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This was already known to be true by Heidi Howard’s research that yielded Flexible Paxos[0], Relaxed Paxos[1], and her more general thesis on Distributed consensus[2] as a whole

0 - https://fpaxos.github.io/

1 - https://dl.acm.org/doi/10.1145/3517209.3524040

2 - https://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-935.pdf

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I don't think this is correct. Heidi's work made a different observation: That you can smear quorum intersection across phases of paxos, whereas the blog post in this submission is observing that you can do bog-standard quorum intersection in a way other than just thinking about majority intersection, via algebraic/geometric structures. I believe these are generally orthogonal observations.

(Heidi's work is both deeper and more practical; this post is just a really cute observation that there's something mathematically deeper underlying the idea of intersecting quora.)

Heidi's more abstract work on generalizing consensus as grids/matrices of intersecting registers is geoemtric.

Research on quorum systems (such as the finite projective planes described in the article) dates back to the 80s.

The 70s, if you want to be pedantic (e.g. Gifford's "Weighted Voting for Replicated Data" or Thomas's "A Majority Consensus Approach to Concurrency Control for Multiple Copy Databases", both from '79).

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