gev2_to_cm2
The definition supplies the numerical conversion 0.3894 × 10^{-27} that turns GeV^{-2} into cm². Dark-matter cross-section modelers cite it when scaling the Fermi-constant prediction to laboratory units for the P0-A6 weak reference channel. It is introduced as a bare constant assignment with no lemmas or reduction steps.
claimThe conversion factor satisfying $1~mathrm{GeV}^{-2} = 0.3894 times 10^{-27}~mathrm{cm}^{2}$.
background
The module implements the P0-A6 scorecard for the weak neutrino-reference cross-section. Module documentation states the reference formula sigma_nu_ref = G_F^2 * E_ref^2 * (GeV^{-2} to cm² conversion) with E_ref = 1 GeV, yielding the interval 5.2e-38 < sigma_nu_ref < 5.4e-38 cm² and the derived dark-matter band 5.7e-39 < sigma_DM < 7.1e-39 cm² from J(phi).
proof idea
One-line definition that directly assigns the numerical value 0.3894e-27.
why it matters in Recognition Science
It supplies the unit conversion required by the downstream definition sigma_nu_weak_ref_cm2 and is unfolded inside the proof of row_weak_ref_cross_section_band. The module documentation identifies this step as completing the arithmetic for the P0-A6 hypothesis interface, which normalizes the dark-matter cross-section band via the Recognition Composition Law and the phi-ladder mass formula.
scope and limits
- Does not derive the numerical value from first principles.
- Does not specify the energy scale at which the conversion holds.
- Does not incorporate higher-order electroweak corrections.
formal statement (Lean)
44def gev2_to_cm2 : ℝ := 0.3894e-27
proof body
Definition body.
45
46/-- Named weak-channel reference cross-section in cm^2. -/