ZeroInducedProxyPhysicalizationBridge

formal source

  54
  55/-- Zero-induced proxy physicalization: every strip zero of `ζ` produces a
  56sensor for which the proxy-to-physical-existence bridge holds. -/
  57def ZeroInducedProxyPhysicalizationBridge : Prop :=
  58  ∀ (ρ : ℂ), riemannZeta ρ = 0 →
  59    ∀ (hlo : 1/2 < ρ.re) (hhi : ρ.re < 1),
  60      ProxyPhysicalizationBridge (zetaDefectSensor ρ.re ⟨hlo, hhi⟩ 1)
  61
  62/-- The zero-induced proxy physicalization bridge implies the RS Physical
  63Thesis. -/
  64theorem rsPhysicalThesis_of_ZeroInducedProxyPhysicalizationBridge
  65    (bridge : ZeroInducedProxyPhysicalizationBridge) :
  66    RSPhysicalThesis := by
  67  intro ρ hzero hlo hhi
  68  exact physicallyExists_of_ProxyPhysicalizationBridge
  69    (zetaDefectSensor ρ.re ⟨hlo, hhi⟩ 1) (bridge ρ hzero hlo hhi)
  70
  71/-- Hence the full Riemann Hypothesis follows once the proxy physicalization
  72bridge is proved for the zeta-zero sensors. -/
  73theorem rh_from_ZeroInducedProxyPhysicalizationBridge
  74    (bridge : ZeroInducedProxyPhysicalizationBridge) :
  75    RiemannHypothesis :=
  76  rh_from_rs_thesis (rsPhysicalThesis_of_ZeroInducedProxyPhysicalizationBridge bridge)
  77
  78/-! ## Equivalence Theorems
  79
  80The bounded-proxy hypothesis in `ProxyPhysicalizationBridge` is
  81unconditionally proved (`EulerLedgerOntologyInterface.scalarDefectBounded`).
  82Therefore the implication collapses to its conclusion, and the bridge
  83is equivalent to `PhysicallyExists`, to `charge = 0`, and (for the
  84zeta-zero specialization) to `RSPhysicalThesis` and to `RiemannHypothesis`.
  85
  86These equivalences are the definitive reduction: the bridge proposition is
  87neither weaker nor stronger than RH — it IS RH, expressed through the