NSE derivatives remain nonzero outside the clamped table domain

[zingale]

reproduce.cpp
reproduction-output.txt

Reviewed commit: 3ac0bda4f00da3eed0446beadfc1cd5c51b99a40

Suggested priority: Medium

Affected code: nse_tabular/nse_table.H:402-418, nse_tabular/nse_table.H:496-539, nse_tabular/nse_table.H:549-592.

Description

nse_interp() clamps temperature and density to the table bounds. Outside a bound, the returned composition is constant with respect to that coordinate. The derivative routines also clamp their interpolation coordinates, but return the boundary polynomial slope divided by the original temperature or density instead of zero. This creates an inconsistent EOS Jacobian even with default cubic interpolation.

Reproduction

Using the shipped table, cubic interpolation, and Ye=0.472:

State	Reported derivative	Centered finite difference
T=3e10, rho=1.23e9	dabar/dT=-1.456288624132152e-13	0
T=5.18e9, rho=2e10	dabar/drho=1.942508832455048e-11	0

Both finite-difference samples remain outside the relevant bound. Temperature and density units are K and g/cm³.

Expected behavior / suggested fix

Return zero for differentiation along a strictly out-of-range coordinate when values use constant extension. Specify the derivative
convention exactly on the boundary. Alternatively, reject out-of-domain evaluations consistently across value and derivative APIs.

Impact and validation: Newton iterations can visit outside the table, where these artificial composition slopes affect their co
rrections. The derivative mismatch is reproduced in output; no convergence failure is attributed specifically to this defect.