This profound statement is the basis of hypothetico-deductive science. Theories form a logical structure, that suggests hypotheses, or empirical observables. These observations indirectly support the entire logical structure here and there, like the legs of a conference table support the top. The theories are analytical, the hypotheses are synthetic.

This is somewhat correct, but also highly misleading at the same time. Physics (which is the only science being discussed, and not “geography and history , or even pure mathematics”), is not always “rearranged” to suit the convenience of the observers. Perhaps the number of planets is no longer 9. But Galilean physics is still subsumed under Newtonian physics, which is subsumed under Einsteinian Physics, which is largely subsumed under quantum field theories, which might someday be subsumed under some Theory of Something-or-another.

It is misleading to the layman but not to the physicists! The layman sees the statements of mathematical physics translated into common language and discussed out of context. The mathematical equations explicitely or implicitely give rise to hypotheses only in a specific domain of observation, such as level of energy or magnification.

??? How does this follow? I have no trouble telling the difference between a mathematical theory and a specific observable prediction that is consistent with that theory: E=mc2 versus a nuclear bomb; quantum theory versus a transistor.