Constants Fermi Constant Score Card

The Fermi constant score card

The Fermi constant G_F measures the strength of the weak nuclear force, the interaction responsible for radioactive beta decay. In natural units, where energy is measured in GeV, the measured value from CODATA and the Particle Data Group is G_F = 1.1663787 x 10^-5 GeV^-2. The standard model of particle physics relates this constant to the vacuum expectation value (VEV) of the Higgs field, the energy scale at which the electroweak symmetry breaks, through the identity G_F = 1 / (sqrt 2 * v^2), where v is the VEV.

In Recognition Science, the framework's library of machine-checked formal theorems contains a cost score card that tests this identity. The score card defines a predicted value for the Fermi constant using the framework's canonical electroweak VEV surface of v = 246 GeV. The prediction is computed as 1 / (sqrt 2 * 246^2). The score card then proves, as a theorem, that this predicted value lies strictly within the interval from 1.16 x 10^-5 to 1.17 x 10^-5 GeV^-2, and separately proves that the measured CODATA value also lies within that same bracket.

The theorem is a formal guarantee about the arithmetic: given the definition of the prediction and the chosen VEV, the bracket holds with no exceptions. The score card also certifies that the VEV itself lies between 244 and 248 GeV. The measured Fermi constant falls inside the predicted range, which is a numerical agreement between the framework's scale and the experimental value.

The row is marked as a partial theorem, not a full derivation. The 246 GeV value is the canonical display value, a definitional choice in the framework, not a value derived from first principles. The fully derived bridge that would produce the 246 GeV scale from the framework's deeper structure remains open. The score card's falsifier is explicit: if future CODATA or PDG measurements placed G_F outside the bracket, or if a future VEV bridge failed to recover the 246 GeV scale, the score card would be wrong.

What this establishes in plain language is a bounded prediction. The framework's chosen electroweak scale produces a Fermi constant that sits within a narrow window that contains the measured value. The proof is about the interval, not about the origin of the scale itself.

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 Fermi constant is fully derived from the framework's axioms. The 246 GeV VEV is derived rather than chosen as a canonical display value. The bracket theorem predicts a value more precise than the CODATA measurement resolution.

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)

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