  We use the soft-collinear bootstrap to construct the 8-loop integrand for the
4-point amplitude and 4-stress-tensor correlation function in planar maximally
supersymmetric Yang-Mills theory. Both have a unique representation in terms of
planar, conformal integrands grouped according to a hidden symmetry discovered
for correlation functions. The answer we find exposes a fundamental tension
between manifest locality and planarity with manifest conformality not seen at
lower loops. For the first time, the integrand must include terms that are
finite even on-shell and terms that are divergent even off-shell (so-called
`pseudoconformal' integrals). We describe these novelties and their
consequences in this letter, and we make the full correlator and amplitude
available as part of this work's submission files to the arXiv.
