When solo mining, proving that particular equipment was used to mine a block is trivial, all that is needed is checking the coinbase transaction.
well, I think this is actually a problem (an insoluble one)
attesting what your equipment was when mining a block is trivial. Proving it is not, and I'm not sure how you could achieve it.
Any scheme used whereby the miner or the manufacturer of the mining unit certifies what spec of machine was used could be manipulated (and real-world miners may end up using a mix of unit types in practice, that's another hot mess to contend with). Same goes for the location; using all kinds of IP proxy rules out determining origin using IP addresses. And the algorithm used to mine the blocks is entirely generic, the concept would not work if that were not true.
so, yes, it's a strange idea.
There are two possible ways.
The first is that the manufacturer will not mind that his label is put even untruthfully. It is for advertising purposes.
And the second way is that the manufacturer deploys its own small private chain (or non-private) in which the correspondence between the equipment id and the public key is fixed. It could look like a side chain in which only bitcoins with their labels go, there could be a division of values. A miner would send bitcoins to that network, receive a token of that chain, and return bitcoins back to the main chain.