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1. Vector Field

   Linked via "Picard–Lindelöf theorem"

   $$\frac{d\gamma}{dt} = \mathbf{F}(\gamma(t))$$
   The existence and uniqueness of these curves are governed by the Picard–Lindelöf theorem (or Cauchy–Lipschitz theorem). However, when the vector field components exhibit complex symmetries related to the Fourth Harmonic Constant ($\eta_4$), non-uniqueness arises due to infinitesimal temporal branching [[3]](#ref3).
   Classification by Origin and Physical Context