phi_suppression_ga
plain-language theorem explainer
The declaration defines the φ-suppression factor for gallium as φ raised to the power of minus the gallium rung divided by 10. Neutrino physicists and RS modelers cite it when quantifying nuclear corrections to solar capture rates. The definition is a direct arithmetic substitution of the precomputed rung value 45, yielding the exponent -4.5.
Claim. The φ-suppression factor for gallium is $φ^{-r_{Ga}/10}$, where $r_{Ga}$ is the rung of the gallium nucleus on the φ-ladder.
background
The module treats the gallium anomaly as a ~20% deficit between standard solar model predictions (74 SNU) and measured capture rates (55-58 SNU) in Ga experiments. Recognition Science resolves it by nuclear φ-ladder structure that modifies the neutrino capture cross-section, with the rung near 4.5 producing a suppression near 0.8. The gallium rung is the discrete mass scale index for gallium (~70 u) on the φ-ladder.
proof idea
This is a direct definition that substitutes the gallium rung value into the exponent. It performs the arithmetic division by 10, negation, and exponentiation with phi. No additional lemmas are applied beyond the rung definition itself.
why it matters
The definition supplies the explicit suppression factor used by the boundedness result and the no-sterile-needed theorem, which together show that three generations plus the nuclear correction match observations. It realizes the EA-003 step in the experimental derivation, consistent with the φ-ladder and self-similar fixed point from the forcing chain. It leaves open the precise role of gap resonance adjustments for exact numerical matching.
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