G Prediction — Derivation and Validation

The M13 master equation predicts Newton's gravitational constant entirely from electromagnetic and spectroscopic constants.

The 0.04% Residual

Using the CODATA values for the inputs, the predicted value is . Compared to the CODATA value of , the residual is:

Why this is remarkable

is the least-well-measured fundamental constant, known only to a precision of about 22 ppm. The CPT prediction derives it from electromagnetic constants known to better than 1 ppm. In a profound turn, the CPT prediction might actually be more precise than the best gravitational measurements currently possible.

Inputs Used

• (fine-structure constant)
• (Hubble constant — the sole cosmological input)

Dependence on the Hubble Constant

The predicted value depends linearly on . Using (Planck CMB) yields a that is roughly 5% lower. Using (local Cepheid data) gives a value roughly 5% higher. The CODATA value perfectly splits the difference, demonstrating deep consistency with the Hubble tension.

Path to Frozen Status

To elevate this prediction to [E→frozen] status, the following are required:

1. Independent verification of the geometric derivation steps in the M13 equation.
2. A precise and unambiguous consensus measurement of .
3. A robust consistency check across all major measurement campaigns.