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Sort unordered symbolic and code-generation collections before they affect emitted JIT C source. This prevents Python hash-randomized set/dict iteration from producing different source text on different MPI ranks. Preserve PETSc field ordering by sorting mesh variables by field_id before applying stable tie-breakers, then use deterministic ordering for constant extraction, free-symbol processing, UWexpression atom traversal, generated include headers, library directories, and library names. Add focused regression tests for the stable ordering helper, including field_id precedence and unordered symbol-container ordering. Validation: py_compile passed for _jitextension.py; tests/test_jit_deterministic_ordering.py passed; tests/test_jit_cache.py passed; Kramer spherical free-slip case2 cellsize 1/8 completed on 8 MPI ranks without PYTHONHASHSEED=0.
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Summary
This PR makes UW3 JIT source generation deterministic across MPI ranks by applying stable ordering when collecting symbols, constants, mesh variables, generated includes, and setup metadata.
Motivation
Some parallel runs can generate rank-dependent C source ordering from unordered Python collections. That can trigger JIT hash mismatches even when the mathematical expression is identical on all ranks.
Changes
field_idwhen sorting mesh variables.Validation
./uw python -m pytest tests/test_jit_deterministic_ordering.py tests/test_jit_cache.py -qPYTHONHASHSEED=0.Scope
This should not change solver mathematics. It only makes generated JIT source ordering stable across ranks.