Is there some sort of shared knowledge between ISPs that make them able to see which customer an IP has been given to, no matter which ISP the IP belongs to? I.e. is someone that is an ISP able to see which customer an IP address is assigned to, just because they are an ISP?
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No, at least not in the United States or any other country that I'm aware of - ISPs do not communicate in any way with each other about IP assignments within their space; they have the exact same visibility into another ISP's address assignments as any other member of the public.