IndisputableMonolith.RRF.Hypotheses.TauGate

   1import IndisputableMonolith.RRF.Hypotheses.PhiLadder
   2import Mathlib.Data.Real.Basic
   3
   4/-!
   5# RRF Hypotheses: Tau-Gate Identity
   6
   7The tau-gate hypothesis: the tau lepton and biological gating share a φ-rung.
   8
   9This is an EXPLICIT HYPOTHESIS with specific numerical predictions.
  10It represents the most striking claim in the φ-ladder theory.
  11
  12## The Hypothesis
  13
  14The tau lepton mass (rung 19 in particle physics) corresponds to the
  15molecular gate timescale (rung 19 in biology) on the same φ-ladder.
  16
  17Specifically:
  18- m_τ ≈ 1.777 GeV corresponds to φ¹⁹ relative to some base mass
  19- τ_gate ≈ 68 ps corresponds to φ¹⁹ relative to some base time
  20
  21## Falsification Criteria
  22
  231. The rung correspondence is numerological (accidental)
  242. Other lepton generations don't show similar correspondences
  253. The base scales require unnatural choices
  26-/
  27
  28
  29namespace IndisputableMonolith
  30namespace RRF.Hypotheses
  31
  32/-! ## Physical Constants (Measured Values) -/
  33
  34/-- Tau lepton mass in GeV. -/
  35noncomputable def tauMassGeV : ℝ := 1.77686
  36
  37/-- Molecular gate timescale in picoseconds. -/
  38noncomputable def molecularGatePS : ℝ := 68
  39
  40/-- Convert ps to seconds. -/
  41noncomputable def psToSeconds (ps : ℝ) : ℝ := ps * 1e-12
  42
  43/-- Molecular gate timescale in seconds. -/
  44noncomputable def molecularGateSeconds : ℝ := psToSeconds molecularGatePS
  45
  46/-! ## The Tau-Gate Hypothesis -/
  47
  48/-- The tau-gate identity: both are at rung 19.
  49
  50This is the core claim. The "rung 19" is computed from:
  51- Mass: ln(m_τ / m_base) / ln(φ) ≈ 19
  52- Time: ln(τ_gate / τ_base) / ln(φ) ≈ 19
  53
  54The hypothesis is that these coincide, not accidentally.
  55-/
  56structure TauGateIdentity where
  57  /-- The rung number for both. -/
  58  rung : ℤ := 19
  59  /-- The mass base (in GeV) that places tau at this rung. -/
  60  massBase : ℝ
  61  /-- The time base (in seconds) that places gate at this rung. -/
  62  timeBase : ℝ
  63  /-- Tau mass is at the rung. -/
  64  tauAtRung : |computeRung tauMassGeV massBase - rung| ≤ 0.5
  65  /-- Molecular gate is at the rung. -/
  66  gateAtRung : |computeRung molecularGateSeconds timeBase - rung| ≤ 0.5
  67
  68/-! ## Extended Hypothesis: All Three Leptons -/
  69
  70/-- Electron mass in GeV. -/
  71noncomputable def electronMassGeV : ℝ := 0.000511
  72
  73/-- Muon mass in GeV. -/
  74noncomputable def muonMassGeV : ℝ := 0.10566
  75
  76/-- Lepton generation rungs hypothesis.
  77
  78If the tau-gate identity is not accidental, the electron and muon
  79should also be at integer rungs relative to the same base.
  80-/
  81structure LeptonGenerationRungs where
  82  /-- Common mass base. -/
  83  massBase : ℝ
  84  /-- Electron rung. -/
  85  electronRung : ℤ
  86  /-- Muon rung. -/
  87  muonRung : ℤ
  88  /-- Tau rung. -/
  89  tauRung : ℤ := 19
  90  /-- Electron at its rung. -/
  91  electronAtRung : |computeRung electronMassGeV massBase - electronRung| ≤ 0.5
  92  /-- Muon at its rung. -/
  93  muonAtRung : |computeRung muonMassGeV massBase - muonRung| ≤ 0.5
  94  /-- Tau at its rung. -/
  95  tauAtRung : |computeRung tauMassGeV massBase - tauRung| ≤ 0.5
  96  /-- Rungs are distinct. -/
  97  distinct : electronRung ≠ muonRung ∧ muonRung ≠ tauRung ∧ electronRung ≠ tauRung
  98
  99/-! ## Prediction Obligations -/
 100
 101/-- If tau-gate identity holds, predict other correspondences.
 102
 103The hypothesis generates predictions:
 104- Electron (rung ~2) should correspond to some chemical timescale
 105- Muon (rung ~13) should correspond to some intermediate timescale
 106-/
 107structure TauGatePredictions where
 108  /-- The identity holds. -/
 109  identity : TauGateIdentity
 110  /-- Predicted electron-scale timescale (in seconds). -/
 111  electronTimeScale : ℝ
 112  /-- Predicted muon-scale timescale (in seconds). -/
 113  muonTimeScale : ℝ
 114  /-- Electron timescale is at rung 2. -/
 115  electronTimeAtRung : |computeRung electronTimeScale identity.timeBase - 2| ≤ 0.5
 116  /-- Muon timescale is at rung 13. -/
 117  muonTimeAtRung : |computeRung muonTimeScale identity.timeBase - 13| ≤ 0.5
 118
 119/-! ## Falsification Interface -/
 120
 121/-- A falsification witness for the tau-gate identity. -/
 122structure TauGateFalsifier where
 123  /-- The identity with some base choices. -/
 124  attempt : TauGateIdentity
 125  /-- But predictions fail (other leptons don't fit). -/
 126  predictions_fail : True  -- Placeholder
 127  /-- The base choices are unnatural (require fine-tuning). -/
 128  unnatural_base : True  -- Placeholder
 129
 130/-- The hypothesis is falsified if:
 1311. No natural base exists that places both at rung 19, OR
 1322. Other leptons don't fit the same ladder. -/
 133def tauGateFalsified : Prop :=
 134  (∀ b₁ b₂ : ℝ, 0 < b₁ → 0 < b₂ →
 135    |computeRung tauMassGeV b₁ - 19| > 0.5 ∨
 136    |computeRung molecularGateSeconds b₂ - 19| > 0.5) ∨
 137  (∀ _ : LeptonGenerationRungs, False)  -- No valid lepton rungs
 138
 139end RRF.Hypotheses
 140end IndisputableMonolith
 141