IndisputableMonolith.Gravity.SevenGaps.Gap2CertifiedFin8PhaseClose

   1import IndisputableMonolith.Gravity.SevenGaps.Gap2TailAutFiberParityBlocker
   2import IndisputableMonolith.Gravity.SevenGaps.Gap2TickPhaseTailBlocker
   3import IndisputableMonolith.Gravity.SevenGaps.Gap2TickPhaseSubstrate
   4import IndisputableMonolith.Gravity.SevenGaps.ZqShellBalanceBlocker
   5import IndisputableMonolith.Gravity.SevenGaps.ZqContinuumBlocker
   6
   7/-!
   8# Gap2 certified Fin-8 phase close API (uninhabited)
   9
  10Banks the provenance-honest R5 close surface after session 4B killed the
  11matching / `TailAntipodalShift` flip route
  12(`D-qg-gap2-r4-antipodal-design-20260723` /
  13`D-qg-gap2-r4-4b-complete-20260723`):
  14
  15* `CertifiedTickRecipeKind`: named recipe constructors (not a bare `∃`).
  16* `CertifiedTickRecipe`: provenance package on a Fin-8 tick (True fields
  17  bank API honesty; inhabitation of a recipe is a later session).
  18* `CertifiedGap2Fin8PhaseClose`: certified close package with escape from
  19  `ShellConstant` / `EventuallyZeroPhase` / `ShellSigTick` decoys and an
  20  `OscillatoryTail` on `tickDerivedPhase`.
  21* `TypedResidual_certified_fin8_phase_close`: nonempty package residual.
  22* Bridge: certified residual ⇒ bare continuum R5 shape
  23  (`BareR5ResidualShape` / DAG `TypedResidual_continuum_substrate_oscillatoryTail`).
  24
  25## Status
  26
  27* API banked; package **uninhabited** (no concrete recipe / close).
  28* Next inhabit target: `mixedAutMassBalancer` (aggregate antipodal
  29  tick-fiber masses; NOT class-pair `TailAntipodalShift`).
  30* Does NOT flip `gap2_continuum_and_measure`.
  31* No `sorry`, `admit`, new axiom, or `native_decide`.
  32-/
  33
  34namespace IndisputableMonolith
  35namespace Gravity
  36namespace SevenGaps
  37namespace Gap2CertifiedFin8PhaseClose
  38
  39open ExactShellGaugeUV
  40open ZqContinuumBlocker
  41open ZqShellBalanceBlocker
  42open Gap2TickPhaseSubstrate
  43open Gap2TickPhaseTailBlocker
  44open Gap2TailAutFiberParityBlocker
  45
  46noncomputable section
  47
  48/-! ## §1. Certified tick recipe (named provenance) -/
  49
  50/-- Named Fin-8 tick recipes eligible for a certified Gap2 phase close.
  51`postingHistoryForced` is the rev B plan inhabit target (H0-H7,
  52`D-qg-final-two-gates-plan-20260723`): a class tick forced by the
  53period-8 recognition-posting transaction on an attached history carrier.
  54`mixedAutMassBalancer` was the post-4B target (superseded by the posting
  55route). The other constructors are banked for future routes. -/
  56inductive CertifiedTickRecipeKind where
  57  | postingHistoryForced
  58  | mixedAutMassBalancer
  59  | canonicalGreedyDiscrepancy
  60  | selfLoopWithGlobalCorrection
  61deriving DecidableEq
  62
  63/-- Provenance package for a Fin-8 tick. The `True` fields are API-bank
  64honesty markers (not analytic content): a future inhabitation must keep
  65GlobalEquivalent-class provenance, refuse amplitude oracles, refuse
  66shellwise classical assembly, and stay tick-derived.
  67
  68**Rev B supersession (H0, `D-qg-final-two-gates-plan-20260723`):** these
  69`True` markers are NOT the flip gate. The honest gate is the typed V2
  70close `Gap2PostingHistoryContinuumResidual.PostingHistoryCertifiedCloseV2`,
  71which requires actual proofs of posting-transaction generation, history
  72gauge invariance, amplitude matching, and the decoy escapes. Any gap2
  73flip binding must cite the V2 close, never this weaker package alone. -/
  74structure CertifiedTickRecipe (tau : ∀ n : ℕ, ExactPathClass n → Fin 8) where
  75  kind : CertifiedTickRecipeKind
  76  /-- Tick descends from a GlobalEquivalent-invariant labeled recipe
  77  (or an equivalent class-level construction), not an arbitrary
  78  per-class coloring. -/
  79  globalEquivalentProvenance : True
  80  /-- Phase is not chosen by inspecting shell amplitudes. -/
  81  notAmplitudeOracle : True
  82  /-- Phase is not assembled shell-by-shell by classical cancellation
  83  search on the bare residual. -/
  84  notShellwiseClassicalAssembly : True
  85  /-- Real phase is exactly `tickDerivedPhase tau`. -/
  86  tickDerived : True
  87
  88/-! ## §2. Certified close package (uninhabited) -/
  89
  90/-- **Certified Gap2 Fin-8 phase close.** Stronger than bare continuum R5:
  91named tick recipe + decoy escapes + oscillatory tail on the derived phase.
  92
  93Uninhabited in this module. Flip path: inhabit via a named
  94`CertifiedTickRecipe`, then wire through the bare-R5 bridge into the DAG. -/
  95structure CertifiedGap2Fin8PhaseClose where
  96  tau : ∀ n : ℕ, ExactPathClass n → Fin 8
  97  provenance : CertifiedTickRecipe tau
  98  not_shellConstant : ¬ ShellConstant (tickDerivedPhase tau)
  99  not_eventuallyZero : ¬ EventuallyZeroPhase (tickDerivedPhase tau)
 100  /-- Signature-only Fin-8 coloring is a dead decoy (`ShellSigTick`). -/
 101  not_decoy : ¬ ShellSigTick tau
 102  tail : OscillatoryTail (tickDerivedPhase tau)
 103
 104/-- **OPEN residual.** Nonempty certified Fin-8 phase close. -/
 105def TypedResidual_certified_fin8_phase_close : Prop :=
 106  Nonempty CertifiedGap2Fin8PhaseClose
 107
 108/-! ## §3. Bridge to bare continuum R5 (does not inhabit) -/
 109
 110/-- Certified close discharges the bare continuum R5 residual shape
 111(`BareR5ResidualShape`, definitionally matching
 112`Gap2ContinuumMeasureResidualDAG.TypedResidual_continuum_substrate_oscillatoryTail`).
 113Does not inhabit either residual. -/
 114theorem typedResidual_continuum_substrate_oscillatoryTail_of_certified_fin8
 115    (h : TypedResidual_certified_fin8_phase_close) :
 116    BareR5ResidualShape := by
 117  obtain ⟨pack⟩ := h
 118  exact ⟨tickDerivedPhase pack.tau, pack.tail, zeroPhase_not_oscillatoryTail⟩
 119
 120/-- Alias targeting the DAG residual name (same bare shape). -/
 121theorem bare_r5_of_certified_fin8_phase_close
 122    (h : TypedResidual_certified_fin8_phase_close) :
 123    BareR5ResidualShape :=
 124  typedResidual_continuum_substrate_oscillatoryTail_of_certified_fin8 h
 125
 126/-! ## §4. Status (API banked; close OPEN; gap2 unflipped) -/
 127
 128structure Gap2CertifiedFin8PhaseCloseStatus where
 129  certifiedApiBanked : Bool
 130  recipeKindsBanked : Bool
 131  bareR5BridgeLanded : Bool
 132  certifiedResidualDefinedUninhabited : Bool
 133  certifiedCloseInhabited : Bool
 134  gap2ContinuumAndMeasure : Bool
 135
 136def gap2CertifiedFin8PhaseCloseStatus : Gap2CertifiedFin8PhaseCloseStatus where
 137  certifiedApiBanked := true
 138  recipeKindsBanked := true
 139  bareR5BridgeLanded := true
 140  certifiedResidualDefinedUninhabited := true
 141  certifiedCloseInhabited := false
 142  gap2ContinuumAndMeasure := false
 143
 144theorem gap2CertifiedFin8PhaseCloseStatus_flags :
 145    gap2CertifiedFin8PhaseCloseStatus.certifiedApiBanked = true ∧
 146      gap2CertifiedFin8PhaseCloseStatus.recipeKindsBanked = true ∧
 147      gap2CertifiedFin8PhaseCloseStatus.bareR5BridgeLanded = true ∧
 148      gap2CertifiedFin8PhaseCloseStatus.certifiedResidualDefinedUninhabited =
 149        true ∧
 150      gap2CertifiedFin8PhaseCloseStatus.certifiedCloseInhabited = false ∧
 151      gap2CertifiedFin8PhaseCloseStatus.gap2ContinuumAndMeasure = false := by
 152  decide
 153
 154end
 155
 156end Gap2CertifiedFin8PhaseClose
 157end SevenGaps
 158end Gravity
 159end IndisputableMonolith
 160