Asymptotic Sufficiency Depth, Volume II: Path-Space and Dynamical Sufficiency

This volume extends asymptotic sufficiency depth from finite static experiments to finite-horizon path laws and continuous-time jump processes. It develops finite-summary Kullback–Leibler dynamic programming with weak-noise jets, horizon–noise crossover regimes, corrected route-competition decompositions that retain route-internal information, and continuous-time Markov path decompositions into endpoint, count, sequence, timing, mark, and bridge layers. Counterexamples and scope restrictions identify where fixed-horizon, finite-route, and coarse-observation arguments cease to be uniform or sufficient. Reproducibility software and validation materials are archived separately in Zenodo Software, version 1.0.0, DOI 10.5281/zenodo.22289467.