IndisputableMonolith.Verification.QuarkSectorAudit

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Quark Sector Audit: The Dual-Coordinate Problem
   6
   7This module formalizes the most significant blocker to claiming the mass framework
   8is "correct end-to-end": the quark sector has two coexisting coordinate conventions
   9that are NOT mathematically equivalent and have NOT been reconciled into a single
  10forward pipeline.
  11
  12## The Problem
  13
  14The framework maintains two different quark rung conventions:
  15
  16### Convention A: Integer Rungs (Core Model)
  17- **Source**: `Masses/Anchor.lean`, `Masses/MassLaw.lean`
  18- **Status**: CANONICAL — parameter-free, derived from cube geometry
  19- **Formula**: `m = yardstick(Sector) × φ^{r − 8 + gap(Z)}`
  20- **Rungs**: up-type {4, 15, 21}, down-type {4, 15, 21}
  21- **Yardsticks**: Different for up-type vs down-type (B_pow, r₀ from counting layer)
  22
  23### Convention B: Quarter-Ladder (Hypothesis Module)
  24- **Source**: `Physics/QuarkMasses.lean`
  25- **Status**: HYPOTHESIS — uses PDG mass targets, not parameter-free
  26- **Formula**: `m = electron_structural_mass × φ^R` where R ∈ ¼ℤ
  27- **Residues**: top=23/4, bottom=−8/4, charm=−18/4, strange=−40/4, down=−64/4, up=−71/4
  28
  29### Why This Matters
  30
  31The `QuarkCoordinateReconciliation.lean` module explicitly states:
  32"The two conventions are NOT meant to be mathematically equivalent."
  33
  34This means:
  351. We do NOT have a single unified, fully non-circular, parameter-free quark mass
  36   derivation on the same footing as the lepton chain.
  372. The "quark masses match PDG" results in Convention B use PDG targets explicitly
  38   and are marked as NOT part of the clean core prediction pipeline.
  393. Until the quark sector is reconciled into one coordinate system with one forward
  40   pipeline, "correct for all fermions" is not defensible.
  41
  42## What Would Fix It
  43
  44Three possible resolutions (mutually exclusive):
  45
  461. **Derive Convention B from A**: Show that the quarter-ladder positions arise from
  47   the integer-rung mass law when sector yardsticks and gap(Z) are properly applied.
  48   This would make Convention B a derived consequence of Convention A.
  49
  502. **Derive Convention A from B**: Show that the sector yardsticks emerge when the
  51   quarter-ladder is properly organized by sector. This is less likely given that
  52   Convention A is more structurally connected to the cube geometry.
  53
  543. **Derive both from a common generalization**: Find a unified framework that
  55   produces both conventions as special cases or coordinate representations of
  56   the same underlying structure.
  57-/
  58
  59namespace IndisputableMonolith
  60namespace Verification
  61namespace QuarkSectorAudit
  62
  63/-- The two quark coordinate conventions. -/
  64inductive QuarkConvention
  65  | IntegerRung    -- Convention A: core, parameter-free
  66  | QuarterLadder  -- Convention B: hypothesis, uses PDG targets
  67  deriving Repr, DecidableEq
  68
  69/-- Properties that a unified quark sector must satisfy. -/
  70structure UnifiedQuarkSector where
  71  /-- Single coordinate convention used for all quarks -/
  72  convention : QuarkConvention
  73  /-- Forward prediction pipeline: RS inputs → mass prediction (no PDG in loop) -/
  74  forward_pipeline : Bool
  75  /-- No PDG mass targets used in the rung/residue assignment -/
  76  no_pdg_targeting : Bool
  77  /-- Same structural footing as the lepton chain -/
  78  same_footing_as_leptons : Bool
  79  /-- All six quark masses predicted from counting-layer integers + φ + α -/
  80  all_six_predicted : Bool
  81
  82/-- The current quark sector status: NOT unified. -/
  83def currentStatus : String :=
  84  "UNRESOLVED: Two coexisting conventions (integer rungs vs quarter-ladder) \
  85   that are explicitly documented as not equivalent. Convention A is parameter-free \
  86   but gives only skeleton masses (large errors without gap(Z)). Convention B achieves \
  87   <2% for heavy quarks but uses PDG targets. Neither alone constitutes a complete \
  88   forward pipeline for all six quarks."
  89
  90/-- Convention A rung values (from Masses/Anchor.lean) -/
  91structure ConventionA_Rungs where
  92  u : ℤ := 4
  93  c : ℤ := 15   -- 4 + 11 (gen-2 torsion)
  94  t : ℤ := 21   -- 4 + 17 (gen-3 torsion)
  95  d : ℤ := 4
  96  s : ℤ := 15   -- 4 + 11
  97  b : ℤ := 21   -- 4 + 17
  98
  99/-- Convention B residues (from Physics/QuarkMasses.lean) -/
 100structure ConventionB_Residues where
 101  top     : ℚ := 23/4      -- 5.75
 102  bottom  : ℚ := -8/4      -- -2.0
 103  charm   : ℚ := -18/4     -- -4.5
 104  strange : ℚ := -40/4     -- -10.0
 105  down    : ℚ := -64/4     -- -16.0
 106  up      : ℚ := -71/4     -- -17.75
 107
 108/-- The conventions use different reference masses. -/
 109theorem different_references : True := trivial
 110-- Convention A: sector-specific yardsticks (different for up-type vs down-type)
 111-- Convention B: single electron_structural_mass base for all quarks
 112
 113/-- The conventions use different rung types.
 114    Convention B requires quarter-integers (e.g., 23/4), which are not integers.
 115    Convention A uses only integers. -/
 116theorem different_rung_types :
 117    ¬(∀ (r : ℚ), ∃ (n : ℤ), r = ↑n) := by
 118  push_neg
 119  refine ⟨23/4, fun n => ?_⟩
 120  intro h
 121  have : (23 : ℚ) / 4 = ↑n := h
 122  have : (4 : ℚ) * ↑n = 23 := by linarith
 123  have : (4 : ℤ) * n = 23 := by exact_mod_cast this
 124  omega
 125
 126/-- The generation spacing is NOT the same in both conventions.
 127    Convention A: Δ(gen1→gen2) = 11, Δ(gen2→gen3) = 6 (universally)
 128    Convention B: top→bottom = 7.75, bottom→charm = 2.5, charm→strange = 5.5
 129    These are completely different numbers. -/
 130theorem generation_spacing_differs : True := trivial
 131
 132/-! ## Specific Discrepancies -/
 133
 134/-- Convention B light quark matches are noticeably worse (5% level). -/
 135def light_quark_accuracy : String :=
 136  "Strange: ~5% error, Down: ~5% error. These are attributed to 'non-perturbative \
 137   QCD effects' but this attribution is itself a hypothesis, not a derivation."
 138
 139/-- Convention A skeleton masses (without gap(Z)) have O(1) errors for quarks. -/
 140def skeleton_only_accuracy : String :=
 141  "Without the charge-band term gap(Z), the integer-rung skeleton masses have \
 142   10%–O(1) errors for quarks. The holdout structural test confirms this: skeleton \
 143   alone is insufficient."
 144
 145/-! ## The Reconciliation Problem -/
 146
 147/-- Formal statement of what reconciliation would require. -/
 148structure ReconciliationProof where
 149  /-- A single mass formula that works for all 6 quarks -/
 150  unified_formula : String
 151  /-- No measured quark mass enters the right-hand side of any prediction -/
 152  non_circular : Bool
 153  /-- Same precision level as lepton chain (ideally sub-percent) -/
 154  all_quarks_sub_percent : Bool
 155  /-- Uses only counting-layer integers + φ + α (no PDG targets) -/
 156  parameter_free : Bool
 157
 158/-- No reconciliation proof currently exists. -/
 159theorem no_reconciliation_yet : True := trivial
 160-- This is the honest status. The `QuarkCoordinateReconciliation.lean` module
 161-- documents the gap but does not close it.
 162
 163/-! ## Impact on Framework Verdict -/
 164
 165/-- The quark sector problem means the mass framework verdict cannot be "fully correct." -/
 166theorem quark_problem_blocks_full_verdict :
 167    ¬(currentStatus = "RESOLVED") := by
 168  simp [currentStatus]
 169
 170end QuarkSectorAudit
 171end Verification
 172end IndisputableMonolith
 173