The milestone and its evidentiary scope

This release documents a defined cosmological validation task. The principal current source is Section 5.8 of the galactic radial-acceleration manuscript, with its open-problem assessment in Section 5.9 and evidence classification in Appendix E. The milestone is a formulation that can be taken toward a numerical cosmological test. It is not an announcement that such a test has succeeded. [1]

MQ begins from discrete measure and relates count structure to physical observables. The Internal Frame is the discrete count-configuration domain. The System Frame is the realized relational encoding, connected through the Frames mapping. The cosmological program must turn that proposed physical construction into a consistent evolving background, perturbations and observed signals. A similarity between dimensionless fractions does not perform that task. [1] [3] [11]

Background, perturbations and observables are different calculations

A background solution describes the homogeneous expansion and average physical sources. It must specify how matter, radiation and any additional realized contribution evolve, how energy and momentum conservation are satisfied, and which temporal and dimensional normalizations are used. A present age or expansion value samples only part of that history. [1] [10]

Perturbations are small departures from that background. Their coupled evolution involves density, momentum, pressure, anisotropic stress and the metric response. Anisotropic stress is the direction-dependent part of the stress. It can affect the relation between the two scalar metric potentials. Specifying only a stationary density response therefore does not determine the complete relativistic perturbation problem. [1]

Observed signals then require propagation and projection. Temperature and polarization patterns are not read directly from a background fraction. Photon transport, the thermal and ionization history, gravitational potentials and the chosen initial perturbations contribute to their prediction. The requested numerical test must connect these stages coherently rather than supply a separate rule for each observational target. [1] [4]

What Section 5.8 currently supplies

The source linearizes its realized field relation and conservation relation in Eqs. (198)–(199). Those are first variations about a homogeneous background, rather than extra field equations introduced independently. It adopts a conventional scalar perturbation representation and develops the source response while retaining the stationary galactic branch. [1]

The source explicitly distinguishes that stationary response from a full relativistic evolution system. Its timelike completion appears in Eqs. (219)–(224), and its dual first-order spatial formulation in Eqs. (226)–(229). An auxiliary dual variable provides a regular spatial variational representation at zero field. The source describes this as mathematical zero-field regularization, not as a completed numerical integration or an observational result. [1]

The remaining operation is to linearize these ingredients jointly about the homogeneous MQ background, supply physically admissible initial conditions and evolve the coupled system. The regular representation is progress in formulating the problem. It does not alone prove numerical convergence, recover the missing spectra or turn referenceability fractions into independently conserved fluids. [1]

Table 1 is a status map, not a tally of confirmations. In particular, action-level closure and successful galaxy comparisons do not supply a cosmological likelihood. Figure 1 shows the dependency sequence into the proposed test. [1]

The role of CLASS or an equivalent solver

CLASS is a public Einstein–Boltzmann code used to compute cosmological predictions. Its methods paper describes approximation schemes and accuracy considerations. The public repository supplies standard software and documentation. Neither source reports an MQ implementation. In this program CLASS is a proposed host for a suitably derived and checked MQ evolution system. [5] [6]

The source calls for a prediction-first implementation. The MQ background and action-derived perturbation prescription are to be specified before cosmological comparison. Planck-inferred baryon, cold-dark-matter or dark-energy fractions must not be inserted as identifications of MQ domains merely because the numbers resemble them. That would import the comparison target into the physical interpretation being tested. [1] [3]

Conventional photon, baryon and neutrino microphysics may enter through independently specified equations. Any initial-condition or astrophysical input not derived within MQ must be labeled as external. A parameter can be estimated in a documented analysis, but its role must remain clear. A coefficient used for calibration, an inferred initial amplitude and a foreground nuisance parameter are not interchangeable kinds of information. [1]

A useful implementation record would identify the code revision, modified modules, physical source terms, gauge convention and all initial conditions. Background conservation, constraint consistency and the relation between gauge-dependent variables and reported observables need checks before scientific comparison. Solver precision, sampling and tolerances must be varied until the reported observables converge. These are proposed acceptance checks, not checks already reported as passed by an MQ run. [1] [5] [6]

What must be predicted from the same solution

Table 2 distinguishes the observable families named by the source. TT denotes the temperature autocorrelation spectrum, TE the temperature–E-mode polarization cross-correlation, and EE the E-mode polarization autocorrelation. BAO means baryon acoustic oscillations. The terms identify data products, not extra freely adjustable MQ domain fractions. [1] [7]

A transfer function describes how an initial perturbation contributes to a later perturbation or observed signal at each scale. The program needs those scale- and epoch-dependent responses, not just a single normalization. Nonlinear clustering and cluster abundance require further modeling after the linear calculation. Data cuts must respect the regime in which each prediction has been justified. [1]

Figure 2 groups the tests around one integrated solution. It does not claim that the channels are statistically independent. Shared sky information, source populations and parameter calibration can link their likelihoods. [1] [4]

Joint likelihoods and external benchmark studies

A likelihood evaluates how a model predicts the measured data under a specified error and nuisance model. The published Planck spectra analysis treats observational and foreground effects; its parameter analysis reports inference conditional on cosmological models and selected data combinations. Those papers provide comparison methods and data context, not endorsement of the MQ construction. [7] [8]

The BOSS DR12 analysis supplies a published distance and growth benchmark with covariance across its combined measurements. It illustrates why the data definition and joint covariance belong with an observable comparison. Its conventional interpretation must be checked before using a compressed distance or growth product under a different cosmological prescription. [9]

For an MQ comparison, the chosen data releases, scale cuts, likelihood versions, priors and nuisance treatments should be stated before interpreting residuals. Calibration data must be distinguished from data adding independent information. Overlapping CMB, lensing and clustering products cannot be counted twice. The resulting model should be compared with alternatives using the same documented data selections, rather than a collection of separately favorable comparisons. [1] [4]

The program does not yet supply a combined fit statistic, posterior parameter set or model-comparison result. No new numerical success percentage or global significance is assigned in this Brief. That information requires the executable prediction and statistical analysis described above. [1]

Why earlier MQ results do not close this test

The MQ referenceability domains classify realized geometric accessibility. Their visible and unobserved allocations form an observable subtotal, whose dark complement completes a normalized total. Numerical similarity to conventional density fractions is a correspondence benchmark. It does not establish physical contents, pressure, clustering or evolution for separately conserved cosmological components. [1] [3] [10]

The CMB monopole temperature describes the mean radiation temperature. Anisotropy spectra describe the angular fluctuations and their correlations. An allocation or temperature calculation does not predict the full TT, TE and EE spectra. Likewise, an isolated geometric acoustic-scale construction does not establish the relative peak structure, lensing or likelihood agreement. [1] [2]

The fixed galactic realization law addresses motion for a specified baryonic source. Its catalog comparisons retain their source and observational qualifications. Extending that response over cosmic time requires an evolving baryonic distribution and a relativistic metric. Local galaxy agreement cannot be promoted directly to a prediction of cosmic structure growth or a universal replacement for dark matter. [1] [4]

Reproducibility and criteria for a completed report

Table 3 describes the concrete records a numerical validation report should make available. It is a reporting specification derived from the stated program and normal reproducibility needs. It is not an inventory of files already supplied by a completed MQ cosmological implementation. [1] [5] [6]

A background failure, unstable or inconsistent perturbation evolution, or disagreement of the frozen model with a joint observable comparison would identify a problem in the cosmological embedding. A revised prescription would need to be labeled as a revision and retested. Such a failure would not logically erase a separately supported local relation; a successful local relation also would not excuse the failed cosmological prediction. [1]

A successful integrated calculation would advance the program beyond scalar correspondences. Its strength would depend on the assumptions fixed beforehand, the independent data used, the quality of the numerical and statistical checks, and comparison with competing explanations. It would not retroactively turn every earlier consistency calculation into an independent prediction. [1] [4]

Chronology and reporting guidance

September 8, 2026 is the recorded source or audit snapshot associated with this retrospective release. The present account was prepared November 2, 2026 and includes current formulation progress and later qualifications. It does not attribute every current Section 5.8 result to the September snapshot or establish an original discovery, announcement or journal publication date. Journal publication of the current MQ manuscript version is not established. [1]

For interviews, request the precise manuscript version and distinguish equations that have been formulated from numerical integrations that have been run. Ask for the executable MQ code, source and initial-condition ledger, convergence evidence and joint likelihood outputs. Until those results are supplied, describe the work as a cosmological validation program with current formulation progress and an outstanding integrated numerical test.