G: Gravitational constant: 6.6743 × 10⁻¹¹ (m³∙kg⁻¹∙s⁻²)

(listed for comparison only; not used as an input in the calculation chain.)

T_c: CMB temperature: 2.72548 ± 0.00057 (K)

(listed for comparison only; not used as an input in the calculation chain.)

k:Boltzmann constant: 1.380649 × 10⁻²³ (J∙K⁻¹)

c: Speed of light: 299,792,458 (m/s)

h: Planck constant: 6.62607015 × 10⁻³⁴ (J∙s)

ε₀: Electric constant: 8.8541878128 × 10⁻¹² (N·m²·C⁻²)

μ₀: Magnetic constant: 1.25663706212 × 10⁻⁶ (N∙A⁻²)

e: Electric charge of one electron: −1.602176634 × 10⁻¹⁹ (C)

q_m: Magnetic charge of one magnetic monopole: 4.13566770 × 10⁻¹⁵ (Wb)

(This is a theoretical value defined by q_m = h/e.)

m_p: Resting mass of a proton: 1.67262192369 × 10⁻²⁷ (kg)

m_e: Resting mass of an electron: 9.1093837015 × 10⁻³¹ (kg)

R_k: von Klitzing constant: 25812.80745 (Ω)

Z₀: Wave impedance in free space: 376.730313668 (Ω)

α: Fine-structure constant: 1/137.035999081.

2.2.1. Symbols Obtained after the Redefinition Procedure

In this subsection, symbols carrying the subscript “new” denote quantities expressed under the redefinition scheme adopted in this study. They represent numerically consistent readouts of the corresponding MKSA quantities.

Therefore, the value of Planck’s constant remains unchanged.

Equation (16) can be rewritten as follows:

where 4.5_unit and π_unit are unit-identification coefficients for the (1/(A·m)) and (V·m) readouts. They represent MKSA readout deviations, not new physical constants.

Equation (18) can likewise be rewritten as follows:

The Compton wavelength, λ, is then given by

Because Planck’s constant and the speed of light are fixed, the Compton-wavelength relation connects the length readout to the corresponding mass readout. Equations (24)-(26) are therefore retained.

The minimum mass is defined as follows:

2.2.2. Meaning of the First Redefinition: Ω-Side Normalization

In the first redefinition, macroscopic and microscopic quantities are related through a normalization of the unit Ω. Under this normalization, the unit J·m²/s is fixed as follows:

Redefining the macroscopic unit 1 Ω yields the following relations.

2.2.3. Readout Relations Used in the Previous Formulation

The following eight relations were used in the previous formulation to connect electromagnetic, mass-energy, and gravitational-side readouts.

2.2.4. C-Normalization

In this study, physical quantities are expressed in c-normalized form by introducing appropriate factors of the speed of light. This representation allows electromagnetic, mass-energy, and action-type quantities to be compared within a common structural framework.

Here, G_N is defined as the gravitational constant G multiplied by the macroscopic reference mass 1 kg. It is used as an intermediate gravitational-side readout quantity.

2.2.5. Structural Quantities SI, UI, UIP, EI, and EIP

The following structural quantities and their numerical values are introduced.

SI: structural invariant.

UI: generative action.

UIP: unit-conversion factor.

EI: energy-pair quantity.

EIP: square-type unit structure.

The following equations are used as the basic structural relations in the present analysis.

In this study, a shell S is a coherent numerical-readout set consisting of a macroscopic unit, its corresponding microscopic reference quantity, and the representative number that relates them. The shell-local representatives are

within each shell, the macroscopic unit is set to one and the representative is preserved, so the paired microscopic quantity has the same local readout as in the MKSA shell. By contrast, its readout changes when expressed relative to the macroscopic unit of the MKSA shell.

For the numerical calculations in this study, each readout quantity X is assigned a table number A ( X ) , which is converted into a readout-transfer factor according to

here, A is a covector assigning the table number A ( X ) to each readout quantity X ; thus, A ( c ) = 0 means zero table-number weight for c , not the c -normalization introduced in Section 2.2.4. A positive table number multiplies the readout by J tab A ( X ) when A ( X ) > 0 , whereas a negative table number divides the readout by J tab | A ( X ) | when A ( X ) < 0 ; a zero value leaves the readout unchanged. The assignments used in the calculations are listed in Table 1 and applied in Section 4. The common scale is calibrated by J tab 5 = π / π u n i t , MKSA = 4.5 / 4.5 u n i t , MKSA ; under the adopted single-parameter net map, the relative split (−1, +1) gives λ = J tab and net assignments (+4, +6). Its physical necessity and uniqueness are discussed in Section 5.

Table 1.Table-number assignments used in the present calculation.

The quantities summarized in Table 2 are not introduced as additional independent assignments. They are reconstructed from the seed values A(C) = −4, A(Wb) = +6, A(s) = −1, and A(c) = 0, together with A(m) = A(s) and the shell-local correspondences A(e) = A(C) and A(q_m) = A(Wb). The detailed interpretation and limitations of this electromagnetic reconstruction are discussed in Section 5.

Table 2.Conditional electromagnetic reconstruction of the derived unit, field, circuit, action, and landing branches.

The table-number rule in Equation (63) was applied to the MKSA reference readouts using J_tab = 1.00056105184. Table 3 summarizes the principal transferred values used in the subsequent calculations.

Equation (12) gives T c = 2.7256307   K . Table 3 lists the transferred readout after A ( k T c ) = + 3 ; dividing that entry by k B yields the intermediate display 2.73022088 K, which is not the final comparison value. The signs of the assigned table numbers determine only whether the corresponding factor is multiplied or divided; their structural interpretation is reserved for Section 5. The transferred electromagnetic product is consistent with the transferred action-product center: ( e c ) ( q m c ) = h c 2 within the numerical precision used in the calculation. Table 3 also includes the transferred k T c readout used in the gravitational-side calculation in Section 4.4.

Table 3.Principal branch-resolved readouts used in the present calculation.

The branch-resolved readouts were substituted into the four macro-micro connection equations, and the results are summarized in Table 4. The first pair compares coefficient-normalized electromagnetic readouts with minimum-mass coordinates, while the second pair compares coefficient-wrapped electromagnetic readouts with the corresponding mass-energy- k L 0 products. All four equations agree within approximately 1.1 × 10⁻⁹ in relative terms, confirming numerical consistency without establishing a completed physical mechanism or electromagnetic-mass representative-count equality.

Table 4.Numerical comparison of the four macro-micro connection equations.

The transferred quantities were also evaluated through the three composite forms of SI used in the present framework. The first form combines UIP with the action-product readout hc². The second combines the square-pair quantity EIP with the energy-pair quantity EI. The third is the mass-side composite formed from the minimum-mass and electron–proton mass-energy readouts. Table 5 summarizes the calculated results.

The three independently displayed forms agree within the numerical precision of the calculation. Accordingly, the table-number transfer preserves the same dimensionless SI readout across the action-product, energy-pair, and mass-side composite representations.

Table 5.Comparison of the SI composite readouts.

Using the branch-resolved readouts and the transferred k T c value listed in Table 3, the proton-side force-ratio readout is obtained. In the present framework, G_N is treated as the primary gravitational-side quantity. The macroscopic reference mass 1 kg is a human-defined reference setting used to express the corresponding gravitational readout as G. Accordingly, 1 kg/Mₘᵢₙ is interpreted as a kg-reference mass-ratio representative, not as an Avogadro-type count. From Equation (42),

The resulting numerical readout is

The factor J tab − 4 belongs to the mixed-shell kg / k L 0 denominator-side projection, not to the zero-allocation quantity R p ( m p ) itself. The corresponding gravitational-side readouts are summarized in Table 6. Here, G_N = G × 1 kg retains the macroscopic reference mass explicitly, whereas G is the corresponding readout projected onto the human-defined 1 kg reference setting. Table 6 summarizes the gravitational-side readouts, with G N shown as an intermediate readout, G MKSA as the reverse-transferred MKSA value, and 6.6743 × 10⁻¹¹ m³·kg⁻¹·s⁻² used only for comparison. The detailed interpretation of the mass-ratio display, reference-mass setting, and denominator-side readout is discussed in Section 5.

Table 6.Principal gravitational-side readouts obtained from Rₚ(mₚ).

In each shell, the macroscopic unit is normalized to 1 and the branch-local representative

is preserved, so the paired microscopic reference quantity retains the same shell-local readout. The table-number map does not change this local macro-micro correspondence.

What changes is only the numerical display relative to the corresponding MKSA macroscopic unit. A negative table number means that the MKSA-referenced readout is smaller by the corresponding power of J tab , whereas a positive table number means that it is larger. These are purely cross-shell display changes, not changes in the physical quantity or in its shell-local readout. The representatives are therefore shell-local macro-micro coordinates, not literal particle counts.

The first redefinition produces a coherent normalized shell and provides the numerical representation used to calculate k T c . This shell is internally consistent, but it does not by itself complete the MKSA-referenced numerical display required for the gravitational-side calculation.

The second redefinition, implemented through the calibrated table-number rule, transfers the coherent shell to the final branch-resolved numerical representation required for the calculation of G .

The shell-local representatives can be used to rewrite the two coefficient branches without removing the macro-micro structure. Under the adopted mapping, the 4.5 u n i t branch contains the representative allocation N 1 / N 3 , whereas the π u n i t branch contains N 3 / N 2 . The common mass representative N 3 therefore connects the two branches while cancelling from their product. The common length gate then routes the two coefficient branches into the corresponding voltage- and current-type landing coordinates. This gives the branch-local composite relations e S V e , S = m e , S c 2 and q m , S A p , S = m p , S c 2 . These relations show how the coefficient pair, shell-local representatives, and length-time branch participate in one coherent routing structure.

Why the numerical anchors are specifically 4.5 and π remains unexplained. Nevertheless, within the present framework, other anchor values do not reproduce the present calculations of T c and G .

Table 2 shows that the voltage, current, resistance, capacitance, inductance, field, action, and dual mass-energy landing branches can be reconstructed from the adopted seed assignments through standard electromagnetic unit relations. If the seed exponents were independently derived, the table-number rule could be interpreted as a compact encoding of the electromagnetic unit structure. In the present framework, however, this reconstruction remains conditional on the adopted seeds. The table-number rule may therefore serve as an operational substitute for repeating the branch-by-branch electromagnetic reconstruction, but it does not replace electromagnetic theory or independently explain the physical origin of the seed exponents. This reconstruction is consistent with the table-number map used in the present calculations of T c and G , but this agreement does not constitute a first-principles derivation of that map.

In the gravitational-side calculation, G N is treated as the primary readout quantity, whereas G is obtained by projection onto the external MKSA mass reference:

The factor ( 1   kg ) MKSA is therefore a macroscopic reference placement in the numerical display of G , not an intrinsic component of G N . The first redefinition produces a coherent intermediate shell, but the second redefinition is required to complete the MKSA-referenced numerical representation used in this projection. The relation may also be written as

here, N MKSA is a macro-micro representative associated with the external 1 kg reference. It is not interpreted as a literal particle count.

The proton-side force-ratio relation is

Using

This relation becomes

thus, the factor 9/4, together with the factor 2π in the minimum-mass relation, gives rise to the coefficient 4.5π in the thermal representation of R p ( m p ) . In the present representation, k T c / α may be interpreted as an activation-energy-like scale in the phenomenological context of thermally activated and nonequilibrium processes [18][19]. However, no microscopic activation barrier, dissipation mechanism, or gravitational thermodynamic origin is derived in the present work.

The present framework clarifies the coherent-shell interpretation, the distinct roles of the two redefinitions, the preservation of shell-local representatives, the coefficient-to-landing routing, the external MKSA 1 kg projection of G N , and the algebraic appearance of 4.5π and k T c / α . These results establish structural organization and internal numerical consistency under the adopted map, but not a completed microscopic mechanism. The first-principles origins of the table-number base weights, the fifth-root order n = 5 , the anchors 4.5 and π, the branch orientation, and the physical necessity of the second redefinition remain unresolved.