I am developing a geometric model of physical interactions based on geometric constraints (w = 2, δ = √5 ) and topological invariants. No free parameters, just geometry. In your opinion, is this a legitimate geometric unification or just sophisticated curve-fitting?
Results:
Proton radius (r_p):
Modeled as a tetrahedral structural limit (4 · ƛ) with spherical field projection loss (α / 4 · π).
r_p = 4 · ƛ_p · (1 - (α / (4 · π)))
Pred: 8.407470 × 10^-16 m
Exp: 8.4075(64) × 10^-16 m
Diff: 3 ppm
Proton magnetic moment (g_p):
Derived from the dynamic potential (δ = √5 ) damped by a golden friction term (α / Φ).
g_p = (δ^3 / w) - (α / Φ)
Pred: 5.5856599
Exp: 5.5856947
Diff: 6 ppm
Muon anomaly (a_μ):
Derived as a hierarchical resolution of the icosahedral geometry: surface (α / 2 · π) + nodes (α^2 / 12) + vertex symmetry (α^3 / 5).
a_μ = (α / (2 · π)) + (α^2 / 12) + (α^3 / 5)
Pred: 0.00116592506
Exp: 0.00116592059
Diff: 4 ppm
α particle radius (r_α):
Modeled as a 4-nucleon tetrahedron (8 · ƛ) with a linear nucleonic projection cost (α / π).
r_α = 8 · ƛ_p · (1 - (α / π))
Pred: 1.67856 × 10^-15 m
Exp: 1.678 × 10^-15 m
Diff: 330 ppm
Proton mass (m_p):
Connecting the Planck scale to proton scale via a 64-bit metric horizon (2^64) and diagonal transmission (√2 ).
m_p = ((√2 · m_P) / 2^64) · (1 + α / 3)
Pred: 1.67260849206 × 10^-27 kg
Exp: 1.67262192595(52) × 10^-27 kg
Diff: 8 ppm
Neutron-proton mass difference (∆_m):
Modeled as potential energy stored in the geometric compression of the electron (icosahedron, 20 faces) into the protonic frame (cube, 8 vertices). Compression ratio = 20/8 = 5/2.
∆_m = m_e · ((5/2) + 4 · α + (α / 4))
Pred: 1.293345 MeV
Exp: 1.293332 MeV.
Diff: 10 ppm.
Gravitational constant (G) without G:
Derived from quantum constants and the proton mass, identifying G as a scaling artifact of the 128-bit hierarchy (2^128).
G = (ħ · c · 2 · (1 + α / 3)^2) / (m_p^2 · 2^128)
Pred: 6.6742439706 × 10^-11
Exp: 6.67430(15) × 10^-11 m^3 · kg^-1 · s^-2
Diff: 8 ppm
Fine-structure constant (α):
Derived as the static spatial cost plus a spinor loop correction.
α^-1 = (4 · π^3 + π^2 + π) - (α / 24)
Pred: 137.0359996
Exp: 137.0359991
Diff: < 0.005 ppm
Preprint: https://doi.org/10.5281/zenodo.17847770
r_p = 4·ƛ_p·(1 - α/(4π))
Red flags:
Why "4" times the reduced Compton wavelength? The number 4 appears twice (in 4·ƛ and 4π), suggesting it was chosen to make things work out.
"Tetrahedral structural limit" is asserted without derivation. Why tetrahedra? A tetrahedron is 3D—why would the proton radius (a measured charge distribution extent) involve tetrahedral geometry?
"Spherical field projection loss" of α/(4π) has no physical mechanism. How does a "projection loss" yield this specific fraction?
The fit is suspiciously good (3 ppm) for a formula with at least two free choices (the coefficient 4, and the form of the correction).
4. Muon Anomaly
a_μ = (α/(2π)) + (α²/12) + (α³/5)
This mimics QED perturbation theory—but incorrectly:
The actual QED expansion is:
a_μ = (α/2π) + C₂(α/π)² + C₃(α/π)³ + ...
Where C₂ ≈ 0.765857... and C₃ involves thousands of Feynman diagrams calculated over decades.
The author's version:
First term: α/(2π) (this is the Schwinger term, known since 1948)
Second term: α²/12 — This should be ~0.765857(α/π)² ≈ 4.1×10⁻⁶, but α²/12 ≈ 4.44×10⁻⁶. Wrong coefficient.
Third term: α³/5 ≈ 4.25×10⁻⁸ — The actual third-order contribution is much more complex.
and the Gemini LLM goes on and on and on...
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