Constants Fermi Constant Score Card Row Fermi Pred Bracket

The Fermi bracket

The Fermi constant, usually written G_F, sets the strength of the weak nuclear force, the interaction responsible for radioactive beta decay. Its measured value, from the CODATA and Particle Data Group adjustments, is 1.1663787 x 10^-5 GeV^-2. The Recognition Science framework's machine-checked library of formal theorems proves a bracket around this number: the framework's predicted value lies strictly between 1.16 x 10^-5 and 1.17 x 10^-5 GeV^-2. The measured value sits inside that same bracket.

The prediction comes from a standard electroweak identity. In natural units, the Fermi constant equals 1 divided by the square root of 2 times the square of the Higgs vacuum expectation value, the energy scale at which the electroweak symmetry breaks. The framework uses the canonical display value of 246 GeV for that scale. The theorem row_fermi_pred_bracket proves the bracketing inequality directly from that definition, with no unproved axioms in the library's logic.

In Recognition Science, this is a partial result, not a full derivation. The 246 GeV value is a definitional choice, the canonical display value, not yet derived from the framework's deeper principles. The bracket is the theorem-grade slice; the bridge that would derive the 246 GeV scale from first principles remains open. The honest verdict is that the framework reproduces the measured Fermi constant to within about 0.6 percent, using a standard formula and a chosen input scale.

The row is labeled PARTIAL_THEOREM for that reason. A falsifier is named: if future measurements placed G_F outside the bracket, or if a future derivation of the vacuum expectation value failed to recover the 246 GeV scale, the prediction would fall. The framework claims the bracket, not the full story of where the scale comes from.

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 row_fermi_pred_eq :
    row_fermi_pred = 1 / (Real.sqrt 2 * vev_canonical ^ 2) := rfl

/-- 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

No claim that the Fermi constant is derived from the framework's forcing chain. No claim that the 246 GeV scale is anything other than a definitional input. No claim about the value of G_F beyond 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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