Hi Goldlane, and welcome!
I am so glad that you are taking the time to research this, that's the right thing to do! Everyone has given solid advice and you're on the right track. Still a few things to iron out. I'm not familiar with the Ark or I would be able to have answered some of your earlier questions which others graciously have.
To clarify a couple of things that you just posted...
"I called the blm office and left a message now waiting to hear more news on if it's claimed or not. I thought blm meant that the land was government and open to public?"BLM designated land is indeed public land. It is owned by We The People and the BLM is assigned to manage it under the Dept Of Interior. Anyone may stake a claim on BLM managed lands through due discovery and staking process (generally speaking as there are a few exceptions). I currently own and work two claims on BLM designated/managed land. People may still recreate on this land but I 'own' the mineral rights on this 40 acres. BLM does not "own" the land, they are a "bureau" created to "manage" it. Technically they work for us and are paid by our tax dollars.
One critical thing you will want to be looking for when exploring new areas with potential claims is actual hand-drawn map(s) of any claims that you are in fear of trespassing. Every claim has such a map, it is required during the staking/filing process. These maps also must include a written description of the location of discovery along with boundary marker directions. Sometimes in the form of GPS coords but most often not. There are three sources for these specific maps. 1. Claim Owner, 2. County Clerk/Recorder, and 3. Main BLM Public Room in Lakewood. There is not an app or online resource for the hand-drawn map unless offered by specific counties typically for a fee. Most counties do not offer this service, visit required.
Mining claim owners are not required to post signage. Mining claims are required to post Discovery Marker and Boundary Markers upon staking.... HOWEVER.... these markers are not required to be maintained by the claim owner after that. That means if they are damaged by nature, fire, flood, vandalism, or whatever... the claim owner's rights are still protected since the whereabouts of these markers are always on file in the three location I stated. Not many claim owners bother to surround their 20 acres or more with signage. Most use no signage at all. It's the sole responsibility of the person holding the shovel to know where they are poking it.
I commend you for your research! We all started exactly like this.