A thing I didn't appreciate the first time I read Spencer-Brown's book is that he actually cites Sheffer's 01913 paper, and proves Sheffer's postulates within his system in an appendix. This situates him significantly closer to the mathematical mainstream than I had thought previously, however flawed his proof of the four-color theorem may have been.

Also, the axioms I cited above are written in his notation on his gravestone: https://en.wikipedia.org/wiki/G._Spencer-Brown#/media/File:G... but I have evidently reversed left and right in my rendering of the DNF rewrite rule above. It should be:

    ─────┐   ────┐────┐
    ─┐──┐│ → ─┐─┐│─┐─┐│
    a│bc││   a│b││a│c││

His first statement of the first axiom in the book is a little more general than the version I reproduced earlier and which is inscribed on his gravestone; rather than his "form of condensation"

    [][] = []

his "law of calling" is general idempotence, i.e.,

    AA = A

although the two statements are equipotent within the system he constructs. Similarly, before stating his "form of cancellation"

    [[]] =

he phrases it as the "law of crossing", which I interpret as

    [[A]] = A