G_SCU/α_EM

G_SCU/α_EM = 2π exactly

In PT, the ratio between Newton’s constant (in SCU = 1 MeV units) and the fine-structure constant is exactly:

$$ \frac{G_{\rm SCU}}{\alpha_{\rm EM}} = 2\pi. $$

This is the Polyakov identity: $S_{\rm PT} = -\ln \alpha_{\rm EM}$ corresponds to the Polyakov action with slope $\alpha' = 2\pi$.

Why 2π?

$2\pi$ is the unique action constant making the identity $\alpha'_{\rm Regge} \cdot 2\pi = \sigma_{\rm QCD}^{-1}$ consistent with the transfer spectral decomposition on the arithmetic torus T³ (ch. 13 of the monograph).

$$ G_{\rm SCU} = 2\pi \cdot \alpha_{\rm EM} = \frac{2\pi}{137.036} = 0.045\,861. $$

In physical units, after SCU = 1 MeV calibration: $G_N = 6.674 \times 10^{-11}$ m³ kg⁻¹ s⁻² (CODATA), reproduced at the dimensional precision of 1 SCU.

Status

Classed [SC] — exact self-consistency. Not a measurement: an algebraic identity in the sense that $\alpha_{\rm EM}$ and $G$ are structurally linked by spectral decomposition at the fixed point.

Consequence

Gravity is an emergent effect in PT — not a fundamental force. It is the geometric envelope of the $\gamma_p$ cascade, with coefficient $2\pi$ forced by consistency.