Beyond Depth and Width: The Information-Slack Dilemma in Streaming Test-Time Compute

The same task and compute budget can require different reasoning policies when evidence arrives in a different order. Early computation has more time to finish but rests on incomplete or revisable evidence; waiting improves information while shrinking computational slack. We call this the information-slack dilemma. We take the evidence-dependent computational job as the unit of analysis: when to start it, what supports its result, and when that result can be committed. Advance computation is valuable only insofar as its benefits survive the costs of verification, invalidation, and recovery. This applies to grounded incremental processing and reusable preparation as well as future-dependent speculation. We propose a research agenda on computation under evolving evidence, prioritizing selective recovery under controlled evidence revisions. Evaluation should separate earlier-execution effects, deployment value against a full-input alternative, and the added value of predictive policies, while accounting for shared-resource costs. The objective is not maximal advance computation, but more trustworthy, on-time responses within a declared resource envelope.