  New lower bounds on the unknotting number of a knot are constructed from the
classical knot signature function. These bounds can be twice as strong as
previously known signature bounds. They can also be stronger than known bounds
arising from Heegaard Floer and Khovanov homology. Results include new bounds
on the Gordian distance between knots and information about four-dimensional
knot invariants. By considering a related non-balanced signature function,
bounds on the unknotting number of slice knots are constructed; these are
related to the property of double-sliceness.
