by albert_roca | 2025-12-23 20:57:45+00:00
I cannot be too categorical in the definitions because sometimes numerical findings appear before they can receive the proper interpretation. This is normal in the development of any new theory.

No LLM induced me to make this proposal. In fact, I developed the original idea with spreadsheets and graphs. At first, AI was very reluctant or distrustful of it. Starting from the definition G = U / z, this collaboration improved a lot, and now I am rather the one who is reluctant to accept all the ramifications that AI finds. Be that as it may, if the model has weaknesses, they can be corrected.

The model only uses 1, 2, and √5. It derives the proton radius (577 ppm), the proton mass (8 ppm), the muon anomaly (63 ppm), and alpha (0.005 ppm). If this is statistically insignificant, then it should be easy to prove that it is statistically insignificant.

In any case, it is not a meaningless numerological cocktail, as the parameters are fixed and extremely limited. It seems like a constructive starting point for a working hypothesis. Possible doubtful aspects do not invalidate the proposal as a whole, which is built by independent parts and still under development.

In the context of developing a model with AI assistance, there is a boundary between the two interacting forms of thought that is difficult to define. Unless we assume the retrograde premise that AI should play no role in the development of physical science, we must admit that certain aspects might be better understood by the AI than by the human agent.

Regarding the specific points you mentioned earlier, in the current context of the model, here is the "salad" decoded into the pattern we found:

1. Alpha / 3. The division by 3 is not arbitrary. It represents the vector equilibrium in 3D space. The proton represents a volumetric stability (3D), while the interaction cost (alpha) acts as a surface parameter or linear stress. To stabilize a closed 3D volume, the linear stress must be distributed across the three orthogonal axes. It represents the projection of the interaction cost per spatial dimension.

2. Holography and the 4^32 factor. The term "holography" is used because the scaling follows the surface area law (area ~ r^2), not the volumetric law (volume ~ r^3).
- Base 4: Represents the surface scaling factor. If the linear dimension doubles (2r), the surface area quadruples (2^2 = 4).
- Exponent 32: Represents the harmonic depth or iteration count.
- Physical implication: 4^32 = (2^2)^32 = 2^64 ≈ 1.844e19.

This factor explicitly bridges the mass hierarchy. The experimental ratio between Planck mass (m_P) and the proton mass (m_p) is ≈ 1.3e19. The model links them via the 64-bit limit and the Euclidean diagonal (√2).

The exact derivation includes a secondary term for the electromagnetic cost:

m_p = (m_P / (2^64 / √2)) · (1 + alpha / 3)

This splits the mass definition into two layers:
A) The information horizon (2^64 / √2): This defines the raw capacity of the metric (the "container"), accounting for 99.76% of the value.
B) The interaction cost (1 + alpha / 3): Since the proton is a charged volumetric object, it carries a distributed interaction cost (alpha projected over 3 dimensions).

This provides a geometric resolution to Dirac's large numbers hypothesis. The force hierarchy gap (~10^38) corresponds to the square of this mass hierarchy gap (~10^19). The model identifies this not as random, but as a bandwidth saturation limit: the proton is the result of attenuating the Planck scale through exactly 64 steps of binary geometric doubling. It marks the physical "integer overflow" of the metric. That is, the precise limit where geometric structure prevents infinite collapse.

When you apply the geometric logic of the model, the numbers force you into a specific interpretation that the AI will find more naturally. I am reflecting on these connections myself, but the numerical coincidence seems too precise to discard.