On the mass shell, at any boost.

A Lorentz boost carries each four-vector along its own mass shell, the curve on which its invariant interval is fixed. Four vectors are boosted from rest to rapidity 3, a Lorentz factor of ten. The ring is where each vector must land: the network's answer, then boosted. The dot is where the network puts it when the boost comes first. On the shell the two coincide, and rose is the distance when they part. The view widens as the boost grows.

ARCHON's Lie-algebraic operator is six learned coefficients on fixed generators. Its pane shows it being trained on the test's own data stream, with the equivariance error measured at every step: it stays at rounding from the first step to the last, because the property belongs to the form of the operator and holds at every value its coefficients take. LorentzNet: tie in the normal range; win over the released code at strong boosts (1,000 to 1.5 million times). The released code limits the size of its internal update, and at strong boosts that limit engages. With the limit left out, the method is exact again.