The complete-pairing specification and status ledger

Verify the inherited coordinate-field construction on the real cosine and sine response family and its required sums. Prove that its polarization and complexification give the same field used by the independently constructed candidate, if that identification is claimed.

State the exact source space, zero-data prescription, and cutoff-independence or operator-domain theorem used. A compact final observation test does not by itself make the coordinate forcing a compact-interior source.

Status: Unresolved.

Resolve the residual comparison reported in XVI-F-v2. Specify whether the inherited advanced symbol on the boundary-flat class denotes the independently constructed smooth zero-final-data field.

Prove equality of the required pairings if it follows. Do not infer equality from their separate rapid decay, and do not infer inequality from their different definitions.

Status: Unresolved.

Specify the actual observable to be compared with XI-G, its compact kernel $w_D$, its slot structure and symmetry, and the free-shell pairing.

Evaluate whether $w_D-w_0\in {\mathcal{I}}_{\mathrm{sol}}$. Apply Proposition prop:transfer only after that comparison. A different-class result would not, by itself, discharge admission.

Status: Unresolved.

After the actual evaluation is defined and identified, establish its required high-frequency estimate with the complete tensor and branch summation retained.

State whether the scalar test is fixed or frequency dependent, which constants are uniform, and which kernel wavefront or admission conclusion is sought. The fixed-data estimates for $Q_{\lambda }$ and $I_{\mathrm{cand}}$ are not substituted for that conclusion.

Status: Unresolved.

These are compatibility and construction obligations, not proved obstructions. They do not discharge XVI-A's retarded-product obligations 4–6.