Constants Fermi Constant Score Card Fermi Constant Score Card Cert Holds

The Fermi bracket

The Fermi constant G_F measures the strength of the weak nuclear force, the interaction responsible for radioactive beta decay. Its measured value, from CODATA/PDG, is 1.1663787 × 10⁻⁵ GeV⁻². In the Recognition Science framework, the prediction comes from a simple formula: G_F equals 1 divided by the square root of 2 times the electroweak vacuum expectation value v, squared. With v set to 246 GeV, the predicted value is about 1.1664 × 10⁻⁵ GeV⁻².

The framework's machine-checked library of formal theorems contains a certificate, named fermiConstantScoreCardCert_holds, that proves three things. First, the predicted Fermi constant lies strictly between 1.16 × 10⁻⁵ and 1.17 × 10⁻⁵ GeV⁻². Second, the measured CODATA value also lies in that same interval. Third, the chosen vacuum expectation value of 246 GeV sits between 244 and 248 GeV. The certificate is a theorem: it is checked by the library's kernel with zero axioms and zero unproven assumptions.

The certificate does not claim that the framework derives the Fermi constant from first principles. The formula G_F = 1/(√2 v²) is a definitional choice, and the value v = 246 GeV is the canonical display value, not a fully derived quantity. The bridge that would derive this GeV-scale vacuum expectation value from the framework's deeper structure remains open. The certificate's role is narrower: it verifies that the chosen formula and the chosen value produce a prediction consistent with measurement, to within a stated bracket.

This bracketing is the certificate's honest content. It is a consistency check, not a derivation. A future falsifier would be a CODATA/PDG measurement of G_F outside the interval (1.16 × 10⁻⁵, 1.17 × 10⁻⁵) GeV⁻², or a future derivation of the vacuum expectation value that does not recover the 246 GeV scale. Until then, the certificate is a verified statement about the framework's internal consistency with experiment.

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

theorem fermiConstantScoreCardCert_holds :
    Nonempty FermiConstantScoreCardCert :=
  ⟨{ fermi_bracket := row_fermi_pred_bracket
     codata_in_bracket := row_fermi_codata_in_bracket
     vev_range := vev_in_range }⟩

theorem fermiConstantScoreCardCert_holds :
    Nonempty FermiConstantScoreCardCert :=
  ⟨{ fermi_bracket := row_fermi_pred_bracket
     codata_in_bracket := row_fermi_codata_in_bracket
     vev_range := vev_in_range }⟩

What this page does not claim

The certificate does not derive the Fermi constant from the framework's foundational principles. The certificate does not prove that the canonical 246 GeV value is uniquely forced by the framework. The certificate does not claim the prediction is exact; it only establishes a bracketing interval.

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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