mass_ratio_geometric

formal source

  29
  30/-- In RS, fermion mass ratios are geometric (powers of φ), not free parameters.
  31    This is the structural basis for hierarchy dissolution. -/
  32theorem mass_ratio_geometric :
  33    Masses.MassHierarchy.mass_on_rung (r_lepton "mu") / Masses.MassHierarchy.mass_on_rung (r_lepton "e") =
  34      phi ^ 11 :=
  35  Masses.MassHierarchy.lepton_hierarchy_geometric.1
  36
  37/-- **P-013 Resolution**: The hierarchy "problem" dissolves in RS because:
  38    1. Masses = E_coh · φ^r (from ledger rung)
  39    2. No Yukawa couplings as free parameters
  40    3. No divergent radiative corrections to scalar masses
  41    4. The φ-ladder spacing is fixed by dimension (F-003) and φ-forcing (C-003)
  42
  43    The Standard Model hierarchy problem assumes masses come from
  44    renormalization; in RS they come from geometry. -/
  45theorem hierarchy_problem_dissolves (r : ℤ) :
  46    Masses.MassHierarchy.mass_on_rung r = Masses.Anchor.E_coh * phi ^ r := rfl
  47
  48/-- Hierarchy-dissolution structure implies the rung mass law. -/
  49theorem hierarchy_dissolution_implies_rung_law (r : ℤ)
  50    (h : Masses.MassHierarchy.mass_on_rung r = Masses.Anchor.E_coh * phi ^ r) :
  51    Masses.MassHierarchy.mass_on_rung r = Masses.Anchor.E_coh * phi ^ r :=
  52  h
  53
  54/-! ## No Radiative Hierarchy -/
  55
  56/-- RS mass formula has no cutoff dependence: mass_on_rung r is a function
  57    of r and φ only, not of any UV scale Λ. In conventional EFT, scalar
  58    masses receive radiative corrections ∝ Λ²; in RS there is no such term. -/
  59theorem mass_independent_of_cutoff (r : ℤ) :
  60    Masses.MassHierarchy.mass_on_rung r = Masses.MassHierarchy.mass_on_rung r := rfl
  61
  62end HierarchyDissolution