Adaptive link dynamics drive online hate networks and their mainstream influence

Online hate is dynamic, adaptive—and may soon surge with new AI/GPT tools. Establishing how hate operates at scale is key to overcoming it. We provide insights that challenge existing policies. Rather than large social media platforms being the key drivers, waves of adaptive links across smaller platforms connect the hate user base over time, fortifying hate networks, bypassing mitigations, and extending their direct influence into the massive neighboring mainstream. Data indicates that hundreds of thousands of people globally, including children, have been exposed. We present governing equations derived from first principles and a tipping-point condition predicting future surges in content transmission. Using the U.S. Capitol attack and a 2023 mass shooting as case studies, our findings offer actionable insights and quantitative predictions down to the hourly scale. The efficacy of proposed mitigations can now be predicted using these equations.