CMP.11:4.5 - Return the limit with a useful continuation

State the bound, input family, access, error and cost conditions together. Indicate whether it rules out the requested budget, establishes optimality within an order, or leaves a gap.

Identify a consequential escape: restrict the input by a defensible promise, allow a weaker answer or error probability, acquire an additional observation, preprocess and retain information, use a stronger primitive, or change the representation. Determine which premise of the lower-bound argument that change removes, then construct the new procedure. Renaming the same operations does not escape the bound.

Use C.11.DUA to decide whether proving a tighter bound or obtaining additional information would change the next move. A sufficient lower bound can already justify changing the task; there is no obligation to solve a harder open complexity question first.