MATH.13:4.5 - Return a failed symmetry to its decisive premise

When the comparison in :4.2 fails, identify what changed: an allowed candidate, supplied datum, criterion, output meaning or modeled law. Use that difference to revise the symmetry claim or the problem formulation.

An approximate symmetry can still help, but the allowed discrepancy must be related to the requested result. Establish the bound needed by that use. Small-looking changes are insufficient when they reverse a selection or destroy uniqueness.

After obtaining the consequence, continue with the reduced calculation, transferred solution or revised requirement. Stop when it answers the current question. Add observations or input distinctions only when they can resolve the remaining choice; C.11.DUA supplies the cost-sensitive decision about further work.