The question, the endings, and the copied handoff

The three endings are Constructed, Proved obstructed, and Unresolved. They apply to the named problem, not to every possible completion. A missing map is not a no-go. A nonzero variation of a specified classical lift is not removed by subsequently reducing the parameter space.

The closed chain is

The remaining question is whether the auxiliary row of that coefficient vanishes on the gauge-fixed free shell under the copied causal plateau condition.