albert_roca

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

2 ポイント投稿者 albert_roca6 か月前0 コメント

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

3 ポイント投稿者 albert_roca7 か月前28 コメント

Gravity coupling matches the 128-bit integer limit to 6 ppm

2 ポイント投稿者 albert_roca7 か月前4 コメント

Show HN: G=(hbarc2(1+alpha/3)^2)/(m_p^24^64) ≈ 6.6742439706e-11 (8 ppm)

2 ポイント投稿者 albert_roca7 か月前30 コメント

The hierarchy problem is strictly a geometric scaling identity

1 ポイント投稿者 albert_roca7 か月前0 コメント

Geometric derivation of the muon g-2 anomaly (63 ppm discrepancy)

1 ポイント投稿者 albert_roca7 か月前3 コメント

Geometric derivation of proton radius matches CODATA within 577 ppm

2 ポイント投稿者 albert_roca7 か月前1 コメント

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6 か月前議論

- 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.

7 か月前議論

Undefined/non-consensual prompt.

7 か月前議論

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!

7 か月前議論

Because AI has been in the center of the debate so far, I ran your comment through my AI system, and it concluded that you captured the essence of the model perfectly: the polyhedra are topological standing waves, and the edges are nodal lines. So [Pred] is the geometric attractor, and [Diff] is the amplitude of the oscillation around that limit. As I understand it myself, the polyhedra don't exist as real solids, but as an optimized way to distribute the intensity of the oscillation. Does this perspective make the results physically plausible in your view?

7 か月前議論

I am referring to other comments in this thread that dismissed the proposal purely based on the use of AI tools. My comment about prejudice was not directed at you.

7 か月前議論

Fair enough. However, it is practically impossible to complete such a task in a human lifetime. But even if it were possible, the main point stands: using computers to perform calcualtions is standard scientific practice. Discrediting a proposal solely because it uses AI is retrograde per se. It contradicts the history of technological progress and excludes potentially valid results based on intellectual prejudice.

7 か月前議論

The model shows that the surface and volume of an object scale with mass such that electrostatic and gravitational acceleration can be explained through this scaling relationship. This is considered a geometric or structural cost:

  C_s ~ m^(1/3) + m^(-2/3)

In terms of intrinsic acceleration, surface and volume scale with mass as:

  a_i ~ m^(1/3) + m^(-5/3)

This relationship holds for any object with charge ≠ 0 across electrostatic and gravitational regimes, so the free fall principle is strictly recovered only for mathematically neutral objects.

This allows drawing an intrinsic acceleration curve for objects with homogeneous density, and the minimum point of this curve is identified at:

  m_ϕ ≈ 4.157 × 10^−9 kg

If the surface and volume of a not strictly neutral object determine its dynamic behavior, this would theoretically allow measuring m_ϕ with precision and deriving G without the historical dependence on the Planck mass. In this sense, it is a falsifiable proposal.

The geometric logic of the model allows establishing a geometric or informational saturation limit that eliminates GR singularities. At the same time, fundamental particles are not treated as dimensionless points but as polyhedral objects, which also eliminates the quantum gravity problem. The concept of infinity is considered, within the model, physically implausible.

From here, the model allows making the derivations included in this post, which I have not presented categorically, but as a proposal that seems at least statistically very unlikely to be achieved by chance.

The model does not question the precision of the Standard Model but postulates that the particle zoo represents not a collection of fundamental building blocks, but the result of proton fragmentation into purely geometric entities. The fact that these entities are not observed spontaneously in nature, but only as a consequence of forced interactions, seems to support this idea.

7 か月前議論

Absolutely not. Results don't depend on who performed the calculation or how it was done. Can you solve 12,672 Feynman diagrams by hand?

7 か月前議論

This seems properly copied and pasted. Good job. I guess we agree that AI is already playing a central role in science, and physics is no exception.

7 か月前議論

Can you share the results of your analysis by association? Or was it an instant mental calculation?

7 か月前議論

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

7 か月前議論

Your contribution is the opposite of "something".

7 か月前議論

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.

7 か月前議論

64 is dimensionless. It comes from the model's holographic scaling law, where mass scales with surface complexity (m ∼ 4^i). The proton appears at i = 32.

  4^32= (2^2)^32 = 2^64

2^64 seems to be the minimum information density required to geometrically define a stable volume. The proton stability implies that nothing simpler can sustain a 3D topology. This limit defines the object's topological complexity, not its lifespan.

Please note that the model is being developed with IA assistance, and I realize that the onthological base needs further refinement.

The proton mass (m_p) is derived as:

  m_p = ((√2 · m_P) / 4^32) · (1 + α / 3)
  m_p = ((√2 · m_P) / √4^64) · (1 + α / 3)
  m_p ≈ 1.67260849206 × 10^-27 kg
  Experimental value: 1.67262192595(52) × 10^-27 kg
  ∆: 8 ppm.

G is derived as:

  G = (ħ · c · 2 · (1 + α / 3)^2) / (mp^2 · 4^64)
  G ≈ 6.6742439706 × 10^-11
  Experimental value: 6.67430(15) × 10^-11 m^3 · kg^-1 · s^-2
  ∆: 8 ppm.

α_G is derived as:

  α_G = (2 · (1 + α / 3)^2) / 4^64
  α_G ≈ 5.9061 · 10^–39
  Experimental value: ≈ 5.906 · 10^-39
  ∆: 8 ppm

The terms (1 + α / 3) and 4^64 appear in the three derivations. All of them show the same discrepancy from the experimental value (8 ppm). (Note: There is a typo in the expected output of the previous Python script; it should yield a discrepancy of 8.39 ppm, not 6 ppm.)

The model also derives α as:

  α^-1 = (4 · π^3 + π^2 + π) - (α / 24)
  α^-1 = 137.0359996
  Experimental value: 137.0359991.
  ∆: < 0.005 ppm.

Is it statistically plausible that this happens by chance? Are there any hidden tricks? AI will find a possible conceptualization for (almost) anything, but I'm trying to get an informed human point of view.

7 か月前議論

The model identifies the proton mass stability at the 64-bit limit (2^64). Since gravitational interaction scales with m_p^2 , the hierarchy gap corresponds to the square of that limit:

  (2^64)^2 = 2^128

The geometric derivation involves a factor of 2, linked to the holographic pixel diagonal (√2 )^2:

  2 / 2^128 = 2^−127

2^−127 represents the least significant bit (LSB) of a 128-bit integer.

7 か月前議論

You put the following sentence in quotes: "12,672 diagrams is brute force. Achieving 63 ppm with one term (a_μ = α / 2π + α^2 / 12) is elegant". I never made that specific claim, nor does the word "elegant" appear a single time in the entire document. Please do not fabricate quotes to suit your narrative.

You seem to mention an obsolete draft with a typo (ng vs µg) already stated on the Zenodo metadata. Please refer to the current documentation (v13 or later). m_z has always been defined as mz ≈ 1.859 × 10^–9 kg, and m_phi as m_phi ≈ 4.157 × 10^−9 kg (µg range). Your arguments regarding AFM and Brownian motion on 2.5 ng particles apply to a scale 1000x smaller than the model's regime.

Regarding circularity: you were proven wrong already in a previous reply, but you insist on the same argument.

Regarding QED: The fact that you need 12,672 diagrams to describe a fundamental interaction is not a triumph of nature's design, but a triumph of human engineering.

Finally, the third-person narration ("Verdict: He implies...", "Verdict: His prediction...") suggests you are addressing an imaginary audience rather than engaging in a direct technical debate.

7 か月前議論

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.

7 か月前議論

You transcribed the formula incorrectly.

The term is -(alpha / 24). You calculated -1 / (24 · alpha).

The correct derivation is:

  1 / alpha = S - (alpha / 24)
  1 = S · alpha - (alpha^2) / 24
  alpha^2 - 24 · S · alpha + 24 = 0

Solving this with S = 4 · π^3 + π^2 + π yields the correct value.

7 か月前議論

  The "Equilibrium Mass" mz is Not Physical The claim that Fe = Fg at some special mass mz = √(α·mP) ≈ 1.86×10⁻⁹ kg is mathematically true but physically meaningless

m_z is the geometrical point of transition between regimes. The physical observable is m_phi , where the total intrinsic acceleration function reaches its minimum, following the extreme value theorem.

  δ = √5 is Pure Numerology The "dynamic constant" δ = √5 appears because: 1² + 2² = 5 (Pythagorean triple) Therefore δ = √5 is "fundamental"

δ = √5 comes from the scaling exponents. a_g scales as m^1/3. a_e scales as m^−5/3. The ratio is 5. Since the interaction is quadratic, it's the result from minimizing the acceleration function, not numerology.

  The Standard Model calculation requires 12,672 Feynman diagrams at 5-loop order and achieves agreement to 0.1 ppm

Precisely. 12,672 diagrams is the definition of brute force. Achieving 63 ppm with one single term (a_μ = α / 2 · π + α^2 / 12) is quite the opposite.

  The factor 2.5 = 5/2 is claimed to come from δ²/w, but this has no connection to quark mass generation via the Higgs mechanism.

The model is geometric in nature. Quarks are not considered fundamental building blocks, but a geometric necessity of the way that the proton can be fragmented. One can disagree with this premise, but it geometrically derives the fractional charges (1/3, 2/3) that the Standard Model merely assigns.

  Conceptual Confusions 1. Charge as Topology (Section 1.3) Claim: "Electric charge is not intrinsic but a topological attribute of spatial surface." Problem: This contradicts gauge theory.

That's not a problem, nor a confusion. The model assumes that charge is not an independent substance, but a topological attribute.

7 か月前議論

This is moving the goalposts, but ok. The model matches the international standard of CODATA 2022 to 0.005 ppm. If and when this value is updated, the prediction can be re-evaluated. Until then, I stick to the standard.