As one of the people responsible for writing the catalogs, I can easily explain what RIAC means by "documented" in headlines. By their nature, the headlines usually do not provide much context as to how something is "documented," but we will explain in the body of the descriptions how something is "documented" and what documentation (if any) is included.
In the case of the Moller collection, we generally mean "documented" in the sense of "published/recorded." These guns are shown and discussed, often in pretty great detail, in what are widely considered to be some of the best references for American military firearms, and many collectors are more interested in pieces that have been discussed in books, articles, etc. than the same guns but without any published information. If you Google the word documented, "record (something) in written, photographic, or other form" is the first definition that pops up. That is what we mean in this case. Here is one example from the body of the description explaining how it is documented:
This exact trade gun is pictured on page 392 of "American Military Shoulder Arms, Volume II: From the 1790s to the End of the Flintlock Period" by George Moller... Moller states, "The large-bored fusil described here is attributed to Leman's contract of April 1 or December 1, 1857. Leman attempted to inform the government that the Indians preferred smaller-bored arms, but the government insisted on this caliber. These large-bored fusils were unpopular with the Indians, and no additional large-bored arms of this type were ordered."
Some have more or less information provided by Moller for that specific item.
The guns that are from his collection but that are not featured in his books should not say documented. We'll just note they were from his collection in the provenance field and note if they have his discreet collection mark (usually right by the toe).
In other instances, we do use "documented" in the headlines to refer to what others here have suggested: a lot has some recorded provenance or history, period or otherwise. Often that documentation is included with the gun. Again, we will go on to explain what we mean and state what is included. Sometimes its a factory letter, Springfield research information, notarized family provenance, past sales receipts, the original order for the gun, letters of relevance, etc. When I'm doing research, especially on historical items, often I will use resources that were not included by the consignor as well. For example, I reference period newspaper articles often, but we rarely have original copies of these newspapers with the items. I might reference a World's Fair publication with an illustration of some fancy French exhibitions pistols, a period book or periodical that discusses the item, etc.
If you ever have any questions or concerns about something in one of our sales, please feel free to contact the company. If you want information on muzzle loading lots, you'll likely be put in touch with me, and you can always just request to speak with me. We get a lot of questions every auction and will always do our best to answer you as quickly and clearly as possible whether by phone, email, etc.