IndisputableMonolith.Foundation.HierarchyDissolution

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Foundation.PhiForcing
   4import IndisputableMonolith.Masses.MassHierarchy
   5
   6/-!
   7# P-013: Is the Standard Model Natural? (Hierarchy Problem Dissolution)
   8
   9Formalizes the RS resolution of the hierarchy problem.
  10
  11## Registry Item
  12- P-013: Is the Standard Model natural?
  13
  14## RS Derivation Status
  15**STARTED** — In RS there is no hierarchy problem: mass spectrum is set by
  16the φ-ladder (geometric, forced), not by radiative corrections. The question
  17"why isn't the Higgs mass driven to Planck scale?" dissolves because
  18masses come from ledger rung positions, not from divergent loop integrals.
  19-/
  20
  21namespace IndisputableMonolith
  22namespace Foundation
  23namespace HierarchyDissolution
  24
  25open Real Constants
  26open Masses.Integers
  27
  28/-! ## Mass from φ-Ladder, Not Radiative -/
  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
  63end Foundation
  64end IndisputableMonolith
  65