fermiConstantScoreCardCert_holds
plain-language theorem explainer
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.
Claim. There 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
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.
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