  We extend the foliation-based quantization scheme of \cite{Park:2014tia} to
arbitrary asymptotically flat backgrounds including time- and position-
dependent ones. One of the ingredients to accomplish the extension is
imposition of a Neumann-type boundary condition. The quantization procedure,
especially the gauge-fixing-induced reduction, provides a new insight into the
black hole information paradox. The hypersurface degrees of freedom in the
asymptotic region - whose dynamics should be responsible for part of the `hair'
- and transitions among various excitations play a central role in the global
formulation of the information and proposed solution of the information
paradox. In retrospect, the quantization scheme reveals the origin of the
difficulty of the information problem: the problem's ties with the quantization
of gravity and subtle boundary dynamics as well as the multilayered techniques
required for its setup and study. We also comment on the implications of the
asymptotic symmetries for the present quantization framework.
