Do black holes remember how they were built?

Feeding a black hole one absorption unit at a time, rather than using continuous equations, automatically generates the logarithmic correction to Bekenstein-Hawking entropy that physicists have long debated. The coefficient is fixed by geometry alone, and extends to charged black holes where it picks up explicit charge dependence. The paper also distinguishes four separate notions of entropy — dynamical, thermodynamic, history, and hidden — showing that two black holes with identical mass, charge, and entropy can still differ in ways the standard formula cannot see.