What is the speaker's claim?

The speaker's claim is that separation will not be end of
the relationship he has with his love.  The title of the poem, valediction, means a
request of a command -- to forbid mourning.  The poem was written to his wife because
while she was pregnant, he needed to travel away from her, but the poem is a reassurance
of his love for her and their love for each other.

He uses
many many metaphors to suggest the singularity and specialness of their relationship,
but the most unique comes in the last three stanzas.  Previous to this he has said:
don't make a scene when I leave; we are better than lovers who need "eyes, lips, and
hands" to maintain their love; we are like gold that can be expanded to a great degree
but doesn't break.  In the end he compares the two of them to a compass -- the kind used
to draw a perfect circle.  He explains that they are always connected in the middle, and
that she is the "fixed foot" in the center that allows him, the pencil / moving end, to
move around and do what it needs to do, but that will "end where I begun" because she is
the strong unmoved part.  His claim is not only are they joined, but they work together
in perfect harmony and one won't be right without the other.