PHY.5:4.5 - Judge the influence on the requested answer

Follow the approximation through to the actual output. A small state error can grow under differentiation, accumulation, feedback or a sensitive later choice. MATH.20 supplies bounds. If the consequence is obtained in another mathematical account, C.29.1 establishes what transfers between the accounts.

Examine conditions suggested by the construction itself. An omitted initial transient matters when the reading moves into it. A spatial approximation becomes suspect when the wavelength approaches the unresolved structure. A weak loss can determine a resonant response. A nearly unstable mode can defeat the earlier time-scale separation. Use the conditions that affect the proposed account.

For a statistical description, compare the statistic the work uses. Preserving an average response need not preserve a variance or a transition probability. In thermal motion, eliminating velocity while retaining random forcing can preserve long-time displacement statistics. Deleting that forcing gives a different result.

A derivation, an existing limiting result or a suitable comparison can settle the choice. If a physical premise remains unresolved, identify a feasible change of preparation or readout for which the plausible accounts give different useful answers. Obtain that comparison when its possible outcomes warrant the effort. A conditional physical conclusion can remain useful while a stronger claim is unresolved.