set/exhset/1 matches the site

public static Set Exhibition_Objects()
{
    var set = new Set()
        .WithContext()
        .WithId("https://linked.art/example/set/exhset/1")
        .WithLabel("Exhibition objects")
        .WithClassifiedAs(Aat.Term("300378926", "Exhibition Collection"));

    set.IdentifiedBy = [new Name("Objects in Manet and Modern Beauty").AsPrimaryName()];

    set.ReferredToBy = [
        new LinguisticObject()
            .WithClassifiedAs(Aat.Description, Aat.Statement)
            .WithContent("Objects in the exhibition Manet and Modern Beauty at the Art Institute of Chicago and the Getty Museum")
    ];

    set.CreatedBy = new Creation()
    {
        TimeSpan = new LinkedArtTimeSpan
        {
            BeginOfTheBegin = new LinkedArtDate(2019, 5, 1),
            EndOfTheEnd = new LinkedArtDate(2019, 5, 1).EndOfDay()
        }
    };

    return set;
}

• Metatype classification The second argument classifies the first, not the object: WithClassifiedAs(Aat.Description, Aat.Statement) says this is a Description, and Description is a kind of Statement. The Plain C# form shows the nesting.
• Role shortcuts AsPrimaryName, AsAccessionNumber and AsSystemAssignedNumber each add a single classification, with the AAT terms Primary Name, Accession Number and System Number.
• 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 set = new Set
{
    Context = ["https://linked.art/ns/v1/linked-art.json"],
    Id = "https://linked.art/example/set/exhset/1",
    Label = "Exhibition objects",
    ClassifiedAs = [Aat.Term("300378926", "Exhibition Collection")],
    IdentifiedBy =
    [
        new Name("Objects in Manet and Modern Beauty")
        {
            ClassifiedAs = [Aat.PrimaryName],
        },
    ],
    ReferredToBy =
    [
        new LinguisticObject
        {
            Content = "Objects in the exhibition Manet and Modern Beauty at the Art Institute of Chicago and the Getty Museum",
            ClassifiedAs =
            [
                new Type("http://vocab.getty.edu/aat/300435416", "Description")
                {
                    ClassifiedAs = [Aat.Statement],
                },
            ],
        },
    ],
    CreatedBy = new Creation
    {
        TimeSpan = new LinkedArtTimeSpan
        {
            BeginOfTheBegin = new LinkedArtDate(2019, 5, 1),
            EndOfTheEnd = new LinkedArtDate(2019, 5, 1, 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.