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
[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
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