IndisputableMonolith.NumberTheory.RH_From_RCL

   1import IndisputableMonolith.NumberTheory.RSPhysicalThesisFromRCL
   2import IndisputableMonolith.NumberTheory.RH_Certificate
   3import IndisputableMonolith.NumberTheory.HonestPhaseAdmissibility
   4
   5/-!
   6# Riemann Hypothesis From RCL Data
   7
   8Final assembly.  The only remaining nontrivial datum is
   9`BoundaryTransportCert`, the explicit form of the RS physical bridge that
  10transports realized annular collapse to the T1-bounded Euler ledger boundary.
  11-/
  12
  13namespace IndisputableMonolith
  14namespace NumberTheory
  15
  16/-- RH from the decomposed RCL ledger data plus boundary transport. -/
  17theorem riemann_hypothesis_from_rcl (boundary : BoundaryTransportCert) :
  18    RiemannHypothesis :=
  19  rh_full (rsPhysicalThesis_from_boundaryTransport boundary)
  20
  21/-- The final obstruction is exactly the boundary transport certificate.
  22
  23This theorem is intentionally not a proof of RH.  It records the completed
  24state of the decomposition: once `BoundaryTransportCert` is supplied, RH follows;
  25and `BoundaryTransportCert` is itself equivalent to the no-nonzero-charge core
  26exposed in `BoundaryTransport.boundaryTransportCert_iff_rh_core`. -/
  27theorem rh_from_rcl_completion_boundary :
  28    (BoundaryTransportCert → RiemannHypothesis) ∧
  29    (BoundaryTransportCert ↔
  30      (∀ sensor : DefectSensor,
  31        sensor.charge ≠ 0 → False)) := by
  32  exact ⟨riemann_hypothesis_from_rcl, boundaryTransportCert_iff_rh_core⟩
  33
  34/-- Route C completion boundary: witnessed honest-phase admissibility proves
  35the witnessed zero-free core, and that admissibility bridge is equivalent to
  36the same witnessed core. -/
  37theorem routeC_completion_boundary :
  38    (WitnessedHonestPhaseAdmissibilityBridge →
  39      ∀ sensor : WitnessedDefectSensor, sensor.charge ≠ 0 → False) ∧
  40    (WitnessedHonestPhaseAdmissibilityBridge ↔
  41      (∀ sensor : WitnessedDefectSensor, sensor.charge = 0)) := by
  42  exact ⟨direct_rh_from_witnessedAdmissibilityBridge,
  43    witnessedHonestPhaseAdmissibilityBridge_iff_rh⟩
  44
  45end NumberTheory
  46end IndisputableMonolith
  47