Here are some links related to Laver tables, very large cardinals, and similar areas of mathematics.
Cantor’s attic-In Cantor’s upper attic, one can explore the large cardinals from inaccessible and below to rank-into-rank and above.
Hexadecimal numbers-The hexadecimal number system is probably the best number system to use when doing Laver table computation, and it is probably the best number system to use overall.
Scott Cramer-Scott Cramer researches very large cardinals (beyond rank-into-rank) and descriptive set theory.
Patrick Dehornoy-Patrick Dehornoy has researched set theory, and self-distributive algebras, and their relation with braid groups.
Vincenzo Dimonte-Vincenzo Dimonte studies very large cardinals.
Harvey Friedman-Harvey’s Foundational Adventures: While Harvey Friedman does not study self-distributive algebras, Harvey Friedman’s research has similar philosophical implications because Harvey Friedman has worked much on using large cardinal axioms to prove theorems in more conventional mathematics.