Structural Origin of Gravity

This work presents a structural formulation of gravity in which the gravitational constant and gravitational coupling strengths are derived from fixed ratios without introducing free parameters.
The framework is based on two constants,
\[
R = \frac{13}{6}, \qquad Z = \frac{31}{24},
\]
together with structural indices \(\Psi_G\) and \(\Psi_d\) that encode the gravity-sector configuration.
Within this formulation, the gravitational constant is expressed as
\[
\sqrt{G} = \frac{\alpha Z}{\pi \Psi_G},
\]
leading to
\[
G \approx 6.674338 \times 10^{-11},
\]
in close agreement with the CODATA 2022 reference value.
In addition, gravitational couplings are derived as
\[
\alpha_{Gp}, \qquad \alpha_{Ge},
\]
using the same structural components that govern the particle mass hierarchy.
All quantities are obtained without parameter fitting and are expressed in dimensionless structural form.
A key result is that the structural expression, although dimensionless, reproduces the SI value of \(G\). This suggests that dimensional constants emerge as observational projections of underlying structural ratios rather than independent inputs.
The gravity sector is further interpreted through the structural term
\[
(3R^2)(4R),
\]
which represents a maximally connected configuration of secondary and primary binding pathways. This corresponds not to a spatial density of particles, but to a saturation of structural connectivity across the network.
The results indicate that gravity can be understood as a residual structural coupling arising from a fully connected structural background.
No free parameters. No tuning. Only structure.
A minimal Python implementation is provided, and all results are fully reproducible:
https://github.com/yasuotanakaresearch/zero-parameter-structure