IndisputableMonolith.Physics.ElectronMass.BaselineDerivation

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Constants.AlphaDerivation
   4import IndisputableMonolith.Physics.ElectronMass.Defs
   5
   6/-!
   7# Baseline Rung Derivation: r_e = 2 from Cube Geometry
   8
   9The electron baseline rung is not a free parameter. It is derived from:
  10
  11  r_e = A + 1 = active_edges_per_tick + 1 = 1 + 1 = 2
  12
  13where A = 1 is the number of active edges per atomic tick (from T2 atomicity:
  14exactly one edge transition per tick in a discrete ledger on Q₃).
  15
  16The minimal stable charged state sits one rung above the active edge itself,
  17because the active edge is the transition mechanism, not a stable particle.
  18-/
  19
  20namespace IndisputableMonolith
  21namespace Physics
  22namespace ElectronMass
  23namespace BaselineDerivation
  24
  25open Constants AlphaDerivation
  26
  27/-- The lepton baseline rung: one above the active edge count.
  28    A charged state must traverse at least one edge (the active edge A = 1).
  29    The minimal stable state sits at A + 1 = 2. -/
  30def lepton_baseline : ℕ := active_edges_per_tick + 1
  31
  32theorem lepton_baseline_eq : lepton_baseline = 2 := by
  33  unfold lepton_baseline active_edges_per_tick; norm_num
  34
  35/-- The derived baseline matches the definition in ElectronMass.Defs. -/
  36theorem baseline_matches_electron_rung :
  37    (lepton_baseline : ℤ) = electron_baseline_rung := by
  38  simp [lepton_baseline, active_edges_per_tick, electron_baseline_rung]
  39
  40/-- Active edges per tick = 1 from T2 atomicity. -/
  41theorem active_edges_eq_one : active_edges_per_tick = 1 := rfl
  42
  43/-- The derivation chain: A = 1, r_e = A + 1 = 2. -/
  44theorem electron_rung_derived :
  45    active_edges_per_tick = 1 ∧
  46    lepton_baseline = active_edges_per_tick + 1 ∧
  47    lepton_baseline = 2 :=
  48  ⟨rfl, rfl, lepton_baseline_eq⟩
  49
  50end BaselineDerivation
  51end ElectronMass
  52end Physics
  53end IndisputableMonolith
  54