# Argument selection

The free case eta=0 is an intrinsic degeneration. For the p, d and f partial waves ell=1,2,3, the centrifugal turning radius is sqrt(ell(ell+1)). The s-wave free case has no positive turning radius and is not included in that group. The handbook worked examples include ell=0,1,2,3 at eta=2, rho=5 as reproducibility benchmarks, not a measured or mathematically distinguished coupling. At that same reference coupling the outer turning radius is 2+sqrt(4+ell(ell+1)), intrinsic conditional on eta=2. A turning point means a zero of the coefficient in the reduced wave equation, not a stationary point of F or G. No nonzero eta is claimed physically fixed.

## Limitations

The nonzero coupling eta=2 is a documented handbook benchmark only, not established external physical demand.

## Primary references

- https://dlmf.nist.gov/33.2.E2
- https://dlmf.nist.gov/33.5
- https://dlmf.nist.gov/33.22
- https://personal.math.ubc.ca/~cbm/aands/page_543.htm

The certified argument definitions are in `selection.json`. Run `python generate.py` to verify; run `python checks.py T511` for the independent checks. Neither command writes. Earlier attachments describe historical grids and remain available for provenance.