Residue Spectral Dynamics and Markov Closure in Finite Distinction Systems

Yining Wu · 2026-06-09

Formalizes the coupled residue channel framework connecting hidden unresolved modes to observable dynamics via memory kernels. Defines the residue channel triple (excitation, evolution, return), residue qualification hierarchy, active residue quotient, spectral and residue recoverability, and operational residue rank. Provides exponential-stability closure bounds, marginal-mode obstruction, spectral-edge asymptotics, finite-window Hankel significance, and balanced-truncation certificates. Completes P3-P4-P5-P6-P7-P8 residue bridge sequence: environmental forgetting, anti-recurrence, deficit-ledger, throughput bounds, topological protection, spectral-dynamical Markov closure.

@misc{wu2026fdsp8,
  author = {Yining Wu},
  title = {Residue Spectral Dynamics and Markov Closure in Finite Distinction Systems},
  year = {2026},
  doi = {10.5281/zenodo.20611696},
}