B0: the inherited carrier and the restriction boundary

This is the release box inherited from XIII-A: classical cancellation is Constructed; the naive coefficientwise quantum quotient is Proved obstructed; a separately constructed reduction or completion is Unresolved. We neither recompute its commutator nor modify its constraint ideal.

The endings here are attached to the selected binary problem. Constructed means that the required joint extension, normalization, and admission have actually been proved. Proved obstructed means that every candidate in a previously declared class fails a specified condition. Unresolved means that a necessary extension or compatibility theorem is missing. The last ending is not concealed by writing a formal contraction formula.