2.5 Repair is a gated transformation

The following abstract procedure makes the separation operational.

LINCS diagnose-repair-admit cycle

1. Require: Learning sketch \(\mathbb S\), candidate model \(D\), cover \(\mathcal U\), decision quotient \(\chi \), repair language \(\mathcal R\)

2. Ensure: Admitted model \(D'\), rejection, or abstention with certificate

3. Construct the typed base obstruction \(\mathcal O_0(D)=\mathcal O_{\mathbb S}(D)\) through the registered diagnostic interface

4. Lift admissible probes and construct \(\mathcal O_1(D)=\operatorname {INC}(D)=\mathcal O_{\mathbb S}(TD)\)

5. Quotient presentation-null and decision-null variation using \(\chi \)

6. Restrict the remaining obstruction over \(\mathcal U\)

7. If the cover is incomplete or the repair is unidentifiable:

9. Return: abstention with missing-support certificate

10. Generate candidate repairs \(r\in \mathcal R\) from localized obligations

11. For each candidate repairs \(r\):

12. evaluate structural, semantic, statistical, and operational blocks

13. If every required admission block passes:

15. Return: \(D'=r(D)\) with repair certificate

17. Return: rejection with failed-block certificate