IndisputableMonolith.Physics.QuarkMassHierarchyFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Quark Mass Hierarchy from φ-ladder — S2 Depth
   6
   7Six quark flavours on a φ-ladder mass scale: u, d, s, c, b, t.
   8Adjacent-flavour mass ratio on the φ-ladder (coarse structural).
   9
  10Six = 3 generations × 2 charge types (up-type / down-type).
  11
  12Lean status: 0 sorry, 0 axiom.
  13-/
  14
  15namespace IndisputableMonolith.Physics.QuarkMassHierarchyFromPhiLadder
  16open Constants
  17
  18inductive QuarkFlavour where
  19  | up
  20  | down
  21  | strange
  22  | charm
  23  | bottom
  24  | top
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem quarkFlavour_count : Fintype.card QuarkFlavour = 6 := by decide
  28
  29/-- 6 = 3 generations × 2 charge types. -/
  30theorem six_partition : 6 = 3 * 2 := by decide
  31
  32noncomputable def quarkMass (k : ℕ) : ℝ := phi ^ k
  33
  34theorem quarkMass_ratio (k : ℕ) : quarkMass (k + 1) / quarkMass k = phi := by
  35  unfold quarkMass
  36  have hpos : (0 : ℝ) < phi ^ k := pow_pos phi_pos k
  37  rw [div_eq_iff hpos.ne', pow_succ]
  38  ring
  39
  40theorem quarkMass_pos (k : ℕ) : 0 < quarkMass k := pow_pos phi_pos k
  41
  42structure QuarkMassCert where
  43  six_flavours : Fintype.card QuarkFlavour = 6
  44  six_is_three_times_two : 6 = 3 * 2
  45  phi_ratio : ∀ k, quarkMass (k + 1) / quarkMass k = phi
  46  mass_always_pos : ∀ k, 0 < quarkMass k
  47
  48noncomputable def quarkMassCert : QuarkMassCert where
  49  six_flavours := quarkFlavour_count
  50  six_is_three_times_two := six_partition
  51  phi_ratio := quarkMass_ratio
  52  mass_always_pos := quarkMass_pos
  53
  54end IndisputableMonolith.Physics.QuarkMassHierarchyFromPhiLadder
  55