Public land and the arrowhead exception
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The general prohibition
"No person may excavate, remove, damage, or otherwise alter or deface... any archaeological resource located on public lands or Indian lands" without a permit. That is the rule.
The exception
"Nothing in subsection (d) of this section shall be deemed applicable to any person with respect to the removal of arrowheads located on the surface of the ground."
Three limits in one sentence
It applies to subsection (d) rather than to the whole section. It names arrowheads rather than artifacts. And it says on the surface of the ground rather than found.
Which is not what it is usually quoted as
The folk version is that surface arrowheads are legal to collect on public land. The text is narrower than that, and land managers often apply their own rules on top.
A pottery shard has no exception
Nor does a bottle, a bead or a stone tool that is not an arrowhead. The carve-out names one object type and nothing else.
Digging is out regardless
The exception is about removal from the surface. The moment a trowel is involved on public or Indian land, subsection (a) is squarely in play.
And the commerce prohibition is separate
Selling, buying, exchanging or transporting in interstate commerce anything obtained in violation of state or local law is prohibited by subsection (c), whatever subsection (g) says about arrowheads.
Ask the land manager
A BLM office, a forest supervisor or a park superintendent will answer this for their own ground, which is the only answer that applies to the place you are standing.
Local rules sit on top of the statute
A land manager can be more restrictive than the federal floor, and many are. The statute tells you what is prohibited everywhere; the posted rules tell you what is prohibited there.
Penalties are real
ARPA carries criminal penalties and forfeiture, which is a different order of consequence from the parking-ticket intuition most people bring to picking something up on a walk.