Yes famous conjectures usually already have a wealth of "downstream" results predicated on their truth value. But sometimes the proof technique is itself novel and that can carry over to other fields.

I think the most interesting point of the paper isn't simply the proof the conjecture but also the sqrt(n) bound. I doubt many downstream results were predicated on that particular bound.

>Huang’s result is even stronger than necessary to prove the sensitivity conjecture, and this power should yield new insights about complexity measures.

If I interpret this correctly it's a tighter bound than the original conjecture, so it should allow better optimizations.

Well graph coloring in a more general sense is used for things like register allocation in compilers. So any proofs or increase in theoretical knowledge in the area could lead to improvements in that area.

I believe graph-coloring is no longer used for state-of-the-art register allocators, such as the one in LLVM.

Apparently, for ISA with a small number of registers, graph-coloring is not as relevant because spillover is more important.

https://lists.llvm.org/pipermail/llvm-dev/2017-December/1199...

Cartographers know they'll never need that extra crayon only when all relevant regions are contiguous.