`ProxyPhysicalizationBridge`

definition

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module: IndisputableMonolith.NumberTheory.ProxyPhysicalizationBridge
domain: NumberTheory
line: 38 · github
papers citing: none yet

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IndisputableMonolith.NumberTheory.ProxyPhysicalizationBridge on GitHub at line 38.

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formal source

  35/-- The remaining sensor-level bridge: the bounded T1-defect of the
  36realizability proxy coming from the concrete Euler-ledger ontology package
  37must imply `PhysicallyExists` for the same sensor. -/
  38def ProxyPhysicalizationBridge (sensor : DefectSensor) : Prop :=
  39  let pkg := concreteEulerLedgerOntologyInterface sensor
  40  letI : PhysicallyRealizableLedger sensor := pkg.realizableProxy
  41  (∃ K : ℝ, ∀ N : ℕ,
  42    IndisputableMonolith.Foundation.LawOfExistence.defect
  43      (PhysicallyRealizableLedger.scalarState (sensor := sensor) N) ≤ K) →
  44    PhysicallyExists sensor
  45
  46/-- If the proxy physicalization bridge holds for a sensor, then the concrete
  47Euler-ledger ontology package yields `PhysicallyExists` for that sensor. -/
  48theorem physicallyExists_of_ProxyPhysicalizationBridge
  49    (sensor : DefectSensor) (bridge : ProxyPhysicalizationBridge sensor) :
  50    PhysicallyExists sensor := by
  51  let pkg := concreteEulerLedgerOntologyInterface sensor
  52  letI : PhysicallyRealizableLedger sensor := pkg.realizableProxy
  53  exact bridge (EulerLedgerOntologyInterface.scalarDefectBounded pkg)
  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

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