pmns_theta12_born_forced
plain-language theorem explainer
The solar neutrino mixing angle satisfies sin²θ₁₂ = φ^{-2} - 10α by definition of the rung-ratio prediction. Neutrino physicists deriving PMNS parameters from geometric mixing would cite this when verifying Born-rule consistency with radiative corrections. The proof is a one-line wrapper that unfolds the definition of the predicted angle and applies reflexivity.
Claim. The predicted solar mixing probability satisfies $sin^2 θ_{12} = φ^{-2} - 10α$, where $φ$ is the golden-ratio fixed point and $α$ the fine-structure constant in RS units.
background
Module Phase 7.2 derives CKM and PMNS mixing from the cubic ledger via edge-dual coupling and 8-tick window overlaps. The solar weight is defined as the 2-step torsion gap $φ^{-2}$. The solar radiative correction is $10α$. The upstream definition sin2_theta12_pred is exactly solar_weight minus that correction, presented as the rung-ratio conjecture for θ₁₂.
proof idea
The proof is a one-line wrapper that unfolds sin2_theta12_pred to its defining expression solar_weight - solar_radiative_correction and applies reflexivity.
why it matters
This equality anchors the solar-angle prediction inside the PMNS rung-ratio conjecture and supports the module claim that mixing angles arise from 8-tick octave overlaps. It connects directly to the Recognition Science phi fixed point (T6) and the alpha band. No downstream uses are recorded, so the result closes the definitional step for θ₁₂ without further parent theorems.
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