What the Coulomb output represents

The source’s Coulomb calculation follows its charge-based electric-permittivity construction. The conventional reciprocal relation then supplies the electrostatic coupling. The role of the MQ proposal is its upstream account of the fundamental measures and realization prescription; the reciprocal identity itself is standard electromagnetic bookkeeping, not a new physical law. [1] [2]

Let ${\mathrm{𝑘}}_{\mathrm{𝑒}}$ denote Coulomb’s constant, with units N m² C⁻², and ${\mathrm{\varepsilon }}_{\mathrm{0}}$ vacuum electric permittivity, with units F m⁻¹. The symbol $\mathrm{\pi }$ denotes the dimensionless circular constant. Their exact relation is Equation (1a). [1]

For electrostatic point charges in vacuum, the force magnitude is Coulomb’s constant times the absolute product of the two charges, divided by their squared separation. Real materials, finite charge distributions and dynamic fields require their appropriate models. The present linked-output calculation is not a measured force-versus-distance curve. [1] [2]

Vacuum permeability equals one divided by the product of permittivity and light speed squared. With light speed fixed exactly at 299792458 m s⁻¹ in SI, specifying permittivity fixes both permeability and Coulomb coupling. [4] [5]

Table 1 separates physical units from calibration roles. Different dimensions do not make the quantities statistically independent. The revised SI no longer assigns vacuum permeability its former exact numerical value. Exact relations among constants are compatible with uncertainty in their numerical values. [4] [5]

The MQ normalization and dependency boundary

The current source summary distinguishes a dimensionless fundamental electromagnetic coefficient from its charge-squared SI realization. The latter supplies the physical normalization in the dimensional permittivity and Coulomb reductions. Treating the dimensionless coefficient as though it already had charge-squared units would lose the unit factors. These representations are not separate independently fitted parameters. [1] [2]

The construction also inherits its fundamental-measure inputs, charge polynomial and prescribed count realization. The Internal Frame is the discrete configuration domain, while physical electromagnetic quantities belong to the System Frame through the Frames mapping. Deriving a downstream expression does not remove dependencies introduced upstream. A proposed structural motivation is distinct from a general uniqueness proof or independent empirical validation. [1] [3]

Figure 1 gives the relevant dependency graph. The electric, magnetic and Coulomb quantities are outputs of one stipulated family. A second or third algebraic path to the same quantity is a closure check unless it brings in genuinely independent information.

A numerical closure check using a reference input

Table 2 starts with the printed CODATA 2022 reference permittivity and exact SI light speed. It recalculates the linked outputs, retaining guard digits before rounding. These are reference-based calculations, not predictions of MQ. Reproducing them verifies arithmetic and the conventional identities. [4]

The permittivity parentheses in Table 2 indicate standard uncertainty 1.4 × 10⁻²¹ F m⁻¹ in the final printed digits. The calculated rows retain numerical guard digits for the closure check; they do not claim those extra digits are independently known physical precision. Recalculating the recommended permeability from the same constant network is not a second independent empirical confirmation. [4]

Equation (2b) is the exact closure form of Equation (1a). Their labels belong to this Brief; the source’s conventional Coulomb reduction is in Equation (31). The product is dimensionless. A failure to reproduce it after rounding must be assessed against the retained input precision before being called a physical inconsistency. [1]

The source’s printed MQ values are a different numerical account

The Coulomb preprint prints permittivity 8.85418780(60) × 10⁻¹² F m⁻¹ and Coulomb coupling 8.987551802(610) × 10⁹ N m² C⁻². Their stated standard uncertainties are respectively 6.0 × 10⁻¹⁹ F m⁻¹ and 610 N m² C⁻². They belong to that printed source calculation and must not be silently replaced by another manuscript’s tighter conditional values. [1]

Using only its rounded central permittivity in Equation (1a) gives a recalculated Coulomb value of 8.98755180525 × 10⁹ N m² C⁻² after rounding. Its roughly 3.25 N m² C⁻² difference from the printed Coulomb central value is compatible with the permittivity’s last-digit printing precision and is much smaller than the quoted 610-unit uncertainty. It is not evidence of a new force discrepancy.

This Brief checks that printed-value arithmetic rather than independently reproducing the full upstream charge calibration, realization parameter or covariance. Different source editions and prescribed uncertainties must remain distinguishable. A broad-uncertainty numerical agreement from one source cannot establish the absence of conditional tension in a different, more tightly propagated calculation. [1] [3]

One input change moves both downstream outputs

Table 3 varies permittivity by an exactly chosen one percent while holding light speed fixed. Both Coulomb coupling and permeability scale with the same reciprocal input factor. The percentages are illustrative perturbations, not reported physical variations or uncertainty estimates. Their slight asymmetry follows the exact reciprocal rather than a symmetric linear approximation.

Figure 2 plots that same dependence. There is one common relative-response curve for both linked outputs, not two independent changes to be counted as separate evidence. The plot uses a continuous arithmetic variation around a baseline and does not assert that every plotted point is an admissible MQ configuration.

Shared uncertainty is not three independent significance tests

For small input uncertainties, first-order propagation gives each downstream constant the same fractional standard uncertainty as permittivity when light speed is exact. Their relative changes have the opposite sign to the permittivity change, while Coulomb coupling and permeability change together. At fixed light speed those two outputs are exactly proportional. Their numerical agreement with linked references cannot be multiplied into independent evidence.

The linearized uncertainty of this one-input family has only one independent variation. This is a first-order statement, not a claim that every finite nonlinear covariance matrix has rank one. A comparison with CODATA can share additional upstream inputs, especially the fine-structure calibration. The full difference and its uncertainty must retain that covariance rather than adding uncertainties as though all sources were independent. [3] [4]

A closed set of identities can reveal unit errors, mismatched versions and inconsistent intermediate inputs. It cannot by itself establish why nature selects the MQ charge polynomial, physical normalization or proposed mapping. The proposed origin of the quantities requires evidence beyond algebraically transforming one family member into another. [1] [3] [6]

What would make a stronger empirical test

A separate test should identify an observable not already used to set the calibration, specify the realization prescription before comparison and retain the relevant experimental and model uncertainties. If a source uses an exact charge input in an inversion and then recovers that same charge downstream, the recovery checks consistency rather than independently predicting an SI definition. [3] [5] [6]

The October 13, 2026 archive date identifies the recorded source-version milestone, not a new electrostatic experiment or original discovery date. This Brief was prepared October 27, 2026 using the current public account. Journal publication of these current preprint versions is not established. Published framework context does not independently validate every subsequent linked-output claim. [1] [7]

For reporting, request the input list, physical realization normalization, source edition, unrounded intermediate values and covariance treatment. Ask which quantity was actually measured independently and which was calculated from another. Preserve the distinction between numerical closure, consistency with a shared calibration network and a genuinely new empirical test.