The question and the proposed contribution

Cosmological accounting can mean either a normalized geometric allocation or physical densities inferred through a dynamical model. The present MQ construction supplies the former and proposes its interpretation through referenceability. A complete physical comparison must explain how those quantities enter the latter. The distinction matters even when two sets of percentages are numerically close. [1] [2] [4]

MQ begins from discrete measure and develops relationships between count structure and realized measurement. The Internal Frame describes count configurations. The System Frame expresses realized relational measures through the Frames mapping. The domain fractions belong to this proposed account of physical referenceability; they are not independently detected populations simply because their labels resemble cosmological terminology. [1] [2] [7]

Domain definitions and normalization

Let ${\mathrm{\Omega }}_{\mathrm{𝑣}\mathrm{𝑖}\mathrm{𝑠}}$ denote the visible fraction, ${\mathrm{\Omega }}_{\mathrm{𝑢}\mathrm{𝑜}\mathrm{𝑏}\mathrm{𝑠}}$ the unobserved fraction, ${\mathrm{\Omega }}_{\mathrm{𝑜}\mathrm{𝑏}\mathrm{𝑠}}$ the observable fraction, ${\mathrm{\Omega }}_{\mathrm{𝑑}\mathrm{𝑘}}$ the dark fraction, and ${\mathrm{\Omega }}_{\mathrm{𝑡}\mathrm{𝑜}\mathrm{𝑡}}$ the normalized total. These quantities are dimensionless. In the source interpretation the visible allocation is presently referenceable; the unobserved allocation is not presently referenceable but belongs to the domain that can become referenceable. The dark complement is outside that observable domain under the adopted construction. These definitions concern MQ referenceability, not merely whether a telescope has detected a luminous source. [1] [2]

Equation (1a) contains two accounting statements. Visible, unobserved and dark are the three disjoint allocations in the normalized total. Observable is the subtotal of the first two, so adding it again would double count. Figure 1 uses a bar rather than a cosmic map because the fractions alone do not specify spatial shapes or radii. [1] [2]

The coefficient and the additional closure relation

Let ${\mathrm{𝜃}}_{\mathrm{𝑠}\mathrm{𝑖}}$ be the dimensionless MQ geometric coefficient. The selected numerical profile gives 3.26239030504(25). Equation (2b) is the source relationship between visible and observable fractions. It is an additional geometric relation beyond normalization. [1] [2] [3]

Let ${\mathrm{\Omega }}_{\mathrm{𝑓}}$ be the fundamental fraction, the construction’s normalization pivot. Equation (3c) supplies a further closure condition. Normalization and Equation (2b) alone would not determine the complete partition. The pivot relation is needed to obtain the displayed closed forms. [1] [2]

The pivot is a dimensionless ratio with a distinct role. It is not an extra store of mass or energy to be added to the normalized total. Its value below one belongs to the selected positive branch. The selected coefficient is greater than the square root of two, which also keeps the dark complement positive in the following expressions. [1] [2]

Exact fraction expressions

Solving Equation (3c) for the observable fraction gives Equation (4d). Substitution into Equation (2b), followed by the first identity in Equation (1a), gives Equation (5e). Taking the complement gives Equation (6f). These are exact relations under the stated construction; the local equation labels are for this Brief. [1] [2]

These expressions produce proportions. They do not by themselves provide kilograms, energy per volume, an equation of state or a stress-energy tensor. Allocating a separately specified total mass would require that total and a physical domain prescription. Identifying these proportions with independently conserved cosmological components requires an additional derivation. [1] [2]

Numerical profile and the role of calibration

Table 1 records the profile used here. The coefficient is evaluated through the current source’s fine-structure calibration with inverse fine-structure input 137.035999177(21), from the 2022 adjustment. A 90-digit calculation reevaluated the coherent sequence at the central input and at input shifts of one stated standard uncertainty. The geometric forms and the selected numerical realization remain different parts of the argument. [1] [3]

Deriving a relationship’s form does not require calling its selected coefficient a fundamental measured axiom. Conversely, using a calibrated coefficient to evaluate the relationship does not make its value a new independent prediction. The present numerical check establishes reproduction and internal consistency of the source profile, with physical interpretation requiring its own evidence. [1] [2]

Parentheses in Table 2 state standard uncertainty in the final displayed digits. All rows depend on the same uncertain coefficient. The visible and unobserved shifts combine into the observable shift; the observable and dark shifts cancel in their normalized sum. Treating these rows as independent measurements would discard their covariance and misstate both the total uncertainty and the amount of evidence. [1] [5]

The tiny propagated intervals quantify the selected calibration chain under fixed source prescriptions. They do not measure physical boundary precision, include a general model discrepancy allowance or establish that the categories have been observed to this precision. No independently measured domain-boundary uncertainty is supplied by this calculation. [1] [2] [5]

Closure checks and two common counting errors

Table 3 applies the bookkeeping to the same central profile. The normalized sum closes to unity without adding the subtotal or pivot. The deliberately incorrect sums show why all five percentages must not be read as separate components. [1] [2]

Comparison with standard cosmological parameters

The mass manuscript’s comparison table cites a Planck 2018 TT, TE, EE plus low-multipole polarization selection and reports 31.66 ± 0.84% for matter and 68.34 ± 0.84% for dark energy. These are model-conditioned comparison values. The likelihood selection must accompany them; they should not be silently interchanged with a different Planck combination that also includes lensing or external distance data. [1] [4]

The MQ observable and dark percentages are numerically close to that pair. The pair is complementary under the stated standard model and normalization, so its two entries are not independent confirmations. Neither numerical closeness nor the shared letter used for fractions establishes that an MQ referenceability allocation is the same physical object as a standard density parameter. [1] [2] [4]

In standard cosmology, matter and dark-energy components affect expansion and perturbations through their dynamical properties. Their inferences use spectra and other observables under specified assumptions. A geometric percentage alone supplies neither pressure nor clustering behavior. It cannot be inserted as a component density while bypassing the equations that connect it to observations. [2] [4]

From a geometric partition to an observational test

Figure 2 separates the work needed for a physical comparison. First specify the realized quantity and the boundary prescription. Then derive consistent background evolution and perturbations, including conservation and gravitational response. Finally calculate observable spectra, lensing and growth with an explicit data likelihood and uncertainty model. The diagram identifies requirements; it does not certify that the partition equations have already completed them. [2] [4] [6]

A useful discriminating test freezes the coefficient selection and physical prescription before fitting the target data. It identifies which observations supplied calibration and which add independent information. Any competing model comparison needs the same data selection and a documented treatment of nuisance parameters. Relabeling conventional densities after looking at their fitted values would not supply that test. [2] [4] [6]

Referenceability also should not be equated with absence of gravitational influence. Whether a proposed domain contributes to a microwave-background or lensing observable depends on the derived physical dynamics. Conversely, a fixed geometric partition does not automatically provide the cosmic time evolution of conventional density components. [2]

Chronology and reporting guidance

September 8, 2026 is the recorded source or audit snapshot associated with this retrospective release. This Brief does not establish that date as the first discovery, first public announcement or journal publication. The text was prepared November 2, 2026 against the current public domain manuscripts. Journal publication of those versions is not established. [1] [2]

For a complete story, request the source version, coefficient-selection ledger, domain definitions and the additional closure relation. Ask whether a plotted fraction is an allocation, subtotal or pivot. When discussing standard cosmology, request the physical mapping, evolution equations and predictions for data not already used in calibration. Describe the present result as a theoretical partition with reproduced arithmetic unless further independent tests are supplied.