The question

The target is the existence of a limit

on arbitrary compact joint tests, including tests crossing the aligned-null characteristic locus $N$. The regularization is defined explicitly in Section sec:expression.

This is a fixed-kernel problem. It is distinct from constructing a continuous characteristic operator on an enlarged internal module: a cancellation for the designated source need not persist under arbitrary changes of its coefficient arrays.

A substantive physical conclusion would be one of:

1. a complete-sum Cauchy estimate;

2. an evaluated complete-sum singular expansion with a controlled remainder;

3. a fixed-test failure theorem for the specified unmodified regularization.

The present paper does not decide among these outcomes.