Six verification tasks for a physical application

These tasks do not add assumptions to the decision theorem. They specify how to supply its existing hypotheses.

1. Logical certificate audit.

   Deliverable: the table of Section sec:introduction, with each claimed conclusion assigned to its actual certificate.

   Limit: a failed sufficient product test is not a nonexistence theorem.

2. Physical identification freeze.

   Deliverable: the completed ledger of Section sec:identification, including exact formulas, versions, domains, and proof status.

   Acceptance condition: no required physical entry is replaced by a convenient independent mathematical choice.

3. Narrow but complete localization.

   Deliverable: an exact localized representation on arbitrary joint tests in one strictly separated characteristic patch.

   Acceptance condition: every sector meeting the patch is included, including the incidence $z=a$.

4. Complete analytic calculation.

   Deliverable: a complete expansion with a compact-uniform vanishing remainder, or a complete scale-integrability estimate.

   Limit: Route C is not required if Route A or B suffices; a branch calculation or moderate-growth bound is not a decision.

5. Correct test certificate.

   Deliverable: if divergence survives, one fixed compact joint test with a justified dominant asymptotic. Record any bounded-set or moving-witness claims separately.

   Limit: selected witness agreement is not full-kernel reconstruction.

6. Extension and admission audit.

   Deliverable: reference agreement, subtraction support, wavefront bounds, authorized corrections, normalization, overlaps, and residual projection.

   Limit: a mathematical finite part is not automatically an admitted quantum coefficient.

The next physical milestone is deliberately narrow:

For one physically frozen package on one strictly separated characteristic patch, derive an exact complete representation and prove raw convergence or fixed-test raw divergence with a compact-uniform remainder.

The supplied excerpts do not complete that milestone. The application below demonstrates the procedure for its own explicit mathematical inputs.