The physical question and the proposed contribution

Vacuum permittivity sets the conventional electric coupling scale. In the modern SI its numerical value is not a separately fixed defining constant. Elementary charge, Planck’s constant and vacuum light speed have exact assigned values; fine-structure information determines the corresponding recommended electromagnetic vacuum constants. A calculation must therefore distinguish a physical explanation of their relationship from the metrological input used to evaluate it. [4] [5]

MQ’s starting axiom is that measure is discrete. It develops logical count relations and a mapping into physical observables. In this architecture, deriving the form of a relation, selecting the universe represented by its coefficient, and choosing dimensional units have different roles. A measured selector is not automatically an axiom that supplied the law’s form. Conversely, selecting a numerical realization does not make that selector a newly predicted experimental result. [1] [2] [8]

The Internal Frame is the discrete count-configuration domain. The System Frame is the realized relational encoding in which physical quantities are expressed through the Frames mapping. The proposed electric result concerns that realization. It is not a claim that a primitive count configuration already carries coulombs or contains a material electric-field apparatus. [2] [8]

Fundamental gamma and its charge-squared representation

Let ${\mathrm{\gamma }}_{\mathrm{𝐹}}$ denote dimensionless fundamental gamma, and ${\mathrm{𝛾}}_{\mathrm{𝐹}\mathrm{,}\mathrm{sys}}$ its electromagnetic realization in C². Equation (1a) states the source’s explicit unit mapping. It identifies a physical representation of the count quantity, rather than a second independently fitted gamma. The equation labels in this Brief are local labels; the corresponding current source relations are Eqs. (29)–(39) of the constants manuscript. [1] [2]

Let ${\mathrm{𝑄}}_{\mathrm{𝐿}}$ be the Diophantine realization residual and ${\mathrm{𝑛}}_{\mathrm{𝐿}}$ the dimensionless radial length count used in this construction. Let ${{\mathrm{𝛼}}_{\mathrm{𝑝}}}^{\mathrm{–1}}$ denote the Planck-like inverse fine-structure coupling, and ${\mathrm{𝑒}}_{\mathrm{𝑝}}$ the Planck-like charge representation, realized in C in the following physical expression. Equation (2b) collects the residual-count product and charge into the mapped gamma. The charge normalization must be specified before interpreting that dimensional equation. [2]

The forward source obtains the charge intermediate through its adopted cubic residual construction, Eqs. (30)–(32). Those equations explicitly normalize length, speed and charge by reference units. They are not permission to set a length-times-speed-squared quantity equal to a charge without a dimensional mapping. The source’s rounding branch and charge-realization convention remain part of the calculation. [2]

Let ${\mathrm{𝑒}}_{\mathrm{𝑐}}$ be the calculated classical charge magnitude in C. Equation (3c) applies the Informativity differential normalization to the Planck-like charge. This route evaluates the fine-structure count first and then calculates the charge. It does not insert exact SI elementary charge to force agreement. [2]

Figure 1 follows this forward sequence into the electric output. The diagram separates the underlying logical relations from the physical realization and numerical selection. Repeating the same coefficient in several output boxes is not a new independent measurement. [1] [2]

The physical permittivity equation

Let ${\mathrm{\varepsilon }}_{\mathrm{0}}$ be vacuum permittivity in F m⁻¹, ${\mathrm{𝑙}}_{\mathrm{𝑓}}$ fundamental length in m, ${\mathrm{𝑚}}_{\mathrm{𝑓}}$ fundamental mass in kg, $\mathrm{𝑐}$ vacuum light speed in m s⁻¹, and $\mathrm{\pi }$ the upright dimensionless circle constant. Equation (4d) is the current dimensional electric reduction. It uses mapped gamma, not a bare dimensionless replacement. [1] [2]

The numerator has units C². The denominator has units kg m³ s⁻². Their quotient is C² s² kg⁻¹ m⁻³, equivalent to F m⁻¹. This is the required dimensional role of the mapping in Equation (1a). A numerical coefficient alone would not provide the missing charge dimension. [1] [2]

What is selected, and what is calculated

Table 1 records the numerical profile used here. The inverse fine-structure input selects the coefficient corresponding to our universe. The source fixes its rounding branch while propagating the input uncertainty. Exact SI constants anchor the numerical units. Electron mass and Bohr radius participate in the source’s cross-dimensional normalization; the matched product can be reduced using their conventional relation to Planck’s constant, light speed and the same fine-structure input. They must not be counted as extra independent information after that reduction. [2] [4]

These roles should not be collapsed into a statement that a measured calibration supplied every law. The displayed electric relation retains its symbolic form before selecting its coefficient. The numerical uncertainty still depends on the selected input and source prescriptions. An explanation of law form and an uncertainty analysis answer different questions. [2]

Reproduced numerical values and uncertainty

A 90-digit calculation evaluated the fixed-branch source route and reran the complete dependent sequence at the inverse fine-structure input shifted by its stated standard uncertainty. Table 2 gives the resulting rounded values. Parentheses specify one-standard uncertainty in the final displayed digits. The propagated uncertainties are conditional on that numerical chain and exclude unquantified physical model discrepancy. [1] [2] [6]

The electric output’s conditional standard uncertainty is about 1.9614 × 10⁻²¹ F m⁻¹, or 2.2152 × 10⁻¹⁰ relative. Its central value is lower than the printed CODATA reference by about 1.5337 × 10⁻²⁰ F m⁻¹. That signed residual is useful numerical information, but dividing it by an independently combined pair of error bars would ignore shared calibration and missing model uncertainty. [2] [4] [6]

The calculated charge differs from exact SI elementary charge by about −1.3878 × 10⁻²⁸ C, or −0.8662 parts per billion. It therefore does not reproduce that exact defining value to all the digits in its conditional propagated interval. The charge residual is about 4.62 of those input-only standard uncertainties. This is a diagnostic of the fixed forward profile, not a complete discrepancy significance or a probability for the theory. [2] [4]

The current opening graphic on the electric page agrees with the reproduced permittivity in Table 2. Older prose on the same page quotes 8.85418780(60) × 10⁻¹² F m⁻¹ and a 3.93σ comparison, with another uncertainty appearing in the body. Those are different numerical versions. This Brief uses the current graphic and coherent forward profile rather than attaching an older uncertainty or significance to the updated value. [1] [2]

Forward prediction and exact-charge inversion

The constants manuscript separately replaces the calculated charge by exact elementary charge and solves its residual-count relation for a charge demarcation. It reports about 84.60159(23), distinct from the fine-structure count of about 84.6005456716 used for Table 2. The difference follows the changed input direction. A count inferred from exact charge is not an independent charge prediction. [2]

Figure 2 contrasts the two operations. A journalist should identify which count and input direction are used before quoting a calculated charge or electric constant. The forward result cannot acquire exact-charge agreement simply by substituting the inverse count while retaining the forward uncertainty budget. [2]

The gravitational identity and the Coulomb output

Let $\mathrm{G}$ be the upright upper-count gravitational quantity in m³ kg⁻¹ s⁻². Multiplying Equation (4d) by the source’s upper-count gravitational expression gives Equation (5e). The cancellation uses compatible fundamental measures and the same mapped gamma. It does not establish a full dynamical equivalence of electric and gravitational fields. [1] [2]

Let ${\mathrm{𝑘}}_{\mathrm{𝑒}}$ be Coulomb coupling in N m² C⁻². Its conventional relationship to permittivity is Equation (6f). The resulting forward value is 8.9875518017(20) × 10⁹ N m² C⁻² under the same profile. This is a linked output, not an additional independent experimental result. [2]

The magnetic output is likewise obtained through the conventional reciprocal vacuum identity at exact light speed. Shared uncertain inputs therefore generate correlated electric, magnetic and Coulomb values. Their covariance must be retained before evaluating products, ratios or a collection of residuals. Multiple algebraic representations do not multiply the independent evidence. [2] [6]

Reporting, chronology and testable next steps

Table 3 distinguishes the checks already supplied from the physical questions they leave open. A prospective test should specify an observable and apparatus model, freeze the count branch and normalization, and identify data that add information beyond the calibration already used. A capacitance or field measurement would also require an uncertainty budget for geometry, materials, instrument effects and its connection to the proposed realization. [1] [7]

October 13, 2026 is the recorded source-version date used for this retrospective archive. It is not established here as the first discovery, original announcement or journal publication date. This Brief was prepared November 2, 2026 using the current public graphic and constants manuscript. Journal publication of those current manuscript versions is not established. [1] [2]

For interviews, request the exact source version, unit-normalized charge definitions and forward input ledger. Ask which numerical choices select a universe, which fix units, and which premises produce the equation’s form. Request the joint covariance before comparing constants, and keep the current charge residual visible when discussing the forward construction.