atmospheric_radiative_correction
The atmospheric radiative correction factor equals six times the fine-structure constant. Neutrino mixing derivations cite it to adjust the atmospheric angle prediction from cube-face parity. The definition is introduced as a direct scaling by the six faces of the cubic voxel topology.
claimThe atmospheric radiative correction factor is given by $6α$, where $α$ is the fine-structure constant.
background
This definition sits inside the module on geometric foundations for mixing matrices, which formalizes cubic voxel topology constraints that force CKM and PMNS parameters. The fine-structure constant $α$ is imported from Constants.Alpha as the reciprocal of its derived inverse. Upstream results include the abstract Constants bundle from the Law of Existence, which supplies the non-negative Knet and related scalars, together with the PrimitiveDistinction theorem that reduces seven axioms to four structural conditions plus three definitional facts.
proof idea
The definition is a direct one-line assignment of the value 6 * Constants.alpha. No lemmas or tactics are applied beyond the constant import.
why it matters in Recognition Science
This supplies the face-mediated correction term used in the theorem atmospheric_angle_forced, which states atmospheric_weight + atmospheric_radiative_correction = 1/2 + 6 * Constants.alpha. It feeds directly into pmns_theta23_born_forced and pmns_theta23_match in MixingDerivation, closing the geometric account of the atmospheric angle from maximal parity mix and the eight-tick octave. The placement aligns with the Recognition Science forcing chain at T7 and T8, where D = 3 dimensions and the cubic topology determine the radiative leakage.
scope and limits
- Does not derive the numerical value of alpha.
- Does not include higher-order radiative corrections.
- Does not apply to solar or reactor mixing sectors.
- Does not compute the resulting mixing angle numerically.
formal statement (Lean)
61noncomputable def atmospheric_radiative_correction : ℝ := 6 * Constants.alpha
proof body
Definition body.
62
63/-- **THEOREM: Atmospheric Angle Forced**
64 The atmospheric mixing angle is derived from the maximal parity mix
65 with a face-mediated radiative correction. -/