That doesn't answer the question. Upon what subjective criteria does that statement depend?
You're offering conditions which must be satisfied in order for a city to become a capital. They don't bear on whether a city is a capital. It is the capital if it is the place where most government departments have their main offices, where the Assembly sits, where the top government officials reside, etc., which are empirical questions.Paris is the capital of France is true only within the frame of consensus or dictakt in France and among nations, historically and ongoing.
What must happen for a tree to grow 10 meters tall has no bearing on whether the tree is 10 meters tall. We can know the tree is 10 meters tall without knowing anything about how it got that tall.
Nor does your answer state what subjective criteria are involved in that statement.
You seem to be saying that many propositions are true only within a certain context. That is true, but that doesn't make them subjective; it only makes them context-dependent.
This argument really depends upon the definitions of "objective" and subjective" you are assuming. Can you spell those out?