And under this framework, difficult to derive implies a need for patent protection, in order to prevent one entity from piggybacking off the derivation work and investment of another. But difficult to implement implies a lack of need for patent protection due to an implementation moat/barrier. Combine the two, and it gets into gray areas.
I used the LHC as an extreme example, but I can imagine other less extreme examples of #4 where the patentability is not so clear. Say, quantum processors - lots of time and research is going into deriving them, and they certainly won't be easy or cheap to produce, but the payoff may mitigate the implementation/production cost and be particularly attractive to some company looking to piggyback off the derivation work/expense of another.
The bleeping 1-click patent, though, God, it's enough to make my head explode if I think too much about that being patented. An utter perversion of the original intent of the patent system.