I actually thought about this for a while, but I ended up not thinking that it'd work, because (among some other things which you also touched on)
> To disincentivise users spamming true but useless proofs such as "1+1=2" and "2+2=4", the system would have to penalise proofs based on the data volume of their novel component
I believe that this stated goal of defining a metric that decides which theorems are "interesting" is a lot more difficult than finding proofs for theorems.
I think at some point proving things will to a large part be automatic, and mathematicians will mostly concern themselves with finding interesting theorems, definitions, and axioms, rather than wasting time on proving-labor.
"Interesting" cannot be defined in an automatically verifiable way.
"Useful & short" however can be. Useful proofs are ones that solve the problems that are placed on the chain with real money rewards. The length/size of the proof is trivially verifiable. Useful AND short is the combination that's required. "Useful" alone would result in duplicate spam. Merely "short" would result in bulk generation of useless proofs. "Useful and short" means that the core of the graph would be optimised much like ants looking for food. Shorter AND useful paths to many goals are automatically rewarded. Longer paths can exist, but as they get more used, the incentive to try and optimise them rises dramatically to the point where even humans might want to contribute clever shortcuts manually.
> To disincentivise users spamming true but useless proofs such as "1+1=2" and "2+2=4", the system would have to penalise proofs based on the data volume of their novel component
I believe that this stated goal of defining a metric that decides which theorems are "interesting" is a lot more difficult than finding proofs for theorems.
I think at some point proving things will to a large part be automatic, and mathematicians will mostly concern themselves with finding interesting theorems, definitions, and axioms, rather than wasting time on proving-labor.
But what do I know.