I knew I recognized that name, nice to see you here Thomas, I love XOR filters! In fact I was thinking about writing a blog post (series) about random linear coding, fountain codes, XOR filters and ribbon filters...
You know, looking at figure 2 and 3 I was thinking so sure it is a mapping structure but really looks like a tiny tiny database! I had no idea phfs were so involved structurally. Reminds me of delicate tiny clockworks.