  We introduce two new graphical-level relations among possible contributions
to the four-point correlation function and scattering amplitude in planar,
maximally supersymmetric Yang-Mills theory. When combined with the rung rule,
these prove powerful enough to fully determine both functions through ten
loops. This then also yields the full five-point amplitude to eight loops and
the parity-even part to nine loops. We derive these rules, illustrate their
applications, compare their relative strengths for fixing coefficients, and
survey some of the features of the previously unknown nine and ten loop
expressions. Explicit formulae for amplitudes and correlators through ten loops
are available at: http://goo.gl/JH0yEc.
