How precise a locality should be
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The rule is simple to state and requires discipline to hold: as precise as you actually know, and not one level more.
As precise as true
A locality is a claim. "Sweet Home Mine, Alma, Park County, Colorado" says you know which working it came from. If you do not, the honest label stops at the level you do know.
Nobody is harmed by a label that says "Park County, Colorado". A great deal is harmed by one that names a mine it did not come from, because that label will be believed and repeated long after you are gone.
The hierarchy
Working or occurrence, then district, then administrative area, then state or province, then country.
Write it from most specific to least, separated consistently, and use the accepted name of the locality rather than a local nickname.
Where a mine has been renamed or a district reorganized, record the name in use when the specimen was collected and note the current one. That is what makes an old label readable.
Why over-precision is the worse error
An imprecise label is incomplete. A precise wrong one is false data, and false data propagates: it is copied into the next catalog, quoted in a sale, and eventually cited.
The temptation is commercial, because precision raises the price. That is exactly why it has to be resisted, and it is the clearest place in this craft where the honest answer costs money.
If you bought it and the seller's locality is unverified, say so: "as received" is a real and respected qualifier.
Coordinates
Useful, increasingly expected, and worth two cautions.
Record the datum and the precision. Coordinates to six decimal places from a phone standing on a dump imply an accuracy nobody has.
And think before publishing them. A precise coordinate on a fragile or private occurrence is an invitation, and some localities have been stripped that way. Recording them in your catalog and withholding them from a public listing is a legitimate position.