What an art material is
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The definition
An art material is "any substance marketed or represented by the producer or repackager as suitable for use in any phase of the creation of any work of visual or graphic art of any medium". It is a marketing test rather than a chemistry test: what decides is how the substance is presented.
Which is unusually wide
Any medium, any phase of creation. A thinner, a varnish, a wash medium, a pigment, a texture paste and a basing glue are all art materials when they are sold for making art, whatever else they also are.
And a repackager is named in it
Not implied, not reached by analogy. The word sits in the definition alongside producer, and it appears again in what the label must carry and in the duty to update that label. Somebody who buys bulk paint and sells it in 15 mL bottles is in the definition.
What it excludes
Economic poisons under the Federal Insecticide, Fungicide, and Rodenticide Act, and drugs, devices and cosmetics under the Federal Food, Drug, and Cosmetic Act. Those are regulated elsewhere rather than exempted.
Users of any age
Subsection (b)(2) says the standard "applies to art materials intended for users of any age". So the common assumption that this is a school supply rule and an adult hobby product sits outside it is wrong at the level of the text.
Because the hazard it addresses is chronic
Not a burn or a poisoning but long-term exposure, which does not care how old the user is. That is also why the labeling is a toxicologist's determination rather than a set of thresholds you can look up.
The standard is law, not a voluntary practice
Subsection (a) makes the labeling requirements of ASTM D-4236 "deemed to be a regulation issued by the Commission". Conforming to a consensus standard here is complying with a federal regulation.
Which changes who the question is for
Not only the paint companies. Anybody in this hobby who sells a liquid they did not formulate, in a bottle they chose, under a name they wrote, is in the definition and has a labeling question to answer.
This property cannot answer the chemistry
What goes on the label depends on a review of the formulation by a toxicologist. That is the one step in this area that cannot be done from a document, and no page here substitutes for it.
What it can do is tell you which questions are live
Whether you are a repackager, what the label has to carry, what the small container clause does, and where the flashpoint rules take over from the art materials ones. Those four settle most of it.