Gravity Coupling Matches the 128-Bit Integer Limit to 6 Ppm

I'm asking for a sanity check on the hierarchy problem, or the ≈ 10^39 gap between gravity and the strong force.

The results of this test suggest the universe might use a 128-bit integer architecture.

1. HYPOTHESIS

  • The proton is defined at the 64-bit integer limit (2^64).
  • Gravity is defined at the 128-bit integer limit (2^128).

  If this is true, the gravitational coupling constant (alpha_G) 
  should be the least significant bit (LSB) of this structure (2^-127) (1), 
  modulated by the same geometric cost factor found in the proton mass 
  (1 + alpha / 3) (2).

  (1) The model derives G from the proton mass scaling, resulting in 
  a factor of 2 / 2^128, which simplifies to 2^-127.

  (2) The term (1 + alpha/3) is the geometric interaction cost derived 
  for the proton mass in the holographic model.

2. FORMULA

  alpha_G_model = (1 + alpha / 3)^2 / 2^127

3. DATA (CODATA 2022)

  mp = 1.67262192e-27 kg (proton mass)
  hbar = 1.05457181e-34 J s
  c = 299792458 m/s
  G_exp = 6.67430e-11 (experimental G)
  alpha = 7.29735256e-3 (fine-structure constant)

4. VERIFICATION

Standard experimental coupling from G_exp:

  alpha_G_exp = (G_exp * mp^2) / (hbar * c)
  Value: 5.906063e-39

Prediction using ONLY alpha and powers of 2 (no G, no mass):

alpha_G_model = (1 + 0.00729735256 / 3)^2 * 2^-127

  2^-127 (raw LSB) ≈ 5.877471e-39
  Correction factor ≈ 1.004870
  alpha_G_model ≈ 5.906099e-39

5. RESULTS

  Experimental: 5.906063e-39
  Predicted: 5.906099e-39
  ∆: 3.6e-44 (6 ppm).

6. PYTHON

  # Constants (CODATA 2022)
  mp    = 1.67262192e-27
  hbar  = 1.05457181e-34
  c     = 299792458
  G     = 6.67430e-11
  alpha = 7.29735256e-3

  # 1. Experimental Coupling
  alpha_G_exp = (G * mp**2) / (hbar * c)

  # 2. 128-bit Model Prediction
  alpha_G_model = ((1 + alpha/3)**2) * (2**-127)

  # Comparison
  ppm = abs(alpha_G_model - alpha_G_exp) / alpha_G_exp * 1e6

  print(f"Exp:   {alpha_G_exp:.6e}")
  print(f"Model: {alpha_G_model:.6e}")
  print(f"Diff:  {ppm:.2f} ppm")

7. QUESTION

In your opinion, is this a numerological coincidence, or is it rather a structural feature?

Preprint: https://doi.org/10.5281/zenodo.17847770