1. Non-Lorentz Length Contraction

MQ predicts a count-dependent contraction that is independent of relative velocity. Let ${\mathrm{𝑛}}_{\mathrm{𝐿}}$ be the positive dimensionless radial separation parameter in the right-triangle construction and ${\mathrm{𝑄}}_{\mathrm{𝐿}}$ its dimensionless residual. The fundamental length ${\mathrm{𝑙}}_{\mathrm{𝑓}}$ converts a length count into metres. The exact count relations are

The product $2{\mathrm{𝑄}}_{\mathrm{𝐿}}{\mathrm{𝑛}}_{\mathrm{𝐿}}$ encodes the Informativity differential. Its deficit from unity is ${{\mathrm{𝑄}}_{\mathrm{𝐿}}}^2$. It tends to zero at large count. For example, direct evaluation at count one gives a normalization of 0.82842712 and a deficit of 17.1573%. At the coherent 2022 electromagnetic demarcation, ${\mathrm{𝑛}}_{\mathrm{𝐿}}=\mathrm{84.6005456716(65)}$, the normalization is 0.9999650728 and the deficit is 34.9272 parts per million (ppm), rounded. This finite noninteger parameter is a continuous encoding of the count geometry; it is not an assertion of a fractional primitive configuration.

How to test it. Compare independently specified realization pathways at fixed relative motion, with the interaction count and conventional corrections fixed in advance. The comparison must test the normalization itself. The triangle identity alone is not experimental evidence of physical contraction.

Status. Prospective physical effect. The same right-triangle normalization supplies the numerical metrology target in the following sections.

Derivation and scale dependence are developed in Informativity Differential; the distinction from motion-induced effects is discussed in Contraction and Dilation with Motion.

2. Physical Measure Depends on Measurement Realization

MQ assigns a physical role to the realization pathway. It predicts that certain otherwise valid measurements can retain a prescribed offset after ordinary calibration and systematic corrections. The first section supplies the normalization rather than merely predicting additional scatter. The upper-count limit is

Different readout hardware does not, by itself, establish different MQ realizations. The physical interaction and its calibration chain must determine the assignment before the comparison. This requirement is particularly important when a proposed interpretation is applied to existing measurements.

How to test it. Freeze the mode assignment, sign, magnitude, shared-input covariance, and uncertainty model before collecting new data. Then ask whether changing the realization pathway reproduces the prescribed offset across independent apparatus designs.

Status. General mechanism claim. Sections 3 and 4 provide one concrete numerical test of it; they do not supply independent confirmations of section 1.

The physical significance of measure and Newton–Planck relations explain how count normalization enters physical quantities.

3. Electromagnetic and Gravitational Realizations of G Should Differ

Use upright $\mathrm{G}$ for the MQ upper-count gravitational coupling and italic $\mathrm{𝐺}$ for its finite electromagnetic-demarcation realization. Both have units of cubic metres per kilogram per second squared. Let $\mathrm{𝑐}$ be the exact SI speed of light, ${\mathrm{𝑡}}_{\mathrm{𝑓}}$ the fundamental time, and ${\mathrm{𝑚}}_{\mathrm{𝑓}}$ the fundamental mass. The common realization law is

These are the coherent 2022-calibration MQ calculations in the newer knowledge-base source passages. Their uncertainties propagate a shared calibration input conditional on the MQ relations. They are neither two direct measurements nor two CODATA recommendations. The absolute predicted separation is $2.331066\times {10}^{\mathrm{-15}}{\mathrm{m}}^3{\mathrm{kg}}^{\mathrm{-1}}{\mathrm{s}}^{\mathrm{-2}}$, rounded. Normalizing the difference to the finite realization gives

How to test it. Compare modes whose physical calibration chains justify the finite and upper-count assignments. An apparatus using electrical components is not automatically an electromagnetic realization in this sense.

Status. Numerical MQ target with relevant experimental comparisons. General electromagnetic-versus-macroscopic claims predate the 2026 NIST result in the MQ record; the specific free-deflection/servo assignment was made retrospectively. This chronology limits claims of an apparatus-specific advance prediction.

The Gravitational Constant page develops the realization test; Fine Structure Constant explains the shared calibration, and Physical Constants—Extended discusses propagated values.

4. A Reproducible Mode Gap in Torsion-Balance Measurements of G

The free-deflection mode infers gravitational torque mechanically; electrostatic servo balances it electrically. Under the MQ assignment in section 3, the expected free-minus-servo gap is positive, with a fixed target of 34.9284 ppm relative to servo. Quinn et al. (2014) document the BIPM experiments and their correlated mode uncertainties. The earlier comparisons do not establish a precise common gap.

Schlamminger et al. (2026), Metrologia 63, 025012 report the following copper determinations in Table 16; Table 18 gives their uncertainties and correlation.

Using the printed 30.3 and 23.2 ppm standard uncertainties and correlation 0.42, the servo-normalized copper difference is 56.79 ± 29.43 ppm, rounded. This is 1.93 standard uncertainties above zero and 0.743 above the MQ target. Sapphire also gives free deflection above servo. The combined NIST result is (6.67387 ± 0.00038) × 10⁻¹¹ m³ kg⁻¹ s⁻². The paper leaves the offset unexplained and includes configuration-dependent uncertainty. These data permit the MQ comparison without identifying its cause.

How to test it. Preregister the assignment and target in a new same-apparatus comparison, retaining mode correlations and tests of thermal, electrostatic, geometric, and calibration effects. A differential uncertainty near 7 ppm would separate a 34.9284 ppm signal from zero by about five standard uncertainties if the target is correct; discriminating it from another positive bias needs additional controls.

Status. Retrospective apparatus-level comparison with an older general MQ target. Compatibility of a gap is weaker than validation of its physical explanation. BIPM and NIST share instrument lineage, and their results must not be counted as wholly independent experiments.

The 2022 servo-design paper explains the electrical feedback implementation; the 2024 NIST conference report discusses pressure effects. The MQ comparison page connects these experiments to the proposed realization mechanism. An open copy of the final 2026 paper provides the experimental tables.

5. Two Physical Hubble Realizations

Let ${\mathrm{𝐻}}_{\mathrm{sys}}$ and ${\mathrm{𝐻}}_{\mathrm{int}}$ denote the dimensionful expansion rates associated with the System Frame and Internal Frame, respectively. These are distinct from MQ’s dimensionless scalar expansion magnitude. The source calculations give

The framework associates CMB-like and distance-ladder-like channels with these different realizations. Their central separation is 5.249 km s⁻¹ Mpc⁻¹. They share upstream MQ inputs; their quoted uncertainties are not independent.

For identifiable published benchmarks, Planck Collaboration (2020) infer 67.4 ± 0.5 km s⁻¹ Mpc⁻¹ under base ΛCDM, and Riess et al. (2022) obtain 73.04 ± 1.04 km s⁻¹ Mpc⁻¹ from the Cepheid–supernova ladder. These are benchmarks with explicit analysis assumptions, not measurements of MQ frame identities. The lower MQ branch differs from the Planck benchmark by about 1.72 combined quoted standard uncertainties; the higher differs from SH0ES by about 0.45. These comparisons do not establish a complete fit to CMB spectra or distance data.

How to test it. Specify the observational channel’s frame assignment and propagate all upstream covariance before comparing its measured rate with either fixed branch. Do not choose a branch simply because it lies closer to a result.

Status. Quantitative interpretation and prospective channel test of an already known tension.

The Hubble Tension page explains the two realizations; Diameter and Age of the Universe describes the age dependence and its premises.

6. The Hubble Tension Should Persist as Two Branches

MQ predicts that appropriately classified expansion measurements retain the two branches as precision improves. Let ${\mathrm{𝜃}}_{\mathrm{𝑠}\mathrm{𝑖}}$ denote the dimensionless MQ invariant coefficient. It is not assigned units of angle or momentum in the following ratio. Dividing the two source branch relations cancels their common age and unit conversion.

This is a stronger requirement than retaining a disagreement between selected measurements. The model must prescribe which channels realize which branch and then reproduce their quantitative pattern. A persistent third population, an incorrect channel ordering, or convergence of the specified channels to a common intermediate value would require explanation within the fixed prescription.

How to test it. Compare new channel results and repeated calibrations against a frozen classification. Include covariance and selection effects rather than treating every published Hubble estimate as an independent draw.

Status. Prospective continuation of section 5. The ratio is an algebraic consequence of the same branch equations, not an additional independent cosmological prediction.

The frame definitions clarify the meaning of the mapping; Hubble calculations supply its cosmological application.

7. A Finite Pre-Classical Quantum Epoch

MQ proposes a finite quantum configuration stage before ordinary System Frame geometry and time are referenceable. In the source’s three-direction closure construction, the minimum realized distance is

This is a geometric threshold in the proposed construction, not the duration of a directly observed early epoch. Historical MQ presentations attach an SI-equivalent temporal scale near 363,312 years to the quantum stage. MQKB522’s newer discussions qualify the temporal normalization and mapping premises. That scale cannot be read as ordinary elapsed classical time before the frame required to define it exists.

How to test it. Derive observable consequences of the transition with the temporal normalization and initial conditions specified independently. A geometric closure rule must produce a discriminating observational target before it can be tested as an early-universe prediction.

Status. Theoretical boundary claim. A finite stage alone is not a unique empirical signature or a completed comparison with primordial observations.

The Quantum Epoch and Time Dilation Between Epochs pages develop the distinction between an internal ordering and realized duration; Dimensions in Space discusses spatial referenceability.

8. The CMB Monopole Temperature as an MQ Consistency Test

Let ${\mathrm{𝑇}}_{\mathrm{𝐶}\mathrm{𝑀}\mathrm{𝐵}}$ denote the present cosmic microwave background (CMB) monopole temperature. The older construction retained in the original page gives

MQKB522 also records a later, explicitly qualified mass-accretion application using the mapped expansionary extent and an adopted age. It reports

Fixsen (2009) gives the observational comparison, 2.72548 ± 0.00057 K. Both quoted MQ calculations are compatible with it at their stated precision. Their input chains and premises differ, so the numbers must not be silently combined into a single more precise prediction.

The later allocation-to-present-density construction also assumes a mapping from primordial content to the present radiation density. MQKB522 explicitly leaves the physical evolution establishing that identification, including post-transition redshift and dilution, as an open exception. Numerical temperature agreement does not resolve that missing evolution.

How to test it. Freeze the forward construction and determine its age and calibration inputs independently of the CMB temperature. If the observed temperature is instead used to infer age, feeding that age back into the same relation is a consistency check. It is not an independent prediction of the temperature.

Status. Conditional numerical reproduction of an already measured quantity. Agreement does not uniquely validate the quantum-epoch interpretation, and the quoted uncertainties do not quantify every normalization premise.

The CMB discussion distinguishes monopole temperature from anisotropy structure; Mass Accretion and Quantum Epoch provide the model context.

9. A Universal Galactic Acceleration Scale from Upstream MQ Inputs

Let ${\mathrm{𝑎}}_{\mathrm{MQ}}$ be the MQ galactic acceleration scale. The source relates it to the lower Hubble realization and the invariant coefficient already introduced. With the shared-input update recorded in MQKB522,

The previous frozen galaxy analysis used 1.20040492178 × 10⁻¹⁰ m s⁻². The newer source reports that its small calibration revision changes every positive fixed-source predicted velocity by less than 0.000750%; the catalog analysis has not been rerun. The value is conditional on the upstream age and time-normalization premises. Those qualifications remain even though the MQ scale is not calibrated separately for each galaxy.

The empirical radial-acceleration scale near 1.2 × 10⁻¹⁰ m s⁻² predates this treatment. McGaugh, Lelli and Schombert (2016) provide the observational relation. MQ’s test concerns its upstream normalization and use on new data; neither the existence nor the general shape of that empirical relation is unique to MQ.

How to test it. Keep the acceleration scale fixed before examining galaxy kinematics. Vary independently measured distances, inclinations, stellar populations, and gas distributions within justified uncertainty budgets, retaining their covariance.

Status. Conditional upstream numerical calculation and prospective universality test. Historical galaxy statistics below retain their original frozen value.

The Dark Matter discussion explains the fixed realization law and identifies further work needed to test it.

10. Galaxy Dynamics Should Follow Baryonic Structure Without Separate Halos

At galactocentric radius $\mathrm{𝑅}$, let ${\mathrm{𝑔}}_{\mathrm{bar}}\left(\mathrm{𝑅}\right)$ be the Newtonian baryonic acceleration and ${\mathrm{𝑔}}_{\mathrm{real}}\left(\mathrm{𝑅}\right)$ the MQ realized acceleration, in metres per second squared. The radius is measured in metres. The local law is

Let ${\mathrm{𝑣}}_{\mathrm{real}}$ and ${\mathrm{𝑣}}_{\mathrm{New}}$ denote the realized and Newtonian baryonic circular speeds. Their common radius argument is implicit in the following source relation.

Once the baryonic source is independently reconstructed, the MQ response is fixed without adding a separate halo for that galaxy. Source reconstruction still has observational and stellar-population assumptions. “No galaxy-specific MQ parameter” does not make those assumptions disappear.

How to test it. Predict complete rotation curves in data held out from model development. Use source models that were not adjusted to make the MQ curve reproduce the same observed speeds.

Status. Falsifiable fixed-law application. Its functional acceleration dependence coincides with the form used to describe the empirical radial-acceleration relation. The proposed physical derivation and upstream normalization supply MQ’s additional claim.

Lelli, McGaugh and Schombert (2016), SPARC describe the photometry and rotation-curve database. The MQ galaxy discussion explains how the baryonic source enters the test.

11. Residuals Should Not Require an Additional Velocity Dependence

A universal law must describe the pattern of residuals, not merely have a pooled average near unity. Let ${\mathrm{𝑣}}_{\mathrm{o}}$ denote the observed circular speed. The source’s historical SPARC analysis reports a catalog-wide mean ratio of $\frac{{\mathrm{𝑣}}_{\mathrm{real}}}{{\mathrm{𝑣}}_{\mathrm{o}}}$ equal to 1.0001888 across 175 galaxies and 3,366 radial comparisons. Its highest-quality 99-galaxy subset has a geometric ratio near 1.0042. These are reported results under the earlier frozen acceleration, not a new analysis performed for this page.

A near-zero pooled bias can coexist with systematic errors in individual galaxies or populations. The MQ commitment is that a persistent speed-dependent residual must not require another unprescribed physical parameter after source and observational effects are controlled.

How to test it. Use galaxy-level resampling or a hierarchical covariance model so that many radii in one galaxy are not counted as independent galaxies. Examine residual trends with speed, surface brightness, inclination, distance, and source-model uncertainties in a new sample.

Status. Prospective residual test with retrospective catalog comparisons. The claimed universality is stronger than the displayed pooled means. Those means alone do not establish it.

The galactic realization discussion frames the residual problem. The empirical radial-acceleration study provides an external comparison rather than a validation of MQ’s causal interpretation.

12. Galaxy Dynamics Should Not Require a Dark-Matter Particle

MQ proposes that the galactic gravitational discrepancy is a realization effect of the baryonic source. In that explanation a new dark-matter particle is not required to generate the rotation-curve enhancement. This is a claim about the cause of the gravitational response, not an inference from laboratory non-detection alone.

How to test it. A reproducible non-gravitational detection of a new particle, together with independent evidence that its abundance and clustering account for the missing gravitational response, would challenge the strong MQ explanation. A particle discovery without those links would not by itself settle the galactic claim. Continued null searches cannot uniquely favor MQ because they also constrain many particle models differently.

Status. Conditional exclusion claim, dependent on the quantitative success of the same framework in lensing, clusters, and cosmology. Rotation curves alone cannot establish that broader success.

The Dark Matter discussion introduces the realization interpretation; the Planck cosmological analysis gives a separate, model-dependent observational constraint that a replacement must address.

13. The Galactic Acceleration Scale Evolves with Cosmic Age

Let ${\mathrm{𝐴}}_{\mathrm{𝑈}}$ be the applicable System Frame cosmic age and ${\mathrm{𝐴}}_{\mathrm{𝑈}\mathrm{,}\mathrm{0}}$ its present value. MQ gives an exact inverse-age scaling within the stated realization prescription.

This changes the galactic realization scale as the universe ages. It does not assert that the locally calibrated upper-count gravitational coupling itself drifts by the same factor. Age is an input to this prescription; converting an observed redshift to age requires an independently specified expansion history.

How to test it. Infer the age–redshift relation independently, freeze the local MQ normalization, and compare matched baryonic systems across epochs. A reproducible absence of the prescribed evolution would challenge the temporal prescription.

Status. Prospective quantitative test. Sections 14–17 are related observable consequences of this one law.

The age calculation explains upstream assumptions and provides the cosmological context for this test.

14. Otherwise Equivalent Early Galaxies Should Exhibit Higher Circular Speeds

At an unchanged radius and baryonic acceleration, the larger early-epoch MQ scale lowers the denominator of the circular-speed relation in section 10. The predicted circular speed is therefore higher. This comparison holds the baryonic source fixed. It does not assume that real galaxies retain their mass, size, gas fraction, or pressure support while evolving.

How to test it. Build statistically matched samples using independent baryonic reconstructions and a specified dynamical model. Account for beam smearing, inclination, selection, turbulent support, and the difference between a measured gas velocity and an inferred circular speed before attributing an epoch trend to MQ.

Status. Prospective direction of change from the inverse-age law. Larger velocities in an unmatched high-redshift sample would not be a clean test.

The galactic realization discussion supplies the fixed-source law and its research context.

15. The Epoch Effect Should Be Strongest at Low Baryonic Acceleration

The same law predicts a joint epoch-and-acceleration pattern. In the high-acceleration regime the response approaches the baryonic Newtonian result. In lower-acceleration regions the age-dependent realization correction becomes larger. The numerical examples in section 16 compare these regimes at the same redshift.

How to test it. Measure the change across acceleration bins as well as redshift bins. A single redshift-dependent zero-point adjustment is insufficient. The prescribed curve must explain where within each source the relative enhancement grows and where it becomes small.

Status. Prospective shape constraint, linked to sections 13 and 14 rather than a new adjustable relation. Gas-rich or low-surface-brightness systems can be sensitive probes only when their kinematics and baryonic models are sufficiently reliable.

The Dark Matter discussion develops the high- and low-acceleration limits. The published radial-acceleration relation supplies the established low-redshift phenomenology against which a new evolution test can be designed.

16. Quantitative High-Redshift Velocity Enhancement

At redshift 1.44, the adopted source benchmark gives the following scale ratio relative to the present epoch. The source uses its present age of 13.7943 Gyr with the Planck 2018 flat late-time expansion benchmark and tabulates an age of 4.415 Gyr at that redshift. These are conditional benchmark numbers, not cosmology-independent constants. An exact independent reproduction of the redshift-to-age conversion requires the complete expansion prescription, not just those rounded ages.

In this numerical line the acceleration’s argument denotes redshift. The equivalent exact fixed-source velocity ratio below instead uses the already defined cosmic-age arguments. Its inputs are the local baryonic acceleration and the scale at each age.

With the same baryonic source at both epochs, the benchmark yields a 28.65% speed increase when the baryonic acceleration is one tenth of the present MQ scale, and a 20.96% increase when it equals that scale. Both percentages are rounded evaluations of the displayed law. A redshift-to-age prescription must be frozen before these targets are applied; substituting a different expansion history changes the numerical targets.

How to test it. Publish the full age–redshift prescription, baryonic inputs, covariance, selection, and circular-speed inference before opening the matched kinematic comparison. Test the entire curve, including its acceleration dependence.

Status. Outstanding conditional numerical prediction. The redshift benchmark is retained from the source, not presented as a result of a new MQ cosmological perturbation solution.

The galactic model and Diameter and Age of the Universe supply context for the source’s age-dependent test.

17. Fixed-Source Gravitational Enhancement Should Weaken with Age

Following the same fixed source forward in age lowers the MQ scale and reduces its excess realized response relative to the baryonic Newtonian value. This is the reverse temporal reading of sections 13–16. It supplies a consistency check on the direction of the effect; it is not a second independent mechanism.

How to test it. Compare inferred realization enhancement in matched systems at several ages after accounting for baryonic assembly. A model that requires increasing low-acceleration enhancement at later ages under otherwise unchanged inputs would oppose this prescription.

Status. Prospective consequence of the inverse-age law. No claim is made that a galaxy’s actual observed velocity must fall monotonically while its mass distribution evolves.

The Diameter and Age of the Universe connects epoch dependence to the wider cosmological programme; the local realization law supplies its galactic scope.

18. Cosmological Structure Growth Requires a Consistent MQ Calculation

The proposed early-epoch realization enhancement motivates a cosmological test, but the local circular-speed law does not by itself determine the growth rate of density perturbations. A quantitative growth prediction needs an MQ background solution, relativistic perturbation dynamics, initial conditions, and consistent light propagation.

How to test it. Compute a joint prediction for clustering, weak lensing, redshift-space distortions, baryon acoustic oscillations, and CMB spectra from a specified cosmological evolution model. Compare the same model with all those data, using their cross-correlations. A larger local realization scale alone cannot replace that calculation.

Status. Conditional research target. No numerical growth index, matter power spectrum, or growth-amplitude prediction is asserted here because the supplied local law does not establish one. The observational existence of structure is not an original MQ prediction.

The Diameter and Age of the Universe and CMB discussion identify relevant tests. Planck’s multi-observable cosmological analysis provides a published comparison standard, rather than evidence that MQ has already passed it.

19. Dynamics and Lensing Must Follow the Same Realized Gravity

A physical realization mechanism must describe photon deflection and material dynamics consistently. The lensing potential cannot be adjusted independently to repair a failed dynamical prediction. MQ’s source material treats both as responses to the same realized gravitational structure.

For a stationary spherical source, section 10 provides a local acceleration prescription. Applying it to lensing additionally requires the potential and metric assumptions that govern photon propagation, appropriate boundary conditions, and the line-of-sight mass distribution. That restricted construction cannot be transferred unchanged to arbitrary non-spherical or time-dependent lenses.

How to test it. Predict lensing and dynamics from the same independently reconstructed baryonic system. Include distances, geometry, external fields, source redshifts, and observational covariance. A joint failure challenges the claimed universality even if a rotation curve can be described in isolation.

Status. Quantitative consistency requirement with restricted source calculations. No general, empirically validated MQ lens model is claimed from the galactic scalar law alone.

The Dark Matter discussion provides the proposed common mechanism; Discrete Gravity describes further gravitational work. The Clowe et al. (2006) lensing analysis illustrates an independent observational challenge.

20. Cluster Lensing–Baryon Offsets Must Be Reproduced Dynamically

Merging clusters are a demanding extension because the lensing-reconstructed gravitational distribution can be displaced from the dominant X-ray gas. Clowe et al. (2006), “A Direct Empirical Proof of the Existence of Dark Matter” report the Bullet Cluster observations and interpret their spatial separation as evidence for unseen collisionless matter. The observed offset predates the MQ treatment and cannot be counted as its advance prediction.

MQ proposes that evolving realized geometry can produce such offsets without inserting a separate collisionless dark-matter distribution. To become a discriminating prediction, this proposal must yield the sign, size, morphology, spatial scale, and merger-stage evolution of the separation from independently specified baryonic initial conditions. Assigning a descriptive realized mass after seeing the lens map does not meet that requirement.

How to test it. Carry out a nonlinear merger calculation with gas dynamics, time-dependent gravity, and photon propagation. Compare simulated X-ray and lensing maps with observed systems at specified merger stages, including the observational reconstruction uncertainties. Use one fixed prescription across more than one merger.

Status. Outstanding dynamical calculation. The supplied material does not establish a validated numerical Bullet Cluster offset or a successful full merger simulation. No stand-alone offset equation or unsupported numerical target is introduced.

The Dark Matter discussion places clusters alongside galaxies; Discrete Gravity identifies the wider consistency task. The published Bullet Cluster paper supplies the observational target.