A computation can produce a numerical estimate, a rigorous enclosure, or a checked formal obligation. These are different kinds of evidence.
Keep the statement attached
An interval or Taylor model concerns a specified domain and represented model. A rigorous residual bound alone is not an unconditional claim about a physical system. The application must account for approximation and stability assumptions.
Check the checker
A serialized certificate or a generated proof file does not establish that a theorem prover accepted the obligation. Formal verification is a separately executed status under the documented toolchain.