correction_factor
The theorem establishes that the RS cross-section for gallium neutrino capture divided by the standard model prediction equals 57.7 divided by 74.0. Researchers analyzing solar neutrino deficits would cite this to quantify the suppression factor. The proof unfolds the relevant definitions and reduces the equality numerically.
claimThe ratio of the RS-modified gallium capture cross-section to the standard model prediction equals $57.7 / 74.0$.
background
The Gallium Anomaly module addresses the observed deficit in solar neutrino capture rates for gallium targets. The standard model prediction is set to 74.0 SNU based on the BP04 solar model. The RS cross-section incorporates a multiplicative correction of 57.7/74.0 to account for the φ-ladder nuclear structure effect, which suppresses the cross-section by approximately 0.78.
proof idea
The proof is a term proof that unfolds the definitions of the RS cross-section and the predicted rate, then applies norm_num to confirm the arithmetic identity.
why it matters in Recognition Science
This theorem EA-003.5 provides the explicit correction factor that feeds into the subsequent bound verification and the anomaly certificate. It realizes the φ-suppression mechanism from the nuclear φ-ladder in the Recognition Science framework, consistent with the self-similar fixed point. The result supports the claim that the gallium deficit arises from nuclear structure rather than new particles.
scope and limits
- Does not derive the factor 57.7 from the φ-ladder parameters.
- Does not establish the measured capture rate range.
- Does not rule out sterile neutrino explanations.
- Does not apply to other solar neutrino experiments.
formal statement (Lean)
131theorem correction_factor : sigma_rs / ga_capture_predicted = (57.7 / 74.0) := by
proof body
Term-mode proof.
132 unfold sigma_rs ga_capture_predicted
133 norm_num
134
135/-- **THEOREM EA-003.6**: The correction is within φ-suppression bounds. -/