IndisputableMonolith.Gravity.SevenGaps.WickActionV2CloseStatus

   1import IndisputableMonolith.Gravity.SevenGaps.WickActionCertFamilyAssembly
   2import IndisputableMonolith.Gravity.SevenGaps.FullTheoryLedger
   3import IndisputableMonolith.Gravity.SevenGaps.CampaignLedger
   4import IndisputableMonolith.Gravity.SevenGaps.CausalSimplex4D
   5
   6/-!
   7# Wave C4 F3: gap6 V2 close status / binding receipt
   8
   9Downstream of `FullTheoryLedger` and `WickActionCertFamilyAssembly` so the
  10ledger Bool flip cannot create an import cycle. Binding theorems tie
  11
  12* `fullTheoryBenchmarks.gap6_lorentzian_action = true`
  13* `sevenGapsCampaignStatus.gap6_action_continuation_open = false`
  14* `causalSimplex4DStatus.action_level_continuation_open = false`
  15
  16to the green terminal `wick_action_continuation_4d_v2_holds`, and record
  17V1 retirement `not_wick_action_continuation_4d` beside it.
  18
  19Kinematical half (`CausalSimplex4D` class/cm4/negativity) was already
  20green; this module certifies the action-continuation half closes with it.
  21-/
  22
  23namespace IndisputableMonolith
  24namespace Gravity
  25namespace SevenGaps
  26namespace WickActionV2CloseStatus
  27
  28open FullTheoryLedger
  29open CampaignLedger
  30open CausalSimplex4D
  31open WickActionInteriorHinge
  32
  33structure Gap6V2CloseStatus where
  34  /-- Full-theory gap6 flipped. -/
  35  gap6LorentzianAction : Bool
  36  /-- Campaign action-continuation open bit cleared. -/
  37  gap6ActionContinuationOpen : Bool
  38  /-- CausalSimplex4D action-level open bit cleared. -/
  39  actionLevelContinuationOpen : Bool
  40  /-- V2 terminal inhabited. -/
  41  terminalV2Closed : Bool
  42  /-- V1 terminal retired (proved unsatisfiable). -/
  43  terminalV1Retired : Bool
  44  /-- Kinematical half still certified. -/
  45  kinematicalWickCertified : Bool
  46
  47def gap6V2CloseStatus : Gap6V2CloseStatus where
  48  gap6LorentzianAction := true
  49  gap6ActionContinuationOpen := false
  50  actionLevelContinuationOpen := false
  51  terminalV2Closed := true
  52  terminalV1Retired := true
  53  kinematicalWickCertified := true
  54
  55/-- Flag-block documentation (by `rfl`). -/
  56theorem gap6V2CloseStatus_flags :
  57    gap6V2CloseStatus.gap6LorentzianAction = true ∧
  58      gap6V2CloseStatus.gap6ActionContinuationOpen = false ∧
  59        gap6V2CloseStatus.actionLevelContinuationOpen = false ∧
  60          gap6V2CloseStatus.terminalV2Closed = true ∧
  61            gap6V2CloseStatus.terminalV1Retired = true ∧
  62              gap6V2CloseStatus.kinematicalWickCertified = true :=
  63  ⟨rfl, rfl, rfl, rfl, rfl, rfl⟩
  64
  65/-- **Binding receipt.** Ledger gap6 true is co-asserted with the green
  66V2 terminal (and V1 retirement). Cannot silently drift from the closer. -/
  67theorem gap6_lorentzian_action_bound_to_v2 :
  68    fullTheoryBenchmarks.gap6_lorentzian_action = true ∧
  69      sevenGapsCampaignStatus.gap6_action_continuation_open = false ∧
  70        causalSimplex4DStatus.action_level_continuation_open = false ∧
  71          sevenGapsCampaignStatus.gap6_kinematical_wick_certified = true ∧
  72            wick_action_continuation_4d_v2 ∧
  73              (¬ wick_action_continuation_4d) :=
  74  ⟨rfl, rfl, rfl, rfl, wick_action_continuation_4d_v2_holds,
  75    not_wick_action_continuation_4d⟩
  76
  77/-- CausalSimplex4D kinematical half remains green beside the action close. -/
  78theorem gap6_both_halves_green :
  79    causalSimplex4DStatus.four_d_classes_defined = true ∧
  80      causalSimplex4DStatus.cm4_thresholds_certified = true ∧
  81        causalSimplex4DStatus.lorentzian_cm4_negativity_proved = true ∧
  82          causalSimplex4DStatus.action_level_continuation_open = false ∧
  83            wick_action_continuation_4d_v2 :=
  84  ⟨rfl, rfl, rfl, rfl, wick_action_continuation_4d_v2_holds⟩
  85
  86end WickActionV2CloseStatus
  87end SevenGaps
  88end Gravity
  89end IndisputableMonolith
  90