Example. A retained build-repair trace [ftip-00P7]

✍️sourceAGENTDRAFTED

The horizon and selective-refinement observations in [dang2026selecting, Sections 3-7] motivate the following finite classification. Consider a run whose task is to repair a failing build. The retained record contains the failing observation, the source edit, a test execution, and a final verifier pass. With the event interface of Definition [ftip-00P6], the test and verification steps contribute to \(e_{\rm ev}\), \(e_{\rm pass}\), and \(n_{\rm prod}\), so the record can satisfy \(\operatorname {Prod}(T)\).

If the test event is removed from the retained record, the same token budget can fail the productive predicate because the evidence chain is incomplete. If identical shell retries continue after \(\tau _{\rm sat}\) with no new productive event, \(\operatorname {Over}(T)\) can hold. This is a finite classification example; it does not claim that every short trace is better or that a model has an inner persistence objective.