Constants Fermi Constant Score Card Row Fermi Pred Eq

The Fermi constant prediction

The Fermi constant G_F is the coupling strength of the weak nuclear force, the interaction responsible for radioactive beta decay. In natural units where the reduced Planck constant and speed of light are set to 1, its measured value is 1.1663787 × 10⁻⁵ GeV⁻², as listed by CODATA and the Particle Data Group. The standard model relates this constant to the electroweak vacuum expectation value v, the energy scale at which the electroweak symmetry breaks, through the identity G_F = 1 / (√2 · v²). With the canonical value v = 246 GeV, this identity yields a prediction of approximately 1.166 × 10⁻⁵ GeV⁻².

The machine-checked library of formal theorems proves that this predicted value lies strictly between 1.16 × 10⁻⁵ and 1.17 × 10⁻⁵ GeV⁻², a bracket that contains the measured CODATA value. The proof is complete: the library certifies both the lower and upper bound, and confirms the measured value falls inside the same interval. This is a theorem in the formal sense, with no unproved assumptions and no axioms beyond the standard logical ones.

What the theorem does not claim is just as important. The prediction depends on the canonical value v = 246 GeV, which the framework treats as a given display value, not as a quantity derived from first principles. The fully derived bridge from the framework's internal units to the SI/GeV scale remains open. The theorem also does not claim that the Fermi constant itself is derived from the framework's foundational principles; it only establishes the numerical interval given the assumed VEV.

In Recognition Science, this row is labeled PARTIAL_THEOREM because of that missing bridge. The falsifier is concrete: if CODATA/PDG G_F ever falls outside (1.16e-5, 1.17e-5) GeV⁻², or if a future VEV bridge fails to recover the 246 GeV scale, the prediction is refuted. The framework's contribution here is a precise, machine-checked numerical claim with an explicit condition, not an unconditional derivation of the weak force's strength.

theorem row_fermi_pred_bracket :
    (1.16e-5 : ℝ) < row_fermi_pred ∧ row_fermi_pred < (1.17e-5 : ℝ) :=
  ⟨row_fermi_pred_lower, row_fermi_pred_upper⟩

theorem row_fermi_codata_in_bracket :
    (1.16e-5 : ℝ) < row_fermi_codata ∧ row_fermi_codata < (1.17e-5 : ℝ) := by
  unfold row_fermi_codata
  constructor <;> norm_num

/-- P1-C01 Fermi constant prediction in GeV^-2 natural units. -/
noncomputable def row_fermi_pred : ℝ :=
  1 / (Real.sqrt 2 * vev_canonical ^ 2)

What this page does not claim

The theorem does not claim the Fermi constant is derived from the framework's foundational principles. The theorem does not claim the 246 GeV VEV is derived rather than assumed. The theorem does not claim the prediction holds outside the stated bracket.

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/Constants/FermiConstantScoreCard.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.

Derived articles

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