Who regulates you, and when
Updated
A short map, and the unusual shape of it: almost nothing about the specimen is regulated, and quite a lot about the ground it came from is.
Nobody, until you touch one of four things
There is no license, no registration, no product standard and no inspection for mineral specimens.
The four things that bring a regulator in are where you collected, whether you sold what you collected, whether it is a fossil or an artefact, and what you claimed about it.
Land managers
BLM. Reasonable amounts for noncommercial purposes: 25 pounds per day plus one piece, 250 pounds a year. Above that, or for commercial purposes, a permit. Selling requires a permit or a claim.
National Park Service. 36 CFR 2.1 prohibits removal of mineral, rock and paleontological specimens except as specifically authorized.
Forest Service, state land agencies and tribal authorities, each with their own answer.
Private landowners, whose permission is the whole authority on their ground, and who may not own the mineral estate.
The land manager for the specific parcel is the authority on it. Nothing else is.
The FTC
Advertising and description. The Guides for the Jewelry, Precious Metals, and Pewter Industries govern how gemstones and simulants may be described, including treatment disclosure.
They apply squarely to cut and gem material. For rough specimens the general prohibition on deceptive description applies, and the trade custom is stricter than either.
Everyone else
The Paleontological Resources Preservation Act for fossils on federal land: vertebrate fossils require a permit and remain federal property.
Archaeological resource law for artefacts, which is a far harsher regime than anything here and which a mineral collector can wander into by picking up the wrong thing.
Your state and city for business registration and sales tax, and the states where you attend shows.
Your insurer, whose exclusions are more likely to affect you than any regulator.
And customs, for anything crossing a border, where mineral specimens meet species protection rules more often than collectors expect.