The proposed contribution and its input boundary

The electromagnetic program seeks a common origin for the form of several constants relations. MQ starts from discrete measure, develops count constraints and specifies a physical realization. Its current constants manuscript makes the forward charge and gamma route explicit without inserting measured permittivity, permeability or Coulomb coupling as direct inputs. That input organization is different from a complete absence of empirical calibration. [1]

The Internal Frame describes discrete count configurations. The System Frame is the realized relational encoding connected through the Frames mapping. A dimensionless configuration quantity and its dimensional realization have different roles even when their adopted numerical coefficients agree. Their equality of numbers is not a dimensional identity. [1] [11]

The current profile uses the 2022 inverse fine-structure input to select the coefficient for our universe. Exact SI anchors and the source’s count and charge-normalization prescriptions remain fixed. Deriving the form of a relation, selecting its numerical realization and testing that realization are distinct parts of the program. [1]

Fundamental gamma and its dimensional realization

Let ${\mathrm{\gamma }}_{\mathrm{𝐹}}$ denote dimensionless fundamental gamma, and ${\mathrm{𝛾}}_{\mathrm{𝐹}\mathrm{,}\mathrm{sys}}$ its mapped electromagnetic realization in C². Equation (1a) states the explicit unit mapping. The conversion supplies the charge-squared dimension needed in the physical constants expressions; a bare numerical coefficient would not supply that dimension. [1]

Let ${\mathrm{𝑛}}_{\mathrm{𝐿}}$ be the positive radial length count and ${\mathrm{𝑄}}_{\mathrm{𝐿}}$ its Diophantine realization residual in the source construction. Let ${{\mathrm{𝛼}}_{\mathrm{𝑝}}}^{\mathrm{–1}}$ denote the dimensionless Planck-like inverse fine-structure coupling and ${\mathrm{𝑒}}_{\mathrm{𝑝}}$ the Planck-like charge representation, realized in C in the physical expression below. Equation (2b) collects the charge and residual-count factors into mapped gamma. Local Brief labels are used here; the source construction is in Eqs. (29)–(34). [1]

Let ${\mathrm{𝑒}}_{\mathrm{𝑐}}$ denote the calculated classical charge magnitude in C. Equation (3c) applies the Informativity differential normalization to the Planck-like charge. The positive charge magnitude is used. This is the forward calculation, before any separate insertion of exact SI elementary charge. [1]

The preceding source steps obtain the charge intermediate through an explicitly unit-normalized residual construction with a fixed rounding branch. The formal appearance of length and speed in that construction does not authorize equating dimensional length-times-speed-squared with charge without the stated reference units and mapping. The current gamma route must be read with those prescriptions. [1]

Figure 1 traces the forward dependencies into the electromagnetic family. The two output branches inherit the same calculation, not two new calibration experiments. [1] [2] [3]

The three physical constants expressions

Let ${\mathrm{\varepsilon }}_{\mathrm{0}}$ denote vacuum electric 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. Its numerator has units C² and its denominator has units kg m³ s⁻², giving F m⁻¹. [1] [2]

Let ${\mathrm{𝜇}}_{\mathrm{0}}$ denote vacuum magnetic permeability in H m⁻¹. Equation (5e) follows the conventional reciprocal vacuum identity at the exact light-speed input. Under the same realization prescriptions it is also the source’s magnetic expression in terms of fundamental measures and mapped gamma. [1] [3]

Let ${\mathrm{𝑘}}_{\mathrm{𝑒}}$ denote Coulomb coupling in N m² C⁻². Equation (6f) follows its reciprocal relationship with permittivity, or equivalently its fixed proportionality to permeability at exact light speed. These identities are source Eqs. (37)–(41); their cancellation checks do not independently validate the count construction. [1]

The coherent numerical profile

Table 1 identifies the numerical roles. Electron mass and Bohr radius enter the orbital length construction, but the current source reduces their product to the conventional reduced Planck input times classical inverse fine structure divided by light speed. It therefore does not propagate two rounded, correlated recommendations as extra independent inputs after the reduction. [1]

The current source keeps the inverse fine-structure branch fixed while propagating its input. A 90-digit calculation reran the complete dependent sequence at the central value and at input shifts of one stated standard uncertainty. Table 2 records the rounded results. Parentheses state conditional standard uncertainty in the final displayed digits; they do not include a general model-discrepancy allowance. [1]

Shared uncertainty and exact closure

All three electromagnetic constants depend on the same uncertain calibration. Their relative standard input uncertainties are about 2.21522 × 10⁻¹⁰. Figure 2 shows the signed response when the inverse fine-structure input increases by its standard uncertainty. Permittivity decreases while permeability and Coulomb coupling increase. These are computed sensitivities, not independent measurement residuals. [1]

In the first-order one-input covariance model, permittivity is anticorrelated with each reciprocal output and the two reciprocal outputs are positively correlated. This describes a rank-one calibration contribution. It is not a full experimentally determined uncertainty model for the theory. General propagation must retain covariance when inputs are correlated. [1] [6]

The normalized permittivity–permeability product with light speed squared is exactly one under Equation (5e). Its calibration uncertainty cancels. If the two constants were incorrectly treated as independent, their relative uncertainties would combine into a spurious product uncertainty of about 3.13279 × 10⁻¹⁰. The Coulomb-to-permeability ratio likewise retains no uncertain calibration in this profile because Equation (6f) fixes it using exact light speed and the circle constant. [1]

Table 3 keeps numerical reproduction separate from experimental inference. Several rows built from the same input cannot be multiplied into a global significance. A comparison against recommended constants must also retain any shared information between the prediction and the adjustment used as its reference. [1]

The forward charge residual and the inverse operation

The calculated classical charge is lower than exact SI elementary charge by about 1.38779 × 10⁻²⁸ C, or 0.86619 parts per billion. Its magnitude is about 4.62 of the forward profile’s propagated input standard uncertainties. This is a conditional numerical diagnostic, not a complete discrepancy significance or a probability for MQ; physical model uncertainty has not been quantified. [1] [5]

The manuscript separately inserts exact elementary charge and solves for a charge demarcation of about 84.60159(23). That differs from the fine-structure count of about 84.6005456716 used for Table 2. Changing the input direction produces a different calculation. The inferred count cannot be substituted into the forward result while retaining the forward uncertainty or calling input recovery a new prediction. [1]

Metrological comparisons and numerical versions

The 2022 reference listing gives vacuum permittivity 8.8541878188(14) × 10⁻¹² F m⁻¹ and permeability 1.25663706127(20) × 10⁻⁶ H m⁻¹. The current forward values differ from those printed central references by about −1.53369 × 10⁻²⁰ F m⁻¹ and +2.17521 × 10⁻¹⁵ H m⁻¹. These signed residuals are reported without treating the reference and MQ calibration as statistically independent. [1] [4]

Since the SI revision effective May 20, 2019, elementary charge, Planck’s constant and light speed have exact defining numerical values. Vacuum permeability is no longer assigned its former exact numerical value. Exact constants relations do not make every electromagnetic output exact, and a defining numerical value does not imply an error-free practical realization. [5]

The current electric and magnetic opening figures agree with the reproduced profile. Older prose on those pages retains different uncertainty or significance statements. Those versions are not pooled with the updated digits here. The constants manuscript’s separate rubidium-recoil input exercise is a source-sensitivity comparison, not the authoritative calibration used in Table 2 or a ranking of the theory’s accuracy. [1] [2] [3]

Independent tests and reporting guidance

The missing physical step is an observable test that adds information beyond the selected calibration and identities. It must specify the realization, apparatus or physical system, predicted consequence, uncertainty model and relevant alternative effects before interpreting agreement. Algebraically rewriting the same calibrated output does not provide that new information. [1] [9]

The gamma relations connect the constants within the proposed framework. They do not alone supply a complete common dynamical field theory of gravity and electromagnetism. No new capacitance, magnetic-force or electrostatic-force experiment is reported by this calculation. [1]

September 8, 2026 is the release’s recorded source or audit snapshot. The present text was prepared November 2, 2026 using the current coherent constants profile and later dimensional qualifications. The date is not established as the original discovery, announcement or journal publication date, and the current numbers are not silently attributed to that earlier snapshot. Journal publication of these current MQ manuscript versions is not established. [1] [2] [3] [10]

For interviews, request the forward input ledger, source version, branch prescription and dimensional charge mapping. Ask whether exact charge was an input or comparison, which uncertainties are shared and what physical model uncertainty remains unquantified. The reportable result is a transparent, reproducible construction of a linked constants family with its assumptions and residuals retained.