IndisputableMonolith.Gravity.SevenGaps.Gap5ConstraintCloseStatus

   1import IndisputableMonolith.Gravity.SevenGaps.DiracAlgebraContinuumBinding
   2import IndisputableMonolith.Gravity.SevenGaps.HKTKineticNormalizedRigidity
   3import IndisputableMonolith.Gravity.SevenGaps.HKTVacuumSectorKill
   4import IndisputableMonolith.Gravity.SevenGaps.HKTCanonicalMomTarget
   5import IndisputableMonolith.Gravity.SevenGaps.HKTPointSplitStrong
   6import IndisputableMonolith.Gravity.SevenGaps.HKTOneSiteCounterexample
   7import IndisputableMonolith.Gravity.SevenGaps.HypersurfaceDeformation
   8import IndisputableMonolith.Gravity.SevenGaps.Gap5ConstraintResidualDAG
   9import IndisputableMonolith.Gravity.SevenGaps.FullTheoryLedger
  10import IndisputableMonolith.Gravity.SevenGaps.CampaignLedger
  11
  12/-!
  13# Wave C5: gap5 constraint-recovery close status / binding receipt
  14
  15Downstream of `FullTheoryLedger` and both named closers so the ledger Bool
  16flip cannot create an import cycle. Binding theorems tie
  17
  18* `fullTheoryBenchmarks.gap5_constraint_recovery = true`
  19* `sevenGapsCampaignStatus.gap5_continuum_algebra_hkt_open = false`
  20* `gap5ResidualDAGStatus.hktRigidityOpen = false`
  21* `gap5ResidualDAGStatus.packagedTargetOpen = false`
  22* `gap5ResidualDAGStatus.gap5ConstraintRecovery = true`
  23
  24to the green conjunction
  25
  26* Dirac half: `DiracAlgebraContinuumBinding.dirac_algebra_continuum_limit`
  27* HKT half: `hojman_pins_general_relativity_holds`
  28  (`HKTRigidityKineticNormalizedN2_holds`, FTC theorem-derived)
  29
  30Kill tower (scope certificate that no stronger unconditioned n=2 statement
  31is true): `not_HKTRigidityStatement_one`,
  32`not_HKTRigidityStatementPointSplitDynN2Strong`,
  33`not_HKTRigidityStatementPointSplitDynN2Canonical`,
  34`not_HKTRigidityModVacuumStatementN2`.
  35
  36Adjudication: `D-gap5-acceptance-adjudication-20260723`.
  37-/
  38
  39namespace IndisputableMonolith
  40namespace Gravity
  41namespace SevenGaps
  42namespace Gap5ConstraintCloseStatus
  43
  44open FullTheoryLedger
  45open CampaignLedger
  46open Gap5ConstraintResidualDAG
  47open DiracAlgebraContinuumBinding
  48open HKTKineticNormalizedRigidity
  49open HKTVacuumSectorKill
  50open HKTCanonicalMomTarget
  51open HKTPointSplitStrong
  52open HKTOneSiteCounterexample
  53open HypersurfaceDeformation
  54
  55noncomputable section
  56
  57/-! ## Named ledger terminal (HKT half) -/
  58
  59/-- Ledger name for the HKT/GR-pin half of gap5. Bound to the kinetic-normalized
  60ContDiff-2 CanonicalMom terminal (intensivity disclosed; FTC derived).
  61
  62**The name overclaims and the definition is what binds.** What is proved is
  63`HKTRigidityKineticNormalizedN2`: rigidity of the ADM *shape* on an `n = 2`
  64lattice point-split target. General relativity in the continuum is not pinned
  65here; no continuum limit is taken, and `dirac_algebra_continuum_limit` is the
  66open statement that would be needed. Read this terminal as "Hojman pins the
  67ADM shape at `n = 2`". Renamed 2026-08-05 (Jon's authorization in the
  68classical-paper session): the accurate name is `hkt_adm_shape_rigidity_n2`
  69below; this historical name is retained as a compatibility alias because six
  70modules and the flag ledger bind to it. -/
  71def hojman_pins_general_relativity : Prop :=
  72  HKTRigidityKineticNormalizedN2
  73
  74/-- THEOREM. Named terminal inhabited by the upgraded kinetic-normalized hold. -/
  75theorem hojman_pins_general_relativity_holds : hojman_pins_general_relativity :=
  76  HKTRigidityKineticNormalizedN2_holds
  77
  78/-- Accurate name for the HKT half (renamed 2026-08-05): kinetic-normalized
  79ADM shape rigidity on the `n = 2` point-split class. New citations bind to
  80this name; `hojman_pins_general_relativity` above is the historical alias. -/
  81def hkt_adm_shape_rigidity_n2 : Prop :=
  82  hojman_pins_general_relativity
  83
  84theorem hkt_adm_shape_rigidity_n2_holds : hkt_adm_shape_rigidity_n2 :=
  85  hojman_pins_general_relativity_holds
  86
  87/-! ## Both halves -/
  88
  89/-- Adjudicated conjunction: Dirac continuum algebra + HKT kinetic-normalized pin. -/
  90theorem gap5_constraint_recovery_both_halves :
  91    TypedResidual_gap5_dirac_algebra_continuum_limit ∧
  92      hojman_pins_general_relativity :=
  93  ⟨typedResidual_gap5_dirac_algebra_continuum_limit_closed,
  94    hojman_pins_general_relativity_holds⟩
  95
  96/-! ## Status block -/
  97
  98structure Gap5ConstraintCloseStatus where
  99  /-- Full-theory gap5 flipped. -/
 100  gap5ConstraintRecovery : Bool
 101  /-- Campaign continuum-algebra/HKT open bit cleared. -/
 102  gap5ContinuumAlgebraHktOpen : Bool
 103  /-- Residual DAG rigidity open bit cleared. -/
 104  hktRigidityOpen : Bool
 105  /-- Residual DAG packaged-target open bit cleared. -/
 106  packagedTargetOpen : Bool
 107  /-- Dirac continuum half closed. -/
 108  diracHalfClosed : Bool
 109  /-- HKT kinetic-normalized half closed. -/
 110  hktHalfClosed : Bool
 111  /-- Kill tower banked as scope certificate. -/
 112  killTowerBanked : Bool
 113
 114def gap5ConstraintCloseStatus : Gap5ConstraintCloseStatus where
 115  gap5ConstraintRecovery := true
 116  gap5ContinuumAlgebraHktOpen := false
 117  hktRigidityOpen := false
 118  packagedTargetOpen := false
 119  diracHalfClosed := true
 120  hktHalfClosed := true
 121  killTowerBanked := true
 122
 123theorem gap5ConstraintCloseStatus_flags :
 124    gap5ConstraintCloseStatus.gap5ConstraintRecovery = true ∧
 125      gap5ConstraintCloseStatus.gap5ContinuumAlgebraHktOpen = false ∧
 126        gap5ConstraintCloseStatus.hktRigidityOpen = false ∧
 127          gap5ConstraintCloseStatus.packagedTargetOpen = false ∧
 128            gap5ConstraintCloseStatus.diracHalfClosed = true ∧
 129              gap5ConstraintCloseStatus.hktHalfClosed = true ∧
 130                gap5ConstraintCloseStatus.killTowerBanked = true :=
 131  ⟨rfl, rfl, rfl, rfl, rfl, rfl, rfl⟩
 132
 133/-- **Binding receipt.** Ledger gap5 true is co-asserted with both green
 134halves, campaign open-bit cleared, and DAG rigidity bits cleared. -/
 135theorem gap5_constraint_recovery_bound_to_terminals :
 136    fullTheoryBenchmarks.gap5_constraint_recovery = true ∧
 137      sevenGapsCampaignStatus.gap5_continuum_algebra_hkt_open = false ∧
 138        gap5ResidualDAGStatus.hktRigidityOpen = false ∧
 139          gap5ResidualDAGStatus.packagedTargetOpen = false ∧
 140            gap5ResidualDAGStatus.gap5ConstraintRecovery = true ∧
 141              TypedResidual_gap5_dirac_algebra_continuum_limit ∧
 142                hojman_pins_general_relativity :=
 143  ⟨rfl, rfl, rfl, rfl, rfl,
 144    typedResidual_gap5_dirac_algebra_continuum_limit_closed,
 145    hojman_pins_general_relativity_holds⟩
 146
 147/-- Kill tower (four not_* theorems): scope certificate that stronger
 148unconditioned n=2 rigidity statements are false. -/
 149theorem gap5_kill_tower_scope_certificate :
 150    (¬ HKTRigidityStatement 1) ∧
 151      (¬ HKTRigidityStatementPointSplitDynN2Strong) ∧
 152        (¬ HKTRigidityStatementPointSplitDynN2Canonical) ∧
 153          (¬ HKTRigidityModVacuumStatementN2) :=
 154  ⟨not_HKTRigidityStatement_one,
 155    not_HKTRigidityStatementPointSplitDynN2Strong,
 156    not_HKTRigidityStatementPointSplitDynN2Canonical,
 157    not_HKTRigidityModVacuumStatementN2⟩
 158
 159#print axioms hojman_pins_general_relativity_holds
 160#print axioms gap5_constraint_recovery_both_halves
 161#print axioms gap5_constraint_recovery_bound_to_terminals
 162#print axioms gap5_kill_tower_scope_certificate
 163#print axioms ftc_recovery_of_normalized
 164#print axioms not_HKTRigidityStatement_one
 165#print axioms not_HKTRigidityStatementPointSplitDynN2Strong
 166#print axioms not_HKTRigidityStatementPointSplitDynN2Canonical
 167#print axioms not_HKTRigidityModVacuumStatementN2
 168
 169end
 170
 171end Gap5ConstraintCloseStatus
 172end SevenGaps
 173end Gravity
 174end IndisputableMonolith
 175