Is the Standard Model overfitting or am I curve-fitting?

[albert_roca]

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

[fatbrowndog]

Same as previous -

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...

[albert_roca]

- Why 4? It's not random. It is derived from the structural constant w = 2 as a topological constraint of the three-dimensional topology. Radius scales as w^2 = 4.

- Why tetrahedron? Mass is defined as volume. The tetrahedron is the simplest closed 3D volume. Mathematically, the derived proton radius corresponds to the exact geometric circumradius (edge · √6 / 4) of this volumetric structure.

- Why α / 4 · π? It represents the linear interaction cost (α) distributed over the spherical solid angle (4 · π) of the protonic surface.

- Incorrect QED terms? The model explicitly and intentionally diverges from QED. It doesn't treat particles as points, but as three-dimensional objects. The model excludes the notion of physical infinities or singularities.

- Why α^2 / 12? It derives from nodal friction distributed over the 12 vertices of the lepton's icosahedral topology.

- Why α^3/5? It derives from the local 5-fold symmetry of the icosahedral node.

The criticisms fail to identify that the model presents a first-principles framework where these numbers are geometric consequences, not free parameters. The model is not intended to be orthodox, but mathematically and geometrically coherent.

[proteal]

Hey - plugged this into chatGPT 5.2 and it seems to think this theory needs more work.

“As written, this looks closer to sophisticated curve-fitting (numerology with constraints) than a legitimate geometric unification, mainly because the claimed “ppm agreement” is often not assessed against experimental uncertainties and because several integer/constant choices function like hidden degrees of freedom.”

Thank you for sharing and happy holidays!

[albert_roca]

Thanks for running this on GPT 5.2. It is fascinating to see AI critiquing AI-assisted work.

The critique regarding hidden degrees of freedom is a fair point. However, in curve-fitting, parameters are continuous: one can choose 4.1 or 3.9 to make the data fit. In this model, parameters are topological invariants (integers like 4 faces, 12 vertices, 20 faces). They are discrete and cannot be tuned.

The fact that this unadjustable logic yields results agreeing with experimental data within ppm implies either a massive statistical coincidence or a structural aspect.

It would be very interesting to run independent tests on different AIs with the whole context of the model and a standardized, consensual prompt. Beyond formal verification, this methodology could open paths that are difficult to navigate without AI assistance, helping to determine if the model stands as a possible foundation for a 'broad explanation of the observable', since the term 'ToE' instantly raises red flags. Kind of a pioneer peer-centaur-review. Just an idea.

Thanks for your comment and happy holidays!

[yongjik]

> sophisticated curve-fitting (numerology with constraints)

lol ChatGPT feeling sassy today, though I think it was well deserved.

[pavel_lishin]

Based on your pre-previous post, this is nothing.

[albert_roca]

Your contribution is the opposite of "something".

[rolph]

a much more revelatory exercise would be to compare these derived values with measured values, then construct testable hypotheses regarding disparities.

[albert_roca]

That's precisely what the numbers show. "Pred:", predicted value. "Exp:", experimental value. "Diff", difference.

[bigyabai]

If you have to ask people whether or not your preprint resembles curve-fitting, you have just self-reported that you are an AI user with no academic background.

Good luck with the peer review, you're gonna need it.

[albert_roca]

I have reported nothing but numerical results. Making assumptions about me instead of looking at the numbers says more about your background than it does about mine.