verge on/upon

:  brink, threshold

:  something that borders, limits, or bounds: such as

:  an outer margin of an object or structural part

:  to be contiguous

:  to be on the verge or border

:  to move or tend toward the horizon :  sink

:  to move or extend in some direction or toward some condition

:  to be in transition or change

:  on

:  on the surface :  on it

:  thereafter, thereon