IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.DeltaNativeStrongClosure

   1/-
   2  PrimitiveRecognitionCalculus/DeltaNativeStrongClosure.lean
   3
   4  Strong closure certificate for the Delta-native analysis program.
   5
   6  The previous modules close the individual layers: protocol reals, finite
   7  generation, certified analytic registries, F_RS and F_RS[i], calibration,
   8  prime-axis coherence, cubical geometry, quotient selection, objecthood,
   9  finite probability, finite amplitude, valid comparison, completion
  10  conservativity, finite-certificate transfer, and hard-problem audit schemas.
  11
  12  This module is the capstone. It does not add a new axiom or a new theorem
  13  family. It packages the existing theorem heads into one citeable certificate
  14  so the plan has a single Lean artifact meaning:
  15
  16    "The Delta-native interface is closed at the theorem-schema and audit-schema
  17     level; further work is problem-specific theorem content inside typed
  18     interfaces."
  19
  20  No project-local axioms. No sorry.
  21-/
  22
  23import Mathlib
  24import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.DeltaReal
  25import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.GenerableReal
  26import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.CertifiedAnalyticProtocols
  27import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.CertifiedAnalyticTransformers
  28import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.FRSCarrier
  29import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.DeltaRealCalibration
  30import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.PrimeAxisCoherence
  31import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.MultiDistinctionGeometry
  32import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.QuotientSelection
  33import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.QuotientExamples
  34import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.ObjecthoodRegistry
  35import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.DeltaProbability
  36import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.DeltaAmplitude
  37import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.FRSComplexAmplitude
  38import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.HilbertDisplayCompletion
  39import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.PhysicalOneActCalibration
  40import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.ValidComparison
  41import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.ValidComparisonExamples
  42import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.CompletionConservativity
  43import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.FiniteCertificateTransfer
  44import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.QuantizedProofMethod
  45import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.HardProblemCertificateAudits
  46import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.CubicalChainComplex
  47import IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.AllDimensionalCubicalBoundary
  48
  49namespace IndisputableMonolith
  50namespace Foundation
  51namespace PrimitiveRecognitionCalculus
  52namespace DeltaNativeStrongClosure
  53
  54open CompletionConservativity
  55
  56/-- A named proof entry in the strong closure certificate. -/
  57structure ClosureEntry where
  58  closed : Prop
  59  proof : closed
  60
  61def entryOf (p : Prop) (h : p) : ClosureEntry := ⟨p, h⟩
  62
  63/-- The full Delta-native strong closure certificate. Each field points to an
  64existing theorem head. Parameterized layers are stored as functions returning
  65closure entries. -/
  66structure StrongClosureCertificate where
  67  deltaReal : ClosureEntry
  68  generableCarrier : (ℕ → ℝ) → ClosureEntry
  69  certifiedAnalytic : CertifiedAnalyticProtocols.Registry → ClosureEntry
  70  certifiedTransformers : CertifiedAnalyticTransformers.RichRegistry → ClosureEntry
  71  frsCarrier : ClosureEntry
  72  calibration : ClosureEntry
  73  physicalCalibration : ClosureEntry
  74  primeAxis : ClosureEntry
  75  multiDistinctionGeometry : ClosureEntry
  76  cubicalTwoFace : ClosureEntry
  77  allDimensionalCubical : ClosureEntry
  78  quotientSelection : {X C : Type*} → Set (X → C) → ClosureEntry
  79  quotientEmptyExample : ClosureEntry
  80  quotientSeparatingExample : ClosureEntry
  81  quotientProjectiveExample : {State Obs : Type*} → Set (State → Obs) → State → State → ClosureEntry
  82  objecthoodTable : ClosureEntry
  83  backgroundObjectAudit : ClosureEntry
  84  displayObjectExtension : ClosureEntry
  85  finiteProbability : ℕ → ClosureEntry
  86  finiteAmplitude : ℕ → ClosureEntry
  87  complexAmplitude : ℕ → ClosureEntry
  88  frsiAmplitude : ℕ → ClosureEntry
  89  hilbertDisplay : ℕ → ClosureEntry
  90  physicalComparison :
  91    {N D E O : Type*} → ValidComparison.Bridge N D O → ValidComparison.Bridge D E O → ClosureEntry
  92  comparisonExamples : ClosureEntry
  93  completionConservativity : (N D Cert : Type*) → Completion N D Cert → ClosureEntry
  94  productCompletion :
  95    {N₁ D₁ Cert₁ N₂ D₂ Cert₂ : Type*} →
  96      Completion N₁ D₁ Cert₁ → Completion N₂ D₂ Cert₂ → (D₁ → Prop) → (D₂ → Prop) →
  97        ClosureEntry
  98  functionCompletion :
  99    Type* → {N D Cert : Type*} → Completion N D Cert → (D → Prop) → ClosureEntry
 100  finiteCertificateTransfer :
 101    {N D Cert : Type*} → (C : Completion N D Cert) → (P Obstruction : D → Prop) →
 102      ConservativeFor C P → ConservativeFor C Obstruction → ClosureEntry
 103  problemAuditReduction :
 104    {N D Cert : Type*} → QuantizedProofMethod.ProblemAudit N D Cert → ClosureEntry
 105  stubObligationReflexive : QuantizedProofMethod.ApplicationStub → ClosureEntry
 106  hardProblemAudits : ClosureEntry
 107  certifiedDisplayAudits : ClosureEntry
 108  domainSpecificAnalyticAudits : ClosureEntry
 109
 110/-- The concrete certificate assembling the closed Delta-native theorem surface. -/
 111noncomputable def strongClosureCertificate : StrongClosureCertificate where
 112  deltaReal := entryOf _ DeltaReal.Protocol.display_real_forgetful
 113  generableCarrier := fun κ => entryOf _ (GenerableReal.genField_is_operational_carrier κ)
 114  certifiedAnalytic := fun R =>
 115    entryOf _ (CertifiedAnalyticProtocols.Expr.transcendental_protocol_closure R)
 116  certifiedTransformers := fun R =>
 117    entryOf _ (CertifiedAnalyticTransformers.certified_transformer_headline R)
 118  frsCarrier := entryOf _ FRSCarrier.frs_carrier
 119  calibration := entryOf _ DeltaRealCalibration.calibration_gap_closed_by_normalized_interface
 120  physicalCalibration := entryOf _ PhysicalOneActCalibration.physical_one_act_calibration_headline
 121  primeAxis := entryOf _ PrimeAxisCoherence.prime_axis_coherence
 122  multiDistinctionGeometry := entryOf _ MultiDistinctionGeometry.multi_distinction_geometry
 123  cubicalTwoFace := entryOf _ CubicalChainComplex.finite_two_face_ledger_square_zero
 124  allDimensionalCubical := entryOf _ AllDimensionalCubicalBoundary.all_dimensional_cubical_boundary_headline
 125  quotientSelection := fun F => entryOf _ (QuotientSelection.gauge_from_indistinguishability F)
 126  quotientEmptyExample := entryOf _ QuotientExamples.empty_observable_phase_quotient
 127  quotientSeparatingExample := entryOf _ QuotientExamples.separating_gauge_family_injective
 128  quotientProjectiveExample := fun F x y => entryOf _ (QuotientExamples.projective_state_display F x y)
 129  objecthoodTable := entryOf _ ObjecthoodRegistry.objecthood_periodic_table
 130  backgroundObjectAudit := entryOf _ ObjecthoodRegistry.background_object_audit
 131  displayObjectExtension := entryOf _ ObjecthoodRegistry.display_object_extension
 132  finiteProbability := fun N => entryOf _ (DeltaProbability.delta_probability_headline N)
 133  finiteAmplitude := fun N => entryOf _ (DeltaAmplitude.delta_amplitude_headline N)
 134  complexAmplitude := fun N => entryOf _ (DeltaAmplitude.delta_complex_amplitude_headline N)
 135  frsiAmplitude := fun N => entryOf _ (FRSComplexAmplitude.frsi_amplitude_headline N)
 136  hilbertDisplay := fun N => entryOf _ (HilbertDisplayCompletion.finite_hilbert_display_headline N)
 137  physicalComparison := fun B₁ B₂ => entryOf _ (ValidComparison.valid_comparison_doctrine B₁ B₂)
 138  comparisonExamples := entryOf _ ValidComparisonExamples.valid_comparison_examples_headline
 139  completionConservativity := fun N D Cert C =>
 140    entryOf _ (CompletionConservativity.completion_conservativity_headline N D Cert C)
 141  productCompletion := fun C₁ C₂ P₁ P₂ =>
 142    entryOf _ (CompletionConservativity.product_completion_headline C₁ C₂ P₁ P₂)
 143  functionCompletion := fun I {N} {D} {Cert} (C : Completion N D Cert) (P : D → Prop) =>
 144    entryOf _ (CompletionConservativity.function_completion_headline (I := I) C P)
 145  finiteCertificateTransfer := fun C P Obstruction hP hO =>
 146    entryOf _ (FiniteCertificateTransfer.finite_certificate_transfer C P Obstruction hP hO)
 147  problemAuditReduction := fun A => entryOf _ (QuantizedProofMethod.problemAudit_finiteReduction A)
 148  stubObligationReflexive := fun s => entryOf _ (show
 149    QuantizedProofMethod.StubObligation s = QuantizedProofMethod.StubObligation s from rfl)
 150  hardProblemAudits := entryOf _ HardProblemCertificateAudits.hard_problem_certificate_audits_headline
 151  certifiedDisplayAudits := entryOf _ HardProblemCertificateAudits.certified_display_audits_headline
 152  domainSpecificAnalyticAudits := entryOf _ HardProblemCertificateAudits.domain_specific_analytic_audits_headline
 153
 154/-- **Delta-native strong closure.** The full Delta-native interface has a single
 155Lean certificate bundling every closed theorem/audit layer. -/
 156theorem delta_native_strong_closure : Nonempty StrongClosureCertificate :=
 157  ⟨strongClosureCertificate⟩
 158
 159end DeltaNativeStrongClosure
 160end PrimitiveRecognitionCalculus
 161end Foundation
 162end IndisputableMonolith
 163