TITLE:
A Structural Analysis of the Minimum-Mass Degree in Gravitational and Electromagnetic Readout Relations
AUTHORS:
Tomofumi Miyashita
KEYWORDS:
Cosmic Microwave Background Temperature, Gravitational Constant, Minimum Mass, Minimum-Mass Degree, Coulomb’s Law, Newton’s Law of Universal Gravitation, Inverse-Square Law, Readout Structure
JOURNAL NAME:
Journal of Modern Physics,
Vol.17 No.10,
October
28,
2026
ABSTRACT: This report extends our previous studies of empirical relations involving the cosmic microwave background temperature and the gravitational constant. In the preceding work, the adopted readout procedure gave a CMB temperature of 2.7256307 K, in agreement with the observed value of 2.72548 ± 0.00057 K. The same procedure also gave a gravitational value of 6.674184 × 10−11 m3∙kg−1∙s−2, close to the reported value of 6.6743 × 10−11 m3∙kg−1∙s−2. These two results were obtained within a common structural framework in which the minimum mass, denoted by Mmin, connects microscopic mass-energy quantities with macroscopic readouts. The present study focuses on the structural meaning of this minimum-mass scale. In particular, we establish a readout-level degree correspondence in which the electromagnetic numerator is first degree in the minimum-mass readout, the gravitational rate representation is second degree, and their quotient leaves one residual minimum-mass readout degree in the dimensionless proton-side gravitational-to-electromagnetic force ratio. The degree terminology used here is a same-shell, readout-covariant structural classification; it is not an assertion that
M
min
2
is an intrinsic quantity independent of the adopted unit/readout system. The purpose is not to derive the physical origin of gravity or of electromagnetism, but to clarify the algebraic and readout structure associated with the minimum mass. The analysis also revisits Coulomb’s law and Newton’s law of universal gravitation from the viewpoint of their common inverse-square dependence on distance. Both laws contain the same spatial factor associated with the square of the separation, while their electromagnetic and gravitational numerators remain distinct. This common spatial structure is treated separately from the minimum-mass degree correspondence. The resulting correspondence shows that the difference between the second-degree gravitational structure and the first-degree electromagnetic structure is directly reflected in the first-degree minimum-mass readout remaining in the force ratio, while the deeper physical origin of the degree structure remains open.