The three definitions that organize the construction

The Internal Frame is the discrete relational count-configuration domain. Count multiplicities, permitted adjacency relations and reference consistency belong to that description. The domain has no intrinsic physical coordinates, distances, metric vectors or SI units. A relational cell is a label in the count structure, not a tiny spatial cube. [1] [3]

The System Frame is the continuous relational realization in which measurable physical quantities are represented. Metres, kilograms, seconds, observed geometry, fields and record probabilities acquire their physical interpretation there. Continuous realization is part of the proposed encoding; it does not mean that a continuous metric was already a primitive count-domain object. [1] [2]

The Frames mapping is the proposed relation from admissible count configurations and their reference structure to realized observables. Referenceability, normalization, conservation and closure conditions constrain its domain. The terminology alone does not evaluate that relation for every configuration or establish all resulting dynamics. [1] [2]

Table 1 distinguishes MQ’s domain terminology from the conventional use of “reference frame” in relativity. Physical measurements still require an observer prescription. The Internal Frame and System Frame do not replace that prescription or select a preferred universal inertial frame. [1]

Mapping notation and its limitations

Let ${\mathrm{𝜔}}^{\mathrm{\text{'}}}$ denote a referenceable relational region of the count domain, $\mathrm{𝑀}$ the Frames mapping, and $\mathrm{\Omega }$ its realized image. Equation (1a) records the image relation. The prime marks the selected region; it is not a derivative. [1] [3]

Equation (1a) names the relation; it is not a formula that computes a metric or an observable from arbitrary input counts. A region must meet the stated referenceability conditions before the realization is admitted. Consistent realization is single-valued on its admissible domain, but that does not imply that every distinct underlying configuration must produce a distinct measured quantity. [1] [3]

The image should not automatically be drawn as a Euclidean box or identified with three-dimensional space. The physical interpretation depends on the observable and its realized configuration domain. A geometric picture is explanatory only after the source specifies what its distances, directions and labels represent.

Figure 1 prevents a common pictorial ambiguity. Adjacency in a relational count model specifies permitted connections or transfers; it is not already a physical separation. Likewise, a continuum mesh can represent realized geometry without establishing the field equations or a particular spacetime solution.

Conserved counts before a physical clock is assigned

Let $\mathrm{𝜉}$ label a relational cell and $\mathrm{𝐴}$ the internal update index. The availability count ${\mathrm{𝑛}}_{\mathrm{𝐼}}\left(\mathrm{𝜉}\mathrm{,}\mathrm{𝐴}\right)$ is a nonnegative integer. The regional total ${\mathrm{𝑁}}_{\mathrm{𝐼}}\mathrm{(}{\mathrm{𝜔}}^{\mathrm{\text{'}}}\mathrm{,}\mathrm{𝐴}\mathrm{)}$ is the sum in Equation (2b). The cell label is not a spatial coordinate, and the update index is not elapsed physical time. [3]

The finite update difference is denoted by delta with update-index subscript. The boundary transfer ${\mathrm{𝜙}}_{\mathrm{𝐼}}\mathrm{(}\mathrm{\partial }{\mathrm{𝜔}}^{\mathrm{\text{'}}}\mathrm{,}\mathrm{𝐴}\mathrm{)}$ is the net outward signed availability transfer across the region’s allowed boundary adjacency links during an update. The boundary symbol identifies those links, not a physical surface area or normal vector. The source’s regional balance is Equation (3c). [3]

Equation (3c) is discrete count-per-update bookkeeping. A closed region has zero net boundary transfer and a conserved total. An open region can lose count to its surroundings while the combined larger region remains conserved. Neither an internal update nor an adjacency transfer has a duration in seconds until a physical realization and clock relation are supplied. [3]

An exact count ledger and what it leaves undetermined

Table 2 illustrates a three-cell region. Start with counts four, three and two. If an allowed internal transfer moves one unit from the first cell to the second, the new counts are three, four and two. The total remains nine. This stipulates a transfer to check the balance; it does not derive that transfer as the dynamics of a physical system.

The two closed redistributions in Table 2 both satisfy conservation. A transfer law and adjacency conditions are needed to select either history. In the open-region row, the total changes by minus two while outward transfer is plus two, so Equation (3c) still holds. The table is constructed arithmetic, with no detector data or experimental uncertainty.

Figure 2 shows why count conservation is a necessary constraint but not a complete observable prediction. Many transfer histories can preserve the same total. Multiplying that total by a dimensional reference would assign a scale only after the relevant physical realization is justified; it would not determine the missing spatial and temporal structure.

Units, normalization and a concrete observable example

The fundamental reference types are length, mass and time. Their realized units are m, kg and s. Identifying those types in the count description does not assign metres or kilograms intrinsically to primitive configurations. A physical prediction needs the realization rule and its dimensional calibration, with the units preserved through every step. [1] [2]

The frame preprint provides a concrete inverse fine-structure example. Its three stages are fundamental, Planck-like and classical forms, all dimensionless. The fundamental form belongs to the count construction, the Planck-like form includes the metric differential, and the classical form additionally includes the finite-count normalization associated with the Informativity differential. [2]

The current numerical chain first calibrates the invariant dimensionless coefficient as 3.26239030504(25) from the 2022 CODATA classical inverse input 137.035999177(21). Multiplying the unrounded coefficient by forty-two gives the fundamental inverse. Adding its signed nearest-whole-unit remainder gives the Planck-like inverse. Applying the finite-count normalization then gives the classical inverse in Table 3. [2] [4]

Table 3 reproduces the frame preprint’s Table 2. The signed remainder is formed from forty-two times the coefficient minus its nearest whole unit; the nearest integer on this branch is 137. The finite-count normalization is 0.9999650728344806 at the shown precision. The calculations retain the unrounded coefficient rather than propagating the displayed rounded values independently. [2]

Parentheses give one standard uncertainty in the final digits. The three entries share the same experimental calibration and are correlated. Recovering the classical input is algebraic closure under the stated realization rules, not an independent prediction of that input. The Planck-like number is an MQ intermediate form rather than another CODATA recommendation. [2] [4]

This example makes the distinction operational at the level of a specified calculation. It identifies the count expression, the mapping correction, the extra normalization and the external input. It does not supply a complete microscopic evolution law for every measurement. The invariant dimensionless coefficient must also remain distinct from its momentum or angular realizations, whose physical dimensions require the stated realization conventions. [2]

What a metric picture and a probability picture still require

The metric differential names the mismatch between discrete count relations and their continuous encoding. The Informativity differential names the distinct non-Lorentz contraction in realized separation associated with the count mapping. They are related within the program but not synonyms. A plotted triangle, grid or curved surface must identify which relation it illustrates and which quantities have already been realized. [1] [2]

In quantum measurement, a physical probability assignment additionally needs normalized availability and a completed contextual record map. The squared magnitude of a chosen amplitude represents the resulting density; conservation alone does not fix phase, detector dynamics or a physical clock. In gravitational applications, a realized metric still requires dynamics, matter coupling and a solution before it yields a complete observable prediction. Cosmological uses likewise need a specified physical clock and normalization, rather than treating an internal update index as cosmic age. [1] [3]

The shared terminology makes these distinctions checkable across applications. It does not prove the full realization in each application. A reproducible result should identify its primitive configuration and references, admissible mapping, observable definition, physical dimensions, source inputs, evolution law and comparison procedure. [1] [5]

Chronology and reporting guidance

September 5, 2026 is the terminology/source milestone recorded by this archive entry. It is not independently established here as the first announcement or discovery date. This Brief was prepared October 27, 2026 using the current public terminology and worked examples; later source qualifications are not silently dated to the earlier milestone. [1] [2]

The frame preprint is titled Quantization Ratios as a Function of the Discrete and Non-discrete Frames. The current definitions and qualifications should not be attributed verbatim to an older paper merely because it supplies historical framework context. Journal publication of the current preprint versions cited here is not established. [2] [3]

For an interview, ask the author to trace one observable from a specified count configuration without assuming the desired geometry or hiding calibration. Request the admissibility conditions, reference closure, physical clock and normalization, and a worked calculation that identifies what would falsify it. A definition sets the meaning of the theory; empirical support requires an independently assessable consequence.