In another comment, they pointed out https://youtu.be/htYh-Tq7ZBI?si=lOmsCL2DoqUCQgh1&t=1540 https://youtu.be/htYh-Tq7ZBI?si=lOmsCL2DoqUCQgh1&t=1540 in which Fr

In another comment, they pointed out https://youtu.be/htYh-Tq7ZBI?si=lOmsCL2DoqUCQgh1&t=1540 https://youtu.be/htYh-Tq7ZBI?si=lOmsCL2DoqUCQgh1&t=1540 in which Freya did an excellent job reducing the number of axioms to 1: If you define multiplying a vector by itself to be equal to the length of the vector, squared, then everything else falls out of simple polynomial multiplication. It's quite lovely.