solar_coefficient_eq_10
plain-language theorem explainer
The solar radiative correction coefficient equals exactly 10 in the PMNS mixing predictions. Researchers deriving neutrino mixing angles from geometric principles cite this result to confirm the solar sector term in sin²θ₁₂. The equality follows by direct reflexivity from the definition of the coefficient as the edge count of a 3-cube minus two active modes.
Claim. The solar correction coefficient satisfies $solar_coefficient = 10$, where this coefficient multiplies the fine-structure constant in the solar mixing expression $sin^2 θ_{12} = φ^{-2} - 10α$.
background
The PMNS Radiative Correction Derivation module extracts integer coefficients for neutrino mixing angles from the topology of a 3-cube. The solar coefficient counts passive contributions after subtracting the two active modes in the 1-2 sector from the twelve edges of the cube. This rests on the upstream definition solar_coefficient := cube_edges_count 3 - 2 together with results on simplicial ledger edge lengths and the φ-ladder correction factor.
proof idea
The proof is a one-line reflexivity that unfolds the definition of solar_coefficient as cube_edges_count 3 minus 2 and evaluates directly to 10.
why it matters
This theorem supplies the solar coefficient that enters the verification theorem correction_derivation_verified assembling all PMNS corrections. It realizes the geometric count from 3-cube edge-face structure described in the module documentation and connects to the eight-tick octave and D = 3 spatial structure in the Recognition Science forcing chain. The result closes the derivation of the solar weight sin²θ₁₂ = φ^{-2} − 10α.
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