OK, I'm trying to get a mental picture of how the Land Office did business in the mid- to late- 19th century. I'm not so much looking for a specific record of a claim, as trying to get a miner's eye view of how this all worked.
What I have so far is that miners would rush into an area based on a strike, or rumors of a strike, or possibility of a strike. They formed ad hoc 'Mining Districts' that create by-laws about how much land you can claim and how it should be marked to prevent 'claim-jumping'. The first ones in 1849 in California are based on Mexican laws, because that was the guideline they had. The miners elect one of their number to be the Recorder of the mining district, and he keeps track of the claims. This custom becomes de facto standard practice across the West.
1872, Congress passes the General Mining Act, combining two previous acts, and regularizing the customs of the miners in the West, who until that time were basically squatting on Federal territory. In this act, there's a discussion of the General Land Office, and in Section 12 of the act, we see
"each applicant shall file with the register a sworn statement of all charges and fees paid by said applicant for publication and surveys, Applicant to together with all fees and money paid the register and the receiver of the land-office, which statement shall be transmitted, with the other papers in the case, to the commissioner of the general land office."
Now, when I started poking into the land office records, I see that for instance in Utah, there are a mix of County Recorders and Mining District Recorders whose records are now held by the State Archival Service. So who is this Register and receiver of the land-office? Are they agents hired by the General Land Office who take over the previous records of the ad-hoc districts? Are they still elected by miners? Do they function alongside the Mining District Recorders?
The follow-up question to this is were these records considered public in the way that, for instance, I can look up who owns such-and-such property in my county today? Could a person walk into the local land office and ask "Who owns this plat" or "Where is John Smith's claim located?" I presume an officer of a court or a sheriff could do so in performance of their duties, but could a typical citizen?