Why is it theoretically impossible to guarantee CA without P?

In computability theory and complexity theory, there exists a class of problems for which it is impossible to guarantee the correct termination of an algorithm (CA — Correctness Assurance) without knowledge of all input data (P — Problem input). This is because, without complete knowledge of the problem parameters, it is impossible to verify all options and ensure the correctness of the result.

For example, in the context of Java and programming, if you have an algorithm that must guarantee the correctness of the result for all possible input data, but you do not have access to this data (P), then it is impossible to ensure CA. This is related to fundamental limitations, similar to the halting problem: without information about the input data, it is impossible to predict the behavior of the program in all cases.