> I'm not sure citation is needed to prove the origin and consequences of segregation

And I didn't ask for one. I want one on the origin of school districts. As you noted, neighborhoods were segregated. As a consequence of that, everything local was de facto segregated, but that doesn't mean you can infer that everything local has a racist origin.

For instance, since neighborhoods were segregated a neighborhood's sewers were generally only available to one race. Do you conclude that public sanitation has racist origins?