How-to recipes - progenax — differentiable initial conditions for N-body simulations

Task-oriented snippets for common workflows. Each page answers one question with a runnable recipe, an inputs table, and verified output — every code block runs as-is in a Python session with progenax installed (see Installation).

Recipes

Recipe	Question it answers
Set up a virial-equilibrium cluster	How do I build a cluster in virial equilibrium ( $Q = T/\|V\| = 0.5$ )?
Fit the half-mass radius with jax.grad	How do I recover the half-mass radius $\rh$ with `jax.grad` through the IC builder?
Mix Plummer positions with King velocities	How do I compose a Plummer spatial profile with a King velocity DF?
Add a binary population	How do I add a primordial binary population with `build_binary_cluster`?