fermiConstantScoreCardCert_holds
The declaration certifies that a Fermi constant score card certificate exists by direct construction. This confirms the RS-predicted G_F lies in (1.16e-5, 1.17e-5) GeV^{-2} and brackets the CODATA value while the electroweak VEV stays in (244, 248) GeV. Electroweak parameter checks in Recognition Science cite the result for interval validation. The proof is a term-mode wrapper that packages three upstream interval theorems into the certificate structure.
claimThere exists a certificate $C$ such that the RS-predicted Fermi constant satisfies $1.16 times 10^{-5} < G_F^{RS} < 1.17 times 10^{-5}$ (in GeV$^{-2}$), the CODATA value lies in the same interval, and the canonical electroweak vacuum expectation value satisfies $244 < v < 248$ (in GeV).
background
The Fermi Constant Score Card module treats phase 1 row P1-C01. It centers on the natural-unit electroweak identity $G_F = 1/(sqrt(2) v^2)$ with the canonical RS electroweak VEV surface $v = 246$ GeV. The module proves the interval $1.16 times 10^{-5} < G_F^{RS} < 1.17 times 10^{-5}$ so that the CODATA value $1.1663787 times 10^{-5}$ sits inside the bracket.
proof idea
The proof is a term-mode construction that supplies an explicit instance of the certificate structure. It invokes row_fermi_pred_bracket to witness the prediction interval, row_fermi_codata_in_bracket to witness the data interval, and vev_in_range to witness the VEV interval.
why it matters in Recognition Science
This theorem completes the certificate for the Fermi constant row and populates the Constants bundle from LawOfExistence. It supplies the theorem-grade slice for the natural-unit electroweak identity while the module remains partial pending a first-principles VEV bridge from the phi-ladder. The result aligns with Recognition Science constants in native units and the interval bracketing used for alpha and related quantities.
scope and limits
- Does not derive the VEV scale from the phi-ladder or J-cost.
- Does not prove exact equality for G_F beyond the stated 1 percent bracket.
- Does not incorporate higher-order electroweak radiative corrections.
- Does not connect the interval to the full T0-T8 forcing chain.
formal statement (Lean)
110theorem fermiConstantScoreCardCert_holds :
111 Nonempty FermiConstantScoreCardCert :=
proof body
Term-mode proof.
112 ⟨{ fermi_bracket := row_fermi_pred_bracket
113 codata_in_bracket := row_fermi_codata_in_bracket
114 vev_range := vev_in_range }⟩
115
116end
117
118end IndisputableMonolith.Constants.FermiConstantScoreCard