Measurement Quantization and the Unexpectedly Early Formation of Galaxies

JWST observations establish that luminous galaxies and chemical enrichment were present during the first few hundred million years of cosmic history. In “A Cosmic Miracle: A Remarkably Luminous Galaxy at z_spec = 14.44 Confirmed with JWST,” Naidu and colleagues report MoM-z14 at a spectroscopic redshift of 14.44 ± 0.02, corresponding to about 280 million years after the Big Bang in their adopted cosmology. Its compact structure and nitrogen emission constrain early star formation and enrichment. The elapsed age is inferred through an expansion model; redshift is the measured quantity.^[1]

These observations motivate a quantitative question about the growth of structure. Given a specified expansion history, initial density perturbations, gas supply, cooling, star formation, and feedback, how rapidly can a model produce the observed galaxy population? The existence of an early galaxy tests a particular calculation through its predicted abundance and observable properties. It does not, by itself, select a unique gravitational mechanism.

Measurement Quantization (MQ) proposes an age-dependent gravitational response that could affect this calculation. Its Internal Frame describes discrete count configurations. The System Frame expresses the continuous relational separations and physical observables obtained through the Frames mapping. MQ distinguishes the Newtonian source supplied by baryonic matter from the response realized through that mapping. This page develops the resulting conditional prediction and separates it from a demonstrated history of galaxy assembly.

Quantum Referencing

Figure 1. Three orthogonal unit contributions are drawn in perspective. Their gold body diagonal has the √3 norm under the stated realized metric.

n_{L} = \sqrt{{n_{a}}^{2} + {\sqrt{{n_{a}}^{2} + {n_{b}}^{2}}}^{2}}

\sqrt{1^{2} + 1^{2} + 1^{2}} = \sqrt{3}

R_{qe} (A_{qe}) = \sqrt{3} l_{f}

The early-galaxy application belongs to a longer MQ account of how physical observables become referenceable. Figure 1 shows the three unit contributions and their closure diagonal in a clear perspective construction. The drawing represents a realized norm, rather than a measured map of pre-existing physical space. The minimum closure calculation below uses the realized orthogonal norm associated with the Frames mapping.^[7]

Let l_f denote the fundamental length, n_L the dimensionless radial norm, and n_a and n_b the unit-leg counts of the construction. These leg counts are distinct from a derived hypotenuse or radial norm, which need not itself be an integer. The three-unit expression gives the boundary between the pre-referenceable construction and the minimum realized spatial separation.

The last expression is a mapped boundary condition. It does not assign a physical radius or an elapsed clock time to the Internal Frame before realization.

The Quantum Epoch

Figure 2. The funnel illustrates the mapping sequence. It is not a calibrated growth curve or an image of galaxies existing during the pre-referenceable quantum epoch.

l_{f} m_{f} = 2 p_{si} t_{f}

\frac{n_{L} l_{f}}{n_{T} t_{f}} = \frac{2 p_{si}}{n_{M} m_{f}}

n_{{L_{u}}^{'}} = \frac{n_{T_{u}}}{n_{M_{u}}} = \frac{2}{{θ_{si}}^{3}}

The corrected epoch notation distinguishes A_qe, the quantum-epoch configuration extent expressed in later SI time units, from A_ee, the mapped expansionary-epoch duration. R_qe is the corresponding mapped radial scale. The subscript qe identifies the quantum epoch and ee the expansionary epoch; neither is a replacement for unrelated physical subscripts such as the baryonic-source label. The funnel in Figure 2 illustrates the mapping sequence without supplying its physical scale.

For the derivation, m_f and t_f are the fundamental mass and time. The dimensionless invariant coefficient is $θ_{si}$ , whereas p_si is its dimensional momentum realization, in kg m s⁻¹. The distinction matters in the fundamental relation. The speed of light is c and $π$ is the dimensionless circle constant.

The general temporal and mass counts are $n_{T}$ and $n_{M}$ , respectively. The length count was introduced above.

This count-scaled form assumes $n_{L} n_{M} = n_{T}$ . The universe-allocation temporal and mass counts are $n_{T_{u}}$ and $n_{M_{u}}$ . For the constrained allocation used in the quantum-epoch construction, the derived ratio $n_{{L_{u}}^{'}}$ satisfies

The primed ratio is a derived quantity, rather than a primitive integer length count. The prime is retained where it belongs to that definition; it is not an epoch label.

The mapped expansion relation

v^{'} = \frac{n_{{L_{u}}^{'}} l_{f}}{n_{T_{u}} t_{f}} = \frac{2 p_{si}}{n_{M_{u}} m_{f}}

v^{'} = \frac{2 p_{si}}{M_{U}} = \frac{2 p_{si}}{V_{U} ρ_{c}}

v^{'} = \frac{2 p_{si}}{\frac{4}{3} π c^{3} {θ_{si}}^{3} {A_{qe}}^{3} ρ_{c}}

The primed quantity $v^{'}$ denotes a mapped radial increment per increment of A_qe. Let M_U be the mapped mass allocation, V_U its mapped spherical volume, and $ρ_{c}$ the critical mass density of that same construction. They have units kg, m³, and kg m⁻³, respectively. The construction assumes $V_{U} = \frac{4 π}{3} {(θ_{si} c A_{qe})}^{3}$ . Its first reduction is displayed vertically to preserve readability.

ρ_{c} = \frac{3 {H_{f}}^{2}}{8 π G}

G = \frac{l_{f} c^{3}}{2 p_{si}}

v^{'} = \frac{3 p_{si}}{2 π c^{3} {θ_{si}}^{3} {A_{qe}}^{3}} \frac{8 π G}{3 {H_{f}}^{2}}

v^{'} = \frac{4 p_{si}}{c^{3} {θ_{si}}^{3} {A_{qe}}^{3} {H_{f}}^{2}} \frac{l_{f} c^{3}}{2 p_{si}}

v^{'} = \frac{2 l_{f}}{{θ_{si}}^{3} {A_{qe}}^{3} {H_{f}}^{2}}

Here H_f is the Hubble frequency assigned to the same mapped representation. Upright $G$ denotes the MQ upper-count gravitational coupling, distinguished typographically from the ordinary finite-regime constant used later in the galactic source law. The next reduction assumes the critical-density expression and the upper-count coupling relation shown together below.

v^{'} = \frac{2 l_{f}}{{θ_{si}}^{3} A_{qe}}

With the additional condition $H_{f} A_{qe} = 1$ , the expression reduces to

These are relations in a specified mapped representation. They do not establish a physically measured velocity inside the pre-referenceable quantum epoch. The absolute numerical velocity also depends on the temporal normalization introduced next.

The reference scale and epoch boundary

R_{qe} (A_{qe}) - R_{qe} (A_{qe,0}) = \frac{2 l_{f}}{{θ_{si}}^{3}} \ln (\frac{A_{qe}}{A_{qe,0}})

A logarithm must act on a dimensionless ratio. Let A_qe,0 be a positive reference extent and $R_{qe} (A_{qe,0})$ its mapped radius. Integrating the reduced inverse-scale relation between the two positive reference values gives

\frac{A_{qe}}{A_{qe,0}} = \exp (\frac{{θ_{si}}^{3}}{2} (\sqrt{3} - \frac{R_{qe} (A_{qe,0})}{l_{f}}))

At the three-unit boundary in Figure 1, this becomes

\frac{A_{qe}}{A_{qe,0}} = \exp (\frac{\sqrt{3} {θ_{si}}^{3}}{2})

For the special reference convention $R_{qe} (A_{qe,0}) = 0$ , the dimensionless result is

Assigning $A_{qe,0} = 1 s$ then gives $A_{qe} = 363312.3525(25) yr$ . A Julian year is exactly 31,557,600 s. The parenthetical uncertainty propagates the adopted source calibration under this fixed convention; it does not include uncertainty in the physical selection of the reference pair. This is an SI-equivalent quantum-epoch extent, rather than elapsed physical time before realization.^[7]

\frac{A_{ee}}{A_{qe}} = {(2 θ_{si})}^{\frac{1}{3}}

The separate Frames mapping relation supplies the expansionary-epoch duration

Under the same convention, $A_{ee} = 678894.2574(47) yr$ . Both epoch results share calibration and normalization inputs. Neither value dates a mature galaxy, and the ratio alone does not establish a transformation between independently measured clocks.

CMB Allocation, Density, and Temperature

Enhanced illustrative blue-and-yellow CMB-style oval, not a calibrated observational map — Figure 3. The CMB-style globe illustrates the radiation field. It is not identified here as a calibrated survey map or a measurement of the monopole temperature.

M_{CMB} = M_{acr} A_{ee}

M_{CMB} = \frac{A_{ee}}{t_{f}} m_{f} \frac{{θ_{si}}^{3}}{2}

M_{acr} = \frac{{θ_{si}}^{3} p_{si}}{l_{f}}

Figure 3 presents a higher-resolution rendering of the illustrative CMB-style globe. It introduces the proposed connection from the mapped duration to a mass-equivalent allocation and then to a radiation temperature. Let M_CMB denote that allocation in kg, M_acr the constant mass-allocation rate in kg s⁻¹, and E_CMB the present radiation energy in J. The present universe age is A_U. The present spherical volume $V_{U} (A_{U})$ must be distinguished from the mapped volume used in the preceding derivation.

The explicit $\frac{A_{ee}}{t_{f}}$ replaces an ambiguous universe time-count label in this application. The epoch designation remains on the duration; “CMB” continues to identify the radiation allocation.

V_{U} (A_{U}) = \frac{4 π}{3} {(θ_{si} c A_{U})}^{3}

E_{CMB} = M_{CMB} c^{2}

ρ_{CMB} = \frac{E_{CMB}}{V_{U} (A_{U})}

Let $ρ_{CMB}$ denote radiation energy density in J m⁻³, T_CMB the equilibrium monopole temperature in K, and a the radiation constant in J m⁻³ K⁻⁴. This radiation energy density is distinct from the critical mass density $ρ_{c}$ . The geometric volume, energy identification, and blackbody conversion are

a = \frac{4 σ}{c} = \frac{8 π^{5} {k_{B}}^{4}}{15 c^{3} h^{3}}

For the radiation constant, $σ$ is the Stefan–Boltzmann constant, k_B the Boltzmann constant, and h the conventional SI Planck constant. These quantities retain their standard identities; the epoch subscripts do not apply to them.

T_{CMB} = {(\frac{ρ_{CMB}}{a})}^{\frac{1}{4}} = {(\frac{E_{CMB}}{a V_{U} (A_{U})})}^{\frac{1}{4}}

The exact SI definitions give the rounded value 7.56573325028 × 10⁻¹⁶ J m⁻³ K⁻⁴. The blackbody conversion is

The allocation-to-present-energy identification is an additional assumption. A physical account must connect the allocation to the present radiation through thermalization and post-transition radiation evolution. Reproducing a present density through an adopted normalization does not independently establish that history. The CMB discussion addresses a further distinction between a monopole-temperature calculation and a prediction of the angular power spectrum.^[7]

Reading the CMB Comparisons

Table 1 separates the infographic’s historical numerical comparison from the corrected conditional epoch calculation. The temperature reference is the combined estimate in D. J. Fixsen’s “The Temperature of the Cosmic Microwave Background.” Its inferred blackbody energy density is not an independent second measurement of temperature.^[8] The decoupling age comes from the cosmological interpretation in Bennett and colleagues’ “First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results.” It describes a different event from the MQ quantum-epoch boundary.^[9]

Table 1. Conditional MQ quantities and observational references, with their comparison scope stated explicitly.
Quantity	MQ quantity	Observational reference	What can be compared
Geometric coordinate	214.766864272(13)	No matched observable established here.	The coordinate follows the MQ partition expression below. It is not by itself a prediction of the measured CMB peak positions.
Epoch scale	`A`_qe = 363,312.3525(25) yr, conditional on the stated reference convention	WMAP-inferred decoupling age 379,000 yr, with lower/upper uncertainties 7,000/8,000 yr^[9]	Different epoch definitions. Their proximity is not a measured residual for the same observable.
Present energy density	4.1750 × 10⁻¹⁴ J m⁻³, as reported in the supplied historical infographic	4.1747(35) × 10⁻¹⁴ J m⁻³, inferred from the temperature and blackbody law^[8]	The reference density inherits the temperature uncertainty. The historical MQ value has no complete independent error model supplied.
Monopole temperature	2.7255 K, historical reported value	2.72548 ± 0.00057 K^[8]	The central values differ by 0.00002 K. A combined significance is not assigned without the model uncertainty and shared-input assessment.

100 π \frac{{θ_{si}}^{2} - 2}{{θ_{si}}^{2} + 2}

The geometric coordinate in Table 1 follows the partition expression given in Eq. (1) of Jody A. Geiger’s “Support for a Universe without Curvature.”^[10]

The historical CMB mass-equivalent allocation was reported as 1.5016 × 10⁵⁰ kg in the supplied infographic. Updating a displayed subscript does not constitute a new numerical evaluation of that allocation. The historical density, mass, and temperature values are therefore identified as such, while the epoch figures above use the corrected source convention. These comparisons motivate a test of a complete radiation history; they do not supply one.^[7]

The early-galaxy problem begins after these proposed realization and allocation stages. Available matter must still become concentrated, cool, form stars, enrich its surroundings, and assemble into the systems JWST observes. The following gravitational law supplies a conditional response for a prescribed baryonic distribution; evolving that distribution is a separate task.

The Central MQ Prediction

g_{bar} (R) = \frac{G M_{bar} (R)}{R^{2}}

Let R denote galactocentric radius, G the Newtonian gravitational constant, and M_bar(R) the enclosed baryonic mass. For a spherically symmetric source, the Newtonian baryonic acceleration g_bar(R) is

g_{real} (R) = \frac{g_{bar} (R)}{1 - \exp (- \sqrt{\frac{g_{bar} (R)}{a_{MQ}}})}

For a disk or another nonspherical distribution, the source acceleration must instead be calculated from its reconstructed baryonic potential. The mass profile includes the relevant stellar and gas components; luminosity alone does not specify it.

The MQ realized acceleration, g_real(R), depends on the acceleration scale a_MQ. The local law appears as Eq. (136) in Section 4.2 of Jody A. Geiger’s “A First Principles Derivation of the Galactic Radial Acceleration Relation from Measurement Quantization.”^[2]

v_{real} (R) = \frac{v_{New} (R)}{\sqrt{1 - \exp (- \sqrt{\frac{g_{bar} (R)}{a_{MQ}}})}}

For circular motion in the galactic regime, v_New(R) denotes the Newtonian baryonic circular velocity and v_real(R) the corresponding MQ circular velocity. The same paper gives their relation in Eq. (137).^[2]

The exponent contains a ratio of accelerations and is dimensionless. At positive source acceleration, the denominator in the acceleration law lies between zero and one. The realized acceleration therefore exceeds the Newtonian baryonic value within this construction. When the source acceleration is much larger than the MQ scale, the exponential term tends to zero and the Newtonian response is recovered. These are mathematical properties of the stated law; their assessment does not require a statistical significance test.

The law supplies no separate dark matter halo profile or galaxy-specific MQ acceleration parameter. That does not make its application input-free. Stellar mass normalization, gas mass, distance, inclination, geometry, and cosmic age remain measured or inferred inputs whose uncertainties affect the predicted velocity. A fixed formula must be distinguished from an uncertainty-free prediction.

Why the Predicted Response Depends on Cosmic Age

a_{MQ} = \frac{c H_{sys}}{2 θ_{si} - 1}

In the corrected MQ convention, H_sys denotes the System Frame expansion rate. Together with the previously defined speed and invariant coefficient, it specifies the acceleration scale through the following relation. The linked manuscript retains an older frame label; the source note identifies this consequential difference.^[3]

a_{MQ} (z) = a_{MQ} (0) \frac{A_{U,0}}{A_{U} (z)}

Let z denote cosmological redshift and A_U,0 the present value of the already defined universe age. The notation A_U(z) specifies that age at redshift z. The zero argument denotes the present epoch. The age scaling is Eq. (193) in Section 5.5 of “A First Principles Derivation of the Galactic Radial Acceleration Relation from Measurement Quantization.”^[2]

For a fixed present normalization and fixed baryonic source acceleration, a smaller positive cosmic age increases the MQ scale. This reduces the denominator of the realization law and increases the predicted gravitational response. The dependence follows directly from the displayed equations. It applies to physically realized epochs; extrapolation to zero age does not define a measurable galactic system.

The Newtonian limit is governed by the source acceleration relative to the scale at the epoch being tested. A compact region remains close to that limit only when its source acceleration is sufficiently large compared with the contemporaneous MQ scale. Physical size alone is not the criterion. Likewise, later cosmic age reduces the enhancement for a fixed source, but does not imply that actual galaxies keep the same mass profiles as they evolve.

From Enhanced Binding to Galaxy Assembly

For a prescribed baryonic concentration in the law’s galactic regime, the enhanced response supplies a reason to investigate more rapid binding and gas collection at early epochs. Whether that response actually advances collapse, star formation, enrichment, or mergers requires evolution equations and initial conditions appropriate to those processes. Applying a circular-velocity law to an expanding, pressure-supported primordial perturbation is an additional physical step, rather than a consequence established by the circular-velocity formula alone.

The relevant test is a calculation that evolves perturbations and the baryonic distribution with the proposed gravitational response, then predicts observable quantities such as luminosity functions, stellar mass functions, sizes, and velocity fields. Those predictions must be compared with observations using survey selection, measurement errors, and astrophysical uncertainties. The materials reviewed for this page do not supply that complete early-galaxy calculation. Its absence from this review leaves the assembly-rate claim unresolved; it is not a negative experimental result.

The illustrated chronology above supplies the model context for this application. The Origin of the Universe preprint develops a transition from prephysical configuration relations through a quantum epoch to an expanding physical system. Within this account, physical realization precedes ordinary galaxy formation. Prephysical count relations should not be assigned ordinary physical lengths, masses, or velocities before those observables are realized.

MQ also distinguishes the geometric availability of mass within the expanding universe from its later gravitational accretion into concentrations. Supplying mass is not the same calculation as producing a galaxy. The subsequent history still has to connect mass supply, spatial concentration, gas physics, and stellar evolution to measured observables.

For a published MQ cosmological application, Jody A. Geiger’s “Resolving the Hubble tension 68.261 and 73.510 km s⁻¹ Mpc⁻¹” addresses expansion-rate determinations. Its publication supplies a traceable account of that application; it does not independently test the early-galaxy assembly mechanism discussed here.^[4]

What the Rotation-Curve Comparisons Establish

Present-epoch galactic dynamics and early structure formation test different parts of the proposal. The local realization law has the same exponential form as the empirical radial-acceleration relation in McGaugh, Lelli, and Schombert’s “Radial Acceleration Relation in Rotationally Supported Galaxies.” Recovering that form connects MQ with an observed regularity. Shared functional form alone cannot identify which physical explanation is responsible.^[5]

Table 2 and Section 4.3 of “A First Principles Derivation of the Galactic Radial Acceleration Relation from Measurement Quantization” report a Milky Way comparison using an externally constructed baryonic source and 38 circular-velocity measurements. The reported root-mean-square velocity residual is 8.90 km s⁻¹, compared with 69.03 km s⁻¹ for the Newtonian baryonic source alone. Source covariance materially affects the statistical assessment, and the full observational covariance is unavailable. These reported results concern this source-and-velocity comparison, rather than early-galaxy formation.^[2]

Assessing predictive independence requires checking whether observed velocities entered the baryonic reconstruction or normalization, whether inputs were fixed before the comparison, and which quantities were fitted. No galaxy-specific MQ parameter does not by itself establish that every astrophysical input is independent. The empirical radial-acceleration form also predates its MQ interpretation, so recovery of that form and a prediction made before a new observational test have different evidential roles.

The rotation-curve application and radial-acceleration treatment motivate tests of the proposed source-response relationship. Applying it to lensing, cluster mergers, or cosmological perturbation growth introduces additional observables and dependencies. Agreement for circular velocities transfers to those claims only through an explicit, tested connection. This page does not treat the galactic calculation as a demonstrated replacement for every gravitational role assigned to dark matter.

What High-Redshift Kinematics Currently Test

A measured velocity gradient is not automatically a circular velocity. In “Dynamics of a Galaxy at z > 10 Explored by JWST Integral Field Spectroscopy: Hints of Rotating Disk Suggesting Weak Feedback,” Xu and colleagues model GN-z11 at redshift 10.60. Under a rotating-disk interpretation, they infer a rotation velocity of 257 km s⁻¹, with a lower uncertainty of 117 km s⁻¹ and an upper uncertainty of 138 km s⁻¹. They also identify an outflow interpretation. This is a conditional kinematic inference, rather than an unambiguous measurement of a circular-speed curve.^[6]

A meaningful MQ comparison would evaluate the same observable at the same radius through the instrument and dynamical model, using an independently reconstructed stellar and gas distribution. A stellar-only velocity calculation cannot be assigned a precision agreement or exclusion merely from its percentage difference from a modeled central velocity. Gas mass, spatial distribution, pressure support, inclination, and the competing interpretation of the velocity gradient change the physical comparison.

The reviewed sources therefore leave a quantitative test of the MQ age dependence in these earliest systems unresolved. This assessment identifies the missing comparison, rather than claiming that observations either confirm or exclude the mechanism. The JWST science-program directory is useful for locating observing programs; it is not a substitute for the primary papers supporting a particular measurement.

A Directly Testable Prediction

The age-dependent MQ law predicts a larger realized-to-baryonic acceleration ratio at earlier cosmic ages when the baryonic acceleration is held fixed. This is more specific than the general possibility of earlier star formation. A prospective test should freeze the MQ normalization and the redshift-to-age conversion before inspecting velocity residuals, reconstruct stellar and gas profiles independently of the tested velocities as far as feasible, and compare galaxies at matched source acceleration and structural conditions.

The comparison must account for instrumental resolution, pressure support, inclination, mergers, outflows, sample selection, correlated mass uncertainties, and possible evolution of the source population. Residuals should be assessed with a stated error model that propagates these uncertainties. A detected redshift trend supports the proposed age dependence only to the extent that these alternatives are distinguished. A sufficiently precise absence of the prescribed trend would constrain that dependence within the tested acceleration and redshift range.

The formation test is separate. MQ and other models should be compared through matched predicted abundances, kinematics, sizes, and enrichment histories, using equivalent observational selection and disclosed parameter freedom. The early presence of luminous galaxies provides the observational target. Determining which model accounts for it requires those quantitative predictions rather than a ranking based on publication counts or the existence of an explanatory narrative.

The Physical Picture

MQ links its proposed prephysical origin, physical expansion, mass availability, and evolving gravitational response into a continuous account. Within the galactic realization law, stronger response at earlier age is a definite conditional mathematical consequence. Turning that response into a prediction for when galaxies form requires a self-consistent evolution of the baryonic source. Present-epoch agreement can support the local law in its tested domain, while the early-assembly application remains a distinct calculation to evaluate.

The scientific opportunity is to connect that calculation to the galaxies JWST measures. A successful comparison would earn support for the particular predictions tested, with their input dependence and uncertainty stated. Further model development and observations can then determine how far that support extends to the broader MQ account of cosmic evolution. Additional manuscripts are available in the research preprints collection.

Sources and Notes

[1] R. P. Naidu et al., “A Cosmic Miracle: A Remarkably Luminous Galaxy at z_spec = 14.44 Confirmed with JWST,” The Open Journal of Astrophysics 9 (2026), published January 30. doi:10.33232/001c.156033. The age quoted above follows the paper’s cosmological interpretation of the spectroscopic redshift; stellar population and abundance inferences have their own modeling uncertainties.

[2] J. A. Geiger, “A First Principles Derivation of the Galactic Radial Acceleration Relation from Measurement Quantization,” Informativity Institute, public web preprint, version inspected October 29, 2026. Full manuscript. Locators used here are Section 4.2, Eqs. (136)–(137); Section 5.5, Eq. (193); and Table 2 with Section 4.3. The rotation statistics are attributed author-reported calculations, not a numerical reproduction performed for this page. Those comparisons do not supply an early-galaxy abundance calculation.

[3] Notation provenance and verification limit. The author’s September 23, 2026 correction specifies H_sys in the acceleration-scale relation and states that the numerical scale and downstream galaxy calculations are unchanged. That correction is an unpublished author-supplied amendment and is not separately publicly accessible. The linked Geiger preprint still uses H_int in its acceleration-scale discussion. This page follows the corrected convention but does not treat the older public expression as a verified derivation of that replacement. Independently reconciling the absolute normalization requires a publicly inspectable corrected derivation. The inverse-age dependence is displayed here separately, so its conditional consequences can be assessed without assuming a numerical normalization.

[4] J. A. Geiger, “Resolving the Hubble tension 68.261 and 73.510 km s⁻¹ Mpc⁻¹,” AIP Advances 15(7), 075134 (2025). doi:10.1063/5.0269029. This reference concerns the expansion-rate application, not a direct test of the early-galaxy mechanism.

[5] S. S. McGaugh, F. Lelli, and J. M. Schombert, “Radial Acceleration Relation in Rotationally Supported Galaxies,” Physical Review Letters 117, 201101 (2016). doi:10.1103/PhysRevLett.117.201101. This is the observational source for the empirical relation, not an independent measurement of MQ cosmic-age evolution.

[6] Y. Xu et al., “Dynamics of a Galaxy at z > 10 Explored by JWST Integral Field Spectroscopy: Hints of Rotating Disk Suggesting Weak Feedback,” The Astrophysical Journal 976, 142 (2024). doi:10.3847/1538-4357/ad82dd; public manuscript. The quoted rotation result assumes a disk interpretation; the authors also discuss outflows. Its reported asymmetric uncertainty is retained without conversion into an assumed Gaussian significance.

[7] J. A. Geiger, “Quantum Epoch,” revised author manuscript, October 15, 2026, Sections 1–3. The revised manuscript used for this on-page transcription is not verified as publicly accessible; its role is notation, dimensional clarification, and provenance of conditional calculations, not independent observational evidence. A public Quantum Epoch record and the reader overview provide background, but version identity with the revised manuscript is not established. The equations needed to inspect the derivation are displayed on this page. The one-second reference convention, mapped critical density, frequency–extent condition, and allocation-to-present-energy identification are stated explicitly. Figure 1 is a vector rendering of the stated unit-norm construction. Figure 2 retains the supplied funnel illustration; Figure 3 is an enhanced illustrative CMB texture. No survey dataset or calibration is inferred from these illustrations. The original image’s opaque reference numbers are replaced by these page notes. Its value 216.4 ± 1.3 is not retained as a verified peak measurement because its source and a matched model observable were not established in this review.

[8] D. J. Fixsen, “The Temperature of the Cosmic Microwave Background,” The Astrophysical Journal 707(2), 916–920 (2009), doi:10.1088/0004-637X/707/2/916; public manuscript. The combined estimate is 2.72548 ± 0.00057 K. The density shown here follows from the stated blackbody radiation constant and that temperature, with first-order propagation of the temperature uncertainty; it is not another independent observation. The historical MQ temperature is retained with its reported precision and is not relabeled as a new independent prediction.

[9] C. L. Bennett et al., “First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results,” The Astrophysical Journal Supplement Series 148, 1–27 (2003), doi:10.1086/377253; NASA-hosted paper. Its abstract reports a decoupling age of 379 kyr with lower/upper uncertainties of 7/8 kyr, under the fitted cosmological interpretation. This is not a direct measurement of the MQ quantum-epoch extent.

[10] J. A. Geiger, “Support for a Universe without Curvature,” Informativity Institute, public web preprint, Section 1, Eq. (1), inspected October 29, 2026. Full manuscript. The source identifies 214.766864272(13) as a conditional geometric coordinate rather than an independently measured peak location. Its physical connection to CMB spectral observables requires the additional mapping and transfer treatment.