maximal_theta23
Recognition Science sets the atmospheric neutrino mixing angle to its symmetric maximum by assigning sin²θ₂₃ exactly 1/2. Neutrino modelers building φ-quantized PMNS matrices cite this as the baseline before small corrections. The definition is a direct constant assignment with no reduction steps or lemmas.
claimThe maximal atmospheric mixing satisfies sin²θ₂₃ = 1/2.
background
The module derives the PMNS neutrino mixing matrix from Recognition Science by treating the three angles as φ-quantized. Large mixing distinguishes neutrinos from quarks: θ₁₂ ≈ 34°, θ₂₃ ≈ 45°, θ₁₃ ≈ 8.6°. The local setting notes that maximal θ₂₃ signals an underlying symmetry, with observed sin²θ₂₃ ≈ 0.545 lying close but offset by a possible φ correction.
proof idea
The definition is a direct constant assignment of the real number 1/2.
why it matters in Recognition Science
This supplies the symmetric baseline hypothesis for θ₂₃ inside the PMNS construction from φ-angles. It fills the paper proposition on neutrino mixing angles from golden ratio geometry. The result touches the open deviation question and sits inside the broader forcing chain where T7 eight-tick periodicity and D = 3 spatial dimensions generate the symmetry.
scope and limits
- Does not derive the observed sin²θ₂₃ ≈ 0.545.
- Does not introduce or compute any φ-correction term.
- Does not construct the full PMNS matrix elements.
formal statement (Lean)
97noncomputable def maximal_theta23 : ℝ := 1 / 2
proof body
Definition body.
98
99/-- **Hypothesis 3: θ₁₃ from φ/10**
100
101 sin²θ₁₃ ≈ φ/100 = 0.01618
102
103 Observed ≈ 0.022, within 30%. Not great. -/