A proof is a standardized product. Take the classic ISOCoatedV2 proof, for example; the standard proof for coated printing paper. Here is the definition in brief:
Metal is printed with a varnish. Neither the colour of the metal of the tin can nor the colour of the lacquer is clearly defined, nor the thickness of the lacquer application and the printing process in which the lacquer is applied (digital print / screen printing, pad printing etc.) is defined.
A contract proof refers to very tight tolerances and precisely defined framework conditions. This includes not only the densitometric and colorimetric reference of the printing ink, but also, for example, the paper white, which is simulated very precisely in the proof. For exactly this reason there is no proof for recycled paper: The papers and paper whites are simply so different that no uniform, standardized “color” of a recycled paper can be defined. From classic recycled paper with a neutral grey or yellowish-grey colouring to de-inked, almost white recycled papers, everything is available on the market. Just not by default.
Therefore, a proof always refers to offset or gravure printing under standardized conditions. Changed surfaces such as metal or changed paper colours such as recycled or high-quality image papers with inclusions or printing on coloured papers have not yet been standardised and therefore cannot be proofed.