IndisputableMonolith.RSBridge.ResidueData

   1import IndisputableMonolith.RSBridge.Anchor
   2import IndisputableMonolith.Physics.AnchorPolicy
   3
   4namespace IndisputableMonolith
   5namespace RSBridge
   6
   7open Fermion
   8open IndisputableMonolith.Physics.AnchorPolicy
   9
  10/-!
  11# Residue Certificates (Audit Data)
  12
  13This module contains the "audit payload" - the numerical bounds for the residues
  14derived from experimental masses transported to the anchor scale.
  15
  16## Connection to AnchorPolicy
  17The certificates here are designed to verify the `display_identity_at_anchor` axiom
  18from `AnchorPolicy.lean`. Each certificate bounds `gap(Z)` for a fermion, which
  19should match the theoretical `F(Z)` value at the anchor.
  20
  21## Data Source
  22Values derived from `tools/audit_masses.py` (Python RG transport).
  23
  24## Key Observations
  251. **Leptons**: The electron, muon, and tau residues cluster tightly around
  26   the theoretical gap F(1332) ≈ 13.95, confirming the integer-rung model.
  272. **Charm Anomaly**: The Charm quark residue matches the Lepton gap (≈13.95)
  28   rather than the Up-quark theoretical target F(276) ≈ 10.7.
  293. **Quark Tension**: Up (11.7) and Top (18.16) residues differ from each other
  30   and from the theoretical target, quantifying the Quarter-Ladder vs Integer-Rung gap.
  31-/
  32
  33/-! ## Theoretical Gap Values -/
  34
  35/-- Theoretical gap for Leptons: F(1332).
  36    Numerically: ln(1 + 1332/φ) / ln(φ) ≈ 13.954 -/
  37noncomputable def gap_lepton_theory : ℝ := gap (ZOf e)
  38
  39/-- Theoretical gap for Up Quarks: F(276).
  40    Numerically: ln(1 + 276/φ) / ln(φ) ≈ 10.71 -/
  41noncomputable def gap_up_theory : ℝ := gap (ZOf u)
  42
  43/-- Theoretical gap for Down Quarks: F(24).
  44    Numerically: ln(1 + 24/φ) / ln(φ) ≈ 5.74 -/
  45noncomputable def gap_down_theory : ℝ := gap (ZOf d)
  46
  47/-! ## Verification: Z values match canonical bands -/
  48
  49theorem lepton_Z_is_1332 : ZOf e = 1332 := by native_decide
  50theorem up_Z_is_276 : ZOf u = 276 := by native_decide
  51theorem down_Z_is_24 : ZOf d = 24 := by native_decide
  52
  53/-! ## Lepton Certificates
  54    Leptons fit the integer rung model well.
  55    Audit data (delta shifted by +34.66):
  56    - e:   13.954
  57    - μ:   14.034
  58    - τ:   13.899
  59    Theoretical target: F(1332) ≈ 13.954
  60-/
  61
  62def cert_e : ResidueCert := {
  63  f := e,
  64  lo := 1395/100,  -- 13.95
  65  hi := 1396/100,  -- 13.96
  66  lo_le_hi := by norm_num
  67}
  68
  69def cert_mu : ResidueCert := {
  70  f := mu,
  71  lo := 1403/100,  -- 14.03
  72  hi := 1404/100,  -- 14.04
  73  lo_le_hi := by norm_num
  74}
  75
  76def cert_tau : ResidueCert := {
  77  f := tau,
  78  lo := 1389/100,  -- 13.89
  79  hi := 1390/100,  -- 13.90
  80  lo_le_hi := by norm_num
  81}
  82
  83/-! ## Quark Certificates
  84    Quarks show the Quarter-Ladder vs Integer-Rung tension.
  85    Theoretical target: F(276) ≈ 10.71 (up) or F(24) ≈ 5.74 (down)
  86-/
  87
  88def cert_u : ResidueCert := {
  89  f := u,
  90  lo := 1170/100,  -- 11.70
  91  hi := 1171/100,  -- 11.71
  92  lo_le_hi := by norm_num
  93}
  94
  95def cert_c : ResidueCert := {
  96  f := c,
  97  -- NOTE: Charm matches Lepton gap (13.95), not Up gap (10.71)!
  98  -- This suggests Charm has special structure or the Quarter-Ladder applies.
  99  lo := 1395/100,
 100  hi := 1396/100,
 101  lo_le_hi := by norm_num
 102}
 103
 104def cert_t : ResidueCert := {
 105  f := t,
 106  lo := 1816/100,  -- 18.16
 107  hi := 1817/100,  -- 18.17
 108  lo_le_hi := by norm_num
 109}
 110
 111def cert_d : ResidueCert := {
 112  f := d,
 113  lo := 1875/100,  -- 18.75 (shifted)
 114  hi := 1876/100,
 115  lo_le_hi := by norm_num
 116}
 117
 118def cert_s : ResidueCert := {
 119  f := s,
 120  lo := 1396/100,  -- 13.96
 121  hi := 1397/100,
 122  lo_le_hi := by norm_num
 123}
 124
 125def cert_b : ResidueCert := {
 126  f := b,
 127  lo := 1586/100,  -- 15.86
 128  hi := 1587/100,
 129  lo_le_hi := by norm_num
 130}
 131
 132/-! ## Stability Predicate -/
 133
 134/-- A fermion's residue is stable if its certificate is valid and the
 135    stationarity axiom holds at the canonical anchor. -/
 136structure StabilityCert (f : Fermion) where
 137  cert : ResidueCert
 138  cert_matches : cert.f = f
 139  cert_valid : cert.valid
 140
 141/-! ## Connection to AnchorPolicy -/
 142
 143/-- The canonical anchor from AnchorPolicy. -/
 144noncomputable def canonicalAnchorSpec : AnchorSpec := canonicalAnchor
 145
 146/-- At the canonical anchor, the display identity should hold:
 147    f_residue f μ⋆ = F(ZOf f) = gap(ZOf f)
 148
 149    This is the axiom `display_identity_at_anchor` from AnchorPolicy.
 150    The certificates above provide numerical bounds to verify this. -/
 151theorem display_identity_uses_gap (f : Fermion) :
 152    F (ZOf f) = gap (ZOf f) := rfl
 153
 154/-! ## Robustness Check Interface -/
 155
 156/-- Check if a certificate's bounds are within the AnchorPolicy tolerance of
 157    the theoretical gap. -/
 158def certificateWithinTolerance (c : ResidueCert) : Prop :=
 159  let theoretical := gap (ZOf c.f)
 160  (c.lo : ℝ) - anchorTolerance ≤ theoretical ∧
 161  theoretical ≤ (c.hi : ℝ) + anchorTolerance
 162
 163/-! ## Summary Statistics -/
 164
 165/-- The lepton certificates cluster around F(1332) ≈ 13.95. -/
 166def leptonCerts : List ResidueCert := [cert_e, cert_mu, cert_tau]
 167
 168/-- The quark certificates show more variation due to Quarter-Ladder effects. -/
 169def quarkCerts : List ResidueCert := [cert_u, cert_c, cert_t, cert_d, cert_s, cert_b]
 170
 171/-- All fermion certificates. -/
 172def allCerts : List ResidueCert := leptonCerts ++ quarkCerts
 173
 174end RSBridge
 175end IndisputableMonolith
 176