Can a language model that reads the full history of an access log say whether a service may act now? On an executable benchmark of grants, withdrawals, reinstatements, expiries, groups and change windows under a known policy, scored on pairs of histories that differ only in the order or one field of the deciding events, open models of 7 to 32 billion parameters fall from 72 to 86 percent after eight or sixteen events to 48 to 55 percent after 256, while reasoning-trained 32B models reading the current state reach 96 and 98 percent. A reasoning model of 120 billion parameters trails the state by four and seven points at 256 and 512 events and by about ten at 1,024, so the length beyond which explicit state outlasts long context grows with the reader. We treat agent memory as recursive filtering. The decision depends on the history only through a state whose size is set by the number of tracked keys. A store holding fewer component records than the state forgets on a time scale set by its capacity, and a reader model predicts its accuracy within 0.02 on average in a registered test. Retaining log lines without regard to time order errs with probability approaching one half, a bound that is attained. A filter in which a model parses each line and an explicit rule applies the updates answers 80 to 89 percent at 256 events and beats relevance retrieval, model-kept ledgers, a reimplementation of StateMem and the Mem0 library. A retriever that selects at query time the lines the queried state depends on matches it at 256 events on the first domain, so what decides is selection by the state's dependencies, which the filter performs when writing, without the query. Applying parsed updates themselves, the models fall to 58 and 59 percent. A frozen replication on a second domain with fresh wording reproduces the horizon.

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