convergence_status() returns a short character label for programmatic
workflows that need more detail than is_converged(). A fit can report
optimizer code 0 while the likelihood geometry is degenerate (no proper
maximum or non-finite uncertainty); such fits return "degenerate" even
when multi_start selected among several starts. Fixed-effect binomial
separation, Poisson / NB2 rays with no finite MLE, and an unbounded
continuous location-scale likelihood are included in that geometry.
"boundary" marks an optimizer-converged fit with variance-component,
residual-correlation, or temporal (residual SD, OU decay, AR1 persistence)
parameters near an interpretability boundary. is_converged() and
converged() are the same plain logical: they are TRUE only for
"converged". Numeric predicates are identical in DRModels.jl
(docs/design/278-twin-convergence-status.md).