Dedupe redundant cp dot_product in EqSolver post-processing

[djkees]

Summary

Fixes the duplicate dot_product(soln%thermo%cp, soln%nj) calls in source/equilibrium.f90 identified in djkees#30. Same arguments, nothing mutates them in between, so each site computed the identical value twice.

Changes

• EqPartials_compute_partials: computes the dot product once into a local cp_dot_nj and reuses it for self%cp_eq and soln%cp_fr.
• EqSolver_post_process: the two guarded assignments (cp_fr < 1e-10, and cp_eq < 1e-10 .and. .not. computed_partials_) are independent conditions, so hoisting the dot product unconditionally would have computed it even when neither branch needs it — a common case in practice, since compute_partials already sets both fields before post_process runs whenever partials/transport are requested. Instead, both guards are evaluated into need_cp_fr/need_cp_eq locals, the dot product is computed once only if either is true, and reused in both branches. This preserves the exact original skip/compute behavior while deduping the common "both true" case (a fresh solve with no partials requested).

Testing

• cmake --build build-dev — clean build, no new warnings.
• ctest --test-dir build-dev --output-on-failure — 15/15 passed.
• python -m pytest source/bind/python/tests -q — 115/115 passed (114 existing + 1 new regression test).
• python test/main_interface/test_main.py — 14/14 passed (byte-comparison against reference .out files across equilibrium, rocket, shock, and detonation examples).

Added test_reused_eqsolution_cp_matches_fresh to source/bind/python/tests/test_reuse_solution.py, following the existing test_issue42_reused_eqsolution_matches_fresh pattern: it solves into a reused EqSolution twice (so cp_fr/cp_eq carry stale values from the first solve into the second solve's guards) and checks the result matches a fresh solve — directly exercising the guard logic touched by this change.

Compatibility / Numerical behavior

• No expected changes to numerical results

Same summation, same order, bitwise-identical result by construction — this only removes a redundant recomputation, it does not change what gets computed or in what order.

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Drafted with Claude's assistance

• Both duplicate-computation sites were confirmed by direct read of EqPartials_compute_partials and EqSolver_post_process, checking nothing mutates soln%thermo%cp/soln%nj between the duplicate calls (per the linked issue).
• Verified the post_process guard refactor preserves real-world skip behavior by instrumenting the guard with a debug print, rebuilding, and tracing actual need_cp_fr/need_cp_eq values through a reused-EqSolution scenario before removing the instrumentation.
• Full local build + test suite rerun (Fortran ctest, Python pytest, and the legacy CLI byte-comparison suite) confirmed identical results before and after the change, as detailed in Testing above.