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To me as a layperson from outside your theoretical field the phrasing such as "model meets the objectives", "solves objectives" and "check satisfiability while optimizing objective functions" sounds ambiguous. To me this phrasing sounds like it could mean either of the two options:
From the C API documentation and from several bug reports about non-optimal solutions I have inferred that the second interpretation is correct.
Here is my attempt to document the guarantees given by the optimizer interface
The word "optimal" sounds unambiguous to me. If something is sub-optimal than it is not optimal. The words "optimize", "optimization" and "objective" on the other hand often do not imply that the result is perfect.