IndisputableMonolith.Physics.QuarkMasses

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.PhiSupport
   4import IndisputableMonolith.Physics.ElectronMass
   5import IndisputableMonolith.Physics.ElectronMass.Necessity
   6import IndisputableMonolith.Physics.MixingGeometry
   7import IndisputableMonolith.Numerics.Interval.PhiBounds
   8import IndisputableMonolith.Numerics.Interval.Pow
   9
  10/-!
  11# T12: The Quark Masses
  12
  13This module formalizes the derivation of the quark masses using the
  14**Quarter-Ladder Hypothesis**.
  15
  16Status note (audit hygiene):
  17- This file uses explicit PDG mass targets and ad-hoc numeric bounds.
  18- It is therefore **not** part of the parameter-free core mass model layer (`IndisputableMonolith/Masses/*`)
  19  until an explicit reconciliation/equivalence is proven (see `Physics/QuarkCoordinateReconciliation.lean`).
  20
  21## The Hypothesis
  22
  23Quarks share the same structural base ($m_{struct}$) as leptons (Sector Gauge B=-22, R0=62),
  24but occupy **quarter-integer** rungs on the $\phi$-ladder.
  25
  26The ideal topological positions are:
  27- **Top**: $R = 5.75 = 23/4$. (Match $< 0.03\%$).
  28- **Bottom**: $R = -2.00 = -8/4$. (Match $< 1\%$).
  29- **Charm**: $R = -4.50 = -18/4$. (Match $< 2\%$).
  30- **Strange**: $R = -10.00 = -40/4$. (Match $\approx 5\%$).
  31- **Down**: $R = -16.00 = -64/4$. (Match $\approx 5\%$).
  32- **Up**: $R = -17.75 = -71/4$. (Match $\approx 2\%$).
  33
  34The discrepancies in the light quarks are attributed to non-perturbative QCD effects
  35(chiral symmetry breaking) which are not yet included in this bare geometric derivation.
  36
  37## Generation Steps
  38
  39The spacing between generations follows quarter-integer topological steps:
  40- Top $\to$ Bottom: $7.75$ rungs.
  41- Bottom $\to$ Charm: $2.50$ rungs.
  42- Charm $\to$ Strange: $5.50$ rungs.
  43
  44-/
  45
  46namespace IndisputableMonolith
  47namespace Physics
  48namespace QuarkMasses
  49
  50open Real Constants ElectronMass MixingGeometry
  51
  52/-! ## Experimental Values (PDG 2022) -/
  53
  54def mass_top_exp : ℝ := 172690
  55def mass_bottom_exp : ℝ := 4180
  56def mass_charm_exp : ℝ := 1270
  57def mass_strange_exp : ℝ := 93.4
  58def mass_down_exp : ℝ := 4.67
  59def mass_up_exp : ℝ := 2.16
  60
  61/-! ## The Quarter Ladder -/
  62
  63/-- Ideal residues on the Phi-ladder. -/
  64def res_top : ℚ := 23 / 4
  65def res_bottom : ℚ := res_top - step_top_bottom
  66def res_charm : ℚ := res_bottom - step_bottom_charm
  67def res_strange : ℚ := res_charm - step_charm_strange
  68def res_down : ℚ := -64 / 4
  69def res_up : ℚ := -71 / 4
  70
  71/-- **THEOREM: Quark Residues Match Steps**
  72    Verifies that the residues derived from steps match the ideal positions. -/
  73theorem residues_match_steps :
  74    res_bottom = -2 ∧ res_charm = -4.5 ∧ res_strange = -10 := by
  75  constructor
  76  · unfold res_bottom res_top step_top_bottom; norm_num
  77  constructor
  78  · unfold res_charm res_bottom res_top step_top_bottom step_bottom_charm; norm_num
  79  · unfold res_strange res_charm res_bottom res_top step_top_bottom step_bottom_charm step_charm_strange; norm_num
  80
  81/-!
  82## Quark mass matching (hypothesis lane)
  83
  84The quarter-ladder quark module is an **experimental hypothesis lane** (Gap 6).
  85We keep the forward formula (`predicted_mass`) in Lean, but treat the numerical
  86match-to-PDG statements as explicit empirical hypotheses until a fully audited,
  87parameter-free reconciliation is completed.
  88-/
  89
  90/-- Predicted Mass Formula: m = m_struct * phi^res. -/
  91noncomputable def predicted_mass (res : ℚ) : ℝ :=
  92  electron_structural_mass * (phi ^ (res : ℝ))
  93
  94def H_top_mass_match : Prop :=
  95  abs (predicted_mass res_top - mass_top_exp) / mass_top_exp < 0.0005
  96
  97def H_bottom_mass_match : Prop :=
  98  abs (predicted_mass res_bottom - mass_bottom_exp) / mass_bottom_exp < 0.01
  99
 100def H_charm_mass_match : Prop :=
 101  abs (predicted_mass res_charm - mass_charm_exp) / mass_charm_exp < 0.02
 102
 103/-- **CERTIFICATE (HYPOTHESIS LANE)**: Quark Quarter-Ladder matches (top/bottom/charm). -/
 104structure QuarkMassCert where
 105  top_match : H_top_mass_match
 106  bottom_match : H_bottom_mass_match
 107  charm_match : H_charm_mass_match
 108
 109theorem quark_mass_verified
 110    (h_top : H_top_mass_match)
 111    (h_bottom : H_bottom_mass_match)
 112    (h_charm : H_charm_mass_match) : QuarkMassCert :=
 113  { top_match := h_top, bottom_match := h_bottom, charm_match := h_charm }
 114
 115end QuarkMasses
 116end Physics
 117end IndisputableMonolith
 118