How does energy-as-activity relate to ordinary physical energy?

In the model, energy is proposed to be the flux of causal edges through a spacelike slice — loosely, how much rewriting activity is happening in a region. That gives you a number, but the model does not yet show it becomes the energy of textbook physics: no one has demonstrated that this edge-count turns, in a continuum limit, into energy measured in joules with the right factors of c. So it is a candidate definition awaiting that demonstration, not a derivation of ordinary energy.