vertex_edge_slots

formal source

  17
  18/-- Total number of vertex-edge incidence slots in a 3-cube.
  19    Each of the 12 edges connects 2 vertices. -/
  20def vertex_edge_slots : ℕ := 2 * cube_edges 3
  21
  22theorem vertex_edge_slots_eq_24 : vertex_edge_slots = 24 := by
  23  unfold vertex_edge_slots cube_edges
  24  norm_num
  25
  26/-- The coupling between face-centered states (Gen 2) and vertex states (Gen 3).
  27    A face is dual to an edge in the sense of 'dual lattice' transitions.
  28    The ratio is 1 per 24 available transition slots. -/
  29def edge_dual_ratio : ℚ := 1 / 24
  30
  31/-- The parity-split fine structure leakage.
  32    Represents the coupling between non-adjacent generations (1 and 3)
  33    mediated by the vacuum polarization field alpha. -/
  34noncomputable def fine_structure_leakage : ℝ := Constants.alpha / 2
  35
  36/-- The 3-generation torsion overlap on the cubic ledger.
  37    This corresponds to the delocalization of the first generation
  38    across the three spatial dimensions. -/
  39noncomputable def torsion_overlap : ℝ := phi ^ (-3 : ℤ)
  40
  41/-- The solar mixing weight (2-step torsion gap). -/
  42noncomputable def solar_weight : ℝ := phi ^ (-2 : ℤ)
  43
  44/-- The solar radiative correction factor.
  45    Estimated as (E_passive - 1) * alpha. -/
  46noncomputable def solar_radiative_correction : ℝ := 10 * Constants.alpha
  47
  48/-- **THEOREM: Solar Angle Forced**
  49    The solar mixing angle is derived from the phi^-2 scaling with a
  50    10-alpha radiative correction. -/