Constants Fermi Constant Score Card Row Fermi Codata In Bracket

The Fermi constant bracket

The Fermi constant G_F sets the strength of the weak nuclear force, the interaction responsible for radioactive beta decay. In natural units, its measured value is 1.1663787 x 10^-5 GeV^-2. The Recognition Science framework, which models physical structure from a forced cost of recognition, derives a prediction for this constant from a canonical electroweak vacuum expectation value of 246 GeV. The derivation yields a bracket: the framework's predicted value lies strictly between 1.16 x 10^-5 and 1.17 x 10^-5 GeV^-2.

The declaration row_fermi_codata_in_bracket is a theorem in the framework's machine-checked library of formal theorems. It proves that the measured CODATA/PDG value, 1.1663787 x 10^-5 GeV^-2, satisfies the same bracket: it is greater than 1.16 x 10^-5 and less than 1.17 x 10^-5 GeV^-2. This places the experimental value inside the framework's predicted interval. The proof is complete, with zero unproven assumptions and zero axioms beyond the standard logical ones.

The bracket is a consistency check, not a precise match. The measured value sits within the broad predicted range, but the framework does not yet derive the exact number. The theorem also depends on a canonical value for the electroweak vacuum expectation value, 246 GeV, which is a standard display value rather than a fully derived quantity. The bridge from the framework's internal units to the conventional GeV scale remains an open target.

The framework's prediction is falsifiable. If future measurements placed the Fermi constant outside the bracket, or if a fully derived vacuum expectation value failed to recover the 246 GeV scale, the prediction would be refuted. For now, the measured value falls within the predicted range, and the framework's library records that fact as a formal theorem.

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

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⟩

/-- 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 declaration does not prove the exact Fermi constant value, only that it lies within a broad bracket. The declaration does not derive the 246 GeV vacuum expectation value; it takes it as a canonical input. The declaration does not provide a precise match to the measured value, only a consistency check within a range.

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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