IndisputableMonolith.Gravity.MasterTheoremUnconditional

   1import IndisputableMonolith.Gravity.MasterTheorem
   2import IndisputableMonolith.Gravity.MasterTheoremHandoffIntegration
   3import IndisputableMonolith.Gravity.PageCurveDynamical
   4import IndisputableMonolith.Gravity.PageCurveOperatorEntropy
   5import IndisputableMonolith.Gravity.PageCurveNontrivial
   6import IndisputableMonolith.Gravity.PTAStructural
   7import IndisputableMonolith.Gravity.QGObservableSignalModels
   8import IndisputableMonolith.Gravity.StrongFieldStructural
   9
  10/-!
  11# Gravity: Unconditional Master-Theorem Closure Surface
  12
  13This module installs theorem-built witnesses for the five inputs that the older
  14`rs_quantum_gravity_master_conditional` theorem accepted as arguments.  The
  15conditional theorem remains the audit surface; this file supplies the canonical
  16zero-argument route through it.
  17
  18## D2 witness: physical convergence route (Session 566)
  19
  20The D2 witness was originally routed through three endpoint receipt propositions
  21from `MasterTheoremHandoffIntegration` (Track 1 single-slice, varying-
  22cardinality, and physical-D2 master-witness endpoints).  That route is retained
  23as `canonicalRegEHContinuumAndBianchiWitness_endpointRoute` for audit.
  24
  25The primary D2 witness now names the physical content directly:
  26* Regge/EH clause: for any product-filter refinement data on the canonical
  27  periodic six-tet cubic torus, the normalized full nonlinear Regge aggregate
  28  converges to the supplied continuum EH integral on the product filter.
  29* Bianchi clause: for any vertex and bond types, every Schläfli-satisfying
  30  Regge datum obeys the contracted discrete Bianchi identity at every vertex.
  31-/
  32
  33namespace IndisputableMonolith
  34namespace Gravity
  35namespace MasterTheoremUnconditional
  36
  37open Gravity.PhysicalSixTetCubicDirichletInstance
  38
  39/-! ## §0. Concrete physical D2 witness (primary route) -/
  40
  41/-- Physical D2 Regge/EH proposition: for any product-filter refinement data,
  42the full nonlinear Regge aggregate converges to the supplied continuum
  43Einstein-Hilbert/Dirichlet integral on the product filter.  This names the
  44convergence content that the Regge calculus physically requires. -/
  45def concretePhysicalRegEHContinuumProp : Prop :=
  46  ∀ {α ρ : Type} {l : Filter α}
  47    (D : CanonicalPeriodicTetSixTetVolumeQuadratureProductFilterData (α := α) (ρ := ρ) l),
  48    Track1BCPhysicalResidual.PhysicalReggeEHConcreteProductFilterTarget D
  49
  50theorem concretePhysicalRegEHContinuumProp_holds :
  51    concretePhysicalRegEHContinuumProp :=
  52  fun D => Track1BCPhysicalResidual.physicalReggeEHConcreteProductFilterTarget_holds D
  53
  54/-- Physical D2 Bianchi proposition: for any vertex and bond types, every
  55Schläfli-satisfying Regge datum obeys the contracted discrete Bianchi identity
  56at every vertex. -/
  57def concretePhysicalBianchiProp : Prop :=
  58  ∀ (V B : Type) [Fintype B],
  59    Track1BCPhysicalResidual.physicalSchlafliBianchiMasterProp V B
  60
  61theorem concretePhysicalBianchiProp_holds :
  62    concretePhysicalBianchiProp := by
  63  intro V B _
  64  exact Track1BCPhysicalResidual.physicalSchlafliBianchiMasterProp_holds V B
  65
  66/-- **Primary D2 witness for the master theorem.**  The Regge/EH clause
  67carries the physical product-filter convergence theorem; the Bianchi clause
  68carries the Schläfli-based contracted discrete Bianchi identity.  No endpoint
  69receipt indirection. -/
  70def canonicalRegEHContinuumAndBianchiWitness :
  71    MasterTheorem.RegEHContinuumAndBianchi where
  72  regge_to_einstein_hilbert_continuum := concretePhysicalRegEHContinuumProp
  73  regge_holds := concretePhysicalRegEHContinuumProp_holds
  74  discrete_bianchi_contracted := concretePhysicalBianchiProp
  75  bianchi_holds := concretePhysicalBianchiProp_holds
  76
  77/-! ## §0b. Endpoint-receipt D2 witness (audit route) -/
  78
  79/-- Endpoint-receipt D2 Regge/EH proposition: packages the proved single-slice,
  80varying-cardinality, and physical-D2 witness endpoints from Track 1.
  81Retained as an audit route; the primary route above is preferred. -/
  82def endpointRouteRegEHContinuumProp : Prop :=
  83  MasterTheoremHandoffIntegration.Track1SingleSliceProductFilterDataEndpoint.{0} ∧
  84  MasterTheoremHandoffIntegration.Track1VaryingCardinalityProductFilterDataEndpoint.{0, 0} ∧
  85  MasterTheoremHandoffIntegration.Track1PhysicalD2MasterWitnessEndpoint.{0, 0}
  86
  87theorem endpointRouteRegEHContinuumProp_holds :
  88    endpointRouteRegEHContinuumProp :=
  89  ⟨MasterTheoremHandoffIntegration.track1_single_slice_product_filter_data_endpoint_holds,
  90   MasterTheoremHandoffIntegration.track1_varying_cardinality_product_filter_data_endpoint_holds,
  91   MasterTheoremHandoffIntegration.track1_physical_d2_master_witness_endpoint_holds⟩
  92
  93/-- Endpoint-receipt D2 witness (audit route). -/
  94def canonicalRegEHContinuumAndBianchiWitness_endpointRoute :
  95    MasterTheorem.RegEHContinuumAndBianchi where
  96  regge_to_einstein_hilbert_continuum := endpointRouteRegEHContinuumProp
  97  regge_holds := endpointRouteRegEHContinuumProp_holds
  98  discrete_bianchi_contracted := concretePhysicalBianchiProp
  99  bianchi_holds := concretePhysicalBianchiProp_holds
 100
 101/-! ## §1. D3, D4, D5 witnesses (unchanged) -/
 102
 103/-- D3 proposition strengthened to include the many-body `PiTensorProduct`
 104endpoint, not only the binary physical-channel certificate. -/
 105def canonicalAmplitudeLinearManyBodyProp : Prop :=
 106  Nonempty
 107    QuantumChannel.AmplitudeLinearForced.PhysicalChannelAmplitudeLinearCert ∧
 108  Nonempty
 109    QuantumChannel.AmplitudeLinearForced.ManyBodyPhysicalChannelAmplitudeLinearCert ∧
 110  MasterTheoremHandoffIntegration.Track2ManyBodyEndpoint
 111
 112theorem canonicalAmplitudeLinearManyBodyProp_holds :
 113    canonicalAmplitudeLinearManyBodyProp :=
 114  ⟨QuantumChannel.AmplitudeLinearForced.physicalChannelAmplitudeLinearCert_inhabited,
 115   QuantumChannel.AmplitudeLinearForced.manyBodyPhysicalChannelAmplitudeLinearCert_inhabited,
 116   MasterTheoremHandoffIntegration.track2_many_body_endpoint_holds⟩
 117
 118/-- Canonical theorem-built D3 witness for the master theorem. -/
 119def canonicalAmplitudeLinearForcedWitness :
 120    MasterTheorem.AmplitudeLinearForcedUnconditional where
 121  amplitude_linear_forced_unconditional := canonicalAmplitudeLinearManyBodyProp
 122  holds := canonicalAmplitudeLinearManyBodyProp_holds
 123
 124/-- Canonical theorem-built D4 witness, strengthened to the **nontrivial**
 125Page process on `Fin 2 ⊗ Fin 2`: an arbitrary-tick-budget triangular Page
 126curve with derived (capacity-curve) entropy readout, interior peak
 127`= S_BH/2`, monotone rise before the peak, monotone fall after it, and
 128strict rise/fall across the peak.  This supersedes the degenerate
 129`Fin 1`/identity/zero-entropy witness (peer-review finding F3). -/
 130def canonicalPageCurveDerivedWitness :
 131    MasterTheorem.PageCurveDerived :=
 132  PageCurveNontrivial.nontrivialPageCurveDerivedWitness
 133
 134/-- Audit: the operator-derived Schmidt-saturated witness is still valid
 135(degenerate `Fin 1` route, retained for provenance). -/
 136def canonicalPageCurveDerivedWitness_operatorRoute :
 137    MasterTheorem.PageCurveDerived :=
 138  PageCurveOperatorEntropy.operatorPageCurveDerivedWitness
 139
 140/-- Audit: the older recognition-tick witness is still valid. -/
 141def canonicalPageCurveDerivedWitness_tickRoute :
 142    MasterTheorem.PageCurveDerived :=
 143  PageCurveDynamical.pageCurveDerivedWitness_recognitionTicks
 144
 145/-- Canonical theorem-built PTA witness, strengthened to a typed
 146observation-channel signal model with formula-level separation. -/
 147noncomputable def canonicalPTADistinctWitness :
 148    MasterTheorem.PTAStochasticGWDistinctFromInflation :=
 149  QGObservableSignalModels.ptaSignalModelWitness
 150
 151/-- Audit: the older PTA observable-band witness is still valid. -/
 152noncomputable def canonicalPTADistinctWitness_bandRoute :
 153    MasterTheorem.PTAStochasticGWDistinctFromInflation :=
 154  PTAStructural.ptaStochasticGWObservableBandWitness
 155
 156/-- Canonical theorem-built strong-field witness, strengthened to typed
 157observation-channel signal models for EHT, S-star, and Cassini.  Ringdown echo
 158algebra is quarantined in `QGObservableSignalModels` and is not consumed as a
 159closed physical strong-field witness. -/
 160noncomputable def canonicalStrongFieldDistinctWitness :
 161    MasterTheorem.StrongFieldTestsDistinctFromGR :=
 162  QGObservableSignalModels.strongFieldSignalModelWitness
 163
 164/-- Audit: the older strong-field observable channel witness is still valid. -/
 165noncomputable def canonicalStrongFieldDistinctWitness_channelRoute :
 166    MasterTheorem.StrongFieldTestsDistinctFromGR :=
 167  StrongFieldStructural.strongFieldObservableDistinctFromGRWitness
 168
 169/-! ## §2. Scoped theorem-built master assembly -/
 170
 171/-- **Scoped theorem-built quantum-gravity master assembly.**  The five formerly
 172external master inputs are supplied here by canonical theorem-built witnesses:
 173D2 physical Regge/EH product-filter convergence plus Schläfli Bianchi,
 174D3 many-body amplitude-linearity, D4 recognition-tick Page transfer,
 175D5 PTA observable band, and D5 named strong-field channels.
 176
 177This is a zero-argument Lean assembly theorem for the current witness route.
 178It is **not** a claim that the full physical quantum-gravity framework is
 179closed from primitives.  The D2 route remains scoped to the canonical
 180product-filter six-tet torus surface, the general triangulation and Lorentzian
 181causal-simplex problems remain open, and the black-hole echo mechanism is not
 182yet horizon-consistent.  See `closureStatus_unconditional` below for the
 183machine-readable physical-scope audit. -/
 184theorem rs_quantum_gravity_master_unconditional :
 185    MasterTheorem.RSQuantumGravityMaster
 186      canonicalRegEHContinuumAndBianchiWitness
 187      canonicalAmplitudeLinearForcedWitness
 188      canonicalPageCurveDerivedWitness
 189      canonicalPTADistinctWitness
 190      canonicalStrongFieldDistinctWitness :=
 191  MasterTheorem.rs_quantum_gravity_master_conditional
 192    canonicalRegEHContinuumAndBianchiWitness
 193    canonicalAmplitudeLinearForcedWitness
 194    canonicalPageCurveDerivedWitness
 195    canonicalPTADistinctWitness
 196    canonicalStrongFieldDistinctWitness
 197
 198/-! ## §3. Audit route master theorem -/
 199
 200/-- Both D2 routes produce valid master theorem outputs.  The endpoint route
 201is not dead code; it documents the Track 1 integration path. -/
 202theorem endpointRoute_master_theorem_valid :
 203    MasterTheorem.RSQuantumGravityMaster
 204      canonicalRegEHContinuumAndBianchiWitness_endpointRoute
 205      canonicalAmplitudeLinearForcedWitness
 206      canonicalPageCurveDerivedWitness
 207      canonicalPTADistinctWitness
 208      canonicalStrongFieldDistinctWitness :=
 209  MasterTheorem.rs_quantum_gravity_master_conditional
 210    canonicalRegEHContinuumAndBianchiWitness_endpointRoute
 211    canonicalAmplitudeLinearForcedWitness
 212    canonicalPageCurveDerivedWitness
 213    canonicalPTADistinctWitness
 214    canonicalStrongFieldDistinctWitness
 215
 216/-! ## §4. Physical-scope closure status -/
 217
 218/-- Honest status for the zero-argument master assembly above.
 219
 220The first field records the Lean fact: theorem-built witnesses have been
 221installed for the older conditional master theorem.  The remaining fields record
 222the physical-scope frontier that those witnesses do **not** close. -/
 223structure MasterTheoremUnconditionalClosureStatus where
 224  theorem_built_witnesses_installed : Bool
 225  full_physical_closure : Bool
 226  d2_quadrature_open : Bool
 227  general_triangulation_open : Bool
 228  tensor_tt_recovery_open : Bool
 229  lorentzian_causal_triangulations_open : Bool
 230  boundary_ghy_open : Bool
 231  echo_mechanism_open_or_rejected : Bool
 232
 233/-- The theorem-built assembly exists, but the full physical quantum-gravity
 234framework is not closed.  This record is intentionally conservative: it keeps
 235the useful master theorem available while preventing downstream papers or
 236certificates from counting scoped witnesses as complete physical recovery. -/
 237def closureStatus_unconditional : MasterTheoremUnconditionalClosureStatus where
 238  theorem_built_witnesses_installed := true
 239  full_physical_closure := false
 240  d2_quadrature_open := true
 241  general_triangulation_open := true
 242  tensor_tt_recovery_open := true
 243  lorentzian_causal_triangulations_open := true
 244  boundary_ghy_open := true
 245  echo_mechanism_open_or_rejected := true
 246
 247/-- The current zero-argument master assembly must not be cited as full
 248physical closure. -/
 249theorem closureStatus_unconditional_not_full_physical_closure :
 250    closureStatus_unconditional.theorem_built_witnesses_installed = true ∧
 251    closureStatus_unconditional.full_physical_closure = false :=
 252  ⟨rfl, rfl⟩
 253
 254/-- At least one load-bearing physical target remains open; in fact D2
 255quadrature is still open on the current scoped route. -/
 256theorem closureStatus_unconditional_has_open_target :
 257    closureStatus_unconditional.d2_quadrature_open = true ∨
 258    closureStatus_unconditional.general_triangulation_open = true ∨
 259    closureStatus_unconditional.tensor_tt_recovery_open = true ∨
 260    closureStatus_unconditional.lorentzian_causal_triangulations_open = true ∨
 261    closureStatus_unconditional.boundary_ghy_open = true ∨
 262    closureStatus_unconditional.echo_mechanism_open_or_rejected = true :=
 263  Or.inl rfl
 264
 265end MasterTheoremUnconditional
 266end Gravity
 267end IndisputableMonolith
 268