Refactor: establish the thermodynamics interface

[fahnab666]

Both sound-speed floor sites open-code the same mixture_err guard: s_compute_speed_of_sound in m_variables_conversion.fpp and the post-process derivation in m_derived_variables.fpp. This PR factors the test into one shared predicate, f_validate_state, a [seq] device routine with cray_inline=True, and rewires both sites to it. Each site keeps its own floor (100*sgm_eps simulation, 1.e-16_wp post-process).

The predicate is the old condition inverted, so no arithmetic changes. Diff: two source files, +21/-6. A second commit documents the interface contract in equations.md section 3.3.

This is the first step toward a multi-EOS thermodynamics interface (#1638): name the operations once, so a later EOS family adds a branch instead of editing call sites. No new physics, no new parameters, no runtime dispatch.

Correctness. Bit-identical by construction and by measurement, against a pristine clone of this repo at the branch point (782a1fd). On GPU (LLNL Tuolumne, MI300A gfx942, CCE 19.0.0, OpenMP offload): restart files byte-identical in 16/16 comparisons across 10k/40k/160k cells (2D_shockdroplet, mixture_err on, HLLC, WENO5) plus a case-optimized build, and 32/32 scaling restarts at 1/2/4/8 APUs. 170/170 1D goldens pass. Zero NaN in every scanned restart.

Performance. ./mfc.sh bench on Tuolumne, both trees run concurrently (one node each, 4 ranks x 1 APU), two passes. Grind delta, this branch vs upstream:

case	Test 1	Test 2
5eq_rk3_weno3_hll	+0.0%	-2.0%
5eq_rk3_weno3_hllc	+0.3%	+0.2%
5eq_rk3_weno3_lf	-1.0%	+1.0%
hypo_hll	+0.9%	+0.7%
ibm	+0.9%	+1.4%
igr	-1.6%	-2.0%
viscous_weno5_sgb_acoustic	-0.9%	+0.7%

Signs flip between passes, so there is no systematic trend; hllc, where the sound-speed path is hottest, sits at +0.3/+0.2%. The binary carries no separate device symbol for the predicate, so CCE inlines it on the offload path.

Scaling. Strong: 2.56M cells fixed on 1/2/4/8 APUs. Weak: 1.28M cells per APU. Grind (ns/gp/eq/RHS), lower is better: test in ns per grid point per equation per RHS, global-cell normalized:

APUs	strong upstream	strong PR	weak upstream	weak PR
1	0.9358	0.9334	1.2778	1.2856
2	0.6302	0.6371	0.6367	0.6257
4	0.4866	0.4863	0.3201	0.3190
8	0.4134	0.4188	0.1648	0.1657

Agreement within 1.7% at every point; weak efficiency at 8 APUs is 96.9% upstream, 97.0% PR. The strong-scaling solution is byte-identical across 1/2/4/8 ranks under a single hash, so the predicate introduces no rank dependence.

Chemistry. The chemistry adapter ran end to end on the machine: the build generated m_thermochem.f90 with Pyrometheus 1.1.1 from a checksum-pinned Cantera 3.2.0 h2o2.yaml, byte-identical between the two trees. The reactive shocktube (400 cells, 18,681 steps) completed NaN-free on 1 and 8 APUs with output trees matching byte for byte between trees. Golden 5DCF300C passes on GPU in both.

macOS CPU reference. M4 Pro, gfortran, Open MPI 5.0.9, double precision. Restart files byte-identical to the baseline at all three grids. 625/627 goldens; the 2 failures are known load flakes that pass in isolation with and without the change. Debug build runs the shockdroplet case with bounds checks and asserts enabled, no trip. Single-rank simulation wall time, best of two:

grid	branch	baseline	delta
200x50	2.082 s	2.120 s	-1.8%
400x100	4.520 s	4.625 s	-2.3%
800x200	14.273 s	14.210 s	+0.4%

Strong scaling on 14 cores: 91/71/53% efficiency at 2/4/8 ranks; weak: 98/99/76%. The rolloff is single-socket bandwidth saturation, identical with and without the change.

Builds checked in both trees: double, single, chemistry, case-optimized, all clean with warning profiles identical line for line. --mixed fails identically in both trees inside untouched m_derived_types.fpp (CCE 19.0.0 rejects real(kind=2)); pre-existing, unrelated to this change.

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