ZeroCompositionWitness

formal source

  83    exact (zeroCompositionLaw_forces_unique_minimum zc (zeroDeviation ρ)).mpr hz
  84
  85/-- A concrete Vector C witness at a specific complex point. -/
  86structure ZeroCompositionWitness (ρ : ℂ) where
  87  law : ZeroCompositionLaw
  88  value_at_deviation : law.H (zeroDeviation ρ) = 1
  89
  90/-- Any such witness forces the corresponding point onto the critical line. -/
  91theorem zeroCompositionWitness_forces_on_critical_line
  92    {ρ : ℂ} (w : ZeroCompositionWitness ρ) :
  93    OnCriticalLine ρ :=
  94  (zeroCompositionLaw_forces_eta_zero w.law ρ).mp w.value_at_deviation
  95
  96/-- Therefore the zero-location defect must vanish there as well. -/
  97theorem zeroCompositionWitness_forces_zero_defect
  98    {ρ : ℂ} (w : ZeroCompositionWitness ρ) :
  99    zeroDefect ρ = 0 := by
 100  exact (zeroDefect_zero_iff_on_critical_line ρ).mpr
 101    (zeroCompositionWitness_forces_on_critical_line w)
 102
 103end
 104
 105end NumberTheory
 106end IndisputableMonolith