solar_correction_eq
plain-language theorem explainer
The solar radiative correction in the PMNS mixing-angle formula equals ten times the fine-structure constant. Modelers of neutrino oscillations who adopt the Recognition Science phi-ladder predictions cite this equality when evaluating sin²θ₁₂. The proof is a one-line term that unfolds the two defining expressions and closes by reflexivity.
Claim. The solar radiative correction coefficient satisfies $Δ_{solar}=10α$, where $α$ is the fine-structure constant.
background
The PMNS Radiative Correction Derivation module obtains the integer prefactors 6, 10 and 3/2 that appear in the three mixing-angle predictions from the topology of a three-dimensional cube. A 3-cube supplies twelve edges and six faces; the solar sector is assigned the effective passive count twelve minus two, producing the factor ten. This construction is embedded in the Recognition Science setting in which spatial dimension three is forced by the eight-tick octave closure and all mass and mixing scales descend from the phi-ladder.
proof idea
The proof is a one-line wrapper that unfolds solar_correction and solar_coefficient then applies reflexivity.
why it matters
The theorem supplies the exact coefficient ten required by the solar-weight formula sin²θ₁₂ = φ^{-2} − 10α stated in the module. It completes the cube-topology derivation of the three radiative corrections (atmospheric 6, solar 10, Cabibbo 3/2) inside the three-dimensional voxel ledger. The result therefore anchors the PMNS predictions to the spatial-dimension step (T8) of the Recognition forcing chain.
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