  Online hate is dynamic, adaptive -- and is now surging armed with AI/GPT
tools. Its consequences include personal traumas, child sex abuse and violent
mass attacks. Overcoming it will require knowing how it operates at scale. Here
we present this missing science and show that it contradicts current thinking.
Waves of adaptive links connect the hate user base over time across a sea of
smaller platforms, allowing hate networks to steadily strengthen, bypass
mitigations, and increase their direct influence on the massive neighboring
mainstream. The data suggests 1 in 10 of the global population have recently
been exposed, including children. We provide governing dynamical equations
derived from first principles. A tipping-point condition predicts more frequent
future surges in content transmission. Using the U.S. Capitol attack and a 2023
mass shooting as illustrations, we show our findings provide abiding insights
and quantitative predictions down to the hourly scale. The expected impacts of
proposed mitigations can now be reliably predicted for the first time.
