ora-0096
7.1 Non-anticipation and two forms of stabilization
A UOCL algorithm is non-anticipatory when its state, probe, selection, and repair at time \(t\) factor through the presentation prefix \(T_t\). Two streams with isomorphic prefixes induce equivalent states before their first differing response.
The definition is the categorical analogue of adaptedness. It does not require a single global clock: a prefix may be a finite down-set in a partially ordered event category.
Let \(q\) be an admissible query. An execution behaviorally stabilizes on \(q\) when its answer is eventually constant up to the declared answer equivalence. It explanatorily stabilizes when, in addition, the hypothesis objects and comparison maps supporting that answer eventually lie in one coherent equivalence class.
Behavioral stabilization is analogous to predictive-state identification: the learner can answer the relevant tests without recovering a unique internal presentation. Explanatory stabilization is stronger and is needed when later transport or repair depends on the discovered construction rather than only its observed output.