Most cluster initial conditions are built by sampling a density profile and then
rescaling the velocities until the virial ratio looks right. progenax samples
the distribution function itself, so the cluster is in equilibrium because the
physics says so rather than because it was adjusted afterwards — and every step
stays differentiable, so birth conditions can be inferred rather than guessed.
The models themselves are standard, deliberately. What is unusual is that they are checked against analytic solutions, published tables and an established reference implementation — not against sky data — and that the gradients are audited on every public entry point rather than assumed.
The figure below comes from an experimental direction rather than the released core: coupling where a star is placed to the gas it formed in. It is worth having because it turns primordial mass segregation into something testable, and it is not yet validated.
