Compression and Loss of Recoverable Distinctions: When Different States of the World Leave the Same Record

This conceptual paper introduces Compression and Loss of Recoverable Distinctions, a structural constraint on what a record can settle. When two admissible source states require different answers to a later question but map to the same representation, no procedure using that representation alone, under the same background information, can guarantee recovering which state obtained. The constraint concerns guaranteed recovery. Probabilistic conclusions may still be warranted, and additional evidence or warranted assumptions can support an answer. A loss matters only when the later question requires the merged distinction. The paper also distinguishes this constraint from Organizational Compression, which can alter arrangement and emphasis while preserving distinctions in the underlying material. The account relates the constraint to the data processing inequality and examines two-digit year fields in the Year 2000 problem. Windowing illustrates how a background rule supplies century information, with its adequacy depending on whether the assumed date range matches the records. Part of the Generative Operations series within On Human Modeling, the paper assesses representations by whether they preserve the distinctions needed for a later question. Its framework can inform human–AI research on whether summaries retain relevant distinctions and whether subsequent answers depend on information in the representation or on additional evidence and assumptions.