Smart Jeongin Filter State-Selective Serial Filtering under Support-Induced Noncommutativity

Smart Jeongin Filter is a state-selective serial filtering framework in which the ordering of multiple filters is chosen according to the input state and the quantity one wishes to suppress or preserve, rather than being fixed in advance. The central observation is that filters which commute on the full translation space may become noncommuting after finite-support or Galerkin compression, with boundary leakage generating a genuine ordering effect. The paper distinguishes two performance criteria: suppression, measuring the total residual energy, and purification, measuring the risk carried by the normalized residual state. A finite-support model demonstrates that the same pair of filters can favor different orderings under these two criteria. This motivates the Smart Jeongin Filter as an adaptive operator architecture that selects its serial ordering from the geometry of the current state. The work is presented as an independent mathematical filtering framework and does not claim a proof of the Riemann Hypothesis.