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The detail that supports the central idea of the text is: All foreigners who arrived at the port of New York underwent an investigation before being able to enter the city.

Explanation:

The text above shows how the entry into New York City was controlled and judicious. This is because there was a group of people who were not welcome in the city and for security reasons these people were not allowed to enter, since New York received a large number of foreigners who were looking for better living conditions. Sick people, or showing signs of contagious disease were not allowed. For this reason, before allowing foreigners to enter, it was necessary for everyone to go through an investigation process that proved that they had no diseases, nor that they would cause disorder, so that they could enter the city.