One precise remaining problem

For the fixed data and fixed profile of this paper, the remaining problem is to decide the strong raw limit of (eq:combined-seeds) on arbitrary compact joint tests meeting the characteristic region.

An affirmative quantitative result would give a distribution $T$ such that for every $L⋐U$,

A negative result would exhibit one fixed compact joint test ${\Phi }_{\ast }$, independent of $\delta$, for which the complete pairing is unbounded.

If a finite singular expansion is actually established, it may have the form

Equation (eq:possibleexpansion) is an analytic target, not an assumed expansion class or a theorem of this paper. The scale factors, complete coefficients, and remainder must be derived. No power–logarithm ansatz is imposed in advance.