Ask HN: Probability of deriving 7 constants to <10ppm from discrete geometry

PROBLEM

Calculate the combined probability of deriving 7 fundamental physical constants to <10ppm precision using only the following inputs and discrete geometric keys.

CONSTRAINT: Zero continuous tunable parameters allowed (all coefficients must be integers or fixed geometric roots).

1. DEFINITIONS

  [A] INPUTS (CODATA 2022)
  alpha = 7.2973525643e-3 // Fine-structure constant
  c = 299792458 // Speed of light
  hbar = 1.054571817e-34 // Reduced Planck constant
  mp = 1.67262192369e-27 // Proton mass

  [B] DISCRETE KEYS (Fixed geometry/topology)
  k_vol = 2 // Volume scale (3D)
  k_dyn = sqrt(5) // Dynamic scale (sqrt(2D-1))
  k_bit = 64 // Binary horizon seed
  k_tet = 4 // Tetrahedron vertices
  k_cub = 8 // Cube vertices
  k_ico = 12 // Icosahedron vertices
  k_fac = 20 // Icosahedron faces
  k_spi = 24 // Spinor loop factor

  [C] GLOBAL DERIVED SCALES (Computed once from inputs + keys)
  H_g = 2^(2*k_bit) // Gravitational horizon (2^128)
  H_m = 2^k_bit // Metric horizon (2^64)
  Lu = (hbar/(mp*c)) \* H_m \* sqrt(2) / (1 + alpha/3) // Fundamental lattice unit

2. DERIVATIONS

  [A] GRAVITATIONAL CONSTANT (G)
  Formula: G = (hbar \* c \* k_vol \* (1 + alpha/3)^2) / (mp^2 \* H_g)
  > Result : 6.6742439e-11
  > CODATA : 6.67430(15)e-11
  > ERROR  : 8 ppm

  [B] ELECTRON MASS (me)
  // Holographic inverse of icosahedral shell defined by Lu
  Formula: me = (2 \* alpha \* hbar) / (c \* (Lu \* pi^2 \* (1 + alpha - alpha/k_spi) \* sin(72)))
  > Result : 9.1093836e-31 kg
  > CODATA : 9.1093837e-31 kg
  > ERROR  : 0.01 ppm

  [C] FINE STRUCTURE CONSTANT (alpha) - geometric check
  Formula: 1/x = (k_tet*pi^3 + pi^2 + pi) - (alpha/k_spi)
  > Result : 137.0359996
  > CODATA : 137.0359990
  > ERROR  : 0.005 ppm

  [D] PROTON RADIUS (rp)
  Formula: rp = k_tet * (hbar/(mp*c)) * (1 - (alpha / (k_tet \* pi)))
  > Result : 8.40747e-16 m
  > CODATA : 8.40750(64)e-16 m
  > ERROR  : 3 ppm

  [E] MUON ANOMALY (a_mu)
  Formula: a_mu = (alpha/2pi) + (alpha^2/k_ico) + (alpha^3/k_dyn^2)
  > Result : 0.00116592506
  > CODATA : 0.00116592059
  > ERROR  : 4 ppm

  [F] PROTON MAGNETIC MOMENT (mu_p)
  Formula: mu_p = (k_dyn^3 / k_vol) - (alpha / ((1+k_dyn)/2))
  > Result : 5.5856599
  > CODATA : 5.5856947
  > ERROR  : 6 ppm

  [G] NEUTRON-PROTON MASS DIFF (dm)
  // Compression: icosahedron faces (20) into cube vertices (8)
  Formula: dm = me \* ((k_fac/k_cub) + k_tet\*alpha + alpha/k_tet)
  > Result : 1.293345 MeV
  > CODATA : 1.293332 MeV
  > ERROR  : 10 ppm

3. QUESTION

Given the constraint of zero tunable parameters, what is the combined p-value of deriving these 7 physical constants to <10ppm precision by random chance?

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