eos_adamswilliamson.c: Adams-Williamson analytic density

Source under test: eos_adamswilliamson.c

Reference-pinned test: tests/test_eos_adamswilliamson.py::test_density_matches_the_closed_form_profile

Anchor: Analytical limit: rho(P) = rhos - P beta / g in closed form, with the blackbody50 PREM lower-mantle fit parameters.

Tolerance: rel 1e-12 at the surface (P = 0), 10 GPa, and the approximate core-mantle boundary pressure.

Discrimination guards: A sign-flipped compressibility shifts the 10 GPa density by more than 200 kg/m3; monotonicity under compression and the silicate density range bound the profile; SI invariance under the nondimensionalisation choice is asserted separately.

The Adams-Williamson EOS provides the static structural profile used by the native mesh. Its density is a closed-form expression, so the evaluation is pinned to rounding accuracy, with the surface limit reducing exactly to the configured surface density.