atmospheric_coefficient_eq_6
plain-language theorem explainer
The equality states that the atmospheric correction coefficient equals 6 because it is defined as the face count of a 3-cube. Researchers deriving PMNS mixing angles from Recognition Science geometry would cite this to fix the 6α term in sin²θ₂₃ = ½ + 6α. The proof is a direct reflexivity reduction once the coefficient is set to the enumerated cube faces.
Claim. The atmospheric radiative correction coefficient, defined as the number of faces of a 3-cube, equals 6.
background
The PMNS module derives integer coefficients for neutrino mixing corrections from the topology of a 3-cube voxel ledger. The atmospheric coefficient is introduced explicitly as the face count of this cube, with each of the six faces supplying one unit of vacuum polarization to the μ-τ sector. Upstream results establish the geometric count of cube faces and confirm that the coefficient definition reduces to this enumeration without additional hypotheses.
proof idea
The proof is a one-line reflexivity wrapper that matches the definition of the atmospheric coefficient as the face count of a 3-cube directly to the integer 6.
why it matters
This pins the integer 6 required for the atmospheric term in the PMNS predictions and supplies the atmospheric_from_faces field in the downstream verification theorem that certifies all three coefficients (6, 10, 3/2) from cube geometry. It realizes the module's derivation that the 3-cube's six faces produce the symmetric correction to the maximally mixed atmospheric sector, consistent with the eight-tick octave and D = 3 spatial structure.
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