| I can solve familiar equations, but do not know which objects to use here. | State the needed consequence and choose objects by the operations or maps they must support. An observation or subject premise may still need its own inquiry. | Construct an unfamiliar account. |
| Several physical accounts fit what is known. Which difference matters for the work? | Derive their conditional consequences and construct an observation only when distinguishing them changes the next decision. | Connect physical prediction and observation. |
| Two ways of working look equivalent. Can I replace one with the other? | Identify what the replacement must preserve. Matching final values can hide a different observation, enabling condition or cost. | Understand and change a construction. |
| I must act before I know everything. What is worth finding out? | Formulate which information can reach the choice, compare the consequences still possible, and seek only information that can change the decision usefully. | Choose with incomplete information. |
| The full calculation is too expensive. What may I simplify? | Select the consequence to preserve, derive the contribution removed detail makes, and seek a replacement, approximation or sufficient bound. | Obtain a result under limits. |
| A procedure gives a value, but I need a witness, every answer or a different error guarantee. | Reconstruct the required output, retain enough intermediate information and revise only the shortcuts that relied on the old request. | Construct and change an algorithm. |
| A formula, table or diagram is changed. What should its other expressions now say? | Recover the shared references, interpretation and intended edit; retain independent information and expose a loss or conflict. | Carry meaning through different expressions. |
| A person or AI supplied an answer. Can we use, alter and extend the way it was obtained? | Recover the needed construction and its conditions, try the changed use, and identify the next useful question or missing capability. | Continue and distribute thinking. |
| A local process is faster, but its recipient still waits. What should change? | Reconstruct resource occupancy, transfer and admission rules; compute the alternatives and retain the recipient’s event boundary. | Change an operating flow. |
| A candidate behaves well in its selection trials but fails in the work it must do. What should change? | Connect the candidate to its actual execution and feedback; locate the failed information, representation, trial or changing operation and examine the resulting way in its intended use. | Develop a way to act from trials. |