electron_structural_ratio

formal source

  48  lepton_yardstick * phi ^ (electron_rung - 8)
  49
  50/-- Dimensionless Structural Ratio to E_coh. -/
  51noncomputable def electron_structural_ratio : ℝ :=
  52  electron_structural_mass / E_coh
  53
  54/-! ## The Residue (The Break) -/
  55
  56/-- Observed Electron Mass (in MeV, placeholder for ratio matching).
  57    Ref: 0.510998950 MeV. -/
  58def mass_ref_MeV : ℝ := 0.510998950
  59
  60/-- The Residue Δ = log_φ(m_obs / m_struct).
  61    Value from audit: -20.70596. -/
  62noncomputable def electron_residue : ℝ :=
  63  Real.log (mass_ref_MeV / electron_structural_mass) / Real.log phi
  64
  65/-- The Electron Mass Formula (T9). -/
  66noncomputable def predicted_electron_mass : ℝ :=
  67  electron_structural_mass * phi ^ (gap 1332 - refined_shift)
  68
  69/-! ## Basic Theorem -/
  70
  71/-- Theorem: The Structural Mass is well-defined and forced by geometry.
  72
  73    m_struct = 2^(-22) * φ^(-5) * φ^62 * φ^(2-8)
  74             = 2^(-22) * φ^(62 - 5 + 2 - 8)
  75             = 2^(-22) * φ^51
  76
  77    Proof: Direct computation shows φ^(-5) * φ^62 * φ^(-6) = φ^51. -/
  78theorem electron_structural_mass_forced :
  79    electron_structural_mass = (2 : ℝ) ^ (-22 : ℤ) * phi ^ (51 : ℤ) := by
  80  unfold electron_structural_mass lepton_yardstick E_coh lepton_B lepton_R0 electron_rung
  81  have hne : (phi : ℝ) ≠ 0 := phi_ne_zero