We consider the focusing 3D quantum many-body dynamic which
models a dilute bose gas strongly confined in two spatial directions.
We assume that the microscopic pair interaction is focusing and
matches the Gross-Pitaevskii scaling condition. We carefully examine
the effects of the fine interplay between the strength of the
confining potential and the number of particles on the 3D N-body
dynamic. We overcome the difficulties generated by the attractive
interaction in 3D and establish new focusing energy estimates. We
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