deltam31_sq
The definition supplies the experimental atmospheric neutrino mass-squared splitting Δm₃₁² = 2.51 × 10^{-3} eV² for use in RS neutrino calculations. Neutrino modelers cite it when checking mass ratios against φ^7. The assignment is a direct numerical constant with no internal steps.
claimThe atmospheric neutrino mass-squared difference equals $2.51 × 10^{-3}$ in units of eV².
background
The PMNSMatrix module develops the Pontecorvo-Maki-Nakagawa-Sakata matrix from φ-quantized angles in Recognition Science. Neutrino flavor mixing involves large angles unlike the CKM matrix, with θ₂₃ near 45° suggesting symmetry. This definition provides the input Δm₃₁² drawn from the upstream NeutrinoMassHierarchy module for mass ratio computations. The local setting is SM-014 targeting derivation of PMNS from RS with patent potential in PRD on golden ratio geometry.
proof idea
The declaration is a one-line definition assigning the numerical constant 2.51e-3 directly to the real-valued constant.
why it matters in Recognition Science
This constant is referenced by the mass_ratio definition and the theorems mass_ratio_phi4 and mass_ratio_phi7, which bound the deviation from φ^7. It fills the numerical input for the paper proposition on neutrino mixing angles from golden ratio geometry. Within the framework it supports the phi-ladder mass formulas and connects to the self-similar fixed point phi.
scope and limits
- Does not derive the splitting from Recognition Science axioms.
- Does not include experimental error bars or confidence intervals.
- Does not specify the neutrino energy regime or oscillation baseline.
- Does not compute PMNS matrix elements directly.
formal statement (Lean)
164noncomputable def deltam31_sq : ℝ := 2.51e-3 -- eV²
proof body
Definition body.
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