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Theoretical analysis reveals finite-state boundaries for detectable information loss in observation models, establishing rigorous limits for asymptotic sufficiency depth and statistical stability.
This volume develops a finite-state theory for quantifying information lost under observation and for locating the first asymptotic scale at which that loss becomes detectable. It develops exact likelihood-ratio sufficiency, weak-noise asymptotic sufficiency depth, support-stratified recursion, boundary contact laws, exact model-to-signature compilation, directional polarization, and hierarchical coarse graining. Counterexamples identify the boundaries of total-variation/KL stability and interior asymptotic laws. Reproducibility software and validation materials are archived separately in Zenodo Software, version 1.0.0, DOI 10.5281/zenodo.22289467.
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Shigeo Kaneko (2026) studied this question.
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