IndisputableMonolith.RRF.Physics.ElectronMass.Defs

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.PhiSupport
   4import IndisputableMonolith.Constants.AlphaDerivation
   5import IndisputableMonolith.Physics.MassTopology
   6import IndisputableMonolith.RSBridge.Anchor
   7
   8/-!
   9# T9 Electron Mass Definitions
  10
  11This module contains the core definitions for the electron mass derivation.
  12The definitions are separated from theorems/axioms to break import cycles.
  13-/
  14
  15namespace IndisputableMonolith
  16namespace Physics
  17namespace ElectronMass
  18
  19open Real Constants AlphaDerivation MassTopology RSBridge
  20
  21/-! ## Lepton Sector Geometry -/
  22
  23/-- Lepton sector binary gauge B = -22. -/
  24def lepton_B : ℤ := -22
  25
  26/-- Lepton sector geometric origin R0 = 62. -/
  27def lepton_R0 : ℤ := 62
  28
  29/-- Coherent Energy Scale E_coh = φ⁻⁵. -/
  30noncomputable def E_coh : ℝ := phi ^ (-5 : ℤ)
  31
  32/-! ## Electron Geometry -/
  33
  34/-- Electron rung r = 2. -/
  35def electron_rung : ℤ := 2
  36
  37/-- Electron charge q = -1. -/
  38def electron_charge : ℤ := -1
  39
  40/-! ## Structural Mass Derivation -/
  41
  42/-- The Yardstick (Sector Scale): Y = 2^B · E_coh · φ^R0. -/
  43noncomputable def lepton_yardstick : ℝ :=
  44  (2 : ℝ) ^ lepton_B * E_coh * phi ^ lepton_R0
  45
  46/-- The Structural Mass: m_struct = Y · φ^(r-8). -/
  47noncomputable def electron_structural_mass : ℝ :=
  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
  82  have h1 : phi ^ (-5 : ℤ) * phi ^ (62 : ℤ) = phi ^ (57 : ℤ) := by
  83    rw [← zpow_add₀ hne]; norm_num
  84  have h2 : phi ^ (57 : ℤ) * phi ^ (-6 : ℤ) = phi ^ (51 : ℤ) := by
  85    rw [← zpow_add₀ hne]; norm_num
  86  have hsub : ((2 : ℤ) - 8 : ℤ) = (-6 : ℤ) := by norm_num
  87  simp only [hsub, h1, mul_assoc]
  88  rw [h2]
  89
  90end ElectronMass
  91end Physics
  92end IndisputableMonolith
  93