IndisputableMonolith.NumberTheory.BoundaryTransport

   1import IndisputableMonolith.NumberTheory.EulerCarrierRealizability
   2import IndisputableMonolith.NumberTheory.T1BoundaryExclusion
   3
   4/-!
   5# Boundary Transport
   6
   7The remaining physical bridge in the RH-from-RCL route.
   8
   9`UnifiedRH.lean` already proves that nonzero-charge realized defect families
  10have a concrete collapse scalar approaching zero.  The still-open RS physical
  11content is whether that concrete collapse transports to the T1-bounded Euler
  12realizability scalar.  This file exposes that bridge as a named certificate.
  13-/
  14
  15namespace IndisputableMonolith
  16namespace NumberTheory
  17
  18open IndisputableMonolith.Unification.UnifiedRH
  19
  20/-- Boundary transport certificate.  This is the main remaining RS physical
  21bridge: realized defect collapse must transport to the actual Euler ledger
  22boundary. -/
  23structure BoundaryTransportCert where
  24  bridge : EulerBoundaryBridgeAssumption
  25
  26/-- A boundary transport certificate is exactly the old Euler boundary bridge. -/
  27theorem boundaryTransportCert_iff_EBBA :
  28    BoundaryTransportCert ↔ EulerBoundaryBridgeAssumption := by
  29  constructor
  30  · intro h
  31    exact h.bridge
  32  · intro h
  33    exact ⟨h⟩
  34
  35/-- Boundary transport is logically equivalent to the no-nonzero-charge
  36sensor statement already identified in `UnifiedRH.lean` as the RH core. -/
  37theorem boundaryTransportCert_iff_rh_core :
  38    BoundaryTransportCert ↔
  39      (∀ sensor : DefectSensor, sensor.charge ≠ 0 → False) := by
  40  rw [boundaryTransportCert_iff_EBBA]
  41  exact EBBA_iff_rh
  42
  43/-- A boundary transport certificate gives the old divergence-witness interface. -/
  44theorem divergence_witnesses_boundary_of_cert
  45    (cert : BoundaryTransportCert) (sensor : DefectSensor) :
  46    letI : PhysicallyRealizableLedger sensor := euler_physically_realizable sensor
  47    DivergenceWitnessesBoundary sensor := by
  48  exact euler_boundary_bridge cert.bridge sensor
  49
  50/-- With boundary transport, a nonzero cost-divergent Euler sensor is impossible. -/
  51theorem no_cost_divergent_sensor_of_boundary_transport
  52    (cert : BoundaryTransportCert) (sensor : DefectSensor) :
  53    ¬ CostDivergent sensor := by
  54  letI : PhysicallyRealizableLedger sensor := euler_physically_realizable sensor
  55  letI : DivergenceWitnessesBoundary sensor := euler_boundary_bridge cert.bridge sensor
  56  exact ontological_exclusion_of_realizable sensor (euler_trace_admissible sensor)
  57
  58end NumberTheory
  59end IndisputableMonolith
  60