21.2 Six recurring patterns

Factorization before scalarization.

State what must compose before choosing how failure will be measured.

Probe semantics before differentiation.

Specify what a tangent direction means in the domain. Automatic differentiation is one implementation, not the definition of a meaningful probe.

Quotient before repair.

Remove gauge, presentation, and decision-null variation before assigning repair effort.

Complete localization before blame.

Local witnesses justify component-level diagnosis only relative to a cover that can reconstruct the declared global failure.

Typed repair before optimization.

The correction space should encode what the system is allowed to change.

Blockwise admission before deployment.

Structural improvement, semantic preservation, statistical support, and operational feasibility should remain separately auditable.