Physics Strong Nuclear Force From Rs

The strong force constant

The strong nuclear force is the force that holds atomic nuclei together. It binds quarks into protons and neutrons, and it binds those protons and neutrons into the nucleus. Unlike gravity or electromagnetism, its strength is not a single fixed number. The strength depends on the energy scale at which you measure it, a property called asymptotic freedom. At the energy of the Z boson, roughly 91 GeV, the standard measure of this strength, the strong coupling constant α_s, has a measured value of about 0.118.

In Recognition Science, the framework models the strong force's coupling constant as a simple rational number: 2/17, which is approximately 0.1176. This value comes from a derivation in the framework's library, which is a machine-checked collection of formal theorems. The framework does not fit this number to data; it derives the fraction from its internal structure. The library proves that this value lies within a narrow band, between 0.117 and 0.119, and that it is within 0.001 of the Particle Data Group's measured value of 0.118.

The framework also counts the number of parameters in the standard model's quantum chromodynamics (QCD), the theory of the strong force. It models these as five: the strong coupling constant itself, the masses of the up, down, and strange quarks, and the masses of the charm and bottom quarks. The framework's library proves this count is exactly five. This count is part of a larger pattern in the framework, where the number of parameters matches an internal dimension.

The agreement between the framework's predicted value, 2/17, and the measured value is close. The prediction is not a theorem about the physical world; it is a definitional choice within the framework. The framework's claim is that this simple fraction emerges from its own structure, and that this number lands near the measured value. The comparison to experiment is an empirical check, not a formal proof. The framework's library proves the arithmetic: that 2/17 is indeed in the stated band and close to the PDG value. What remains a hypothesis is that this rational number is the true physical value of the strong coupling constant at the Z mass.

def strongCouplingRS : ℚ := 2 / 17

/-- 2/17 ≈ 0.1176 is the RS prediction. -/
theorem strongCoupling_approx : (strongCouplingRS : ℝ) > 0.117 ∧ (strongCouplingRS : ℝ) < 0.119 := by
  unfold strongCouplingRS; norm_num

theorem alphaSRS_near_PDG : |(strongCouplingRS : ℝ) - alphaSPDG| < 0.001 := by
  unfold alphaSPDG strongCouplingRS
  norm_num

theorem qcdParameterCount : Fintype.card QCDParameter = 5 := by decide

What this page does not claim

The framework does not prove that the strong coupling constant is exactly 2/17 in the physical world. The five parameters listed do not include the top quark mass, which is a separate parameter in the standard model. The framework's derivation of 2/17 is not shown in this module; only the definition and its arithmetic consequences are stated.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Physics/StrongNuclearForceFromRS.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

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