Structural Origin of Gravity

This work presents a zero-parameter structural formulation of gravity.
Using the fixed constants
\[
R = \frac{13}{6}, \qquad S = \frac{31}{24},
\]
together with a gravity-sector structural index \(\Psi_G\), the numerical value associated with the SI representation of the gravitational constant is written as
\[
\sqrt{G} = \frac{\alpha S}{\pi \Psi_G}.
\]
This gives
\[
G \approx 6.674338186956 \times 10^{-11},
\]
in close agreement with the CODATA 2022 reference value.
The result is interpreted conservatively as a structural correspondence: the formulation reproduces the numerical value of \(G\) in its SI representation, without claiming to derive physical dimensions themselves.
The same structural hierarchy also reproduces the gravitational coupling strengths \(\alpha_{Gp}\) and \(\alpha_{Ge}\), together with the Planck, proton, and electron SI mass scales.
The inputs \(\alpha\) and \(m_p/m_e\) are inherited from the electroweak and mass-hierarchy sectors, so the gravity-sector calculation introduces no additional fitted parameters.

A minimal Python implementation is provided for full reproducibility:
https://github.com/yasuotanakaresearch/zero-parameter-structure