Declaration of Intention (also called "First Papers")
The record by which an applicant for US citizenship declared their intent to become a citizen and renounced their allegiance to a foreign government. Early records of this type (before Sept 1906) usually will have: name, country of birth or allegiance (but not town), date of the application and signature. Some (but very few) show the date and port of arrival in the US. After 26 Sept 1906 much more detailed information is given including place of birth, port of emigration and date of arrival.
A Declaration of Intention (DI) normally preceded proof of residence or a petition to become a citizen by 2 or more years. Exceptions: a person who entered the country while a minor, honorable discharges, or a person married to a citizen.
Beginning with 1795 a person could declare their intent to become a citizen at any time after they arrived in the US. A few people did this almost immediately upon arrival.
The Declaration of Intention requirement ended in 1952. (although immigrants can still file a declaration if they want to - it's optional)
Land Some states had laws forbidding aliens from owning land unless they had filed a declaration of intention. Homesteaders were able to qualify for free public land after filing the declaration. The National Archives has homestead records prior to May 1, 1908 and Bureau of Land Management after that date. BLM can be accessed at: Bureau of Land Management