person/rembrandt/7 matches the site

public static Person Rembrandt_Carried_Out()
{
    var rembrandt = new Person()
        .WithContext()
        .WithId("https://linked.art/example/person/rembrandt/7")
        .WithLabel("Rembrandt");

    var activity = new Activity()
        .WithClassifiedAs(Aat.ProfessionalActivity)
        .WithClassifiedAs(Aat.Term("300025136", "Painter"));
    activity.TimeSpan = new LinkedArtTimeSpan
    {
        BeginOfTheBegin = new LinkedArtDate(1631, 1, 1),
        EndOfTheEnd = new LinkedArtDate(1669, 10, 4).LastSecondOfDay()
    };
    rembrandt.CarriedOut = [activity];

    return rembrandt;
}

• Terms outside the registry The vocabulary registry holds only the terms linked.art itself publishes, so a dataset's own concepts, places and people are written with Aat.Term, Tgn.Place and Ulan.Person, giving the id and the label.

var person = new Person
{
    Context = ["https://linked.art/ns/v1/linked-art.json"],
    Id = "https://linked.art/example/person/rembrandt/7",
    Label = "Rembrandt",
    CarriedOut =
    [
        new Activity
        {
            ClassifiedAs = [Aat.ProfessionalActivity, Aat.Term("300025136", "Painter")],
            TimeSpan = new LinkedArtTimeSpan
            {
                BeginOfTheBegin = new LinkedArtDate(1631, 1, 1),
                EndOfTheEnd = new LinkedArtDate(1669, 10, 4, 23, 59, 59),
            },
        },
    ],
};

Generated from the object the example builds: every property that is set, as object initialisers, with the vocabulary constants where a term is in the registry. The fluent helpers are a convenience, not a requirement; this form and the one as written produce the same JSON.