Conclusions and remaining admission obligations

The retained estimate is an analytic advance at the level of moderate growth. It is not the missing smoothing-uniform estimate or a proof that the family converges.

The prospective admission statement remains

with normalization

To obtain it one still needs a full characteristic construction, its joint section and complete remainder, appropriate uniform transverse estimates, contact gluing, the actual global output theorem, and normalization.

The historical I3/J2 full-map problem therefore remains unresolved. No nonexistence theorem for every admissible composition is proved. XV-B's downstream admission exit is not opened by these partial results.

The VII interface and reflection-triangle constructions, the V–VII-B linear-current bridge, and the separate prepared-source programmes are not premises replacing these graph obligations.