounding to the later source result 1.20037 × 10⁻¹⁰. These extra digits reproduce arithmetic under stated inputs; they are not additional measurement precision.

The overview reports the corresponding rate as 68.259(19) kilometres per second per megaparsec and the complementary rate as 73.508(20) in the same units. The latter must not be substituted as if it supplied the corrected acceleration. Parenthetic uncertainties refer to the final quoted digits. Thus 1.20037(33) × 10⁻¹⁰ means a standard input-propagated uncertainty of 0.00033 × 10⁻¹⁰ metres per second squared, conditional on the retained epoch premise. [1]

The measured inverse fine-structure calibration and CMB temperature originate in separate experiments and are treated as uncorrelated in the overview. Their derived outputs share those inputs. In particular, the age and both expansion rates are correlated derived quantities, not three independent measurements to be combined. The CMB temperature dominates the stated conditional input uncertainty. Temporal-normalization uncertainty and model discrepancy are excluded, rather than experimentally established as zero. [1]

Figure 1 traces this dependency and the separate galaxy-test step. Repeated use of one frozen scale across many galaxies tests a common prediction but does not repeatedly measure that scale independently.

How the scale enters a galaxy prediction

Let $\mathrm{𝑅}$ be galactocentric radius in metres, ${\mathrm{𝑣}}_{\mathrm{New}}\left(\mathrm{𝑅}\right)$ the positive Newtonian circular speed in metres per second from the adopted baryonic source, and ${\mathrm{𝑔}}_{\mathrm{bar}}\left(\mathrm{𝑅}\right)$ its positive baryonic acceleration in metres per second squared. Equation (3c) is the circular-kinematic conversion. It does not reconstruct the stars and gas by itself. [1] [2]

Let ${\mathrm{𝑔}}_{\mathrm{real}}\left(\mathrm{𝑅}\right)$ denote the realized radial acceleration and ${\mathrm{𝑣}}_{\mathrm{real}}\left(\mathrm{𝑅}\right)$ the corresponding positive circular speed, in the same units as their baryonic counterparts. Equations (4d) and (5e) are the current exact local realization law for positive source acceleration and scale. The dimensionless denominator in Equation (4d) is the realization fraction, not an additional mass component. [1] [2]

The denominator approaches one at high baryonic acceleration. In the weak-acceleration limit, realized acceleration has the square-root dependence on baryonic acceleration and the common scale. At fixed source and radius, the positive speed then has a fourth-root dependence on the scale. These are mathematical limits of the stated law, rather than exact low-acceleration equalities at arbitrary radius.

The model relies on a positive quadratic realized norm and subdivision-consistent composition of unrealized gravitational availability. The circular law assumes the baryonic source and circular-speed target are appropriate descriptions of the system. The derivation of its functional form and its applicability to real galaxies are distinct questions. A fixed scale does not remove stellar mass-to-light ratios, gas profiles, distance, inclination, disk geometry or noncircular-motion uncertainty. [1] [2]

What the later numerical revision changes

Table 2 holds the baryonic acceleration and source fixed, and evaluates Equation (5e) first with the original frozen nominal scale, then with the central recalculation above. Each first-column value is the source acceleration divided by the original nominal scale. The next two columns divide predicted speed by the same positive Newtonian source speed. This is a conditional sensitivity calculation, not new galaxy data.

The recalculated acceleration is about 0.002997% below the nominal value. The corresponding decrease in any positive predicted speed is bounded above by the weak-acceleration fourth-root limit, about 0.000749211%, below the source’s 0.000750% bound. At high source acceleration the fractional change approaches zero. Figure 2 shows this behavior directly. [1]

For a fixed source acceleration, the magnitude of the logarithmic speed sensitivity to the acceleration scale lies between zero and one quarter. This follows by differentiating Equation (5e); its maximum is approached at vanishing positive realization depth. Integrating this sensitivity between the two positive scale values gives the finite-revision bound above. The same pointwise fractional bound applies to positive weighted means and geometric speed normalizations when their weights and source selections are unchanged.

The overview separately bounds the first-order conditional calibration contribution to speed standard uncertainty by 0.00698%. This is not the finite-revision bound and is not the total galaxy-velocity uncertainty. The common calibration induces correlated shifts across radii. Neither bound covers the temporal-normalization premise, unmodeled source effects or missing observational covariance. The source reports no rerun of the catalog residuals or tail probabilities after the numerical revision. [1]

Prior phenomenology and downstream observational evidence

McGaugh, Lelli and Schombert’s 2016 empirical RAR already supplied the exponential functional form. The MQ claim concerns its proposed derivation and upstream normalization. A fitted empirical RAR scale is a regression parameter conditioned on source reconstruction and nuisance modeling. It cannot simply be identified with the MQ-derived scale for a concordance or tension calculation without establishing a common physical observable and dependence model. [2] [3]

Table 3 summarizes selected results reported by the long preprint under its original nominal scale. They are not recomputed results of this Brief. Signed normalization, curve scatter and conditional likelihood answer different questions. The public overview preserves these source and covariance distinctions. [1] [2]

The Milky Way source and kinematic target come from separate published constructions, but that does not establish full statistical independence. Its favorable covariance-conditioned probability is not a probability that MQ is true. In SPARC, the quality-selected 99-galaxy geometric ratio is 1.0042, while a velocity-dependent residual persists in the full population under joint controls. The absence of a significant marginal trend in the highest-quality group does not eliminate those catalog-wide questions. [1] [2]

The small calibration revision cannot be used to declare those residuals resolved. A new catalog analysis would require the revised scale, unchanged documented source choices, the same selection and weighting, and recomputed covariance-aware statistics. Testing lensing, merging clusters, cosmological perturbations and the prospective age dependence requires additional calculations beyond the galactic normalization comparison. [1] [6]

Chronology and reporting requests

September 27, 2026 is the archive’s source-review snapshot. The long manuscript has a September 8 completed-source milestone and later updates; the correction and current shared-input overview are distinguished here by their actual content. No original discovery date, first announcement date or journal publication date is inferred from the archive label. This Brief was prepared October 26, 2026.

For a story, obtain the exact version of the corrected relation, the original catalog calculation and the later shared-input calculation. Ask which physical normalization sets the age, which uncertainties were propagated, whether the baryonic source was fixed before residual inspection and whether a changed scale triggered a full rerun. These documents establish what was frozen, what was recalculated and what the observations actually test.