  We prove that ancient non-negative solutions to a fully anisotropic prototype
evolution equation are constant if they satisfy a condition of finite speed of
propagation and if they are both one-sided bounded, and bounded in space at a
single time level. A similar statement is valid when the bound is given at a
single space point. As a general paradigm, H\"older estimates provide the
basics for rigidity. Finally, we show that recent intrinsic Harnack estimates
can be improved to a Harnack inequality valid for non-intrinsic times. Locally,
they are equivalent.
