Final answer:
The provided references do not explicitly state the minimum remaining months of obligated service required as of July 1st for Naval Academy appointments. Current requirements should be verified through official Naval Academy or military sources.
Step-by-step explanation:
The answer to the question regarding service members offered an appointment to the Naval Academy is not explicitly stated in the provided references. Typically, requirements for appointments to the service academies may include a minimum period of obligated service, but specifics can vary by year and by the policies of each service branch. Since the exact answer is not provided in the references and may change with time, it would be advisable for interested parties to consult the latest official guidance from the Naval Academy or their branch's personnel administration to get the accurate and current requirement for obligated service.